Strojniški vestnik Journal of Mechanical Engineering no. 10 year 2019 volume 65 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, Aškerčeva 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: Papirografika, printed in 300 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: Precise 3D measurements, performed on the Alicona InfiniteFocusSL measuring system, used to assess the chipping of ceramic workpiece edges after milling. Image courtesy: University of Ljubljana, Faculty of Mechanical Engineering, Chair of Machining Technology Management, Slovenia ISSN 0039-2480, ISSN 2536-2948 (online) International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, King Fahd U. of Petroleum & Minerals, Saudi Arabia Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, University of Ljubljana, Slovenia Filippo Cianetti, University of Perugia, Italy Franci Čuš, University of Maribor, Slovenia Janez Diaci, University of Ljubljana, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Jožef Duhovnik, University of Ljubljana, Slovenia Igor Emri, University of Ljubljana, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Janez Grum, University of Ljubljana, Slovenia Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, University of Maribor, Slovenia Soichi Ibaraki, Kyoto University, Department of Micro Eng., Japan Julius Kaplunov, Brunel University, West London, UK Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Jernej Klemenc, University of Ljubljana, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, University of Ljubljana, Slovenia Gorazd Lojen, University of Maribor, Slovenia Thomas Lubben, University of Bremen, Germany Jure Marn, University of Maribor, Slovenia George K. Nikas, KADMOS Engineering, UK Tomaž Pepelnjak, University of Ljubljana, Slovenia Vladimir Popovič, University of Belgrade, Serbia Franci Pušavec, University of Ljubljana, Slovenia Mohammad Reza Safaei, Florida International University, USA Marco Sortino, University of Udine, Italy Branko Vasič, University of Belgrade, Serbia Arkady Voloshin, Lehigh University, Bethlehem, USA General information Strojniški vestnik - Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue). 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Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10 Contents Contents Strojniški vestnik - Journal of Mechanical Engineering volume 65, (2019), number 10 Ljubljana, October 2019 ISSN 0039-2480 Published monthly Papers David Muženič, Jaka Dugar, Davorin Kramar, Matija Jezeršek, Franci Pušavec: Improvements in Machinability of Zinc Oxide Ceramics by Laser-Assisted Milling 539 Daniel Miler, Stanko Škec, Branko Katana, Dragan Žeželj: An Experimental Study of Composite Plain Bearings: The Influence of Clearance on Friction Coefficient and Temperature 547 Thangavel Yuvaraj, Paramasivam Suresh: Analysis of EDM Process Parameters on Inconel 718 Using the Grey-Taguchi and Topsis Methods 557 Fariha Mukhtar, Faisal Qayyum, Hassan Elahi, Masood Shah: Studying the Effect of Thermal Fatigue on Multiple Cracks Propagating in an SS316L Thin Flange on a Shaft Specimen Using a Multi-Physics Numerical Simulation Model 565 Mohammad Hadi Izadi, Shahrokh Hosseini Hashemi, Moharam Habibnejad Korayem: Buckling of Joined Composite Conical Shells Using Shear Deformation Theory under Axial Compression 574 Roman Satošek, Michal Valeš, Tomaž Pepelnjak: Study of Influential Parameters of the Sphere Indentation Used for the Control Function of Material Properties in Forming Operations 585 Chang Wang, Jun Liu, Zhiwei Luo: Suppression of Self-Excited Vibrations in Rotating Machinery Utilizing Leaf Springs 599 Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 © 2019 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2019.6133 Original Scientific Paper Received for review: 2019-05-09 Received revised form: 2019-07-17 Accepted for publication: 2019-08-13 Improvements in Machinability of Zinc Oxide Ceramics by Laser-Assisted Milling David Muzenic* - Jaka Dugar - Davorin Kramar - Matija Jezersek - Franci Pusavec University of Ljubljana, Faculty of Mechanical Engineering, Slovenia In this paper, an attempt Is made to advance the understanding of Laser-Assisted Milling (LAMill) of zinc oxide (ZnO) electronic ceramics. A series of conventional milling and LAMill experiments with varying laser power were conducted to determine the effect of laser assistance on the machinability of this material. Improved machinability in terms of reduction in machined surface roughness and edge chipping was achieved by adjusting laser power. At an optimal laser power of 120 W, determined for the machining parameters used, Ra and Rz were reduced by 37 % and 46 %, respectively, while the average and maximum chipping widths were reduced by 15 % and 17 %, respectively Keywords: zinc oxide (ZnO) ceramics, machinability, laser-assisted milling, surface roughness, edge chipping Highlights • This paper deals with LAMill of ZnO electronic ceramics; milling of ZnO electronic ceramics has not been researched previously • Conventional milling and LAMill experiments using various levels of laser power were conducted. • The effect of laser power on the machined surface integrity was determined in terms of surface roughness and interior edge chipping. • Optimal level of laser power was proposed for the used machining conditions. 0 INTRODUCTION Machinability in cutting processes, which is the ability to economically machine a certain material, is usually closely related to the performance of the to-be-cut material. Engineering ceramics are known for their poor machinability due to high hardness and brittleness. Thus, often the state-of-the-art in precision shaping of these materials are low material-removal rate processes, e.g. grinding and lapping, resulting in high machining costs. Nowadays, new ceramic materials are being developed in different areas of the industry (e.g. electronic ceramics). These ceramics are usually not known for high hardness or strength, yet high brittleness and low fracture toughness that lead towards excessive edge chipping. Therefore, machinability of these materials is significantly reduced. Edge chipping of ceramics is sudden edge damage on the macro- or microscale, caused by fractures usually while the cutting tool either comes in contact or separates from the workpiece. Ng et al. [1] described three types of edge chipping, namely entry edge chipping, interior edge chipping and exit edge chipping (Fig. 1), while milling a tetrasilicic mica glass ceramic. On finished parts, the presence of edge chipping is detrimental to the mechanical characteristics as well as dimensional and geometrical accuracy, and often severely limits the productivity of ceramic machining processes. Direction of r toolpath Interior "^chipping Fig. 1. Types of edge chipping [1] Some improvements in machinability of both structural and electronic ceramics were achieved by optimizing the conventional fixed abrasive machining processes [2]. Besides improvements in conventional processes, large reductions in cutting forces and edge chipping in ceramics fixed abrasive machining were achieved with ultrasonic oscillations of the cutting tool during machining [3]. Another hybrid approach to fixed abrasive machining of silicon nitride (Si3N4) structural ceramics was presented by Guerrini et al. [4]. The authors proposed a combined process wherein a laser source is used to induce controlled cracking of the workpiece material surface, which aids the consequent grinding process. Zhang et al. [5] have adopted a similar shaping approach for zirconium oxide ceramics. Besides improvements in fixed abrasive machining processes, other non-traditional or hybrid processes such as electrical-discharge machining [6], laser machining [7] and thermally *Corr. Author's Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva cesta 6, Ljubljana, Slovenia, david.muzenic@fs.uni-lj.si 539 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 enhanced machining [8] have been used to address the poor machinability of ceramic materials. In thermally enhanced machining, a heat source is used to heat the workpiece material right before the cutting zone, resulting in local softening of the to-be-cut material. By heating ceramic materials above a certain temperature, a reduction in hardness can be achieved as well as the change in deformation behaviour from brittle to ductile [9]. Amongst the thermally enhanced machining processes, laserassisted machining (LAM) has been shown to be superior method for improving the machinability of different structural ceramics due to the ability of a fast, local and controlled input of heat into the workpiece material. In comparison to grinding and lapping, much higher material-removal rates can be achieved in LAM, leading to a significant reduction in machining costs. Lei et al. [10] evaluated the potential of laser-assisted turning (LAT) as an economically viable process for the fabrication of precision Si3N4 ceramic parts. Compared to the conventional diamond grinding, a decrease in the thickness of the subsurface damage layer was observed, while achieving tool life, comparable to metal cutting. Tian et al. [11] also report on achieving tool life, comparable to metal cutting, while successfully producing Si3N4 parts with complex geometry. Pfefferkorn et al. [12] demonstrated the feasibility of LAT of magnesia-partially-stabilized zirconia (PSZ) by achieving a process with 0 % flaws, which would cause a workpiece to be scrapped. The experiments showed that at a laser power of 100 W, the material removal temperature rises to 530 °C and the material can be successfully machined, although a PCBN-tipped tool life was only 3 min. Further increasing the laser power to 250 W leads to a material removal temperature of 1210 °C and a drastic increase in tool life (up to 120 min). While several studies on LAT of structural ceramics are reported in literature, the authors found only two reports on laser-assisted milling (LAMill) of these materials. The possible reasons for that are that LAMill is generally more complex than LAT with regards to the laser setup and in the case of brittle materials, milling is significantly more subjected to workpiece edge chipping than turning. Tian et al. [13] achieved good surface finish, repeatable performance and acceptable tool wear in LAMill of Si3N4 ceramics using TiAlN coated carbide tools, although the problem of edge chipping was not addressed in this study. A detailed study on edge chipping mechanisms in LAMill of this material was presented by Yang et al. [9]. The authors concluded that by heating the material above the softening point, edge chipping is reduced due to the reduction in cutting forces. By heating the material further, above the brittle/ductile transition temperature, edge toughness of Si3N4 is increased significantly, resulting in a further reduction of edge chipping. In this study, an attempt is made to advance the understanding of LAMill on the machinability of zinc oxide (ZnO) based electronic ceramic. Detailed information about the composition and preparation of this ceramic is provided in [14]. Lapping process represents the state of the art in machining of ZnO ceramic. Achieving a successful milling operation, however, would result in a drastic increase in quality, achievable material removal rate and consequently a decrease in machining costs. No reports on machining of this material can be found in literature, nor information about the material edge toughness or edge chipping tendencies. The authors performed preliminary studies on conventional milling of ZnO ceramics and concluded that conventional milling is not appropriate for its machining and that edge chipping is the main factor, reducing its machinability. The latter is supported by comparing the fracture toughness of zinc oxide ceramics (2.10 MPa^m1/2 to 2.16 MPa^m1/2 [15]) to previously discussed structural ceramics (for example Si3N4, 4 MPa^m1/2 to 8 MPa^m1/2 [16]). Based on the similarities between ZnO ceramics and other electronic ceramics, or even structural ceramics, the authors assume that laser assistance should provide significant machinability improvement in milling of ZnO ceramic material. Therefore, the aim of this study is defining the effect of laser assistance on the machinability of zinc oxide ceramics. To observe laser assistance significance, only laser power was varied throughout the experimental repetitions, while the machining parameters were kept constant at levels that were found as optimal by the preliminary conventional milling experiments. 1 EXPERIMENTAL PROCEDURE 1.1 Laser-Assisted Milling Experiments The laser-assisted dry milling experiments were performed on a 3-axis Mori Seiki Frontier M1 vertical machining center, equipped with a 400 W YLR-400-AC continuous wave fiber laser from IPG Photonics with a wavelength of 1070 nm and the collimated laser beam diameter of 5 mm. The cutting tool used in the experiments was a DIXI 72420 PCD end mill with a diameter of 4 mm and a single cutting edge. 540 Muzenic, D. - Dugar, J. - Kramar, D. - Jezersek, M. - Pusavec, F. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 A depth and width of cut of 0.1 mm and 0.33 mm, respectively, a feed velocity of 250 mm/min, a spindle speed of 6250 rev/min (vc = 78.5 m/min and f = 0.04 mm) and the position of the laser spot relative to the cutting tool (Fig. 2) were kept constant throughout all experimental repetitions. For every experimental repetition, a 4 mm wide and 0.1 mm deep slot was milled at the centre of the workpiece in the x-direction without laser assistance and then two consecutive LAMill passes with the same width of cut in the positive >>-direction were performed, as shown in Fig. 2. The measurement setup used for surface integrity analysis is shown in Fig. 3. Fig. 2. Laser-assisted milling strategy Table 1 shows the plan of laser-assisted milling experiments. Experiments N° 1 to 6 were performed with two repetitions with the same experimental parameters, each time on a new workpiece. As the results indicated an area of interest between the two used levels of laser power, four more experiments (N° 7 to 10) were performed, with one repetition per laser power used. 1.2 Surface Integrity Analysis Surface integrity was evaluated in terms of interior edge chipping and machined surface roughness. For the purpose of surface integrity analysis, a 3D scan including the edge and the surface, generated in the two machining passes, shown in Fig. 2, was executed on an Alicona InfiniteFocusSL measurement system. Fig. 3. Surface integrity measurement setup Edge chipping was evaluated by fitting a reference plane on the portion of un-machined surface in the scan and extracting the intersection curve of a plane 5 ^m below the reference plane and the scanned surface. A plot of the distance from the reference plane for the case 0Wb where the lower limit of the colour scale was set to - 5 ^m and thus evidencing the detected edge as the border of the black-coloured area is shown in Fig. 4a). A portion of the detected edge around the maximum detected chipping for the case 0W1 is shown in Fig. 4b). Edge chipping is characterized by the chipping widths, wc,n, which are the normal distances from the ideal edge, without edge defects (green line), to the local extremes (red marks) of the detected edge (blue line), as shown in Fig. 4 b). Two parameters were chosen to evaluate edge chipping, namely maximum (wcmax) and average (wc,avg) chipping width, which are the maximum and mean value of the detected chipping widths in an experimental repetition, respectively. Surface roughness at the machined surface (black area in Fig. 4a) was measured on three different randomly selected 5 mm long profiles in the x-direction for every experimental repetition. For each profile an average of 5 profiles, each 10 ^m Table 1. Plan of laser-assisted milling experiments N° 1 2 3 4 5 6 7 8 9 10 P [W] 0 0 80 80 160 160 110 120 130 140 label 0W1 0W2 80W1 80W2 160W1 160W2 110W1 120Wi 130W1 140W1 Improvements in Machinability of Zinc Oxide Ceramics by Laser-Assisted Milling 541 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 5.00000mm I -5 A -2 0 2 location of wcma)t for measurement 0W, b) E 0.2 — 0.1 * 0 10 12 14 16 18 20 distance from reference plane [pm] edgeid -edgereal »detected chippings 1 1 W Jf / ---- -V" w c,n 1 1 i i -1.5 -1 -0.5 0.5 0 x [mm] Fig. 4. Edge chipping: a) detection methodology and b) definition 1.5 apart in the >>-direction, was taken into account and a cut-off wavelength of 800 ^m was used to eliminate waviness. 2 RESULTS AND DISCUSSION The effects of laser power on the surface integrity of milled ZnO ceramic parts was evaluated in terms of machined surface roughness (chapter 2.1) and interior edge chipping (chapter 2.2). Furthermore, optimal level of laser power is discussed in chapter 2.3. 2.1 Surface Roughness To evaluate the machined surface roughness, Ra and Rz were chosen as representative parameters. Fig. 5 shows the results of surface roughness measurements, grouped by the laser power used. Each vertical bar represents the highest and lowest measured value, while the connecting line represents the mean value for each group of experiments. Note that for laser powers of 0 W, 80 W and 160 W, six measurements are included in the group, while only three measurements are included in the other groups. The results are showing that both Ra and Rz decrease with laser power almost linearly from 0 W to 110 W, followed by a sharp decrease at 120 W and a slight increase with further increasing the laser power. This suggests that 120 W is the optimal laser power level when milling ZnO ceramics with the proposed machining parameters. Furthermore, the difference between the highest and lowest measured Ra or Rz, for a fixed laser power, decreases drastically when increasing the laser power above 80 W. This suggests an improvement in process stability while increasing 542 the laser power above a threshold value between 80 W and 110 W. Fig. 5. Effect of laser power on machined surface roughness The results are indicating that machined surface roughness is in direct correlation with the occurrence of grain pull-out during machining. The latter is facilitated by the brittleness of the thin layer of Bi-rich intergranular phase, through which the cracks propagate during brittle fracture of this material at room temperature. By preheating the workpiece material before cutting, the intergranular phase softens, inhibiting grain pull-out. Furthermore, the authors assume that at a threshold value of laser power between 80 W and 110 W, the material is heated above the glassy transition temperature of the Bi-rich intergranular phase (~350 °C [17]), resulting in changes in the deformation behaviour and the material removal mechanism. A brittle/ductile transition, like in the case of Si3N4 [9], where random cracks during brittle fracture are replaced by the viscous flow of the workpiece material, would explain the increase in process stability. This means that, optimally, the laser power should be kept just above that point (120 W), Muzenic, D. - Dugar, J. - Kramar, D. - Jezersek, M. - Pusavec, F. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 Fig. 6. Sample edge, achieved with a) conventional milling and b) LAMill using a laser power of 160 W and c) area around the maximum detected edge chipping for every experimental repetition Improvements in Machinability of Zinc Oxide Ceramics by Laser-Assisted Milling 543 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 as using higher power does not lead to improvements in surface roughness and results in cracks on the machined surface (Fig. 8). 2.2 Edge Chipping Laser assistance has also a significant effect on interior edge chipping; however, its correlation with laser power differs from the findings of surface roughness. A sample edge, achieved with conventional milling in 0W1 and a sample edge from 160Wb where the best results regarding edge chipping were achieved, are presented in Fig. 6a) and b), respectively. Fig. 6 c) shows the area around wcmax (centred at x = 0) for every experimental repetition and the detected chippings. It can be seen that the definition of a chipping differs from the literature [9] and [18]. To clarify, in this work, a chipping detection algorithm based on local extremes was constructed and used. In contrast with the other definitions of a chipping, several detected chippings in the area of a single, longer (in the x-direction) chipping are detected. However, as stated by Yang et al. [9], the maximum chipping width and the chipping area, which is the area surrounded by the real and ideal edges in Fig. 4, are independent of the chipping definition. Moreover, as the plot of chipping area shows the same trend as the wc,avg in Fig. 7, the authors consider the algorithm to be appropriate for edge chipping evaluation. The dependence of wc and wc on laser power is presented in Fig. 7. A trend line is added to the data as a third degree polynomial fit. It can be seen that both wcmax and wc,avg increase with laser power, for low laser powers, and then decrease linearly for laser powers above 80 W, with the values at 80 W still being significantly larger than at 0 W. This suggests that the optimal laser power for the machining parameters used is outside the tested range, above 160 W. It can be seen in Fig. 7 that the benefits of laser assistance are only achieved with laser powers exceeding 110 W, where both wcmax and wc,avg are reduced, compared to those, achieved by conventional milling. This suggests that the glassy transition of the Bi-rich intergranular phase plays an important role in interior edge chipping as well as in the previously discussed surface roughness. Similarly, for the case of Si3N4, Yang et al. [9] report that there are two factors, contributing to edge toughness. Firstly, edge chipping is reduced due to reduction in cutting forces in LAMill and secondly, while increasing laser power so to heat the material above the glassy transition temperature, the edge toughening mechanism takes place, further reducing edge chipping. 2.3 Optimal Level of Laser Power This study showed that positive effects on the machinability of ZnO ceramics in terms of reduction of interior edge chipping and improved machined surface quality can be achieved with laser assistance by adjusting laser power. At a laser power of 120 W, Ra and Rz were reduced by 37 % and 46 %, respectively, compared to conventional milling, and a 4.5- and 7-fold reduction in the difference between the highest and lowest measured values was observed for Ra and Rz, respectively at this laser power. The highest reduction of edge chipping was obtained at the highest laser power used, 160 W, where the average and maximum chipping widths were reduced by 55 % and 60 %, respectively. However, using this level of laser power resulted in cracks in the workpiece due to thermal shock, as shown in Fig. 8. The stresses, as a consequence of excessive temperature gradient are causing this problem. Based on this, the minimum power above the glassy transition point is considered as the most reliable choice by the authors (i.e. 120 W). By using a laser power of 120 W, the average and maximum chipping widths were reduced by 15 % and 17 %, respectively. Fig. 7. Edge chipping for different laser powers Fig. 8. Thermal crack, formed when using a laser power of 160 W 544 Muzenic, D. - Dugar, J. - Kramar, D. - Jezersek, M. - Pusavec, F. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 539-546 3 CONCLUSIONS The paper contributes to an advanced understanding of laser assistance and represents a pioneering work in the field of LAMill of ZnO electronic ceramics. Conventional milling and LAMill experiments, using various levels of laser power, were conducted to determine the effect of laser power on the machined surface integrity. The key findings of this research are summarized as follows. • Edge chipping is the main factor, reducing the machinability of ZnO ceramics. Laser assistance can improve the machinability of ZnO ceramics by reducing edge chipping and improving surface roughness. For the machining parameters used, an optimal level of laser power exists, where the highest improvement in machinability was achieved. • At the optimal level of laser power of 120 W, Ra and Rz were reduced by 37 % and 46 %, respectively. • By using a laser power of 120 W, the average and maximum chipping widths were reduced by 15 % and 17 %, respectively. Higher reductions in edge chipping were achieved at higher levels of laser power, but cracks due to thermal shock started to appear on the machined surface. Although the novel approach of LAMill applied in this study showed an improvement in the machinability of this material, many areas are yet to be researched to fully understand and implement LAMill in ZnO ceramic part production. As concluded previously, edge chipping is considered the main factor reducing the machinability of ZnO ceramics and LAMill of this material is limited by thermal shock. Therefore, a thermal model that can reliably predict temperatures near the edges of the workpiece after laser heating is crucial for further studies of LAMill of this material. Furthermore, the mechanisms that result in the improvement of surface integrity, while machining ZnO at high temperatures have to be researched to master LAMill of ZnO. 4 ACKNOWLEDGEMENTS The authors would like to thank the Slovenian Research Agency (ARRS) for their financial support through the P2-0266 Research Program and prof. dr. Slavko Bernik from the Department for Nanostructured materials at the Jožef Stefan Institute for his support with knowledge in the field of ZnO ceramics. 5 REFERENCES [1] Ng, S.J., Le, D.T., Tucker, S.R., Zhang, G. (1996). Control of Machining Induced Edge Chipping on Glass Ceramics. Institute of System Research, University of Mariland, College Park. [2] Shih, A.J., Denkena, B., Grove, T., Curry, D., Hocheng, H., Tsai, H.-Y., Ohmori, H., Katahira, K., Pei, Z.J. (2018). Fixed abrasive machining of non-metallic materials. CIRP Annals, vol. 67, no. 2, p. 767-790, DOI:/10.1016/j.cirp.2018.05.010. [3] Wang, J., Zhang, J., Feng, P., Guo, P. (2018). Damage formation and suppression in rotary ultrasonic machining of hard and brittle materials: A critical review. Ceramics International, vol. 44, no. 2, p. 1227-1239, DOI:10.1016/j.ceramint.2017.10.050. [4] Guerrini, G., Fortunato, A., Melkote, S.N., Ascari, A., Lutey, A.H.A. (2018). 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D0l:10.5545/sv-jme.2019.6108 Original Scientific Paper Received for review: 2019-04-18 Received revised form: 2019-08-10 Accepted for publication: 2019-08-21 An Experimental Study of Composite Plain Bearings: The Influence of Clearance on Friction Coefficient and Temperature Daniel Miler1 - Stanko Škec12* - Branko Katana1 - Dragan Žeželj1 1 University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Croatia 2 Technical University of Denmark, Denmark Plain bearings are often used due to their compact dimensions and low cost. Their frictional and wear properties are affected by several parameters: load, sliding velocity, temperature, and surface roughness, among others. In this article, the authors have experimentally investigated the influence of clearance size on the friction and wear in composite plain bearings. An experimental rig was designed to enable the testing of plain bearings in working conditions similar to those encountered throughout their exploitation. Two load levels, two lubrication types, and four clearance levels were varied, resulting in 48 experiments, as each was replicated twice. The friction coefficient and bearing temperature were measured during the experiment, while the material loss and change in surface roughness were determined postexperiment. The results have shown that clearance affects the friction in both the dry running specimens and specimens lubricated using a solid lubricant (polytetrafluoroethylene). Keywords: clearance, composite, friction coefficient, plain bearing. Highlights • The influence of plain bearing clearance on friction coefficient, temperature, and wear was studied. • The experiment was designed as the full factorial; loads, lubrication regimes, and clearance sizes were varied. • In dry running specimens, the friction coefficient reduces as the clearance size is increased, while in PTFE-lubricated specimens local minimum must be found. • In specimens tested at 65 N load, the linear relation between the friction coefficient and the bearing temperature was found. 0 INTRODUCTION The bearings enable relative linear or rotational motion between the two parts by reducing the friction coefficient. Plain bearings are a frequently used bearing sub-type, most likely due to their fairly simple geometry and low manufacturing cost. Since no additional rolling elements are required, their outer diameter is small, while the large contact surface increases the load-carrying capacity. The performance of a plain bearing can be evaluated through a number of criteria, such as its efficiency [1], durability [2], or load-carrying capacity [3]. As such, it is influenced by several parameters: load, sliding velocity, operating temperature, surface roughness, clearance between the plain bearing and the shaft [4], and material. Composite materials are often used in the design of machine elements to provide engineers with a wider range of possibilities in terms of material mechanical properties. The composites have diverse mechanical properties, which are usually achieved by combining different matrix, filler, and reinforcement materials. For example, polymer matrices are chemically resistant but are adversely affected by an increase in temperature. As noted by Prehn et al. [5], a chemically resistant polymer matrix (polyetheretherketone and epoxy resin were used in the referenced study) embedded with fibre reinforcement (CF) and filler (SiC) has improved wear properties while also enabling use in adverse environments, such as seawater [6]. Further, the working temperature often narrows the suitable matrix materials to thermally resistant ones; for example, an increase in temperature decreases the mechanical properties of polymers [7], such as the tensile strength, permissible Hertzian stress, and Young modulus, rendering them unusable. Increase in temperature reduces the tensile strength, permissible Hertzian (contact) stress, and Young modulus of polymer materials. Building on these premises, a compromise during the selection of composite materials may be required to achieve the desired bearing properties, such as the high load capacity or low power losses. As a plain bearing material, composites have several advantages when compared to the traditionally used bronze alloys [8]: higher chemical resistance, lower wear rate, vibration damping, and lower weight. For that reason, there has been a steady rise in composite use for plain bearing manufacturing. It should be noted that the composites used as plain bearing materials are thermal insulators, meaning that an increase in the working temperature will be higher. Moreover, to better understand the overall performance and limitations of the composite plain *Corr. Author's Address: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lucica 5, 10002 Zagreb, Croatia, stanko.skec@fsb.hr 547 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 bearings, most of the current research efforts are focused on the analysis of tribological properties [9] and [10], the optimization of design itself [11] and [12], application of novel materials and coatings [13] and [14], or studying the lubrication models [15]. Generally, the research on tribological properties includes studying the adhesion, friction, wear, and lubrication of surfaces in contact [16]. The tribological properties of the composite materials such as the friction coefficient and wear rate can be improved by altering the orientation, volume fraction, and shape of the reinforcements. For example, El-Sayed et al. [17] found that, for the observed composite material, the lowest friction coefficient is achieved using either transversal or longitudinal fibre orientation. Moreover, increased volume fraction was found to have a beneficial effect on both the wear rate and friction coefficient. By varying the whisker aspect ratios, Ji et al. [18] determined whether the reinforcement shape affects the frictional and wear properties of the composite. Whiskers with lower aspect ratios resulted in more stable mechanical properties. Masripan et al. [19] studied the effect of hardness on a plain bearing's tribological properties. The authors concluded that using the hardest test specimen will result in the lowest friction and, consequently, the lowest wear. The design can be enhanced by altering the microgeometry; with surface texturing being one of the methods. Rahmani and Rahnejat [12] used analytical methods to optimize texture geometry of composite reinforcements. Orientation and layout of the surface fibre were varied to increase the load capacity. When aiming to improve the performance of a bearing-shaft system, in addition to the design and material selection, the use of lubricant is essential. It reduces the friction and material wear in plain bearings and, consequently, improves their efficiency and service life [20]. The lubricants can be either liquid (greases, oils), solid or gaseous. In composite materials with a polymer matrix, lubricants can be impregnated into the matrix, or the running can be dry (no lubricant). This research study is focused on solid lubricants, which are most often used when a continuous adherent film is required in the rubbing surfaces [21], a case encountered in plain bearings. The key advantage to solid lubricants in bearing design is simplicity; there is no need for a lubricating system. Additionally, they ensure uniform friction coefficient and increased permissible contact stresses at the cost of a limited lifetime and modest heat dissipation properties [22]. For lubrication of polymer materials the diamond-like carbon (DLC), polytetrafuoroethylene (PTFE), and MoS2 are the most widely used solid lubricants, with PTFE often described as promising [23]. For the dry running specimen, Rezaei et al. [4] conducted an experimental study using the oscillatory motion, often found in mechanical joints. The clearance was found to have a significant impact on the contact stress distribution. No further studies considering the influence of clearance on dry running plain bearings were found. For this reason, in this article, the authors investigated whether the clearance has an influence on friction coefficient and wear in plain bearings operating at constant rotational speed, as found in mechanical transmissions. The rotational shaft movement was used instead of the oscillatory one to more precisely simulate a bearing-shaft system [4]. 1 METHODS The main goal of this experimental study was to determine how the clearance affects the friction coefficient between the bearing and shaft, and the wear of the composite bearing itself. The experimental rig is described in Section 2, while the variables of interest and associated levels are given in Section 2.1. The plain bearing specimens made of NORDEN Marine 605 composite are coupled with the shaft made of AISI 316. The composite consists of a thermosetting resin reinforced with synthetic fabric and impregnated with solid lubricants to enhance the dry running capabilities. As such, it is an orthotropic material. Its mechanical properties are shown in Table 1. Additional manufacturer-provided data that includes the composite material specifications, machining recommendations, and handling information can be found in [24]. The influence of clearance on the composite plain bearing performance regarding the bearing efficiency and durability was assessed for both the dry running and lubricated specimens. Solid lubricants were applied instead of the liquid ones to avoid the swelling of the polymer matrix. Within the study, polymer swelling is undesirable since it affects the clearances that must remain the same during the test run. PTFE was selected as a lubricant due to its tribological properties (low friction) and convenient application. The conducted study is based on the approach used by Rezaei et al. [4], who studied the clearance influence on the contact stresses in polymeric composite journal bearings. Rezaei et al. conducted an experiment using two different bearings, each having a different vertical load, clearance, and width. PTFE filler was used as a lubricant in both bearings. 548 Miler, D., - Skec, S. - Katana, B. - Zezelj, D. Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 In this research study, a full factorial experimental design was used (more details in Section 2.2). Two lubrication types were combined with two load and four clearance levels, resulting in a total of 16 required measurements per replication. Three replications were made for each specimen to obtain statistically relevant data. Each measurement lasted 120 minutes to avoid the transitional phenomena, thus ensuring the robustness of results. Level selection is explained in Section 2.1. Table 1. NORDEN Marine 605 mechanical properties [24] Property Maximum tensile strength [N/mm2] 60 Maximum safe static load [N/mm2] 110 Maximum safe dynamic load [N/mm2] 55 Density [kg/m3] 1300 Maximum water swell [%] 0.15 Maximum working temperature [°C] 100 2 EXPERIMENTAL The experimental rig was created to emulate the working conditions, and the loads plain bearings have to endure during their working life (Fig. 1). The rig enables the adjustment of bearing load Fw by using weights, which are attached to the ball bearing to keep a constant orientation of load vector. The ball bearing is fitted on the outer side of the plain bearing housing, as shown in Fig. 1. The torque T used to overcome the frictional losses is provided by an alternating current (AC) electric motor and is measured using the torque meter. The torque meter of accuracy class 0.2 and a nominal torque of 20 Nm was used. A plain bearing is mounted in the housing using the press fit. The shaft diameter is 34 mm. During the experiment, the rotational speed of the shaft is constant. The rotation causes relative movement between the static plain bearing and the shaft. At the end of the upper rig arm, a load cell (accuracy class 0.2, a nominal force of 500 N) is mounted to enable the measurement of force Fm. Sensors were connected to the data acquisition unit operating using professional software. The rig geometry is defined as follows; the distance L = 150 mm is the distance between the shaft axis and the load cell. An increase in length L enables the use of a lower capacity load cell, the advantage of which is higher test rig accuracy, as the cell sensitivity is specified as a percentage of the maximum capacity. Due to a higher thermal expansion coefficient of the polymer matrix composites, an increase in temperature will result in a larger decrease in the clearance, when compared to the steel parts. A thermometer has been installed to keep track of the change in temperature, which causes thermal expansion. The highest temperature is expected in the contact zone between the bearing and shaft, where it cannot be measured directly. For this reason, the thermometer beam is focused on the plain bearing side, near the contact point. The contactless thermometer (declared accuracy of ±1%) was used to measure the plain bearing temperature 9. The disadvantages of using the above-described method to determine the polymer temperature are shown in [25]. Fig. 1. Experimental rig 2.1 Experimental Variables Preliminary variable analysis and selection were necessary due to a limited number of runs. The experimental variables can be divided into three groups: independent variables, dependent variables, and control variables. Independent variables serve as input and are manipulated to determine their influence on the dependent variables, which is measured throughout the experiment, while the control variables remain unchanged to prevent them from affecting the results. Influences of the following independent variables were considered in this experimental study: Clearance - the primary aim of the study was to conclude whether the clearance influences the plain bearing friction and wear. The clearance size S, defined as the difference between the internal bearing and shaft diameter, was varied. Bearings were made with bore widths of 34.15 mm, 34.25 mm, 34.5 mm, An Experimental Study of Composite Plain Bearings: The Influence of Clearance on Friction Coefficient and Temperature 549 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 and 34.9 mm, resulting in clearances of 0.15 mm, 0.25 mm, 0.5 mm and 0.9 mm respectively. To diminish the influence of manufacturing error on the experimental results, specimens were measured before the experiment. An internal micrometer with a precision of 0.001 mm was used. Bearing load - is equal to the radial force applied to the bearing through the shaft. It is included as an independent variable since, at both ends of the load spectrum (light and heavy loads), load effect on the friction coefficient was found. The former was presented by Myshkin et al. [26] in a review article, in which an overview of research articles studying load influence on friction in various polymers was shown, mostly using the ball-on-disc method. For light loads, the friction decreases as the load increases, while the opposite is correct for the heavy loads [27]. Since the Norden Maritim 605 has a polymer matrix, results are relevant to the case observed in the study at hand. To account for bearing load (Fw) influence, two load levels were used. A load of 65 N was chosen to represent the regular working load, while 115 N represents the higher end of the load spectrum. Lubrication - the lubricant is used to reduce the friction coefficient between the two parts in relative motion and as such influences the friction coefficient. Thus, the two lubrication types were included as independent variables; the dry running specimens were compared to specimens lubricated using a solid lubricant, PTFE. It should be emphasized that the lack of oil film in solid lubrication eases the thermometer beam focusing. The following dependent variables were measured or calculated during the experiment: Friction coe fficient - is one of the key factors for assessing the efficiency of a power transmission [28]; reducing the friction coefficient will result in lower power losses. The defined test rig geometry (moment arm lengths L and r) and the known forces Fm and Fw enable the friction coefficient calculation using Eq. (1), as follows: F ■ L (1) where Fm [N] is the load cell measured load; L [mm] the distance between the shaft axis and the load cell; r [mm] the inner plain bearing radius, and Fw [N] the applied weight. Temperature - is known to affect the friction coefficient between the parts [26]. Moreover, an increase in the temperature causes thermal expansion, reducing the previously measured clearances. The low thermal conductivity of the matrix should also be noted, as the expected contact temperature could be higher than the measured one. To enable the assessment of thermal influence on the friction coefficient, it is selected as a dependent variable and tracked throughout the experiment. As described in Section 2, a contactless thermometer was used to measure the change in temperature close to the point of contact. By keeping track of the changes in temperature, it is possible to determine the magnitude of thermal expansion. Wear - to determine the influence of the clearance on composite plain bearing wear, specimens were weighed before and after the experiment [29]: Am = minitial - mfinal' (2) where minitial [mg] and mfinal [mg] are bearing masses before and after the experimental run, respectively. The digital scale with an accuracy of 0.001 g was used to weigh the specimens. The PTFE-lubricated specimens were weighed before and after lubrication. Surface roughness - although the influence of surface roughness on the friction coefficient exists, as demonstrated in [30], it was not considered in this study. However, mean surface roughness was measured before and after the experiment to keep track of the smoothing effect. All the specimens were to be manufactured with the equal mean surface roughness of Ra = 3.2 ^m. Its values are measured in the axial direction before and after the experiment to provide data for possible future studies. The authors used a roughness tester with a resolution of 0.002 ^m at a 25 ^m range. Lastly, the following variables were chosen as constants: Sliding velocity - the sliding velocity influences both the friction and wear [8], but was not considered within this research study. According to Myshkin, et al. [26], for insignificant variations in contact temperature, independence of friction coefficient in relation to the sliding velocity can be assumed. The sliding velocity vs = 0.53 m/s was selected for all the specimens. Temperature measurements were used for the validation of the sliding velocity simplification procedure. Bearing width - plain bearing width was 27 mm for all test specimens. Outer bearing diameter - a value of 39 mm was used for all the test specimens. 550 Miler, D., - Skec, S. - Katana, B. - Zezelj, D. Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 2.2 Design of Experiment The experiment was organized as full factorial since it was difficult to predict the possible interactions between variables, and whether there are saddle points within the interval at hand. The clearance size, lubrication, and bearing load selected as independent variables (see Fig. 2). Additionally, measurements were replicated twice to increase the reliability, resulting in a total of 48 experimental runs. Fig. 2. Design of experiment schema The clearances between the shaft and the bearings were measured to determine the scale of manufacturing error (see Table 2). Table 2. Clearances Lubri- Bearing load, Fw [N] Theoretical clearance Sh, [mm] Measured clearance S, [mm] cation I II III 0.15 0.128 0.13 0.133 65 0.25 0.224 0.235 0.243 CT 0.5 0.511 0.52 0.562 = 0.9 0.866 0.872 0.882 ^ 0.15 0.145 0.17 0.19 o 115 ■ 0.25 0.224 0.241 0.246 0.5 0.532 0.535 0.541 0.9 0.91 0.918 0.919 0.15 0.145 0.147 0.147 LL? 65 0.25 0.241 0.242 0.243 1— GL 0.5 0.532 0.535 0.536 nt a 0.9 0.917 0.918 0.93 ic ubr 0.15 0.165 0.168 0.186 ■O 115 0.25 0.251 0.253 0.282 o 00 0.5 0.505 0.55 0.58 0.9 0.925 0.935 0.94 3 RESULTS A total of 48 measurements have been carried out. All the specimens were inspected after the experiment to avoid erroneous measurements. The inspection procedure consisted of disassembling the experimental rig and removing the test specimen, which was then cleaned using the solvent cleaner. After the cleaning, visual inspection using a magnification lens was carried out. During the visual inspection, the focus was on detecting failure modes caused by the manufacturing process or inaccurate assembly (i.e. uneven wear). Failure modes that develop slowly, such as corrosion or fatigue failure were not considered since the experiment lasted for only 120 minutes. Uneven wear was the only defect the authors detected within the study. The authors assume that it was caused by a misalignment of the plain bearing and shaft axes. For all the specimens where a defect was detected, a measurement was repeated. The relation between the friction coefficient, the plain bearing temperature, and the clearance is shown in Fig. 3 (for additional plots see Appendix, Fig. 7). Dry running specimens displayed inconclusive results; trends were not consistent for loads of 65 N and 115 N. In the former, greater clearance caused a decline in the friction coefficient. Measurements on clearances of 0.25 mm and 0.5 mm found no significant difference in friction coefficient. For the load of 115 N, friction coefficients displayed a different trend. The lowest friction coefficient ^ = 0.184 was found at the 0.15 mm clearance, followed by ^ = 0.192 at the 0.9 mm clearance. In PTFE-lubricated specimens, results are consistent for both load levels. The highest friction coefficient was found at the clearance of 0.15 mm. With the increase in clearance, up to 0.5 mm, the friction coefficient was reduced. The change was more prominent for the higher load level; the lowest friction coefficient values were measured for clearance of 0.5 mm. Further increase in the clearances resulted in an increased friction coefficient. Lastly, when compared to the PTFE-lubricated specimens, the calculated friction coefficients were higher for the dry running specimens. As shown in Fig. 3, changes in the measured temperatures are related to the changes in friction coefficient. The relationship is the most prominent for dry running specimens under the load of 65 N. The exceptions were 0.15 mm clearances, for which no relation with the friction coefficient was found. The largest deviations were found in dry running specimens loaded with 65 N and the lubricated specimen loaded with 115 N. Dry running specimens displayed similar An Experimental Study of Composite Plain Bearings: The Influence of Clearance on Friction Coefficient and Temperature 551 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 behaviour at both load levels except for 0.15 mm clearance. Increase in the clearances resulted in minor decreases in the temperatures. For the PTFE-lubricated specimens, the highest temperatures were measured at the clearance of 0.15 mm. Increases in clearance resulted in lower temperatures up to clearance of 0.5 mm; the lowest temperature was measured for both load levels. Further increase in clearance resulted in increased temperature. On average, the difference in measured temperature between the dry running and PTFE-lubricated specimens was 4.26 °C at the load level of 65 N, and 4.35 °C at 115 N. When comparing the load level influence on the temperatures, the average difference in temperature between the 115 N and 65 N load was 7 °C for dry running and 6.7 °C for PTFE-lubricated specimens. a) --&-- 65 N O- 115N —*—& (65 N) • 3(1 ISN) 0.32 0.28 iS 0.24 0.2 0.16 b) 0.22 0.18 0.14 0.1 0.06 A •— — -• • -G vO O . O 1 0.2 0.4 0.6 0.8 1 O \ \ O -A O 48 ' 44 40 a 36 -3 -j Xi 32 § 44 - 40 ■ 36 - 32 60 a ■R 28 0.2 0.4 0.6 0.8 Clcarancc, S [mm] Fig. 3. Influence of clearance on a friction coefficient and temperature a) dry running and b) PTFE-lubricated The weighing of specimens has shown that clearance has an impact on bearing wear (Fig. 4). By using the experiment data, the average mass loss was calculated for each test condition. As expected, higher wear is measured in dry running specimens at both load levels; on average, usage of the PTFE lubricant reduced the lost material mass by 1 mg for 65 N and 0.66 mg for 115 N load. The lowest wear was found in 0.5 mm clearance bearings for both lubrication regimes and load levels. When compared to 0.9 mm clearance, using 0.15 mm and 0.25 mm clearances causes a more prominent increase in wear. When comparing the influence of load levels, dry running specimens displayed inconclusive results. For clearance of 0.15 mm, lower load resulted in lower wear, while for the 0.25 mm and 0.5 mm clearances higher load coincided with the lower wear. At the 0.9 mm clearance, average mass losses due to wear were equal. The behaviour observed in PTFE-lubricated specimens was similar; at clearances of 0.15 mm and 0.5 mm, lower wear was recorded for 65 N load, in contrast to 0.25 mm and 0.9 mm clearances, which favoured the higher load. As noted in Section 2.1, mean surface roughness was measured both before and after the experiment. For the dry running specimens, the average change in mean surface roughness was 0.87 ^m at 65 N, and 0.89 ^m at 115 N. Lubricated specimens displayed greater smoothing effect; average change in mean surface roughness was 1.56 ^m at a load of 65 N and 1.28 ^m at 115 N. 0,25 0.5 Clcarancc, S [mm] Fig. 4. Bearing mass loss for different clearances 4 DISCUSSION In plain bearings working under constant rotational speed, the clearance size affects the friction coefficient, differing from the results for oscillating movement presented in [4]. For example, at 65 N loads, the lowest friction coefficient was measured for 0.5 mm clearance. In the vicinity of that value lays the optimal clearance for a corresponding set of selected parameters. By either increasing or decreasing the clearance, the friction coefficient increases. Lowering the clearance size results in an increase in the friction coefficient, thus increasing 552 Miler, D., - Skec, S. - Katana, B. - Zezelj, D. Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 the risk of bearing failure. The former statement was validated by repeating the experiment for the bearings with clearances of 0.05 mm (Fig. 5). Each test run, regardless of load level and lubrication regime, resulted in bearing seizure within the first hour. The average friction coefficients for the duration of the experiment were ranging from 0.782 to 0.819 for dry running and from 0.636 to 0.65 for PTFE-lubricated specimens. Similar results were reported by Brockwell and DeCamillo in [31], where a small decrease in clearance size resulted in a steep increase of the temperature, restricting the rotational velocities. 10 15 20 25 Time, t [min] Fig. 5. Results for PTFE-lubrlcated specimen (115 N) On the other side of the spectrum, for the dry running specimens, the increase in clearance size resulted in a lower friction coefficient. In PTFE-lubricated specimens, however, larger clearance sizes also resulted in higher friction coefficients. With an increase in clearance size, contact surface decreased, causing the contact pressure to rise. Using the procedure presented in [32], in specimens loaded with 65 N contact pressure of 0.8 MPa was calculated for 0.15 mm, and 1.9 MPa for 0.9 mm clearance. At a higher load level, values were 1 MPa and 2.5 MPa, respectively. It should be added that a study carried out by Domitran, et al. [25], in which the authors used polyethylene (PET) samples with the addition of PTFE, has shown that an increase in contact pressure also increased the friction coefficient. Building on these premises, an increase in contact pressure could affect the increase in friction coefficient in lower clearance sizes. When assessing the relationship between the bearing load and friction coefficient, higher friction coefficients were calculated for higher loads, regardless of the lubrication regime. Furthermore, the friction coefficient trendlines in dry running specimens had a similar shape for 65 N and 115 N loads. The same was found in PTFE-lubricated specimens. Exceptions to former statements were the dry running specimens with 0.15 mm clearance and PTFE-lubricated specimens with 0.25 mm clearance. The differences regarding the lubrication regime were also noted. In dry running specimens, the lower friction coefficient was achieved by increasing the clearance size. For PTFE-lubricated specimens, optimal clearance must be found. The optimal clearance will be a trade-off between the seizure at the low clearance sizes and an increase in contact pressure in higher clearance sizes. The clearance affects the temperature of bearing near the contact point (Fig. 5). However, those changes are low; the largest difference in temperature A#max = 5.6 °C was measured for bearings operating at 115 N load with no lubricant. Accordingly, as the A9max is rather low and comparable to the fluctuations in the ambient temperature, the assumption regarding the use of constant sliding velocity is valid (see Section 2.1, [26]). The bearing load was also shown to affect the bearing temperature. In specimens loaded with 65 N loads, changes in clearance size resulted in a linear relationship between the friction coefficients and measured bearing temperature (Fig. 6). It was more prominent in PTFE-lubricated specimens, likely due to a more uniform surface resulting from the application of solid lubricant. No distinct trends were noted for the specimens operating under a heavier load. The lower friction coefficient results in a lower frictional force, which in turn reduces the amount of heat transferred to the bearing and its wear. Consequently, the lower temperature was measured in PTFE-lubricated specimens. By further increasing the clearance size to 0.9 mm, the temperature started to increase. For the dry running specimens, the bearing temperature decreased with the increase in clearance. The lowest mass loss was measured for 0.5 mm clearances, which proved to be optimal regarding the wear for all the specimens. Furthermore, with the increase of clearance size from 0.15 mm to 0.5 mm, mass loss in specimens working under 115 N load decreased, after which it rose at a clearance of 0.9 mm. The similar behaviour was observed in the friction coefficient. For loads of 65 N, highest wear was found in 0.25 mm clearances. It was also observed that, contrary to the higher load level, specimens working at 65 N load have multiple local minima, suggesting the need for including additional clearance size levels in the future studies. An Experimental Study of Composite Plain Bearings: The Influence of Clearance on Friction Coefficient and Temperature 99 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 15 N / dry x■' " i t , -x- -X 115 N / PTFE A---------- Ai' X << 65 N/dry ............................ .....O A 65 N / PTFE a , tet -■H'"' 0.07 0.12 0.17 0.22 0.27 Friction coefficient, ju Fig. 6. Relationship between the friction coefficient and bearing temperature (not sequenced by the clearance) Similarly to the friction coefficient and temperature, the higher load caused more intensive wear. The larger frictional force, caused by higher friction coefficient and normal load, resulted in more intensive bearing wear. Thus, it was expected that a mass loss will increase as the friction coefficient increases. However, the experimental results were not in agreement with the former statement; even though the increase in wear is expected as the load level rises [33], no consistency in mass loss depending on the load was found. The use of lubricant resulted in lower wear for all the clearances and load levels, as expected. The mass loss reduction was lower for the higher bearing load. When considering the surface roughness, even though the lowest average values were found in 0.5 mm clearance specimens, differences were rather modest. No bearing load impact was observed as the lowest change was recorded in the dry running specimens at 65 N load. 5 CONCLUSIONS The study of the influence of clearance on the friction coefficient and wear in composite plain bearings has been carried out. A total of 48 experimental measurements have been conducted. The performances of composite plain bearings manufactured with different clearances were observed under two levels of load and two different lubrication regimes; dry running and solid lubricant applied (PTFE). Not accounting for the manufacturing error, four different clearances were observed. The results have shown that the friction coefficient is affected by clearance. For the dry running specimens, the results have shown that 554 the friction coefficient reduces as the clearance size is increased. In PTFE-lubricated specimens, the optimum must be found, as the local friction coefficient minimum was found inside the observed clearance size interval. When considering the bearing temperature, in specimens tested under the 65 N loads, the linear relation between the friction coefficient and the bearing temperature was found. The relation between the temperature and friction coefficient was found only at the lower load level (65 N), while no general trends were observed for the wear and surface roughness change. Even though the study has shown that clearance affects the friction coefficient, temperature, and wear in dry running and PTFE-lubricated specimens, initial results point out that the further work is required to determine its optimal values. By decreasing the interval between the different clearance size levels, the optimal solution could be found. Increase of a number of clearance size levels could mitigate the possible saddle points found when observing wear. 6 ACKNOWLEDGEMENTS This paper reports on work funded by the Croatian Science Foundation project IP-2018-01-7269: Team Adaptability for Innovation-Oriented Product Development (TAIDE). 7 NOMENCLATURES b bearing width, [mm] Fm measured force, [N] Fw bearing load, [N] Ffr frictional force, [N] L distance between the load cell and shaft axis, [mm] Am plain bearing mass loss, [g] r inner bearing radius, [mm] ARa difference between the initial and final mean surface roughness, [^m] S clearance between the plain bearing and the shaft, [mm] T motor-provided torque, [Nm] vs sliding velocity, [m/s] 9 bearing temperature, [°C] H friction coefficient, [-] Miler, D., - Skec, S. - Katana, B. - Zezelj, D. Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 547-556 8 REFERENCES [1] Hirani, H., Suh, N.P. (2005). 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D0l:10.5545/sv-jme.2019.6194 Original Scientific Paper Received for review: 2019-06-13 Received revised form: 2019-08-26 Accepted for publication: 2019-09-10 Analysis of EDM Process Parameters on Inconel 718 Using the Grey-Taguchi and Topsis Methods Thangavel Yuvaraj* - Paramasivam Suresh Muthayammal Engineering College (Autonomous) Rasipuram, Department of Mechanical Engineering, India Nickel-based superalloys are gaining importance for their growing usage in aerospace industries. Amidst the various advanced machining processes, electro discharge machining (EDM) is considered to be an important one for its ability to machine materials irrespective of its intrinsic properties. In this study, Inconel 718 is considered as a work material, and an L18 orthogonal array (OA) experimental plan is utilized to machine the work material. The influential factors, which affect the EDM performance characteristics, are identified using analysis of variance (ANOVA). Not much work has been done regarding using grey-Taguchi technique for order of preference by similarity to ideal solution (TOPSIS) methods, although these methods can be easily applied for multi-objective optimization. These methods provide the best results with the available sparse data. The best combination of machining factors is determined using grey-Taguchi and TOPSIS methods. Based on the conducted experiments, voltage (V) and pulse off-time (toff) show a notable contribution on output performance. The optimal combination of input parameter through grey-Taguchi is found to be 10 A, 30 V 200 ys, and 20 ys respectively for the EDM parameters: current (I), V, pulse on-time (ton) and toff for improved response. Moreover, the best parameter setting (I = 10 A, V = 30 V, ton =100 ys and toff = 20 ys) is identified using the TOPSIS method for the performance measures machining rate (MR), tool wear rate (TWR), overcut (OC), and taper overcut (TOC). Further tool wear behaviour is also studied through scanning electron microscope (SEM) images by varying the voltage. Keywords: Inconel, ANOVA, grey-Taguchi, overcut, taper Highlights • EDM process parameters(voltage, current, pulse on- time and pulse off- time) were optimized through the L18 orthogonal experimental design method, and the grey relational analysis (GRA) method, considering multi-responses, such as machining rate (MR), tool wear rate (TWR), overcut (OC), and taper overcut (TOC). • The methods grey-Taguchi and TOPSIS were used to study the influential parameters that provide the best results with the available sparse data. • Based on GRA and TOPSIS, the optimum level parameters for EDM have been identified. Furthermore, the tool wear behaviour is also studied through SEM images by varying the voltage. • The optimal combination of the input parameter to acquire better responses based on grey-Taguchi has been found to be (10 A), V (30 V), ton (200 ys), and toff (20 ys). According to ANOVA, the voltage and toff plays a prominent role in machining Inconel 718. • The best combinations identified using the TOPSIS method for better performance measures is 10 A, 30 V, 100 ys and 20 ys. 0 INTRODUCTION Electro discharge machining (EDM) has a one-off significant process for the machining of hard materials and superalloys. Heat-resistant superalloys (HRSA), especially the Inconel alloy, find applications in aerospace and marine components, cryogenic storage tanks, and nuclear reactor components. Understanding the importance of the Inconel alloy, manufacturing scientists and engineers are attempting to understand the behaviour of it through EDM processes. In the machining of Inconel 718, Shen et al. [1] applied high-speed EDM with air as a dielectric medium and produced components with better surface quality. The importance of powder-mixed dielectric fluid in the EDM for machining Inconel alloy was analysed by Talla et al. [2]. The researchers revealed better results for surface quality and accuracy while using different powders, such as graphite, silicon, and aluminium [3] and [4]. Torres et al. [5] investigated the behaviour of an Inconel 600 alloy through EDM process. They studied the electrical parameters' influence and concluded that the change in polarity has a significant influence on surface quality.Tanjilul et al.[6] reported that a novel flushing method and a machining current significantly influences the debris removal. The size of the debris particles increases with increasing machining current. Rajesha et al. [7] studied the effect of process parameters such as current, duty cycle, sensitivity control, inter-electrode gap control, and flushing pressure on the material removal rate (MRR) and surface roughness (SR). They found that the pulse current and duty factor has the highest influence. Kuppan et al. [8] reported that the MRR and SR increase with the increase in peak current, duty factor, and electrode speed. *Corr. Author's Address: Department of Mechanical Engineering, Muthayammal Engineering College (Autonomous), Rasipuram, India,yuvarajt2019@gmail.com 557 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 557-564 Mohanty et al. [9] conducted an L9 orthogonal array (OA) and optimized the EDM process parameters of Inconel 825 using grey relational analysis (GRA). The parameters combination ( I (1A), ton (10 ^s), and duty cycle (75 %)) showed good results for the rate of material removed, surface quality, and radial overcut. Mohanty et al. [10] highlighted the importance of cryogenic treatment of tool in EDM on output performance using technique for order of preference by the similarity to ideal solution (TOPSIS) method and teaching-learning-based optimization algorithm. Dang [11] optimized the EDM parameters using a kriging model and particle swarm optimization method,finding that the model and method is suitable for the optimization of EDM process. Lin et al. [12] optimized and enhanced the EDM process parameters for Inconel 718 through multi-objective optimization technique using grey-Taguchi. Muthuramalingam and Mohan [13] machined SS 201 through EDM and established the importance of peak current. Lin et al. [14] conducted experiments on Ti-6Al-4V alloy through Micro-EDM and studied the influence of process parameters and gaps using the grey relational analysis (GRA)-Taguchi technique. The use of the GRA with Taguchi technique yields better results for tool electrode wear and overcut.Based on the above literature, the characteristics of EDM for machining holes on Inconel 718 are influenced by various input parameters. Each performance characteristic has different combinations of optimal process parameters and thus, in the case of multiple responses, the selections of optimal machining parameters are difficult. The grey system, proposed by Deng [15], handles the vague information and thus the GRA method is recommended as a principal method for multiple response optimisation. Therefore, researchers optimized the machining of Inconel 718 using electrical parameters and inter-electrode gap (IEG).In this paper, EDM process parameters: I, V, ton and tf were optimized through the L18 orthogonal experimental design method, and the GRA method considering multi-responses, such as machining rate (MR), tool wear rate (TWR), overcut (OC) and taper overcut (TOC). Not much work has been done using the grey-Taguchi and TOPSIS methods although these can be easily applied for multi-objective optimization. The significant contribution of this research is in using these methods to study the influential parameters that provide the best results with the available sparse data.Based on GRA and TOPSIS, the optimum level parameters for EDM have been identified. Furthermore, the tool wear behaviour is also studied through scanning electron microscope (SEM) images by varying the voltage. 1 EXPERIMENTAL The experimental set-up for EDM machining process is shown in Fig. 1. It consists of a maximum working voltage of 415 V, maximum current of 25 A, work table size of 600 mm x 400 mm, a maximum electrode length of 400 mm, and a servomotor for inter-electrode gap control. Inconel 718 has been selected as a workpiece material, whereas a brass electrode of 0 0.5 mm is used with EDM oil as the dielectric medium. Tables 1 and 2 provides the details of chemical and mechanical properties of Inconel 718 [16]. The thickness of workpiece is 3.1 mm. Since the discharge energy is primarily determined by current (I), voltage (V), pulse on-time (ton), and pulse off-time (tf), these factors are used as the input parameters. These parameters are selected based on the literature review, and levels are identified based the preliminary experiments;10 A, 12 A and 14 A have been considered as current variables; 30 V, 40 V and 50 V have been chosen as voltage variables;100 ^s, 150 ^s and 200 ^s have been chosen as ton values with tf values of 20 ^s, 30 ^s and 40 ^s. Table 3 shows the experimental layout using an L18 OA. MR is calculated by dividing the length of the through hole with the machining time required to complete the through hole. TWR is calculated using the relation mass is p x v, where p is brass density, v volume of brass tool (nr2h), h brass tool height. During the start and end of each Fig. 1. Experimental setup 558 Thangavel, Y. - Paramasivam, S. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 557-564 Table 1. Chemical composition of Inconel 718 (weight %) C Mn Si Cr Ni Co Mo Nb+Ta Ti Al Fe 0.040 0.08 0.08 18.37 53.37 0.23 3.04 5.34 0.98 0.50 17.80 experiment, the length of the brass tool is measured, and the difference is noted as h; this value is used to calculate the volume of brass electrode. The ratio of volume of electrode wear to the time taken to complete the experiment is called TWR. OC is calculated using optical microscopic images. OC is defined by AR=Re -Rt, where Re is the entrance radius of the machined hole and Rt the tool electrode radius.The difference in Re and Rt results in OC. TOC is defined by TOC=D - d/ (2L), where, D is entry diameter of the machined hole, d exit diameter of the machined hole, and L thickness of the workpiece. Table 2. Mechanical properties of Inconel 718 Hardness [HB] Yield limits [MPa] Tensile stress [MPa] 388 1 375 1170 2 RESULTS MR is the measure of machinability of the material. Hence, for a characteristic like MR, "larger-the-better" Table 3. L18 orthogonal array Range of factors Actual value of parameters Experiment No. No. A B C D I V ton D"S] toff D"s] MR [mm/min] TWR [g/min] OC [mm] TOC [mm] 1 1 1 1 1 0.019137 0.00261 0.2419 0.04839 2 1 2 2 2 0.042738 0.00466 0.1630 0.06966 3 1 3 3 3 0.065654 0.00205 0.1978 0.03706 4 2 1 1 2 0.056586 0.00351 0.1885 0.05388 5 2 2 2 3 0.049971 0.00410 0.1328 0.03871 6 2 3 3 1 0.062078 0.00317 0.1398 0.04179 7 3 1 2 1 0.090978 0.00905 0.1398 0.01508 8 3 2 3 2 0.051362 0.00366 0.1143 0.06070 9 3 3 1 3 0.072961 0.00675 0.0911 0.04752 10 1 1 3 3 0.044799 0.00371 0.1398 0.03871 11 1 2 1 1 0.039450 0.00436 0.1027 0.04284 12 1 3 2 2 0.032244 0.00559 0.1444 0.04806 13 2 1 2 3 0.081764 0.00526 0.1537 0.03786 14 2 2 3 1 0.050321 0.00456 0.1491 0.05987 15 2 3 1 2 0.043268 0.00399 0.1003 0.04493 16 3 1 3 2 0.070008 0.00488 0.1676 0.06497 17 3 2 1 3 0.062579 0.00699 0.1235 0.11196 18 3 3 2 1 0.081983 0.00456 0.1769 0.09516 is considered and the obtained MR data values are homogenized as shown below [14]: ... x-(i)-min x-(i) x* (i )=—iArr' (1) min Xj (i) - -in xj (i) where x* (i) are the homogenized MR after the preprocessing, is the signal-to-noise ratio of the MR, where i = 1 for MR; i = 1, 2, 3, ..., 18 for experiments 1 to 18. EDM performance is also measured using TWR, OC and TOC. Hence, to achieve better machining quality, the "smaller-the-better" is considered in view of minimizing TWR, OC, and TOC. Therefore the actual sequence must be normalized as follows [14]: , . . max x- (i)- x. (i) X (.) =-- • (.x' (2) max Xj (i)-mm xj (i) where x* (i), A0j (i), xj (i) are reference sequence, deviation sequence and comparability sequence, respectively. Ao j ()=K ()- xj ( )|. (3) Analysis of EDM Process Parameters on Inconel 718 Using the Grey-Taguchi and Topsis Methods 559 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 557-564 Similarly, other computation was carried out for 18 experiments and the values of all A0;- for j = 1, 2, 3, ..., 18 are represented in Table 4. In continuation of data preprocessing, a coefficient for grey relational analysis is found using the relation given below [14]: Table 4. Performance characteristics of the processed data Experiment Performance characteristics after data processing Deviation sequences run reference MR TWR OC TOC MR TWR OC TOC sequence [mm/min] [g/min] [mm] [mm] [mm/min] [g/min] [mm] [mm] 1 0.0000 0.9197 0.0000 0.6562 1.0000 0.0803 0.0000 0.3438 2 0.3285 0.6270 0.5231 0.4366 0.6715 0.3730 0.5231 0.5634 3 0.6475 1.0000 0.2924 0.7731 0.3525 0.0000 0.2924 0.2269 4 0.5213 0.7921 0.3539 0.5995 0.4787 0.2079 0.3539 0.4005 5 0.4292 0.7069 0.7231 0.7561 0.5708 0.2931 0.7231 0.2439 6 0.5977 0.8399 0.6769 0.7243 0.4023 0.1601 0.6769 0.2757 7 1.0000 0.0000 0.6769 1.0000 0.0000 1.0000 0.6769 0.0000 8 0.4486 0.7697 0.8462 0.5291 0.5514 0.2303 0.8462 0.4709 9 0.7492 0.3289 1.0000 0.6652 0.2508 0.6711 1.0000 0.3348 10 0.3572 0.7634 0.6769 0.7561 0.6428 0.2366 0.6769 0.2439 11 0.2827 0.6695 0.9231 0.7135 0.7173 0.3305 0.9231 0.2865 12 0.1824 0.4937 0.6462 0.6596 0.8176 0.5063 0.6462 0.3404 13 0.8718 0.5416 0.5846 0.7649 0.1282 0.4584 0.5846 0.2351 14 0.4341 0.6418 0.6154 0.5377 0.5659 0.3582 0.6154 0.4623 15 0.3359 0.7221 0.9385 0.6919 0.6641 0.2779 0.9385 0.3081 16 0.7081 0.5952 0.4923 0.4851 0.2919 0.4048 0.4923 0.5149 17 0.6047 0.2939 0.7846 0.0000 0.3953 0.7061 0.7846 1.0000 18 0.8748 0.6418 0.4308 0.1734 0.1252 0.3582 0.4308 0.8266 Table 5. Computed Grey relational grade Experiment No. GRC Grey relational grade (GRG) MR Zm TWR OC Zm MR Zm y= 1/4 • (Z(l) + Z(2) + Z(3) + Z(4)) 1 0.3333 0.8617 1.0000 0.5926 0.6969 2 0.4268 0.5727 0.4887 0.4702 0.4896 3 0.5865 1.0000 0.6310 0.6879 0.7263 4 0.5109 0.7063 0.5856 0.5552 0.5895 5 0.4669 0.6304 0.4088 0.6722 0.5446 6 0.5542 0.7574 0.4248 0.6446 0.5952 7 1.0000 0.3333 0.4248 1.0000 0.6895 8 0.4755 0.6847 0.3714 0.5150 0.5117 9 0.6660 0.4270 0.3333 0.5989 0.5063 10 0.4375 0.6788 0.4248 0.6722 0.5533 11 0.4108 0.6020 0.3514 0.6357 0.5000 12 0.3795 0.4969 0.4362 0.5949 0.4769 13 0.7959 0.5217 0.4610 0.6802 0.6147 14 0.4691 0.5826 0.4483 0.5196 0.5049 15 0.4295 0.6428 0.3476 0.6188 0.5097 16 0.6314 0.5526 0.5039 0.4927 0.5451 17 0.5585 0.4146 0.3892 0.3333 0.4239 18 0.7997 0.5826 0.5372 0.3769 0.5741 £ ( i) _ A min + Z ' Amax (4) ^ A0 ;(k ) + Z'Amax' where Z is a unique coefficient and Z is considered as 0.5 because all parameters are given equal weight. The grey relational grade (GRG) presented in Table 5 is calculated by averaging the GRC and overall 560 Thangavel, Y. - Paramasivam, S. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 557-564 assessment of the multiple objective optimization determined using Eq. (5). Yj = b £x (a)' (5) ° a=l where yj is the GRG of jth experiment and b is the number of performance characteristics. 3 DISCUSSION The multi-response performance index presented in Table 6 presents the average value of the GRG for every level. The highest value of GRG indicates the best possible level of the process parameters. The calculated higher GRG value indicates the closeness to the optimal value. The total mean of the GRG for the eighteen runs was estimated and is presented in Table 6. The optimal parameter combination for better MR and lesser TWR, OC and TO is found to be (AjBjCsDj) as given in Table 6. Table 6. Multi response performance index Symbol Level 1 Level 2 Level 3 Main effect (max-min) A 0.5738 0.5598 0.5418 0.0321 B 0.6148 0.4958 0.5648 0.1191 C 0.5377 0.5649 0.5728 0.0351 D 0.5934 0.5204 0.5615 0.0730 y, = = 0.5585 Moreover, Fisher's test (F test) is also performed to establish machining parameters' influence on the performance characteristic [17]. ANOVA for GRG is presented in Table 7. Based on the ANOVA, table voltage and pulse off-time show a higher percentage contribution, hence voltage and pulse off-time are dominant parameters that affect the MR, TWR, OC and TOC. In EDM, increase voltage increase the current required for machining which improves the ionization effect between the tool and electrode. This ionization effect increases the temperature of the tool and electrode, resulting in melting of workpiece material. The molten material resulted from heating is evaporated during pulse off time of the EDM process. Hence, the voltage and pulse off-time are considered as significant factors in EDM. Table 7. ANOVA table Factors DoF SS MSj F ratio

se=se + zKe> Yse = rSe + zKse, Ysz = rl, Yez = /1 £o _dU k o _0 +dW dx ds ds 0 1 {tt ■ dV sa =-1 Usina+ Wcosa + - ee (2) R( s) 0 1 {dU T/ . ) dV y e =-1--V sin a 1 + —, se R(s) [de ) ds 1 (a • dPe -1 Bs sina^-^ R(s) [ s de (3) K = - R(s)(i-BeSin«) + dBe, 1 ( dW R(s) ^ de V cosa 1 + Be- In which es, s0, ys0, ysz and y0z represent the strains of each point of the shell. Also, es0, yQse, y0z and Yez are the strains of the middle surface of shell and ks, k0 and ks0 are the curvatures of the middle surface of shell. In addition, R(s) is the curvature radius of each point on the conical shell and can be expressed as follows: R(s) = R + s sin a. (4) Below is the stress-strain relationship for the cross-ply joined composite conical shell [48] N M Qee Qss [A] [B]- [B] [D] = K 0 A (5) 576 Fig. 1. Coordinate systems of two joined conical shells Izadi, M.H. - Shahrokh, H.H. - Habibnejad Korayem, M. 0 z 44 0 Strajniski vestnik - Journal of Mechanical Engineering 65(2019)10, 1-584 where N and M are the force and moment resultants, which are expressed: moreover, N| r a/2 (a d M\~J-a/21 za Z' nl _ A =lXq»\ +i- zk )> k=1 1 nl _ Bj= 2 Hj (zk2+i- z2 )' 2 k=1 1 nl _ Dj=1 TiQij), ((i- zk 3 k=1 (6) (7) in which k represents the kth layer of laminated shell, and A{ coefficients. shell, and Ay, By and Dtj are the laminated stiffness Qii = Qucos4 9 + Q22 sin4 9, Q12 = Q12 (C0S4 9 + Sin4 9^ Q22 = Q11Sin4 9 + Q22C0S4 Q66 = Q66 (C0s4 9 + Sin4 9^ Q44 = Q44 COS2 9 + Q55 Sin2 9, Q55 = Q55 COS2 9 + Q44 Sin2 9, U12 = U21 Q = E1 E1 E2 , Ql1 Q = U12 E2 12 (8) 1 U12U21 1 U12U21 Ô22 =^ 1 U12U21 066 G12> Q44 G23' Q55 G13' where q> is the fiber angle of laminated shell. The principle of minimum potential energy shall be derived as follows: S(U -W s -W e ) = 0, (9) in which U is the strain energy^ Ws is the work of body and surface forces and We is the work of external loading. These parameters are presented as: ^ 22 SUJ = i i i (as5ss + aoSso + aseSYst _ L -h 2 2 +vj7sz +°ezSYez )Rdedsdz, (10) J L/2 _L/2 ' L/2 SW s = \\ 2(qSu + qgSv - qzSw) RdQds, lp fL/2 1 dw -, f f 1 W(—fRd0ds, JoJ-L/2 9 r)v where U is the in-plane compressive axial buckling force resultant. By integrating around the circumstances of one conical shell, the relation between the axial buckling load (Pcr) and U can be calculated as below: N = - 2nR cosa (11) By substituting the displacement field in strain-displacement and stress-strain relationships, the general form of equilibrium equations for each conical shell based on FSDT can be extracted in terms of U(s, 0), V(s, 0), W(s, 0), ps(s, 0) and p0(s, 0) as follows: [L ]{,V ,W, ps, pe]T =(4 (12) [L] is the matrix of the partial differential operators with partial derivatives with respect to s and 0, given in the Appendix. Additionally, using integration by parts, hereby, following is the extracted general form of boundary conditions: f {(( -N) + (MS -M) +(( -Ne)sv + (e - Me)e+( - Qss )8w\rde. (13) Upon this basis, various sets of boundary conditions were obtained from the above relationship, such as five boundary conditions at each end. Besides, at the interface of the two cones, displacements and forces would be equal; these continuity conditions ensure that all displacements and forces at the interface are equal; consequently, no distortion is possible at the interface (i.e., the connection is rigid). Due to the satisfaction of the continuity constraint at the interface of the cones, relationships should be considered equally for the two cones in general and common coordinates. In this regard, the relationships for displacements and forces are equal along the cone's axis and normal to cone's axis then related to each other. Accordingly, continuity conditions at interface of the two shells are as follows. U cosaj - W1 sinaj = U2 cosa2 - W2 sina2, Uj sinaj + W1 cosaj = U2 sina2 + W2 cosa2, Vj = V2, Psj = Ps 2, Pej = Pe2, Nsj cosaj - Qsj sinaj = Ns2 cosa2 - Qs2 sina2, Nsj sinaj + Qsjcosaj = Ns2sina2 + Qs2cosa2, (14) Nsej = Msj = Ms2 , Meej = Mse2. 2 Jo J-L/2 2 ds Lh Buckling of Joined Composite Conical Shells Using Shear Deformation Theory under Axial Compression 577 Strajniski vestnik - Journal of Mechanical Engineering 65(2019)10, 1-584 2 SOLUTION METHOD To solve the extracted equations, firstly, the Fourier expansions were performed along the circumferential direction as follows: U (s,O) = u (s )cos nO, V (s,O) = v (s )sin nO, W (s,O) = w (s )cos nO, (15) ps (s,O) = Js (s )cos nO, pO (s,O) = p~O(s )sin nO. Secondly, the solution of the problem along s-axis was considered in terms of a power series (PS): _ » _ » _ » u (s ) = ^ amsm, v (s ) = ^ bmsm, w(s ) = ^ cmsm, m=0 m=0 m=0 _ » _ » Ps (s ) = Z dmSm, Pe(s ) = £ emSm. (16) m=0 m=0 Now, by substituting the above-mentioned series into Eq. (12) and sorting similar powers regarding 5, one may end up with recursive relationships in terms of other coefficients. Using such relationships, one can obtain all constant coefficients in the series, except a0, a1, b0, b1, c0, c1, d0, d1, e0, e1 as well. Therefore, these 10 coefficients shall be derived by applying the boundary conditions and continuity constraints on the joined shells. The boundary conditions used in the present paper as the following forms: Clamped(C): u = v = w = = = 0, Simply-Supported(S): v = w = Pe = Ns = Ms = 0, (17) Free(F): Ns = Ms = Ns0 = Ms6 = Qs = 0. Evaluation of the above relationships for each conical shell under the boundary conditions and subject to the continuity conditions can be led to a system of 20 algebraic equations in terms of the coefficients of the series. By setting the determinant of coefficients matrix to zero, the value of critical buckling load for any given value of n can be extracted. For this purpose, 30 terms of power series have been used. 3 RESULTS AND DISCUSSION First, the dimensionless buckling parameters are presented in Table 1 for cross-ply cylindrical shells. If a1 and a2 are equal to zero, the conical shells change to cylinders. So, the buckling load of structure can be compared to the buckling load of cylinders in other researches. Hence, the results of the present study have been compared to Khdeir et al. [49] as well as Shadmehri et al. [43] studies. In Table 1, L/R = 1, h/R = 0.1, E1 /E2 = 40, w12 = 0.25, G23 = 0.5 E2 and G12 = G13 = 0.6 E2 have been assumed as the geometric and material properties of cylindrical shells. The present results are in good agreement with other research results. Table 1. Dimensionless critical buckling parameters (IV = NL2j(100 h3E2) )for cross-ply cylindrical shells BC Lamination sequences CST& Levy[49] FSDT& Levy [43] Present FSDT & Present study Single shell Single shell Joined Shells SS [0/90/0] 0.2765 0.2813 0.2763 [0/90] 0.1525 0.1670 0.1629 CC [0/90/0] 0.4168 0.4197 0.4145 [0/90] 0.2406 0.2508 0.2454 SC [0/90/0] 0.3411 0.3452 0.3409 [0/90] 0.1851 0.1969 0.1923 In continue, to come up with comparable results to other references, dimensionless buckling load is defined as follows: Pcr = PJP, cyto ' (18) where Pcr is critical buckling load, denotes dimensionless buckling load, and Pcylx is defined as follows [50]: 2nElh2 cos2 a p =. cylm V3 (-U122 ) (19) To undertake comparisons, the results of two joined cones at identical semi vertex-angles are compared to a single conical shell. Tong and Wang [51], Abediokchi et al. [52] and Sharghi et al. [53], using Donnell-type shell theory, present a procedure for buckling analysis of laminated conical shells. The composite considered in those researches is an asymmetrically cross-ply laminated shell made from carbon/epoxy. E2 = 10 GPa, u12 = 0.25, EJ E2 = 40, G12¡E2 = 0.5. (20) The obtained results in Table 2 are for a constant thickness ratio of shells (h/ R = 0.01) and different length of shells (L/ R), number of composite layers (Nl) and semi-vertex angles (a), which falls within the scope of thin shells. The results are extracted for simply-supported boundary conditions at both ends. The results show a good agreement between the present and other results. 578 Izadi, M.H. - Shahrokh, H.H. - Habibnejad Korayem, M. Strajniski vestnik - Journal of Mechanical Engineering 65(2019)10, 1-584 Table 2. Pcr for S-S anti-symmetric laminated cross-ply conical shells (h/R = 0.01, a = 45°) L /R Nl Tong and Wang [51] Sharghi et al. [53] Abediokchi et al. [52] Present study CST & PS CST & PS CST & GDQ FSDT & PS 2 0.1146(8) 0.1146(8) 0.1146(8) 0.1129(8) 0.2 4 0.2488(7) 0.2487(7) 0.2488(7) 0.2438(7) 6 0.2732(7) 0.2732(7) 0.2733(7) 0.2664(7) co 0.2927(7) 0.2927(7) 0.2927(7) 0.2857(7) 2 0.06751(6) 0.06735(6) 0.06734(6) 0.06581(6) 0.5 4 0.1054(6) 0.1054(6) 0.1053(6) 0.1033(6) 6 0.1117(5) 0.1117(5) 0.1117(5) 0.1079(5) co 0.1158(5) 0.1158(5) 0.1158(5) 0.1129(5) 2 0.06743(6) 0.06757(6) 0.06748(6) 0.06582(6) 1 4 0.1063(5) 0.1065(5) 0.1064(5) 0.1036(5) 6 0.1122(5) 0.1122(5) 0.1121(5) 0.1082(5) 00 0.1165(5) 0.1165(5) 0.1165(5) 0.1118(5) Table 3 demonstrates the results using FSDT by assuming identical thickness, length, and material for both cones. The non-dimensional critical buckling load of two joined cross-ply laminated conical shells is expressed for two orders of lamination sequences. As shown in Table 3, in all cases, the minimum values occurred when the lower shell is very similar to circular plate. The results illustrate that the order of lamination sequence is not very effective on the critical buckling load of joined asymmetrically cross-ply laminated shell. However, the use of [90, 0] lamination sequence obtains lower values than [0, 90]. Using the finite element (FE) and analytical methods, Table 3 presents the effects of the lamination stacking sequence on the critical buckling load of joined cross-ply laminated cones. The finite element modelling is implemented using the finite element method (FEM)-based software (ABAQUS/CAE). As an appropriate choice, a 4-nodes element with 24 degrees of freedom (DOFs) for each element (three rotational and three translational DOFs at each node) is used for FE analyses. This type of element reveals the effect of FSDT. Also, the effects of mesh refinement and mesh convergence on the FEM solution have been surveyed. The percentage differences shown in Table 4, expresses the difference between FEM and analytical solution results. The results indicate an acceptable amount of difference of approximately 1.2561% to 1.8484%. The effect of ordering of the layers on non-dimensional critical buckling load can be calculated with the following expression LSD = Prl9-] -P xl00 %, (21) Pcr[90] where LSD stands for lamination sequence differences. As is obvious from Table 4, the values of the axial buckling loads are minimum for the single-layer [0], whereas single layer [90] values are maximum. The impact of the lamination sequence on the critical axial load increases when the number of [90] layers grows, especially in outer layers. Fig. 2 investigates the influence of changes in a1 on dimensionless buckling load. Table 3. Non-dimensional buckling load (Pcr) for simply-supported laminated cross-ply conical shells (L/ R = 0.1, h/ R = 0.1) [0, 90] [90, 0] a1 a2 Nl 2 4 Sym. 2 4 Sym. 0 0.2697 0.3749 0.3109 0.2650 0.3714 0.4101 0 30 0.4030 1.0305 0.8455 0.3963 1.0217 1.1494 60 0.2863 0.6916 0.6527 0.2805 0.6801 0.7718 90 0.0049 0.0125 0.0167 0.0048 0.0124 0.0217 0 0.4355 1.0593 0.8523 0.4324 1.0502 1.1506 30 30 0.2522 0.3507 0.2952 0.2438 0.3435 0.3805 60 0.2673 0.6689 0.5763 0.2634 0.6643 0.7350 90 0.0048 0.0126 0.0170 0.0047 0.0125 0.0221 0 0.2970 0.6831 0.6163 0.2871 0.6757 0.7821 60 30 0.2715 0.6658 0.5410 0.2665 0.6519 0.7173 60 0.1216 0.1690 0.1456 0.1155 0.1651 0.1799 90 0.0047 0.0127 0.0171 0.0047 0.0126 0.0222 Buckling of Joined Composite Conical Shells Using Shear Deformation Theory under Axial Compression 579 Strajniski vestnik - Journal of Mechanical Engineering 65(2019)10, 1-584 Table 4. Effects of lamination sequences on Pcr for S-S cross-ply conical shells («j = 30° a2 = 75° NL = 4, L /R1 = 0.1, h / R1 = 0.1) Stacking sequences FEM Present study Difference [%] LSD [%] [0] 0.3491 0.3440 1.4609 83.594 [0/90/0] 0.3787 0.3717 1.8484 82.273 [0/0/90]S 0.4086 0.4022 1.5663 80.818 [0/90/0/90] 0.4427 0.4363 1.4457 79.192 [0/0/90/0] 0.6774 0.6689 1.2548 68.099 [0/0/90] 0.7482 0.7357 1.6707 64.913 [0/90/0]S 0.8290 0.8178 1.3510 60.998 [0/90/90]S 0.8859 0.8720 1.5690 58.413 [0/0/90/90] 0.9076 0.8962 1.2561 57.259 [0/90/90] 1.1197 1.1001 1.7505 47.534 [90/90/0] 1.1318 1.1138 1.5904 46.881 [90] 2.1319 2.0968 1.6464 - As can be seen, with increasing the a2 angle from negative values toward zero (cylindrical shell), the value of buckling load goes up, and given the short length of the shells, critical buckling load decreases abruptly as semi-vertex angles of the two shells get closer to one another. In other words, a sharp decrease in buckling load occurs when the semi-vertex angles come close together. If two joined conical shells have the same semi-vertex angles, one cone could be shaped with a longer length. Accordingly, the buckling of the longer cone under axial compression occurs sooner and critical buckling load decreases. Furthermore, the minimum buckling load varies with semi-vertex angles. Increasing the semi-vertex angles decreases the minimum buckling load. R -h/R=0.0l cr — — h/R=0.05 1 h/R=0.1 ■ i. 0.8 i h \ / / / ✓ \ \ / / fi.6 i \ \ \\ // ^^ // / .7 / .7 / 0.4 \ : -if. V: r U V V. \ V 0.2 \ // / -90 -60 -30 30 60 90 Fig. 3. Effect of changes in h / R1 ratio on buckling load (a1 = 30° Nl = 4, L /R1 = 0.1) Fig. 3 demonstrate the effect of changes in L /Rj ratio at different values of semi-vertex angle that considers a case where aj = 30°, L/Rx = 0.1, and the number of layers is four. Upon increasing the h /Rj ratio, the value of the dimensionless buckling load increases. In Fig. 4, the effects of variations in L/Rx on dimensionless buckling load have been shown. Fig. 2. Effect of changes in a1on buckling load (h /R1 = 0.1, NL = 4, L / R1 = 0.1) Fig. 4. Effect of changes in L /R1 ratio on buckling load a = 30° Nl = 4, L/R1 = 0.1J As mentioned before, in shorter shells, as semi-vertex angles of the two shells come closer to one another, a significant decrease occurs in buckling load; however, this rarely happens in longer shells. 580 Izadi, M.H. - Shahrokh, H.H. - Habibnejad Korayem, M. Strajniski vestnik - Journal of Mechanical Engineering 65(2019)10, 1-584 Fig. 5 presents the influence of changes in NL on a dimensionless buckling load. It is observed that the buckling load is very low in the case of being two layers. Due to the asymmetry of the shell at the low number of layers, it is rising by increasing the number of layers. Also, the minimum point changes by the number of layers and reaches to a2. As shown in Fig. 6, for a special case, dimensionless buckling load was calculated for different thicknesses using classical shell theory (CST) of Donnell type based on the solution approach proposed by Shakoori and Kouchazadeh [31], and the obtained results were compared to those of the present research where FSDT was implemented. it i 0.2 \J -90 -60 -30 0 30 60 90 Q2 Fig. 5. Effect of changes in NLon buckling load (h/ R1 = 0.1: a1 = 30° L /R1 = 0.1J As observed in Fig. 6, with increasing the thickness, the differences between classic theory and FSDT grow; i.e. the effects of shear force cannot be neglected, and the classic theory no longer provides acceptable results. The provoking point is that, in all cases, the results of FSDT are lower than those from the classic theory, and differences are presented even in the scope where the classic theory applies to thin shells (h /R1 < 0.05), although those can be neglected adequately. Fig. 7 presents the influence of boundary conditions on dimensionless buckling load. The value of dimensionless buckling load decreased as one moved from C-C, S-C, F-C and S-S to F-S state. The clamped condition at each end of shell raises the value of dimensionless buckling loads because of the increasing rigidity of the structure. 0.3-1-1-1-1-1-1-1-1-1— 0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 h/Rj Fig. 6. Comparison between the results of classic theory and FSDT at different thicknesses The results reveal that the value of Pcr in simply-supported conditions is slightly near to free conditions. In addition, it is necessary to explain that the critical buckling loads decrease abruptly when two joined conical shell have the same semi-vertex angles in all boundary conditions. -®~CC Per SC FC -90 -60 -30 0 30 60 90 Fig. 7. Effect of boundary conditions on buckling load (a1 = 30°, L / R1 = 0.1, h / R1 = 0.1) 4 CONCLUSIONS In this research, the buckling of two joined composite conical shells has been investigated using FSDT and CST, and the following general conclusions have been achieved. Effect of shear deformation is Buckling of Joined Composite Conical Shells Using Shear Deformation Theory under Axial Compression 581 Strajniski vestnik - Journal of Mechanical Engineering 65(2019)10, 1-584 negligible in thin shells. In thick shells; however, the results will be considerably different from real values in which shear deformation is ignored. In all cases, the results of FSDT are lower than those of classic theory, and differences are present even in the scope where the classic theory applies to thin shells (h/R < 0.05), though those can be neglected adequately. Therefore, the usage of classic shell theory is not suggested in thick shells. A sharp decrease in buckling load occurs where the semi-vertex angles come close together. In other words, in shorter shells, as semi-vertex angles of the two shells come closer to each other, buckling load decreases at a high rate. In conclusion, it is highly recommended to use two joined shells with appropriate semi-vertex angles instead of a single cone. In thin shells, the highest rigidity of the structure occurs at nearly identical semi-vertex angles. However, in thicker shells, the rigidity of shells from thickness is more effective than semi-vertex angle of the shells resulted from geometry. 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A„smacosa L =—^— d -- 22 R( s) R (s) r = (A22 + A44 )C0Sa d L32 = t>2,_\ °6' R (s) L33 ~ A55 . srna _ d.. +-d. R( s) A44 d A22 cos a R2(s) ee R2(s) 2nR(s)cosa R(s) , . 8,cosa L A„sina B„smacosa l34 = | 4s —^— Id---- R(s) R (s) l35 = - R(s) R (s) = Bud. + . - 11 ss R(s) s B-, sin a B R (s) R (s) cosa. A, sina cosa L„ = —-d s —-- R(s) R (s) L4=Bndss+s -^^+%de 14 11 ss R(s) s R (s) R2 e j (B12 + B33 ) d (B22 + B33 )sina d ¿15 ~ s0 n2, ■ ¿21 = R(s) (A12 + A R(s) R z(s) 33, ( + A33 )sina . 0.a +---r^-00 R (s) L22 = A33 sina . sin2 a d +--d---— ss R(s) s R (s) A., cos2 a A22 d ^ x44 V an R (s) R (s) L _ (A22 + A44 )cosa d L23 _ R2(s) e' r _(B12 + B33 ) d , (B22 + B33 )si L24 R(s) + R2(s) sina L25 _ B33 sina _ sin2 a d.. +-d -■ B,. R 2(s) R(s) s R2(s) cosa '+ R( s) ' r _(B12 + B33 ) d (B22 + B33 )s'n« d L42 _ 0sO „2, °° R( s) R 2(s) L _ 1 B12cosa B22 sina cosa L43 _- 1 rs R2(s) ' L = D d + Diisinad - D22 sin2 a + D33 g - A R(s) s R2(s) R2(s) 66 55' _(Di2 + D33) d (P22 + D33 )si sin a R (s) L _(B12 + B33 ) d , (B22 + B33 )Sina d L51 _ d s« + „2/ R (s) L52 _ B33 sm^ sin a d..+-d- R(s) s R2(s) B R (s) L53 _ ^44cosa R(s) A44 B22cosa R(s) R 2(s) 1 " j (D12 + D33 ) d , (D22 + D33 )sina d L54" R(s) dR2(s) de L55 = D33 sin^ sin a d +--d-- R(s) s R2(s) i D22 d - A R 2(s)dee A44' 45 e' 584 Izadi, M.H. - Shahrokh, H.H. - Habibnejad Korayem, M. Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 585-598 © 2019 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2019.6312 Original Scientific Paper Received for review: 2019-09-02 Received revised form: 2019-09-24 Accepted for publication: 2019-09-25 Study of Influential Parameters of the Sphere Indentation Used for the Control Function of Material Properties in Forming Operations Roman Satošek1 - Michal Valeš2 - Tomaž Pepelnjak1,* University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 2Czech Technical University in Prague, Faculty of Mechanical Engineering, Czech Republic The uncertainties of modern, adaptable sheet metal forming systems are classified into model errors and disturbances. To improve the control of production, disturbances in the forming process need to be reduced. For this purpose, a new data flow system was introduced. It connected the data flow of all influencing material parameters into the "material property control function". To control on-line the forming production line and acquire necessary material data, an indentation test was implemented. The main parameters to follow in this test are pile-up or sink-in values after the embossing of the ball-shaped tool into the material where the innovative approach of fully anisotropic material description was used. To set-up an optimal indentation test, parametric studies were performed with material data of AW 5754-H22. Finite element simulations were used to evaluate the influences of indenter diameter, contact friction and forming history of used the material. Fully anisotropic material behaviour was considered. Novel to this approach were a) the linking of the linear correlation of pile-up with the indentation depth described by gradient k, and b) the linking ofgradient k with different pre-strains by a new power function. Keywords: indentation test, anisotropy, on-line control system, forming process, parametric study Highlights • A new set-up of the control function influenced by the material properties, which is intended for the direct control of the sheet metal-forming production process via on-line indentation testing. • Influential parameters of indentation testing at different indentation depths shows following scientific innovations: • The pile-up effect is dominant when the spherical indenter is embossed into AW 5754-H22. • A linear relationship exists between pile-up and indentation depth at different indenter diameters, in which the pile-up value has a smaller gradient in the case of a bigger indenter diameter and vice versa. • If no elastic region exists under indentation, the observed relationship between indenter diameter and pile-up value is not linear. • The relationship between Coulomb friction coefficient p and pile-up value expresses larger values of the linear gradient at a smaller value of friction coefficient p. • A linear relationship exists between the pile-up and indentation depth at various values of normal anisotropy. Examining the cold roller anisotropic material, it was found that the pile-up at 8 = 45° has the nearest slope to the isotropic one while at 8 = 0° the slope is increased and, vice versa, at 8 = 90° it is lower as in the case of isotropic material.. • The most important contribution to the research of indentation is a novel definition of power function correlations among strain hardening, anisotropy and pile-up. 0 INTRODUCTION The autonomous operation of modern metal-forming processes is essential. An appropriate response of the flexible sheet metal forming lines can only be provided if the properties of the incoming material can be identified online. All deviations of the finished part from the design are coming from the uncertainties of the forming process. Allwood et al. [1] have described in an overview paper of this research field those uncertainties in metal forming processes and divided them into model errors and disturbances. According to this classification, the model errors include all process design errors (necessary forces, friction, etc.) while disturbances include all those uncertainties that are not included in model errors (variations in input material thickness, equipment vibration, temperature differences, differences in the material forming properties, etc.). One of the major goals in designing modern metal forming processes is to have the majority of all influential parameters described as model errors and to minimize the amount of disturbances. To follow major goals in designing the modern metal forming processes, we need to move uncertainties caused by the changes of metal forming properties from disturbance to model errors. This transition can be made with the implementation of the indentation test. A spherical indentation test is commonly used for determining the hardness of the material. However, with special approaches, we can also make evaluations with its constitutive properties, fracture toughness, *Corr. Author's Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, tomaz.pepelnjak@fs.uni-lj.si 585 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 585-598 residual stresses, and creep properties. The indentation test is classified as a non-destructive [2] or quasi-nondestructive [3] localized test that can be used for nonstandard specimens. Indentation test is a simple test but extracting the aforementioned properties from a specimen is far from easy. The biggest challenge is non-uniform strain beneath the indenter. This paper evaluates the constitutive properties of the material based on the indentation test. Such evaluations with similar methods have been done by several authors [4] to [17], and they have used the strain-hardening coefficient n based on the Hollomon hardening power law (Eq. (1)). = C - ^s = R + i-A°f. (7) (8) As mentioned, when defining material properties of the AW 5754-H22, the presented paper uses the Swift approximation power low due to better fitting of its material properties. Finally, no indentation test method considering the Swift hardening power law was found in the literature. The indentation test at different forming steps i was simulated using the Swift hardening law. Since at 300 250 200 Oh S150 tT 100 300 250 CTf45 200 fin Rv 150 ¿T 100 50 0 a) <7. „-.t^^ p-t-0-- Rp Pre-forming (sheet metal rolling) Forming (deep draw) • • Annealed —Pre-forming - - Forming 3 0.02 0.04 0.06 0.08 0.1 £e.p [/] b) „ _ i = 60 % ^flOO f m 9 * 70 % '' = 85 % Aof i = 45 "/ ; = 30»/ / = 15 % Virtual shift -^Initial -»- ¡ = 45 % 0.02 0.04 0.06 0.0 Se.p [/] 0.1 Fig. 12. Material property of- £e,p curve: a) production life cycle b) usage in FEsimulation Fig. 13. Material property history described with of- £ep curves compression loading significantly higher strains can be reached prior to material failure, as in the case of tensile loading, the maximal plastic strain of the initial material in all FE simulations of indentation test were set to £e,p,max = 1. The su versus h correlations at rolling direction (0 = 0°) obtained from FE simulations are presented in Fig. 14a. The maximum values of each obtained line correspond to the obtained value of selected maximal plastic strain. However, the factors Study of Influential Parameters of the Sphere Indentation Used for the Control Function of Material Properties in Forming Operations 595 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 585-598 i are connected to the percentage of pre-strain values presented in Fig. 14a for these pre-strain values, the maximal attainable plastic strain was decreased, as shown in Fig. 14a. It can be observed that the indenter depth depends on percentage i of the pre-strain, where at higher forming percentages i lower indentation depth h is reached. The present study shows that percentage of the pre-strain i increases the gradient of the linear correlation describing the su-h relationship (steeper slope). Fig. 14b is an example of the increased gradient of the su-h line due to the pre-strain difference between initial and i = 45 % pre-strained material. It is also evident that anisotropy does not influence the gradient increase if pile-up in different directions (8 = 0°, 8 = 45° and 8 = 90°) was observed (Fig. 14b). function. An entirely new correlation is introduced, as shown in the Eq. (9): o 0 0.05 0.1 0.15 h [mm] Fig. 14. Influence of strain history on ball Indentation test a) complete pre-strain range and b) only Initial and i = 45 % For each FE simulated set of data points at particular pre-strain, the linear trendline was approximated in order to obtain the parameters of linear correlation, and the gradient k was extracted. Fig. 15 presents the relationship between gradient k and pre-strain values. It is evident that the relationship k versus ee,p can also be described with a power k = a • (( +£ep) (9) where a is the constant of the introduced power function, f0 initial shift regarding the coordinate system and b the function's exponent. Particular parameters of the determined power function are shown in Table 5 for all three directions regarding the material rolling. The introduced function is valid for the AW 5754-H22 material and its generalization needs to be further analysed. However, this function can be introduced into the DFMCF system. Table 5. Power function parameters 8 [°] a [-] fo [-] b [-] 0 0.372 0.0214 0.186 45 0.339 0.0239 0.222 90 0.3 0.0211 0.242 Fig. 15. Relations between the k (gradient of the linear trendline) and true strain s. e,p 5 CONCLUSIONS The following conclusions can be stated from the presented study: a) To reduce disturbances (Allwood classification) in the sheet metal-forming process we, introduce the concept of DFMCF aimed for the feedforward controls of sheet metal production lines. This data flow has three groups of modules among which one is designated as knowledge build-up. The present study focuses on the FE simulation module as a part of knowledge build-up group. If we are following the material properties control function data flow for FE simulation, the material properties have to be experimentally acquired. In the presented work, the uniaxial tension test for 596 Satosek, R. - Vales, M. - Pepelnjak, T. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 585-598 aluminium alloy AW 5754-H22 was conducted and approximated with Swift hardening power law. b) The pile-up effect is influenced by indenter diameter D and corresponding indenter depth hp. The combination of indenter diameter D, indenter depth hp and material thickness 5 was analysed to select proper dimension D for experimental work, for which the existence of the elastic area under the indenter must be present. The relation between indenter depth hp and the value of the pile-up 5u have to be linear for quality measurements. The slope of the linear relationship 5u - hp depends on indenter diameter D its smaller value leads to a steeper line. In the case of the missing elastic area under the contact surface (e.g., when the material thickness 5 is too small), the relationship between indenter depth hp and pile-up value 5u becomes non-linear, and the gradient of the curve starts to decrease. Material AW 5754-H22 with a thickness of 5 = 3 mm and the indenter with diameter D = 1 mm were selected for experimental verification. c) Friction has significant influence on the pile-up effect, and it decreases the pile-up value 5u. Therefore, for the numerical simulations a proper friction coefficient needs to be inserted into the FE models. Comparative analyses among FE simulations of the indentation process and experimental work have shown good fit for friction coefficient of f = 0.2 being used for all consecutive numerical analyses. d) The anisotropic behaviour of material properties plays a significant role in pile-up mapping. In the case of anisotropic material, the pile-up values are directional dependent. Evaluating the relationship 5u - h, it was found that the pile-up at 6 = 45° has the nearest slope to the isotropic one while at 6 = 0° the slope is increased and, vice versa, at 6 = 90° it is lower as in the case of isotropic material. In the future research work, the indentation test will be integrated into the sheet metal forming process, and the relation between pile-up values and Lankford's r-values will be determined. e) The forming history can be recorded with the indentation test shown on the case of aluminium alloy AW 5754-H22. Various material pre-strains caused by cold rolling deliver steeper 5u - h lines, and the target true equivalent plastic strain ee,p is reached at smaller indentation depth h. f) An entirely new correlation of the slope of the linear relationship of 5u versus h as a function of pre-strain was introduced, leading the AW 5754- H22 material to the potential equation correlating the factors k, ee,p and new introduced parameters a, f0 and b. g) Further research work is oriented towards the design of an experiment to establish the connection between the knowledge build-up group and control function generator group and experimentally prove the presented on-line forming process feed-forward control function. 6 ACKNOWLEDGMENTS This paper is part of research work within the program Nr. P2-0248 entitled Innovative Production Systems financed by the Slovene Ministry of Education, Science and Sport. The authors are very grateful for the financial support. 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Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 599-608 © 2019 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2019.6112 Short Scientific Paper Received for review: 2019-04-22 Received revised form: 2019-07-08 Accepted for publication: 2019-08-13 Suppression of Self-Excited Vibrations in Rotating Machinery Utilizing Leaf Springs Chang Wang1 - Jun Liu12* - Zhiwei Luo3 1-rianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of Technology, China 2National Demonstration Centre for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, China 3Organization of Advanced Science and Technology, Kobe University, Japan When rotating machinery is operated above the major critical speed, self-excited vibrations appear due to internal friction of the shaft. Internal frictions are classified into hysteretic damping due to the friction in the shaft material and structural damping due to the dry friction between the shaft and the mounted elements. In this paper, a method to suppress the self-excited vibration using leaf springs are proposed. The structural damping is considered as the internal damping. The characteristics of a rotor with leaf springs are investigated systematically by using simulative and theoretical analyses. The validity of the proposed method is also proved by experiments. Keywords: self-excited vibration, internal damping, vibration suppression, leaf spring, experiment Highlights • A rotor system with internal frictions and leaf springs is analysed by using numerical simulations and theoretical analyses systematically, and self-excited vibrations occur above the major critical speed. • The self-excited vibrations can be suppressed by using leaf springs on the rotor system with internal frictions. • The effectiveness of the proposed suppressing method is verified by experiments, simulations, and theoretical analyses. 0 INTRODUCTION In rotor systems, the friction created between a rotational part and a stationary part, such as a rotating disk and the surrounding air, is called external friction, and another friction that works within two rotating parts is called internal friction. In addition, the internal friction is further classified into hysteretic damping, which works in the inside part of the shaft material, and structural damping, which occurs due to the sliding between the shaft and mounted elements such as bearings and gears. It is well known that the self-excited vibration occurs above the major critical speed when the internal friction works in the rotor system [1]. Regarding the self-excited vibration caused by internal friction, many scholars have conducted extensive research. Queiroz [2] studied flow-induced instabilities known as "whirl" and "whip" on the lightly-loaded shaft supported by fluid-film bearings and analysed self-excited vibrations. Bonello and Pham [3] presented a generic technique for the transient nonlinear dynamic analysis (TNDA) and the static equilibrium stability analysis (SESA) of a turbomachine running on foil air bearing (FABs). Their research revealed stabilities and self-excited vibrations of the rotor system. Boyaci et al. [4] carried out an investigation of the stability and bifurcation phenomena of the rotor-bearing system and found self-excited vibrations with very high amplitudes. Bykov and Tovstik [5] studied synchronous whirling and asynchronous self-excited vibrations on the statically imbalance rotor under action conditions of external and internal damping forces. Because the nonlinear characteristics of the internal friction are very complicated, obtaining succinct expression of the theory is very difficult. The mechanism of self-excited vibrations caused by the internal friction was understood [1] to [5]. Ishida and Yamamoto [6] investigated characteristics of the subharmonic resonance of the order of 1/2 on the rotor-bearing system with a nonlinear spring-restoring force and an internal damping force. The phenomena were understood that self-excited vibrations occurred under the forced autonomous system. In addition, many researchers studied self-excited vibrations due to other causes on the rotor system. Coudeyras et al. [7] presented a novel nonlinear method called the Constrained Harmonic Balance Method (CMBM), which is applied to solve the specific problem of disc brake squeal with extensive parameters and to predict self-excited vibrations. Han et al. focused on the experimental study for the dynamic characteristics of a permanent magnet (PM) disk-type motor rotor supported by an aerostatic gas bearing and analysed low-frequency vibrations caused by self-excited gas films [8]. Vlajic et al. [9] studied dynamic *Corr. Author's Address: Tianjin University of Technology, No. 391 Bin Shui Xi Dao Road, Tianjin, China, liujunjp@tjut.edu.cn 599 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 599-608 characteristics of a modified Jeffcott rotor with the torsional deformation and the rotor-stator contact and investigated self-excited backward whirling motions with the continuous stator contact. Hua et al. [10] presented the basic excitation mechanism and vibration characteristics on the coupled bending and torsional nonlinear dynamic model of a rotor system with a nonlinear friction, and the results revealed multiform complex nonlinear dynamic responses of the rotor system under rubbing. Nishimura et al. [11] explained self-excited vibrations in the vertical pump with a journal bearing and demonstrated the nonlinear steady-state vibration analysis of self-excited vibrations. Tadokoro et al. [12] focused on self-excited vibrations induced by the velocity-weakening friction in rotary contact systems. Chouchane and Amamou [13] analysed the bifurcation of the steady-state equilibrium point of the journal centre and predicted stable or unstable limit cycles from the equilibrium point at the major critical speed. Peletan et al. [14] proposed a quasi-periodic harmonic balance method (HBM) to deal with self-excited vibrations of the steady-state dynamic behaviour of rotor-stator contact problems. It is well known that harmonic resonances can be avoided by controlling rotational speeds. However, since the self-excited vibrations occur within a wide range of rotational speeds, it is difficult to escape the occurrence of self-excited vibrations. In addition, the amplitude of vibrations increases with exponential growth if there is no limit cycle. Based on the two characteristics mentioned above, it is concluded that self-excited vibrations are more dangerous than the harmonic resonance. Some methods of suppressing self-excited vibrations have been proposed. Kligerman et al. [15] investigated the nonlinear behaviour of shaft supports at the boundaries and stability of a rotating system with an electromagnetic noncontact damper, and a closed-form solution for the radius of the limit cycle and the frequency of self-excited vibrations are obtained. Inoue et al. [16] researched the occurrence region and vibration characteristics of self-excited vibrations caused by the ball balancer. The results are also validated experimentally. However, the theoretical analyses of self-excited vibrations have been less commonly proposed. In this paper, based on self-excited vibrations by causing the structural damping, a suppressing method by using leaf springs is proposed. The vibration characteristics of a rotor with leaf springs are systematically investigated using theoretical analyses and numerical simulations. The validity of proposed method is also verified by experiments. 1 THEORETICAL MODEL 1.1 Dynamic Equations The theoretical model of the rotor system with leaf springs is shown in Fig. 1. The two degrees of freedom (2DOF) inclination model with the gyroscopic moment is adopted, and a rigid disk is mounted at the centre of a massless elastic shaft. To suppress self-excited vibrations due to the internal damping, a bearing is fitted to the shaft, and four groups of leaf springs are placed to contact with the outer race of the bearing in four directions shown in Fig. 1. The rectangular coordinate system O-xyz is established, and the z-axis coincides with the bearing centreline. The point O is the geometrical centre of the disk. The line OA is the centreline of the disk, and the line OB is the tangent of the shaft at Point O. t is the angle between lines OA and OB, which represents the imbalance of the rotor system. 0 is the angle between lines Oz and OB, and it is the inclination angle of the shaft at the position of the disk. 0x and 0y are projections of 0 on planes xz and yz, respectively. It is assumed that the internal damping caused by the sliding between the disk and the shaft works in this system. In addition, the sliding here means that the inclined elastic rotor whirls with an angular velocity different from the rotational speed m, and the disk cannot move torsionally on the shaft. The dimensionless dynamic equations of the 2DOF rotor system can be obtained by reference to the study [1]. Considering effects of the internal damping and leaf springs, the dimensionless equations of motion of the rotor system are shown as follows: e + + cex+e+kLex - d - dLx = F cos at 9y - ipadx + c6y +ey + kLQy - Dy - DLy = F sin cat' , (1) where F = (l - ip )co2, c is the coefficient of the external damping, and ip is the ratio of the principal axis of the polar moment of inertia of the disk and the diametrical moment of inertia of the disk. Dix and Diy represent the internal damping force in x and y directions, and DLx and DLy represent the damping force of leaf springs in x and y directions. kL is the increase of spring stiffness of the rotor due to leaf springs. They will be illustrated later in this paper. 1.2 Internal Damping (Structural Damping) The pre-tightening force needs to be large enough to mount the disk on the shaft. When the deflection 600 Wang, C. - Liu, J. - Luo, Z. Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 599-608 of the shaft is comparatively large, the fibres of the shaft elongate or contract with the changes of the shaft orbit, which causes the pre-tightening force to be insufficient. Thus, the static friction cannot prevent the sliding between the shaft and the disk, and the type of friction has been transformed into dry friction. The dry friction, as internal friction, will cause structural damping. In addition, a large deflection of the shaft means that there is hysteretic internal damping due to frictions in the shaft material. In order to discuss influences of the structural damping on self-excited vibrations, it is necessary to eliminate the effects of the hysteretic internal damping caused by the deflection motion, which is the reason that the 2DOF model with an inclination motion is adopted. Here, the Coulomb friction is applied to approximate the dry friction between the shaft and the disk. The internal damping force is determined by the difference in the whirling angular velocity and rotational speed. Fig. 1. Rotor model with leaf springs and coordinate system Therefore, the internal damping force is discussed in the rotational coordinate system O- d'xd'y shown in Fig. 1. For simplicity of representation, complex variables z=6x + i6y in the coordinate system O- 0x0y and z'=0'x + i0'y in the coordinate system O-d'xd'y are introduced. Based on the previous studies [1], the expression of the internal damping force in the rotational coordinate system O-d'xd'y is obtained as follows: The expression of the internal damping force is converted to the expression in the stationary coordinate system O-0x0y as follows: , t œ + mdv ) + i(dv -mdr ) D, = D'em' = -h—-y-—^-— D = -h px +œdy )2 + (dy -wOx )2 œ+®Qy ) (3) Diy =-h- pz +mdy)2 + (dy -mdx)2 ^ (0y -m Px) ex+m ey )2+(ey -m ex )2 where h is a constant coefficient. 1.3 Damping Force and Elastic Force of the Leaf Spring The damping force and elastic force of leaf springs work on the elastic shaft by the contact between the bearing and leaf springs shown in Fig. 1. Under the condition with effects of the elastic force of leaf springs, the spring stiffness of the rotor system becomes larger. It is considered that the change of the spring stiffness is linear, and the increase of the restoring force of the rotor system are as follows: FLx =-kLt FLy =-k£ (4) The leaf springs periodically deform with the motion of the rotor system. The dry friction of leaf springs is not negligible in the system. The restoring force has a hysteresis characteristic due to the dry friction, as shown in Fig. 2. The damping forces of leaf springs can be approximately described as follows: 9, D, -K ¡|. D„ ft. (5) where hL is a function of the magnitude of a relative velocity |$x| or |$y . This damping force increases with the increase of the preload between leaves, and the viscous damping force increases in proportion to the velocity of the movement. Here, the dry friction is also approximated by the Coulomb friction. With the above approximation, hL is considered as a constant coefficient, and coulomb damping force is independent of the velocity. 1.4 Natural Frequency Equation and Major Critical Speed D' = DX + iD[, =-hf~;. (2) With regard to leaf springs, the natural frequency equation of the rotor system is obtained as follows: Suppression of Self-Excited Vibrations in Rotating Machinery Utilizing Leaf Springs 601 Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, 599-608 (1 + h) + ipmp - p2 = 0. (6) Fig. 2. Hysteretic characteristic of leaf springs The relationship between natural frequencies and the rotational speed is obtained by solving Eq. (6), and the results are shown in Fig. 3. There are two natural frequencies pf < 0 and pb > 0 shown in Fig. 3. The pf is a natural frequency of a forward whirling mode and pb is that of a backward whirling mode. In addition, the major critical speed can be expressed as follows: = (1+h) (i - iP)' (7) 2- o, >> o § 1 CT" 3 "3 2 -1 - -2 S ' Pf^^ V CO Pb i = 0.3 k, = 0.25 P L- 012345678 Rotating speed w Fig. 3. Natural frequency of the 2 DOF system 2 THEORETICAL ANALYSIS WITHOUT IMBALANCE In this chapter, the theoretical analysis is executed under the case without an imbalance (t = 0). Because self-excited vibrations occur above the major critical speed, the following analyses will set the case of m > mc. In addition, because the self-excited vibration does not appear under the case of m < mc, the solutions with zero-amplitude are stable. 2.1 Theoretical Analysis When the imbalance is not considered, and the rotational speed considers the case of m > mc, solutions for self-excited vibrations are as follows: (8) \QZ = R cos( pft + 5) = Rsin(pft + 5)' Substitute solutions Eq. (8) into the equations of motion, and represent the order of magnitude by the notation O(e) in this following. Based on the assumption that the amplitude R and the phase angle 8 change slowly, the cos(pyt + 8) and sin(pft+8) will be compared with the accuracy of O(e2) to obtain their coefficients. The internal damping force can be expanded as follows: r R cos( pft + 5) ^ D = -h R(m- pf) - RS + O(s2) R(pf +S)sin( pft + S) - R(a-pf) - RS + O(s2) a>R sin( p ft + S) + O(s2) +-f-=-1- R(a- pf) - RS + O(s ) , I . . _. R cos(pft + S) ■--h nh/4. The results of the above analyses show that leaf springs can effectively suppress self-excited vibrations in the wide rotational speed range. 3 THEORETICAL ANALYSIS WITH IMBALANCE Due to the existence of internal damping terms, the multi-scale perturbation method and the harmonic balance method, it is difficult to theoretically analyse the vibration characteristics of the rotor system. In this paper, the improved shooting method is used to solve approximate solutions of the harmonic component. 3.1 Theoretical Analysis Firstly, we reduce the order of Eq. (1). Putting Ae =6z, Ae =6y, Eq. (17) with four variables can be obtained as follows: f (, Aflx ,9y, Agy ) f ((, A9,9y, A9y ) /3 (, A9 9, A9y ) f ((, A9,9y, A9y ) A F cos ©t - ip a>A9y - c A9x - (1 + kL 9 + Dx + DLx A9y yx Fsinœt + ip œA9x - c A9 - (1 + kL)9y + Dy + DLy , (17) y 9 Suppression of Self-Excited Vibrations in Rotating Machinery Utilizing Leaf Springs 603 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 599-608 where D.x = -h Dy =-h \ +®6y )2 +( ~a0x ) DLx =-hL] \ +m0y )2 +(( ~m0x )2 and DLy = -hL | The components of the harmonic vibration are the main interest in the theoretical analyses, and it is considered that vibration components of constant terms are small. Therefore, we can assume the solutions to be as follows: fa = P»x C0s (mt + % ) \ = PAto sin ( + % ) | °y = Pey Sin (mt + % ) \ = PA9 C0S (mt + % ) (18) Substituting the solution Eq. (18) into Eq. (17), we make rat=2nn (n represents the number of cycles in the system response) to eliminate time parameters in the system. Nonlinear equations of five variables can be obtained as follows: -Pexosin (Pi ) \ocos (Pi ) P0y° C0S (Pi ) ®Sin (Pi ) \ Sin (Pi ) F - ip mPAg cos (cot + pi )-cPhg sin (cot + pi ) - (1 + kL ) pez cos ( + Pi ) + D + D'Lx Py C0S (Pi ) ip Sin (0t + Pi ) - C PA9y C0S (0t + Pi ) - (i + kL )pey sin o + Pi ) + D'y + DLy (19) Therefore, the optimal numerical solution of each parameter in Eq. (19) can be solved by using the genetic algorithm. 3.2 Stability Analysis of the Solution This paper applies the first Lyapunov method for the stability of approximate solutions. According to Eq. (17), the Jacobian matrix A can be obtained as follows: A = df df d\ d0y ÔAo df2 f 3/2 dA0 d0y ÔAo f f f f d0x d0y dAe df4 f f dAo d0y DAe (20) Substituting theoretical solutions into matrix A to obtain the coefficient matrix, the characteristic equation of the rotor system can be obtained as follows: = 0. (21) The stability of theoretical solutions can be investigated by judging the positive and negative of the real part of the eigenvalue A,. If all the real parts of eigenvalues are negative, the solution is stable. If there is at least one positive real part and others are negative, the solution is unsteady. 2.0 all — X «12 «13 «14 «21 «22 — X «23 «24 a31 «32 «33 — X «34 «41 «42 «43 «44 — X z-planes parameters in rotational coordinate system parameters in rotational coordinate system ratio of the principal axis of the polar moment of inertia of the disk and the diametrical moment of inertia of the disk damping coefficient internal damping forces damping forces of the leaf spring increase of the spring stiffness amplitude of the excitation initial phase angle of the excitation time rotational speed, [rpm] major critical speed, [rpm] inclined angle of the rotor (imbalance) constant coefficients of the internal damping force natural frequencies of the rotor system amplitude of vibrations of the rotor system, [mm] amplitude of vibrations in x and y directions first derivative term of amplitude of vibrations in x and y directions phase angle of vibrations of the rotor system orders in magnitude of parameters small variations of O(e) variation in the complex field eigenvalue of the characteristic equation of the rotor system p c Suppression of Self-Excited Vibrations in Rotating Machinery Utilizing Leaf Springs 607 Strojniski vestnik - Journal of Mechanical Engineering 65(2019)10, 599-608 9 REFERENCES [1] Yamamoto, T., Ishida, Y. 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Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10 Vsebina Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 65, (2019), številka 10 Ljubljana, oktober 2019 ISSN 0039-2480 Izhaja mesečno Razširjeni povzetki (extended abstracts) David Muženič, Jaka Dugar, Davorin Kramar, Matija Jezeršek, Franci Pušavec: Izboljšanje obdelovalnosti keramike na osnovi cinkovega oksida s frezanjem z lasersko asistenco SI 67 Daniel Miler, Stanko Škec, Branko Katana, Dragan Žeželj: Eksperimentalna študija kompozitnih drsnih ležajev: vpliv zračnosti na količnik trenja in temperaturo SI 68 Thangavel Yuvaraj, Paramasivam Suresh: Analiza parametrov procesa elektroerozijske obdelave Inconela 718 po metodah Grey-Taguchi in Topsis SI 69 Fariha Mukhtar, Faisal Qayyum, Hassan Elahi, Masood Shah: Numerična simulacija vpliva toplotnega utrujanja na napredovanje razpok v tanki gredni prirobnici iz jekla SS316L SI 70 Mohammad Hadi Izadi, Shahrokh Hosseini Hashemi, Moharam Habibnejad Korayem: Uklon spojenih kompozitnih koničnih lupin pod aksialnimi tlačnimi obremenitvami po teoriji strižnih deformacij SI 71 Roman Satošek, Michal Valeš, Tomaž Pepelnjak: Študija vplivnih parametrov vtiskovanja krogle za opredelitev nadzorne funkcije lastnosti materiala pri preoblikovalnih operacijah SI 72 Chang Wang, Jun Liu, Zhiwei Luo: Omejevanje samovzbujenih vibracij pri rotacijskih strojih z listnatimi vzmetmi SI 73 Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, SI 67 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-05-09 Prejeto popravljeno: 2019-07-17 Odobreno za objavo: 2019-08-13 Izboljšanje obdelovalnosti keramike na osnovi cinkovega oksida s frezanjem z lasersko asistenco David Muženič* - Jaka Dugar - Davorin Kramar - Matija Jezeršek - Franci Pušavec Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija Keramika na osnovi cinkovega oksida (ZnO) je elektronska keramika, ki se večinoma uporablja pri komponentah za zaščito pred impulzi zelo visoke napetosti (nekaj 100 kV). Za doseg pravilnega delovanja takšnih komponent je ena ključnih zahtev oster rob, ki nastane po končni obdelavi sintranega surovca. Zaradi same sestave te keramike, je le-ta izredno krhka, kar posledično privede do krušenja robov izdelka med končno obdelavo. Trenutno stanje tehnike pri končni obdelavi izdelkov iz ZnO keramike je postopek lepanja. Hitrosti odnašanja materiala so pri postopku lepanja veliko manjše, kot pri postopkih odrezavanja (struženje, frezanje), kar privede do visokih proizvodnih stroškov takih komponent. Uspešna uvedba npr. frezanja v proizvodni proces komponent iz ZnO keramike bi tako privedla do občutnega znižanja proizvodnih stroškov takih komponent. Kot je bilo ugotovljeno v predhodnih študijah avtorjev tega prispevka na frezanju ZnO keramike, je krušenje robov glavni faktor, ki znižuje obdelovalnost tega materiala in konvencionalen proces frezanja ni primeren za končno obdelavo izdelkov iz ZnO keramike. Z namenom izboljšanja obdelovalnosti tega materiala je bila v konvencionalni proces frezanja uvedena laserska asistenca (angl. Laser-Assisted Milling - LAMill), pri čemer se z uporabo laserja material obdelovanca pred rezalno cono segreje in s tem zmehča. Za določitev vpliva laserske asistence na proces frezanja, je bila izvedena serija eksperimentov konvencionalnega frezanja ter frezanja z lasersko asistenco, pri katerih so bile uporabljene različne moči laserskega žarka. Rezultati so pokazali, da laserska asistenca lahko izboljša obdelovalnost ZnO keramike preko zmanjšanja krušenja robov ter izboljšanja hrapavosti obdelane površine. Za uporabljene parametre frezanja (globina in širina frezanja ap = 0,1 mm in ae = 0,33 mm ter podajalna in rezalna hitrost vf = 250 mm/min in vc = 78,5 m/min) je bilo ugotovljeno, da obstaja optimalna moč laserskega žarka, pri kateri je izboljšanje obdelovalnosti največje. Pri optimalni moči laserskega žarka 120 W je bilo zmanjšanje parametrov hrapavosti obdelane površine Ra in Rz 37 % ter 46 %. Pri tej moči je bilo doseženo tudi 15 % zmanjšanje povprečne ter 17 % zmanjšanje največje širine odkruškov na robu, nastalem med obdelavo. Pri večjih močeh laserskega žarka je bilo doseženo dodatno zmanjšanje odkruškov, vendar so se pri teh močeh laserskega žarka na obdelani površini pojavile razpoke, za katere avtorji sklepajo, da so posledica termičnega šoka. Čeprav je inovativni pristop k obdelavi ZnO keramike s frezanjem z lasersko asistenco, predstavljen v tem članku, pokazal potencial za izboljšanje obdelovalnosti tega materiala, je potrebno še veliko raziskav, da bi povsem razumeli vpliv laserske asistence na obdelovalnost tega materiala ter bi lahko tak postopek uvedli v proizvodni proces elektronskih komponent. Krušenje robov, nastalih pri končni obdelavi takih komponent je glavni faktor, ki znižuje obdelovalnost tega materiala in aplikacija laserske asistence v postopek frezanja je omejena s termičnim šokom, ki ga hitro ogrevanje z laserskim žarkom povzroči v materialu obdelovanca. Naslednji korak, nujen za razumevanje tega procesa je torej formacija modela prenosa toplote, s katerim se lahko zanesljivo napove temperatura blizu robov obdelovanca, kot posledica segrevanja z laserjem. Poleg tega je za obvladovanje tega procesa potrebno raziskati mehanizme, ki povzročijo povečanje obdelovalnosti tega materiala pri povišanih temperaturah. Ključne besede: keramika na bazi cinkovega oksida (ZnO), obdelovalnost, frezanje z lasersko asistenco, hrapavost obdelane površine, krušenje robov *Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva cesta 6, Ljubljana, Slovenija, david.muzenic@fs.uni-lj.si SI 67 Strojniški vestnik - Journal of Mechanlcal Englneerlng 65(2019)10, SI 68 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-04-18 Prejeto popravljeno: 2019-08-10 Odobreno za objavo: 2019-08-21 Eksperimentalna študija kompozitnih drsnih ležajev: vpliv zračnosti na količnik trenja in temperaturo Daniel Miler1 - Stanko Škec12* - Branko Katana1 - Dragan Žeželj1 1 Univerza v Zagrebu, Fakulteta za strojništvo in ladjedelništvo, Hrvaška 2 Danska tehniška univerza, Danska Drsni ležaji so se uveljavili zaradi svoje kompaktnosti in cenovne dostopnosti. Ti ležaji ne potrebujejo dodatnih kotalnih elementov in imajo zato manjši zunanji premer, velika kontaktna površina pa izboljšuje njihovo nosilnost. Na torne in obrabne lastnosti drsnih ležajev vpliva več parametrov, med drugim obremenitev, drsna hitrost, temperatura in površinska hrapavost. Pri pregledu literature niso bile odkrite študije, ki bi opisovale vpliv zračnosti na trenje v drsnih ležajih. Zato je bila opravljena eksperimentalna študija s ciljem določitve vpliva zračnosti na količnik trenja, temperaturo, obrabo in površinsko hrapavost pri drsnih ležajih. Eksperiment je bil zasnovan kot faktorski poskus z dvema ravnema obremenitev (65 N in 115 N), dvema vrstama mazanja (suho, s PTFE) in štirimi vrednostmi zračnosti (0,15 mm, 0,25 mm, 0,5 mm in 0,9 mm). Vsaka serija eksperimentov je bila ponovljena dvakrat zaradi zagotavljanja zanesljivosti rezultatov. Skupaj je bilo opravljenih 48 serij, vsaka pa je trajala dve uri. Ležaji so bili izdelani iz kompozita NORDEN Maritim 605. Vsi ležaji so bili enake širine in nazivnega premera, razlikovali pa so se v zračnosti. Količnik trenja je bil izračunan iz velikosti sil na preizkuševališču, izmerjenih z merilno celico. Žarek termometra je bil usmerjen na drsni ležaj v bližini točke stika. Obraba je bila določena s tehtanjem preizkušancev pred eksperimentom in po njem, na enak način pa je bila izmerjena tudi površinska hrapavost. Rezultati so pokazali, da zračnost vpliva na trenje tako v ležajih brez mazanja kot v ležajih, podmazanih s trdnim mazivom (PTFE). Pri ležajih brez mazanja se je količnik trenja zmanjševal s povečevanjem zračnosti. Pri ležajih, mazanih s PTFE, je treba poiskati optimum, saj je bil ugotovljen lokalni minimum količnika trenja znotraj opazovanega intervala zračnosti. Pri obravnavi temperature ležajev, obremenjenih s silo 65 N, je bila ugotovljena linearna odvisnost med količnikom trenja in temperaturo ležaja. Splošno veljavni trendi za obrabo in spremembo površinske hrapavosti niso bili ugotovljeni. Čeprav je študija pokazala, da zračnost vpliva na količnik trenja, temperaturo in obrabo ležajev brez mazanja in ležajev, mazanih s PTFE, so prvi rezultati pokazali, da bodo za določitev optimalnih vrednosti potrebne še dodatne raziskave. S povečanjem števila ravni zračnosti bi se tako bilo mogoče izogniti morebitnim sedlastim točkam pri ugotavljanju obrabe. Za izboljšanje kakovosti rezultatov bi bilo mogoče med spremenljivke poleg zračnosti dodati še nazivni premer ležajev. Članek je prispevek k boljšemu razumevanju vpliva zračnosti na lastnosti drsnih ležajev. Množina zbranih podatkov bo lahko dobra osnova za nadaljnje študije in za pridobivanje novih zaključkov. Ključne besede: drsni ležaj, zračnost, kompozit, količnik trenja, mazanje, eksperimentalna študija SI 68 *Naslov avtorja za dopisovanje: Univerza v Zagrebu, Fakulteta za strojništvo in ladjedelništvo, Ivana Lučica 5, 10002 Zagreb, Hrvaška, stanko.skec@fsb.hr Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, SI 69 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-06-13 Prejeto popravljeno: 2019-08-26 Odobreno za objavo: 2019-09-10 Analiza parametrov procesa elektroerozijske obdelave Inconela 718 po metodah Grey-Taguchi in Topsis Thangavel Yuvaraj* - Paramasivam Suresh Tehniški kolidž Muthayammal (avtonomni), Oddelek za strojništvo, Indija Elektroerozijska obdelava (EDM) je postopek posebnega pomena za obdelavo trdih materialov in superzlitin. Toplotno obstojne superzlitine (HRSA) in še posebej Inconel so razširjene v letalski in vesoljski industriji, v pomorstvu, kriogenih skladiščnih rezervoarjih in jedrskih reaktorjih. Pregled literature je pokazal, da na elektroerozijsko obdelavo lukenj v Inconelu 718 vplivajo različni vhodni parametri. Za doseganje optimalnih rezultatov za vsak posamezni parameter obdelave so potrebni različni parametri procesa, izbira optimalnih parametrov obdelave pa je zato težavna naloga. Sistem Grey, ki ga je predlagal Deng, omogoča večciljno optimizacijo po metodi GRA. V članku je predstavljena optimizacija parametrov procesa EDM I, V, ton in tojj z ortogonalno zasnovo eksperimenta L18 in metodo GRA z več odzivi, kot so stopnja odvzema materiala (MR), stopnja obrabe orodja (TWR), nadmera (OC) in konična nadmera (TOC). Čeprav sta metodi Grey-Taguchi in TOPSIS primerni za večciljno optimizacijo, do sedaj še nista bili uporabljeni na tem področju. Pomemben prispevek te raziskave je v uporabi metod za preučevanje vplivnih parametrov, ki dajejo najboljše rezultate z razpoložljivimi podatki. Določene so bile optimalne vrednosti parametrov EDM po metodah GRA in TOPSIS. Obraba orodja pri različnih napetostih je bila preiskana z vrstično elektronsko mikroskopijo (SEM). Uporabljena je bila medeninasta elektroda 0 0,5 mm in olje za EDM kot dielektrik. Debelina obdelovanca je bila 3,1 mm. Parametri so bili izbrani na osnovi pregleda literature in vrednosti so bile določene na osnovi preliminarnih eksperimentov. Uporabljene so bile vrednosti toka 10 A, 12 A in 14 A ter vrednosti napetosti 30 V, 40 V in 50 V. Vrednosti ton so bile 100 ^s, 150 ^s in 200 ^s, vrednosti toff pa 20 ^s, 30 ^s in 40 ^s. Oblikovana je bila zasnova eksperimenta L18 OA. Optimalna kombinacija vhodnih parametrov za boljši odziv po metodi Grey Taguchi je bila I = 10 A, V = 30 V, ton = 200 ^s in tojj = 20 ^s. Analiza variance je pokazala, da imata poglavitno vlogo pri obdelavi Inconela 718 napetost in čas toff. Potrditveni preizkusi so pokazali znatno izboljšavo vrednosti GRA pri optimalni kombinaciji parametrov, z 0,6969 na 0,7122. Potrditveni preizkus je dokazal, da je metoda GRA primerna za optimizacijo parametrov procesov EDM v proizvodni industriji in s tem za izboljšanje konkurenčnosti. Najboljša kombinacija za izboljšanje zmogljivosti po metodi TOPSIS je bila 10 A, 30 V, 100 ^s in 20 ^s. Obraba orodja pri različnih napetostih je bila preiskana z vrstično elektronsko mikroskopijo. Mikroposnetki SEM potrjujejo odvisnost vzorcev obrabe od napetosti. V prihodnje bo tako mogoče opraviti podrobnejše analize in optimizacijo električnih parametrov. Pomemben prispevek raziskave je v uporabi metod za preučevanje vplivnih parametrov, ki dajejo najboljše rezultate z razpoložljivimi podatki. Z metodama GRA in TOPSIS so bile tako določene optimalne vrednosti parametrov za EDM. Ključne besede: Inconel, ANOVA, Grey-Taguchi, nadmera, konus, TOPSIS *Naslov avtorja za dopisovanje: Tehniški kolidž Muthayammal (avtonomni), Oddelek za strojništvo, 637408 Rasipuram, Indija, yuvarajt2019@gmail.com SI 69 Strojniški vestnik - Journal of Mechanlcal Englneerlng 65(2019)10, SI 68 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-04-18 Prejeto popravljeno: 2019-08-10 Odobreno za objavo: 2019-08-21 Numerična simulacija vpliva toplotnega utrujanja na napredovanje razpok v tanki gredni prirobnici iz jekla SS316L Fariha Mukhtar1 - Faisal Qayyum2 - Hassan Elahi3* - Masood Shah1 1 Tehniška univerza, Oddelek za strojništvo, Pakistan 2 Tehniška univerza Bergakademie Freiberg, Inštitut za preoblikovanje kovin, Nemčija 3 Univerza v Rimu Sapienza, Oddelek za strojništvo in letalsko tehniko, Italija Tudi po več kot desetletju raziskovanja pojava razpok v komponentah jedrskih reaktorjev zaradi toplotnega utrujanja še vedno obstajajo vrzeli v znanju. Obstaja potreba po znanju o napredovanju razpok in vplivih razpok na utrujenostno trajnostno dobo jeklenih komponent zaradi intenzivnega toplotnega utrujanja. Raziskovalci so se v preteklosti ukvarjali z eksperimentalnimi preiskavami, ki zaradi omejitev pri zbiranju podatkov zagotavljajo le omejeno razumevanje. Raziskovalna tema je bil tudi razvoj analitičnih in numeričnih metod z različnimi aproksimacijami, ki ne dajejo zanesljivih rezultatov. Točni modeli za numerične simulacije lahko pripomorejo k boljšemu razumevanju vpliva različnih dejavnikov na napredovanje razpok. V predstavljeni raziskavi je bil razvit model za numerično simulacijo na osnovi končnih elementov s pomočjo komercialne programske opreme ABAQUS. Cilj je bil pridobitev vpogleda v napredovanje in zaustavitev širitve razpok v tanki gredni prirobnici iz jekla SS316L. Sestav je bil hlajen od znotraj, vir cikličnih toplotnih obremenitev pa je bil postavljen na obod prirobnice. Opravljeni so bili eksperimenti na posebnem preizkuševališču s tuljavo za indukcijsko ogrevanje zunanjega oboda. Za določitev natančnega temperaturnega profila so bili uporabljeni termoelementi, radialno pritrjeni na obod. Modelu so bili dodeljeni realnočasovni in temperaturno odvisni podatki o elastoplastičnih lastnostih materiala. Robni pogoji in toplotni profil za numerični model so bili usklajeni s podatki eksperimentov. Pridobljeni rezultati simulacije so bili za validacijo primerjani z rezultati eksperimentov. V predstavljenem delu so ovrednotene napetosti, ki povzročijo začetek razpok, vpliv števila in dolžine razpok na napetosti, absorbcija energija na vrhu razpoke v vsakem toplotnem ciklu in pragovne vrednosti razpok. Ugotovljeno je bilo, da se vrednost CMOD povečuje neodvisno od števila ali dolžine razpok in zato ni primerna za identifikacijo poškodb zaradi toplotnega utrujanja. Razviti model za simulacijo pripomore k boljšemu razumevanju evolucije napetosti in deformacij zaradi cikličnih toplotnih obremenitev v disku iz jekla SS316L. Ugotovljeno je bilo, da je nastanek razpok posledica obodnih napetosti v prirobnici. Razviti model omogoča boljše razumevanje pojavov napredovanja razpok in sproščanja energije na vrhu razpok ter bo uporaben pri prihodnjih raziskavah na področju projektiranja komponent, ki so izpostavljene toplotnemu utrujanju, npr. v jedrskih elektrarnah. Ključne besede: toplotno utrujanje, numerična simulacija, SS316L, obodna napetost, napredovanje razpoke, J-integral SI 70 *Naslov avtorja za dopisovanje: Univerza v Rimu Sapienza, Oddelek za strojništvo in letalsko tehniko, Via Eudossiana 18, 00184 Rim, Italija, hassan.elahi@uniroma1.it Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, SI 71 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-05-18 Prejeto popravljeno: 2019-07-29 Odobreno za objavo: 2019-08-21 Uklon spojenih kompozitnih koničnih lupin pod aksialnimi tlačnimi obremenitvami po teoriji strižnih deformacij Mohammad Hadi Izadi - Shahrokh Hosseini Hashemi* - Moharam Habibnejad Korayem Iranska univerza za znanost in tehnologijo, Oddelek za strojništvo, Iran Članek obravnava kritične uklonske obremenitve pri spojenih koničnih lupinah pod vplivom aksialnega tlaka. Konične lupinaste konstrukcije se uporabljajo v raznih aplikacijah kot so rezervoarji za skladiščenje ogljikovodikov, naprave v rafinerijah, hladilni stolpi, ohišja in vmesniki izstrelkov, trupi letal, šobe izstrelkov in reaktivnih motorjev, cevovodi in tankerji za transport kapljevin, naprave v elektrarnah, turbine in tlačne posode, trupi podmornic ter različne konstrukcije in silosi. Pregled literature je pokazal, da obstaja le malo študij spojenih lupin. Večina raziskav je omejenih na spojene cilindrično-konične lupine in na tanke lupine. Obravnavane lupine so bile poleg tega pogosto izdelane iz elastičnih izotropnih homogenih materialov. V predstavljeni študiji so bile raziskane uklonske lastnosti spojenih koničnih lupin pod aksialno obremenitvijo ob upoštevanju vpliva strižne deformacije. Klasični linearni uklon spojenih stožcev, izdelanih iz križnih laminatov, ojačenih z vlakni, je bil preučen z analitičnim pristopom. Vodilne enačbe so bile določene po teoriji strižne deformacije prvega reda (FSDT) in za določitev kritičnih uklonskih obremenitev je bila uporabljena analitična rešitev. Sistem parcialnih diferencialnih enačb je bil razrešen z ločitvijo spremenljivk z razvojem v Fourierjevo vrsto in po metodi razvoja v potenčno vrsto. Preučen je bil vpliv števila slojev, vrstnega reda laminacije, polkota ob vrhu, debeline lupin, dolžine lupin in robnih pogojev na stabilnost spojenih stožcev. Validacija je bila opravljena s primerjavo rezultatov pričujoče in predhodnih študij. Za analizo po metodi končnih elementov je bila uporabljena programska oprema ABAQUS/CAE. Rezultati predstavljene metode se dobro ujemajo z rezultati simulacije po metodi končnih elementov in drugimi. V območju približevanja polkotov nastopi ostro zmanjšanje uklonske obremenitve. Z drugimi besedami: pri krajših lupinah se uklonska obremenitev hitro zmanjša na mestu, kjer se približata polkota dveh lupin. Sledi ugotovitev, da ima uporaba dveh spojenih lupin z ustrezno izbranima polkotoma prednost pred uporabo enotnega stožca. Pri tankih lupinah je konstrukcija najbolj toga pri skoraj identičnih polkotih, pri debelejših lupinah pa ima togost lupin zaradi debeline večji vpliv kot polkoti lupin, ki izhajajo iz geometrije. Uklonska obremenitev je minimalna, ko je ena od lupin ploščata. Pridobljene ugotovitve za debele lupine bo mogoče primerjati z rezultati prihodnjih raziskav na osnovi HSDT. Raziskati bo mogoče tudi vpliv transverzalnih in rotacijskih obremenitev ter aksialnih in obodnih ojačitev na stabilnost spojenih lupin. Prihodnje raziskave se bodo lahko osredotočile tudi na eksperimentalno analizo uklona spojenih stožcev. Uklon spojenih koničnih lupin končno tudi še ni bil analiziran po metodi GDQM in rezultate GDQM bo tako mogoče primerjati z rezultati razvoja v potenčno vrsto. Ključne besede: uklon, spojena laminirana konična lupina, strižna deformacija prvega reda, potenčna vrsta, MKE, aksialni tlak, križna laminacija *Naslov avtorja za dopisovanje: Iranska univerza za znanost in tehnologijo, Oddelek za strojništvo, Narmak, Teheran, Iran, shh@iust.ac.ir SI 71 Strojniški vestnik - Journal of Mechanlcal Englneerlng 65(2019)10, SI 68 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-04-18 Prejeto popravljeno: 2019-08-10 Odobreno za objavo: 2019-08-21 Študija vplivnih parametrov vtiskovanja krogle za opredelitev nadzorne funkcije lastnosti materiala pri preoblikovalnih operacijah Roman Satošek1 - Michal Valeš2 - Tomaž Pepelnjak1,* Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 2Češka tehniška univerza v Pragi, Fakulteta za strojništvo, Češka republika Odstopanja od predpisanih lastnosti preoblikovanega izdelka v sodobnih, prilagodljivih preoblikovalnih procesih se delijo na napake in motnje delovanja proizvodnega procesa. Za boljši nadzor nad proizvodnjo je potrebno zmanjšati motnje v procesu preoblikovanja. V ta namen je bil uveden nov in inovativen sistem pretoka podatkov, ki je za vse materialne parametre povezan v novo opredeljeno "funkcijo nadzora lastnosti materiala". Za sprotni nadzor proizvodne linije pri procesih preoblikovanja in pridobivanje potrebnih materialnih podatkov je bil izveden preizkus vtiskovanja krogle v merjen material. Glavni parametri, ki jih je treba pri tem upoštevati, so vrednosti izbočenja ali vbočenja preoblikovane okolice kalote po vtisnjenju orodja v obliki krogle ob upoštevanju anizotropnega popisa materiala. Parametrična študija primernosti preskusa vtiskovanja krogle je izvedena na podlagi materialnih podatkov aluminijeve zlitine AW 5754-H22. Metoda končnih elementov (MKE) je uporabljena za oceno vplivov premera krogle orodja, kontaktnega trenja in zgodovine preoblikovanja uporabljenega materiala. Novost tega pristopa in znanstven doprinos dela pri vtiskovanju krogle v material sta: a) povezava linearne korelacije izbočenja z globino vtiskovanja krogle opredeljeno z naklonom k, in b) povezava naklona k z različnimi prednapetostmi z novo potenčno funkcijo. Slednja predstavlja nov koncept parametričnega popisa vplivov materiala na proces vtiskovanja in se ga bo v bodoče integriralo v krmilne sisteme preoblikovalnih procesov. V članku je predstavljena linearna korelacija ter definicija nove potenčne funkcije opredeljene s parametri a, f in b povezave med gradientom razmerja su napram h v odvisnosti od tehnološke zgodovine materiala izvedena za primer aluminijeve zlitine AW 5754-H22. Za njen popis potrebujemo opredelitev naslednjih robnih pogojev: velikosti vtiskovane krogle, vpliva debeline materiala, globine odtisa ter kontaktnega trenja. Našteti robni pogoji so s pomočjo MKE vrednoteni napram višini izbočenja po vtiskovanju krogle v material. Za primer analize trenja so dobljeni numerični rezultati tudi eksperimentalno preverjeni. Ugotovljeno je ujemanje med MKE in eksperimentom pri koeficientu Coulombovega trenja z vrednostjo ^=0.2, ki se v nadaljevanju raziskav uporabi pri izvedbi študije o vplivu anizotropije ter tehnološke zgodovine opazovanega materiala. V MKE je uporabljen Hillov potencialni kriterij tečenja, ki upošteva anizotropne lastnosti materiala. Za popis Hillovih potencialov je uporabljena napetost tečenja v smeri valjanja ter eksperimentalno pridobljeni Lankfordovi parametri anizotropije materiala r (r0, r45 in r90). Trenje ima pomemben vpliv na izbočenje in zmanjšuje njegovo vrednost. V primeru anizotropnega materiala je izbočenje odvisno od smeri valjanja. Popis odvisnosti se prikaže z naklonom linije v su - h diagramu. Naklon v smeri 0=45 ° je najbližji naklonu pri izotropnem material, medtem ko je pri 0=0 ° nagib povečan in obratno, pri 0 = 90 ° je manjši kot pri izotropnem materialu. Tehnološko zgodovino materiala je mogoče zabeležiti s pomočjo linearne odvisnosti med izbočenjem in globino kalote pri čemer ob večjem gradientu navedene odvisnosti, ki je posledica pred-utrjevanja zaradi tehnološke zgodovine materiala, dosežemo opazovano ciljno deformacijo pri nižjih kalotah kot v primeru mehko žaljenega deviškega materiala. Študija omogoča nadaljevanje raziskav opredeljenega modela generatorja kontrolnih funkcij za nadzor preoblikovalnega procesa. Prav tako odpira vprašanja generalizacije novo opredeljene potenčne funkcije povezave med gradientom razmerja su napram h v odvisnosti od tehnološke zgodovine na različne kovinske materiale, njeno generalizacijo in njeno implementacijo v krmilno funkcijo za nadzor preoblikovalnega procesa. Ključne besede: test vtiskovanja, anizotropija, sprotni nadzorni sistem, preoblikovalni proces, parametrična študija SI 72 *Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, tomaz.pepelnjak@fs.uni-lj.si Strojniški vestnik - Journal of Mechanical Engineering 65(2019)10, SI 73 © 2019 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-04-22 Prejeto popravljeno: 2019-07-08 Odobreno za objavo: 2019-08-13 Omejevanje samovzbujenih vibracij pri rotacijskih strojih z listnatimi vzmetmi Chang Wang1 - Jun Liu12* - Zhiwei Luo3 1 Državni laboratorij za napredne mehatronske sisteme in inteligentno vodenje, Tehniška univerza v Tianjinu, Kitajska 2 Nacionalni demonstracijski center za eksperimentalno delo pri pouku strojništva in elektrotehnike, Tehniška univerza v Tianjinu, Kitajska 3 Organizacija za napredno znanost in tehnologijo, Univerza v Kobeju, Japonska Pri delovanju rotacijskih strojev nad zgornjo kritično hitrostjo se zaradi notranjega trenja na gredi pojavljajo samovzbujene vibracije. V članku je preučen mehanizem nastanka samovzbujenih vibracij in predstavljena učinkovita metoda za omejevanje samovzbujenih vibracij z listnatimi vzmetmi. Lastnosti rotorjev z listnatimi vzmetmi so bile sistematično preučene z numeričnimi simulacijami in teoretično analizo. Teoretična analiza vibracijskih lastnosti rotorskih sistemov po večskalni perturbacijski metodi in metodi harmoničnega ravnovesja je težavna zaradi notranjih dušilnih členov. V tej študiji je bila uporabljena izboljšana strelna metoda za pridobivanje aproksimativnih rešitev za harmonično komponento. Veljavnost predlagane metode omejevanja vibracij je bila preverjena tudi eksperimentalno. Pojavi notranjega trenja se razvrščajo v histerezno dušenje zaradi notranjega trenja v materialu gredi in v strukturno dušenje zaradi suhega trenja med gredjo in zunanjimi elementi. Strukturno dušenje rotorja v tem primeru šteje v notranje dušenje. Ob upoštevanju sil dušenja in elastičnih sil listnatih vzmeti so bile pridobljene enačbe dinamike rotorskega sistema. Na podlagi analize lastnih frekvenc je bilo ugotovljeno, da imajo sile dušenja listnatih vzmeti velik vpliv na glavno kritično hitrost rotorskega sistema, ki se povečuje z rastjo koeficienta dušilnih sil. Za pridobivanje aproksimativnih rešitev za rotorski sistem v pogojih ravnotežja in neravnotežja sta bili uporabljeni metoda harmoničnega ravnotežja in izboljšana strelna metoda. V kombinaciji z numeričnimi simulacijami so bili pridobljeni resonančni odzivi za analizo vibracijskih lastnosti rotorskega sistema. Amplituda samovzbujenih vibracij v pogojih brez neravnotežja se je bistveno zmanjšala s povečanjem koeficienta dušilnih sil. Ko ta doseže kritično vrednost, ne more priti do samovzbujenih vibracij. Harmonične vibracije in samovzbujene vibracije v pogojih brez neravnotežja so praktično neodvisne, skoraj periodična gibanja pa se pojavljajo zaradi seštevanja harmoničnih in samovzbujenih vibracij. Listnate vzmeti lahko učinkovito omejijo samovzbujene vibracije v širokem razponu vrtilnih frekvenc. Za preverjanje učinkovitosti predlagane metode omejevanja je bil zgrajen enorotorski sistem z listnatimi vzmetmi. Puša omogoča nastavitev sile prednapetosti med pušo in gredjo, notranja sila dušenja pa se prilagaja z uravnavanjem sile zategovanja puše. Pod diskom je vgrajen kroglični ležaj. Štirje paketi listnatih vzmeti se dotikajo zunanjega obroča ležaja na štirih mestih. Vsak paket listnatih vzmeti je sestavljen iz treh listov različnih dolžin in med listi nastane suho trenje. Brez listnatih vzmeti pri vrtilnih frekvencah nad zgornjo kritično hitrostjo nastopijo samovzbujene vibracije in validacija mejnega cikla ni mogoča. Rezultati eksperimentov z listnatimi vzmetmi so pokazali odsotnost samovzbujenih vibracij nad glavno kritično hitrostjo tudi ko je rotorski sistem z listnatimi vzmetmi izpostavljen ponavljajočim se motnjam. Raziskava je bila osredotočena na vibracijske lastnosti pri vrtilnih frekvencah v bližini glavne kritične hitrosti. V prihodnje bodo raziskane še vibracijske lastnosti v bližini podharmonične resonance reda 1/2, saj ima rotorski sistem eliptične orbite. Rezultate teoretičnih analiz in numeričnih simulacij potrjujejo tudi rezultati eksperimentov: z listnatimi vzmetmi je mogoče omejiti samovzbujene vibracije nad glavno kritično hitrostjo. Ključne besede: rotorski sistem, samovzbujene vibracije, notranje dušenje, omejevanje vibracij, listnata vzmet, eksperiment *Naslov avtorja za dopisovanje: Tehniška univerza v Tianjinu, No. 391 Bin Shui Xi Dao Road, Tianjin, Kitajska, liujunjp@tjut.edu.cn SI 73 Information 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 10 pages. Longer contributions will only be accepted if authors provide juastfication 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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