Journal of Mechanical Engineering no. 7-8 year 2021 volume 67 Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s). Editor in Chief Vincenc Butala University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Founding Editor Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerceva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Demat d.o.o., printed in 250 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Mitjan Kalin University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Vice-President of Publishing Council Bojan Dolšak University of Maribor, Faculty of Mechanical Engineering, Slovenia Cover: The cover image shows a complex sinusoidal mesh surface machined through single point diamond turning technology. In actual machining, the tool path significantly affects the quality of the machined surface. To realize the determined machining accuracy effectively, the tool path that meets the machining accuracy demand can be derived by reverse application of the error calculation process according to the requisition of residual error and chord error. Courtesy: Jilin University, School of Mechanical and Aerospace Engineering, China International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, King Fahd U. of Petroleum & Minerals, Saudi Arabia Josep M. 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Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8 Contents Contents Strojniški vestnik - Journal of Mechanical Engineering volume 67, ( 2021) , number 7-8 L jubljana, July-August 2021 ISSN 0039-2480 Published monthly Papers Peixing Ning, Ji Z hao, Shijun Ji, Jingjin Li, Handa Dai: Ultra-Precision Single-Point Diamond Turning of a Complex Sinusoidal Mesh Surface Using Machining Accuracy Active Control 343 Yang-zhi Chen, Chao He, Yue-ling Lyu: Basic Theory and Design Method of Variable Shaft Angle Line Gear Mechanism 352 Myron Chernets, Marek Opielak, Anatolii Kornienko, Oleg Radko: Predictive Estimation of Sliding Bearing Load-Carrying Capacity and Tribological Durability 363 Raj Vardhan Patel, Anshul Yadav, Jerzy Winczek: Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 369 Anna Rudawska, Magd Abdel Wahab: Mechanical Properties of Adhesive Joints Made with Pressure- Sensitive Adhesives 380 Tomasz Bucki, Marek Konieczny, Dana Bolibruchova, Sylwia Rzepa: Characterization of the AZ 31/ AW-6060 Joint Fabricated using Compound Casting with a Z n Interlayer at Relatively Low Temperature Conditions 389 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 343-351 Received for review: 2021-03-20 © 2021 Journal of Mechanical Engineering. All rights reserved. Received revised form: 2021-05-18 DOI:10.5545/sv-jme.2021.7172 Original Scientific Paper Accepted for publication: 2021-06-17 U ltra-Precision Single-Point D iamond Turning of a Complex S inusoidal Mesh Surface U sing Machining Accuracy A ctive Control Peixing Ning1 – Ji Z hao1,2,* – Shijun Ji1 – Jingjin Li1 – Handa Dai1 1Jilin University, School of Mechanical and Aerospace Engineering, China 2Northeastern University, School of Mechanical Engineering and Automation, China Single-point diamond turning (SPDT) assisted with slow tool servo (STS) is the most commonly utilized technique in the fabrication of optical modules. However, the tool path significantly affects the quality of the machined surface. In order to realize the determined machining accuracy effectively, a tool path generation (TPG) method based on machining accuracy active control (MAAC) is presented. The relationship between tool path and machining error is studied. Corner radius compensation (CRC) and the calculation of chord error and residual error are detailed. Finally, the effectiveness of the proposed approach is verified through a machining error simulation and a cutting experiment of a complex sinusoidal mesh surface fabrication. Keywords: machining accuracy active control (MAAC), machining error prediction, complex sinusoidal mesh surface, single-point diamond turning (SPDT) Highlights • A tool path generation method based on active control machining error is proposed; the relationship between tool path generation parameters and machining error, including chord error and residual error, is studied. • The analytical geometry method and tool contact point discretization method are used to realize tool path planning. • The presented method can predict machining error and achieve the surface accuracy control before actual processing. 0 INTRODUCTION Single point diamond turning (SPDT) is an economical and efficient fabrication technology that can achieve an optical finish without subsequent machining [1] and [2]. At present, complex surfaces are widely used in various areas [3] and [4]. Therefore, scholars have conducted many studies on the ultra-precision machining technology of complex optical surfaces. Kong et al. [5] presented a hybrid tool servo (HTS) process and proposed a tool path generation (TPG) method. A microstructure array compound freeform surface machining experiment verified the validity of the proposed theory. Z hang et al. [6] put forward a termed toroid-surface-based slow tool servo (STS) turning method to generate discontinuously structured micro-lens arrays. Tian et al. [7] developed a novel fast tool servo system and experimented with rear-view mirrors fabrication using that system. Based on the principle of automatic dynamics analysis of mechanical systems, Khagani and Cheng [8] introduced an innovative approach for TPG. In their research, the Newton-Raphson method was used to generate the tool paths of very complex freeform surfaces; the study revealed that the time step size is very important in that method [8]. Li et al. [9] investigated a systematic approach for TPG and a theory for surface topography simulation in SPDT. A sinusoidal grid and micro-lens array sample were machined and measured to validate the effectiveness of the proposed theoretical research. Chen et al. [10] put forward a triangle rotary method; the results of the simulations and experiments showed that the presented approach was very feasible for position-velocity-time (PVT) interpolation. The presented method can decrease the interpolation error. Wei et al. [11] set up a progressive addition lens design model and proposed an optimized TPG method for diamond turning of the optical freeform surface. Ji et al. [12] designed and machined a compound freeform surface using an optimized TPG approach. Fang et al. [13] studied a cylindrical coordinate machining method for freeform surfaces fabrication, in which a typical non­uniform rational B-spline (NURBS) was utilized to fit the feature points. They also carried out a machining experiment of a compound eye structure surface to prove the theory. The above research studies mainly focused on TPG, corner radius compensation (CRC) and machined surface topography analysis. However, few studies have been conducted on the basis of TPG to ensure machining accuracy. In this study, a TPG method based on machining accuracy active control (MAAC) is proposed, and the relationship between TPG parameters and machining error, including chord error and residual error, is studied. This paper proposed a TPG method by MAAC for complex surface SPDT assisted by STS. In Section 2, the presented method and CRC are described minutely. The relationship between tool path and machining errors is studied. An experiment for a complex sinusoidal mesh surface fabrication utilizing the proposed method is carried out in Section 3. Finally, Section 4 s ummarizes the paper. 1 TPG BASED ON MAAC 1.1 Machining Accuracy Active Control Method In the process of complex mirror-like surface machining, TPG is the first and the most critical step, which has a visible impact on surface topography and surface finish of the machined workpiece. The SPDT technology is based on spindle rotary motion and linear reciprocating motion. The spindle rotation and the Z -axis reciprocating motion produce the chord error in the direction of cutting motion, and the X -axis linear motion produces the residual error in the direction of feed motion. Considering the above two principle errors, the TPG method based on MAAC can be used as the selection basis of cutting contact points (CCPs). Thus, the tool path for SPDT of the complex surface that meets the requirements of machining errors can be obtained. The method is generally divided into the following two steps: Firstly, the feed f should be calculated according to the requirement of residual error. Because there is a certain interval between two adjacent circles of the tool path, and the shape of the cutting edge is a circular arc, the cutting residue will be produced in the direction of cutting motion during the machining process. To calculate the residual error, the section curve in radial direction z = f (r) should be obtained, and the curvature radius R at CCP P (r, z ) should be i iii calculated by Eq. (1): ( ()232 1 (1 °fr'i)) / Ri˜˜ , (1) Kifr() '' i where K is the curvature at each CCP, f (r) is the ii first derivative of the section curve, f (r) is the i second derivative of the section curve. According to the difference of curvature, the calculation of cutting residual height can be divided into three forms [14]; the principle is indicated in Fig. 1. Fig. 1. Schematic diagram of residual error calculation Fig. 2. Schematic diagram of chord error calculation hen the requirement of residual error is res, the Repeating the above process with Pj+ 1 as the feed f at CCP P (r, z ) can be obtained through Eqs. initial point, the TPG can be finally achieved based on iiii (2) and (3) : active control for chord error.   f2 ..°2 r) R˜0 1.2 Corner Radius Compensation (CRC) ˜°( 1 resres.i (2 R)( .°2 r) ˆ.°2 R.. °..°2 r resresires.resi . f˜ R.0, (2) In the SPDT process, if the vertex of the cutting edge 2( .°R) i resi always moves along the CCPs, overcut will occur °...2 R)( .°2 r) ˆ...R2 r. resresires.resi. (2 when curvature is not zero, and a large machining f3 ˜ Ri0 ( ..R) resi error will be leaded. To make the cutting edge always f= min{ fff}. (3) ,, i123 Secondly, the TPG could be completed on the basis of the requirement of chord error. In the cutting process, the tool path between two adjacent CCPs is a straight line rather than an ideal curve. The chord error is the linear error between a realistic tool path and an ideal curve, as presented in Fig. 2. The analytical mathematical optimization TPG method can be used to realize active control for chord error: The tool path can be expressed as z = f (f). Because the distance between two adjacent CCPs is very small, the tool path between two points can be approximated as a circular arc. Therefore, the chord error c ho ˜ dc hord . According to the geometric relationship of incipient point Pj and required chord error ho, the next CCP c Pj+ 1 could be derived from Eq. (4) : PP jj.1 2 2 ˜cho°.chord=Rj. Rj.( ). (4) 2 tangent to the section curve in the radial direction of the proposed surface in the machining process, the CRC is needed. Unlike the process of milling, the CCPs needs to be compensated in three directions of space. Since there is no Y direction motion in SPDT, the CRC only needs to consider the compensation in the X Z plane. The principle of CRC is detailed in Fig. 3. Fig. 3. Schematic diagram of CRC The black line is the original position without CRC. At this point, the shaded area indicates that overcut occurred. To avoid overcut and keep the cutting point position constant, the trajectory of the CCPs P (r, z ) offsets a length of corner radius along iii the normal vector direction nri and the CLPs P (r, z ) iii is obtained, as written in Eq. (5) : .fr() ' i r'˜°rr ˆii. 2 1 .fr''() ˆi . (5 ) . 1 ˆ z'zr ˜. ii. ˆ 2 1 .fr ''() .i  Fig. 4. Form chart of complex sinusoidal mesh surface machining 2 MACHINING EXPERIMENT AND DISCUSSION surface with a gradual amplitude gradient. Therefore, the mathematical model can be established as Eq. (6 ): To prove the feasibility of the proposed method, a 2 . . h 1 Rw h 1 .ˆ. .. machining experiment of a complex sinusoidal mesh Z ˜ °  . . ˆ. Rw r . r sin surface is conducted. Fig. 4 presents the flowchart of Rw l 2 SPDT process for the surface machining. . . h 2 h 2 .ˆ.  2 .. . 2  ° (6) ˆ. . r  sin 2 r , Rw Rw 2.1 Complex Sinusoidal Mesh Surface Model Establishing where ...ˆ.. Rw h 1 h 1 ...ˆ..  r ˜°° The designed complex sinusoidal mesh surface is combined with umbrella surface and radial sinusoidal expresses sin r Rw l Rw the errors are all maintained ithin 0.5 m as shon ° . ° in Fig. 7. .ˆ w h2 R 2  .. w h2 R ..ˆ umbrella surface and ˜ . indicates complex radial sinusoidal surface; h1 and h2 are amplitudes of the two surfaces; l and . are the number of sinusoids with complete periods in circumferential and radial directions, respectively; r is polar radius, R is radius of the workpiece, f is polar w angle. 2.2 TPG and Machining Error Prediction The designed complex sinusoidal mesh surface is modelled as Eq. (10) with the maximum amplitude hmax= 0.2 mmm, h1= h2= hmax/4, the number of sinusoids with complete periods in a circumferential direction is l = 8, the number of sinusoids with complete periods in radius direction is .= 3 2/15, the radius of workpiece R = 8 mm, as shown in Fig. 5. w The res is set as 0.5 m and ho is also set as 0.5 m. c The TPG method based on MAAC is used for tool path planning of the designed surface. Fig. 6 presents the planning result. .. r sin r Fig. 5. Complex sinusoidal mesh surface model Fig. 6. Tool path planning of complex sinusoidal mesh surface machining Reversing the calculation process of TPG applied above, the prediction of machining errors can be realized. The prediction consequence indicated that a) b) Fig. 7. Machining error prediction; a) chord error prediction, and b) residual error prediction The CLPs after CRC, which can be directly applied to computerized numerical control (CNC) machine for complex sinusoidal mesh surface fabrication, is depicted in Fig. 8: Fig. 8. CLPs and CCPs trajectory of complex sinusoidal mesh surface machining 2.3 Machining and Measurement Experiments The processing experiment is conducted by using a Nanoform 250S PDT machine. The workpiece is made of Al6061 . The cutting parameters are summarized in Table 1. The machine tool system and successfully machined sample are exhibited in Fig. 9. Table 1. Cutting parameters Parameters Value Tool rake angle . 0° Tool clearance angle a 10° Tool included angle e 120° Corner radius re 0.496 mm Depth of cut a p 5 ”m Feed f 0.0402 mm Average cutting speed vc 166.72 mm/min a) b) Fig. 9. The machining experiment; a) machine tool system, and b) the machined complex sinusoidal mesh surface sample To verify the machining quality, the machined surface is measured using a newview 9000 white light interferometer profiler Z ygo, as shown in Fig. 10. The measurement conditions are as follows: the enlargement factor of zoom lens was set as 1.0Ś (standard). The enlargement factor of the objective lens was set as 50Ś . The filter tray was set as Standard F1, which can be used for most surfaces measurement. The bandwidth of the filter tray Standard F1 is 125 nm, and the centre wavelength is 550 nm. The field of view in object-space was set as 0.87 mm Ś 0.87 mm. The measurement adopts the method of distributing points at equal distances. The number of distributing points in the X and Y directions are all 1000. Due to the limitation of the measurement vision field, eight areas on different radii of the machined surface were randomly selected for measurement, including peak areas, valley areas and interim areas. The measurement results and the obtained machining errors are presented in Fig. 11. Figs. 11 (a1) to (h1) are reconstructed surfaces using the measurement data, and Figs. 11 (a2) to (h2) are machining errors after removing the form component of the machined surface from the original measurement data. Because the residual error and the chord error are coupled, which is inconvenient to measure and analyse separately, the machining quality can be evaluated through the peak valley (PV) value of the machined surface. PV represents the maximum peak-valley deviation of the form error of the machined surface. The residual error and the chord error could be negative. So the predicted PV can be calculated through Eq. (7) : ( res( res2 . PV ˜°.°cho) ..°.°cho) ˜m. (7 ) From Fig. 11, excluding the random error, the overall deviation (actual PV) of the machined complex sinusoidal mesh surface is about 2.45 m, which is a little bit larger than the predetermined PV 2 m, because there are some other uncontrollable factors such as measurement error, machine tool error, tool wear and cutting temperature. Therefore, it also can be demonstrated from the experiment result that the TPG by MAAC is usable. 3 CONCLUSIONS In this paper, a TPG method based on MAAC is presented by studying the mapping relationship between tool path and processing errors. The simulation and experiment of a complex sinusoidal mesh surface machining attest to the validity of the method. The conclusions are drawn as follows: 1. According to the requisition of residual error and chord error, the tool path that meets the machining a1) a2) b1) b2) c1) c2) d1) d2) e1) e2) f1) f2) g1) g2) h1) h2) Fig. 11. Measurement results and machining errors; (a1 to h1) reconstructed surfaces, and (a2 to h2) machining errors accuracy demand can be derived by reverse application of the error calculation process. 2. Using the proposed method, the TPG and CRC for a complex sinusoidal mesh surface machining are carried out systematically. The machining error simulation manifests that the generated tool path can meet the machining accuracy requirement. 3. Machining and measurement experiment results show that the PV of the machined complex sinusoidal mesh surface is not significantly different from the predetermined PV, which attest to the effectiveness of the TPG method by MAAC. 4 ACKNOWLEDGEMENTS This work is supported by Key R& D Projects of the Ministry of Science and Technology of China (Grant Nos. 2017Y FA0701200 and 2018Y FB1107600) National Natural Science Foundation of China (Grant No 51775237) , Graduate Innovation Fund of Jilin University (Grant No. 101832020C X 122). 5 REFERENCES [1] Zhang, S.J., Zhou, Y.P., Zhang, H.J., Xiong, Z.W., To, S. (2019). Advances in ultra-precision machining of micro-structured functional surfaces and their typical applications. International Journal of Machine Tools and Manufacture, vol. 142, p. 16-41, DOI:10.1016/j.ijmachtools.2019.04.009. [2] He, C.L., Zong, W.J., Xue, C.X., Sun, T. (2018). An accurate 3D surface topography model for single-point diamond turning. International Journal of Machine Tools and Manufacture, vol. 134, p. 42-68, DOI:10.1016/j.ijmachtools.2018.07.004. [3] Cai, H.B., Shi, G.Q. (2019). Tool path generation for multi-degree-of-freedom fast tool servo diamond turning of optical freeform surfaces. Experimental Techniques, vol. 43, p. 561­569, DOI:10.1007/s40799-019-00307-1. [4] Fountas, N.A., Vaxevanidis, N., V., Stergiou, C.I., Benhadj-Djilali, R. (2019). Globally optimal tool paths for sculptured surfaces with emphasis to machining error and cutting posture smoothness. International Journal of Production Research, vol. 57, p. 5478-5498, DOI:10.1080/00207543.2018.153046 8. [5] Kong, L.B., Ma, Y.G., Ren, M.J., Xu, M., Cheung, C.F. (2019). Generation and characterization of ultra-precision compound freeform surfaces. Science Progress, vol. 103, no. 1, DOI:10.1177/0036850419880112. [6] Zhang, L., Naples, N.J., Zhou W.C., Yi, A.Y. (2019). Fabrication of infrared hexagonal microlens array by novel diamond turning method and precision glass molding. Journal of Micromechanics and Microengineering, vol. 29, no. 6, DOI:10.1088/1361-6439/ab10ff. [7] Tian, F.J., Yin, Z.Q., Li, S.Y. (2015). Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors. International Journal of Advanced Manufacturing Technology, vol. 80, p. 1759-1765, DOI:10.1007/s00170-015-7152-9. [8] Khaghani, A., Cheng, K. (2019). Investigation on multi-body dynamics based approach to the tool path generation for ultraprecision machining of freeform surfaces. Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture, vol. 234, no. 3, p. 571-583, DOI:10.1177/0954405419863961. [9] Li, D., Qiao Z., Walton, K., Liu, Y., Xue, J.D., Wang, B., Jinag, X. (2018). Theoretical and experimental investigation of surface topography generation in slow tool servo ultra- precision machining of freeform surfaces. Materials, vol. 11, no. 12, DOI:10.3390/ma11122566. [10] Chen, X., Kang, M., Wang, X.S., Hassan, M., Yang, J. (2017). Tool path optimal design for slow tool servo turning of complex optical surface. Proceedings of the Institution of Mechanical Engineers Part B: Journal of Engineering Manufacture, vol. 231, no. 5, p. 825-837, DOI:10.1177/0954405416654192. [11] Wei, Y., Zhai, P., Chen, X.Y., He, L. (2020). Study on design and diamond turning of optical freeformsurface for progressive addition lenses. Mathematical Problems in Engineering, vol. 2020, art. ID 2850606, DOI:10.1155/2020/2850606. [12] Ji, S.J., Li, J.F., Zhao, J., Feng, M., Sun, C.R, Dai, H.D. (2018). Ultra-precision machining of a compound sinusoidal grid surface based on slow tool servo. Materials, vol. 11, no. 6, art. ID 1001, DOI:10.3390/ma11061001. [13] Fang, F.Z., Zhang, X.D., Hu, X.T. (2008). Cylindrical coordinate machining of optical freeform surfaces. Optics Express, vol. 16, no. 10, p. 7323-7329, DOI:10.1364/OE.16.007323. [14] Lin, R.S., Koren, Y. (1996). efficient tool-path planning for machining freeform surfaces. Journal of Engineering for Industry, vol. 118, no. 1, p. 20-28, DOI:10.1115/1.2803642. Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 352-362 Received for review: 2021-04-08 © 2021 Journal of Mechanical Engineering. All rights reserved. Received revised form: 2021-06-09 DOI:10.5545/sv-jme.2021.7216 Original Scientific Paper Accepted for publication: 2021-07-01 Basic Theory an d D esign Method of Variable Shaft Angle L ine Gear Mechanism Yang-zhi Chen1,* – Chao He1 – Yue-ling Lyu2 1South China University of Technology, School of Mechanical and Automotive Engineering, China 2Sun Yat-sen University, School of Biomedical Engineering, China In this paper, a novel line gear mechanism is proposed; it is called the variable shaft angle line gear mechanism (VSALGM). VSALGM has two rotational degrees of freedom, one is the rotation of the two gears with a constant transmission ratio, and the other is the relative swing of the two gears shafts. First, a novel contact model of VSALGM composed of one driven contact curve and one driving line teeth working surface (DLTWS) was proposed. With the concept, the basic design equations for VSALGM were derived on the basis of the space curve meshing theory of line gear. Moreover, the design criterion of pressure angle for VSALGM was analysed and proposed on the basis of the contact model. A basic design method for VSALGM was thus developed. A design example was given, and prototypes were manufactured using three-dimensional (3D) printing. Kinematic experiments and gear contact spot testing were carried out on a self-made kinematic test rig by the prototypes. The results show that the VSALGM designed in this paper can achieve a continuous, smooth and stable meshing transmission while the shaft angle is continuously changed within its setting range. Keywords: line gear, variable shaft angle, degree of freedom, pressure angle, space curve meshing theory Highlights • A variable shaft angle line gear mechanism (VSALGM) was proposed, which achieves a smooth meshing transmission with variable shaft angle. • The basic theory and design of VSALGM were derived. • Experiments were carried out to verify its kinematic performance. 0 INTRODUCTION Conventional gear pairs, including cylindrical gear pairs, bevel gear pairs and, non-cylindrical gear pairs, have a fixed shaft angle, meaning that they have only one rotational degree of freedom while working. Some applications, such as angle grinder [1], flexible joint [2] and manipulator [3], need the functions of both the constant transmission ratio and the two rotational degrees of freedom, but conventional gear pairs cannot satisfy these demands alone. Those applications [1] to [3] are generally achieved by a series connection of universal joints and gearboxes, because a universal joint has two rotational degrees of freedom, and a gearbox provides a constant transmission ratio. However, the series connection of universal joint and gearbox leads to a large structure and low transmission efficiency. Although involute gear pairs with two rotational degrees of freedom [4] and [5] have been developed, their designs are complex. A line gear based on the space curve meshing theory [6] and [7] is dissimilar from conventional gear based on the space surface meshing theory [8] to [10]. In theory, two space conjugate curves can guarantee the transmission accuracy of line gear [11]. Common line gear mechanisms, including parallel axes line gear mechanisms [12], intersecting axes line gear mechanisms [13] and skew axes line gear mechanisms [14], have only one rotational degree of freedom; specifically, these common line gear mechanisms have a fixed shaft angle. The feature of common line gear mechanisms is that their driving contact curve and driven contact curve is a couple of space conjugate curves. Based on the space curve meshing theory, a new line gear mechanism referred to as variable shaft angle line gear mechanism (VSALGM) is proposed. VSALGM has a constant transmission ratio and two rotational degrees of freedom. One of the two rotational degrees of freedom is the rotation of the two gears with a constant transmission ratio, and the other rotational degree of freedom is the relative swing of the two gear shafts. VSALGM is composed of a pair of driving line gear and driven line gear. Different from common line gear mechanisms, VSALGM has a variable shaft angle. Specifically, VSALGM maintains a continuous, smooth and stable meshing transmission with a constant transmission ratio; its shaft angle can be continuously changed within a range. For VSALGM, the driving contact curve and the driven contact curve are always a couple of space conjugate curves under different shaft angle, wherein the driving contact curve changes with *Corr. Author’s Address: School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China, meyzchen@scut.edu.cn different shaft angles, but the driven contact curve remains unchanged. The set of driving contact curves constitutes a driving line teeth working surface (DLTWS). As long as the accuracy of the DLTWS and the driven contact curve are high, the transmission accuracy of VSALGM will be high. In addition to having the advantages of common line gear mechanisms, such as small size, a number of teeth, and a large transmission ratio, more importantly, VSALGM has the features of variable shaft angle and two degrees of freedom, which can provide a better choice for the design cases on the requirement of both constant transmission ratio and two rotational degrees of freedom. Also, it should be noted that VSALGM can only design to transmit the motion in one direction, either in the clockwise direction (CW) or counter-clockwise direction (CCW), which means there is no reversibility of VSALGM. In this paper, the basic design equations for VSALGM were established, and the design criterion of pressure angle for VSALGM was proposed. Furthermore, based on the pressure angle rule, a parameters selection method of the basic design equations is given. According to the method, a design example was given, and kinematics experiments were completed. Finally, the gear contact spot testing was carried out. 1 METHODS 1.1 Basic Design Equations for VSALGM For VSALGM, the driving line gear and the driven line gear rotate around their axis with a constant angular velocity, respectively; meanwhile, the shaft angle of VSALGM can be continuously changed shafts of line gear A and line gear B; they are collinear with axis and z p axis, respectively. Line gear A rotates around the axis for an angle f by a uniform a angular velocity . Line gear B rotates around the a z p axis for an angle fb by a uniform angular velocity . In this paper, line gear A is the driven wheel, line b gear B is the driving wheel; curve C1 represents the driving contact curve, curve C2 represents the driven contact curve; the transmission ratio is denoted as i , and i = f/ f. ba Fig. 1. Space curve meshing coordinates for VSALGM According to [13], the contact curves of intersecting axes line gears are a couple of space conjugate curves, composed of one cylinder helix curve and one cone helix curve. In this paper, the cone helix curve is defined as the driving contact curve and the cylinder helix curve as the driven contact curve. The equations for the driving contact curve and the driven contact curve are given as Eqs. (1) and (2) in their coordinate systems, respectively.  M b..˜macos ..˜n...0 ° ˜°˜.°ntb°sin . within a range. The design equations are deduced in the following section. VSALGM can transmit under different shaft angle; its coordinates system is as shown in Fig. 1. The design equations for VSALGM are denoted in the space curve meshing coordinates, as shown in x 0 z z ˆcos ˜t.° ii. ˜° yb.˜ma° cos ..nntb°sin .°, ˜.˜...(1) M 0z 0z ˆsin ˜t.° ii. ˜°.ma0 sin ..n.nt.0 cos . b˜.°˜.tb° z M z z Fig. 1. The coordinate system O xy is set as a fixed Cartesian coordinate system arbitrarily. The coordinate system O p x pypz p is determined by the position of the coordinate system O xyz . The x pO pz p plane coincides with the xO plane. The distance from O p to axis is denoted as a 0, the distance from O p to x axis as b 0, and the included angle between axis and z p axis as .z. .z is the shaft angle, the range of .z is from 0° to 90° ; The designed minimum shaft angle is denoted as .z min and the designed maximum shaft angle as – .z – max. The gear shaft a and the gear shaft b are the . ˆ.. a ˜° .xM .mcos t˜° yM a.msin, (2) t .a ˜° zM .n.nt where m denotes the helix radius of the driven contact curve; n is the pitch parameter of the driven contact curve, denoting the pitch as p, n = p/ 2p; .z is the nn shaft angle; t is an independent variable, which also indicates the scope of the driven contact curve, that t= [ 0, 2p] means a circle of the driven contact curve. The lengths of driving contact curve and driven contact curve are directly controlled by the scope of t on demand. For VSALGM, its shaft angle is another independent variable. It can be seen from Eq. (1) that different driving contact curves are corresponding to different shaft angles. In other words, there are a series of corresponded driving contact curves when the shaft angle is continuously changed in a certain range. Accordingly, a DLTWS is constituted by the set of the driving contact curves. The equation for the DLTWS is denoted as Eq. (3) in the coordinate system O p x pypz p. ˜°b˜˜.°˜n..°° x..macos ...ntbsin . M 0z 0z ˆcos ˜t..° ii b y˜°.macos ...ntb°sin .° ˜˜.° ˜n.. M 0z 0z , (3) ˆsin ˜t. ii.°˜°°.tb. zb.˜ma.sin ..˜n.nt.°cos M 0z 0z .z ..t1 where .z denotes the shaft angle of VSALGM, which is an independent variable in this paper, and t1 represent the scope parameter of the shaft angle. It should be indicated that .z is a constant in Eq. (1) but a variable in Eq. (3) . The basic design equations for VSALGM are set as Eqs. (2) and (3) , respectively. 1.2 Contact Model for VSALGM Based on the above basic design equations, the contact model for VSALGM was established by the Wolfram Mathematica software, as shown in Fig. 2.    Fig. 2. Contact model for VSALGM VSALGM can transmit under different shaft angles; its meshing process is similar to the common line gear mechanisms when it transmits under a fixed shaft angle. Different driving contact curves on the DLTWS always mesh with the same driven contact curve, while the shaft angle is continuously changing within the setting range. Two points need to be explained further. One is that VSALGM can only mesh in one direction, either CW or CCW. The other is that the two degrees of freedom of VSALGM do not impact each other. The shaft angle can be changed whether the gears rotate or not; and VSALGM can mesh while the shaft angle continuously changing. A constant transmission ratio remains unchanged when the transmission was conducted from the driving wheel to the driven wheel. 1.3 Analysis of Pressure Angle for VSALGM For gears, pressure angle (denoted as a) has a great influence on the transmission performance: the larger the pressure angle is, the smaller the effective transmission force will be [15]. It is worse for VSALGM that large deformation would be caused by the radial and axial components of the contact force applied on the cantilevered teeth [16]. Even more so, self-lock would be caused by excessive pressure angle, which would make the gear pair unable to be driven. In other words, the value of driving torque must be greater than the value of maximum friction torque for mA.......................................................w..............................................- the driven wheel. In this paper, the driving torque is mA.......................................................w..............................................- denoted as M , and M F cosa, where F denotes the a contact force; aThe maximum friction torque is denoted as M ”, and the static friction coefficient is as ”. In mA.......................................................w..............................................- order to avoid self-lock, the value of driving torque must be greater than the value of maximum friction torque, which is that M ” ”F M F cosa [17]. In a other words, the value range of pressure angle is as follows: a arccos ”. Therefore, the allowable value of pressure angle depends on the maximum static friction coefficient of the gear pair. For commonly-used materials of line gear pairs [18], the typical value of the maximum friction coefficient is no greater than 0.7 under the condition of poor or no lubrication [19]. Therefore, the allowable value of pressure angle is derived as follows: a 45. Moreover, the design criteria of pressure angle for involute gear and non-circular gear is used as a reference. For the involute gear, the standard pressure angle is equal to 20° in the China standard [20], and the maximum pressure angle is approximately equal to 45° when the addendum coefficient is equal to 1 or 0.8 [21]. For the non-circular gear, the maximum pressure angle must be designed to less than 65° [22]. In summary, the design criterion of pressure angle for VSALGM is as follows: a 45. 1.4 Parameters Selection Method for VSALGM Based on Pressure Angle Rule The value of the pressure angle is determined by the parameters of the basic design equations for VSALGM. The parameters selections are diversified in the basic design equations when designing a pair of line gear. To ensure that the pressure angle is within the allowable range, a parameter selection method was given. First, the calculation formula for the pressure angle was derived. The pressure angle exists during the transmission between the driving wheel and the driven wheel. The pressure angle is defined as the acute angle between the direction of the contact force and the direction of linear velocity at the meshing point on the driven wheel. The contact form of line gear belongs to point contact. According to the contact t. icos °iiˆ.°°.a0 .m.cos .z .isin .z °nt°. model, at the meshing point, the direction of the force for the driven wheel is overlapped with the normal direction of the DLTWS, and the expression of the normal vector of the DLTWS is as Eq. (4) . i1 f ˜xt°x° . z .... In Eq.( 4) , i 1, j1 and ˆ... j1 k1 yt°zt°. (4) y°z° . zz k 1 represent the three unit vectors in a Cartesian coordinate system, xt' , yt' and zt' represent the partial derivative of t, x °˜z, y.z and z °˜z represent the partial derivative of .z. Next, the parameters are substituted into Eq. (4) , at the meshing point, the expression of the normal vector of the DLTWS in the coordinate system O xyz can be obtained as Eq. (5) . b bbb  ˆ..b.2 .nnt°.ˆ..bsin °t.. 0 .° 0 .iiˆfb°.°°.°.2 (5) ˜innt°.ˆ..b0 cos iit.ˆ..isin iit.ˆ.°°.a0 .mcos . z .isin .z n°t.ˆ..b0 .. .isin °.2 .bnt..2 .2 °.nt.. 2 ..ma.-°.ˆia. mb.°.ˆcos 2 z0 °00 °0 .z .. 2 ° At the meshing point, the expression of the linear . velocity for the driven wheel in the coordinate system O xyz is as shown in Eq. (6) . a aaa msin ..t v a ˜ ...ˆ mcos 0 ..t  .  Eq. (5) can be seen as the expression of the direction of the contact force. To calculate the pressure angle, the expression of the direction of the contact force needs to be converted from the coordinate system O xyz to the coordinate system O xyz . b bbba aaa (6) The transformation matrix from the coordinate system O xyz to the coordinate system O xyz is as b bbba aaa shown in Eq. (7) .  . . coscos .cos .°sin .sin .cos .sin ..cos .cos .sin .cos .sin .°cos .ˆbsin ..acos .. z abababz babz bzz °.os ...sin . coscos .sin .°cos .sin .co.cos .°cos .sin .sin .°sinsin .ˆ°acos ..bsin z abbaabz abz bzz b Mba˜.(7) ° cos .sin .°sinsin .cos .°bcos .° .asin . azz az zz 0 001  For the driven wheel, the expression of the In order to analyse the values and distributions direction of the contact force in the coordinate system of the pressure angle more intuitively, calculation O xyz is as follows: F= Mf. example 1 was given referring to [13], and the a aaaa bab Finally, according to the calculation formula for parameters of VSALGM were as follows: m= 12.5 the spatial angle between two vectors, for VSALGM, mm, n = 6 mm, a 0 = 30 mm, b 0= 10 mm, i = 0.5 mm, its calculation formula of the pressure angle is .z= [0°, 90° ] and t= [ 0, 10] . In calculation example 1, deduced as Eq. (8) . the values and distributions of the pressure angle were ˆ... obtained by using Eq. (8) , and the distribution graph fv aa . (8) was plotted by using Wolfram Mathematica software, a . ˜ ...° arccos fv as shown in Fig. 3. a Fig. 3. The pressure angle distribution graph in calculation example 1 It can be seen from Fig. 3 that the pressure angle goes beyond the allowable value in some parameter ranges, which may cause self-lock. Therefore, acceptable design parameters must be chosen to ensure that the pressure angle is always within the allowable range. Parameters including m, n , a 0, and b 0 are usually selected according to the geometric parameters selections of line gear pairs [23], and the transmission ratio i is selected on the requirement of practical design. From Fig. 3, it can be seen that different areas in the pressure angle distribution graphs can be selected by .z and t, which means that the pressure angle can be controlled within the allowable range when a reasonable range of .z and t are selected. In general, the value range of .z is determined on the requirement of practical design. The value range of t is chosen under the conditions of that a 45 and that the contact ratio of line gear greater than 1 with non­interference [24]. The above analysis shows that the value of pressure angle can be controlled by the selection of the variable t. Therefore, the basic design method for VSALGM can be summarized as follows: On the first step, the basic design equations for VSALGM are calculated. On the second step, parameters i and .z are selected on the requirement of practical design; Parameters m, n , a 0, and b 0 are selected according to the geometric parameters selections of line gear pairs [23], and parameter t is selected according to the design criterion of pressure angle. On the third step, the 3D models are designed by using the 3D Design Software. In short, the basic design method for VSALGM can be described by the design flow chart in Fig. 4. Fig. 4. Design flow Chart for VSALGM Usually, the driving gear and driven gear are installed in their corresponding position. When the driving gear and driven gear have to swap positions, it is necessary to recalculate whether the pressure angle is within the allowable range or not; the calculation method refers to the above analysis. 2 EXPERIMENTAL 2.1 Design Example 2 According to the basic design method for VSALGM proposed in Section 1, design example 2 was derived based on calculation example 1. It is necessary to indicate that the range of shaft angle is selected on specific requirements. In design example 2, the original parameters were set as follows: m= 12.5 mm, n = 6 mm, a 0= 30 mm, b 0 = 10 mm, i = 0.5 mm, .z= [75° , 90° ] and t= [ 5, 9] . The pressure angle distribution graph of design example 2 was shown in Fig. 5. .x˜°.˜17 5 ˆ.6 t°sin ˆ° b˜...cos 2 t .cos 610 Mz z  ˜° yM b..˜17 5 ˆz .˜6 .6t.°sin ˆz °sin 2 (9) .cos .610 t. ˜° b˜..° z..17 5 .sin ˆ.6 .6 t10 cos ˆ  Mz z  When the relevant parameters are substituted into Eq. (2), the equation for the driven contact curve is obtained as Eq. (10). a ˜° .xM .12 5 .cos t. a ˆyM .12 5 t ˜°.sin . (10) .a ˜° z.6 .6 t .M . The tooth model of the driven gear was established by using the Unigraphics NX software. Specifically, a completed DLTWS was fitted and constructed depending on six driving contact curves, which correspond to six shaft angles (74° , 78° , 82° , 86° , 90° , 94 ° ). In order to make VSALGM work properly in the theoretical scope, the practical value range of .z is slightly greater than the theoretical scope. The structures of the areas, where the shaft angle is out of the setting scope, only play a role of support, but do not participate in transmission. By using the Unigraphics NX software, the fitted DLTWS and the tooth model were obtained, as shown in Fig. 6. The six curves on the driving tooth surface in Fig. 6 represent the six driving contact curves of the above design. Fig. 6. 3D model of VSALGM; a) fitted DLTWS, b) fitted tooth model, c) driving line gear model, and d) driven line gear model Fig. 6a shows one driving tooth surface, Fig. 6b shows a driving tooth model, Fig. 6c shows the driving line gear model, and Fig. 6d shows the driven line gear model. According to the construction method of the normal line gear teeth, the driven tooth was generated by the function of ScanTo3D in the SolidWorks software, with the driven contact curve as the boundary and a 5 mm diameter circle as the outline, as shown in Fig. 6. The designed structure of line gear has a small volume and light weight. The line gear has the characteristic of a small number of teeth. The tooth number of the driving line gear was set as 4, and the driven line gear as 2. The completed line gear was obtained by connecting the line gear teeth. 2.2 Kinematics Experiments for VSALGM The prototypes were made by 3D printing according to the above model, as shown in Fig. 7. According to the product manual, the tolerance of the 3D printing line gears is 200 microns. Fig.7. Prototypes of VSALGM: a) driving wheel, and b) driven wheel It can be seen from Fig. 7b that the driven gear consists of a small spiral tooth; therefore, VSALGM can only be used for small loads. The kinematics performance of VSALGM was verified in the self-made kinematics test rig, as shown in Fig. 8. Fig. 8. The test rig for VSALGM According to [25], kinematics experiments for VSALGM were carried out using the self-made kinematics test rig, as shown in Fig. 8. The two gears were installed. The geared servo motor 1 generated a clockwise motion, and the driving wheel transmitted the motion to the driven wheel. The geared stepper motor 2 generated another motion making the shaft angle be changed. There were two encoders installed on the driving wheel and the driven wheel for recording the angular displacements of the two gears, respectively. A magnetic powder brake connected to the driven wheel, which generated the load. The speed and angular displacement of the geared servo motor 1 can be quantitatively controlled through the motion controller installed on a personal computer. The pulse signals of the two encoders (output 20000 pulses per revolution) are obtained by the data acquisition card installed on the personal computer. The angular displacement of each gear can be obtained from the collected pulse signals. The kinematics experiments were conducted by three groups, and each group included the testing of fixed shaft angle (88 ° , 82° and 76° ) and the testing of continuously changing shaft angle. The three groups were conducted on the condition of different loads. VSALGM is only suited for small loads. Therefore, the load was set as 0 N·mm in group 1, 30 N·mm in group 2 and 60 N·mm in group 3. The geared servo motor 1 was set as 1.67 rpm. The sampling frequency of the two encoders was set as 20 Hz in the experiment. The geared stepper motor 2 was set as 0.0347 rpm, for continuously changing the shaft angle from 90° to 75° . The transmission performance of VSALGM varies periodically relating to the number of teeth. In this paper, the driving line gear and the driven line gear rotated 2 revolutions and 4 revolutions, respectively, during the tests, which mean the testing time equal to 72 s . 2.3 Gear Contact Spot Testing In this paper, the red lead powder was used as the developer in the gear contact spot testing to research the contact form of VSALGM. The developer was evenly smeared on the driving gear tooth surface, as shown in Fig. 9. When the two gears are meshed, the developer will stick to the driven wheel from the driving wheel at the contact point, and the developer will be driven away at the contact point because of the contact force. The contact spots on the two gear tooth surfaces can be observed after the two gears meshed. In the gear contact spot testing, the gear pair was installed on the self-made gear kinematics test rig, and the load was set to 30 N·mm. The gear contact spot testing was successively conducted under two different shaft angles (82° and 76° ), and the contact spots on the two gears tooth surfaces were obtained. Fig. 9. Diagram of the gear contact spot testing 3 RESULTS In order to study the kinematic performance of VSALGM, the experiments were conducted when the designed gears meshed at different shaft angles. The transmission error is the difference between the real angular displacement and the theoretical angular displacement of the driven line gear shaft [26]. According to [27], the data of the transmission error were measured through the collected encoder’ s data when the designed gears meshed at different shaft angles, as shown in Figs. 10 to 12. a) .z = 88°; b) .z = 82°; c) .z = 76°; d) .z changing from 90° to 75° In Figs. 10 to 12, the four different curves in each figure show the three fixed shaft angle testing results and the changing shaft angle testing result on the condition of different loads. For each transmission error curve, the curve between the bottoms of every two peaks represents 1 tooth rotation, and the bottom of each peak represents the contact conversion between two teeth. The transmission errors data analyses are tabulated as Table 1, including the peak-to-peak value, amplitude and standard deviation of the transmission error. In the gear contact spot testing, the meshing traces appeared on both driving line gear and driven line gear after the two gears meshed. The results of the gear contact spot testing were obtained after rotating the gear pair, as shown in Fig. 13. Table 1. Transmission errors for the kinematics experiments Load Shaft angle Peak-to-peak Amplitude Standard [N·mm] [°] value [°] [°] deviation [°] 88 0.9 0.576 0.284 82 0.9 0.576 0.284 0 76 0.9 0.576 0.286 90 to 75 1.152 0.738 0.357 88 1.026 0.684 0.307 30 82 76 1.026 1.026 0.666 0.63 0.308 0.306 90 to 75 1.296 0.792 0.385 88 1.206 0.684 0.358 60 82 76 1.206 1.206 0.666 0.648 0.356 0.352 90 to 75 1.674 0.9 0.494 4 DISCUSSION It can be seen from the kinematics experiments that VSALGM can achieve a continuous, smooth, and stable meshing transmission under the setting range of shaft angle, meaning that VSALGM has two degrees of freedom. The range of shaft angle is selected on specific requirements. In this paper, the range of the shaft angle is from 90° to 75° , but for other designs, in practically, the range of shaft angle has different options. It can be seen from Figs. 10 to 12 and Table 1 that the transmission error is a consistent level under different fixed shaft angles on the condition of the same load. However, the transmission error of the testing of continuously changing shaft angle is greater than the testing of fixed shaft angles; it is because of the installation error other than the shaft angle variations. According to the experiment results, the transmission error increases with the increase of the load. Due to the cantilevered teeth, the loads will cause deformations on the teeth of VSALGM, which lead to the errors of the real meshing contact curves and cause the transmission error. Therefore, VSALGM can only conduct transmission under small loads. The transmission error of VSALGM in the kinematics experiments is mainly due to the errors of the instrument and the test prototypes, which includes the encoder error, the motor vibration error, the gears installation error and the test prototypes error. The different sources of error were analysed for VSALGM. Theoretically, the gear installation error of VSALGM includes axial error and eccentricity error; it mainly depends on the accuracy of the test rig. For the test rig in Fig. 8, the tolerance of the manufactured parts is 20 m, the tolerance of the gear shaft is 10 m, the tolerance of the bearing is 10 m, and the tolerance of the positioning pin is 10 m. A slide calliper rule ith an accuracy of 20 m as used to assist the gear installation. Therefore, the gear installation error analysis can be obtained, as shown in Fig. 14. As shown in Fig. 14, for the gear installation error, both the axial tolerance and the eccentricity tolerance are about 140 m. In addition, the tolerance of the line gear prototypes is 200m, and the deformations on the teeth of VSALGM increases with the load. The accuracy of the encoder is 1.08. The motor vibration error will cause the driving wheel to rotate reverse instantaneously with a small angle. In this paper, a reducer and an elastic coupling were used to reduce the influence of motor vibration. It is difficult to study the accuracy of the gear installation error based on the above experimental equipment. However, the experiments in this paper focus on verification of the basic theory and design method of VSALGM, which have proved that VSALGM has two degrees of freedom and maintains a smooth transmission while continuously changing the shaft angle. In the future, the precision testing bench and precision line gears will be developed to investigate the transmission error and dynamic performance for VSALGM. For the gear contact spot testing, it can be seen from Fig. 13 that there are two different meshing traces on the driving tooth surface and only one meshing trace on the driven line gear after the gear pair meshing under the two different shaft angles. The meshing trace on the driven line gear is a cylindrical helix curve under the two different shaft angles. The gear contact spot testing proved that for VSALGM, different driving contact curves always mesh with the same driven contact curve under different shaft angle. The gear contact spot testing also proved that VSALGM belongs to point contact. Finally, it can be seen from the kinematics experiments and the gear contact spot testing that whether it is a theoretically designed driving contact curve or a fitted driving contact curve, they all can achieve a smooth meshing transmission by meshing with the same driven contact curve. 5 CONCLUSIONS In this paper, a line gear mechanism with two rotational degrees of freedom referred to as Variable Shaft Angle Line Gear Mechanism (VSALGM) is proposed. The main work is summarized as follows: (1) Based on the space curve meshing theory of line gear, the basic design equations for the proposed VSALGM were established. The design criterion of pressure angle was proposed, and a parameter selection method was given. (2) The prototypes of VSALGM were manufactured by using 3D printing. Based on the prototypes, the kinematic experiments for VSALGM were conducted under different shaft angles. The kinematic experiments results have proved that VSALGM has two degrees of freedom and maintains a smooth transmission while continuously changing the shaft angle. (3) The gear contact spot testing were carried out, which have shown that there are different driving contact curves meshing with the same driven contact curve under different shaft angle for VSALGM. However, many problems remain to be studied, such as the non-interference between two gears, parameters optimization, structural design, strength formula and sliding ratio for VSALGM, the efficiency and friction losses, the transmission error. More importantly, we will manufacture precision prototypes and develop a practical precision testing bench for testing the integrated performance of transmission for VSALGM in future. 6 ACKNOWLEDGEMENTS The authors gratefully acknowledge the supports from the National Natural Science Foundation of China [ No. 51575191] , Natural Science Foundation of Guangdong Province [ No. 2018A 030310404] and 2019 Guangzhou technology project [ No.201904010368] . It is our honour to thank the reviewers and editors for their valuable criticisms and comments. 7 NOMENCLATURES a The distance from point O p to axis 0 b The distance from point O p to x axis 0 m The helix radius of driven contact curve n A pitch parameter of driven contact curve .The shaft angle of VSALGM z i The transmission ratio t The scope parameter of helix curve fThe rotation angle of driven wheel a fThe rotation angle of driving wheel b The angular velocity of driven wheel a The angular velocity of driving wheel b F The value of contact force M The value of driving torque a M The value of maximum friction torque of line ” gear ” The static friction coefficient of line gear pair a The pressure angle fThe normal vector in the coordinate system b O – x byb at the meshing point bb vThe linear velocity of driven gear at the meshing a point MThe transformation matrix from O – x yz to ba bbbba aaa O – x yz 8 REFERENCES [1] Reinvee, M., Aia, S., Pääsuke, M. (2019). Ergonomic benefits of an angle grinder with rotatable main handle in a cutting task. Human Factors, vol. 61, no. 7, p. 1112-1124, DOI:10.1177/0018720819827184. [2] Alam, W., Mehmood, A., Ali, K., Javaid, U., Alharbi, S., Iqbal, J. (2018). Nonlinear control of a flexible joint robotic manipulator with experimental validation. Strojniški vestnik - Journal of Mechanical Engineering, vol. 64, no. 1, p. 47-55, DOI:10.5545/sv-jme.2017.4786. [3] Yadmellat, P., Shafer, A.S., Kermani, M.R. (2013). Design and development of a sin-gle-motor, two-DOF, safe manipulator. IEEE/ASME Transactions on Mechatronics, vol. 19, no. 4, p. 1384-1391, DOI:10.1109/TMECH.2013.2281598. [4] Jian, G., Wang, Y. , Zhang, P., Xie, Y., Zhao, J. (2020). Analysis of lubricating performance for involute spur gear under vibration. Lubri-cation Science, vol. 32, no. 7, p. 344-357, DOI:10.1002/ ls.1507. [5] Zhao, Y., Wei, W., Dong, X. (2008). Some problems on the 2DOF theory of gearing. Mechanism and Machine Theory, vol. 43, no. 8, p. 1024-1037. DOI:10.1016/j. mechmachtheory.2007.07.002. [6] Chen, Y.Z., Lv, Y.L., Ding, J., Chen, Z. (2013). Fundamental design equations for space curve meshing skew gear mechanism. Mechanism and Machine Theory, vol. 70, p. 175­188, DOI:10.1016/j.mechmachtheory.2013.07.004. [7] Chen, Y., Xiaoyong, X., Liang, L. (2009). A corrected equation of space curve meshing. Mechanism and Machine Theory, vol. 44, no. 7, p. 1348-1359, DOI:10.1016/j. mechmachtheory.2008.11.001. [8] Litvin F.L., Demenego, A., Vecchiato, D. (2001). Formation by branches of envelope to parametric families of surfaces and curves. Computer Methods in Applied Mechanics & Engineering, vol. 190, no. 35-36, p. 4587-4608, DOI:10.1016/ s0045-7825(00)00334-0. [9] Kiekbusch, T., Sappok, D., Sauer, B., How-ard, I. (2011). Calculation of the combined torsional mesh stiffness of spur gears with two- and three-dimensional parametrical FE models. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 11, p. 810-818, DOI:10.5545/sv-jme.2010.248. [10] Guangjian, W., Lin, C., Li, Y., Shuaidong, Z. (2017). Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method. Mechanism & Ma-chine Theory, vol. 109, p. 1-13, DOI:10.1016/j. mechmachtheory.2016.11.006. [11] Chen, Y., Hu, Y., Lyu, Y., He, G. (2020). Development of a form milling method for line gear: principle, CNC machine, cutter, and testing. International Journal of Advanced Manufacturing Technology, vol. 107, no. 3-4, p. 1-11, DOI:10.1007/s00170­019-04771-2. [12] Chen, Y.Z., Yao, L. (2016). Design formulae for a concave convex arc line gear mechanism. Mechanical Sciences, vol. 7, no. 2, p. 209-218, DOI:10.5194/ms-7-209-2016. [13] Chen, Y., Huang, H., Lv, Y. (2016). A var-iable-ratio line gear mechanism. Mechanism and Machine Theory, vol. 98, p. 151­163, DOI:10.1016/j.mechmachtheory.2015.12.005. [14] Chen, Y.Z., Lv, Y.L., Ding, J., Chen, Z. (2013). Fundamental design equations for space curve meshing skew gear mechanism. Mechanism and Machine Theory, vol. 70, p. 175­188, DOI:10.1016/j.mechmachtheory.2013.07.004. [15] Marimuthu, P., Muthuveerappan, G. (2013). Influence of pressure angle on load sharing based stresses in asymmetric normal contact ratio spur gear drives. Applied Mechanics and Materials, vol. 465-466, p. 1229-1233, DOI:10.4028/www. scientific.net/amm.465-466.1229. [16] Ding, J., Chen, Y.Z., Lv, Y.L., Song, C. (2014). Position-parameter selection criterion for a helix-curve meshing-wheel mechanism based on sliding rates. Strojniški vestnik - Journal of Mechanical Engineering, vol. 60, no. 9, p. 561-570, DOI:10.5545/sv-jme.2013.1574. [17] Litvin, F.L., Fuentes, A., Hayasaka, K. (2006). Design, manufacture, stress analysis, and experimental tests of low-noise high endurance spiral bevel gears. Mechanism and Machine Theory, vol. 41, no. 1, p. 83-118, DOI:10.1016/j. mechmachtheory.2005.03.001. [18] Kulkarni, N., Gautham, B.P., Zagade, P., Panchal, J., Allen, J.K., Mistree, F. (2014). Exploring the geometry and material space in gear design. Engineering Optimization, vol. 47, no. 4, p. 561-577, DOI:10.1080/0305215x.2014.908868. [19] Bjrling, M., Miettinen, J., Marklund, P., Lehtovaara, A., Larsson, R. (2015). The corre-lation between gear contact friction and ball on disc friction measurements. Tribology International, vol. 83, p. 114-119, DOI:10.1016/j.triboint.2014.11.007. [20] Wu, X.T. (2009). Principle of Gearing. Jiaotong University Press, Xi’an. (in Chinese) [21] Li, X., Sosa, M., Olofsson, U. (2015). A pin-on-disc study of the tribology characteris-tics of sintered versus standard steel gear materials. Wear, vol. 340-341, p. 31-40, DOI:10.1016/j. wear.2015.01.032. [22] He, J., Wu, X., Cui, Y. (2004). Gearing principle and geometric design of conical in-volute gear pairs with crossed axes. Proceedings of the Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science, vol. 218, no. 12, p. 1517-1526, DOI:10.1243/0954406042690461. [23] Chen, Y.Z. (2014). Line Gear. Science Press, Beijing. (in Chinese) [24] Chen, Y.Z., Luo, L., Hu, Q. (2009). The contact ratio of a space-curve meshing-wheel transmission mechanism. Journal of Mechanical Design, vol. 131, no. 7, art. ID 074501, DOI:10.1115/1.3116343. [25] Wang, G., Su, L., Zou, S. (2020). Uneven load contact dynamic modelling and trans-mission error analysis of a 2K-V reducer with eccentricity excitation. Strojniški vestnik - Journal of Mechanical Engineering, vol. 66, no. 2, p. 91-104, DOI:10.5545/sv-jme.2019.6298. [26] Yu, L., Wang, G., Zou, S. (2018). The ex-perimental research on gear eccentricity error of backlash-compensation gear device based on transmission error. International Journal of Precision Engineering and Manufacturing, vol. 19, p. 5-12, DOI:10.1007/s12541-018-0001-7. [27] Guangjian, W., Lin, C., Li, Y., Shuaidong, Z. (2017). Research on the dynamic transmis-sion error of a spur gear pair with eccentricities by finite element method. Mechanism and Machine Theory, vol. 109, p. 1-13, DOI:10.1016/j. mechmachtheory.2016.11.006. Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 363-368 Received for review: 2021-02-21 © 2021 Journal of Mechanical Engineering. All rights reserved. Received revised form: 2021-05-11 DOI:10.5545/sv-jme.2021.7139 Original Scientific Paper Accepted for publication: 2021-06-21 Predictive Estimation of Sliding Bearing L oad-Carryi ng Capacity and Tribological D urability Myron Chernets1 – Marek Opielak2 – Anatolii Kornienko1,* – Oleg Radko3 1Aerospace Faculty, National Aviation University, Ukraine 2Lublin University of Technology, Poland 3 National Defence University of Ukraine named after Ivan Cherniakhovskyi, Ukraine A computational method is presented as a method for solving a plane contact problem of the theory of elasticity to determine the contact strength and tribological durability of sliding bearings. The effect of load and radial clearance on the initial contact pressures and their reduction due to wear is studied. The durability of the bearing is estimated. Qualitative and quantitative regularities of changes in contact parameters and durability from the factors under study are established. In particular, it has been shown that both contact angles and maximum contact pressures are approximately linearly dependent on the load, and the durability decreases nonlinearly with increasing load. Keywords: sliding bearing, wear-contact problem, contact and tribocontact parameters, wear, durability Highlights • A computational method for sliding bearings is presented. • A tribokinetic wear model for sliding friction has been developed. • Evaluation of contact pressures and durability has been carried out. • Regularities of the influence of wear on contact characteristics and resources have been established. 0 INTRODUCTION The use of sliding bearings as one of the common friction units (Fig. 1) currently remains quite significant, where the use of rolling bearings is impossible or impractical. The main recommendations for their use are high load capacity, use at miniature or large shaft diameters, at significant speeds, at shock loads, small radial dimensions, low noise, damping capacity, etc. The range of their application in practice is very diverse [1]. They work in various conditions, not only at liquid conditions but also at boundary and dry friction in separate cases. Under certain operating conditions, special alloys can be used to make the shaft, for example [2]. It should be noted that the number of new types of composite materials for metal bearings is growing rapidly [3]. Therefore, the estimated assessment of their bearing capacity, wear, and durability at the design stage is an urgent task. The solutions of the corresponding wear-contact problems for such sliding tribosystem are known in the literature [4] to [16]). In particular, in [7] and [8], a model of the sliding bearing wear in conditions of boundary friction was obtained in the form of dependence of the wear rate on the dimensionless complexes of contact pressure and sliding velocity. The parameters of wear resistance in the model were determined by the calculation-experimental method on the basis of wear tests with the “ cone – three balls” structure under variable contact conditions. Such a non-standard friction structure (ISO 7 148­ 2) significantly limits the use of this wear model. Paper [9] presents the results of an experimental and numerical study of fibre-reinforced polymer bearings. The authors developed a two-dimensional finite-element model to study the stresses in the bearing and researched three-dimensional quasi-static and two-dimensional dynamic models. A study on the effect of the clearance on the contact stresses and kinematics of large-scale composite bearings in [10] was conducted experimentally, using the finite element method. The results of the wear study are not given. Paper [11] presents an adaptive wear-modelling method in plain bearings. Validation was done for a laminated polymeric composite bearing. A study of the effect of clearance on the wear and the evolution of contact pressure due to wear was performed. In [12], the method of triboelements and the modelling of the behaviour of sliding tribosystems on the basis of Archard’ s law of abrasive wear with use of ANSYS are presented. Paper [13] aimed to study the wear of a fine elastic layer with the rigid bearing and shaft with the same method. Numerical analysis of the effect of the external load scattering and the initial radial clearance in the bearing on its wear was carried out. Paper [14] presents the results of a numerical simulation with the triboelement method to determine the wear of a thin elastic layer on a hard bushing of a cylindrical linear plain bearing. These orks use Arhards la of wear. Methods for estimating the parameters of the durability model under the mechanism of high-cycle fatigue under sliding friction conditions are proposed in [15]. The results are recommended for analysing the reliability and durability of friction units of machines under fatigue wear conditions. For the numerical modelling of the wear kinetics of tribosystems, an iterative approach is presented in [16], which takes into account the discrete states and operational factors affecting wear. The wear of the tribosystem elements is calculated. The abovementioned methods have not yet found proper practical application due to the use of a simplified Archard’ s law of abrasive wear assuming the wear intensity linear dependence on the contact pressure and the friction path, although this type of wear is unacceptable in sliding bearings. Today, in engineering practice and in the design calculations of sliding bearings, it is customary to use two main parameters: the average pressure p and the parameter pv. This simplification is very approximate, because the contact area characteristics depend not only on the load and the diameter of the shaft journal but also significantly on the radial clearance in the bearing and the elastic characteristics of the element materials. The last of the specified significant factors of influence are not considered in any way in the specified criteria, and the problem of predictive evaluation of sliding bearings durability at the design stage is not considered here at all. Therefore, reasonable methods for calculating bearings should be based on the contact problems of the theory of elasticity for cylindrical bodies of close radii. This study aims to use the author’ s generalized computational method [4] and [17] to [23] to estimate tribocontact pressures and durability when the bearing wears. This method is based on the concept [4], [17] and [18] of near-surface layers frictional-fatigue destruction of tribosystem elements in the process of sliding friction. In particular, in [17], the author presented a method of approximate solution of cylindrical sliding tribosystem consisting of elements with small non-circularity of its contours for the first time. The model of the triboprocess and the method of calculating the contact pressures were considered; in [18], a set of different contact problems is considered, taking into account wear for cylindrical tribosystems consisting of elements with non-circular contours; in [19], a cumulative analytical model of wear and durability of plain bearings is presented and schemes of plain bearings with different faceting of the shaft and the bushing are investigated; in [20], a generalized method for solving the contact problem for a cylindrical joint with complex faceting is presented. The parameters of one- and two-region contact are determined; in [21], according to the author’ s cumulative model of wear of plain bearings with technological ovality of adjacent parts, the accuracy of calculations of their service life was evaluated. The developed express calculation method of the tribocontact interaction of the shaft and the bushing is given; in [22], the generalized cumulative model of research of wear kinetics for the plain bearings in the case of one- and two-region contact is given. The results of solving the nonclassical contact problem and the wear contact problem are presented; in [23], the solution of the wear-contact problem for a bearing with different faceting of the shaft is given. Using the cumulative model, the influence of the faceting on the service life of the bearing at the complete one-region and mixed-region contact was investigated. Based on the above methods of solving a complex wear-contact problem of the theory of elasticity, an easier-to-implement engineering method is presented below. 1 WEAR TRIBOKINETIC MODEL OF SLIDING FRICTION According to [4], the materials’ wear kinetics in sliding tribosystem is described by a system of ordinary differential equation: 1d h ˜k.k.k() °.1, (1) vd t where his the linear wear function of tribosystem k elements; .k is the wear rate of their materials; v is the sliding speed; t is the triboprocess time (t) is the basic parameter of the model as the characteristic function of wear resistance of tribocouple materials; k = 1, 2 is the numbering of tribosystem elements. The specific force of friction in mechanics and tribology is determined by the Amonton-Coulomb formula: ˜.f°r, (2) where f is the sliding friction coefficient; sr =–p(a) is the contact stress calculated according to the methods of the elasticity theory; p(a) are the contact pressures. The characteristic function (t) of wear ii resistance of materials for discrete values of specific friction forces t is established by the results of tribo- i experimental studies according to the method [18] and [19]: L ˜i°i.hii, (3) .. where L= vt is the friction path; .= 1, 2, 3, ... are the levels of load in the tribo-experiment. Approximation of experimental values of wear resistance functions F(t) is carried out by the relation ii [18] and [19]: k ° ˜..°.Bkm0, (4) kkmk°°k0 . .ˆ where B kmk , tk 0 are the wear resistance characteristics of materials in the tribocouple. 2 FORMULATION OF A TRIBOCONTACT PROBLEM The arrangement of the sliding bearing is presented in Fig. 1. Shaft 2 rotates at a constant angular velocity .2. Under the influence of the reduced external load N = F/l , the contact pressures p(a) unknown in distribution and magnitude arise in the contact area. There is the radial clearance e= R 1 R 2> 0 in the bearing. The materials of the shaft and the bushing usually have different elastic properties and different wear resistance. The bearing elements have different wear areas: the bushing 1 in the area 2R 2a0 and shaft 2 along the contour. The problem is solved as a plain problem of the elasticity theory, where the external load F on the shaft is related to the length of the journal l . Fig. 1. Scheme of the sliding bearing When solving the problem, it is necessary to determine: initial contact angle 2a0; maximum initial contact pressures p(0); tribocontact angle 2maximum tribocontact a; at pressures wear0h.. permissible wear h; bearing elements wear h during kk the accepted service life t . NREC(7) 4, hhh20sin ..ˆ . According to the methods in [4], [18], and [20], the equilibrium Eq. (5) is used to determine the initial . .ˆ contact semi-angle a0 under the action of the reduced load N = F/l , the journal radius R 2 and the radial °  clearance e. . 0 ° NRp˜RE ˜22204()cossind, (5)  .4 ˆ 0 ˜ 2 ecos °./4 .4 EE where E˜0, e˜12,0 ˜°.0 °90 ˜, R2 Z ( E34, k tA.......................................................w..............................................- 0 ˜°. .2 . 2 t........-A.......................................................w..............................................- 4 (0, ); bearing durability at the accepted elements thtp..Z..E..˜°˜°°°°°..(1)())(),k are Young’s modules and Poisson’s ratios of E”, shaft 1 and bearing bushing 2 materials. Eq. (5) is solved using the method of successive approximations, bky ensuring the equality of its left and right parts with the accepted accuracy. Accordingly, to determine the k1211maximum initial (0), which contact pressurespcharacterize the bearing load-carrying capacity, the 1 developed method uses the formula: (6) Ep0tan .Determining the tribocontact semi-angle a0h while shaft and bearing bushing wear is carried out by a similar dependence as for the contact semi-angle a:0.ˆ.˜.where hh ˜°., hktkkhKh°.max()12 h 1, Kt(1)= 1, Kt(2) ˜°. are the overlap coefficients; Ch > 0 is the 0 wear rate indicator; h1 is the permissible bushing wear: 1 ˆ.B.m..m 21 ..0 ....h11.2 h1 ˜°°°Kt, m h1 ˆ.... 2 ..B...m20221 220 10 .m hˆ..B......m 1 2 220 ..1 h2 ˜°°°Kt, m h2 ˆ1 ...B......m102112 110 20 ˆ is the maximum specific friction force acttaning at 20the wear process beginning when = 0; h1, h2 are the linear wear of bushing and shaft, respectively. Maximum contact pressure p(0, h) in the bearing at elements wear: where ˜.fp() .fE°..0  parameters 1 °m MS°t () 2 , (11) 2 °() S M2  ˆ 1 . . ° m 2 The results of solving the considered wear­ ( () ph,.(8) pt0 ,,hp) ˜0 °(0 ) The change in the maximum initial contact pressure p(0, h) due to bearing elements wear is calculated as follows: p(0 ,h)EChh tan 0 h.(9) 2 Since the bushing material is less wear-resistant than the shaft material and the bushing wears at a limited contact area, the bearing service life is determined by the bushing durability when it reaches the maximum permissible wear. According to [4], [22], and [23], taking into account the dependences, Eqs. (1), (2), (4) , (6) and (9) , the bearing service life t is calculated by the formula: 1 °B.m1 t*˜10. '(1) vCS.°.1 h.ˆ.1 °mK ˆ hh11 t 1 °m 1 °m1 1 .() S°.SCS.hhhˆ, (10) where S = f · p(0) / e, Sh = f · p(0, h) / (eh Ch), v= .· R 2. If it is necessary to estimate the shaft wear ..ˆ h2 along its entire contour over time t , the wear is calculated as follows (after the corresponding  °.. transformation of Eq. (10)): . 1 h2 ˜ 2 '2 () () CSKhh°hKt .t2 ..ˆ ˜ The calculation of contact semiangle a0, maximum contact pressure p(0), tribocontact semiangle a0h, maximum contact pressure at wear p(0, t, h), bearing service life t and linear shaft wear * h2 was performed according to the given flow diagram (Fig. 2). Fig. 2. The flow diagram of calculation of contact and tribocontact vA.......................................................w..............................................- A.......................................................w..............................................-m hA.......................................................w..............................................- 2 Bˆm where M2 ˜202 , and 2 '2 () () vCS(1 °m) .K°h..K hh2 t2 t ()2 1 ˜°/KhhK() ˜. 2 tt1 3 RESULTS OF NUMERICAL SOLUTION Data for calculation of contact and tribocontact parameters, durability: N = 25 N, 62.5 N, 125 N, F = Nl ; D 2 = 50 mm; l= D 2; .2 = 1 s–1, 5 s–1; = 25 mm/s, 125 mm/s; e = 0.125 mm, 0.25 mm; f = 0.05 at boundary friction; h1 0.5 C = 0.05. Bushing material: teen bronze .1 = 1.2· 10P, 5 ”1 = 0.34; B 1 = 1.9· 109 , m1 = 0.76, t01 = 0.1 MPa; shaft material: hardened steel .2 = 2.1· 10P, ”2 = 0.3; 5 B 2 = 4.9· 109 , 2 = 0.66, t02 = t01. contact problem are presented in Figs. 3 t o 5. e = 0.25 m m e = 0.25 m m e = 0.125 m m e = 0.125 m m Fig. 3. Dependences of initial contact angles on loading and their changing at wear: 2a0 in dashed lines, and 2a0h in solid lines For the initial contact angle 2a0 in the studied range of loads, there is an almost linear dependence in their increase. Naturally, with smaller radial clearances, these angles will be larger. When the accepted permissible wear is reached, the tribocontact angles 2a0h increase up to 2 times at both values of the radial clearances. e = 0.25 m m e = 0.25 m m e = 0.125 m m e = 0.125 m m Fig. 4. Dependences of initial contact angles on loading and their changing at wear: p(0) in dashed lines, p(0, th ) in solid lines At relatively low loading, a nonlinear increase in the initial maximum pressures p(0) is observed, and a further increase in the load leads to their linear increase. The wear of the bronze bushing contributes to a significant reduction in pressure. Tribocontact pressures p(0, th ) depend to varying degrees on radial clearance and wear. Fig. 5. Dependence of the bearing service life on loading As the load increases, the bearing service life decreases nonlinearly. With a fivefold increase in angular velocity, there is a directly proportional decrease in service life. 4 CONCLUSIONS 1. The presented method of predictive estimation of sliding bearings load-carrying capacity and tribological durability allows carrying out substantiated and effective research on such basic factors of influence as external loading, shaft diameter, radial clearances, and wear. 2. An important feature of the method is the ability at the design stage to perform both the calculation of bearing service life, and the solution of inverse problem: the assessment of the bushing and shaft wear accepted service life. The solution is presented in a closed form, and this allows its implementation using the simplest software, starting from Excel (Figs. 3 t o 5) . 3. It should also be noted that the method (presented in Section 2) can be used without any restrictions not only for the calculation of bearings with metal elements, as presented above, but also when the friction surfaces are coated with different composition and purpose (protective, antifriction, wear-resistant) coatings. 4. On the basis of this method, it is possible to carry out the optimization on criteria of contact strength, wear resistance and durability, as well as an optimum choice of materials at the stage of the bearings designing. It is also very promising to use the method for hybrid bearings, with materials that are significantly different in their properties are used. 5. It is an advanced method for the calculation of metal-polymer bearing assemblies, because there are no calculation methods for such friction assemblies. 6. Solutions of this type of wear-contact problems can also be used to estimate the error of calculations obtained by various numerical methods (the finite element method, the boundary element method, etc.). 4 REFERENCES [1] Lawrowski, Z. (2007). Sliding bearings. History, current state, development prospects. Tribologia, vol. 26, no. 6, p. 7-61. [2] Cherepova, T., Dmitrieva, G., Tisov, O., Dukhota, O., Kindrachuk, M. (2019). Research on the properties of Co-TiC and Ni-TiC HIP-sintered alloys. Acta Mechanica et Automatica, vol. 13, no. 1, p. 57-67, DOI:10.2478/ama-2019-0009. [3] Panarin, V. Ye., Kurdyumov, G.V., Svavil’nyy, M. Ye., Khominych, A.I., Kindrachuk, M.V., Kornienko, A.O. (2017). Creation of a diffusion barrier at the interphase surface of composite coatings reinforced with carbon nanotubes. Journal of Nano- and Electronic Physics, vol. 9, p. 06023-1–06023-5, DOI:10.21272/jnep.9(6).06023. [4] Andreikiv, A.E., Chernets, M.V. (1991). Evaluation of the Contact Interaction of Rubbing Machine Elements. Naukova Dumka, Kiev. [5] Kuzmenko, A.G. (2010). Development of Methods of Contact Tribomechanics. KhNU, Khmelnytsky. [6] Zwiezycki, W. (1999). Predicting the Reliability of Wearing Machine Elements. Institute for Sustainable Technologies, Radom. [7] Dykha, A., Sorokatyi, R., Makovkin, O., Babak, O. (2017). Calculation-experimental modeling of wear of cylindrical sliding bearings. Eastern-European Journal of Enterprise Technologies, vol. 5, no. 1, p. 51-59, DOI:10.15587/1729­4061.2017.109638. [8] Dykha, A., Marchenko, D. (2018). Prediction the wear of sliding bearings. International Journal of Engineering & Technology, vol. 7, no. 2.23, p. 4-8, DOI:10.14419/ijet.v7i2.23.11872. [9] Rezaei, A., Ost, W., Van Paepegem, W., De Baets, P., Degrieck, J. (2011). Experimental study and numerical simulation of the large-scale testing of polymeric composite journal bearings: Three-dimensional and dynamic modelling. Wear, vol. 270, no. 7-8, p. 431-438, DOI:10.1016/j.wear.2010.11.005. [10] Rezaei, A., Ost, W., Van Paepegem, W., De Baets, P., Degrieck, J. (2012). A study on the effect of the clearance on the contact stresses and kinematics of polymeric composite journal bearings under reciprocating sliding conditions. Tribology International, vol. 48, p. 8-14, DOI:10.1016/j. triboint.2011.06.031. [11] Rezaei, A., Van Paepegem, W., De Baets, P., Ost, W., Degrieck, J. (2012). Adaptive finite element simulation of wear evolution in radial sliding bearing. Wear, vol. 296, no. 1-2, p. 660-671, DOI:10.1016/j.wear.2012.08.013. [12] Sorokatyi, R.V. (2002). Modeling the behavior of tribosystems using the method of triboelements. Journal of Friction and Wear, vol. 23, no. 1, p. 16-22. [13] Sorokatyi, R.V. (2003). Solution of the problem of wear of a fine elastic layer with a rigid bearing mounted on a rigid shaft using the method of triboelements. Journal of Friction and Wear, vol. 24, no. 1, p. 35-41. [14] Sorokatyi, R.V. (2003). Evaluation of efficiency of sliding bearings during reciprocation. Journal of Friction and Wear, vol. 24, no. 2, p. 136-143. [15] Sorokatyi, R., Chernets, M., Dykha, A., Mikosyanchyk, O. (2019). Phenomenological model of accumulation of fatigue tribological damage in the surface layer of materials. Mechanisms and Machine Science, vol. 73, p. 3761-3769, DOI:10.1007/978-3-030-20131-9_371. [16] Dykha, A., Sorokatyi, R., Pasichnyk, O., Yaroshenko, P., Skrypnyk, T. (2020). Machine wear calculation module in computer-aided design systems. IOP Conference Series Materials Science and Engineering, vol. 1001, art. ID 012040, DOI:10.1088/1757-899X/1001/1/012040. [17] Chernets, M.V. (1996). On the issue of assessing the durability of cylindrical sliding tribosystems with boundaries close to circular. Friction and Wear, no. 3, p. 340-344. [18] Chernets, M.V. (2009). Contact Problems for Cylindrical Systems with Low Angularity of Contours When Worn. Drohobycz State Pedagogical University, Lviv. [19] Chernets’, M.V., Andreikiv, O.E., Liebiedieva, N.M., Zhydyk, V.B. (2009). A model for evaluation of wear and durability of plain bearing with small non-circularity of its contours. Materials Science, vol. 2, p. 279-290, DOI:10.1007/s11003-009-9176-5. [20] Chernets’, M.V. (2009). Contact problem for a cylindrical joint with technological faceting of the contours of its parts. Materials Science, vol 45, p. 859-868, DOI10.1007/s11003­010-9252-x. [21] Chernets’, M.V., Zhydyk, V.B., Chernets’, Yu.M. (2014). Accuracy of evaluation of the service life of a plain bearing according to the generalized cumulative model of wear. Materials Science, vol. 50, p. 39-45, DOI:10.1007/s11003­014-9689-4. [22] Chernets, M., Chernets, Ju. (2015). Generalized method for calculating the durability of sliding bearings with technological out-of-roundness of details. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 229, no. 2, p. 216-226, DOI:10.1177/1350650114554242. [23] Chernets, M.V. (2015). Prediction of the life of a sliding bearing based on a cumulative wear model taking into account the lobing of the shaft contour. Journal of Friction and Wear, vol. 36, p. 163-169, DOI:10.3103/S1068366615020038. Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 369-379 Received for review: 2021-03-09 © 2021 Journal of Mechanical Engineering. All rights reserved. Received revised form: 2021-05-18 DOI:10.5545/sv-jme.2021.7156 Original Scientific Paper Accepted for publication: 2021-06-28 Exp erimental Investigation and Mathematical Modelling of H eat Transfer Coefficient in D ouble Slope Solar Still Raj Vardhan Patel1,2 – Anshul Yadav1,2 – Jerzy Winczek3* 1Kamla Nehru Institute of Technology, India 2CSIR-Central Salt and Marine Chemicals Research Institute, India 3 Czestochowa University of Technology, Poland In this study, a double slope solar still has been designed and fabricated with the help of locally available materials for the climatic condition of Sultanpur, India. The experimental study was performed to investigate the effect of basin water, wind velocity on the heat transfer coefficient (convective, evaporative, and radiative) and yield of solar still. A mathematical model is developed to understand the impact of wind velocity and basin water depth in the double slope solar still on the heat transfer coefficient. It was found that the convective heat transfer coefficient depends upon the water mass and the temperature of basin mass, and glass cover temperature. The maximum value of hew (55.05 W/(mČK) and 31.80 W/(mČK)) and hcw , (2.48 W/(mČK) and 2.38 W/(mČK)) found for depths of 2 cm and 5 cm, respectively. The radiative heat transfer coefficient found to be a maximum of 8.31 W/(mČK) for 2 cm depth, and it increases as the condensation increases, because the glass surface temperature increases as vapour transfers its energy to the surface. On increasing the depth from 2 cm to 5 cm, the yield from the solar still decreases by 25.45 %. The maximum yield of 2.5 l/mČ/day was found for a 2 cm water depth. The theoretical and experimental yield agreed with an error of 7.5 %, 3.25 %, 7.4 %, and 8.4 % for water depths of 2 cm, 3 cm, 4 cm, and 5 cm, respectively. It was also found that the yield from the solar still increases as the wind speed increase because this leads the faster condensation at the glass surface. Keywords: double slope solar still; solar energy; distillation; heat transfer coefficient Highlights • A mathematical model is developed to find the yield and heat transfer coefficient for double slope solar still with the experimental findings on the yield and heat transfer coefficient. • Convective and evaporative heat transfers were the most critical parameters for a solar distillation unit. • The radiative heat transfer coefficient increases as the condensation increase because, due to condensation, the glass surface temperature increases as vapour transfers its energy to the glass surface. • The yield from the still increases as the basin water depth decreases. The evening time production is higher for higher basin mass because of the heat-storing capacity of basin mass. • The yield of solar still increases as the wind speed increases because this leads to higher condensation on the glass surface. 0 INTRODUCTION Currently, energy and fresh water supplies are major challenges in remote areas. Only 1 % of the total water available on the earth can be used for drinking. Current distillation methods use conventional fuel, which are a limited resource, and there is environmental pollution when such fuels are used to generate power. Solar stills are simple devices that can be used to produce potable water. They can be an effective solution for providing potable water in remote areas [1] and [2]. Solar stills are generally classified into two categories: active and passive [3] and [4]. Solar stills require only solar energy for their operation, which is freely available and eco-friendly, and work on the simple principle of evaporation and condensation. Solar distillation removes salts and other impurities [5] and [6]. It is used to produce potable or pure water for hospitals, laboratories, and commercial products [7] and [8]. The yield of a conventional solar still depends on the water mass in the basin. The effect of that water mass on the solar heat transfer still has been investigated by various researchers [9] to [11]. The studies concluded that as the mass of basin water increases, the yield from the system decreases. Dev et al. [9] investigated the inverted absorber single slope solar still, and found higher production of freshwater with 1 cm depth compared to 2 cm and 3 cm depths. Phadatare and Verma [10] studied water depth on the internal heat and mass transfer in the single-basin double-slope solar still (DSSS). Tripathi and Tiwari [11] concluded that the yield from the system decreases as the mass of basin water increases. The experimental and analytical study performed by Feilizadeh et al. [12] reported that the production from the solar still increases as the water depth and distance between the water basin and the condensing cover is lower. The radiative and convective heat transfer decrease as the water mass in the basin increases. The influence of wind on the production of solar stills was investigated by El-Sebaii [13] and [14], who determined that the increase in wind speed up to a critical value increases the yield of still. Higher wind speed decreases the yield because it decreases the basin temperature. An experiment conducted by Danish et al. [15] to enhance the performance of the solar still by using a vacuum pump and geothermal energy found that the increases in wind speed have a detrimental effect on the yield of solar still, because the increase in speed increases the heat loss from the basin water. The production rate of solar stills is low; therefore, they cannot be used as a conventional water purifier. The yield from a solar desalination unit increased by incorporating phase change materials (PCM) [16] and [17] and nanofluids [18] and [19] to the basin water. Mathematical modelling has been as subject of some interest as it can optimize the efficiency and production by changing the different operational and geometrical parameters without losing its inherent feature of low cost; the main advantage associated with modelling analysis that much effort and cost can be minimized for carried out the experimentation [20] and [21]. Rahbar and Esfahani [22] proposed a numerical correlation to determine the productivity of a solar still by assuming the fixed water depth and glass temperature. The trends of water production are similar to the convective heat transfer coefficients. Madhlopa [23] modelled the radiative heat transfer inside a solar still with and without considering the view factor, and the numerical model with view factor involving provides better yield. Keshtkar et al. [24] proposed a novel transient model to calculate transient temperature and concentration distribution and also production from a solar still without specifying the water and glass surface temperatures as the boundary condition. The production of a solar still is dependent on the rate of heat transfer in the solar still, basin water, and wind velocity (which provides glass cover cooling), and similar factors. The present study focuses on studying the variation of the heat transfer coefficient with basin water temperature and wind velocity for the acrylic solar still for the summer climatic condition of Sultanpur, India. The different heat transfer coefficient associated with DSSS is compared for different water depths, and the comparisons have been made for the orientations (i.e., east and west sides). 1 EXPERIMENTS 1.1 Solar Distillation Unit The schematic diagram and the experimental setup of the DSSS are shown in Figs. 1 and 2, respectively. A passive DSSS is designed and fabricated to investigate the effect of climatic and operational parameters on a solar still for the summer climatic condition of Sultanpur (latitude: 26.2648° N and longitude: 82.0727° E) Uttar Pradesh, India. The basin of the solar still is fabricated frin a black acrylic sheet of a thickness of 4 mm. The basin size of the still is 1 m Ś 1 m Ś 0.1 m. Plywood of 12 mm thickness is used for support and insulation of solar still basin in order to reduce the heat transfer from the bottom and side of solar still basin. The acrylic material has been selected due to its low thermal conductivity and high water-resistant nature. The still is designed for the maximum water depth of 10 cm. Glass of 3.5 mm thickness used as the condensing cover, which is inclined at an angle of 30° . The condensing cover inclination is equal to the latitude of Sultanpur to receive maximum radiation from the sun. The basin of the still is painted black to enhance the capacity of the basin to receive the maximum solar radiation. A V-shaped trough of length 1.02 m is provided below the condensing cover to collect the condensed water from the glass surface. M-seal and putty were used to make still airtight and prevent water leakage. Fig. 1. A schematic diagram of solar still 1.2 Experimental Measurements The experiments were performed in March and April 2016. The solar still was placed in the east-west orientation for the experiments. Seven digital temperature sensors were used to record the temperature reading at the different locations of solar still. Global solar radiation, ambient temperature, and wind speed data were taken from the solar radiation resource assessment (SRRA) station installed at the KNIT, Sultanpur, India. A digital anemometer was used for measuring the wind velocity. The temperature readings were recorded at a one-hour interval. The experiments were carried out for different water depths, of which 2 cm, 3 cm, 4 cm, and 5 cm are presented in this study. Fig. 2. Experimental setup of solar still 1.3 Error Analysis of Experimental Measurements The errors associated with the different measuring instruments (solarimeter, digital thermometer, digital anemometer, and measuring jar) have been calculated based on the least count and the least value measured from that instrument during the experimentation. The minimum error is the ratio of the least value that an instrument can measure to the least value measured from that instrument. Table 1 shows the error percentages associated with the different measuring instruments. Table 1. List of measuring devices and their accuracy and error Instrument Range Accuracy Error [%] Solarimeter 0 W/mČ to 2500 W/mČ ±1 W/mČ 0.707 Thermometer –50 °C to 150 °C ±0.1 °C 0.37 Anemometer 0 m/s to 15 m/s ±0.1 m/s 9.17 Measuring jar 0 ml to 1500 ml ±1 ml 10 2 THERMAL CALCULATION FOR THE MODEL 2.1 Mathematical Model for Heat Transfer in Solar Still The heat transfer can be classified into two categories: internal and external heat transfer in a solar distillation system. The different heat interactions in the solar distillation unit are explained below. 2.1.1 Internal Heat Transfer The internal heat transfer is the heat transfer between basin water and glass cover by convection, evaporation, and radiation. 2.1.2 Convective Heat Transfer The heat transfer is taking place across the air, which is inside the solar still. As the system is airtight, there is no external velocity provided to the inside air to cause heat transfer. The air is humid because of vapour evaporating from the water surface; the heat transfer is due to the buoyancy only, meaning that free convection heat transfer occurs inside the still casing. The rate of convective heat transfer ( q.cw) from the water surface to condensing glass cover is given by: q. ˜h.T°T.. (1) cwcwwg The convective heat transfer coefficient depends on the operating temperature range of still and physical properties of the fluid at this operating temperature, condensing cover geometry and flow characteristics of the fluid. Dunkle [25] developed an equation for evaluation of the internal heat transfer coefficient: 1 3 hcw˜0 0884 ( °T . *), (2) * ..P.P.Tˆ. . .273 15 wgw where ˜T°.T.T.ˆ. wg. .Pw 268 9103  . 2.1.3 Evaporative Heat Transfers The evaporative heat transfer occurs between the water surface and the inner glass surface of the DSSS. The rate of evaporative heat transfer ( q. ew) from the water surface to glass cover surface is given by: q. ˜h.T°T., (3) ewewwg and the evaporative heat transfer from the water surface to the glass surface is given by: q. ˜0 0162°h.P.P. .. (4) ewcwwg The above equation can be rearranged as: .3 .Pw.Pg.q. ˜16 273 °10 hT.T., . .(5) ewcwwg .T.T. wg .P.P. where h˜. °10 hwg 16 273 .3, ewcw .T.T. wg where Pw and Pg are partial saturation pressures [ W/m2] and given by [26]: 5144 Pg˜exp 25 317 °, . (6) T.273 15 . .gi. 5144 P˜exp 25 317 (7) .°. wT.315 273. .w. 2.1.4 Radiative Heat Transfer Coefficient The rate of radiative heat transfer ( q. ) from the water surface to glass cover for these infinite parallel surfaces is given by: q. ˜T°273 15 .4 .T27315 4 . (8) .. rweff.w.g°. The rate of radiative heat transfer is also given by: q. ˜h.T°T.. (9) rwrwwg The (hrw) is the radiative heat transfer coefficient . from the water surface to the glass cover and is given ..rwby (by comparing Eqs. (8) and (9)): rweffw. ..g°27315 2 54630 . . q ..2 hTT˜°°27315 . .TT°°(10) . wgwhere iseffective emissivity of water and glass e–8surface, Stefan-Boltzmann constant (5.67Ś10s2.1.5 External Heat Transfers . q ff 4 . q.ˆˆ.ˆ2W/(mK)). ˆ....ˆ.ˆ The external heat transfer is primarily governed by conduction, convection, and radiation process, which are independent of each other. These heat transfers occur outside the solar distiller, from the glass cover and the bottom and side insulation. 2.1.6 Top Loss Coefficient Due to the small thickness of the glass cover, the temperature of the glass may be assumed to be uniform. The external rate of heat transfer radiation (q. rg), convection (q. cg) and total heat (q.tg) losses from the glass to the ambient surroundings are expressed as: ˜°, (11) tgrgcg q. ˜ˆ.T°27315 4 T°273 15 .4  . ...., (12) rgggsky .. q. ˜h.T°T.. (13) rgrgga  Comparing the above Eqs. (12) and (13) , we obtain: 44 T273 15 ...T°. g.g°. sky273 15 . ˆ. hrg˜, (14 ) .T.T. ga .. where T sky = Ta – 6 [27], eg emissivity of the glass surface. The ambient emissivity is assumed to be 1, as it behaves as a black body [8]. (In case of clear and cloudy sky, the difference between ambient ˆ.. temperature and effective sky temperature was assumed to be 6 ° C) and the rate of convective heat transfer from the glass surface to ambient is given by: q. ˜h.T°T.. (15 ) cgcgga On substituting the value of (q. rg) and (q. cg) in Eq. (11), we obtain: q. ˜h.T°T., (16) tgtgga where htg = hrg + hc g . The expression for (htg ) and (h) is given by cg Watmuff and Charters [27]: htg = 5.7 + 3.8 V , (17) hc g = 2.8+ 3 V , (18 ) where V is wind velocity [ m/s] , htg is, hrg and h total, cg radiative, and convective heat transfer coefficient [ W/mČ ] from the top glass surface, respectively. 2.1.7 Bottom and Side Loss Coefficient Heat is also lost from the water in the basin to the ambient through the insulation, subsequently by convection and radiation from the bottom or side surface of the basin. The bottom loss coefficient (U ) b can be written as: 1 11 Ub˜°. (19 ) hh .wb. The side loss coefficient (U ) can be expressed as: e UA Ue= bSS, (20) AS where A SS is a sidewall surface area [ m2] in contact with basin water and A area of the basin of the S distiller [ m2] . A is very small in comparison to A , SSS for small water depth. Therefore, it can be neglected. The rate of heat loss per m2 from the basin liner subscripts w, g , a , and i indicate the basin water, glass to ambient can be written as: surface, ambient and insulation respectively. .˜.°., (21) qhTT bwa3 RESULTS AND DISCUSSIONS .ti1 ˆ1 where h˜°, where hw and h are b..b Kh°h .icbrb. convective and overall heat transfer coefficient from basin liner to ambient through the bottom, t thickness, i K thermal conductivity of the insulation material at ithe bottom, hc b and hrb convective and radiative heat transfer coefficient basin liner to ambient through the bottom. 2.1.8 Determination of Distillate Output The hourly distillate output per m2 from the solar still can be obtained as: hT°T q. ew.wg. ew m= 3600, or m˜3600, (22) ewew LL where L is latent heat of vaporization [ J/kg] for less than 70° and given by [27]: 6 .4 L˜2 4935 °10 .. °10 T . .ˆ19 4779 .72 .93 ... .. 1 3132 °10 T.4 7974 °10 T, where temperatures are in ° C and heat transfer coefficients are in W/(m2K). The heat transfers rate presented in the thermal modelling are in W/m2. The The present experimental work has been carried out for heat transfer analysis of the east-west orientation of DSSS for various basin water depths (2 cm, 3 cm, 4 cm and 5 cm). The east-west orientation has been chosen because the still gives maximum yield for this orientation. The experimental measurements were recorded and accurately from 8: 00 h to 17: 00 h. The mathematical equations which are used in the thermal model have solved analytically. As the difference between basin water and glass cover increases, the rate of heat transfer, as well as the production from the DSSS increases. 3.1 Variation of Basin Water Temperature with Basin Water Depth In Fig. 3, the variation of basin water temperature with the depth of basin water and wind velocity are represented. It can be seen that the basin water temperature for 2 cm water depth is higher compared to 3 cm, 4 cm, and 5 cm water depths. This is because the basin water with 3 cm, 4 cm and 5 cm depths have high thermal inertia compared to 2 cm water depth. Therefore, the basin filled with 2 cm water depth will be heated faster than other water depths. During the experiments, it was found that the Fig. 3. Variation of basin water temperature with basin water depth and wind velocity maximum temperature for 2 cm, 3 cm, 4 cm, and 5 cm depths are 69.0 ° C, 62.6 ° C, 58.5 ° C, and 54.4 ° C, respectively, between 13: 00 h and 14: 3 0 h. The peak starts shifted towards the right side as basin water depth increases from 2 cm to 5 cm. This is because 5 cm water depth requires more time to be heated, due to the higher mass present in the basin. The basin water temperature was found to be maximum for 2 cm depth. The temperature decrease for 2 cm water depth was higher than other higher water depth after 14: 00 h because of lower heat storage capacity. During the experimentation, the average wind velocity was found to vary between 2 m/s to 3 m /s. 3.2 Variation of Heat Transfer Coefficients with Basin Water Depth Figs. 4 to 6 show the variation of heat transfer coefficients (convective, evaporative, and radiative, respectively) for DSSS for the east and west glass. The curves are drawn for the positive value of temperature difference between basin water and glass cover surface (dT). The yield from the solar still increases either increase in evaporation temperature or decrease in condensing surface temperature. In both cases, the (dT) increases and the heat transfer rate increases. Fig. 4 shows the variation of the convective heat transfer coefficient obtained from Eq. (2). The convective heat transfer rate is strongly dependent on the temperature difference between the water and glass cover surface. Fig. 4 s hows that the average heat transfer coefficient for 2 cm water depth is maximum because of the higher temperature difference than higher water depths. This is because the lesser mass present in the basin with 2 cm depth requires less time to be heated. The maximum value of hw were c 2.48 W/(mČ K), 2.25 W/(mČ K), 2.21 W/(mČ K), and 2.38 W/(mČ K) for 2 cm, 3 cm, 4 cm, and 5 cm depths, respectively. The heat transfer coefficients are higher than the results obtained in the experimental studies by Shukla and Rai [28]. The maximum heat transfer occurs around 13: 00 to 14: 00 h, while in the case with 5 cm depth, the maximum value of hoccurs at 16: 00 cw h. This is because of the higher wind speed, which leads to faster cooling of the glass. Thus, the heat transfer of convection increases. The heat transfer coefficient is lower for 2 cm depth compared to 5 cm depth after 16: 00 h. This is because of the higher thermal storage capacity of 5 cm water depth, which leads to higher basin water temperature. Fig. 5 shows the variation of the evaporative heat transfer coefficient (calculated from Eq. (5) ) with basin water depth for the experimental setup. It can be observed from Fig. 5 that the hew is high for west glass because there is no direct sun heating of it in the morning, but as the evaporation starts and vapour start condensing on the west glass surface, the heat released during condensation heated the glass surface which leads the increase in the surface temperature of the glass. Thus, as the process continued, the temperature of west glass approaches saturation temperature, and due to this, condensation starts decreasing after 13: 00 h, 13: 30 h and 14: 00 h, and 14: 30 h for 2 cm, 3 cm, 4 cm, and 5 c m water depths. It is seen that from Figs. 4a and 5a that in the morning for 2 cm water depth, the rate of h and hew cw is maximum for the west glass because basin water, as well as the east glass, is heated; therefore, the dT is higher for the west glass as compared to the east glass. After 13: 00 h, the variation becomes closer for east and west glass because solar radiation does not directly fall on one glass only. This is also due to the higher basin water temperature as it absorbs solar energy since morning. However, in the case of higher water depths (i.e., 3 cm, 4 cm, and 5 cm), the east and west variation is almost eliminated because of the heating due to solar radiation and cooling due to wind. While 2 cm depth variation of heat transfer is faster than other depths, the wind velocity is higher with the 5 cm water depth; this is because of higher thermal energy storing capacity with the 5 cm depth consequent the slower cooling of the basin water. The h of east and west surfaces for the present solar still cw is higher for the period of 15: 00 to 17: 00, compared to Shukla and Rai [28]. This is because of the higher basin temperature and low thermal conductivity of acrylic material of solar still, which reduces the heat loss of the basin water. The average evaporative heat transfers were higher for 2 cm depth than other water depths (3 cm, 4 cm, and 5 cm). Therefore, the yield in the case of 2 cm water depth is maximum as the evaporation rate is the main driving parameter for the production from the solar still. From Fig. 5, the hew starts decreasing at a faster rate for 2 cm depth compared to other water depths. This is not only because of low heat-storing capacity for 2 cm water depth but also because of the lower heating rate for the other higher depths; thus, from the evening, the production rate starts decreasing faster for lower and nocturnal production is more for higher depths. The maximum value of hew is found to be 55.05 W/(mČ K), 49.23 W/(mČ K), 31.25 W/(mČ K) and 31.80 W/(mČ K) for 2 cm, 3 cm, 4 cm and 5 cm water depths. The peak of hew shifted to the right as the mass in the basin starts increasing; this is due Fig. 4. Variation of the convective heat transfer coefficient with basin water depth for: a) east glass, and b) west glass Fig. 5. Variation of evaporative heat transfer coefficient with basin water depth for a) east glass b) west glass Fig. 6. Variation of radiative heat transfer coefficient with basin water depth for a) east glass b) west glass to lower thermal inertia for 2 cm depths compared are found to be 2.48 W/(mČ K) and 55.05 W/(mČ K) to others depth. The maximum value of h and hew for the west glass, respectively, for 2 cm depth. cw There are some fluctuations in heat transfer because of uncontrolled wind speed over the DSSS glass surfaces. From Fig. 5, it can be seen that the heat transfer coefficient increases for higher water depths. This is due to an increase in wind speed which leads to better evaporation as well as condensation. When the results are compared with those of Shukla and Rai [28], the maximum and average evaporative heat transfer coefficients are found to be higher in this study. This is due to the higher temperature difference obtained with the present experimental setup. This higher temperature difference is because of higher basin temperature also due to the insulating nature of acrylic. Fig. 6 shows the variation of radiation heat transfer’ s coefficient (calculated from Eq. (8) ) for 2 cm, 3 cm, 4 cm and 5 cm water deptha for the experimental setup for the east and west glass of DSSS. The radiation heat transfer mainly depends on the basin water and glass surface temperature and the emissivity of basin water and glass surface. As the evaporation increases, the surface temperature of the glass surface increases due to the condensation of vapour on the glass surface. Therefore, the radiation heat transfer coefficient increases. The maximum heat transfer coefficients are found to be 8.32 W/(mČ K), 8.21 W/(mČ K), 7.47 W/(mČ K) and 7.41 W/(mČ K) for 2 cm, 3 cm, 4 cm and 5 cm water depths, respectively. Shukla and Rai [28] showed a lower radiative heat transfer coefficient than the present study did. This is because of the higher evaporation and condensation associated with the design of DSSS. In the present Fig. 7. Hourly yield from per m2 area of the solar still at 2 cm, 3 cm, 4 cm and 5 cm water depth; a) theoretical, and b) experimental study, the radiative heat transfer coefficient for 2 cm and 3 cm depth are higher because of the high basin temperature and higher evaporation associated with these depths, leading to increases in glass temperature as the hrw is the function of both glass and basin water temperature. It was also observed that the hew (west surface) was much higher for 3 cm compared to hrw, but the variation in hrw for 2 cm and 3 cm (Fig. 6b) is closer due to higher evaporation compensated by higher basin temperature for 2 cm depth. Fig. 7 shows the theoretical (calculated from Eq. (17) ) and experimental yield from the still for 2 cm, 3 cm, 4 cm, and 5 cm water depths in the basin. The theoretical yield from the still is higher than the experimental yield, but sometimes it is lower than experimental because of the atmospheric condition like wind speed; due to this, the vapour is condensed rapidly, whereas the theoretical yield depends on the temperature difference between the glass and basin water; also. the data recorded are average data. The yield for 2 cm water depth is higher than 3 cm, 4 cm. and 5 cm water depths. This proves that the yield is higher for a lower basin mass. After 15: 00 h, it can be seen that the yield for 2 cm depth is decreasing at a faster rate compared to other higher depts. This is due to the heat-storing capacity of the basin mass. This proves that the evening and off-sun time production is higher for higher basin mass. Before the afternoon, the yield rate is higher for 2 cm depth because of the higher evaporation rate as compared to other water depths. The wind has a positive effect on yield with higher depth compared to a lower depth. This is because the lesser depth (2 cm) of basin water’ s temperature decreases faster, which enhances the yield. While for higher depth (4 cm), this has a less negative effect due to the higher energy storing capability of water mass. It can be seen from Figs. 3 and 7b that the yield is higher when wind speed increases. This is because of the higher temperature gradient between the basin water condensing glass cover for 4 cm compared to the 2 cm depth water depth. The yield from the still is higher for the 4 cm depth between 13: 00 h and15: 00 h not only because of the wind speed but also due to the higher water mass, which stores more thermal energy and release during this time period. From Fig. 7b, it can be seen that the rate of production increases for 2 cm as well as 4 cm depths at a very high rate. This is due to an increase in wind speed and the high solar radiation during this period. 4 CONCLUSIONS The DSSS of acrylic with basin area 1 m with an inclination angle of 30° was fabricated for the climatic condition of Sultanpur, Uttar Pradesh, India. Various experiments were performed on this setup to analyze the effect of parameters, including different depths (2 cm, 3 cm, 4 cm and 5 cm), the wind velocity effect on the yield, and heat transfers. The experimental and theoretical yields have been compared. The following conclusions have been drawn from the present study. 1. Convective and evaporative heat transfers are the most critical parameter for a solar distillation unit. The maximum value of h (55.05 W/(mČ K), 49.2 W/(mČ K), 31.25 W/(mČ K) and 31.80 W/(mČ K)) and h(2.48 W/(mČ K), 2.25 W/(mČ K), 2.19 W/ (mČK) cawnd 2.38 W/(mČ K)) was found for 2 cm, 3 cm, 4 c m, and 5 c m depths, respectively. 2. The radiative heat transfer coefficient is found to be a maximum of 8.39 W/(mČ K) for 2 cm depth, and it increases as the rate of condensation increases on the glass surface. 3. The yield from the still increases as the basin water depth decreases because the lower basin water requires less time to come into steady-state, and due to this, the evaporation starts earlier. 4. On increasing the depth from 2 cm to 4 cm, the ewA.......................................................w..............................................- yield decreases by 17.62 % . In comparison, it decreases by 25.45 % when the water depth is 5 cm. The maximum yield of 2.5 l/m per day is found for 2 cm water depth. The theoretical and experimental yield from solar still agreed with an error of 7.5 % , 3.25 % , 7.4 % and 8.4 % for 2 cm, 3 c m, 4 c m and 5 c m water depths, respectively. 5. The afternoon production is higher for the higher basin mass because of the heat-storing capacity of basin mass. 6. During the initial time duration of still (i.e. 1 h to 2 h of operations), the rate of convective, evaporative, and radiative heat transfer coefficients is less. This is due to the slow heating of water mass in the basin because of the outer glass surface at a higher temperature than the lower surface. 7. The yield of DSSS increases as the wind speed increase because this leads to faster condensation at the glass surface. The higher basin mass temperature is less affected by the variation in wind velocity. 5 NOMENCLATURES q. cwrate of convective heat transfer from water to glass cover, [ W/m2] hconvective heat transfer coefficient from water to cw condensing cover, [ W/(m2K)] q. ewrate of evaporative heat transfer from water to glass cover, [ W/m2] hew evaporative heat transfer coefficient, [ W/(m2K)] q. rwrate of radiative heat transfer from water to glass cover, [ W/m2] hrw radiative heat transfer coefficient, [ W/(m2K)] eef f effective emissivity of glass and water, [ -] eg emissivity of glass, [ -] ew emissivity of water, [ -] 4 . Stefan Boltzmann constant, [ W/(m2K)] q. grate of total heat transfer from glass cover to ambient, [ W/m2] q. rgrate of radiative heat transfer from glass cover to ambient, [ W/m2] hrg radiative heat transfer coefficient from glass cover to ambient, [ W/(m2K)] q. rate of convective heat transfer from glass cover cgto ambient, [ W/m2] hc g convective heat transfer coefficient from glass surface to ambient, [ W/(m2K)] q.tgrate of total heat transfer from glass cover to ambient, [ W/m2] htg total heat transfer coefficient from glass surface to ambient, [ W/(m2K)] U bottom heat loss coefficient, [ W/(m2K)] b U side heat loss coefficient, [ W/(m2K)] e hw convective heat transfer coefficient from basin liner to water, [ W/(m2K)] hc b convective heat transfer coefficient from basin liner to ambient, [ W/(m2K)] hrb radiative heat transfer coefficient from basin liner to ambient, [ W/(m2K)] hb overall heat transfer coefficient from basin liner to ambient through bottom, [ W/(m2K)] Tg temperature of condensing cover, [ ° C] T temperature of basin, [ ° C] b T water temperature, [ ° C] w T water vapour temperature, [ ° C] T sky temperature of sky, [ ° C] T ambient temperature, [ ° C] a V wind velocity, [ m/s] tthickness of insulation material, [ m] i Ki thermal conductivity of insulation material, [ W/(m· K)] P partial vapour pressure at water temperature, w [ N/m2] Pg partial vapour pressure at glass temperature, [ N/m2] mew distillate output, [ kg/m2/h] L latent heat of vaporization, [ J/kg] hoverall heat transfer coefficient from basin liner b to ambient through bottom insulation, [ W/(m2K)] A SS surface area in contact with water, [ m2] AS area of the basin of the distiller, [ m2] 6 REFERENCES [1] Kannan, N., Vakeesan, D. (2016). Solar energy for future world: A review. Renewable and Sustainable Energy Reviews. vol. 62, p. 1092-105, DOI:10.1016/j.rser.2016.05.022. [2] Patel, R.V.P., Kumar, A. (2017). Experimental investigation of double slope solar still for the climatic condition of Sultanpur. International Journal of Engineering and Technology, vol. 9, no. 6, p. 4019-4033, DOI:10.21817/ijet/2017/v9i6/170906309. [3] Patel, R.V., Bharti, K., Singh, G., Mittal, G., Singh, D.B., Yadav, A. (2021). Comparative investigation of double slope solar still by incorporating different types of collectors: A mini review. Materials Today: Proceedings, vol. 38, p. 300-304, DOI:10.1016/j.matpr.2020.07.338. [4] Misra, S., Patel, R.V., Kumar, A., Yadav, A., Patel, V. (2021) Effect of Climatic Conditions and Water Depth on Yield of Single Slope Solar Still. Current Advances in Mechanical Engineering: Select Proceedings of ICRAMERD 2020, p. 137­147, DOI:10.1007/978-981-33-4795-3_14. [5] Sharshir, S.W., Ellakany, Y.M., Algazzar, A.M., Elsheikh, A.H., Elkadeem, M.R., Edreis, E.M.A., Waly, A.S., Sathyamurthy, R., Panchal, H., Elashry, M.S. (2019). A mini review of techniques used to improve the tubular solar still performance for solar water desalination. Process Safety and Environmental Protection, vol. 124, p. 204-212, DOI:10.1016/j. psep.2019.02.020. [6] Tiwari, A.Kr., Tiwari, G.N. (2006). Effect of water depths on heat and mass transfer in a passive solar still: in summer climatic condition. Desalination, vol. 195, no. 1-3, p. 78-94, DOI:10.1016/j.desal.2005.11.014. [7] Zarasvand Asadi, R., Suja, F., Ruslan, M.H., Jalil, N.A. (2013). The application of a solar still in domestic and industrial wastewater treatment. Solar Energy, vol. 93, no. 63-71, DOI:10.1016/j.solener.2013.03.024. [8] Ali, M.T., Fath, H.E.S., Armstrong, P.R. (2011). A comprehensive techno-economical review of indirect solar desalination. Renewable and Sustainable Energy Reviews, vol. 15, no. 8, p. 41874199, DOI:10.1016/j.rser.2011.05.012. [9] Dev, R., Abdul-Wahab, S.A., Tiwari, G.N. (2011). Performance study of the inverted absorber solar still with water depth and total dissolved solid. Applied Energy, vol. 88, no. 1, p.252­264, DOI:10.1016/j.apenergy.2010.08.001. [10] Phadatare, M.K., Verma, S.K. (2007). Influence of water depth on internal heat and mass transfer in a plastic solar still. Desalination, vol. 217, no. 1-3, p. 267-275, DOI:10.1016/j. desal.2007.03.006. [11] Tripathi, R., Tiwari, G.N. (2006). Thermal modeling of passive and active solar stills for different depths of water by using the concept of solar fraction. Solar Energy, vol. 80, p. 956-967, DOI:10.1016/j.solener.2005.08.002. [12] Feilizadeh, M., Karimi Estahbanati, M.R., Ahsan, A., Jafarpur, K., Mersaghian, A. (2016). Effects of water and basin depths in single basin solar stills: An experimental and theoretical study. Energy Conversion and Management, vol. 122, p. 174­181, DOI:10.1016/j.enconman.2016.05.048. [13] El-Sebaii, A.A. (2011). On effect of wind speed on passive solar still performance based on inner/outer surface temperatures of the glass cover. Energy, vol. 36, no. 8, p. 4943–4949. DOI:10.1016/j.energy.2011.05.038. [14] El-Sebaii A.A. (2004). Effect of wind speed on active and passive solar stills. Energy Conversion and Management, vol. 45, no. 7-8, p. 1187–1204, DOI:10.1016/j. enconman.2003.09.036. [15] Danish, S.N., El-Leathy, A., Alata, M., Al-Ansary, H. (2019). Enhancing solar still performance using vacuum pump and geothermal energy. Energies, vol. 12, no. 3, art. ID 539, DOI:10.3390/en12030539. [16] Thalib, M.M., Manokar, A.M., Essa, F.A., Vasimalai, N., Sathyamurthy, R., Garcia Marquez, F.P. (2020). Comparative study of tubular solar stills with phase change material and nano-enhanced phase change material. Energies, vol. 13, no. 15, art. ID. 3989, DOI:10.3390/en13153989. [17] Singh, R., Kumar, A., Yadav, A. (2019). Performance analysis of the solar photovoltaic thermal system using phase change material. IOP Conference Series: Materials Science and Engineering, vol. 577, art. ID 012166, DOI:10.1088/1757­899X/577/1/012166. [18] Safaei, M.R., Goshayeshi, H.R., Chaer, I.. (2019). Solar still efficiency enhancement by using graphene oxide/ paraffin nano-PCM. Energies, vol. 12, no. 10, art. ID 2002, DOI:10.3390/en12102002. [19] Nazari, S., Safarzadeh, H., Bahiraei, M. (2019). Performance improvement of a single slope solar still by employing thermoelectric cooling channel and copper oxide nanofluid: An experimental study. Journal of Cleaner Production, vol. 208, p. 1041-1052, DOI:10.1016/j.jclepro.2018.10.194. [20] El-Sebaey, M.S., Ellman, A., Hegazy, A., Ghonim, T. (2020). Experimental analysis and CFD modeling for conventional basin-type solar still. Energies, vol. 13, no. 21., art. ID 5734, DOI:10.3390/en13215734. [21] Rahbar, N., Esfahani, J.A. (2013). Productivity estimation of a single-slope solar still: Theoretical and numerical analysis. Energy, vol. 49, no. 289-297, DOI:10.1016/j. energy.2012.10.023. [22] Setoodeh, N., Rahimi, R., Ameri, A. (2011). Modeling and determination of heat transfer coefficient in a basin solar still using CFD. Desalination, vol. 268, no. 1-3, 103-110, DOI:10.1016/j.desal.2010.10.004. [23] Madhlopa, A. (2014). Modelling radiative heat transfer inside a basin type solar still. Applied Thermal Engineering, vol. 73, no. 1, p. 707-711, DOI:10.1016/j.applthermaleng.2014.07.065. [24] Keshtkar, M., Eslami, M., Jafarpur, K. (2020). A novel procedure for transient CFD modeling of basin solar stills: Coupling of species and energy equations. Desalination, vol. 481, art. ID 114350, DOI:10.1016/j.desal.2020.114350. [25] Dunkle, R.V. (1961). Solar wter distillation: the roof type still and a multiple effect diffusion still. International Developments in Heat Transfer, ASME, Proceeding of International Heat Transfer, part V, p. 895. [26] Fernández, J., Chargoy, N. (1990). Multi-stage, indirectly heated solar still. Solar Energy, vol. 44, no. 4, p. 215-223, DOI:10.1016/0038-092X(90)90150-B. [27] Watmuff, J.H., Charters, W.W.S., Proctor, D. (1977). Solar and wind induced external coefficients-solar collectors. CMES, p. 56. [28] Shukla, K.S., Rai, A.K. (2008). Analytical thermal modeling of double slope solar still by using inner glass cover temperature. Thermal Science, vol. 12, no. 3, p. 139-152, DOI:10.2298/ TSCI0803139S. Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 380-388 Received for review: 2021-05-12 © 2021 Journal of Mechanical Engineering. All rights reserved. Received revised form: 2021-06-17 DOI:10.5545/sv-jme.2021.7253 Original Scientific Paper Accepted for publication: 2021-07-09 Mechanical Properties of Adhesive Joints Made w ith Pressure-Sensitive Adhesives Anna Rudawska1,* – Magd Abdel Wahab2,3 1 Lublin University of Technology, Faculty of Mechanical Engineering, Poland 2Duy Tan University, Institute of Research and Development, Vietnam 3 Ghent University, Faculty of Engineering and Architecture, Belgium The paper aims to determine the mechanical properties of the adhesive joints made with acrylic pressure-sensitive adhesives. Two types of double-sided acrylic pressure-sensitive adhesive tapes are used. Three construction materials are used to prepare the adhesive joints: structural steel sheet (C45), aluminium alloy sheet (EN-AW 5754), and titanium sheet (Grade 2). Strength tests of adhesive joints made with the pressure-sensitive adhesive tapes are carried out both after conditioning time at room temperature (23 °C) and subjected to thermal shocks (500 cycles: +60 °C / –40 °C). Strength tests are carried out based on the DIN EN 1465 standard on a Zwick/Roell Z150 testing machine. The main conclusion from the tests carried out was the positive effect of thermal shocks on the mechanical strength of joints bonded with pressure-sensitive adhesive tape. Keywords: adhesive joint, pressure-sensitive adhesive, mechanical properties, thermal shocks Highlights • In the investigated range of the thermal shocks, the post-conditioning does not appear to trigger the deterioration of the mechanical properties of the adhesive joints bonded with the pressure-sensitive adhesive tapes. • The increase in the adhesive joints’ strength is also associated with the type of adherend. • There is a positive correlation between the thermal shocks and the mechanical strength of the adhesive joint bonded with the pressure-sensitive adhesive tapes. • The pressure-sensitive adhesive tapes exhibit a good capacity for bonding the considered adherends under the considered conditions. 0 INTRODUCTION Assembly joints can be made using various joining methods, including bonding [1] to [3]. One type of adhesive material used in assembly processes is pressure-sensitive adhesives. Pressure-sensitive adhesive tape is an alternative to conventional mechanical joining methods, including screws, rivets, dowels and other fasteners. In addition to bonding, i.e., their primary function, adhesive tape is also used for sealing purposes, by protecting bonded components against penetration by an external medium [1], [4], and [5]. Manufacturers of industrial pressure-sensitive adhesive tapes will sometimes develop their products tailored to specific assembly and industry needs [6] to [8]. The term “ pressure-sensitive” describes adhesives that are aggressively and permanently tacky in the dry form at room temperature and firmly adhere to a variety adherends’ surfaces upon mere contact, without the need of more than hand pressure [9]. Pressure-sensitive adhesives consist mainly of tacky polymeric materials that adhere to adherends surface upon applying a contact pressure [9] to [11]. Pressure-sensitive adhesives require a balance of cohesive strength and viscoelastic properties. Such adhesives can be easily detached from the adherend surface and may be reusable [12]. An essential property of pressure-sensitive adhesive tapes is their tack performance, which relates the adhesive force generated by a small short-term pressure on the tapes [12]. One of the important features of pressure-sensitive adhesive tapes is their flexibility (even exceptional flexibility), which allows for relative component movement in the assembly related to the thermal expansion of adherends [4], [5], [13], and [14]. Various issues of mechanical properties related to pressure-sensitive adhesives are presented in many works [7], [11], [12], and [15] to [17]. Czech and Milker [7] underlined that pressure-sensitive adhesives (PSA) presented a novel generation of self-adhesives with a large number of excellent properties. In this work, several groups of pressure-sensitive adhesives were described. Foster et al. [15] defined bonding principles for the development of commercial water-bone pressure-sensitive adhesive. Z osel [17] presented that the correlations between shear resistance and the mechanical properties of pressure-sensitive adhesives. Also, issues related to the rheological properties of pressure-sensitive *Corr. Author’s Address: Lublin University of Technology, Nadbystrzycka 38D, Lublin, Poland, a.rudawska@pollub.pl adhesive on the mechanical behaviour were discussed, among others in the works [10], [16], and [18] to [20]. Dynamic mechanical properties of pressure-sensitive adhesives were presented by Chu [10]. Marin and Derail [20] investigated the relationship between rheological and peeling properties for hot-melt pressure-sensitive adhesives based on homopolymers or copolymers blended with tackifier resins. Sun et al. [21] indicated that the mechanical properties of pressure-sensitive adhesives are usually described by tack, shear resistance and peel strength. Sosson et al. [22] investigated the shear failure mechanisms of pressure-sensitive adhesive. The effect of tackifier on the adhesive properties of pressure-sensitive adhesives tape was investigated by Sasaki et al. [23]. The article characterizes adhesive joints formed using industrial pressure-sensitive adhesive tapes that were subjected to temperature shock testing. The major finding emerging from the tests was the positive effect of thermal shocks on the mechanical strength of pressure-sensitive adhesive tape bonded joints. 1 METHODS AND EXPERIMENTAL 1.1 Adherends and Pressure-Sensitive Adhesives The substrates bonded using the tested adhesive tapes were: C45 steel sheets (PN/EN 10083 -2), EN­AW 5754 aluminium alloy sheets (PN-EN 573-3) and Grade 2 titanium sheets (according to American standard ASTM F67: 2000-Ti Grade 2). The thickness of the adherends was 1 ± 0.02 mm. Two pressure-sensitive adhesives in the form of double-sided tapes were subjected to testing: 3M VHB double-sided tape (3M company, VHB brand, No. 4 947F , 3 M Deutschland GmbH) and 3M Scotchź double-sided pressure-sensitive adhesive tape (3M company, Scotchź Brand, 3M Deutschland GmbH). Table 1 lists the characteristics of the 3M VHB tape. The presented characteristics have been prepared based on the information provided on the manufacturer’ s websites [24] to [26]. Table 1. Characteristics of 3M VHB pressure-sensitive adhesive tape Properties Details/value Adhesive tape specification Double-sided adhesive tape Adhesive type Multi-purpose acrylic Foam type Acrylic foam Density 720 kg/mł Liner PE film The maximum and minimum operating temperatures are + 90 ° C and –40 ° C. Short- and long­term temperature resistance are 149 ° C and 93 ° C, respectively. Selected properties of the 3M Scotchź double-sided pressure-sensitive adhesive tape are shown in Table 2. The maximum and minimum operating temperatures are + 93 ° C and -35 ° C. Table 2. Characteristics of 3M Scotchź pressure-sensitive adhesive tape Properties Details/value Adhesive tape specification Double-sided adhesive tape Adhesive type Modified acrylic Liner PET 1.2 Adhesive Joints and Adhesives Samples Two research objects were used in the study: single-lap adhesive joints of three construction materials, i.e., structural steel sheet (C45) , aluminium alloy sheet (EN-AW 5754) and titanium sheet (Grade 2), joined with pressure-sensitive adhesives, and a pressure-sensitive adhesive in the form of rectangular samples. The single-lap adhesive joints (Fig. 1) have the following dimensions: sheet width (ws) 20 ± 0.12 mm, sheet length (Ls) 100 ± 0.32 mm, overlap length after curing process (l ad ) 20 ± 0.58 mm, sheet thickness g = 1 ± 0.02 mm, adhesive tape thickness (tad ): 3M VHB pressure-sensitive adhesive tape 1.1 mm, 3M Scotch 1.9 m m. Fig. 1. The parametric scheme of single-lap adhesive joints For each type of adherends and pressure-sensitive adhesives, 8 adhesive joints were made. A total of 96 adhesive joint samples were subjected to strength tests (3 types of adherends Ś 2 types of pressure-sensitive adhesives, tapes Ś 2 variants of testing conditions Ś 8 samples). The dimensions of rectangular samples of pressure-sensitive adhesives are 100 mm Ś 20 mm. For each pressure-sensitive adhesive variant, 6 adhesive samples were made. 1.3 Bonding Technology The adhesive joints were prepared in several steps: adherend surface preparation, cutting off the pressure-sensitive adhesive tape, applying the adhesive onto adherends surfaces, and curing. 1.3.1 Surface Treatment and Applying the Adhesive The surface treatment of adherends prior to bonding consisted of degreasing with acetone. Specifically, the degreasing agent was applied in 3 repetitions onto the surfaces: after the first two applications, it was wiped off with dust-free swabs; after the third application, the samples were allowed to dry for approx. 2 minutes. The surface treatment procedure was performed at 26 ± 1 ° C and humidity 40 ± 1 % . The pressure-sensitive adhesive tape was cut with scissors to the required overlap length of 20 mm. Next, it was applied onto one of the adherend surfaces and pressed appropriately once the adherend and the adhesive tape were in line. Given that the bond strength is relative to the condition and the size of the contact surface (according to theoretical mechanics), an even amount of pressure needed to be applied. To ensure better contact between the tape and the bonded surface, and thus to increase the strength of the fixture, the proper pressure was applied with a hand roller. 1.3.2 Curing Once the joint was assembled, it was subjected to curing, according to the following procedure: 2-hour subjecting under a load of 0.20 MPa, at a temperature of 26 ± 1 ° C and humidity of 41 ± 1 %, hold at a temperature of 150 ± 1 ° C for 10 minutes (Fig. 2), cooling at 26 ± 1 ° C for 1 hour. During curing, the joints were heat-treated at an elevated temperature to accelerate and improve the deposition of the tape adhesive in the irregularities of the adherends. The curing was carried out in a climatic chamber SH-661 ( Klimatest, Poland). The bonded joints were subsequently conditioned at 23 ± 1 ° C and relative humidity of 28 ± 1 % for 24 hours, upon which time their quality was verified in visual inspection. Finally, the specimens were divided into two test batches that differed in terms of the thermal post-treatment. 1.3.3 Thermal Post-Conditioning Prior to failure strength tests, the specimens from the first test group (RT) conditioning in room temperature, whereas for the second variant (TS) the specimens were additionally subjecting using thermal shocks, carried out using a thermal shock chamber STE 11 (ESPEC, Klimatest, Poland). The test groups are described in Tables 3 a nd 4. Table 3. Description of test groups Test group RT TS variant (without thermal shocks) (with thermal shocks) Temperature: 23 ± 1 °C 500 cycles Conditions RH: 28 ± 1 % 1 cycle: +60 °C / 15 min. Time: 24 h and -40 °C / 15 min. Table 4. Description of test adhesive joints Adherend (designation) Adhesive tape 3M Test group Designation of adhesive joints Steel VHB Scotchź RT S/VHB/RT S/S/RT (S) VHB Scotchź TS S/VHB/TS S/S/TS Aluminium alloy VHB Scotchź RT Al/VHB/RT Al/S/RT (Al) VHB Scotchź TS Al/VHB/TS Al/S/TS Titanium (Ti) VHB Scotchź RT Ti/VHB/RT Ti/S/RT 1.4 Strength Test The shear strength tests of adhesive joints were conducted according to the DIN EN 1465 standard test temperature 23 ± 1 ° C and during the test speed of 50 mm/min, using Z wick/Roell Z 2.5 testing machine (Z wick/Roell GmbH& Co. KG, Ulm, Germany). The elongation strength tests pressure-sensitive adhesive samples were performed at test temperature 23 ± 1 ° C and during the test speed, according to DIN EN ISO 527-1 standard, using Z wick/Roell Z 2.5 testing machine (Z wick/Roell GmbH& Co. KG, Ulm, Germany). 2 RESULTS 2.1 Mechanical Properties of Adhesive Joints - RT Variant: Conditioning in Room Temperature Figs. 2 and 3 compare the results from shear strength tests of steel sheet, aluminium alloy sheet and titanium sheet adhesive joints bonded using two pressure-sensitive adhesive tapes. Specifically, Fig. 2 reports the strength performance of these joints, and Fig. 3 compares the elongation at break of joints under testing conditions. The designations in the charts in Figs. 2 and 3 have been adopted in accordance with the designations presented in Table 5. From the data presented in Fig. 2, it can be seen that adhesive joints bonded with the acrylic adhesive tape tended to develop higher strength, regardless of the adherends. With respect to the material of adherends, the aluminium alloy was shown to develop the highest shear strength of all the joints, both when bonded with the 3M VHB (0.38 MPa) and the 3M Scotchź (0.28 MPa) pressure-sensitive adhesive tapes. For these types of joints, the difference in the shear strength amounted to approx. 27 % . The lowest shear strength was recorded for the adhesive joints of titanium sheets. This applies to both types of pressure-sensitive adhesive tapes: 3M VHB (0.35 MPa) and 3M Scotchź (0.15 MPa). The shear strength of titanium adhesive joints joined with 3M Scotchź pressure-sensitive adhesive tape corresponded to approx. 40 % of the shear strength of adhesive joints made with 3M VHB pressure-sensitive adhesive tape. Fig. 2. Shear strength of tested adhesive joints - RT variant A meaningful difference in shear strength was also observed in the case of steel sheet joints. The strength of joints made with the 3M VHB pressure-sensitive adhesive tape is 0.35 MPa and 0.18 MPa with the use of 3M Scotchź pressure-sensitive adhesive tape, which corresponds to almost 50 % of the difference between the strength of the compared adhesive joints. In general, in all material cases, greater strength was observed when using 3M VHB pressure-sensitive adhesive tape. As indicated in the previous paragraph, significantly greater differences in the strength values were observed in the joints bonded with 3M Scotchź pressure-sensitive adhesive tape (nearly 50 % ), which can be interpreted as the effect of this type of tape sensitivity to the type of adherend used in the bonding processes. Similar dependencies result from the analysis of the elongation of adhesive joints (Fig. 3) . Average Standard deviation Elongation at break [ mm] Fig. 3. Elongation at break of tested adhesive joint – RT variant Considering the elongation values (Fig. 3) , it can be seen that there are no statistical differences of elongation between the different tapes (3M VHB and 3M Scotchź pressure-sensitive adhesive tapes) for the same material due to the relatively high standard deviations. Considering all variants of the samples of adhesive joints depending on the base material, it can be seen that the highest elongation was obtained in aluminium alloys adhesive joints, and the lowest in titanium adhesive joints. Moreover, for the pressure-sensitive adhesive tapes used, the difference between the highest and lowest average elongation is similar and amounts to approximately 10 % ; however, it has also been shown that the type of adherends affects the properties of the joints (including the elongation) in strength tests. 2.2 Mechanical PROPERTIES of Adhesive Joints - RT Variant: Conditioning in Room Temperature The results obtained from the shear strength tests conducted on adhesive joints of steel and aluminium alloy sheet substrates that were bonded with the two types of pressure-sensitive adhesive tapes are reported in Figs. 4 a nd 5. Several observations emerge from the comparative analysis of the performance (shear strength and elongation at break) of pressure-sensitive adhesive tape joints subjected to 500 thermal shock cycles (Figs. 4 a nd 5) : Fig. 4. Shear strength of tested adhesive joints - TS variant 0 1 2 3 4 5 6 7 8 91011 Average Standard deviation Elongation at break [ mm] Fig. 5. Elongation at break of tested adhesive joint – TS variant the strength parameters of adhesive joints of aluminium alloy determined in tests were higher compared to the steel adhesive joints, which applies to both types of pressure-sensitive adhesive tapes, the aluminium alloy adhesive joints bonded with the 3M VHB pressure-sensitive adhesive tape were stronger than the steel adhesive joints by 27 % on average, the difference in joint strength was less significant in the case of the 3M Scotchź pressure-sensitive adhesive tape, amounting to 3 % on average, when comparing the elongation of specimens bonded using the 3M VHB pressure-sensitive adhesive tape, the difference between the adherends was equal to 4 % , while for the 3M Scotchź pressure-sensitive adhesive tape it was 11 % on average. The bonded joints of titanium sheets exhibited the lowest strength, regardless of the type of adhesive type used and were therefore excluded from thermal shock testing. 2.3 Mechanical Properties of Adhesives The results of strength parameters pressure-sensitive adhesive tapes shown that the average value of the tensile strength of the 3M VHB pressure-sensitive adhesive tape was 0.43± 0.03 MPa, whereas the average value of the tensile strength of 3M Scotchź pressure-sensitive adhesive tape was 0.3 4 ± 0.06 MPa. The modulus of the 3M VHB pressure-sensitive adhesive tape was 1.30 ± 0.12, and the modulus of the 3M Scotchź pressure-sensitive adhesive tape was 0.23 ± 0.09. It can be seen that 3M VHB pressure-sensitive adhesive tape is characterized by a 20 % higher value of tensile strength than Scotch pressure-sensitive adhesive tape. In the case of the tensile modulus, it was observed that the 3M Scotchź pressure-sensitive adhesive tapes have almost 5 times lower value compared to the VHB pressure-sensitive adhesive tape. Elongation at break was at a similar level, and no significant differences were observed, i.e., for the 3M VHB pressure-sensitive adhesive tape was 720 ± 43 % , and was 733 ± 30% for the 3M Scotchź pressure-sensitive adhesive tape. 3 DISCUSSION The comparison of the results of shear strength of adhesive joints curing and conditioning in room temperature (RT) and additionally subjected to thermal shocks (TS) was presented in Figs. 6 a nd 7. Based on the results presented in Fig. 6, it can be seen that the strength of steel adhesive joints that were subjected to thermal shocks is higher than those of joints that were conditioned at ambient temperature. However, the extent to which the presence of thermal shocks contributes to improving the strength properties of steel adhesive joints depends on the type of pressure-sensitive adhesive tape in use. The adhesive joints bonded with the 3M VHB pressure-sensitive adhesive tape were observed to develop strength increased by 37 % when thermal shock treatment was applied. The difference was even higher in adhesive joints bonded with the 3M Scotchź pressure-sensitive adhesive tape, in which case the increase in the strength of adhesive joints exceeded 8 0 %. Fig. 6. The shear strength of steel adhesive joints subjected and not subjected to thermal shock testing Considering the correlation between the type of adherend of adhesive joints after thermal shock and the type of pressure-sensitive adhesive tapes, it was observed that the steel adhesive joints prepared with the 3M Scotchź pressure-sensitive adhesive tape showed a 15 % higher strength than the steel adherends bonded with the 3M VHB pressure-sensitive adhesive tape: 0.63 MPa and 0.54 MPa, respectively. In the adhesive joints not subjected to thermal shocks, the opposite mechanism occurred: steel adhesive joints bonded with the 3M VHB pressure-sensitive adhesive tape were capable of resisting higher loads than the 3M Scotchź pressure-sensitive adhesive tape-bonded joints. Also, the difference was far more significant, reaching close to 50 % . What may be then inferred from the observation is that thermal shocks contribute to a certain “ levelling-off” of the strength properties of pressure-sensitive adhesive tape, and thus exhibit a positive effect on the strength of adhesive joints. Considering the shear strength of adhesive joints of aluminium alloy sheets not subjected to and subjected to thermal shock, significant differences in the results of this strength parameter were observed (Fig. 7) . Adhesive joints subjected to thermal shocks were characterized by higher shear strength of their joints, and this difference is more than twofold. After the thermal shock, the adhesive joints of aluminium alloy sheets joined with 3M VHB pressure-sensitive adhesive tape (0.77 MPa) are almost 15 % more durable than joints made with 3M Scotchź pressure-sensitive adhesive tape (0.66 MPa). As in the case of bonding steel sheets, there is a clear discrepancy between the strength of adhesive joints prepared with 3M VHB and 3 M Scotchź pressure-sensitive adhesive tapes not subjected to thermal shocks: it amounted to approx. 27 % . Therefore, it can be assumed that the heat causes the pressure-sensitive adhesive to cross-link further, as a result of which the properties of the adhesive joints become similar. Nevertheless, other factors were likely to have contributed to this, such as their specific material properties Thermal shocks are widely known to be among the factors degrading polymer materials, including adhesives. According to the definition of the term, degradation is a process of structural modification that may result from physical or chemical changes occurring within the polymer under the long-term impact of various external factors [4] and [5]. Okba et al. [5] presented that the decrease of residual compressive and tensile strengths depends on the type of polymer adhesive, level of elevated temperature, type of applied stress and, to a lesser degree, on exposure time. The residual bond strength was reduced, and the mode of failure changed due to the high temperature, prolonged exposure time, type of polymer adhesive and the increase in the surface area of the bond. Gilbert et al. [19] investigated the effect of the rheological properties of industrial hot-melt and pressure-sensitive adhesives on the peel behaviour at various temperatures. In the conducted tests, it was noticed that the failure was cohesive with regard to the adhesive layer, and the cracks appeared at the beginning of the adhesive joint overlap. However, as it could be inferred from the results reported here, in certain cases in the first phase of degradation, the properties of an exposed material may actually improve, particularly its mechanical strength. This is a result of additional cross-linking of the material structure that is induced by heat, for example. It is only at a later stage (over a prolonged effect of degradation factors) that other processes begin to contribute, e.g., excessive cross-linking or molecular weight reduction, initiating the deterioration of such material properties, such as strength or elongation, as underlined by Benedek and Feldstein [14] and also Chang [8]. The information from the preceding paragraph and the results from the strength and elongation tests seem to suggest that, in the reported cases, the mechanical strength of adhesive joints bonded with specific pressure-sensitive adhesive tapes was increased by subjecting the specimens to 500 thermal shock cycles, carried out at + 6 0 ° C and –40 ° C. It should be noted that the applied temperatures did not exceed the values recommended by the manufacturer regarding their maximum (+ 90 ° C for VHB pressure-sensitive adhesive tape and + 93 ° C for 3M Scotchź pressure-sensitive adhesive tape) or minimum operating temperatures (–40° C for VHB pressure-sensitive adhesive tape and –35° C for 3M Scotchź pressure-sensitive adhesive tape, although in the last pressure-sensitive adhesive tape the minimum temperature was slightly exceeded). However, it is probable that a greater number of cycles, i.e., increased duration of thermal shocks, could lead to a reduction in the strength of the joints under consideration due to, for instance, excessive cross-linking of the adhesive or molecular weight reduction. The results of elongation of the adhesive joint specimens bonded with the pressure-sensitive adhesive tapes under investigation that were or were not subjected to thermal shocks are presented in Fig. 8 (steel adhesive joints) and in Fig. 9 (aluminium alloy adhesive joints). Several observations can be drawn from the elongation tests carried out on the steel adhesive joints subjected and not subjected to thermal shocks (Fig. 8) : Fig. 8. Elongation at break of steel adhesive joints with and without thermal shock thermal shocking improved the elongation at break of adhesive joints bonded with the 3M VHB pressure-sensitive adhesive tape (9 .09 mm). The difference between the elongation at break of adhesive joints prior to an after thermal shocks is 13 % ; adhesive joints bonded with the 3M Scotchź pressure-sensitive adhesive tape did not respond positively to thermal shocks: slightly better elongation properties were exhibited by the non-post treated joints (8.24 mm versus 7.70 mm), and this difference was approx. 6 % ; following the series of thermal shocks, adhesive joints bonded with the 3M VHS pressure-sensitive adhesive tape showed a 15 % higher elongation at break value than the 3M Scotchź pressure-sensitive adhesive tape-bonded specimens. Fig. 9. Elongation at break of the aluminium alloy adhesive joints with and without thermal shock Considering the results from the elongation tests presented in Fig. 9, i t can be seen that: with respect to the type of pressure-sensitive adhesive tape bonding the aluminium alloy adherends, higher elongation at break was obtained after subjecting the adhesive joints specimens to a specific cycle of thermal shocks; after thermal shocks, adhesive joints bonded with the 3M VHS pressure-sensitive adhesive tape showed higher elongation at break value (by about 10 % ) compared with the 3M Scotchź tape – similarly to the steel sheet joints; the difference in the elongation at break of the adhesive joints of the aluminium alloy adherends bonded with the 3M VHB pressure-sensitive adhesive tape subjected and not subjected to thermal shocks is 10 % , while in the same adherends adhesive joints joined with the 3M Scotchź pressure-sensitive adhesive tape, the difference is negligible – approx. 2 % . The results above (Figs. 8 and 9) confirm that, with the exception of a single case, the applied number and type of thermal shock cycles increase the elongation at break of adhesive joints prepared with the tested pressure-sensitive adhesive tapes. Sun et al. [21] underlined that the adhesion properties of pressure-sensitive adhesives strongly depend on surface roughness, tackifier compatibility, monomers, cross-linking degree and others. On the basis of the obtained results, it can be observed that the type of adherends play an important role in the mechanical properties of adhesive joints prepared by pressure-sensitive adhesives. By bonding thicker (stiffer) elements, a greater strength of the joints is obtained but lower maximum stress of the joined materials under failure load. This was also confirmed in the work of Sun et al. [21] and in the work of Peykova et al. [27], who also indicated that different surface also affects the cavity growth mechanisms. According to Dimas et al. [28], several factors determine the mechanical properties of pressure-sensitive adhesive, e.g., the type of adhesive. Although both acrylate-based pressure-sensitive adhesives were used in the study, the type of acrylic was probably different (the information is very general from the manufacturer on this subject); the thickness and the different base were different. That is, the factors mentioned by Dimas et al. [28] could have influenced the noticeable differences in the strength of the adhesive joints of the materials joined with the use of both tapes. According to Chu [10] the performance of PSA is related to the viscoelastic response of the bulk adhesives as well as to the surface energies of the adhesives and adherend. Differences in the strength of adhesive joints made with two different pressure-sensitive adhesives (Fig. 2) can probably be explained by the different structures of the adhesive layer and its thickness. The results presented by Poh and Kwo [29] highlighted the importance of the thickness of the adhesive layer on the adhesive substrate. They presented that, generally, peel and shear strength increase with coating thickness. The type of materials forming the pressure-sensitive adhesive is an equally important factor, which was emphasized in the works of, among others, Rodrigez et al. [18], Chang [8], and Marin and Derail [20]. 4 CONCLUSIONS The experimental data suggest that in the investigated range of thermal shocks (the number of cycles, temperature and duration of positive and negative temperatures), commonly regarded as a degradation factor, the post-conditioning does not appear to trigger the deterioration of the mechanical properties of adhesive joints bonded with pressure-sensitive adhesive tapes; nevertheless, the increase in strength is also associated with the type of adherend. Thus, there is a positive correlation between thermal shocks and the mechanical strength of adhesive joint bonded with pressure-sensitive adhesive tapes, which should be linked primarily with additional cross-linking of the adhesive material structure under exposure to heat, and the resulting increase in the mechanical strength of the adhesive joints. An implication of this is that pressure-sensitive adhesive tapes exhibit a good capacity for bonding the considered adherends under the considered operating conditions. 5 REFERENCES [1] Adams, R.D., Comyn, J., Wake. W.C. (1997). Structural Adhesive Joints in Engineering Book. Springer, London. [2] Mojškerc, B., Kek, T., Grum, J. (2016). Pulse-echo ultrasonic testing of adhesively bonded joints in glass façades. Strojniški vestnik - Journal of Mechanical Engineering, vol. 62, no.3, p. 147-153, DOI:10.5545/sv-jme.2015.2988. [3] Tušek, J., Klobcar, D. (2004). Current development trends for material joining in the automotive industry. Strojniški vestnik - Journal of Mechanical Engineering, vol. 50, no. 2, p. 94-103. [4] Blackburn, B.P., Tatar, J., Douglas, E.P., Hamilton, H.R. (2015). Effect of hydrothermal conditioning on epoxy adhesives used in FRP composites. Construction and Building Materials, vol. 96, p. 679-689, DOI:10.1016/j.conbuildmat.2015.08.056. [5] Okba, S.H., Nasr, E.-S.A., Helmy, A.I.I., Yousef, I.A.-l. (2017). Effect of thermal exposure on the mechanical properties of polymer adhesives. Construction and Building Materials, vol. 135, p. 490-504, DOI:10.1016/j.conbuildmat.2016.12.067. [6] Abderrahmen, R, Gavory, C., Chaussy, D., Briançon, S., Fessi, H., Belgacem, M.N. (2011). Industrial pressure sensitive adhesives suitable for physicochemical microencapsulation. International Journal of Adhesion and Adhesives, vol. 31, no. 7, p. 629-633, DOI:10.1016/j.ijadhadh.2011.06.003. [7] Czech, Z., Milker, R. (2005). Development trends in pressure-sensitive adhesive systems. Materials Science Poland, vol. 23, p. 1015-1022. [8] Chang, E.P. (1991). Viscoelastic windows of pressure-sensitive adhesives. Journal of Adhesion, vol. 4, p. 189-200, DOI:10.1080/00218469108026513. [9] Czech, Z. (2004). Development in the area of UV-crosslinkable solvent-based pressure-sensitive adhesive with excellent shrinkage resistance. European Polymer Journal, vol. 40, no. 9, p. 2221-2227, DOI:10/1016/j.eurpolymj.2004.05.012. [10] Chu, S.G. (1991). Dynamic mechanical properties of pressure-sensitive adhesives. Lee, L.-H. (ed.), Adhesive Bonding. Springer Science+Business Media, New York, p. 97-138, DOI:10.1007/978-1-4757-9006-1_5. [11] Creton, C. (2003). Pressure-sensitive adhesives: An introductory course. MRS Bulletin, vol. 28, p. 434-439. DOI:10.1557/mrs2003.124. [12] Takahashi, K., Shimizu, M., Inaba, K., Kishimoto, K., Inao, Y., Sugizaki, T. (2013) Tack performance of pressure-sensitive adhesive tapes under tensile loading. International Journal of Adhesion and Adhesives, vol. 45, p. 90-97, DOI:10.1016/j. ijadhadh.2013.05.005. [13] Schneider, B., Beber, V.C., Schweer, J., Brede, M., Mayer, B. (2018). An experimental investigation of the fatigue damage behavior of adhesively bonded joints under the combined effect of variable amplitude stress and temperature variation. International Journal of Adhesion and Adhesives, vol. 83, p. 41-49, DOI:10.1016/j.ijadhadh.2018.02.011. [14] Benedek, I., Feldstein, M.M. (2009). Technology of Pressure-Sensitive Adhesives and Products. CRC Press Taylor & Francis Group, Boca Raton. [15] Foster, A.B., Lovell, P.A., Rabjohns, M.A. (2009). Control of adhesive properties through structured particle design of water-borne pressure-sensitive adhesives. Polymer, vol. 50, no. 7, p. 1654-1670, DOI:10/1016/j.polymer.2009.01.054. [16] Kajtna, J., Alic, B., Krajnc, M., Šebenik, U. (2014). Influence of hydrogen bond on rheological properties of solventless UV crosslinkable pressure sensitive acrylic adhesive prepolymers. International Journal of Adhesion and Adhesives, vol. 49, p. 103-108, DOI:10.1016/j.ijadhadh.2013.12.016. [17] Zosel, A. (1994). Shear strength of pressure sensitive adhesives and its correlation to mechanical properties. Journal of Adhesion, vol. 44, p. 1-16, DOI:10.1080/00218469408026613. [18] Rodriguez, I., Lim, Ch.T., Natarajan, S., Ho, A.Y.Y., Van, E.L., Elmouelhi, N., Low, H.Y., Vyakarnam, M., Cooper, K. (2013). Shear adhesion strength of gecko-inspired tapes on surfaces with variable roughness. Journal of Adhesion, vol. 89, no. 12, p. 921-936, DOI:10.1080/00218464.2013.767198. [19] Gibert, F.X., Allal, A., Marin, G., Derail, C. (1999). Effect of the rheological properties of industrial hot-melt and pressure-sensitive adhesives on the peel behavior. Journal of Adhesion Science and Technology, vol. 13, no. 9, p. 1029-1044, DOI:10.1163/156856199X00497. [20] Marin, G., Derail, C. (2006). Rheology and adherence of pressure-sensitive adhesives. Journal of Adhesion, vol. 82, no. 5, p. 469-485, DOI:10.1080/00218460600713618. [21] Sun, S., Li, M., Liu, A. (2013). A review on mechanical properties of pressure sensitive adhesives. International Journal of Adhesion and Adhesives, vol. 41, p. 98-106, DOI:10.1016/j.ijadhadh.2012.10.011. [22] Sosson, F., Chateauminois, A., Creton, C. (2005). Investigation of shear failure mechanisms of pressure-sensitive adhesives. Journal of Polymer Science B: Polymers Physics, vol. 43, no. 22, p. 3316-3330, DOI:10.1002/polb.20619. [23] Sasaki, M., Fujita, K., Adachi, M., Fujii, S., Nakamura, Y., Urahama, Y. (2008). The effect of tackifier on phase structure and peel adhesion of a triblock copolymer pressure-sensitive adhesive. International Journal of Adhesion and Adhesives, vol. 28, no. 7, p. 372-381, DOI:10.1016/j.ijadhadh.2007.11.002. [24] Pressure-sensitive adhesive tape, from https://www.3m. co.uk/3M/en_GB/company-uk/3m-products/~/3M-VHB­tape-4947/, accessed on 2021-03-08. [25] Pressure-sensitive adhesive tape, from https:// www.3mpolska.pl/3M/pl_PL/firma-pl/all-3m-products, accessed on 2021-03-08. [26] Pressure-sensitive adhesive tape, from https://www.conrad. com/p/3m-40021915-industrial-tape-scotch-grey-l-x-w-15-m­x-19-mm-15-m-547078, accessed on 2021-03-08. [27] Peykova, Y., Lebedeva, O.V., Diethert, A., Mler-Buschbaum, P., Willenbacher, N. (2012). Adhesive properties of acrylate copolymers: effect of the nature of the substrate and copolymer functionality. International Journal of Adhesion and Adhesives, vol. 34, p. 107-116, DOI:10.1016/j. ijadhadh.2011.12.001. [28] Dimas, D.A., Dallas, P.P., Rekkas, D.M., Choulis, N.H. (2000). Effect of several factors on the mechanical properties of pressure-sensitive adhesives used in transdermal therapeutic systems. AAPS PharmSciTech, vol. 1, p. 80-87, DOI:10.1208/ pt010216. [29] Poh, B.T., Kwo, H.K. (2007) Peel and shear strength of pressure-sensitive adhesives prepared from epoxidized natural rubber. Journal of Applied Polymer Science, vol. 105, no. 2, p. 680-684, DOI:10.1002/app.26072. Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, 389-397 Received for review: 2021-05-23 © 2021 Journal of Mechanical Engineering. All rights reserved. Received revised form: 2021-07-01 DOI:10.5545/sv-jme.2021.7262 Original Scientific Paper Accepted for publication: 2021-07-12 Characteriz ation of the AZ 31/ AW-6060 Joint Fabricated using Compound Casting w ith a Z n Interlaye r at R elatively L ow Temperature Conditions Tomasz Bucki1,* – Marek Konieczny1 – Dana Bolibruchova2 – Sylwia Rzepa3 1Kielce University of Technology, Faculty of Mechatronics and Mechanical Engineering, Poland 2University of Z ilina, Faculty of Mechanical Engineering, Slovak Republic 3 COMTES FHT a.s., Mechanical Testing and Thermophysical Measurement Department, Czech Republic The work deals with the fabrication of a joint between AZ31 magnesium alloy and AW-6060 aluminium alloy with the use of a Zn interlayer. The Zn layer was produced on the surface of an AW-6060 alloy insert by diffusion bonding. The insert was then placed inside a steel mould and kept at room temperature. The joint was produced using compound casting by filling the mould with liquid AZ31 alloy, heated to 650 °C. The microstructure of the bonding zone formed between joined alloys was analysed using an optical microscope and a scanning electron microscope equipped with an energy dispersive X-ray spectroscope. The properties of the joint were examined using Vickers microhardness measurements and simple shear strength testing. As a result of the experiment, the 400 ”m thick bonding zone with a complex microstructure was formed between the alloys. The microstructural analysis showed that the bonding zone reveals a high concentration of Zn and Mg. The layers of a eutectoid (a MgZn phase + a solid solution of Al and Zn in Mg), a Mg5Al2Zn2 phase and a Mg(Al,Zn)2 phase with fine particles of other phases were observed there. The bonding zone was characterized by relatively high microhardness, which was related to the brittleness of the constituents. The shear strength of the examined joint was 19.6 ± 2.5 MPa. Keywords: compound casting, magnesium alloy, aluminium alloy, zinc interlayer, microstructure, mechanical properties Highlights • The AZ31/AW-6060 joint was fabricated by compound casting with the use of a Zn interlayer. • The Zn layer was produced on the surface of the AW-6060 alloy insert to act as an interlayer. • The compound casting involved pouring the liquid AZ31 magnesium alloy at 650 °C onto a solid AW-6060 aluminium alloy insert placed in a steel mould and kept at room temperature. • The study focused on the analysis of the microstructure and examinations of microhardness and shear strength of the fabricated joint. 0 INTRODUCTION In recent years, there has been a noticeable increase in the application of bimetallic elements based on various metals and their alloys. Such products have unique properties that cannot be achieved with a single alloy. A promising solution is the production of bimetals based on light alloys: magnesium and aluminium. The combination of these materials into one element allows taking the advantages of both alloys: the low density of the magnesium alloy and good resistance to corrosion and abrasion of the aluminium alloy [1] and [2]. The literature review shows that the following methods are used to join magnesium alloys with aluminium alloys: diffusion bonding [3], ultrasonic welding [4], resistance spot welding [5], friction stir welding [6]; explosive welding [7], tungsten inert gas (TIG), metal inert gas (MIG) and laser welding techniques [8] to [10], and compound casting [11]. The advantages of compound casting over other joining techniques include the possibility of producing joints with complex shapes, high efficiency, and a relatively simple and economical production process. The joining of magnesium to aluminium alloys by compound casting seems to be a promising direction that may contribute to the increase in the use of light alloys in various industries, mainly in the automotive industry. This technique involves pouring a liquid alloy onto a product made of a different material. The literature data [11] shows that joints with favourable properties can be fabricated by pouring liquid magnesium onto a solid aluminium insert placed in a casting mould. The typical bonding zone has a complex structure composed of continuous layers of Al3 Mg2 () and Mg17 Al12 () intermetallic phases, as well as a layer of a eutectic (a Mg17 Al12 phase + a solid solution of Al in Mg). Mg-Al intermetallic phases are characterized by high brittleness, related to the low strength of the joint and the brittle nature of the fracture. The thickness of the bonding zone depends on the parameters of the casting process, such as the temperature of molten magnesium and temperature of the mould with an aluminium insert [12], Mg-to-Al volume ratio [13] and [14], method of casting [15], and pressure in the mould [16]. The research results on the properties of such joints show that favourable strength is achieved for the joints with a thin bonding zone. Some studies have focused on the fabrication of joints between Mg and Al alloys, e.g., AZ 91/ A356 [17] and [18], AZ 91/ AlSi17 [19] and [20], AZ 91/ AlSi12 [21], Z E41/ AlSi12 [22], AZ 31/ AW-6060 [23]. The results of the above-mentioned works indicate that the presence of alloying elements may lead to significant modification of the structure of the created bonding zone and can affect the mechanical properties of the joint. The properties of the joint can also be improved by using interlayers. Such modification is meant to reduce or block the possibility of the formation of Mg-Al intermetallic phases and replace them with other phases with better properties. Recent studies showed that good results can be achieved when the Z n [23], Ni [24] or Ni + Cu [25] interlayers are used. Fig. 1. Isothermal cross-section of the Mg-Al-Zn phase diagram at the temperature of 25 °C [29] © MMMS and ASM Int. In order to understand the processes of formation of the Mg alloy/Al alloy joint with the use of a Z n interlayer, it is necessary to become acquainted with the Mg-Al [26], Mg-Z n [27] and Al-Z n [28] phase diagrams as well as the Mg-Al-Z n ternary diagram [29]. Fig. 1 shows the isothermal cross-section of the Mg-Al-Z n phase diagram at the temperature of 25 ° C. The system, beyond the binary phases, also includes to ternary phases, marked as (also knon as Mg5 Al2Z n2 [30]) and (Mg32 (Al,Z n)49 [29]). The authors note that in all binary phases in the system, the solubility of the third element is low, except for the phase (Mgn2). Due to the high solubility of Al in MgZ n2, this phase can also be stated as Mg(Al,Z n)2. However, the results by Czerwinski [31] indicate that Z n atoms can replace some Al atoms in the Mg17 Al12 phase. It can be then defined as Mg17 (Al,Z n)12. This work is a part of a larger project on the joining of Mg and Al alloys with the Z n interlayer by compound casting. In our previous paper [23], we focused on the effects of the Z n interlayer on the microstructure and properties of the joint formed between the AZ 31 magnesium alloy and AW-6060 aluminium alloy. The research involved the formation of a 100 m thick n layer on the surface of A­6060 insert by diffusion bonding. The insert was next placed inside a steel mould and heated to 170 ° C. Then the AZ 31 alloy, heated to 660 ° C, was poured into the mould. As a result, a continuous bonding zone ith a thickness of 500 m as formed beteen the alloys. The findings showed that the microstructure of the joint was complex. The layer of a eutectic (a Mg5 Al2Z n2 phase + a solid solution of Al and Z n in Mg), a layer of a Mg32 (Al,Z n)49 phase, and a layer of a eutectic (a Mg32 (Al,Z n)49 phase + a solid solution of Mg and Z n in Al) were detected in the bonding zone. Furthermore, the bonding zone contained the fine particles of other phases, identified as Mg17 Al12, Mg2Si, Al6 (Fe,Mn), and Al5 FeSi. The analysed joint was characterized by relatively high shear strength. The average shear strength was 42.3 ± 2.8 MPa. The strength of the joint formed without an interlayer was much lower. The highest shear strength values (8.1 ± 2.3 MPa) were noted for the joint produced with the following process parameters: pouring temperature 660 ° C, mould temperature 300 ° C. It was shown that the low strength and high brittleness of the analysed joint are correlated with the presence of brittle Mg-Al intermetallic phases in the bonding zone. In this case, the thickness of the bonding zone (approx. 400 m) as loer than for the joint fabricated ith the Z n interlayer, despite the use of a higher temperature of the insert. The present paper deals with the fabrication of an AZ 31/ AW-6060 joint by compound casting at temperature conditions significantly lower than those applied in our previous work. For this reason, an AW-6060 insert with a Z n surface layer with a steel mould was kept at room temperature. A greater reduction in the temperature of the insert would be inappropriate. Therefore, it was also decided to reduce the temperature of pouring of the AZ 31 alloy. This alloy was thus heated to 650 ° C and then poured into the mould. The study focuses on the microstructure analysis and examinations of microhardness and shear strength of the fabricated joint. 1 EXPERIMENTAL DETAILS AZ 31 magnesium alloy and AW-606 0 aluminium alloy were used as the materials to be joined. The chemical compositions of the alloys are listed in Table 1. Table 1. Chemical compositions of AZ31 and AW-6060 alloys [at.%] Alloy Mg Al Zn Si Mn AZ31 bal. 3.07 1.05 - 0.31 AW-6060 0.45 bal. - 0.50 0.19 The 30 mm in diameter and 10 mm thick specimens were cut from an AW-6060 alloy rod. After cutting, the specimens were subjected to grinding with abrasive papers up to 800 grit and to degreasing with ethanol. The Z n layer was formed on the surface of the AW-6060 alloy by diffusion bonding, by annealing the specimen in contact ith a 100 m thick n foil. The annealing was conducted in a vacuum furnace at 375 ° C for 20 minutes. The pressure of 3 MPa was exerted to ensure good contact with the materials. The insert with Z n surface layer was next placed in a steel mould and kept at room temperature. The mould was then filled with liquid AZ 31 alloy, heated to 650 ° C under an inert argon atmosphere. The specimens for microscopic observations were prepared using standard metallographic procedures. The final polishing was carried out using 0.05 m colloidal silica. o etching as used due to the sufficient revealing of the microstructure of the specimens in contact with water. The microscopic observations were conducted with a Nikon ECLIPSE MA 200 optical microscope (OM) and a JEOL JSM­7100F scanning electron microscope equipped with an energy dispersive X -ray spectroscope detector (SEM/ EDS). The microhardness was tested by Vickers method, using a MATSUZ AWA MMT Vickers microhardness tester at a load of 100 g. The strength of the joints was examined by a simple shear test with a LabTest 5.20S P1 universal testing machine, using the setup described in the previous study [23]. The specimens with dimensions of 7 mm Ś 7 mm Ś 20 mm were cut from the central part of the joints. The shear strength was tested at a displacement of 10 mm/min. 2 RESULTS AND DISCUSSION Fig. 2a presents the microstructure of the layer fabricated on the surface of AW-60 60 alloy by diffusion bonding in contact ith the 100 m thick Z n foil. Microscopic analysis showed that diffusion processes during bonding resulted in forming a continuous joint between the materials used. As a result, Al and Z n form a simple phase diagram with no intermetallic phases [28]. The SEM observations at high magnification (Fig. 2b), together with the results of the EDS analysis (e.g., 52.16 at.% Z n, 47.84 at.% Al), suggested that the interface layer between the Z n and AW-6060 alloy had a lamellar microstructure and was composed of a solid solution of Al in Z n and a solid solution of Z n in Al. Fig. 2. Microstructure of the layer fabricated on the surface of AW-6060 alloy by diffusion bonding in contact with the Zn foil; a) OM image, b) high magnification SEM image Fig. 3 shows the microstructure of the bonding zone formed by pouring the liquid AZ 3 1 alloy at 650 ° C onto the solid AW-6060 alloy insert with a Z n surface layer, which was kept at room temperature. The microscopic observations revealed that the joining process resulted in the formation of a continuous bonding zone with a complex structure. The overall thickness of the bonding zone as about 400 m. Fig. 3. Microstructure of the bonding zone formed by pouring the liquid AZ31 alloy at 650 °C onto the solid AW-6060 alloy insert with a Zn surface layer, which was kept at room temperature Fig. 4 shows the results of an EDS linear analysis throughout the analysed bonding zone. The distribution of elements along the marked line shows a high content of Z n and Mg, while the concentration of Al was relatively low. The higher content of Al was recorded only in the transition region, which can be distinguished at the interface between the two characteristic layers of the bonding zone. Fig. 4. Results of an EDS linear analysis throughout the bonding zone formed between the AZ31 alloy and AW-6060 alloy with a Zn surface layer The details of the microstructure of the bonding zone observed in SEM are shown in Fig. 5. The results of EDS point analysis performed in marked points are presented in Table 2. The comparison of the result of analysis carried out in areas marked in Fig. 5a as 1 and 2 showed that the AZ 31 alloy in the immediate vicinity of the bonding zone was enriched with Z n. The layer of the bonding zone at the AZ 31 alloy side was characterized by a two-phase microstructure. The analysis results carried out in points 3 and 4 suggested that this region was composed of a eutectoid containing a MgZ n intermetallic phase and a solid solution of Al and Z n in Mg. The chemical composition of the highly dispersed two-phase area (marked as 5) also indicated a eutectoid (a MgZ n phase + a solid solution of Al and Z n in Mg). In the transition region, which was observed in the central part of the bonding zone, light particles with high content of Mg, Z n, and Al were located (point 6 in Fig. 5b) . The composition of these particles indicated a Mg5 Al2Z n2 ternary phase. The analysis carried out in point 7 showed that the chemical composition of the region observed below the eutectoid is also close to a Mg5 Al2Z n2 phase. In the next layer of the bonding zone (analysis in point 8) , a light matrix was observed. Its chemical composition indicated a Mg(Al,Z n)2 phase. In the structure of this region, fine particles of other phases were also distributed. The results of microscopic observations showed that the particles marked as 9 have a two-phase structure. The small size of these particles made it impossible to perform quantitative analysis in single phases. The result of the analysis in point 9 and the high magnification image presented in Fig. 5c suggests that these particles may be composed of a eutectic containing a Mg(Al,Z n)2 phase and a solid solution of Mg and Z n in Al. The high content of Mg and Si in particles marked as 10 indicated that the darker particles were composed of a Mg2Si intermetallic phase, which may originate from the AW-6060 alloy. It can also be formed as a result of diffusion processes between the elements present in the alloys. For example, in [17] and [18], the authors showed that pouring of Mg alloy onto the Si-containing Al alloy insert resulted in the formation of fine particles of the Mg2Si phase in the bonding zone. The results of the analysis in the area marked as 11 in Fig. 5d showed that the bonding zone on the AW­6060 alloy side also consisted of a Mg(Al,Z n)2 phase with some particles of other phases. Throughout the bonding zone, the light particles containing Al, Fe and Mn or Al, Si and Fe were also found (e.g., 89.67 at.% Al, 7.98 at.% Fe, 2.35 at.% Mn or 78.26 at.% Al, 13.4 7 at.% Si, 8.27 at.% Fe, respectively). They probably were particles of multicomponent phases originating from the AW-6060 a lloy. Fig. 6 illustrates the effects of microhardness measurements in AZ 31 and AW-6060 alloys and in the bonding zone formed between them. The results Fig. 5. Details of the microstructure of bonding zone; a) region close to AZ31 alloy, b) the central region, c) high magnification image of the light matrix observed in the central region, d) region close to AW-6060 alloy showed that a relatively high hardness characterizes the bonding zone. The layer with a two-phase structure (a MgZ n phase + a solid solution of Z n and Al in Mg), which was observed on the AZ 31 alloy side, had a microhardness in the range from 214.4 HV0.1 to 225.1 HV0.1. The microphotography presented in Fig. 6b shows that the measurements in this region did not lead to the formation of cracks. In the transition region containing a Mg5 Al2Z n2 phase (Fig. 6c ), a higher microhardness was noted. In this area, the cracks propagating from the corners of Vickers tester impressions were observed. The presence of fine cracks indicates a certain brittleness of this area. The highest microhardness (31 1.5 HV0.1 to 329.9 HV0.1) was reported in the region adjacent to the AW-6060 alloy, which consisted of a Mg(Al,Z n)2 phase and particles of other phases. Fig. 6d shows that the microhardness measurements in this region also resulted in the formation of fine cracks indicating the brittleness of the phases. Table 2. Results of the EDS analysis at points marked in Fig. 5 (at.%) Point Mg Al Zn Si 1 96.40 3.03 0.57 - 2 93.71 4.46 1.83 - 3 51.13 2.58 46.29 - 4 90.99 5.81 3.20 - 5 68.79 5.75 25.46 - 6 57.93 17.79 24.28 - 7 56.14 18.42 25.44 - 8 32.63 2.88 64.49 - 9 27.66 15.15 57.19 - 10 66.14 1.14 0.98 31.74 11 30.98 5.59 63.43 - Fig. 6. Results of Vickers microhardness measurements in the bonding zone; a) low magnification image, high magnification of the indentation left in: b) the region close to AZ31 alloy, c) the central region, d) the region close to AW-6060 alloy alloy and AW-6060 alloy with a Z n surface layer. The microscopic observations revealed that only fine pores could be found locally in the bonding zone, as shown in Fig. 7. Fig. 8 presents the results of a simple shear test performed for the analysed joint. The average shear strength of the tested specimens was 19.6 ± 2.5 MPa. The shape of the stress-displacement curves was typical of brittle materials. No symptoms of plastic deformation were observed. A comparative analysis of the presented results and the findings from our previous work [23] allowed us to conclude that using a Z n interlayer may result in substantial changes in the microstructure of the AZ 31/ AW-60 60 joint produced by compound casting at a wide range of process parameters. The use of the Z n interlayer permitted a significant reduction in the pouring temperature and the temperature of the insert. The presence of Z n also limited the formation of Mg-Al binary phases and led to the creation of phases containing Z n. In addition, the bonding zone in the joint formed with the Z n interlayer, which was analysed in the present study, was characterized by higher microhardness and better shear strength in comparison to the direct joint. This phenomenon is worth highlighting because the high hardness of such materials typically corresponds with their brittleness and low strength. The results of the present research showed, however, that the Mg-Al intermetallic phases present in the direct joint were characterized by high brittleness, as indicated by significant cracks at the corners of the indentations left by the microhardness tester. Some cracks were also observed for the joint with Z n interlayer, but the crack dimensions were much smaller despite the higher hardness. Important insights can be drawn when comparing the joints produced with the Z n interlayer at different pouring temperatures and Al alloy insert temperatures. The results show that depending on the temperature conditions, the diffusion of the elements occurs at different rates. The higher temperature led to the greater content of Al in the bonding zone, while for the joint produced at the lower temperature, the amount of Al remained low. It results in significant differences in the phase composition of the bonding zone. The results of the study are in good agreement with the Mg-Al-Z n phase diagram. The greater content of Al in the first case resulted in the formation of phases rich in Mg, Al, and Z n, while the lower content of Al in the other bonding zone led to the presence of phases rich in Mg and Z n. Furthermore, the joint made at a higher temperature was characterized by the lowest brittleness and the highest shear strength among all analysed variants. 3 CONCLUSIONS The AZ 31/ AW-6060 joint was fabricated by the compound casting process. A 100 m n layer as produced on the surface of the insert to act as an interlayer. The compound casting involved pouring the liquid AZ 31 magnesium alloy at 6 50 ° C onto a solid AW-6060 aluminium alloy insert with a Z n layer, which was placed in a steel mould and kept at room temperature. As a result of the experiment, a continuous, a 400 m thick layer as formed beteen the alloys. The bonding zone has a complex structure. On the AZ 31 alloy side, it was composed of a eutectoid containing a MgZ n intermetallic phase and a solid solution of Al and Z n in Mg. In the central part of the bonding zone, the particles of a Mg5 Al2Z n2 ternary intermetallic phase and the thin layer of this phase were observed. The region adjacent to the AW-6060 alloy consisted of a Mg(Al,Z n)2 phase matrix with fine particles, whose composition indicated that they were the particles of a Mg2Si phase, a eutectic (a Mg(Al,Z n)2 phase, and a solid solution of Mg and Z n in Al) and multicomponent phases rich in Al, Fe and Mn or Al, Fe and Si. The bonding zone was characterized by higher microhardness than that of the joined alloys. The highest microhardness values were observed in the region containing a Mg(Al,Z n)2 phase and in the layer composed of a Mg5 Al2Z n2 phase. The microhardness measurements in these areas led to the propagation of small cracks in the vicinity of Vickers tester indenters. Observed cracks indicate a noticeable brittleness of the phases. The average shear strength of the joint was 19.6 ± 2.5 M Pa. 4 REFERENCES [1] Kumar, D.S., Phanden, R.K., Thakur, L. (2021). A review on environment friendly and lightweight Magnesium-Based metal matrix composites and alloys. Materials Today: Proceedings, vol. 38, p. 359-364, DOI:10.1016/j.matpr.2020.07.424. [2] Ahmad, A., Yunxin, W., Hai, G., Lei, L. (2019). Determination of the effect of cold working compression on residual stress reduction in quenched aluminium alloy 2219 block. Strojniški vestnik - Journal of Mechanical Engineering, vol. 65, no. 5, p. 311-318, DOI:10.5545/sv-jme.2018.5938. [3] Zhang, J., Luo, G., Wang, Y., Xiao, Y., Shen, Q., Zhang, L. (2013). Effect of Al thin film and Ni foil interlayer on diffusion bonded Mg-Al dissimilar joints. Journal of Alloys and Compounds, vol. 556, p. 139-142, DOI:10.1016/j.jallcom.2012.12.106. [4] Patel, V.K., Bhole, S.D., Chen, D.L. (2012). Microstructure and mechanical properties of dissimilar welded Mg-Al joints by ultrasonic spot welding technique. Science and Technology of Welding and Joining, vol. 17, no. 3, p. 202-206, DOI:10.1179/ 1362171811Y.0000000094. [5] Hayat, F. (2011). The effects of the welding current on heat input, nugget geometry, and the mechanical and fractural properties of resistance spot welding on Mg/Al dissimilar materials. Materials & Design, vol. 32, no. 4, p. 2476-2484, DOI:10.1016/j.matdes.2010.11.015. [6] Zettler, R., Da Silva, A.A.M., Rodrigues, S., Blanco, A., Dos Santos, J.F. (2006). Dissimilar Al to Mg alloy friction stir welds. Advanced Engineering Materials, vol. 8, no. 5, p. 415­421, DOI:10.1002/adem.200600030. [7] Mr, S., Mola, R., Szota, P., Stefanik, A. (2020). Microstructure and properties of 1050A/AZ31 bimetallic bars produced by explosive cladding and subsequent groove rolling process. Archives of Civil and Mechanical Engineering, vol. 20, p. 1-15, DOI:10.1007/s43452-020-00084-4. [8] Liu, F., Zhang, Z., Liu, L. (2012). Microstructure evolution of Al/ Mg butt joints welded by gas tungsten arc with Zn filler metal. Materials Characterization, vol. 69, p. 84-89, DOI:10.1016/j. matchar.2012.04.012. [9] Zhang, H.T., Song, J.Q. (2011). Microstructural evolution of aluminum/magnesium lap joints welded using MIG process with zinc foil as an interlayer. Materials Letters, vol. 65, no. 21­22, p. 3292-3294, DOI:10.1016/j.matlet.2011.05.080. [10] Scherm, F., Bezold, J., Glatzel, U. (2012). Laser welding of Mg alloy MgAl3Zn1 (AZ31) to Al alloy AlMg3 (AA5754) using ZnAl filler material. Science and Technology of Welding and Joining, vol. 17, no. 5, p. 364-367, DOI:10.1179/13621711 2X13333824902080. [11] Hajjari, E., Divandari, M., Razavi, S.H., Emami, S.M., Homma, T., Kamado, S. (2011). Dissimilar joining of Al/Mg light metals by compound casting process. Journal of Materials Science, vol. 46, p. 6491-6499, DOI:10.1007/s11431-008-0345-9. [12] Mola, R., Bucki, T., Dziadon, A. (2016). Formation of Al-alloyed layer on magnesium with use of casting techniques. Archives of Foundry Engineering, vol. 16, no. 1, p. 112-116, DOI:10.1515/afe-2016-0013. [13] Emami, S.M., Divandari, M., Arabi, H., Hajjari, E. (2013). Effect of melt-to-solid insert volume ratio on Mg/Al dissimilar metals bonding. Journal of Materials Engineering and Performance, vol. 22, p. 123-130, DOI:10.1007/s11665-012-0243-y. [14] Jiang, W., Fan, Z., Li, G., Yang, L., Liu, X. (2016). Effects of melt-to-solid insert volume ratio on the microstructures and mechanical Properties of Al/Mg bimetallic castings produced by lost foam casting. Metallurgical and Materials Transactions A, vol. 47, p. 6487-6497, DOI:10.1007/s11661-016-3788-9. [15] Emami, S.M., Divandari, M., Hajjari, E., Arabi, H. (2013). Comparison between conventional and lost foam compound casting of Al/Mg light metals. International Journal of Cast Metals Research, vol. 26, no. 1, p. 43-50, DOI:10.1179/1743 133612Y.0000000037. [16] Li, G., Yang, W., Jiang, W., Guan, F., Jiang, H., Wu, Y., Fan, Z. (2019). The role of vacuum degree in the bonding of Al/Mg bimetal prepared by a compound casting process. Journal of Materials Processing Technology, vol. 265, p. 112-121, DOI:10.1016/j.jmatprotec.2018.10.010. [17] Li, G., Jiang, W., Yang, W., Jiang, Z., Guan, F., Jiang, H., Fan, Z. (2019). New insights into the characterization and formation of the interface of A356/AZ91D bimetallic composites fabricated by compound casting. Metallurgical and Materials Transactions A, vol. 50, p. 1076-1090, DOI:10.1007/s11661­018-5022-4. [18] Jiang, W., Li, G., Fan, Z., Wang, L., Liu, F. (2016). Investigation on the interface characteristics of Al/Mg bimetallic castings processed by lost foam casting. Metallurgical and Materials Transactions A, vol. 47, p. 2462-2470, DOI:10.1007/s11661­016-3395-9. [19] Mola, R., Bucki, T., Dziadon, A. (2017). Effects of the pouring temperature on the formation of the bonding zone between AZ91 and AlSi17 in the compound casting process. IOP Conference Series: Materials Science and Engineering, vol. 179, p. 1-6, DOI:10.1088/1757-899X/179/1/012053. [20] Mola, R., Bucki, T. (2018). The microstructure and properties of the bimetallic AZ91/AlSi17 joint produced by compound casting. Archives of Foundry Engineering, vol. 18, no. 1, p. 71­76, DOI:10.24425/118814. [21] Mola, R., Bucki, T. (2020). Characterization of the Bonding zone in AZ91/AlSi12 bimetals fabricated by liquid-solid compound casting using unmodified and thermally modified AlSi12 alloy. Strojniški vestnik - Journal of Mechanical Engineering, vol. 66, no. 7-8, p. 439-448, DOI:10.5545/sv­jme.2020.6703. [22] Mola, R., Bucki, T. (2018). Characterization of the bonding zone in a ZE41/AlSi12 joint fabricated by liquid-solid compound casting. Archives of Foundry Engineering, vol. 18, no. 2, p. 203-208, DOI:10.24425/122529. [23] Mola, R., Bucki, T., Gwozdzik, M. (2019). The effect of a zinc interlayer on the microstructure and mechanical properties of a magnesium alloy (AZ31)–aluminum alloy (6060) joint produced by liquid–solid compound casting. JOM, vol. 71, p. 2078-2086, DOI:10.1007/s11837-019-03405-y. [24] Li, G., Jiang, W., Guan, F., Zhu, J., Yu, Y., Fan, Z. (2020). Effect of different Ni interlayers on interfacial microstructure and bonding properties of Al/Mg bimetal using a novel compound casting. Journal of Manufacturing Processes, vol. 50, p. 614­628, DOI:10.1016/j.jmapro.2020.01.017. [25] Li, G., Jiang, W., Guan, F., Zhu, J., Zhang, Z., Fan, Z. (2021). Microstructure, mechanical properties and corrosion resistance of A356 aluminum/AZ91D magnesium bimetal prepared by a compound casting combined with a novel Ni-Cu composite interlayer. Journal of Materials Processing Technology, vol. 288, p. 1-12, DOI:10.1016/j. jmatprotec.2020.116874. [26] Okamoto, H. (1998). Al-Mg (aluminum-magnesium). Journal of Phase Equilibria, vol. 19, p. 598, DOI:10.1361/105497198770341815. [27] Okamoto, H. (1995). Mg-Zn (magnesium-zinc). Journal of Phase Equilibria, vol. 16, p. 474-475, DOI:10.1007/ BF02645363. [28] Okamoto, H. (1995). Al-Zn (aluminum-zinc). Journal of Phase Equilibria, vol. 16, p. 281-282, DOI:10.1007/BF02667316. [29] Liang, H., Chen, S.-L., Chang, Y.A. (1997). A thermodynamic description of the Al-Mg-Zn system. Metallurgical and Materials Transactions A, vol. 28, p. 1725-1734, DOI:10.1007/ s11661-997-0104-8. [30] Cheng, K., Sun, J., Xu, H., Wang, J., Zhou, J., Tang, S., Wang, [31] Czerwinski, F. (2002). The oxidation behaviour of an AZ91D X., Zhang, L., Du, Y. (2021). On the temperature-dependent magnesium alloy at high temperatures. Acta Materialia, diffusion growth of F-Mg5Al2Zn2 ternary intermetallic vol. 50, no. 10, p. 2639-2654, DOI:10.1016/S1359­compound in the Mg-Al-Zn system. Journal of Materials 6454(02)00094-0. Science, vol. 56, p. 3488-3497, DOI:10.1007/s10853-020­05439-z. Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8 Vsebina Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 67, ( 2021) , številka 7-8 L jubljana, julij-avgust 2021 ISSN 0039-2480 aa eeo R az širjeni povz etki (extended abstracts) Peixing ing, Ji hao, Shijun Ji, Jingjin Li, Handa Dai: Ultranatancno tockovno diamantno struženje kompleksne sinusoidne površine z aktivnim nadzorom tocnosti obdelave SI 45 Yang-zhi Chen, Chao He, Yue-ling Lyu: Osnovna teorija in metoda za konstruiranje linijskih zobniških mehanizmov z variabilnim kotom gredi SI 46 Myron Chernets, Marek Opielak, Anatolii Kornienko, Oleg Radko: Napoved nosilnosti in tribološke trajnosti drsnih ležajev SI 47 aj Vardhan Patel, Anshul adav, Jerzy inczek: Eksperimentalna raziskava in matematicni model toplotne prehodnosti dvokapnega solarnega destilatorja SI 48 Anna Rudawska, Magd Abdel Wahab: Mehanske lastnosti lepljenih spojev, izdelanih z lepili, obcutljivimi na tlak SI 4 Tomasz Bucki, Marek Konieczny, Dana Bolibruchova, Sylwia Rzepa: Karakterizacija spoja AZ 31 /AW-6060, izdelanega po postopku sestavljenega litja z vmesno plastjo Z n pri razmeroma nizkih temperaturah SI 50 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, SI 45 Prejeto v recenzijo: 2021-03-20 © 2021 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2021-05-18 Odobreno za objavo:2021-06-17 ltraatao tooo diaato tree olee ioide orie atii adoro tooti odelae Peixing Ning1 – Ji Z hao1,2,* – Shijun Ji1 – Jingjin Li1 – Handa Dai1 1Univerza v Jilinu, Šola za strojništvo in letalsko tehniko, Kitajska 2Severovzhodna univerza, Šola za strojništvo in avtomatizacijo, Kitajska Tockovno struženje z diamantnim orodjem (SPDT) v kombinaciji s tehnologijo Slo Tool Servo (STS) je najbolj razširjena tehnika izdelave opticnih modulov. Priprava poti orodja je prvi in kljucni korak, ki ima velik vpliv na topografijo in kakovost površin izdelka po obdelavi. Dosedanje raziskave tehnologije ultranatancne obdelave kompleksnih opticnih površin so bile usmerjene predvsem v pripravo poti orodja, kompenzacijo radija zaokrožitev in analizo topografije obdelanih površin. Le malo pa je študij na temo priprave poti orodja za doseganje tocnosti obdelave. V clanku je predstavljena metoda priprave poti orodja na osnovi aktivnega nadzora tocnosti obdelave (MAA), ki ucinkovito zagotavlja zahtevano tocnost obdelave. Pri tehnologiji SPDT se uporablja kombinacija rotacijskega gibanja vretena in linearnega reciprocnega gibanja. Vrtenje vretena in reciprocno gibanje po osi Z povzrocata napako tetive v smeri rezanja, linearno gibanje v smeri X pa preostalo napako v smeri podajanja. Preucena je bila odvisnost med potjo orodja in napako obdelave ob upoštevanju omenjenih glavnih virov napak. V clanku sta podrobneje predstavljena kompenzacija radija zaokrožitev ter izracun napake tetive in preostale napake. Pot orodja, ki izpolnjuje zahteve glede tocnosti obdelave, je tako mogoce izpeljati po obratnem postopku izracuna napake. a preverjanje ucinkovitosti predlagane metode sta bila opravljena simulacija napak obdelave in eksperiment z obdelavo kompleksne sinusoidne površine. Mejna vrednost preostale napake res in napake tetive ho je bila c nastavljena na 0,5 m. a nacrtovanje poti orodja, ki prinaša oblikovano površino, je bila uporabljena metoda priprave poti orodja na podlagi MAAC. Simulacija napak obdelave je bila izvedena po obratnem postopku zgornjega izracuna poti orodja. Ugotovljeno je bilo, da so vse napake znotraj 0,5 m. a dokazovanje ucinkovitosti predlaganega pristopa pri realni obdelavi je bil opravljen eksperiment na stroju Nanoform 250 za SPDT. Obdelana površina je bila izmerjena z opticnim profilometrom na belo svetlobo ygo nevie 000. aradi omejitev merilnega vidnega polja je bilo nakljucno izbranih osem predelov obdelane površine razlicnega polmera, vkljucno z vrhovi, dolinami in vmesnimi obmocji. Preostala napaka in napaka tetive sta povezani, zato ju je težko meriti in analizirati loceno. Kakovost obdelave površin je mogoce ocenjevati z najvecjo višino profila (PV) obdelane površine. ezultati meritev po izkljucitvi nakljucnih napak so pokazali, da je celotno odstopanje (dejanska vrednost PV) obdelane kompleksne sinusoidne površine približno 2,45 m. Vrednost ne odstopa signifikantno od vnaprej dolocene vrednosti PV 2 m. Ti rezultati so dokazali, da je metoda MAA primerna za pripravo poti orodja. Predstavljena metoda je prispevek k raziskavam nadzora tocne obdelave kompleksnih površin s tehnologijo SPDT. bstajajo pa še drugi dejavniki, ki jih ni mogoce nadzorovati merilne napake, napake obdelovalnega stroja, obraba orodja in delovna temperatura – zaradi katerih dejanska vrednost PV nekoliko presega vnaprej doloceno vrednost PV. V prihodnje bo treba preuciti tudi vpliv teh dejavnikov na napake obdelave površin za doseganje zahtevane tocnosti. le eede atii ador tooti odelae aoedoae aae odelae olea ioida oria tooo tree diaati orode Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, SI 46 Prejeto v recenzijo: 2021-04-08 © 2021 Journal of Mechanical Engineering. All rights reserved. Prejeto popravljeno: 2021-06-09 Prejeto popravljeno: 2021-07-01 O snovna teorija in metoda z a konstruiranje linijskih z obniških mehaniz mov z variabilnim kotom gredi Yang-zhi Chen1,* – Chao He1 – Yue-ling Lyu2 1Fakulteta za strojništvo in avtomobilsko tehniko, Tehniška univerza Južne Kitajske, Kitajska 2Univerza Sun at-sen, ueling Lyu, Fakulteta za biomedicinski inženiring, Kitajska V clanku je predstavljen nov linijski zobniški mehanizem z variabilnim kotom gredi (VSALM). Mehanizem VSALGM ima dve rotacijski prostostni stopnji: prva je vrtenje zobniške dvojice s konstantnim prestavnim razmerjem, druga pa predstavlja relativni zasuk gredi. Mehanizem je tako primeren za aplikacije, ki zahtevajo konstantno prestavno razmerje in dve prostostni stopnji. Najprej je podan predlog novega kontaktnega modela VSALGM, ki ga sestavljata ena gnana kontaktna krivulja in ena gonilna delovna površina linijskega zobnika (DLTS). Površino DLTS sestavlja množica gonilnih kontaktnih krivulj. a osnovi teorije prostorske ubirnice linijskih zobnikov so bile izpeljane osnovne enacbe za konstruiranje po kontaktnem modelu VSALM. Ker ubirni kot pomembno vpliva na ucinkovitost zobniškega prenosnika, je bil narejen primer izracuna ubirnega kota na osnovi kontaktnega modela VSALM. ezultati izracunov kažejo, da lahko pri nekaterih kombinacijah parametrov nastopi blokada oziroma nezmožnost vrtenja zobniške dvojice. Z ato je bil analiziran in predlagan kriterij ubirnega kota VSALGM na osnovi kontaktnega modela. Iz tega je bila izpeljana osnovna metoda za konstruiranje VSALGM. Podan je tudi primer konstrukcije zobniške dvojice na osnovi zgornjega primera izracuna ubirnega kota, na podlagi katerega so bili 3D-natisnjeni prototipi. a preizkus delovanja VSALM je bilo zgrajeno kinematicno preizkuševališce, ki omogoca spreminjanje kota gredi. a njem so bile opravljene tri skupine kinematicnih eksperimentov s prototipi, v vsaki skupini pa so bili zajeti testi s fiksnim in zvezno spremenljivim kotom gredi. Skupine so se razlikovale po obremenitvah. Nato so bili izvedeni še preizkusi kontaktnih površin zobnikov. ezultati kinematicnih eksperimentov so dokazali, da ima VSALGM dve prostostni stopnji in da zagotavlja gladek prenos tudi med konstantnim spreminjanjem kota gredi. Iz analize kontaktnih površin sledi ugotovitev, da razlicne gonilne kontaktne krivulje pri razlicnih kotih gredi VSALM ubirajo z vedno isto gnano kontaktno krivuljo. Analiza napak prenosa VSALM v kinematicnih eksperimentih je pokazala, da so le-te predvsem posledica napak instrumenta in testnih prototipov. Trenutno bi bilo zaradi nizke natancnosti eksperimentalne opreme težko analizirati tocnost montaže zobnikov. V prihodnje bodo razviti natancno preizkuševališce in natancni linijski zobniki za analizo napak prenosa in dinamicne zmogljivosti VSALM. ezultati eksperimentov so pokazali, da se napaka prenosa povecuje z obremenitvijo. Z dajšnji mehanizmi VSALGM so primerni le za manjše obremenitve. Njihova konstrukcija bo v prihodnje izpopolnjena za povecanje obremenljivosti. VSALGM ima v primerjavi s predhodnimi rešitvami tovrstnih zobniških dvojic dve prostostni stopnji ter zagotavlja gladek prenos tudi med konstantnim spreminjanjem kota gredi. le eede liii oi ariaile ot redi rotota toa iri ot teoria rotore irice ieatii eeriet oii reoV Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, SI 47 Prejeto v recenzijo: 2021-02-21 © 2021 Strojniški vestnik. Vse pravice pridržane. Prejeto popravljeno: 2021-05-11 Odobreno za objavo: 2021-06-21 aoed oiloti i trioloe traoti dri leaeY Myron Chernets1 – Marek Opielak2 – Anatolii Kornienko1,* – Oleg Radko3 1acionalna univerza za letalstvo, Fakulteta za letalski in vesoljski inženiring, Ukrajina 2Tehniška univerza v Lublinu, Poljska 3 acionalna univerza za obrambo Ivana ernjahovskega, Ukrajina Uporaba drsnih ležajev ima pomembno vlogo pri tehnicnih aplikacijah, kjer uporaba kotalnih ležajev ni možna oz. prakticna. a njihove delovne naloge so znacilne zelo razlicne obremenitve, premeri gredi, vrtilne frekvence, širine in uporabljeni materiali. Ti ležaji obratujejo v razlicnih delovnih pogojih ter v prisotnosti fluidov (plinov), mejnega trenja in tudi v pogojih suhega trenja. Metode za izracun trajnosti tovrstnih ležajev iz literature se v praksi niso uveljavile zaradi uporabe Archardovega zakona abrazivne obrabe, ki ne nastopa v pogojih mejnega trenja. Pri projektiranju drsnih ležajev se pogosto uporabljajo izracuni na osnovi povprecnega tlaka p in Z einerjevega kriterija pv. Poenostavitev pri racunanju nosilnosti na osnovi tlaka p je velik približek. Velikost kontaktnega tlaka ni odvisna le od obremenitve in od premera gredi, temvec v veliki meri tudi od radialne zracnosti ležaja in od elasticnosti materialov. menjeni kriteriji ne upoštevajo omenjenih dveh dejavnikov. V fazi konstruiranja prav tako ni vkljuceno napovedovanje obrabe drsnih ležajev. Ustrezna metoda za izracun ležajev mora temeljiti na kontaktnih problemih teorije elasticnosti za cilindricna telesa podobnih polmerov ob upoštevanju mehanizma obrabe s tornim utrujanjem. Pricujoci clanek predstavlja novo analiticno metodo na podrocju teorije elasticnosti, ki omogoca racunanje kontaktne trdnosti in življenjske dobe drsnih ležajev. Metoda temelji na avtorjevi metodologiji za preucevanje kinetike torno-utrujenostnega loma materialov v triboloških sistemih pri pogojih drsnega trenja. Predstavljen je tribokineticni matematicni model obrabe, metode za racunanje zacetnega kontaktnega tlaka in njihova transformacija zaradi obrabe ležajnih elementov, kakor tudi izracun življenjske dobe ležajev do maksimalne linearne obrabe puše. a podlagi rezultatov numericne simulacije je bil preucen vpliv obremenitve in radialne zracnosti na izhodišcne kontaktne tlake in njihovo zmanjševanje zaradi obrabe. Izdelana je bila racunska ocena življenjske dobe ležaja. Ugotovljene so bile kvalitativne in kvantitativne odvisnosti sprememb parametrov kontakta in trajnosti od obremenitve, kotne hitrosti gredi ter radialne zracnosti ležaja. Metoda omogoca izracun trajnosti ležajev z dovoljeno obrabo puše ter dolocitev obrabe puše in gredi v dolocenem obratovalnem obdobju. Predstavljena je zaprta oblika rešitve problema tribološkega kontakta za prakticno uporabo s preprostimi programskimi orodji, zlasti s programom Microsoft Excel. azvita metoda je uporabna brez omejitev za preracun kovinskih ležajev, tudi v prisotnosti razlicnih prevlek (zašcitnih, za zmanjšanje trenja, obrabno obstojnih). Metoda veliko obeta tudi pri hibridnih (kovinsko-polimernih) ležajih, ki so izdelani iz materialov z znatno razlicnimi lastnostmi. Postopki konstruiranja za take ležaje še ne obstajajo. Predstavljena metoda za racunsko napovedovanje zmogljivosti drsnih ležajev omogoca kakovosten in ucinkovit izracun kontaktne trdnosti in tribološke trajnosti v inženirski praksi. Metoda zagotavlja optimizacijo kriterijev kontaktne trdnosti, obrabne obstojnosti in trajnosti ter izbiro optimalnih materialov pri konstruiranju ležajev. ešitve tovrstnih problemov kontaktne obrabe omogocajo tudi ocenjevanje napak pri numericnih izracunih. Metoda ima znanstveno vrednost na podrocju tribologije, teoreticno vrednost na podrocju tribomehanike in prakticno vrednost na podrocju tribotehnike. le eede dri lea role otate orae araetri otata i triootata oraa trajnost Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, SI 48 Prejeto v recenzijo: 2021-03-09 © 2021 Strojniški vestnik. Vse pravice pridržane. Prejeto popravljeno: 2021-05-18 Odobreno za objavo: 2021-06-28 Eerietala raiaa i ateatii odel tolote prehodnosti dvokapnega solarnega destilatorja Raj Vardhan Patel1,2, Anshul Yadav1,2, Jerzy Winczek3,* 1Inštitut za tehnologijo Kamla Nehru, Indija 2CSIR - centralni inštitut za raziskave soli in morskih kemikalij, Indija 3 Tehniška univerza v enstohovi, Poljska Z mogljivost solarnih destilatorjev je odvisna od prenosa toplote v destilatorju, vode v posodi, hitrosti vetra (za hlajenje steklene strehe), itd. Pricujoca študija obravnava odvisnost toplotne prehodnosti od temperature vode v posodi in hitrosti vetra pri akrilnem solarnem destilatorju, ki je zasnovan za poletne klimatske razmere v Sultanpuru v Indiji. Opravljene so bile eksperimentalne študije za preucitev vpliva vode v posodi in hitrosti vetra na toplotno prehodnost (s konvekcijo, uparjanjem in sevanjem) in kapaciteto solarnega destilatorja. azvit je bil matematicni model za preucitev vpliva globine vode v posodi in hitrosti vetra na prenos toplote in zmogljivost solarnega destilatorja. Ta je bil za poskuse postavljen v smeri vzhod-zahod. S sedmimi digitalnimi temperaturnimi tipali so bile zabeležene vrednosti temperature na razlicnih mestih v destilatorju. Podatki o soncnem obsevanju, temperaturi okolice in hitrosti vetra so bili pridobljeni iz postaje za spremljanje soncnega sevanja SAna inštitutu KITv Sultanpuru v Indiji. Hitrost vetra je bila izmerjena z digitalnim anemometrom. Trenutna temperatura je bila odcitana vsako uro. Matematicni model je bil uporabljen tudi za primerjavo zmogljivosti in toplotne prehodnosti dvokapnega solarnega destilatorja z rezultati eksperimentov. Ugotovljeno je bilo, da je konvektivna toplotna prestopnost odvisna od mase in temperature vode v posodi ter od temperature steklene strehe. Najvišji vrednosti hew (55,05 W/(m2K) in 31 ,80 W/(m2K)) ter h(2,4 8 W/(m2K) in 2,38 W/(m2K)) sta bili ugotovljeni pri globinah 2 cm oz. 5 cm. ajvecja sevalna toplotna prestopnost znaša 8,31 W/(m2K) pri globini 2 cm in se povecuje s kondenzacijo. Vodna para med kondenziranjem namrec oddaja toploto stekleni površini in jo tako segreva. Ko se globina poveca z 2 cm na 5 cm, se zmogljivost destilatorja zmanjša za 25,45 . ajvecja dnevna zmogljivost 2,5 lm2/dan je bila ugotovljena pri globini vode 2 cm. mogljivost destilatorja se povecuje s porastom hitrosti vetra, saj kondenzacija na stekleni cw površini poteka hitreje. Do tega pride zaradi povišanja temperaturne razlike med stekleno streho in vodo v posodi. Prednost pasivnih solarnih destilatorjev je v nizki ceni in v nižjih stroških vzdrževanja, njihova pomanjkljivost pa je majhna zmogljivost. a vecjo zmogljivost so potrebni aktivni solarni destilatorji. mogljivost pasivnih destilatorjev je odvisna od dejavnikov, kot so hlajenje steklene strehe, materiali posode itd. V študiji niso bili upoštevani vpliv hlajenja steklene strehe zaradi tekoce vode, vpliv razlicnih materialov posode, debelina steklene strehe in vpliv oblike posode. Te dejavnike bo mogoce upoštevati v prihodnjih študijah solarnih destilatorjev. Preuciti bo mogoce tudi vkljucitev soncnih kolektorjev in virov odpadne toplote. azvoj matematicnega modela optimalne integracije soncnih kolektorjevbi pripomogel k prihodnjim raziskavam solarnih destilatorjev. Tudi masni pretok tekocine, ki kroži skozi kolektorje, ima pomembno vlogo pri izkorišcanju toplote. Možna je optimizacija masnega pretoka in globine vode v posodi destilatorja. Prenos toplote v destilatorju bi bilo mogoce še dodatno povecati z uporabo nanofluidov. Možnost za izboljšanje prehajanja toplote iz posode na stekleno streho in s tem kapacitete predstavljajo tudi rebra v posodi in notranji odsevniki. V vsakem primeru je izkoristek solarnega destilatorja odvisen od temperaturne razlike med vodo v posodi in stekleno streho. le eede doai olari detilator oa eeria detilacia oeiciet reoa tolote Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, SI 49 Prejeto v recenzijo: 2021-05-12 © 2021 Strojniški vestnik. Vse pravice pridržane. Prejeto popravljeno: 2021-06-17 Odobreno za objavo: 2021-07-09 Mehanske lastnosti lepljenih spojev, iz delanih z lepili, otliii a tlaN Anna Rudawska1,* – Magd Abdel Wahab2,3 1Tehniška univerza v Lublinu, Fakulteta za strojništvo, Poljska 2Univerza Duy Tan, Razvojno-raziskovalni inštitut, Vietnam 3 Univerza v hentu, Fakulteta za inženiring in arhitekturo, Belgija lanek obravnava mehanske lastnosti lepljenih spojev, izdelanih z akrilnimi lepili, obcutljivimi na tlak. Lepljeni spoji z industrijskimi lepilnimi trakovi, obcutljivimi na tlak, so bili v preskusih izpostavljeni vec temperaturnim ciklom. V preskusih sta bili uporabljeni dve vrsti akrilnih lepilnih trakov in tri vrste gradbenih materialov: plocevina iz konstrukcijskega jekla (45), plocevina iz aluminijeve zlitine (E-A: 5754) in titanova plocevina (kvalitete 2). Trdnostni preskusi lepljenih spojev so bili opravljeni po kondicioniranju na sobni temperaturi (23 ° C) in po 500 temperaturnih ciklih v obmocju 60 40 . Trdnostni preskusi so bili izvedeni po standardu DI E 1465 na stroju Z wick/Roell Z 150. Pri lepljenih spojih, ki so bili izpostavljeni temperaturnim ciklom, ni bilo ugotovljeno poslabšanje mehanskih lastnosti. Lepilni trakovi, obcutljivi na tlak, imajo dobro sposobnost lepljenja obravnavanih materialov v danih pogojih. Glavna ugotovitev raziskave je, da temperaturni cikli pozitivno vplivajo na mehansko trdnost spojev, izdelanih z lepilnimi trakovi, obcutljivimi na tlak. ovost pricujoce raziskave je v izpostavitvi omenjenih spojev temperaturnim ciklom v imenovanem obmocju. ezultati bodo uporabni pri nacrtovanju spojev z uporabo lepilnih trakov, obcutljivih na tlak, zlasti tistih, namenjenih obratovanju v prisotnosti temperaturnih ciklov. le eede lelei o elo aliiea litia leilo otlio a tla eae latoti temperaturni šoki Strojniški vestnik - Journal of Mechanical Engineering 67(2021)7-8, SI 50 © 2021 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2021-05-23 Prejeto popravljeno: 2021-07-01 Odobreno za objavo: 2021-07-12 K arakteriz acija spoja AZ 31/ AW -6060, iz delanega po postopku sestavljenega litja z vmesno plastjo Z n pri raz meroma niz kih temperaturah Tomasz Bucki1,* – Marek Konieczny1 – Dana Bolibruchova2 – Sylwia Rzepa3 1Tehniška univerza Kielce, Fakulteta za mehatroniko in strojništvo, Poljska 2Univerza v ilini, Fakulteta za strojništvo, Slovaška republika 3 MTES FHT a.s., ddelek za mehanske preiskave in termofizikalne meritve, eška republika Vzadnjih letih je opazen znaten porast uporabe bimetalnih elementov na osnovi lahkih kovin, natancneje aluminija in magnezija. Uveljavljajo se na mnogih podrocjih, npr. v avtomobilski industriji, kjer prispevajo k zmanjšanju mase vozil in s tem porabe goriva. Magnezijeve in aluminijeve zlitine je mogoce kombinirati z razlicnimi tehnikami. Pri metalurškem spajanju Mg in Al se obicajno formirajo intermetalne faze Mg-Al, ki so same po sebi krhke in povzrocijo, da ima spoj slabe mehanske lastnosti. Sestavljeno litje je postopek spajanja podobnih ali raznorodnih zlitin z nalivanjem raztaljene zlitine na drugo zlitino, ki je v trdnem stanju. Proces omogoca razmeroma preprosto in ekonomicno proizvodnjo bimetalov v najrazlicnejših oblikah in dimenzijah. lanek obravnava izdelavo spoja magnezijeve zlitine A31 in aluminijeve zlitine A-6060 z vmesno plastjo n. Uporabljeno je bilo temperaturno obmocje, ki je v primerjavi s podatki iz literature razmeroma nizko. Po postopku difuzijskega spajanja je bila na površino vložka A-6060 nanesena plast n. Vložek je bil vstavljen v jeklen kalup na sobni temperaturi in spoj je bil nato izdelan po postopku sestavljenega litja tako, da je bil kalup napolnjen s tekoco zlitino A31, ogreto na 650 . Predmet študije sta bili analiza mikrostrukture ter preiskava mikrotrdote in strižne trdnosti izdelanega spoja. Mikrostruktura je bila preucena pod opticnim mikroskopom in z vrsticnim elektronskim mikroskopom, opremljenim z energijsko disperzijskim rentgenskim spektrometrom. Izmerjena je bila tudi mikrotrdota po Vickersu. Trdnost spoja je bila dolocena s strižnim preskusom. Ugotovljeno je bilo, da se je med zlitinama oblikoval 400 m debel spoj. Mikrostrukturna analiza je pokazala, da je za obmocje spoja znacilna visoka koncentracija n in Mg. Spoj na strani A31 sestavljata evtektoid z intermetalno fazo Mgn ter trdna raztopina Al in n v Mg. V osrednjem delu obmocja spoja so bili ugotovljeni delci ternarne intermetalne faze Mg5 Al2Z n2 in tanek sloj te faze. V obmocju zraven A-6060 je bila ugotovljena osnova Mg(Al,Z n)2 s finimi delci drugih faz. a obmocje spoja je znacilna višja mikrotrdota kot pri obeh zlitinah. ajvišje vrednosti mikrotrdote so bile ugotovljene v obmocju s fazo Mg(Al,n)2 ter v sloju, sestavljenem iz faze Mg5 Al2Z n2. Meritve mikrotrdote v tem predelu so povzrocile širjenje manjših razpok v okolici konice merilnika trdote po Vickersu, ki dokazujejo opazno krhkost faz. Povprecna strižna trdnost spoja je znašala 19,6 ± 2,5 M Pa. ezultati študije bogatijo znanje na podrocju spajanja Mg in Al zlitin po postopku sestavljenega litja. Ugotovljen je bil vpliv vmesne plasti n na oblikovanje spoja. Uporaba te plasti je omogocila oblikovanje spoja brez krhkih faz Mg-Al. Predstavljeni spoj je glede na podatke v literaturi manj krhek in ima boljše mehanske lastnosti kot spoji, izdelani brez vmesne plasti. Ugotovljeno je bilo tudi to, da temperaturne razmere pomembno vplivajo na oblikovanje spoja z vmesno plastjo Z n. Pri nizkih temperaturah so se formirale faze, bogate z Mg in Z n, pri povišanih temperaturah pa je bila ugotovljena višja vsebnost Al. Iz predstavljenih rezultatov sledi sklep, da je uporaba vmesnih plasti obetavna rešitev za spajanje zlitin Mg in Al. Z ustrezno modifikacijo mikrostrukture spoja je mogoce znatno izboljšati njegove mehanske lastnosti, s tem pa uporabnost materialov. le eede etaleo lite aeiea litia aliiea litia cioa ea lat mikrostruktura, mehanske lastnosti Guide for Authors All manuscripts must be in English. Pages should be numbered sequentially. The manuscript should be composed in accordance with the Article Template given above. The maximum length of contributions is 12 pages (approx. 5000 words). Longer contributions will only be accepted if authors provide justification in a cover letter. For full instructions see the Infor­mation for Authors section on the journal’s website: http://en.sv-jme.eu . 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Ašker°eva 6, 1000 Ljubljana, Slovenia, e-mail: info@sv-jme.eu http://www.sv-jme.eu Contents Papers 343 Peixing Ning, Ji Zhao, Shijun Ji, Jingjin Li, Handa Dai Ultra-Precision Single-Point Diamond Turning of a Complex Sinusoidal Mesh Surface Using Machining Accuracy Active Control 352 Yang-zhi Chen, Chao He, Yue-ling Lyu: Basic Theory and Design Method of Variable Shaft Angle Line Gear Mechanism 363 Myron Chernets, Marek Opielak, Anatolii Kornienko, Oleg Radko: Predictive Estimation of Sliding Bearing Load-Carrying Capacity and Tribological Durability 369 Raj Vardhan Patel, Anshul Yadav, Jerzy Winczek: Experimental Investigation and Mathematical Modelling of Heat Transfer Coefficient in Double Slope Solar Still 380 Anna Rudawska, Magd Abdel Wahab: Mechanical Properties of Adhesive Joints Made with Pressure-Sensitive Adhesives 389 Tomasz Bucki, Marek Konieczny, Dana Bolibruchova, Sylwia Rzepa: Characterization of the AZ31/AW-6060 Joint Fabricated using Compound Casting with a Zn Interlayer at Relatively Low Temperature Conditions