Strojniški vestnik Journal of Mechanical Engineering 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: Koštomaj printing office, printed in 275 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Mitjan Kalin University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Vice-President of Publishing Council Bojan Dolšak University of Maribor, Faculty of Mechanical Engineering, Slovenia Cover: The cover image shows a scaled-down spinning machine intended for research of the mineral wool fiberization process that can operate in 2, 3 or 4 wheel configuration. Instead of high-temperature mineral melt, molten isomalt sugar is used as a working medium to allow for easier and safer device operation in the lab. Image courtesy: University of Ljubljana, Faculty of Mechanical Engineering, Courtesy of Laboratory for water and turbine machines, 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. 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Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5 Contents Contents Strojniški vestnik - Journal of Mechanical Engineering volume 66, (2020), number 5 Ljubljana, May 2020 ISSN 0039-2480 Published monthly Papers Benjamin Bizjan, Brane Širok, Marko Blagojevič: Analogue Experimental Study of Fiber Formation on Two-Wheel Spinner 279 Hongwei Yan, Yajie Li, Fei Yuan, Fangxian Peng, Xiong Yang, Xiangrong Hou: Analysis of the Screening Accuracy of a Linear Vibrating Screen with a Multi-layer Screen Mesh 289 Wiktor Kamycki, Stanislaw Noga: Application of the Thin Slice Model for Determination of Face Load Distribution along the Line of Contact and the Relative Load Distribution Measured along Gear Root 300 Da Cui, Guoqiang Wang, Huanyu Zhao, Shuai Wang: Research on a Path-Tracking Control System for Articulated Tracked Vehicles 311 Vytautas Martinaitis, Dovydas Rimdžius, Juozas Bielskus, Giedre Streckiene, Violeta Motuziene: Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan 325 Aida Parvaresh, Mohsen Mardani: Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 337 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288, © 2020 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6557 Original Scientific Paper Received for review: 2020-01-16 Received revised form: 2020-04-02 Accepted for publication: 2020-04-23 Analogue Experimental Study of Fiber Formation on Two-Wheel Spinner Benjamin Bizjan* - Brane Sirok - Marko Blagojevic University of Ljubljana, Faculty of Mechanical Engineering, Slovenia In this paper, the process of mineral fiber formation was investigated experimentally on a two-wheel spinner by means of high-speed imaging. Analogue isomalt melt was fiberized at different rotational speeds of spinner wheels, melt flow rates and impingement positions so that the fiberization process was dynamically similar to an industrial mineral wool production process. Images of fiber formation and transport reveal highly complex dynamics of these processes, as fibers mostly occur in form of 3D mutually intertwined structures such as clusters, strands and veils periodically shedding from the melt film. Despite the complexity of flow structures, there is a clear trend of increasing mean fiber length and expansion angle of the coaxial fiber-laden flow as the Weber number and the ratio of melt film velocity to blowing air velocity are increased. The fiberization efficiency (ratio of fiber mass deposited on the collecting mesh to the mass of melt poured) is affected by the impingement position and flow rate of melt as well as the Weber number of melt film. The optimum efficiency was attained at 30° (1 o'clock) impingement position and the ratio of melt film to blowing air flow velocity close to unity. Keywords: spinner, fiber formation, mineral wool, multiphase flow, primary layer, high-speed imaging Highlights • Fiber formation from melt was studied on a two-wheel spinner by high-speed imaging. • Fibers are intertwined into complex 3D structures before separation from melt film. • Fiber structure complexity further increases by interaction with turbulent airflow. • Mean fiber length increases with Weber number of the melt film. • Fiberization efficiency depends on melt flow, impingement position and wheel speed. 0 INTRODUCTION Turbulent fiber-laden flows are of great importance in manufacturing of fiber-based materials such as mineral wool insulation, paper, composites and non-woven fabrics [1] and [2]. Fibers for these applications are commonly produced by air-assisted spinning machines (also known as spinners) with two prevailing designs: hollow rotors with perforated walls [3] and [4] and multi wheel spinners where melt cascades between wheels and is fiberized from a free surface [5] and [6]. The former type is used for fiberization of melts with temperatures up to 1000 °C, while the latter type is employed with very high temperature melts (up to 1600 °C) in the manufacturing of stone and slag wool and will be the focus of research presented in this paper. The basic operating principle of a multi-wheel spinner is the scattering of melt to ligaments from a radial film formed on each wheel, followed by solidification and transport to the fiber deposition area where the primary layer of fibers is formed [5]. Both fiberization and primary layer formation processes are highly complex and not well understood on the micro scale despite the fact that centrifugal fiberization is a mature technology that has been in use for many decades. This is largely due to the fact that mineral fibers are typically very thin (under 10 ^m) and initially travelling at velocities in excess of 100 m/s, effectively preventing the observation of individual fibers even with state-of-the-art high-speed cameras. To overcome these issues, different approaches have been employed. Simplified theoretical models of fiber formation were proposed by Vad and Morlin [7] and Zhao et al. [8]. Bizjan et al. [9] modelled the fiberization process on a scaled-down, single wheel spinning machine using an isothermal Newtonian liquid. Results of these experiments were successfully reproduced in a numerical simulation by Mencinger et al. [10], while a similar study that also considered solidification of ligament breakup droplets was conducted by Peng et al. [11]. Nevertheless, a full three-dimensional (3D) simulation of the spinner fiberization process has not yet been attempted due to an extreme computational expense when all fiberization-related phenomena are considered. Another possible method for investigation of fiberization and primary layer formation is to employ a low-temperature melt that can be safely handled in the laboratory environment. Several authors investigated the fiberization process as an undesired phenomenon in the dry centrifugal granulation process using a rosin-paraffin melt [12] to [14], but with little regard to fiber formation dynamics. Speaking of the fibrous primary layer formation process, several studies *Naslov avtorja za dopisovanje: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, benjamin.bizjan@fs.uni.lj.si 279 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 have been conducted. Bajcar et al. [15] investigated the dependence of the primary layer texture on aerodynamic characteristics within the collection chamber. Bizjan et al. [16] modelled the bulk density and distribution of deposited sucrose fibers produced by an air-assisted cotton candy machine. A similar study was performed on the collecting drum of an industrial stone wool production line [17]. These studies did not focus on the flight of fibers between the spinner and the collecting mesh. This segment was covered on a more fundamental level by Lin et al. [1] and Capone et al. [18] who modelled transport of short rigid fibers in the axial airflow. In light of above-presented studies dealing with different stages of fiber formation and transport, the present paper aims to improve the understanding and modelling of realistic fiber formation and transport processes with regard to spinner operating conditions, particularly on small length and time scales. For this reason, a two-wheel spinner resembling industrial spinning machines for production of fibers [5] and powders [19] was designed, and the flow of fibers was investigated experimentally by high-speed imaging. 1 EXPERIMENTAL SET UP AND METHODOLOGY We = p-g2 R3 7 (1) Ohnesorge number (ratio of viscous forces relative to inertial and surface tension forces acting on the melt): Oh =- JpRy' Dimensionless velocity ratio: (2) (3) Fig. 1. Experimental set-up for high-speed imaging of melt fiberization u w = V B Experimental set-up (Fig. 1) consisted of a spinner with two counter-rotating aluminum wheels, a pivoting cup liquid supply system, blowing and suction air systems, and a high-speed imaging system. The radius of the first spinning wheel was R1 = 45 mm, while the second wheel with R2 = 52.5 mm was installed so that the minimum clearance (gap) between wheels was 5 mm (Fig. 1, front view). Both wheels were 60 mm long and propelled by a direct-drive electric motor that was powered by a variable frequency drive (VFD), with rotational speed of the wheel varied in the range 40 Hz < /< 100 Hz. The spinner used in our experiments is a scaled-down version of a four-wheel industrial mineral wool spinning machine (approximately 1:3 scale). Only wheels 1 and 2 were installed for the purpose of the present study as such setup is adequate to investigate fiberization-related phenomena without the unnecessary complexity of the flow visualization setup required for a four-wheel device. Operating parameters in our experiment were selected so that similarity criteria with industrial spinners were satisfied. Three main dimensionless numbers were introduced for this purpose in Eqs. (1) to (3): Weber number (ratio of inertial to surface tension forces acting on the melt): 280 The working medium in our experiments was molten isomalt, a sugar alcohol commonly used in the food industry. The main advantage of using isomalt instead of sucrose is its low susceptibility to caramelization, recrystallization and moisture absorption [20], while its glass transition temperature (Tg = 63.6 °C [21]) is sufficiently high to ensure fiber solidification to a glassy state when cooled to ambient temperature. On the other hand, unlike aforementioned rosin-paraffin mixtures, solid isomalt residues can be cleaned with water instead of organic solvents, and the isomalt melt is also safer to handle due to its low volatility and low flammability. The properties of isomalt melt [20] and [21] used in our experiments are provided in Table 1 along with the properties of typical mineral melts [22] and [5]. Also provided in Table 1 is a comparison of Oh, We and w dimensionless numbers that confirms a good similarity of model spinner from the present study with industrial spinning machines. Consequently, the findings presented in this paper can be largely applied to the mineral wool manufacturing process. Once the melt was homogenized at its desired temperature, it was filled into a polytetrafluoroethylene (PTFE) cup with 70 mm inner diameter (Fig. 2a) preheated to the same temperature to prevent Bizjan, B. - Širok, B. - Blagojevič, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 Table 1. Comparison of model and industrial spinner parameters, including physical properties of melts and dimensionless similarity criteria for model and industrial spinners Spinner Material T[°C] Tg [°C] p [kg/m3] Y [N/m] / [Pa-s] We [x106] Oh w Model isomalt 195 63.6 1418 0.070 0.21 0.19 to 1.16 0.09 to 0.10 0.44 to 1.1 Indus. min. melt 1400 to 1600 750 to 900 2600 0.4 to 0.5 0.5 to 1.5 0.5 to 10 0.05 to 0.15 0.5 to 1 Fig. 2. a) Melt pouring from the pivoting cup, and b) spinner in operation (frontal view) premature solidification of melt. In all experiments, the mass of the melt batch (mM) was approximately 150 g. The cup was then rotated 180° by a pivoting mechanism powered by a stepper motor, pouring the melt onto the spinner until completely empty. Two different angular velocities were used (6 °/s and 9 °/s), resulting in a mean volume flow rate of melt Q= 18.3 mL/s and Q= 24.8 mL/s, respectively. The main advantage of using the pivoting cup melt supply is a good repeatability of the pouring process, and a negligible residual mass of melt left in the cup. The melt flowing from the pivoting cup impacted the first spinner wheel at an impingement angle q> (Fig. 2b, q> = 0° corresponds to 12 o'clock position on the wheel) and was deflected towards the second wheel. The impingement angle was varied between 15° and 60°. A radial melt film was formed on both spinning wheels and was continuously disintegrated to melt ligaments that rapidly solidified to fibers. Fibers were transported from the spinner with the aid of coaxial airflow distributed through circular nozzles (1 mm diameter, 5 mm above wheel surface) of two blowing rings (Fig. 2b) connected to a utility compressed air system, and the suction airflow generated by axial fans on the other end of the collection chamber channel. The transparent plexiglass channel was 1 m long with a 0.5 m x 0.5 m cross-section. Blowing and suction air flow rates were set to qB = 10 L/s and qS = 140 L/s, respectively (ambient air temperature and relative humidity were 23 °C and 62 %, respectively). The resulting ratio qS / qB = 14 was close to ratios used in the mineral wool industry, 10 to 12, [5]. The velocity of the coaxial blowing air flow above the center of the wheel mantle where melt film was formed was approximately 30 m/s. As the fiber-laden flow reached the collecting mesh, fibers were deposited, forming a layer of fibrous material also known as the primary layer [16] and [17]. The process of fiberization, fiber flight and primary layer deposition was recorded from the side and top of the spinner casing (fiberization imaging setup shown in Fig. 1) using a high-speed camera (Fastec HiSpec4) with 50 mm fixed zoom lens and recording at 2500 frames per second. In all cases, a diffuse LED light source was used for illumination of fibrous structures from the opposite side of the focal plane. Analogue Experimental Study of Fiber Formation on Two-Wheel Spinner 281 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 2 RESULTS AND DISCUSSIONS 2.1 Fiberization Process and Fiber Transport The process of fiber formation from the melt film was visualized on wheel 2 at three different rotational speeds (Fig. 3) and a 1200 * 492 pixels resolution. As seen in Fig. 3 and Table 2, low wheel speeds (f= 40 Hz, u = 13.2 m/s) resulted in fiber trajectories nearly parallel to the wheel surface and a strong recirculation zone behind the wheel, where a significant amount fibers accumulated (note that the front face of both wheels was hollow). A few relatively large droplets generated in the fiberization process (mean radial velocity: rDR=9.0 m/s) are visible and are mostly transported away by the blowing air flow. In the intermediate range of wheel velocities ( f= 70 Hz, u = 23.1 m/s), the recirculation zone can be seen to disappear, and the fibers are transported following a horizontal trajectory downstream of the wheel. However, the number and velocity of melt droplets is increased (Table 2), resulting in droplets penetrating the air flow in the radial plane (rDR = 15.5 m/s). A further increase of the wheel rotational speed to 100 Hz (u = 33 m/s) causes an even larger number and velocity of penetrating melt droplets (rDR = 19.1 m/s). The ratio ^d r / u can be seen to decrease with the rotational speed of the wheel, most likely due to increased aerodynamic drag acting on melt droplets. Also decreasing is the mean diameter of droplets (cD) that roughly follows the values predicted by the head droplet size model dHD = 1.95\fi* We-045 [9], suggesting that most visible droplets are produced by pinching of molten ligament heads. Besides, fibers can also be seen to partly penetrate the coaxial air jet, as indicated by an increased concentration of low velocity fibrous structures below the jet that gradually reenter the blowing air flow. As the circumferential velocity of the wheel increases, radial and tangential velocities of emerging fibers also increase while the axial component does not change significantly (blowing air velocity was kept constant), resulting in a larger spreading angle of the fibrous flow that can be seen as a steeper initial flight path of fibers in Fig. 3. This Fig. 3. High-speed images of fiberization process on wheel 2 at different wheel rotational speeds (V = 30°, Q = 24.8 mL/s, Oh = 0.092) is also evident from Fig. 4 where vertical profiles of the gray level standard deviation aG are shown at x= 10 mm and x= 50 mm (consider coordinate system in Fig. 3). The value of aG was normalized to the maximum possible gray level of images (i.e. 255). Besides the shift of the peak aG position, an increase in wheel rotational speed also results in larger mean values of aG , while the difference between profiles drawn at x= 10 mm and x= 50 mm diminishes. Both findings indicate a marked increase in the turbulent intensity of the fiber-laden flow with the rotational speed of the wheel. A very important parameter for characterization of the fiberization process is the fiber length L (Fig. Table 2. Dependence of droplet diameters on spinner operating conditions (values calculated for wheel 2) f [Hz] We *^D,R [m/s] u [m/s] w vd,R / u *dD [mm] dHD [mm] *Lm ± al [mm] 40 1.85 105 9.00 13.2 0.44 0.682 0.41 0.436 13.1±5.4 70 5.67 105 15.49_231_077_0.671_0.35_0.264_14.5±6.2 100 1.16-106 19.13_330_1.10_0.580_0.27_0J.9_16.9±6.5 * parameters manually measured from Images using IrfanVlew software with on-screen ruler and subpixel Interpolation (100 measurements for each set of operating conditions, each measurement accurate to 0.1 pixels / 11 |jm). 282 Bizjan, B. - Širok, B. - Blagojevič, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 Fig. 4. Standard deviation profiles of the image gray level for different wheel speeds and axial positions 5), and its arithmetic mean Lm (Table 2). Length statistics presented in Table 2 and in Fig. 5 suggest that the fiber length distribution is quite wide, and both the mean and the standard deviation of the length tend to increase with the rotational speed of the wheel. For experiments with the highest Weber number ( /= 100 Hz, We = 1.16-106), the length of 95 % of fibers was between 10 mm and 30 mm, and the Lm / R ratio was approximately 0.32. These figures are consistent with values reported on industrial spinning machines (Lm ~ 10 mm, Lm /R= 0.3, ..., 0.4; [5]), where Fig. 5. Histogram of the fiber length based on 100 length measurements at each rotational speed used fiberization process is hydrodynamically similar to our experiments as it occurs in a similar range of We, Oh and wnumbers (Table 1). Similarity is considered valid for as long as dimensionless numbers for model and industrial devices are by less than factor 10 apart [5]. Nevertheless, cold experiments performed by Bizjan et al. [23] suggest that much longer fibers are produced in the absence of the blowing air flow, a ratio of Lm /R~ 1.1 was reported on a wheel Fig. 6. High-speed images of fiber formation near the melt film (y = 30°, Q = 24.8 mL/s, Oh = 0.092), frame separation 0.4 ms Analogue Experimental Study of Fiber Formation on Two-Wheel Spinner 283 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 with R= 45 mm. This finding is also supported by experience in the mineral wool industry [5], although the exact fiber length is difficult to measure due to the fragility and mutual intertwining of fibers. A better insight into the microscale dynamics of the fiberization process can be gained by examination of high-speed images in the region adjacent to the melt film (Fig. 6). Regardless of the wheel rotational speed and Weber number, a similar general mechanism can be observed. Liquid ligaments are initially extended from the melt film in a direction perpendicular to the axis of wheel rotation. In this phase, the ligament growth is largely governed by hydrodynamic instabilities such as the Rayleigh-Taylor and Kelvin-Helmholtz instability [24]. As the ligament head enters the high velocity zone of the coaxial air jet, the ligament is gradually curved towards the axial direction. When the circumferential velocity of the wheel and thus the melt film velocity is much lower than the air flow velocity (e.g. at f= 40 Hz, Fig. 6), most ligaments are immediately deflected towards the axial direction, some reattaching to the wheel surface downstream of the melt film. However, as the ratio between the melt film velocity and the air current velocity approaches unity (w^ 1), the radial extent of ligaments from the melt film is increased, and the deflection towards the air jet direction is complete at a farther distance from the origin point of ligaments (as already noted, some ligaments can even penetrate the air jet). Since there is a large number of liquid ligaments attached to the melt film, deflection by the air current inevitably causes ligaments to come in contact, stick to each other and form relatively large clusters upon solidification to fibers. Due to the ongoing ligament formation, such fiber clusters grow continuously while remaining attached to the melt film for extended periods of time. Once a critical size is reached, a part of the cluster is separated under the action of the centrifugal force and the aerodynamic drag force and is transported away from the wheel by the blowing air flow. In our experiments, the most common frequency of fiber cluster shedding was between 150 % and 200 % of the wheel rotational frequency f, while the size of both attached and separated clusters significantly decreased with f. Apart from the cluster formation, some ligaments that did not immediately intertwine can be seen to extend far downstream of the melt film and solidify to long and thin strands (Fig. 3). Complex fluid-structure interaction phenomena occur as these fiber strands interact with the coaxial air flow and with each other while still attached to the rotating melt film. Eventually, the partly intertwined fiber strands are torn away from the wheel surface, forming veil-like structures of varying sizes and exhibiting a complex 3D motion in the transporting air flow - consider Fig. 7 for flow images recorded from a top-down view immediately downstream of spinning wheels. Fig. 7. Typical fibrous structures downstream of the model spinning machine, top-down view (y = 30°, Q = 24.8 mL/s); wheel gap position marked by dashed lines The fact that there is a strong interaction between fibers implies that existing fiberization models assuming a single fiber in the airflow [7], [8] and [25], whilst useful for prediction of fiber diameters, cooling rates and initial trajectories, become inadequate once fibers are mutually intertwined. Particularly the process of fiber tearing from the melt film and subsequent fiber breakage in the blowing air flow is still poorly understood. As noted by Westerlund and Hoikka [25], tensile load calculated by a single fiber model is by an order of magnitude lower than the tensile strength of mineral fibers, while the final fiber length is significantly overestimated. Consequently, it is likely that fiber breaking mechanisms are closely linked to the interaction of fibrous structures with the turbulent air flow that is not considered by any of the known models. 284 Bizjan, B. - Širok, B. - Blagojevič, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 As already said, the multiphase fiber-laden flow downstream of the spinner is highly complex, a finding confirmed by flow images shown in Fig. 7. Multiple different types of fibrous structures including clusters and strands are visible, often occurring mutually intertwined. Consistent with observations regarding the initial fiberization process (Fig. 6), flow images in Fig. 7 suggest a decreasing trend for the mean size of fibrous structures as the wheel rotational speed is increased. Despite the decreasing size, the bulk density of fiber clusters remains relatively high, as indicated by low light transmittance of these structures (note very dark image areas where the light source is obstructed by clusters). 2.2 Formation of the Primary Layer of Fibers on the Mesh Apart from fiber formation and transport in the airflow, the process of fiber settling on the collecting mesh determines the structure and quality of the primary layer (Fig. 8a) of deposited fibers [5]. The fiber settling process was recorded in the area adjacent to the collecting mesh (Fig. 8b, image size 880*646 pixels). A sample flow image shown in Fig. 8b indicates the presence of complex and interconnected three-dimensional fibrous structures near the collecting mesh. As evident from Fig. 9, fibrous structures of very different size and morphology (strands, Fig. 8. a) Primary layer of fibers on the collecting mesh; and b) typical fibrous structures in flight near the mesh ( f= 70 Hz, qB = 10 L/s, qS = 140 L/s) Fig. 9. Fiberization image sequences (f = 70 Hz, qB = 10 L/s, qs = 140 L/s); frame separation: 2 ms (upper row), 100 ms (lower row); viewing area size: 61.6 mm x 45.2 mm (all tiles); Note the thickness of the primary layer (right edge of tiles) increasing with time Analogue Experimental Study of Fiber Formation on Two-Wheel Spinner 285 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 veils, clusters) can appear in a single fiberization experiment, including shorter time periods where little or no airborne fibers are observed. Despite the predominant axial velocity component, the motion of fibers is three-dimensional, including rotation and deformation of structures. High-speed images of the fiber settling process were used to measure the thickness of the primary layer (h) and the relative mass flow rate of fibers (M). M was calculated as the time series of mean image brightness (leftmost 100 pixels of each image were included, Fig. 8b), and normalized to the value range of [0, ..., 1]. In Fig. 10, large fluctuations in the value of M can be observed and are consistent with the large fiber structure variability presented in Fig. 9. However, the estimated cumulative mass of deposited fibers Im calculated by temporal integration of M increases in a fairly linear manner with time despite the mass flow rate fluctuations, suggesting a quasi-steady fiber deposition process. A similar linear trend can be observed for the growth of the primary layer thickness h. Visible oscillations of h (rapid increases followed by periods of fairly constant h) are likely related to spatially random thickening of the primary layer, as well as redistribution and fluttering of large fiber structures on the mesh, all leading to alternating positive and negative errors in measurement of h. Oscillations also indicate the possibility of unsteady rate of layer compression, although further research is needed in this regard. Fig. 10. Relative mass flow rate, relative deposited mass of fibers and primary layer thickness (f= 70 Hz, qB = 10 L/s, qs = 140 L/s, hmax = 15.1 mm) The fact that the time-averaged growth rate of the thickness h was fairly constant (approximately 9.2 mm/s) indicates that compression of fibrous structures mostly occurred when these structures settled on the collecting mesh, while subsequent additional compression due to deposition of new fibers and resulting increased pressure difference across the mesh was negligible. This can be explained by a low suction pressure in our experiments (approximately 15 Pa when mesh was covered by fibers). On the other hand, high-capacity industrial collecting chambers where the mesh is moving often operate with suction pressures in excess of 500 Pa, resulting in a higher degree of primary layer compression. After each fiberization experiment, fibers were removed from the mesh and weighed. Collected fiber mass mF was used to calculate the fiberization efficiency n0 = mF /mM (Fig. 11) and its relative value n calculated by normalization to the peak efficiency of a given curve. Curves presented in Fig. 11 suggest that fiberization efficiency initially increases with the rotational speed of spinner wheels and melt impingement angle. After passing an optimal setting (^ ~ 30°, f= 65 Hz to 80 Hz), n begins to decrease. Fig. 11. Diagrams of relative fiberization efficiency as a function of wheel rotational speed, melt impingement position and flow rate time At q> = 30°, the n (f) efficiency curve of the lower flow rate used (Q = 18.3 mL/s) exhibits a narrower range of efficiency than the curve for Q = 24.8 mL/s, and is less sensitive to non-optimal wheel speed settings. This suggests that the higher flow rate used in our experiments is near the maximum flow rate of melt that can be fiberized in the present spinner arrangement, and deviations from optimal settings of f and q> result in a significant mass fraction of melt remaining unfiberized. When the melt impingement position is low (q> > 45°), a large part of melt flows through the spinner wheel gap without adhering to the melt film [5]. Since wheels 3 and 4 were not installed in this study, this melt could not be fiberized once passing through the gap and was therefore lost. A different melt loss mechanism occurs when melt flow rates are used with high impingement positions, though. In this case, a significant proportion of melt 286 Bizjan, B. - Širok, B. - Blagojevič, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 279-288 is lost immediately after the impingement due to the splashing [5]. The splashing phenomenon can be explained by the occurrence of a hydraulic jump [26] when a stream of liquid or melt impinges a highspeed moving surface. The study by Keshavarz et al. [26] was conducted by liquid impact on a horizontal moving surface, while in our case the melt impacts a rotating surface with a relatively low curvature radius and is partly deflected towards the second spinning wheel. We suspect that the detachment of the melt jet with superimposed hydraulic jump structures may further intensify the splashing, and should be researched in future studies. 3 CONCLUSIONS In this work, the process of melt fiberization and primary layer formation was studied on a two-wheel spinner. The effect of operating parameter variation including rotational speed of spinner wheels, melt impingement position and flow rate was investigated by high-speed imaging of the fibrous flow at different locations in the collection chamber channel. The ratio of melt film velocity to blowing air velocity, as well as the melt film Weber number significantly affect fiber trajectories and structure, mean fiber length and fiberization efficiency, with optimum fiberization quality and efficiency near w= 1 and log(W?) ~ 6. The fiberization efficiency is also governed by the impingement position of the melt on the spinner and is highest when y ~ 30°. The mean fiber length and its standard deviation both gradually increase with w and We, but fibers produced are relatively short when w^ 1 (LM / R~ 0.3). The fiber formation and breakage process cannot be adequately described by single-fiber models due to the fact that molten ligaments and solidified fibers mutually intertwine in complex 3D structures such as clusters, strands and veils. These structures interact with the turbulent blowing air flow and are torn away from the melt film with a mean frequency higher than the rotational frequency of spinner wheels. The complexity and randomness of fibrous flow structures increases from the spinner towards the collecting mesh where the primary layer is formed. Nevertheless, the primary layer formation is quasi-steady when observed on a sufficiently long timescale, and there is little compression of existing layer when new fibers are accumulated. Further research should investigate the effect of the blowing air velocity on fiberization. Also relevant for more in-depth research is the process of primary layer formation, particularly with regard to the influence of suction flow velocity and pressure on the structure and density of deposited fibrous layer. 4 ACKNOWLEDGEMENTS The authors acknowledge the financial support from the Slovenian Research Agency - ARRS (research core funding No. P2-0401, and grant Z7-8271). 5 NOMENCLATURES G image gray level, [-] h primary layer thickness, [m] hmax maximum primary layer thickness, [m] Im relative cumulative mass of deposited fibers, [-] L fiber length, [m] Lm mean fiber length, [mm] mF mass of fibers collected on the mesh, [kg] mM mass of poured melt batch, [kg] M relative mass flow of fibers, [-] Oh Ohnesorge number, [-] Q volume flow rate of melt, [m3/s] qB volume flow rate of blowing air flow, [m3/s] qS volume flow rate of suction air flow, [m3/s] R spinner wheel radius, [m] t time since the start of melt pouring, [s] T melt pouring temperature, [°C] Tg melt glass transition temperature, [°C] u wheel circumferential velocity, [m/s] v melt velocity, [m/s] vB blowing air velocity, [m/s] w ratio of wheel/melt film circumferential velocity to blowing air velocity, [-] W acquisition window width, [m] We Weber number, [-] Y melt surface tension, [N/m] n relative fiberization efficiency, [-] p melt viscosity, [Pa-s] p melt density, [kg/m3] y liquid impingement position, [°] aG normalized standard deviation of image gray level, [%] aL normalized standard deviation of fiber length, [%] m angular velocity of the wheel, [rad/s] 6 REFERENCES [1] Lin, J.Z., Liang, X.Y., Zhang, S.L. 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D0l:10.5545/sv-jme.2019.6523 Original Scientific Paper Received for review: 2019-12-19 Received revised form: 2020-04-02 Accepted for publication: 2020-04-15 Analysis of the Screening Accuracy of a Linear Vibrating Screen with a Multi-layer Screen Mesh Hongwei Yan - Yajie Li - Fei Yuan - Fangxian Peng - Xiong Yang - Xiangrong Hou North University of China, School of Mechanical Engineering, China This paper investigates the screening characteristics of the multi-layer vibrating screens. A portable linear screen with a three-layer screen mesh and the vibrating screening experimental platform were designed and simulated. Based on the discrete element method (DEM), the influences of the motor excitation frequency, the pulverized coal mass flow rate, and the shape of the particles on the screening accuracy of each layer of the screen and the total energy contained in the particles were analysed. The simulation analysis found that, during the vibration screening process, with the increase of the frequency of motor excitation, the screening accuracy of each screen layers increased first and then decreased. The ratio of the sieving accuracy of the first screen and the third screen is reduced first and then increased. The energy contained in the particles gradually increases. With the increased pulverized coal mass flow rate, the screening accuracy of each layer gradually decreased, while the ratio of the screening accuracy of the first layer to that of the third layer gradually increased. The energy contained in the particles gradually decreases. Similarly, the increased percentage of non-spherical particles generated slightly decreased screening accuracy and an increased ratio of the screening accuracy of the first and third screens. The particles also contain much less energy than spherical particles do. A simulation was carried out on the vibrating screening experimental platform with screening materials such as soybeans and red beans. The experimental results matched the discrete element simulation. The screening accuracy was proved to be higher when the excitation frequency lay in 18 Hz to 20 Hz, and the particles mass flow rate stayed below 0.4 kg/s. This study demonstrated that changing the shape of particles is a practical way of managing real screening work. It also provided a theoretical basis and reference for the design and applications of multi-layer vibrating screens. Keywords: vibration sieve, discrete element method, screening accuracy, excitation frequency, mass flow rate, particle shape Highlights • According to the design requirements, a three-layer linear vibrating screen is established. • Taking the excitation frequency, the mass flow rate and the shape of particles as variables, the screening accuracy of the vibrating screen is simulated and analysed by using the discrete element method and verified by experiments. • This paper analyses the screening efficiency, the ratio of the first screen to the third screen, and the energy content of particles. • Adjusting the proportion of non-spherical particles can make the simulation results closer to the actual working process. • The results show that the optimum excitation frequency is 18 Hz to 20 Hz, and the maximum mass flow rate is less than 0.4 kg/s. 0 INTRODUCTION A linear vibrating screen has many advantages, such as large material handling capacity, long service life, easy maintenance, etc. It has been widely used in coal mining, the chemical industry, the medical industry, etc., [1] and [2]. With the increasing accuracy requirements for screening materials, existing vibrating screens (such as ZKB-type vibrating screens) have been unable to meet current production needs because of its single motion trajectory and low screening accuracy, [3] and [4]. Therefore, it is necessary to explore a new method to simulate and analyse the running state of material particles on the vibrating screen for the problem of the low screening efficiency of current vibrating screens. The discrete element method (DEM) was first proposed by Cundall [5] and [6], of the Royal Academy of Engineering and American Academy of Engineering, based on the principle of molecular dynamics in 1971. It is an analytical method for discrete granular materials. Its basic idea is to treat the whole medium as composed of a series of discrete and independent particle elements, which have certain geometric, physical, and chemical characteristics; motion is controlled using a conventional motion equation. The deformation and evolution of the whole medium are described by the movement and position of each element. By tracing and calculating the micromotion of each element, the macro-motion law of the whole research object can be obtained. At present, the research mainly takes the traditional single-layer screen vibrating screen as the research object and develops the related screening accuracy theory. Zhao et al. [7] and [8] carried out a three-dimensional discrete element simulation on the vibrating screening process to study the influence of the vibration parameters of the vibrating screen on the screening efficiency of the material during the screening process. Li et al. [9] and [10] proposed *Corr. Author's Address: North University of China, School of Mechanical Engineering, Taiyuan, China, aweigeyan@nuc.edu.cn 289 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 289-299 that the increase of vibration intensity can improve the screening efficiency of materials to a certain extent but would also increase the loss of materials during the screening process. Elskamp and Harald [11] and [12] conducted vibratory screening research on materials with different particle sizes and shapes. It was found that when the horizontal velocity component of the material is higher than the vertical velocity component, the screening accuracy of the material is higher; otherwise, the screening accuracy is reduced. Dong and Yu [13] studied the influence of the size and shape of the vibrating screen pore on the screening efficiency and analysed the screening of materials under different geometric parameters of the vibrating screen. Suitable motor excitation frequency and the mass flow rate of the particles can improve the screening accuracy, and it is also an important parameter to measure the screening accuracy of the vibrating screen. Therefore, the linear vibrating screen is taken as the research object, with the shape of material particles, the mass flow rate and the excitation frequency of motor as the control variables. The discrete element method is used to simulate and analyse the influence law of the screening precision of each layer of sieve, which provides a reference for further understanding the screening mechanism of the particle group on the multi-layer sieve vibrating screen. 1 STRUCTURAL DESIGN OF LINEAR VIBRATING SCREEN Based on the traditional ZKB vibrating screen, an optimization scheme is proposed to design a portable linear vibrating screen containing a multi-layer screen. The structure is mainly composed of a sieve hopper, a screen frame, a column, a screening motor and a screen, and is fixed on the bottom plate. Fig. 1 shows the three-dimensional model of the vibrating screen. The two screen motors are arranged on both sides of the vibrating screen, and the output end is connected to the eccentric wheel with eccentric block. The eccentric wheel rotation generates a certain intensity of exciting force. The component forces parallel to the direction of the screen offset each other, while the component forces perpendicular to the direction of the screen are superimposed on each other, to increase the throwing index of the vibrating screen and improve the vibration intensity. Based on the theory of dynamic balance and Lagrange dynamics theory analysis, it is concluded that the spatial motion trajectory of any point on the vibrating screen is like an ellipse, and the relationship between the stiffness of the supporting spring and the relative sensitivity of the screen vibration is analysed, [14] and [15]. The geometric parameters of this vibrating screen member are shown in Table 1. Fig. 1. Portable linear vibrating screen model Table 1. Shaker design size parameters Name Geometric parameters [mm] Total length 390 Total width 310 Total height 417 Screen length 300 Screen width 150 Eccentric radius 12 Front pillar height 180 Rear pillar height 224 2 DISCRETE ELEMENT MODEL In this paper, the discrete element method is used to simulate the motion of particles on a vibrating screen. Its parameter input includes the physical properties of particles and geometry, the contact model, etc. [16] and [17]. First, the geometry model is imported, and the material properties of the pulverized coal particles and the screen are input, as shown in Table 2. The factors affecting the accuracy of the sieve are mainly the shape, size, concentration ratio, mass flow rate, related geometric parameters, and related geometric parameters, including excitation frequency, vibration direction angle, etc. According to Zhang [18] and [19], the research on the effect of coal crushing found: the particle size 290 Yan, H.W. - Li, YJ. - Yuan, F. - Peng, F.X. - Yang, X. - Hou, X. R. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 289-299 Table 2. Material property parameter Item Density [kg/m3] Elastic recovery coefficient Static friction factor Rolling friction factor Poisson's ratio Shear modulus [GPa] Pulverized coal 1300 0.5 0.6 0.05 0.3 1 Screen 7861 0.5 0.4 0.05 0.29 79.9 Fig. 2. Non-spherical particle model; a) 0.7 mm; b) 1.4 mm; c) 2.8 mm; and d) 5 mm of coal powder crushing is mostly concentrated in 0.5 mm to 5 mm. Therefore, the screen mesh size is set to 5 mesh, 10 mesh, and 18 mesh in the design process of the vibrating screen, respectively. The relative particle size (the ratio of particle size to mesh size) is 0.7. Therefore, the pulverized coal particles are set to spherical particles of 0.7 mm, 1.4 mm, 2.8 mm, and 5 mm, respectively. The concentration ratio is 1:1:1:1, and the total mass is set to 0.3 kg. The vibration form of the vibrating screen is simplified as follows: the amplitude is 1.5 mm, the swing angle is 0.5°, and the vibration direction angle is 45°. To simulate the screening situation as well as possible, four kinds of particles were structurally improved, and their corresponding aspheric particle models were designed. The method of equivalent radius is chosen as the method of equivalent volume radius, with which spherical particles and non-spherical particles have the same volume, different shapes, but equal mass [20]. Fig. 2 shows four non-spherical particle models. At present, particle contact models are mainly divided into hard sphere model and soft sphere model. The hard sphere model does not consider the deformation of particles. It is described by the coefficient of recovery and the coefficient of friction. Based on the law of momentum conservation, the integral result of force to time is described as the velocity change before and after particle collision. It is mainly used in the numerical model of fast motion and low concentration particle system. The model simplifies the contact force between particles by elastic and damping coefficients and calculates the contact force according to its normal overlap and tangential displacement. Thus, the velocity variation of particles can be obtained, which is more suitable for the numerical simulation of engineering problems. The soft sphere model uses the elastic and the damping coefficient to simplify the contact force between the particles. The contact force is calculated according to the normal overlap amount and the tangential displacement, so that the velocity variation of particles can be obtained, which is more suitable for numerical simulation of engineering problems. Therefore, the soft sphere model is used to simulate the collision behaviour between particles in the screening process, [21] and [22]. Its mathematical model is shown in Fig. 3. ¿il rVVV\Ai where dn is normal damping, kn is normal stiffness, dt is tangential damping, kt is tangential stiffness, dr is rolling damping, and dk is rolling stiffness. According to the theory of the mechanics of particulate matter, the motion analysis equation of the /h particulate matter can be expressed as follows: Analysis of the Screening Accuracy of a Linear Vibrating Screen with a Multi-layer Screen Mesh 291 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 289-299 dvi ^nhi^ ^ \ jM *, + T s j=1 where mt is the mass of inertia of spherical particles, is the and moment of inertia of spherical particles, n is the total number of spherical particles, vt is the movement speed of material particles, and mt is the rotational angular velocity of material particles. Among them, FniJ (the normal force), FtiJ (the tangential force), TtiJ (the tangential moment), T,y (the friction torque) can be obtained according to the theory of mechanical properties of granular materials, [23] and [24]. 3 SIMULATION ANALYSIS The movement state of the material particles on the vibrating screen is as follows: when the screening starts, four kinds of material particles are generated in a certain proportion in the granular factory. When the motor rotates at a certain frequency, the vibrating screen also periodically vibrates, the material particles on the net are thrown forward. Under the dual effects of the excitation force and gravity, the particles and the screen frame come into contact and collide to generate energy exchange, which causes the particles to move relative to each other. Particles with a particle size smaller than the mesh size of the screen are screened, while particles having a larger particle size remain on the screen surface until they exit the discharge port. Fig. 4 shows the screening status of the vibrating screen in the simulation. This paper mainly analyses the running state of material particles on the vibrating screen, taking the motor vibration frequency, particle mass flow rate and its shape and concentration ratio as the control variables, taking the screening accuracy of each screen layer and the ratio of the screening accuracy of the first layer to the third layer as the research variables, and the scheme with the highest screening accuracy under this condition is selected. 3.1 Influence of Vibration Frequency on Screening Accuracy The vibration frequency of the motor affects the transmission capacity of the vibrating screen and affects the stability of the particle flow screening. According to the discrete element simulation analysis, the screening accuracy of each screen layer is changed, as shown in Fig. 5, under different vibration frequencies. From Fig. 5, it can be seen that with the increase of motor vibration frequency, the screening accuracy of each screen layer increases first and then decreases. When the vibration frequency is 16 Hz, the screening accuracy of the first layer screen is the highest, reaching 95.6 %; when the vibration frequency is 18 Hz, the screening accuracy of the second layer and the third layer screen is the largest, respectively 94.5 % and 91.2 %. Under the same vibration frequency, the screening accuracy of each screen layer is also different. The screening accuracy of the upper screen is always slightly higher than the screening accuracy of the lower screen. This is because the first screen is screened by four different particle sizes, while the third screen only screens particles with the smallest size, so the first layer screen has higher screening accuracy than other screens. The screening precision ratio of the first layer screen and the third layer screen is as shown in Fig. 6. 100 90 80 70 60 50 —First layer screen - - Second layer screen —Third layer screen Fig. 4. Simulating the screening process of vibrating screen Motor excitation frequency [Hz] Fig. 5. Relationship between excitation frequency and screening accuracy It can be seen from Fig. 6 that as the vibration frequency of the motor increases, the ratio of the 12 14 16 18 20 22 24 26 28 292 Yan, H.W. - Li, YJ. - Yuan, F. - Peng, F.X. - Yang, X. - Hou, X. R. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 289-299 screening accuracy of the first layer screen and the third layer screen decreases first and then increases. When the vibration frequency is 18 Hz, the ratio of the screening accuracy of the first layer to the third layer is at least 1.04. Currently, the screening accuracy of each layer of the screen is also relatively high. As can be seen from Fig. 6, when the vibration frequency of the motor is too low or too high, the shielding precision of each layer of the screen is relatively low, and the shielding precision ratio of each layer of the screen is also large. The reason for this phenomenon is shown in Fig. 7. increases, the energy contained in the particles gradually increases, indicating that the collision between particles is intensified, and the screening process can be completed, and the screening time is gradually shortened. When the excitation frequency is increased to 24 Hz, because the excitation frequency is too large, the particles collide violently, the energy obtained is also large, and the screening time is also significantly shortened. However, a large number of small particles come out of the screen in advance with the large particles, and the screening efficiency is greatly reduced. 8.X1 1 12 14 24 26 16 18 20 22 Motor excitation frequency [Hz] Fig. 6. Relationship between excitation frequency and screening accuracy ratio 28 a) b) Fig. 7. Schematic diagram of pulverized coal screening at different frequencies; a) f = 12 Hz; and b) f = 28 Hz Fig. 7 shows the vibration screening state of the 2 s time node. It can be seen in Fig. 7 that when the motor vibration frequency is as low as 12 Hz, the material particles cannot obtain energy through contact collision, and it is difficult to be effectively thrown loose. There is a large amount of material at the inlet of each layer of the screen, severely hindering its passage. When the motor vibration frequency is as high as 28 Hz, the particles collide violently, get too much energy, make it fly about in the air, fill the vibrating screen and even fly away from the screening area, greatly reducing screening accuracy. From an energy point of view, when the excitation frequency is 12 Hz, most 5 mm particles remain on the upper sieve within the specified sieving time. The particles have no or only a small amount of energy and are difficult to move. As the frequency 2 12 14 24 26 16 18 20 22 Motor excitation frequency [Hz] Fig. 8. Energy relationship of particles at different excitation frequencies Therefore, the optimal excitation frequency is about 16 Hz to 20 Hz. 3.2 Influence of Mass Flow Rate on Screening Accuracy During the screening process, different mass flow rates are bound to have an impact on the screening accuracy of the pulverized coal on each layer of the screen. According to the discrete element simulation analysis, the relationship between different mass flow rates and the screening accuracy of each layer of mesh is shown in Fig. 9. 100 90 80 70 60 50 40 —First layer screen - - Second layer screen —Third layer screen 0.3 0.4 0.5 0.6 m Mass flow rate [kg/s] Fig. 9. Relationship between mass flow rate of pulverized coal and screening accuracy It can be seen from Fig. 9 that as the mass flow rate of the pulverized coal increases, the screening accuracy of each layer of the screen is accelerated to decrease. When the mass flow rate of pulverized coal 6 4 Analysis of the Screening Accuracy of a Linear Vibrating Screen with a Multi-layer Screen Mesh 293 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 289-299 is 0.1 kg/s, the screening accuracy of the first layer screen is the highest, at about 96.38 %. When the mass flow rate is 1 kg/s, the screening accuracy of the third layer screen is the lowest, about 42.41 %. This is because when the mass flow rate of the pulverized coal is small, the amount of pulverized coal flowing into the screen at the same time is small, and the pulverized coal can be sufficiently thrown under the action of the exciting force, thereby facilitating the sieving of the pulverized coal. When the mass flow of pulverized coal is large, more pulverized coal flows into the screen at the same time, which is not conducive to the loosening of the pulverized coal by contact collision, which, in turn, is not conducive to the sieving of coal powder. When the mass flow rate of pulverized coal is constant, the screening accuracy of each screen layer is also that the screening accuracy of the upper screen is slightly higher than that of the lower screen. The screening accuracy ratio of the first layer screen and the third layer screen is as shown in Fig. 10. 1.7 1.6 _ ^ 15 - o § 1.4 _ o 0 ° 1.3 ii I 1.2 - 4 / V5 Kd2 / Kg / Kd5 Kd3 / Kg / Kdg Kd5 / Kj / Kg Kd5 / Kj / Kd4 Kd5 / K i / Kt d5 e Z Z e The corresponding membership function is shown in Fig. 7. The control method for the ATV is expressed as follows: (1) When the deviation of the distance and heading angle is high, Kp assumes a higher value for a fast response. With a decrease in the total deviation, the increase in Kp enables the vehicle to maintain the current direction approaching the pre-set path. When the distance deviation of the articulated tracked vehicle is further reduced, the heading angle is the main deviation, and the Kp should be higher. (2) The parameter K is primarily used to eliminate the residual error caused by the proportional link. Although the parameter can improve the control accuracy and accelerate the response of the system, it can also make the system produce higher oscillation amplitudes. In the process of approaching the pre-set path, K should be smaller when the deviation of the distance and heading angle is high to avoid excessive oscillation of the system. When the deviation is small, increasing K can correspondingly improve the accuracy of the system. After passing the marking line, K is higher to increase the response speed of the system and make the vehicle return to the pre-set path as soon as possible. (3) Parameter Kd has an excellent regulating effect on the dynamic characteristics of the system. When Fig. 7. Membership function of PID controller parameters the deviation of distance and heading angle is large, Kd assumes a higher value to reduce the shock of the system. When the deviation of the Fig. 8. Relationship between fuzzy control output variables and input variables 318 Cui, D. - Wang, G. - Zhao, H. - Wang, S. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 311-324 Fig. 9. Control block diagram of the fuzzy PID controller using RecurDyn/Simulink system is small, the Kd value is reduced, to enable the integral link to adjust the error better and to increase the adjusting precision of the system. The fuzzy rule for the control system, which is designed based on previous work in [20] and [34] and modified through simulation tests, is shown in Table 1. The relationship between the inputs and outputs are shown in Fig. 8. straight path in AT-plane. It can be seen from these figures that the overshoot by the classical PID controller is approximately 26 % and settling time is approximately 110 s, while the overshoot by the fuzzy PID controller is approximately 15 % and the settling time is approximately 90 s. The fuzzy PID shows faster response and less overshoot than the classical PID controller because of the fuzzy system. 3 SIMULATION RESULTS To verify the effectiveness of the controller proposed in this paper, a virtual prototype simulation analysis is conducted in two typical driving conditions of the ATV The accuracy of the vehicle path-tracking control system is determined by analysing the distance and heading angle deviations between the actual path and the pre-set path of the vehicle during driving. The main parameters of the model are shown in Table 2. The Simulink control block diagram of the controller is shown in Fig. 9. For the straight driving condition, the initial distance and heading angle deviations between the centre of mass of the ATV and the pre-set path are 5.6 m and 30°, respectively. The driving speed of the centre of mass of the vehicle is 0.56 m/s. The results of two controllers for the straight driving condition are shown in Fig. 10. Fig. 10a and Fig. 10b illustrate the time-history of the distance deviation and heading angle deviation of the ATV, respectively. Fig. 10c shows the trajectory of the ATV and reference Table 2. Design parameters for simulation Values Ground contact length: l 1953 mm Mass: m 14.78 t Vehicle Parameters Track gauge: b 1500 mm Track width: h 600 mm Pitch radius of the sprocket: r 375 mm Distance from the articulation point to the centre of mass: d 2625 mm Soil shear deformation modulus: K 0.02 m Apparent cohesion: c 70000 Angle of internal shear: $ 0.67 Terrain Friction coefficient between 0.9 Parameters the tracks and the terrain: / Coefficients of lateral motion resistance: /1 0.8 Coefficients of longitude motion resistance: /f 0.6 For the curved driving conditions, the pre-set path is an arc with a radius of 25.2 m, and the initial distance and heading angle deviations are both zero, Research on a Path-Tracking Control System for Articulated Tracked Vehicles 319 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 311-324 a) b)=: Fig. 10. Simulation results for the two controllers in a straight trajectory; a) distance deviation, b) heading angle deviation, and c) trajectory of the XY-plane a) b) 0 5 10 15 20 25 c) x[m] Fig. 11. Simulation results for the two controllers in a circular trajectory; a) distance deviation, b) heading angle deviation, and c) trajectory of the XY-plane and the driving velocity of the vehicle is 0.56 m/s. Fig. 11a and Fig. 11b show the time-history of the distance deviation and heading angle deviation and Fig. 11c shows the trajectory of the ATV. From Fig. 11, it can be understood that by using the fuzzy system for tuning the PID gains improves performances. 4 EXPERIMENTAL VERIFICATION The control effect of the ATV path-tracking control system is experimentally investigated to verify the fuzzy PID control algorithm. The overall scheme of the ATV path tracking control test platform is shown in Fig. 12. The test platform is composed of the ATV test prototype, data acquisition and processing scheme, and computer control system. The latter is mainly employed to run the path tracking control system based on visual navigation and collect and analyse relevant data. Image acquisition Image binaryzation Fuzzy-PID controller Execution deviee Trajectory fitting Computer LabVlEW Deviation calculation Eg. (32) cRIO contrôler module Driver DC motor t i i I r* Linear actuator Track sprockets Experimental articulated tracked vehicle Fig. 12. General scheme of the path tracking control test platform Sprocket DC-motor Fig. 13. Overview of the path-tracking control test platform In the experiment, the pre-set path is set on the horizontal ground. A reduced scale model was employed for the experimental prototype with a ratio of 14:1. Since the purpose of the experiment is to c) 320 Cui, D. - Wang, G. - Zhao, H. - Wang, S. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 311-324 verify the feasibility of the control algorithm based on visual navigation, the adoption of a small-sized model is acceptable. The data acquisition and processing scheme are input into the computer control system to obtain the running state of the test prototype in the process. The fuzzy PID controller provides the control commands to the actuator of the ATV to follow the pre-set path. The path tracking control platform based on visual navigation is shown in Fig. 13. a) d) -S 2 ¿5 ^ I- Left track (front vehicle) Right track (front vehicle) Left track (rear vehicle) Right track (rear vehicle) ¡A 0 20 80 100 40 60 e) Tim« M Fig. 14. Experimental results from a straight path; a) distance deviation, b) heading angle deviation, c) trajectory of the XY-plane, d) articulated angle of rotation and e) velocities of sprockets A monocular camera is used to collect road information in front of the test prototype. The collected image is processed using binarization to identify clear landmark information. A matrix is created by extracting the values of each pixel in the binary image. The sudden change in pixel values is determined and recorded from the starting position to obtain the centreline coordinates of the navigation line. The least-squares method is used to fit the centreline coordinates, and the fitting curve of the road navigation line is obtained. According to the similarity principle and the triangle relationship, the lateral deviation ey and heading angle deviation ev can be calculated. According to the road navigation information collected by the visual navigation path-tracking system and by using the designed fuzzy PID controller, the test prototype is automatically controlled to run along the pre-set path. The distance and heading angle deviations between the actual running and the pre-set path and the track speed on both sides of the prototype are analysed in straight and curve driving conditions. In the straight travelling condition, the initial distance and heading angle deviations between the centre of mass and the path of the test prototype are 0.4 m and 30°, respectively. The speed of the driving track is set to 0.1 m/s. Fig. 14a and 14b illustrate the variation in the distance and heading angle deviations with time. Fig. 14c shows the trajectory in the XY-plane. The control inputs are shown in Fig. 14d and 14e. In the case of driving along a curved path, the pre-set path is a curve with a 2.5 m radius. The initial distance and heading angle deviations between the centre of mass and the pre-set path are 0.4 m and 30°, respectively. Fig. 15a and 15b show the variation in the distance and heading angle deviations with time. The XY-plane motion is shown in Fig. 15c. The corresponding control inputs are demonstrated in Fig. 15d and 15e. According to the tests and analysis, the control system can effectively realize the path tracking of the ATVs by adjusting the sprocket velocity of both sides and the deflection angle of the articulated points in accordance with the different driving paths. 5 CONCLUSIONS A control system for path-tracking for an ATV based on the fuzzy PID algorithm is proposed in this study. The control system uses the distance and heading angle deviations between the actual trajectory and the pre-set path as inputs, and the outputs are the b) c) Research on a Path-Tracking Control System for Articulated Tracked Vehicles 321 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 311-324 Fig. 15. Experimental results from a circular path; a) distance deviation, b) heading angle deviation, c) trajectory of the XY-plane, d) articulated angle of rotation and e) velocities of sprockets deflection angle and track velocity on both sides of the ATV. The fuzzy PID controller is the core of the control system, which adjusts the parameters Kp, Ki, and Kd according to the prescribed fuzzy rules to achieve effective vehicle tracking. The mathematical model of the ATV is proposed, and a virtual prototype model of the ATV is established in RecurDyn. The validity of the virtual prototype model is verified by a simulation comparison between the prototype and mathematical models. A fuzzy PID control system model is established in Simulink, and the virtual prototype co-simulation analysis is conducted for two typical working conditions, i.e., straight and curve path travelling. The simulation results show that the ATV can effectively track the pre-set path under the control of the fuzzy PID controller. An ATV path tracking control test platform that is based on visual navigation was developed to test the effects of the control system in a practical application. The vision navigation system is used to collect path tracking information. The fuzzy PID controller is applied for real-time control of vehicle tracking. The distance and heading angle deviation variations during tracking are analysed using the path tracking test for straight and curved driving paths, and the deflection angle and track speed on both sides of the articulated track are adjusted. The experimental results show that the ATV tracking control system is effective in practice. 6 ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant No. 51775225) 7 NOMENCLATURES x - y centroid point velocity component of front vehicle, [m/s] centroid point velocity component of front vehicle, [m/s] yaw angle, [rad] deflection angle between the front vehicle and the rear vehicle, [rad] side slip angle, [rad] centroid coordinates of front vehicle in global coordinate system, [m] front and rear vehicle centroid velocity, [m/s] mass of the single vehicle, [kg] grounding length of the crawler, [m] track gauge, [m] distance between the centre point and the articulated point, [m] width of link pad, [m] the moment of inertia of the single vehicle, [kgm2] track slips of front vehicle track slips of rear vehicle mL, mR sprocket velocity of front vehicle, [rad/s] mL', mR sprocket velocity of front vehicle, [rad/s] actual velocity of the crawlers of front vehicle, [m/s] x - y V- V' Ô P- P' X- Y v- v' M L B D H Iz iL, iR iL, iR VL, VR 322 Cui, D. - Wang, G. - Zhao, H. - Wang, S. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 311-324 vL\ vR actual velocity of the crawlers of rear vehicle, [m/s] Fl , Fr tractive force of the crawlers of the front vehicle, [N] Fl, FR tractive force of the crawlers of the rear vehicle, [N] Rl , Rr longitudinal resistance of the front vehicle, [N] Rl, RR longitudinal resistance of the rear vehicle, [N] Ftx, Fy force component between front vehicle and articulated point, [N] Ftx', Fy force component between rear vehicle and articulated point, [N] M drag moment of centroid point in front vehicle, [Nm] M' drag moment of centroid point in rear vehicle, [Nm] Fmax maximum tractive force produced by a track, [N] Tmax maximum shear strength of the terrain, [N/m2] c apparent cohesion, [N/m2] $ angle of internal shearing resistance of the terrain, [N/m2] p normal pressure, [kPa] K soil shear deformation modulus, [m] coefficient of longitudinal motion resistance, [-] ^ T coefficients of lateral motion resistance, [-] fy, fy lateral resistance force of the front vehicle and rear vehicle respectively, [N] 50, 50' longitudinal slip of track velocity instantaneous centre, [m] Mj, M} turning moment produced by longitudinal forces, [Nm] Mr, Mr' turning moment produced by lateral forces, [Nm] Xr, Yr, yr components of reference pose, [-] ex, ey, ew deviation components between current pose and reference pose, [-] Kp proportional gain, [-] K integral gain, [-] Kd derivative gain, [-] 8 REFERENCES [1] Watanabe, K., Kitano, M., Fugishima, A. 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D0l:10.5545/sv-jme.2019.6379 Original Scientific Paper Received for review: 2019-10-11 Received revised form: 2020-04-07 Accepted for publication: 2020-05-11 Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan Vytautas Martinaitis - Dovydas Rimdzius - Juozas Bielskus - Giedre Streckiene* - Violeta Motuziene Vilnius Gediminas Technical University, Department of Building Energetics, Lithuania Flow-mixing is common in technological processes, and both ejectors and turbofans can produce an interaction between flows with different energy potentials. Ejectors have been extensively used, and their analytical models have been widely presented. To the best of the authors' knowledge, there is a lack of studies exploring the efficiencies of turbofans. The goal of this paper is to compare thermodynamic processes in these devices. Their efficiencies are compared in terms of compression and entrainment ratios. A comprehensive one-dimensional subsonic thermodynamic models of the ejector and turbofan are presented. The quantitative indices are obtained for the same initial conditions expressed as the ratio of differences in enthalpies for ideal compression and ideal expansion. When initial conditions are equal to the numeric value of the combination of the isentropic efficiency of the evaluated components (numerical case 0.16), both devices have the same efficiencies; at lower initial conditions (numerical case 0.10), a turbofan's entrainment ratio is 1.5 times and compression efficiency 1.25 times higher; at higher values of initial conditions (numerical case 0.28), the ejector is more efficient. Such distinctive characteristics of turbofans and the nature of their variation may correspond to the specific application areas of technological equipment that require certain flow-mixing parameters. Keywords: ejector, turbofan, thermodynamic model, flow mixing, efficiency of compression, entrainment ratio Highlights • Thermodynamic processes of gas mixing in the ejector and the turbofan are compared. • The efficiency of compression and entrainment ratios are compared in subsonic mode. • When entrainment ratios are low, the ejector is more advantageous than turbofan. • Turbofan can be applied where a relatively higher passive flow rate is required. • Isentropic efficiencies are highly dependent on the features of each component. 0 INTRODUCTION Flow-mixing processes are common in the devices of many technological systems. These processes are realized in components such as ducts, nozzles, diffusers, throttling valves, mixing chambers, turbines, compressors, and ventilators. Mixing flows with different parameters in the mixing chamber are usually aimed at the increase of the efficiency and operational abilities of these devices. The presented analysis relates to different flow-mixing devices in which the mixing of two gas flows takes place due to different energy potentials. Such cases are sketched in Fig. 1. The ejector (Fig. 1a) is a very well-known device, and the roof turbine ventilator (Fig. 1b) has become ubiquitous over the last decade as a device using renewable wind energy for building ventilation. Turbofans - gas mixers (Fig. 1c) are used rarely, although they have been known for a long time as gas burners' mixers. Despite similarities with other mentioned devices, turbofans - engines (Fig. 1d) will not be discussed further because of their complexity and significant differences in scope of operation compared to other above-described mixers. The roof turbine rotor (Fig. 1b) on the side from which the wind blows operates as turbine, and as a fan from the opposite side. Ejection processes are also happening in it. During the operation of this device, very complex processes occur, which could be why, to the best of the authors' knowledge, there has been no theoretical, thermodynamic model to describe the operation of the roof turbine ventilator to date. In the provided examples, the interaction and mixing between flows that have varying energy potentials are common. The models of classical thermodynamic analysis enable understanding the operation of the technical system; determing the places and causes of the irreversibility of energy conversion processes, as well as comparing the performance of the technical systems that are described in the same way. This paper focuses on a conceptual comparison of the two shown devices: the ejector (Fig. 1a) and the turbofan-gas mixer (Fig. 1c). The ejector will be used as baseline for such comparison, as ejectors thermodynamic models have strong practical and scientific validation. The turbofan (Fig. 1c) has a separated turbine and fan; therefore, it preliminary comparison requires less debatable assumptions (e.g. in comparison to the roof turbine ventilator (Fig. 1b)) and has a close logical sequence same as ejector. *Corr. Author's Address: Vilnius Gediminas Technical University, Department of Building Energetics, Sauletekio ave. 11, Vilnius, Lithuania, gie-dre.streckiene@vgtu.lt 325 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 Nowadays, the application of ejectors has spread to various thermal engineering facilities. Ejectors are used in various areas: vapor-compression refrigeration systems [1]; in buildings and vehicles ventilation [2], district heating [3], etc. However, recently the application and improvement of ejectors in refrigeration equipment has been at the centre of most studies [4]. A review of various research on the mathematical models of the hydrodynamic and thermodynamic nature of the ejector is provided in [5]. The thermodynamic model of the ejector is developed based on balance equations of mass, momentum and energy with specific interpretations for the ejector or its sections. According to the review [5] in the majority of cases the flows inside the ejector can be treated as steady and one-dimensional. The friction of flows and non-ideal mixing leads to a non-isentropic process, which is evaluated by isentropic efficiencies in the nozzle, mixing and diffuser sections [1] and [6]. The compression efficiency of the ejector [5] and [7] is evaluated in terms of the energy recovered by the secondary flow with respect to the energy available in the primary flow. The above-mentioned ejectors' models [5], characteristics of their properties [1] and [8] are widely validated experimentally or tested in practice. As was mentioned and shown above (Fig. 1c), a turbofan has a turbine and fan located on a common axis. There are application examples in which the renewable energy driven wind turbine is employed to rotate fans to ventilate road tunnels [9]. This type of turbofan is often applied in industrial applications [10] when burning natural gas. When discussing the turbofans, one should bear in mind the idiosyncrasies of microturbines [11]. These devices were first used in dental medicine [12] before spreading to small-scale energy systems [13] or other micro systems [14]. In the context of the present analysis, it is important to note that the performance indicators of microturbines differ significantly from traditional energy turbines [15]. There are dozens of patents, the majority of which involve gas burners [16] and [17]. Unfortunately, scientific papers rarely focus on such specifics; to the best of authors' knowledge, no thermodynamic models opeartions are described in a manner similar to the way ejectors are described, which hinders the preliminary assessment of their applicability. The distinctive characteristics of turbofans as well as the nature of their variation may correspond to the specific application areas of the technological equipment (e.g. ventilation, air conditioning, refrigeration), which require certain flow-mixing parameters. These may be relatively new areas, such as personalized ventilation [18], compressed air energy storage [19], or integration in road tunnel ventilation [9] and [20]. When considering the potential Fig. 1. Devices, the functionality of which is obtained by using the potential and kinetic energy of flows by mixing them: a) ejector; b) roof turbine ventilator; c) turbofan - gas mixer; d) turbofan - engine 326 Martinaitis, V. - Rimdzius, D. - Bielskus, J. - Streckiené, G. - Motuziené, V. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 application of a turbofan, preliminary indications about the basic characteristics, such as the efficiency of compression and entrainment ratios, are required. For these applications, supersonic flow is not typical, so the methodology developed below in the paper is limited to the analysis of subsonic modes. There is a knowledge gap regarding which turbofan or ejector is superior or inferior to each other. The goal of this paper is to compare thermodynamic processes in the ejector and the turbofan when they have the same initial states of active and passive flows. The path to obtaining a turbofan's characteristics based on the adapted thermodynamic model of the ejector was chosen. The proposed model is compared to well-known, broad-mode and fluid range validated ejector thermodynamic models. The latter have been modified and detailed here to allow symmetric comparison of ejector and turbofan thermodynamic models. It is very important to determine the internal irreversibility (losses) of the processes. Quantitative indicators required to solve the tasks are defined using analytical, empirical, and numerical models as well as a combination of their equations. The presented preliminary comparison of performance thermodynamic models for the mentioned devices has not been described elswhere in the literature. The present article should be considered as a theoretical or conceptual one. The analytical equations of flow processes and their interpretations found in the textbooks of engineering thermodynamics are chosen for this case and prevail in the article. The authors believe that using/selecting five process irreversibility coefficients for the produced entropy enabled minimizing the empiricism taht common in technical sciences. This article is structured as follows: Section 1 explains the ideal processes in ejector and turbofan. Section 2 describes in detail the adapted thermodynamic model of the process in the ejector. Section 3 presents the thermodynamic model of the turbofan in parallel with the main accents of the ejector model. The assessment and comparison of the main performance indicators (compression and entrainment ratios as the resulting comparative parameters) of both devices for the case study are presented in Section 4. The conclusions are summarized in Section 5. mixing chamber and diffuser. The main components of the TF in Fig. 3 are the air turbine and fan. Fig. 2. Simplified scheme of the ejector (the numbers next to the cross-sections correspond with the indices used in equations and diagrams Fig. 3. Simplified scheme of the turbofan: T - turbine, F - fan The purpose of these devices is to create a mixture that has the required flow mass ratio M = M0/Mj and to provide this mixture with pressure Pm. In both devices, the passive flow of enthalpy h0 (or pressure P0) is induced by the active flow expressed as enthalpy hj (or pressure P1). These flows are mixed, and the mixture attains the state of enthalpy hm (or pressure Pm). The following relationship exists between the states that define these processes: Po < Pm < Pi or ho < hm < hi . (1) 1 IDEAL PROCESSES IN THE EJECTOR AND TURBOFAN Simplified schemes of the compared devices with their characteristic parameters are presented: ejector (EJ) in Fig. 2 and turbofan (TF) in Fig. 3. The main components of the EJ depicted in Fig. 2 are: nozzle, The above-mentioned common states for both devices and related ideal gas processes are shown in the h - s diagram (Fig. 4). At first, consider these processes to be ideal when the internal irreversibility in each section is expressed by ASir = 0 and let us denote states that correspond with that with the ' index. Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan 327 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 In an ideal case, the initial state of active flow is marked as state 1 and for a passive flow 0. For the ideal processes, the initial state of the mixture (3') is on the P0 isobar that connects states 0 and 2'. Finally, the resulting state of the mixture is state 4', which is on the line that connects states 0 and 1. The ratio of ideal compression and ideal expansion (h4,- h3) / (hl - h2) is considered to be an indicator of the identity of the initial conditions of both devices. [kJ/(kg-: Fig. 4. Ideal mixing processes in ejector and turbofan In this case the first law of thermodynamics (FLT) and the second law of thermodynamics (SLT) are expressed as follows: (MjT + M0)/ Mjt h + M0+ h0 = Ail s1 + = ^Mr + (2) (3) The parametric equation resulting from the FLT and SLT enables to determine the specific location of point 4' for the enthalpy and entropy of this mixture: M i si +M cSo M i+M o and h4, = M y K+M 0 ho M y +M o (4) One of the most important indicators of such a process is the ratio between the flow mass rates, entrainment ratio M : M = ^ MM y h - K h - h0 (5) The location of point 4' on the diagram allows determining the pressure Pm of the mixture in the idealized process. Another important performance indicator would be the efficiency of compression, which demonstrates the ratio of the achieved result and the accompanying costs: or Vm = (( + M0) (h 4'- h,')/ My(hy - h Vm =(1 + m) ^ (hi - h2 (6a) (6b) These two indicators together characterize the performance of the device. They must be defined for actual processes, i.e. evaluate the irreversibility of all processes in the devices. Ideal expansion from 1 to 2' and compression from 3' to 4' and relevant actual processes from 1 to 2 and from 3 to 4m for both devices are drawn analogously, as shown in Fig. 5. Thus, from a graphical point of view, i.e. from the first approach, the processes do not differ in these devices. Both in the nozzle of the EJ and the turbine of the TF the conversion of the state of the active component (that has a higher total energy or enthalpy) to another state takes place. However, there is a difference. Transformations linked to kinetic energy take place in the EJ. In the nozzle of the EJ a flow Fig. 5. Energy conversion processes on the h-s diagram in the components of the ejector and the turbofan: a) the turbine (T) and the nozzle; b) the compressor or the fan (F) and the diffuser s,, = 4 328 Martinaitis, V. - Rimdzius, D. - Bielskus, J. - Streckiené, G. - Motuziené, V. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 process takes place, i.e. the energy of the active component is converted to flow velocity C2 (kinetic energy of the flow C| / 2 ). The energy form obtained in the turbine is expressed specific mechanical work of the turbine eT. Analogously, only opposite processes occur in the diffuser and the fan. Actual processes properties depend both on the above mentioned inherent differences of the processes, as well as on specific irreversibility properties of their specific components, which will be discussed further, as thermodynamic models for each device are presented. The processes in this paper are limited to cases in which both fluids are of the same nature and incompressible, and the flow is subsonic. This limitation has no significant effect on the planned essential assessments of the thermodynamic analysis of devices (balance equations and graphical representation) as well as the comparison of processes that take place therein and the efficiency thereof. The thermodynamic statement, when and how much the device with the energy transformation through mechanical work is more efficient than another device, in which the kinetic energy is directly transferred between the two streams, is the interest of this work. This statement will be proven based on equivalent thermodynamic models for both devices. The proposition of such balanced minuteness models is an important part of this study. 2 THE THERMODYNAMIC MODEL OF THE PROCESS IN THE EJECTOR This work compares and discusses the thermodynamic models of two devices, the ejector and the turbofan, designed to prepare a mixture of the selected mass ratio and state for the two ideal gas subsonic flows. We start with the EJ as a widely-known yet specific device used for flow mixing. Its specific feature is that the energy of the active flow (the flow that has a higher total enthalpy) is used to entrain the passive flow (the flow that has a lower total enthalpy) and to provide the mixture thereof with the momentum required to create the potential and kinetic energy of that mixture and to transport it between the devices in the system. The structure of thermodynamic ejectors' models designed to assess the processes that take place and related cases have been presented in the introduction. The model is based on balance equations of mass, momentum and energy for the EJ or its sections. In the majority of cases the flows inside the EJ can be treated as steady and one-dimensional. The specifics of each model usually reflect the objectives and specifics of this paper. The usual sequence is followed in this paper. In order to correctly compare the EJ and TF, certain adjustments have been made. To compare actual and idealized processes they are drawn on the same h - s diagram (Fig. 6). Dry air when subsonic flow is present has been selected for the case study. The influence of air humidity is not investigated as it is negligible in the context of this research. The initial state is 1 (1.9 bar) for the active flow and 0 (1.01325 bar) for the passive flow. The same pressure Pm is to be obtained in the actual process. For this, the mass flow rate from idealized to actual processes should be increased Mi > Mv . In addition, the state of the resulting mixture in this case on this Pm isobar would shift to the right from point 4' to 4m. We will discuss this transformation step-by-step. Fig. 6. The depiction of the analyzed processes in the ejector on the h - s diagram In the actual process, the active flow that flows out of the nozzle expands until it reaches pressure P0, state 2 and velocity C2, which is expressed as follows: C2 =V2( - h) =72( - h)VNs , (7) where nNs= (h1 - h2) / (h1 - h2) - the isentropic efficiency of nozzles (see the h - s diagram). Having thus evaluated the internal irreversibility of the flow in the nozzle, the state of the mixture before the diffuser on the h - s diagram will shift from point 3' to the right AsN = A53. _ 3* to point 3*. Then, after the ideal diffuser we would have the equivalent of point 3* _ point 4* on the pressure line Pm. If we consider the velocity equalizing process of both components in the mixing section as isobaric, P2 = P3 = P0, we can assess the internal irreversibility of this process in terms of the produced entropy Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan 329 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 AsM = As3* _ 3. We have the corresponding enthalpy h3 and the isentropic efficiency of mixing chamber nMs. The authors propose expressing this efficiency, using the process parameters depicted on the h - s diagram, as follows: ^Ms - {¡i - ¡3* {¡i - ¡3 (8) and after the ideal diffuser point 4 on the pressure line Pm would be obtained. When transitioning to the actual diffuser, it is necessary for the velocity C3 at the rear of the mixing chamber (i.e., before the diffuser) to become C4 ~ 0 once the flow reaches the rear of that diffuser on cross-section 4, and that its pressure and enthalpy remain Pm and h4m, respectively. Having linked this to the actual process in the diffuser: c3 '4m - h3 ) = 2 K - h ) = L {h4' - h VDs VDs (9) (h4 " h3 ) (h4' " h3') where ^Ds = --- = --- is the isentropic (h4m - h3 ) (h4m - h3 ) efficiency of the diffuser. In Eq. (9) and the expression of nDs the enthalpy difference was changed in accordance with the equation observed in the process on the h - s diagram, h4 - h3 = h4* - h3* = h4- h3, because isobars Pm and P0 are almost parallel and the distance in the direction of s in terms of the entire diagram is small. Velocities C0, C2 and C3 are related by the process in the mixing chamber, which is denoted by a dashed line in Fig. 2. In quantitative terms, it is defined by the momentum equation using these velocities and corresponding cross-sections: P2 A2 + P0 Ao + MC + M0C0 = = P3 A3 + (M0 + M ) C3 + F2 - 2-3' (10) where F2-3 is the force between cross-sections 2 and 3. When analysing ejectors, it is assumed that the mixing process takes place at a constant pressure P2 = P3 = P0, areas of cross-sections are linked + A = ^3> F2-3 = 0 and C0=0. To assess these assumptions in quantitative terms, in this paper, we propose using the isentropic efficiency of the mixing chamber and the corresponding produced entropy. Therefore the momentum Eq. (10) can be expressed as MjC2^j77Ms = (mM0 + M^ C3 and readjusted as follows: Mn ■C, TT = -1 - or M -1. (11) M, C C3 11 Having used Eq. (7) and Eq. (9), as actual processes take place in the EJ, it follows that: Mn M = - M, - A^Ns^Ms^Ds (h -h) (h4'~ ^ ) -1. (12) Using this equation we can find the actual flow rate of the active fluid Ail under actual conditions of the process efficiency, evaluated by nNs, nMs, nDs. The initial state of the active flow, according to the h - s diagram, is 1 and the initial state of the passive flow (flow to be transported) is 0 and its mass flow rate M0. When analysing the h-s diagram, these initial conditions can be expressed as follows: h4' - h0 hA* - h' 1 - h - h -i3- --— or M'=-1—0- -1, (13) h1 - h0 h1 - hr 1 + M' h4' - h0 and then the equation that expresses the relationship between the main indicators of the actual and ideal ejectors (i.e., the entrainment ratio and coefficients of isentropic efficiencies of processes), is valid: M = ^nJIMMDS f1 + M) "1. (14) 3 THE PROCESS IN THETURBOFAN ALONGSIDE THE PROCESS IN THE EJECTOR In the nozzle of the EJ a flow process takes place with energy losses, evaluated as the isentropic efficiency of the nozzle nNs. In this case there is no mechanical work. A work process takes place in the turbine, with corresponding energy losses, evaluated as the isentropic efficiency of the turbine nT= (hj - h2) / (hj - h2). Even though this expression is analogous to qNs, their numeric values differ due to different As2 _2., which depends on the distinctive properties of the component (turbine or nozzle). When presenting the processes in the TF below, the device will be compared with the process in the EJ which was discussed in chapter 2. The work obtained in the turbine and the momentum obtained in the nozzle are used in the next elements of the corresponding device. We have chosen the aggregation of most common losses which occur in the TF. As a result, we used "isentropic efficiency of the turbine" and "isentropic efficiency of the fan". It is hardly possible to estimate all losses that occur in practice. 330 Martinaitis, V. - Rimdzius, D. - Bielskus, J. - Streckiené, G. - Motuziené, V. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 In our research, these efficiencies are accepted on the basis of engineering practice and published investigations; the losses in microturbines have been analysed widely in [12], [13], [15] and [16]. The specific mechanical work of the turbine is eT or power ET = eTMl, while the internal irreversibility of this process is evaluated as the isentropic efficiency of the turbine nT. This power is transmitted to the fan installed on the same shaft without any energy losses. As in any fan, the change of state of the flow that is being mixed Mj + M0 takes place here, which is evident as an increase of enthalpy. The internal irreversibility of this process, including mixing and the restoration of pressure in the diffuser that is assigned to the fan, is evaluated as the isentropic efficiency of the fan nT. In a more detailed analysis it can be divided into impeller, mixing and diffuser losses nF=n fi n fmn fd. In quantitative terms, the process in the TF is expressed using the mechanical work of components, which is expressed by the power balance equation: eTMl = eF (M + M0 ). (15) Both compression processes on h - s diagrams (Figs. 5 and 7) are depicted using process lines with the same indices. Fig. 7 is a simplified version of Fig. 6. The main processes on the h - s diagram for the EJ and the TF are depicted in an analogous manner. Fig. 7. The processes of the change of state of components that are being mixed in the EJ and the TF Eqs. (11) and (15) serve as the basis of the dependence on the entrainment ratio for each of the compared devices: and - C Mej = C - 1 C3 Mtf = ^ -1. eF (16a) (16b) In general, the velocity of the flow that leaves the nozzle at the defined difference of enthalpies and the isentropic efficiency of the nozzle (the ratio of the difference of actual and isentropic kinetic energies) nNs is expressed as follows: C =V2(h - K^n (17) The specific work in the turbine is calculated likewise: e = (h-h2')ilT . (18) Then Eqs. (16a) and (16b) can be rewritten as: (19a) _ I ((- h2 mej = An NAMR*---- 1 and mtf Wfi^fm^fd (h4, - h3: (h _h) -1. (,•_ hi) (19b) The efficiency of compression, based on Eq. (6) for actual process: = (M, + M0) (h 4 - h )/Mi (h, - h2,), (20a) or nm = (1 + M w(i + m . (20b) 1 '(hi - h2) '(hi - h2) The enthalpy difference could be changed in accordance with the equation observed in the process on the h - s diagram, h4 - h3 = h4 - h3< , because isobars Pm and P0 are almost parallel and the distance in the direction of s in terms of the entire diagram is small. On the basis of Eqs. (19) and (20) the expressions of the efficiency of the EJ and TF are obtained: ,, =JnM , (21a) and nrF nrnFinFMnFD (K-K) (hi-h2') ((-hv) (h4-h) (21b) (h4' h3' ) (hi - h2' ) Having applied the previous assumption that h4* - h3* = h4 - h3 = h4 ■ - h3 ■: Vej = An NAMAD (h4, - hy and nrF nrnFinFMnFD (( - K)' (( - K) ( 4 - h3 ) (h4'- h3') (hi - h2' ) (22a) . (22b) When comparing the efficiencies of these two devices it follows that: Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan 331 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 tf Vej VtVfiVfmVfd (h4, - h,, (( -hT] (23) and the entrainment ratio proportion thereof, with the same main starting thermodynamic parameters (h - h2)/(h4- h»): Mt ^t'Hfi'Hfm'Hfd (( - hT (h4, - h,, -1 Me Mns^mNds (hi -(h4, - h,, (24) -1 4 RESULTS OF THE THERMODYNAMIC ANALYSIS 4.1 Processes that The Place in the Ejector The numeric analysis of the presented model under the initial conditions listed in Table 1 (dry air and subsonic flow) is presented below. Table 1. Initial air state parameters for the numerical examples h [kJ/kg] 5 [kJ/(kgK)] P [Pa] 1 308.6 1.55 190000 0 292.0 1.675 101325 2' 257.8 1.55 101325 The h -s diagram in Fig. 8 and Table 2 present the results of three numeric examples of the analytical explanation provided above. These cases correspond with the structure of the detailed diagram depicted in Fig. 6, where the numeric case of M0 / M1< = 1.33 is shown. For the purpose of an equivalent comparison of the essential results, identical isentropic efficiencies nNs, nMs, nDs were selected for all cases (0.85; 0.90; 0.85, respectively [9]). In Figs. 5 to 8, closed dots depict the states of the actual process, while open dots are used to convey the concept of thermodynamic models (see Fig. 6). It should once again be noted that this paper presents a case in which the pressure Pm and mass flow rate M0 of the mixture obtained in the ideal process following the proportions of the component should be preserved when transitioning to the actual process. For this purpose, the mass flow rate of the active fluid is increased in terms of the ideal case, Mj > Mr . As the M0 component relatively increases, Pm moves towards the pressure line of M0 (1.01325 bar). The enthalpy of the mixture decreases while the entropy increases, in turn increasing the internal irreversibility of the process. The relationship between Eqs. (13) and (14) shows that this mass flow rate has to be increased. Compared with the ideal process for each case, M0 / Mr= 2.5; 5; 9, the mass flow rate of the active flow has to be increased almost five times while the efficiency of compression is nearly halved. This is depicted in Fig. 9. Other cases are possible; for example, the aim to preserve the initial ratio of mass flow rates M, i.e., they should remain the same in both ideal and actual cases. Then the pressure of the mixture would be Table 2. The results for three cases when subsonic flows of air are mixed in the ejector Numeric cases in accordance with Eq. (18) M0 / My = 2.5 M0 / My = 5 M0 / My = 9 nNS nMs nDs nNs nMs nDs nNs nMs nDs 0.85 0.9 0.85 0.85 0.9 0.85 0.85 0.9 0.85 State parameters typical of the process h [kJ/kg] s [kJ/(kgK)] P [Pa] h [kJ/kg] s [kJ/(kgK)] P [Pa] h [kJ/kg] s [kJ/(kgK)] P [Pa] 2 265.4 1.579 101325 265.4 1.570 101325 265.4 1.579 101325 3' 282.2 1.639 101325 286.3 1.654 101325 288.6 1.663 101325 4' 296.8 1.639 121331 294.8 1.654 113029 293.7 1.663 108696 3* 284.6 1.648 101325 287.7 1.659 101325 289.4 1.665 101325 4* 299.2 1.648 121331 296.2 1.659 113029 294.5 1.665 108696 3 286.7 1.655 101325 290.2 1.668 101325 292.1 1.675 101325 4 301.5 1.655 121331 298.8 1.668 113029 297.2 1.675 108696 4m 304.1 1.664 121331 300.3 1.673 113029 298.2 1.678 108696 Main results M0 / M1 M0 / My nm M0 / M1 M0 / My nm M0 / M1 M0 / My nm Eq. (12) Eq. (13)/ Eq. (14) Eq. (20) Eq. (12) Eq. (13)/ Eq. (14) Eq. (20) Eq. (12) Eq. (13)/ Eq. (14) Eq. (20) 0.509 4.916 0.438 0.975 5.128 0.334 1.550 5.806 0.258 332 Martinaitis, V. - Rimdzius, D. - Bielskus, J. - Streckiené, G. - Motuziené, V. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 Fig. 8. The depiction of numeric examples of the process in the ejector on the h-s diagram: a) when M0/M1= 2.5; b) when M0/M1= 5; c) when M0/M1= 9. Other data correspond with Tables 1 and 2 Fig. 9. Variation in actual active mass flow rate and the efficiency of compression of the ejector subject to the selected mass flow ratio in the idealized process lower than Pm, significantly reducing the efficiency. The results of the comparison of the TF and EJ are presented below. 4.2 Assessment of the Main Performance Indicators of the Ejector and the Turbofan Fig. 10 shows the results of the comparison of the most important performance characteristics for the processes that take place in the EJ and TF, obtained using Eqs. (22) to (24). All those dimensionless or ratio-based characteristics are given depending on the previously mentioned initial conditions (h4 ■ - A3 )/(h - h2 ). These conditions are unambiguously related to the entrainment ratio of the ideal EJ, expressed by Eqs. (13) or (5). Fig. 10 shows the numerical link between the following initial conditions and three cases of M0 / Mv (see Table 2) for the EJ: 2.5, 5.0 and 9.0. The figure shows that according to the equations obtained during the analysis, the devices compared here have different sensitivities to the initial conditions. When both Eqs. (23) and (24) are equal to 1 (see also 1 in the ordinate axis), the performance indicators for the same initial flow conditions for both devices are the same. From here towards lower values of (h4 - h3 )/(Aj - h2 ) (on the left side of the diagram) the TF has an advantage over the EJ. As shown in the figure, the actual efficiency of compression of the EJ at that location is about 33 % (Eq. 21a) and the entrainment ratio is almost 1 (Eq. 19a). The intersection of the indicators depicted in the diagram (coloured dots) depends on the numeric values of the combination of isentropic efficiencies nTnF and nNs nMs nDs. The above are commonly assumed to be (point and lines - green): nT= 0.5; nFI= 0.8; nFM = 0.9; nFD = 0.9. Thus, nF= 0.8 x 0.9 x 0.9 = 0.65. For EJ -nNs=0.85, nMs=0.90, nDs=0.85. This competitiveness boundary of the compared devices is determined analytically as (nTnF)2 / (nNsnMsnDs), which would be an indicator comparing the degree of irreversibility of the processes in these devices, for which no flow state parameters are required. In this case study it equals 0.16 from (0.5 x 0.65)2/(0.85 x 0.90 x 0.85) while the corresponding M0/Mr equals 5.07. When we increase the isentropic efficiency of EJ components, we will have the case < 0.16 (the point of intersection of the comparative parameters will move to the left, see Fig. 10). When we increase the isentropic efficiency of microturbine or fan, we will have a case > 0.16. Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan 333 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 Fig. 10. The comparison of the main performance indicators of the ejector and turbofan under the same starting conditions (¿4- h, )/(h - ¿2'), Eq. (13) These isentropic efficiencies are highly dependent on the size and other features of each evaluated component. While in a wide range nNsnMslDs are rather stable and well-researched, when it comes to small devices (micro-turbines with partial admission and micro-fans or micro-compressors) nfnF can move quite far from 1. This is demonstrated by additional sensitivity analysis by changing the efficiency of the microturbine, which is the parameter whose value has the least certainty at this stage of the research. The ejector's isentropic efficiencies are assumed as constant (see also Table 2) As already mentioned, in the case of Fig. 10, isentropic efficiency of microturbine is nf= 0.5. In the case of nf= 0.40, it is understood that the advantages of TF occur at the EJ entrainment ratio values higher than 1. These would be the cases to the left of MEJ « 1.5 (point and blue lines). In the case of nf= 0 30 of TF, the benefits appear for cases already to the left of MEJ «2.3 (point and red lines). The developed analytical model and this fragment of the sensitivity analysis show that particular attention must be paid at the microturbine's design in the design of TF. The advantage of the TF over the EJ increases as the entrainment ratio on the basis of mass M = Mi J Ml increases. This means that based on 334 the h-s diagram, when the initial and resulting state parameters are the same, the TF with the selected active flow rate will allow a higher amount of the passive flow to be pumped. Due to the higher efficiency of compression and the accompanying entrainment ratios the TF could be relevant in terms of gas burners, roof turbofans and other specific devices. Natural gas burners that use full mixing require M ~ 18. When entrainment ratios are low, the EJ has an advantage in terms of these indicators. The processes that take place in the TF and EJ are rather simplified in this paper, which allows the authors to easily demonstrate or emphasize that in order to achieve higher entrainment ratios, converting the available energy to mechanical work enables the possibility of achieving better performance when compared with conversion to kinetic energy. More thorough experimental research is required to determine the values of M and the absolute values of M1 and M0 at which it is efficient to use the TF. In addition to this, this device has moving parts, making its manufacturing process more complicated. 5 CONCLUSIONS In this paper, the authors have analysed the thermodynamic processes in the ejector and the Martinaitis, V. - Rimdzius, D. - Bielskus, J. - Streckiené, G. - Motuziené, V. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 325-336 turbofan when they have the same initial states of active and passive flows. This analysis is based on the parallel comparison of two thermodynamic models: one of them is created for turbofan, and one is adapted from the classical ejector. The characteristics that demonstrate their efficiency - the efficiency of compression and entrainment ratios - were defined and compared at the subsonic flow mode conditions. The following conclusions were made: 1. The main cause of the resulting differences is the following. The mixing process in the EJ is realized via the interaction of kinetic energies that is expressed by the momentum balance equation. In the TF this occurs by transforming the energy of the active flow into the turbine work transferred to the fan, which conveys the passive flow. The process is defined by the work balance equations. 2. The case of numerical examples for the comparison of thermodynamic processes in the EJ and the TF when they have same initial states of active and passive flows (h4 - h3 )/(h1 - h2) shows that the TF has an advantage over the EJ at lower values of these starting conditions (< 0.161). The advantage of the TF over the EJ increases as the entrainment ratio on the basis of mass increases M=MJ mx. In this case the turbofan could be relevant in terms of gas burners, roof turbofans or other specific devices for which a relatively higher passive flow rate is required. 3. The boundary between the advantage of the TF over the EJ on the basis of efficiency of compression and entrainment ratio indicators for the same initial flow conditions is determined analytically. These cases correspond to ((nrnF?)/ (nNsnMsIDs). It is 0.16 in the case of numerical examples and depends on the combination of isentropic efficiency of the components of both devices. In order to determine these specifics for the TF, a thorough experimental study is required, especially if a microturbine with partial admission is used. The numerical results obtained comparing the models discussed in the paper are limited to air-to-air flows mixing at the subsonic regime. Considering similarities to EJ, turbines and ventilators, the presented thermodynamic model could serve as a basis for the creation of the theoretical model for roof turbine ventilators. The developed model could also serve as a basis for its development into supersonic analysis. 6 ACKNOWLEDGEMENTS This project has received funding from the European Regional Development Fund project No 01.2.2-LMT-K-718-01-0016 under a grant agreement with the Research Council of Lithuania (LMTLT). 7 NOMENCLATURE A cross-section area, [m2] C velocity, [m/s] E mechanical power, [kW] e specific mechanical work, [kJ/kg] F2-3 power between cross-sections 2 and 3, [N] h enthalpy, [kJ/kg] M mass flow rate, [kg/s] M entrainment ratio (ratio of mass flow rates), [-] P pressure, [Pa] S entropy, [kJ/K] s entropy, [kJ/(kgK)] n efficiency, [-] nDs the isentropic efficiency of diffuser, [-] nF the isentropic efficiency of fan, [-] nFD the efficiency of fan diffuser, [-] nFI the efficiency of fan impeller, [-] nFM the efficiency of mixing in fan, [-] nMs the isentropic efficiency of mixing chamber, [-] nMs the isentropic efficiency of nozzles, [-] nT the isentropic efficiency of turbine, [-] Superscripts ' idealized state + in - out Subscripts 0 to 4 air flow states at the cross-section (according to Fig. 2) D diffuser EJ ejector F fan ir irreversible M mixing chamber m mixture N nozzle T turbine TF turbofan 8 REFERENCES [1] Ma, Z., Bao, H., Roskilly, A.P. 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D0I:10.5545/sv-jme.2019.6499 Original Scientific Paper Received for review: 2019-12-06 Received revised form: 2020-04-06 Accepted for publication: 2020-04-14 Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks Aida Parvaresh1 - Mohsen Mardani2* 1K.N. Toosi University of Technology, Iran 2ACECR, Sharif University of Technology Branch, Iran This paper presents a data-driven approach that utilizes the gathered experimental data to model and control a test rig constructed for the high-powered gearboxes. For simulating a wide variety of operational conditions, the test rig should be capable of providing different speeds and torques; this is possible using a torque-applying system. For this purpose, Electro-Hydraulic Actuators (EHAs) are used. Since applying accurate torque is a crucial demand as it affects the performance evaluation of the gearboxes, precise modelling of the actuation system along with a high-performance controller are required. In order to eliminate the need to solve complex nonlinear equations of EHA that originate from friction, varying properties of flow and similar, a data-driven system based on neural networks is used for modelling. In this manner, the model of the system, which captures the whole dynamic of the system, can be obtained without any simplifying assumptions. The model is validated with experimental data, and the learning factors are set to zero to reduce the high computational costs. After that, another network of neurons is used as a controller. The performance of the proposed controller under normal conditions and in the presence of disturbances are investigated. The results show a good tracking of this controller for various reference inputs in different conditions with acceptable characteristics. Additionally, the obtained results are compared with a conventional proportional-integral-derivative (PID) controller results, and the superior features of the proposed scheme is concluded. Keywords: identification; data-driven system; closed-loop test rig; hydraulic actuator; neural networks Highlights • Presenting a straight-forward procedure for accurate modelling of the actuation system in the test rig for testing the high-powered gearboxes. • Eliminating the requirement for the application of simplifying assumptions to reach the linear analytical model. • Providing the possibility of applying different scenarios for testing the gearboxes performance under different operational conditions. • Achieving the precise control of the actuation system even in the presence of disturbances. 0 INTRODUCTION Ensuring safety and performance along with the reduced maintenance costs of high-powered gearboxes, which are mostly used in helicopters and wind turbines, are of great importance in industrial applications. Since in-field testing of such equipment is often impossible, time-consuming, and not cost-efficient, test rigs are developed [1] and [2], for primary assessment of the capability and performance of the components in industrial use. Full-sized test rigs can provide realistic conditions so that the performance and operation of the systems can be evaluated. These test rigs can be designed both in closed-loop or open-loop schemes. Test rigs operating based on the closed-loop principle can reduce energy consumption up to 95 % compared to open-loop schemes, so they are superior in testing high-powered gearboxes when a great amount of energy is required. Different types of test rigs have been developed to investigate different features based on desired parameters to be tested. In a study by Âkerblom [3], a closed-loop recirculating power test rig was developed for testing gearboxes under controlled environments. Different parameters, including noise, gearbox life, and efficiency, were studied in a gearbox system consisting of two similar gearboxes. In the studied system, one gearbox was tilted using a hydraulic cylinder. In [4], Arun et al. reviewed different test rigs; they also fabricated a new test rig. A novel test rig was proposed by Mihailidis and Nerantzis [5], which was consisted of a planetary gear box for applying variable torques and speeds. Palermo et al. [6] constructed a precise closed-loop test rig to evaluate the dynamic behaviour of gear pairs in different operational conditions. Their fabricated test rig consisted of a test side to test the desired gearbox and reaction side to close the power train. Mozafari et al. [7], represented the preliminary, conceptual, and detailed design of a test rig that was developed for high-powered gearboxes. Their rig was a closed-loop mechanical type and used hydraulic torque applying system for providing the desired torque. In order to reach the desired position of the hydraulic actuators, they implemented on-off and proportional-integral- *Corr. Author's Address: ACECR, Sharif University of Technology Branch, Iran, mardani@acecr.ac.ir 337 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 derivative (PID) controllers [8] as well as fractional order PID [9]. For conducting dynamic tests in high-powered gearboxes and for actuating the system, the torque should be applied automatically employing a torque-applying system. These systems should be able to provide variable torques and speeds to simulate the operational conditions of high-powered transmissions. Different systems can be used for this purpose, among which, hydraulic systems would be the best choice due to their superior features. Compared to the other equipment for applying torque, electro-hydraulic actuators (EHAs) can provide higher power-to-weight ratios considering the volume limitations, higher forces, reduced size of equipment as well as the robustness improvement. In addition, they are inherently more stiff and rigid so that the precise position control can be achieved. Also, they provide faster response, which is a desirable feature in industrial applications [10] and [11]. However, despite the noticeable advantages of these systems, their dynamic behaviour is highly nonlinear due to the nonlinear characteristics of flow and pressure, including varying bulk modulus, compressibility, and viscosity [12]. So, prior to the control of these systems, an accurate model, which represents the complete dynamic behaviour of the system should be developed. Despite the extensive published studies, a lack of precise and appropriate modelling is observed. Different methods have been utilized to overcome these problems. Some researchers attempt to overcome this problem via the linearization of equations and using linear control procedures to control these systems. However, by the use of linear control strategy, some portion of the dynamic system behaviour would be lost during the linearization of the system. Some researchers also used simplifying assumptions, such as neglecting leakage or flow compressibility. The obtained model by these approaches would be valid just in the adjacent of the linearization point. Additionally, the use of linear controllers would not lead to high-performance control. In some other researches, higher-order linear models were used to design controllers. However, these models also suffer from the validity problem in other points rather than operating points. In [13], a method for parameter identification of nonlinear terms in the model of the system was proposed. It was observed that considering the identified nonlinear effects, increases the accuracy of the model, significantly. In addition, in another study [14], the identification of the nonlinear effects, including friction coefficient was conducted using the input-output data. The control of EHAs and developing an appropriate controller to satisfy the desired requirements are of great importance regarding their various applications. The control scheme can be designed either in a force control mode or displacement control mode. Considering the easier implementation of displacement control mode from the practical point of view, better performance as well as disturbance rejection characteristics, this mode is widely used in controlling EHAs [15]. Many nonlinear adaptive control approaches were used for controlling EHA, among them, the usage of sliding mode controller [16], back-stepping [17] and [18], feedback linearization controller [19] and [20] and so on can be mentioned. Deticek and Zuperl [21], presented a novel hybrid-fuzzy control scheme for positioning the EHA in practical applications. Nonlinear control schemes are rarely utilized in industrial applications due to their need for a mathematical model as well as the complexity of tuning the parameters. Achieving high accuracies in the position tracking of hydraulic actuators are of great importance; however, parametric uncertainties, as well as nonlinearities, are the major problems in this field [22]. Parametric uncertainties can be compensated by the use of adaptive control schemes, while nonlinearities can be handled by robust controllers. To take advantage of these two schemes simultaneously, intelligent controllers are proposed. Guan and Pan [18] presented a nonlinear adaptive robust control procedure with unknown parameters for an EHA, by combining a back-stepping technique and a simple robust control. Haung et al. [17] used an incremental nonlinear dynamic inversion control technique for controlling a hydraulic actuator in the presence of system uncertainties. They implemented their proposed approach on a 6-degree-of-freedom (DOF) hexapod hydraulic robot. In industrial applications, sometimes the use of popular theoretical control methods, which represents superior performance, is not possible due to the occurrence of some unpredicted and unexpected effects [23]. Model-free controllers, which do not require an explicit model of the plant, are the best choice in these applications, such as classic PID controllers. In these types of controllers, high and intensive modelling work are not required. Among the advantages of model-free control schemes, easy implementation and tuning of the coefficients can be mentioned. The model-free procedure provides good control features without considering an accurate model of the system [24]. These models aim to approximate the system dynamics using the gathered information from the embedded sensors that are 338 Aida Parvaresh, A. - Mardani, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 estimated and updated in each time samples. It is evident that through using this control scheme, we can overcome the difficulties in mathematical modelling and improve the practical implementation. Some model-free control schemes were used for controlling EHA. Neural networks (NNs) are universal approximators, which means that they can be used as a black-box estimator applicable for the systems with parametric uncertainties and nonlinearities [25]. Tremendous interest has been devoted to NNs, according to their outstanding performances in learning, adaptation, generalization, optimization, and control [26]. From the theoretical point of view, a continuous function can be approximated to a desired accuracy, which enables the modelling of the complex nonlinear system using NNs. In many research studies, NNs are used for control and modelling [27]. These structures are used to learn the features and characteristics of the system, which can be used as the model, instead of obtaining the explicit dynamic of the system. According to some studies, these controllers can be classified as model-free controllers as they do not use the exact model of the system. The existing complexities in the control problem of industrial systems make the neural network approach as a popular method. Learning the control scheme using NNs was proposed for enhancing the trajectory tracking performance. Yao et al. [25] developed an advanced nonlinear controller for the hydraulic system to obtain position tracking in the presence of various disturbances. They used a neural network estimator to improve the disturbance compensation. In general, using these networks have significant advantages over other controllers. In this paper, we aim to take the advantages of NNs for modelling and controlling of a hydraulically-actuated test rig. The rest of the paper is organized as follows: In Section II, a brief introduction of the fabricated test rig, which is a mechanically closed-loop test rig with a hydraulically-driven torque applying system, is presented. Then, in Section III, the data acquisition procedure required for modelling of the system is explained. After that, in Section IV, the proposed algorithm for modelling and controlling the actuation system using neural networks is described. Then, the results of neural-network modelling and controlling for different conditions are presented in Section V. Finally, Section VI is dedicated to the conclusions derived from this research. 1 SYSTEM DEFINITION The studied test rig is a mechanically closed-loop test rig that was designed and fabricated in Sharif University of Technology branch of Academic Centre of Education, Culture and Research (ACECR). The mentioned test rig was designed so that it has low energy loss; it also provides wide ranges of torques and speeds. Therefore, it is appropriate for testing the high-powered gearboxes that are commonly used in aeronautic industries. The specification of the test rig and torque-applying system are provided in Table 1. In Fig. 1, the schematic and real test rig are depicted. To apply the required torque to the testing system, a torque-applying system that consists of a planetary gearbox is used. By rotating the ring of this planetary gearbox, the system is rotated. The rotation of the ring of this planetary gearbox is provided by the linear hydraulic actuators, which are depicted in Fig. 2. It is noteworthy that all criteria, including stresses, strains, safety fractures, and failure and similar, are provided in the design procedure [7]. For sensing the displacement of the actuator rod, two displacement sensors are utilized with the maximum measurement course of 75 mm, which is larger than the course length of the actuator. A hydraulic circuit is designed for controlling the hydraulic actuator; in addition, a 4/3 directional valve is used for changing the direction of the hydraulic actuator. The actuation system consists of a three-phase electrical motor, a positive displacement pump, a container, a safety valve, and a pressure indicator. More information about this test rig and actuation is provided in [28]. Table 1. Specifications of the test rig and torque applying system Specification Value Test Rig Max loading capacity 365 kW Max rotational speed 3000 rpm Max hydraulic actuator course 60 mm Torque applying Max required force 10 kN system Force applying arm 175 mm Max rotation 20 deg 2 DATA ACQUISITION The model obtained from the neural network structure does not require any mathematical relationships. It is a data-driven system, which uses input and output data of the system for training the desired network. Therefore, gathering data is an important step for modelling. The data collection procedure is depicted in Fig. 3. Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 339 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 Fig. 1. The schematic and real test rig for high-powered gearboxes Fig. 2. The schematic and real test rig for high-powered gearboxes Fig. 3. Data- acquisition procedure According to Fig. 3, the generated excitation signal in the computer is converted to the current of Iv. Then, it is multiplied by Kv, which is the constant gain of the servo valve, to produce Xv, the signal for displacing the spool of 4/3 servo valve. By displacing the spool, the flow rate of QL would be changed; thus, the piston would be displaced. Then, this displacement is measured by the displacement sensors that are embedded in the system. The combination of sine signals is the best choice for excitation signal in the cases in which the system would be operated in determined frequencies, and the quality of the collected data in those signals are important. The frequency of the excitation signal should be selected according to the operational frequencies of the system [21]. In this research, the excitation signal is considered as follows: : ^at cos a.ts (1) where Sexc is the excitation signal, n is the number of sine signals that are summed together, ts is the sampling time, a{ is the amplitude of /h sine signals, and mj is the frequency of the signals. The gathered input-output signal is depicted in Fig. 4. 340 Aida Parvaresh, A. - Mardani, M. exc =1 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 10 -Input kç^r A M ilJL, rrWV Y\ 10 20 30 Time [s] 40 40 20 -20 -Output (\ A \ P V 0 10 20 30 40 Time [s] Fig. 4. Input-output data set for training the system 3 PROBLEM DEFINITION For obtaining the model of the actuation system for the torque-applying system, we aim to use a procedure that captures the system dynamics completely and uses no simplifying assumptions and can overcome the existing nonlinearities and uncertainties. Precise modelling is of great importance, as it directly affects the performance of the controller for the actuation system and consequently, the performance of the testing procedure for high-powered gearboxes. As mentioned, EHA is a single-input singleoutput (SISO) discrete-time nonlinear system. The system can be described using the following relation [23]. ^u(k), u(k -1),..., u(k - na ^x(k), x(k -1),..., x(k - nb) x(k +1) = M (2) This structure provides a nonlinear mapping from input space Kn to output space Km and defined using [u(k) u(k- 1) ... u(k-na)] and [u(k) u(k- 1) ... u(k-nh)] vectors. In this relation, x(k) denotes the output of the system at time instant k, which is the rod displacement. M(.) e K is a function from Kn ^ Km and represents the model structure of the system, which is a function of previous inputs and previous outputs of the system. The controller for this plant can be defined as: ^ u(k-1),u(k - 2),...,u(k - n ) ^ u(k ) = C ec (k +1), ec (k +1),..., ec (k - nd ) (3) In Eq. (3), u(k) is the current control signal, which is defined by the use of [u(k- 1) u(k- 2) ... u(k-nc)] and [ec(k- 1) e(k- 2) ... e(k-nd)]. [u(k- 1) u(k- 2) ... u(k-)] denotes the past control inputs, with the nc representing the maximum previous input; while [ec(k- 1) ec(k- 2) ... ec(k-nd)] denotes the past errors, with nd representing the maximum past errors. In addition, C(.) is a nonlinear function representing the controller structure. ec is the tracking error that is defined as: ec = x(k ) - xdes (k ), (4) where xde(k) is the desired output. In order to obtain the model and controller structure practically, some assumptions should be considered as follows: Assumption 1: The partial derivatives of M(.) are continuous for ke N and M(.) e M is a smooth function of Mn ^ Mm. This assumption is a general condition for nonlinear systems. Assumption 2: The model of the system as described in Eq. (2), is generalized Lipchitz; hence a positive constant C exists, so that the |Ax(K+ 1)| < C|\&|\, Zk= [Ax(k), Au(k)]. This assumption represents the direct influence of the inputs variation on variation rate of the system output. According to this assumption, the outputs of the system are bounded if the inputs are varied in the bounded region [29]. According to the above assumptions, Eq. (2) can be defined by the use of in the following form: x(k +1) = x(k ) + = = x(k ) + Ax(k k + Au(k (5) In Eq. (5) represents the nonlinear dynamic of the system. The main problem is the estimation of In this paper, the neural networks are used for approximating this function. A neural network is defined as a system of neurons locating at different layers. With the appropriate selection of the activation functions, bounding the input values to SBe Mn, as well as adjusting the hidden layers number, weights and biases, the M(x), which represents the model of the plant can be defined in the form of: M ( x) = H2TaM (HTx ) + s m ( x). (6) In the above equation, H1 is the matrix representing the weights (ma) and biases (ba) of the first hidden layer; while weights (ml2) and biases (b2) of the second hidden layer are included in H2. Additionally, the vectors of activation functions are denoted by aM. Moreover, eMX) is the approximation error by the neural network structure. With the use of a suitable NN for approximation, which means the appropriate selection of H, H2 and aM, it is necessary 5 0 0 0 Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 341 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 to obtain M(x) so that the approximation error (sM(x)) becomes less or equal to the acceptable error: Mx) < sMR for all samples. sMR is the acceptable error, which is defend by the problem dynamics and proposed application. It should be noted that the computational costs would be increased for the lower amount of this value. After that, the appropriate estimation for the model is achieved, all the biases and weights are considered fixed, and their learning rate set to zero (ma, bi1, mi2 and bi2, = const., hence, Hj, H2 and aM = const.). Therefore, that the fixed model of the system is available for the further uses in the controller. The schematic of the proposed procedure is depicted in Fig. 5. As is obvious, two networks are used in the proposed process; one represents the model of the EHA while the other is used as a controller. The neuron inputs (current and previous inputs; in this research past two inputs are used) are multiplied by the corresponding weights, then the resultant products are summed together their summation with biases are fed into a transfer function. and the output is generated as follows: x = m HH+1 +s,) j. (7) The adaption of NN weights are based on Levenberg-Marquandt algorithm. Another neural network structure is used as the controller of the EHA. C(x) can be defined as the following structure, which includes two hidden layers. C(x) = H4TaC [H3Tx) + eC (x). (8) In Eq. (8), H3 is the matrix representing the weights (mi3) and biases (bi3) of the first hidden layer in the controller structure. Weights (mi4) and biases (bi4) of the second hidden layer in the controller design are included in H4. Additionally, the vector of activation functions is denoted by aC. By using suitable NNs for the controller structure, which means the appropriate selection of H3, H4 and aC, it is necessary to obtain C(x) so that the controller steady-state error (eC(x)) is located in the acceptable range: edx) < sCR for all samples. In summary, the outputs of the first neural network (controller section) is the controller command for the model, which is obtained through the second neural network (model section). In this research, the modelling is conducted offline, meaning that first the data is collected and then, it is transferred to the personal computer (PC) for processing and obtaining the model. Once the model is obtained, there is no need for calculation in further uses. Because the actuation system is responsible for running the whole system, controlling the displacement of the hydraulic actuator is very important. Different parameters, including the type of input/output signals, the number of inputs/outputs and the appropriate controlling y L Fig. 5. The proposed procedure for modelling and controller design 342 Aida Parvaresh, A. - Mardani, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 algorithm, should be considered in the control scheme. In the desired test rig, hydraulic actuators are in displacement control mode, which means that the command signal that is fed to the servo valve is based on the difference between the desired displacement and measured displacement by the sensors. The steps taken for modelling and controlling the system are depicted in Fig. 6. 3.1 Model Estimation and Validation The criterion for selecting the model with the best quality is the root mean square error (RSME) criteria. This criterion is the most-widely used measure of difference between the predicted values through the obtained model and observed values through the embedded sensors. This criterion is defined as follows: rsme - XII * (k )- / n, (9) where, x(k) and x(k) are the real and predicted outputs of the system and n is the sample number. This term is always between 0 and 1; smaller values indicate the high quality of the predicted values. In addition, the error mean and std (standard deviation) are also checked. The error mean is the average of the errors; while std provides an indication of how far the responses deviate from the mean. 4 RESULTS AND DISCUSSION In this section, the obtained results are provided and discussed. The results are represented in two sections; the first section is dedicated to the modelling, and the second section is devoted to the controlling results. Mode! structure Design of ■ Excitation ■ Data | experiment ■ signal ■ acquisition Model structure selection Neural network selection Model estimation Model Set learning validation ^BM rate to zero Controller structure Defining controller inputs Controller output Neural network selection Selection of parameters Checking performance Fig. 6. Neural-Network based model and controller Fig. 7. Modelling results: The blue line: Target values and red line: Output values Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 343 =1 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 4.1 Modelling Results The results of modelling the system are depicted in Fig. 7. As shown in this figure, the estimated model can capture the dynamic of the system with an acceptable error. A magnified portion of the figure between the 2.49 s and 2.51 s shows the small deviation between the real and estimated models. In addition, the RSME, mean and std (standard deviation) of error are shown in Fig. 8. According to Fig. 8, the RSME of the error is equal to 0.0055726, which confirms the validity of the estimated model. Since it is close to zero, it clarifies the quality of the model. Additionally, std is equal to 0.0005574, and its low value indicates the closeness of the values to the mean value. Fig. 8. RSME and error properties for modelling results; a) RSME diagram (RSME=0.00055726), and b) Error mean and standard deviation diagram (errormean=7.0024e-0.6, std=0.0005574) 4.1 Controller Result As mentioned, a neural network controller was utilized for controlling the position of the hydraulic actuator. The performance of the designed controller in different conditions is investigated in the following sections. The desired reference is considered in the workspace of the hydraulic actuator, in which the model was trained. Two constant and variable step references are considered as the references for the system and the performance of the system in two conditions, normal condition and in the presence of the disturbance, is studied. The results are provided in Figs. 9 to 12. As can be seen in Fig. 9 for the constant reference in normal condition, the controller output tracks the reference output in less than 0.25 s. According to this figure, no overshoot is seen in the controller output; in addition, it tracks the reference without any steady-state error. For the variable step reference, the controllers track the reference without any steady-state error. The settling time is different 0.15 o.io g 0.05 § 0 % 0.15 0.10 0.05 0 -.........!..........!..........;..........;....... Reference Controller Output /.....;.......................................... {.......!........................................... : 3.5 0 0.5 1 1.5 2 2.5 3 Time [s] Fig. 9. Controller performance for constant reference 1.5 2 2.5 3 Time [s] Fig. 10. Controller performance for variable reference 1 1.5 2 2.5 3 Time- [s] Fig. 11. Controller performance for constant reference in the presence of disturbance Reference -Controller output f : v. Time (Second) Fig. 12. Performance of the controller for variable reference in the presence of disturbance 344 Aida Parvaresh, A. - Mardani, M. Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 for different steps. After a maximum of 0.3 s, the controller output tracks the determined variable step. The performance of the controller in the presence of the disturbance are presented in Figs. 11 and 12 for constant reference and variable references, respectively. The disturbance in the form of dist = 0.04(t > L50)(t < 1.55) -- 0.02(t > 1.55)(t < 1.7), was applied to the system in the time duration of 1.50 s and 1.7 s. According to Fig. 11 and Fig. 12, the controller can damp the disturbance well and the systems tracks the reference after that the disturbance is applied for a short period. 4.2 Comparison with PID Control Scheme In order to highlight the superiority of the obtained results from the NN controller, we aimed to provide a comparison with conventional PID results. This controller is also considered to be a model-free controller. The control goal was to track a constant reference. For this purpose, the PID controller is defined as: t u (t ) = Kpe(t) + Ki J e(t )dt K de(t ) dt ' (10) In which, Kp, Kt and Kd denote the proportional, integral, and derivative coefficients, respectively. Additionally, e(t) represents the error, which is defined as: e(t ) = (t ) - x(t ). (11) where xj(t) is the desired output and x(t) is the output, obtained from the controlled plant. The aim was to provide the minimum error by the use of the controller. The PID control scheme is depicted in Fig. 13. The result of implementing PID controller along with NN controller is plotted in Fig. 14 for tracking the constant reference. According to this figure, the NN controller provides faster convergence with the reference input. In both controllers, no steady-state error is seen; however, the settling time for the PID controller is much bigger compared to the NN controller. g -o 8- 1) -i-1- 0.05 -NN Controller -PID Controller -- -Reference -0.1 0.15 -0 7 Fig. 13. The PID control scheme Time [s] Fig. 14. Comparison between the results of NN controller and PID controller For the NN controller, the settling time is approximately 0.25 s; while for the PID controller, this value is 4.35 s. In both controllers, no overshoot was observed. Therefore, it can be concluded that the NN controller performs better. 5 CONCLUSION Different methods were used for ensuring the safety and performance of the high-powered gearboxes that are mostly used in aeronautic industries. The usage of real-sized test rigs for evaluating the performance of system components is known to be one of the reliable methods. In order to provide variable torque and speed, torque applying systems are required. In this paper, we investigated the hydraulically-driven actuation system for the torque applying system of the test rig that was designed and fabricated in Sharif University of Technology branch of ACECR. First, identification and data-driven modelling of the hydraulically-actuated torque applying system of a mechanically closed-loop test rig were conducted by neural networks. The advantage of the proposed scheme is capturing the whole system dynamic, which was problematic due to the existing nonlinearities in the dynamic of the EHA, In addition, the modelling was conducted without any simplifying assumptions. Therefore, the precise model of the EHA was obtained without performing time-consuming mathematical calculations. After that, the model was obtained, a neural network controller was designed to track the desired output; the parameters of this network was adjusted so that the tracking error becomes very small. According to the obtained results, the system was modelled with the RMSE of 0.00055726 and std of 0.0005574, which indicates the good quality of the model. For the controller, it was obvious that the controller output reached to the reference output in approximately 0.25 s, without any overshoot and 0 Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 345 Strojniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 steady-state error. In addition, the controller tracked the variable reference very well. For the case in which the disturbance was presented, the controller was able to deal with the applied disturbances and followed the reference after 0.13 s. In summary, a good tracking feature of the controller was obtained in different conditions; in addition, good disturbance rejection feature was observed. It should be mentioned that the use of two neural networks increases the computational cost of the system. In order to solve this problem, in this paper, it was proposed to set the learning factors of the model section to zero. Finally, to highlight the superior characteristics of the proposed data-driven algorithm, the results of this paper was compared with the results of the conventional PID controller. In general, the proposed Neural Network modelling, and the Neural Network controller provide acceptable results, in which the system dynamics include uncertainty and non-modelled nonlinearity. 6 REFERENCES [1] Averous, N.R., Stieneker, M., Kock, S., Andrei, C., Helmedag, A., De Doncker, R.W., Hameyer, K., Jacobs, G., Monti, A. (2017). Development of a 4 MW full-size wind-turbine test bench. 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Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 347 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5 Vsebina Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 66, (2020), številka 5 Ljubljana, maj 2020 ISSN 0039-2480 Izhaja mesečno Razširjeni povzetki (extended abstracts) Benjamin Bizjan, Brane Širok, Marko Blagojevič: Analogna eksperimentalna študija tvorbe vlaken na dvokolesni centrifugi SI 37 Hongwei Yan, Yajie Li, Fei Yuan, Fangxian Peng, Xiong Yang, Xiangrong Hou: Analiza natančnosti sejanja večetažnega linearnega vibracijskega sita SI 38 Wiktor Kamycki, Stanislaw Noga: Uporaba modela tankih rezin za določitev porazdelitve sil vzdolž nosilne ploskve in relativne porazdelitve sil, izmerjenih na korenskem delu zoba SI 39 Da Cui, Guoqiang Wang, Huanyu Zhao, Shuai Wang: Raziskava sistema vodenja zgibnih goseničnih vozil s sledenjem poti SI 40 Vytautas Martinaitis, Dovydas Rimdžius, Juozas Bielskus, Giedrè Streckienè, Violeta Motuzienè: Preliminarna primerjava termodinamičnih modelov podzvočnega ejektorja in turbopuhala SI 41 Aida Parvaresh, Mohsen Mardani: Sistem za obremenjevanje z navorom na mehanskem zaprtozančnem preizkuševališču: vodenje na osnovi podatkov in brez modela z nevronskimi mrežami SI 42 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, SI 37, © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2020-01-16 Prejeto popravljeno: 2020-04-02 Odobreno za objavo: 2020-04-23 Analogna eksperimentalna študija tvorbe vlaken na dvokolesni centrifugi Benjamin Bizjan - Brane Širok - Marko Blagojevič Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija Članek predstavlja študijo razvlaknjenja na dvokolesni centrifugi, ki je bila zasnovana kot pomanjšana industrijska centrifuga, pri kateri smo namesto mineralne taline uporabili nizkotemperaturno sladkorno talino (izomalt pri 195 °C). Namen študije je bil preučiti pojave, povezane z nastankom vlaken in transportom le-teh s filma taline na kolesih centrifuge na mrežo zbiralne komore, ter s tem povezane karakteristike vlaknastega toka. Z uporabo nizkotemperaturne taline smo se želeli izogniti tehnološkim in varnostnim omejitvam, ki jih prinaša delo z visokotemperaturno mineralno talino. Ker je bila pri tem dosežena dobra dinamična podobnost z visokotemperaturnim industrijskim procesom razvlaknjenja, je mogoče rezultate modelne študije aplicirati na tudi na realni industrijski proces. Eksperimenti so bili izvedeni pri različnem naboru spreminjanih obratovalnih pogojev: vrtilna frekvenca koles (od 40 Hz do 100 Hz), volumski pretok taline (od 18 mL/s do 25 mL/s) in položaj natoka taline na kolo (od 15° do 60°). Volumski pretok zraka za odpih in odsesa sta bila tekom meritev konstantna in v medsebojnem razmerju 1:14. V vsaki obratovalni točki smo večfazni vlaknast tok posneli s pomočjo hitre kamere, iz visokohitrostnih posnetkov pa nato določali lastnosti toka in vlaken. Posnetki kažejo na izrazito kompleksnost strukture in dinamike vlaknastih struktur, saj se vlakna ob interakciji s turbulentnim tokom odpiha oblikujejo v tridimenzionalone medsebojno prepletene strukture v obliki kosmov, niti in tančic, medtem ko se kvazi-periodično trgajo s filma taline s frekvenco, višjo od vrtenja kolesa. Kljub kompleksnosti vlaknastega toka smo pri kvantitativni analizi pojavov opazili jasno izražene trende spreminjanja lastnosti vlaknastega toka. Dolžina vlaken se pri naraščanju razmerja obodne hitrosti filma taline glede na aksialno hitrost toka odpiha povečuje, večji pa postaja tudi raztros dolžine vlaken. Poleg tega se z obodno hitrostjo filma zmanjšuje velikost nerazvlaknjenih perl, kljub temu pa tok odpiha lažje prebijejo zaradi večje radialne hitrosti. Podoben učinek ima obodna hitrost kolesa tudi na vlakna, saj se kot njihovega širjenja v odpihu s hitrostjo kolesa povečuje, medtem ko pri nizkih hitrostih glede na hitrost odpiha lahko pride do recirkulacije toka za kolesi. Z oddaljevanjem od koles centrifuge se velikost in kompleksnost vlaknastih struktur povečuje, dokler se ne usedejo na mrežo zbiralne komore. Trend naraščanja debeline plasti je linearen, vendar prihaja do periodičnih oscilacij. V zvezi z usedanjem vlaken smo definirali tudi izkoristek razvlaknjenja kot razmerje med maso na mreži zbranih vlaken in maso dobavljene taline. Izkazalo se je, da je izkoristek močno odvisen od vrtilne frekvence kolesa, volumskega pretoka in položaja natoka taline. Optimalni izkoristek v modelni študiji je dosežen pri kotu natoka 30°, Webrovemu številu filma taline okrog 106 in ko je obodna hitrost kolesa približno enaka aksialni hitrosti toka odpiha. Z vidika metodologije in rezultatov članek predstavlja znaten napredek pri raziskavah razvlaknjenja mineralne volne, saj so se do zdaj uporabljali manj natančni eksperimentalni modeli na osnovi opazovanja industrijskega procesa na večjih velikostnih skalah, in pa poenostavljeni numerični modeli z enim vlaknom, ki ne upoštevajo niti strjevanja vlaken niti njihove medsebojne interakcije. V članku predstavljena metodologija pa omogoča sočasno spremljanje snovnih in transportnih pojavov, ki se odvijajo na zelo različnih velikostnih skalah. V nadaljnjih študijah je smiselno podrobneje raziskati še vpliv hitrosti odpihnega in odsesnega toka ter tlačne razlike preko plasti vlaken na zbiralni mreži. Ključne besede: centrifuge, razvlaknjenje, mineralna volna, večfazni tok, primarna plast, hitre kamere *Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, benjamin.bizjan@fs.uni.lj.si SI 37 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, SI 38, © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-12-19 Prejeto popravljeno: 2020-04-02 Odobreno za objavo: 2020-04-15 Analiza natančnosti sejanja večetažnega linearnega vibracijskega sita Hongwei Yan - Yajie Li - Fei Yuan - Fangxian Peng - Xiong Yang - Xiangrong Hou Šola za strojništvo, Kitajska severna univerza, Kitajska Večina vibracijskih sit na trgu ima majhno učinkovitost sejanja, obenem pa zasedajo veliko prostora. V pričujočem članku je podan predlog majhnega in učinkovitega linearnega vibracijskega sita. Analizirana je natančnost sejanja tega vibracijskega sita po metodi diskretnih elementov in določena sta najboljša frekvenca vzbujanja in masni pretok materiala. Ti rezultati so pomembna osnova za izboljševanje natančnosti sejanja manjših vibracijskih sit. Na podlagi opravljene raziskave trga so bile določene konstrukcijske zahteve za vibracijsko sito in postavljen je bil tridimenzionalni model. Določeni so bili tudi parametri vibracij za simulacijo in analizo gibanja kosov premoga na vibracijskem situ. Nato je bila postavljena eksperimentalna platforma za simulacijo procesa sejanja zmesi z uprašenimi delci premoga in določeni so bili optimalni parametri vibracij. Za simulacijo gibanja delcev na vibracijskem situ je bila uporabljena metoda diskretnih elementov, za analizo rezultatov simulacije pa metoda kontrolne spremenljivke. Rezultati eksperimentov so bili nato primerjani z rezultati simulacij za izluščenje najboljše frekvence vzbujanja in masnega pretoka. Predhodne simulacije so pokazale, da na učinkovitost sejanja vibracijskega sita vplivata predvsem vzbujalna frekvenca in masni pretok delcev. Primerjava rezultatov eksperimenta in simulacije je pokazala, da je najboljša vzbujalna frekvenca 18 Hz do 20 Hz. Previsoka ali prenizka vzbujalna frekvenca povzroči poslabšanje učinkovitosti in hitrosti sejanja. Analiza masnega pretoka materiala je pokazala, da sejanje pri pretokih od 0,6 kg/s naprej ne deluje zaradi visoke stopnje mašenja. Pri masnem pretoku 0,4 kg/s je stopnja mašenja manjša in sejanje lahko poteka normalno. Sledi sklep, da je zgornja meja masnega pretoka za normalno delovanje vibracijskega sita 0,4 kg/s. Omejitve raziskave, implikacije: (1) V fazi simulacije je bil privzet soobstoj sferičnih in nesferičnih kosov za opis dejanskega procesa sejanja. Vseeno pa obstajajo določena odstopanja od dejanskega procesa in za nadaljnje simulacije bo zato treba izdelati tudi model uprašenih delcev premoga. (2) Izbran je bil model trkov med delci na osnovi diskretnih elementov, ki pa ne omogoča simulacije in analize trkov med mokrimi delci ali delci v vlažnem okolju. Zato bodo potrebne nadaljnje analize mokrega premogovega prahu oz. drugih materialov za boljši popis dejanskega procesa sejanja. (3) V simulaciji z diskretnimi elementi je bila privzeta nespremenljiva oblika delcev in med trki tako ne prihaja do nobenih deformacij ali drobljenja. V nadaljevanju bo zato treba razviti kontaktni model, ki bolje popisuje dejanske pogoje. V članku je bil privzet soobstoj sferičnih in nesferičnih kosov za čim boljšo simulacijo dejanskega procesa sejanja premoga. Za simulacijo trkov delcev je bila uporabljena metoda diskretnih elementov, primerjava rezultatov eksperimenta z rezultati simulacij pa je pokazala dobro ujemanje. Metoda diskretnih elementov ima določene praktične tehnične prednosti za analizo sejanja z vibracijskimi siti. Sejanje je torej potencialno področje za širšo uporabo metode diskretnih elementov. Metoda bo tako lahko osnova za prihodnje optimizacije vibracijskih sit kot razvojnega področja izbrane metode. Ključne besede: vibracijsko sito, metoda diskretnih elementov, natančnost sejanja, vzbujalna frekvenca, masni pretok, oblika delcev SI 38 *Naslov avtorja za dopisovanje: Kitajska severna univerza, Šola za strojništvo, Taiyuan, Kitajska, aweigeyan@nuc.edu.cn Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, SI 39, © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-12-19 Prejeto popravljeno: 2020-04-02 Odobreno za objavo: 2020-04-15 Uporaba modela tankih rezin za določitev porazdelitve sil vzdolž nosilne ploskve in relativne porazdelitve sil, izmerjenih na korenskem delu zoba Wiktor Kamycki* - Stanislaw Noga Tehniška univerza v Rzeszowu, Oddelek za strojništvo in aeronavtiko, Poljska Zobniki so sestavni del sistemov za prenos moči. Vsak prenosnik ima lahko napake v izdelavi, ki jih je treba predvideti že v fazi konstruiranja. Ena od pomembnejših napak pri prenosnikih je napaka v poravnavi zobnikov, ki povzroči neenakomerno porazdelitev sil po nosilni ploskvi zobnikov v ubiranju. Neenakomerne obremenitve povzročijo koncentracijo napetosti v določenih predelih zob, ki postanejo dovzetnejši za porušitev. Gostota moči prenosnikov nenehno narašča, obenem pa so vse strožje tudi zahteve po njihovi zanesljivosti. Zato obstaja potreba po natančni opredelitvi porazdelitve sil po širini zob, v idealnem primeru po metodi A, ki jo predpisuje standard ISO 6336-1 (z merilnimi lističi na korenskem delu zoba). Z meritvijo raztezka vzdolž korenskega dela zoba je mogoče določiti korenski koeficient porazdelitve sile po širini zoba KFß. Neposredne meritve bočnega koeficienta porazdelitve sile po širini zoba KHß trenutno niso možne in za izpeljavo tega faktorja so potrebne dodatne pretvorbe na osnovi geometrije zobnika in znanega korenskega koeficienta porazdelitve sile KFß. Namen pričujoče raziskave je zato razvoj algoritma za preučevanje odvisnosti med koeficientoma porazdelitve sil KFß in KHß, ki bo upošteval vpliv porazdelitve sil po širini zoba za upogibne in za kontaktne napetosti. Za analizo vpliva porazdelitve sil po širini na kontaktne napetosti in na napetosti v korenu so bile uporabljene štiri metode: • smernice ISO 6336, ki določajo ugotavljanje koeficientov porazdelitve sile, • model tankih rezin, ki je bil razvit v programski opremi MATLAB za namene tega dela, • metoda končnih elementov, • namensko preizkuševališče v kombinaciji z naprednim sistemom za telemetrijo. Izračuni in simulacije pri vseh štirih metodah so bili opravljeni na osnovi parametrov planetnega gonila (sončni in planetni zobnik) vetrne turbine z močjo 2 MW. Opravljena je bila verifikacija razvitega modela tankih rezin s praktičnimi metodami analize porazdelitve sil na zobnikih. Štiri metode za analizo odvisnosti med koeficienti porazdelitve sile predstavljajo nov pristop k reševanju problema. Osnova za analizo je bilo opazovanje odgovora metod na tri posebne obremenitvene primere, ki so značilni za normalno obratovanje prenosnikov. S primerjavo se odpirajo priložnosti za iskanje združljivosti in nepravilnosti metod. Model tankih rezin je bil verificiran na osnovi smernic iz ISO 6336-1 v pogojih realnih obremenitev. Opažena sta bila dva glavna pojava: pojav sklopitve in robni pojav. Oba vplivata na odvisnosti med porazdelitvijo intenzitete sil za kontakt in upogib. Pojav sklopitve predstavlja nagnjenost zoba zobnika k prenašanju odklonov po širini zoba. Vsi odkloni zoba se prenašajo po širini s strižnimi silami. Robni pojav je povezan s področji koncentracije napetosti v okolici robov zoba zaradi Poissonovega pojava. Večja podajnost zoba v bližini roba verjetno pomembno vpliva na porazdelitev sil po nosilni ploskvi. Analize kažejo ustrezen odziv modela tankih rezin z ozirom na učinek sklopitve. Potreben pa bo še dodaten razvoj za zagotavljanje občutljivosti orodja na robni pojav in odpravo nezveznosti odklona, ki so se pojavile pri posebnih obremenitvenih primerih. V prihodnjih raziskavah bo uporabljeno posebno preizkuševališče za dinamične preskuse v skladu z delovnimi pogoji, ki se pojavljajo v prenosnikih. Članek osvetljuje pomen meritev porazdelitve sil na zobeh zobnikov z merilnimi lističi. Izpostavlja tudi problem določitve porazdelitve kontaktnih napetosti vzdolž nosilne ploskve in predlaga učinkovito rešitev. Razviti model tankih rezin bo lahko uporaben v industriji kot orodje za analiziranje porazdelitve sil po širini zob. Ključne besede: zobnik, porazdelitev sil, koeficient porazdelitve sil, porazdelitev napetosti, meritev raztezkov, meritev napetosti *Naslov avtorja za dopisovanje: Tehniška univerza v Rzeszowu, Oddelek za strojništvo in aeronavtiko, Al. Powstancow Warszawy 12, 35-629 Rzeszow, Poljska, wiktor.kamycki@gmail.com SI 39 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, SI 40, © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-12-19 Prejeto popravljeno: 2020-04-02 Odobreno za objavo: 2020-04-15 Raziskava sistema vodenja zgibnih goseničnih vozil s sledenjem poti Da Cui - Guoqiang Wang - Huanyu Zhao - Shuai Wang* Univerza Jilin, Šola za strojništvo in letalsko tehniko, Kitajska Zgibna gosenična vozila (ATV) so sestavljena iz dveh dvogoseničnih enot, ki sta povezani z zgibnim mehanizmom, uporabljajo pa se npr. v vojaški industriji, kmetijstvu in gozdarstvu. Kompleksna in nevarna delovna okolja zahtevajo uporabo avtonomnega sistema za navigacijo, ki zmanjšuje izpostavljenost ljudi tveganjem. Namen predstavljene študije je razvoj optimalnega sistema vodenja ATV s sledenjem poti. Vodenje gibanja ATV je zaradi edinstvenih krmilnih mehanizmov kompleksen problem. Na voljo so različne metode vodenja, med njimi pa je najprimernejša proporcionalno-integrirno-diferencirna regulacija (PID), ki lahko stabilizira nelinearne sisteme in je bila dobro sprejeta zaradi preproste zgradbe, nezahtevnega projektiranja in cenovno ugodne izvedbe. S klasičnimi regulatorji PID pa je težko doseči optimalno zmogljivost vodenja nelinearnih in kompleksnih sistemov. Za doseganje želene zmogljivosti sledenja poti ter optimalne zmogljivosti vodenja je bil zato uporabljen PID-regulator v kombinaciji z mehko logiko. Študija analizira zmogljivost krmiljenja ATV in vpeljuje dinamični model ATV. Na osnovi odmika od referenčne poti in odstopanja smernega kota vozila kot vhodnih spremenljivk ter odklonskega kota v točki tečaja in hitrosti pogonskih zobnikov kot izhodov regulatorja je bil razvit sistem vodenja ATV s sledenjem poti na osnovi algoritma vodenja, ki kombinira mehko logiko in PID. Za preverjanje uspešnosti predlaganega sistema vodenja sta bila izvedena virtualna simulacija prototipa in eksperiment s fizičnim prototipom v dveh značilnih režimih vožnje ATV. Rezultati simulacij so pokazali, da je sistem vodenja ATV zmožen uspešnega sledenja poti, mehki PID pa zagotavlja hitrejši odziv in manjši prenihaj kot klasični PID-regulator. Zasluga za to gre sistemu mehke logike. Rezultati eksperimentov se ujemajo z rezultati simulacij in sledi sklep, da lahko predlagani regulator uspešno sledi referenčni trajektoriji. V pričujoči študiji je predstavljen regulator, ki vozilom ATV omogoča sledenje referenčni poti. Zmogljivost regulatorja je bila ocenjena na podlagi rezultatov predhodne študije. Največji prenihaj je bil nastavljen na 20 %, čas umiritve ts pa na 10ey,max/v, kjer je ey,max največji odmik in v želena hitrost. Preden bo samodejno vodenje vožnje ATV primerno za praktično uporabo, bo treba izboljšati njegovo zmogljivost, zato bodo prihodnje raziskave usmerjene v izboljševanje zmogljivosti regulatorja. V študiji je predstavljen predlog novega sistema vodenja ATV za sledenje poti na podlagi algoritma, ki predstavlja kombinacijo mehke logike in PID. Podan je predlog matematičnega modela ATV in postavljen je model virtualnega prototipa ATV v paketu RecurDyn. Rezultati simulacije kažejo, da lahko ATV pod vodstvom mehkega PID-regulatorja uspešno sledi referenčni poti. Razvita je bila eksperimentalna platforma za preučevanje sistemov vodenja ATV s sledenjem poti na osnovi vizualne navigacije, ki omogoča testiranje njihove uspešnosti v praksi. Simulacije in fizična eksperimentalna platforma oblikujejo temelje za prihodnje aplikacije na področju samodejne navigacije ATV. Ključne besede: zgibno gosenično vozilo, dinamično modeliranje, sledenje poti, mehki PID-regulator, kosimulacija, vizualna navigacija SI 40 *Naslov avtorja za dopisovanje: Univerza Jilin, Šola za strojništvo in letalsko tehniko, Kitajska, wangshuai_jlucn@163.com Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, SI 41 © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-10-11 Prejeto popravljeno: 2020-04-07 Odobreno za objavo: 2020-05-11 Preliminarna primerjava termodinamičnih modelov podzvočnega ejektorja in turbopuhala Vytautas Martinaitis - Dovydas Rimdžius - Juozas Bielskus - Giedre Streckiene* - Violeta Motuziene Tehniška univerza Gediminas v Vilniusu, Oddelek za gradbeno energetiko, Litva Mešanje tokov je del tehnoloških procesov. Za realizacijo interakcij med tokovi z različnimi energijski potenciali se med drugim uporabljajo ejektorji in turbopuhala. Ejektorji so danes v široki uporabi in njihovi analitični modeli so dobro znani. Po vedenju avtorjev pa manjkajo študije, ki bi preučevale učinkovitost turbopuhal in pogoje, v katerih imajo lahko turbopuhala prednost pred ejektorji ali obratno. Pričujoči članek je namenjen primerjavi učinkovitosti termodinamičnih procesov v teh napravah. V ta namen sta uporabljeni stopnji kompresije in odnašanja, določena pa je tudi notranja nepovračljivost procesov (izgube). Predstavljena sta celovita enorazsežnostna termodinamična modela podzvočnega ejektorja in turbopuhala. Osnova za primerjavo so podatki o ejektorjih, saj so termodinamični modeli ejektorjev praktično in znanstveno potrjeni. Turbopuhalo ima jasno ločeno turbino in puhalo, zato v preliminarno primerjavo vstopa z manj domnevami, ki so odprte za razpravo, obenem pa ima podobno kot ejektor logično zaporedje korakov. Članek je teoretične oz. konceptualne narave: v njem so bile za obravnavani primer uporabljene analitične enačbe tokovnih procesov in njihove interpretacije iz učbenikov inženirske termodinamike. Kvantitativni indikatorji za razrešitev naloge so definirani z analitičnimi modeli in kombinacijo tamkajšnjih enačb. V obstoječih virih ni bilo mogoče najti preliminarnih primerjav termodinamičnih modelov omenjenih naprav. Avtorji verjamejo, da je z uporabo petih količnikov nepovračljivosti procesa za nastalo entropijo zagotovljen minimalen vpliv empiričnega pristopa, ki je sicer značilen za tehniške vede. Meja, na kateri turbopuhalo pridobi prednost pred ejektorjem na osnovi indikatorjev izkoristka kompresije in stopnje odnašanja, je določena analitično kot kombinacija izentropnih izkoristkov vrednotenih komponent (nr nF)2/(nNs nMs nDs). V tem primeru gre za izentropne izkoristke turbine, puhala, šobe, mešalne komore in difuzorja. Kvantitativni indikatorji so določeni za enake začetne pogoje, izražene kot razmerje razlike entalpije za idealno kompresijo in idealno ekspanzijo. Če so začetni pogoji enaki numerični vrednosti kombinacije izentropnega izkoristka vrednotenih komponent (numerični primer 0,16), imata obe napravi enak izkoristek. Pri nižjih začetnih pogojih (numerični primer 0,10) je stopnja odnašanja turbopuhala za 1,5* in izkoristek kompresije za 1,25* višji, medtem ko je pri višji vrednosti začetnih pogojev (numerični primer 0,28) učinkovitejši ejektor. Turbopuhala s svojimi značilnimi lastnostmi in naravo njihove variabilnosti so lahko primerna za različna področja uporabe tehnološke opreme, ki zahtevajo določene parametre mešanja tokov. Glavni vzrok razlik je v procesu mešanja. V ejektorju je ta realiziran z interakcijo kinetičnih energij, ki je izražena z enačbo ravnovesja momentov. V turbopuhalu se energija aktivnega toka pretvori v delo turbine, ta pa se prenese na puhalo, ki ustvarja pasivni tok. Proces je opredeljen z enačbami ravnovesja dela. Izentropni izkoristek je specifična lastnost komponent. Vrednosti nNs, nMs, nDs so v širokem območju razmeroma stabilne in dobro raziskane, pri mikroturbinah z delnim natokom in mikropuhalih pa se lahko vrednosti nT, nF precej odmaknejo od 1. Numerični rezultati primerjave modelov v članku so omejeni na mešanje zračnih tokov v podzvočnem režimu. Predstavljeni termodinamični model je zaradi podobnosti z ejektorjem, turbino in puhalom primeren tudi kot osnova za gradnjo teoretičnega modela strešnih turbinskih ventilatorjev. Razviti model bo lahko tudi podlaga za razvoj na področju analize nadzvočnega režima. Ključne besede: ejektor, turbopuhalo, termodinamični model, mešanje tokov, izkoristek kompresije, stopnja odnašanja *Naslov avtorja za dopisovanje: Tehniška univerza Gediminas v Vilniusu, Oddelek za gradbeno energetiko, Sauletekio ave. 11, Vilnius, Litva, gie-dre.streckiene@vgtu.lt SI 41 Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, SI 42, © 2020 Strojniški vestnik. Vse pravice pridržane. Prejeto v recenzijo: 2019-12-19 Prejeto popravljeno: 2020-04-02 Odobreno za objavo: 2020-04-15 Sistem za obremenjevanje z navorom na mehanskem zaprtozančnem preizkuševališču: vodenje na osnovi podatkov in brez modela z nevronskimi mrežami Aida Parvaresh1 - Mohsen Mardani2* tehniška univerza K. N. Toosi, Iran 2ACECR, Sharifova tehniška univerza, Iran Zagotavljanje pravilnega delovanja visokozmogljivih prenosnikov je pomembno za varnost in višino skupnih stroškov, še zlasti v letalski industriji. V ta namen so bila razvita različna preizkuševališča za testiranje stanja in zmogljivosti omenjene opreme. Ena najzanesljivejših metod za vrednotenje zmogljivosti sistemskih komponent je uporaba preizkuševališč v naravni velikosti. Preizkuševališča morajo zagotavljati čim manjše energijske izgube in ta pogoj izpolnjujejo mehanski zaprtozančni sistemi. Preizkuševališče, ki je bilo konstruirano v Sharifovi tehniški univerzi akademskega središča za izobraževanje, kulturo in raziskave (ACECR), je mehansko zaprtozančno preizkuševališče, namenjeno testiranju visokozmogljivih prenosnikov v različnih obratovalnih pogojih. Preizkuševališče mora biti za simuliranje najrazličnejših delovnih pogojev sposobno doseganja različnih vrednosti hitrosti in navora, kar je izvedljivo s sistemi za obremenjevanje z navorom. Za vodenje teh sistemov so na voljo različne rešitve, med katerimi imajo prednost elektrohidravlični aktuatoiji (EHA). Ti omogočajo ustvarjanje velikih sil in točno pozicioniranje, obenem pa ne zasedejo veliko prostora. Natančno obremenjevanje z navorom je ključnega pomena, saj vpliva na vrednotenje zmogljivosti prenosnikov. Zato je nujno natančno modeliranje sistema v kombinaciji z visokozmogljivim regulatorjem. Za odpravo potrebe po reševanju kompleksnih nelinearnih enačb EHA, ki so povezane s trenjem, spreminjajočimi se tokovnimi lastnostmi itn., je bil pri modeliranju uporabljen sistem z nevronskimi mrežami na osnovi podatkov. Na ta način je mogoče pridobiti model sistema brez poenostavitev, ki popisuje celotno dinamiko sistema. Natančnost in zanesljivost modela je bila potrjena z eksperimentalnimi podatki, ki so bili zbrani med uporabo izdelanega sistema vodenja. Vrednosti korena povprečne kvadratne napake 0,00055726 in standardnega odklona 0,0005574 nakazujeta visoko kakovost modela sistema. Po določitvi modela so bili učni faktorji nastavljeni na vrednost nič za zmanjšanje visoke računske zahtevnosti iterativnega procesa. Nato je bila zasnovana nova nevronska mreža za sledenje sistema za obremenjevanje z navorom želeni trajektoriji. Parametri mreže so bili prilagojeni za čim manjšo napako sledenja. Preučena je bila zmogljivost predlaganega krmilnika v običajnih razmerah in v prisotnosti motenj za pokrivanje vseh scenarijev, ki se lahko pojavijo pri delovanju sistema v praksi. Rezultati kažejo, da izhod regulatorja doseže referenčni izhod v približno 0,25 s, brez prenihaja ali pogreška v ustaljenem stanju. Regulator poleg tega zelo dobro sledi variabilni referenčni vrednosti. V primeru vnosa motnje je le-to lahko obvladal in sledil referenčni vrednosti v času 0,13 s. Sledi sklep, da lahko regulator zagotavlja dobro sledenje pri različnih referenčnih vhodih oz. v različnih pogojih. Rezultati so bili za oceno zmogljivosti predlagane rešitve primerjani z rezultati običajnega proporcionalno-integralno-diferencialnega (PID) regulatorja, pri čemer so bile potrjene odlične lastnosti predlagane rešitve. Glavni prispevek študije je v predstavitvi preprostega postopka na osnovi podatkov za natančno modeliranje in regulacijo hidravličnega aktuatorja na obstoječem preizkuševališču, kakor tudi v odpravi potrebe po poenostavitvah in reševanju kompleksnih nelinearnih enačb. Ključne besede: identifikacija, sistem na osnovi podatkov, zaprtozančno preizkuševališče, hidravlični aktuator, nevronske mreže SI 42 *Naslov avtorja za dopisovanje: ACECR, Sharifova tehniška univerza, Iran, mardani@acecr.ac.ir Guide for Authors All manuscripts must be in English. 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Define acronyms in the text, not in the nomenclature. - References must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript. - Appendix(-icies) if any. SPECIAL NOTES Units: The SI system of units for nomenclature, symbols and abbreviations should be followed closely. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms-1, K, min, mm, etc.). Please also see: http://physics.nist.gov/cuu/pdf/sp811.pdf . Abbreviations should be spelt out in full on first appearance followed by the abbreviation in parentheses, e.g. variable time geometry (VTG). The meaning of symbols and units belonging to symbols should be explained in each case or cited in a nomenclature section at the end of the manuscript before the References. 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References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. Please add DOI code when available. Examples follow. Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code. [1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent cross-linked simulations. Strojniški vestnih - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013. Journal titles should not be abbreviated. Note that journal title is set in italics. Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication. [2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken. Note that the title of the book is italicized. Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages. [3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordič, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553576. Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages. [4] Štefanič, N., Martinčevič-Mikič, S., Tošanovič, N. (2009). Applied lean system in process industry. MOTSP Conference Proceedings, p. 422-427. Standards: Standard-Code (year). Title. Organisation. Place. [5] ISO/DIS 16000-6.2:2002. Indoor Air - Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva. WWW pages: Surname, Initials or Company name. Title, from http://address, date of access. [6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 200909-07. EXTENDED ABSTRACT: When the paper is accepted for publishing, the authors will be requested to send an extended abstract (approx. one A4 page or 3500 to 4000 characters or approx. 600 words). The instruction for composing the extended abstract are published on-line: http://www.sv-jme. eu/information-for-authors/ . COPYRIGHT: Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original work by the authors and not be published elsewhere in any language without the written consent of the publisher. The proof will be sent to the author showing the final layout of the article. Proof correction must be minimal and executed quickly. Thus it is essential that manuscripts are accurate when submitted. Authors can track the status of their accepted articles on http://en.sv-jme.eu/. PUBLICATION FEE: Authors will be asked to pay a publication fee for each article prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 380 EUR (for articles with maximum of 6 pages), 470 EUR (for articles with maximum of 10 pages), plus 50 EUR for each additional page. The additional cost for a color page is 90.00 EUR (only for a journal hard copy; optional upon author's request). These fees do not include tax. Strojniški vestnik -Journal of Mechanical Engineering Aškerčeva 6, 1000 Ljubljana, Slovenia, e-mail: info@sv-jme.eu http://www.sv-jme.eu Contents Papers Benjamin Bizjan, Brane Sirok, Marko BLagojevic: Analogue Experimental Study of Fiber Formation on two-Wheel Spinner Hongwei Yan, Yajie Li, Fei Yuan, Fangxian Peng, Xiong Yang, Xiangrong Hou: Analysis of the Screening Accuracy of a Linear Vibrating Screen with a Multi-layer Screen Mesh Wiktor Kamycki, Stanistaw Noga: Application of the Thin Slice Model for Determination of Face Load Distribution along the Line of Contact and the Relative Load Distribution Measured along Gear Root Da Cui, Guoqiang Wang, Huanyu Zhao, Shuai Wang: Research on a Path-Tracking Control System for Articulated Tracked Vehicles Vytautas Martinaitis, Dovydas Rimdzius, Juozas BieLskus, Giedre Streckiene, VioLeta Motuziene: Preliminary Comparison of the Performance of Thermodynamic Models of the Subsonic Ejector and Turbofan Aida Parvaresh, Mohsen Mardani: Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 279 28 300 9770039248001