1 Introduction Swash plate design axial piston units are often used as pumps and motors in mobile and stationary applications. Figure 1 shows the assembly of an unit consisting of a drive shaft (1), which is connected to the cylinder (10). The cylinder is connected via the port plate (7) to suction port (8) and high-pressure side (5) using the Aus Wissenschaft und Forschung 9 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0028 EHL Simulation Model for an Abstracted Piston-Bushing Test Rig Markus Gärtner, Achill Holzer, Felix Fischer, Katharina Schmitz* Eingereicht: 30. Juli 2019 Nach Begutachtung angenommen: 11. November 2019 Am Institut für Fluidtechnische Antriebe und Systeme der RWTH Aachen University (ifas) wird das tribologische Verhalten des Systems Kolben - Buchse in Schrägscheibenpumpen - seit einigen Jahren experimentell an einem Einkolbenprüfstand untersucht. In der vorliegenden Publikation wird die simulative Modellbildung mithilfe des Mehrkörpersimulationswerkzeugs FIRST der IST GmbH diskutiert. Drei verschiedene Simulationsmodelle mit unterschiedlicher Modellierungstiefe werden hinsichtlich des Aufwands der Modellbildung, der erforderlichen Randbedingungen und der Berechnungsdauer verglichen. Abschließend erfolgt ein kritischer Vergleich der Berechnungsergebnisse anhand der Verlustkenngrößen axiale Reibkraft und Leckage. Weiterhin werden Ansätze zur Verbesserung der Simulationsmodelle genannt. Schlüsselwörter Kolben-Buchse-Kontakt, EHD-Simulation, Mehrkörpersimulation, hydrodynamische Schmierung, Grenzreibung, Reibkraft, Leckage At the Institute for Fluid Power Drives and Systems of RWTH Aachen University (ifas) the tribological behaviour of the piston - bushing contact in swash plate pumps has been investigated experimentally on a single piston test rig for several years. In the present publication simulation modelling is discussed with the help of the multi-body simulation tool FIRST, developed by the IST GmbH. Three different simulation models with different modeling depths are compared with respect to the effort of modelling, the required boundary conditions and the calculation duration. Finally, differences in the calculation results are critically compared on the basis of the loss characteristics of axial friction force and leakage. Furthermore, approaches for improving the simulation models are mentioned. Keywords piston-bushing contact, EHL simulation, multi-body simulation, hydrodynamic lubrication, boundary lubrication, friction force, leakage Kurzfassung Abstract * Dipl. -Ing. Markus Gärtner Orcid-ID: https: / / orcid.org/ 0000-0001-8040-351X Pleiger Maschinenbau GmbH & Co. KG Achill Holzer, M.Sc. Orcid-ID: https: / / orcid.org/ 0000-0003-1190-1819 Felix Fischer, M.Sc. Orcid-ID: https: / / orcid.org/ 0000-0002-4558-333X Univ.-Prof. Dr.-Ing. Katharina Schmitz Orcid-ID: https: / / orcid.org/ 0000-0002-1454-8267 Institute for Fluid Power Drives and Systems (ifas) RWTH Aachen University control plate (6) as fast-acting valve. Pistons (11) with slipper pads (12) are kinematically driven and supported by the swashplate (13) and retaining plate (2). A control unit (4) allows to rotate the swashplate by the stroke piston (3) to a certain angle. Figure 1: Assembly of an axial piston unit [Bos08] TuS_6_2019.qxp_T+S_2018 28.11.19 14: 53 Seite 9 tact surfaces are modelled with EHL couplings is an established method. Typical applications include various hydrodynamic and partially hydrostatic bearings in internal combustion engines (for example piston ring cylinder liner or connecting rod bearing, crankshaft bearings and camshaft bearings) or friction pairings in hydrostatic machines, such as hydraulic or high-pressure pumps (common rail) [Bar13, Bob08, Hei17, Sch01, Lan97, Pel12]. With the goal of refeeding of the introduced friction force to the temperature of the affected components and in particular of the fluid, the thermo-elastohydrodynamic coupling (TEHL) is the subject of current research [Sha16, Sha18, Sol06]. However, it is not implemented in this work. 3 Single piston test rig The measurements, that are basis of the simulation presented here, are executed on a single piston test rig in the ifas laboratory (see Figure 2). Experimental measurements have been performed and will be published on a later stage. It consists of an asynchronous motor (6) which is connected to a fly wheel (5). The test rig housing (3) contains the swashplate machine and is described further below. Using an auxiliary shaft (3), the motor also drives the rotary valve (2), which, together with the valve block (1), allows a precise timing of the inand outlet flows. This test rig is suitable for experimental analyses of axial and tangential friction force (likewise friction work), leakage and temperature distribution in the piston-bushing contact. The kinematic chain of the test rig is inverted with respect to that of a swashplate machine and corresponds to that of a wobble plate machine. Figure 3 shows the guide unit of the test ring in cross section. Due to the inverted kinematic chain, both bushing and bushing carrier (4) are mounted stationary. This allows easy mounting of various sensors close to the regarded Aus Wissenschaft und Forschung 10 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0028 The power loss of those units is mainly caused by the tribological contacts cylinder block - valve plate, slipper - swashplate and piston-bushing. The piston-bushing contact is in contrast to the other two tribological systems slipper - swashplate and cylinder block - valve plate usually not hydrostatically balanced. Thus, hydrodynamic pressure build-up and solid contact forces support the piston lateral forces. The complex friction behaviour in the considered contact is the subject of numerous publications [Fan95, Man99, Iva12, Bre06, Brä06]. In the context of this paper, modelling will be discussed using an established computer program. The test results, among others from Vatheuer [Vat16], provide a broad basis for the validation of the simulation results. In particular, in cases where measurement data cannot be reliably detected according to the current state of the art, whether due to the measuring position or the inevitable influence of the measuring subject, further findings can be obtained by numerical methods. In the investigations described below, the program package FIRST of IST GmbH [IST11] is used, which is suitable for the calculation of conformal contacts. The focus is on the calculation of the piston - bushing contact. In a model analysis, the adjacent contacts slipper - swash plate and the ball joint, which connects slipper and piston, are considered. 2 State of the art The piston-bushing contact has been a subject of research for several decades. The experimental and analytical work of Renius [Ren74] and Regenbogen [Reg78] is often cited. About 20 years ago, numerical approaches were published for the first time. In the face of the low computing power at that time, the focus was on efficient algorithms and simple mathematical modelling. Often, elastic deformations and boundary lubrication were not considered [Ole01, Kle02]. Nowadays the calculation of tribological problems using multi-body simulation models, in which lubricated con- Figure 2: General view of the single piston test rig TuS_6_2019.qxp_T+S_2018 28.11.19 14: 53 Seite 10 contact. Driven by the swash plate (1), piston (3) and slipper (2) perform a forced axial movement within the bushing carrier. The latter is bolted to a plate (12), which is connected to the test rig housing (7) with four piezo load cells (11). The compensation piston (9) establishes a hydraulic connection to the rotary valve, without a significant force shunt on the force sensors. The compensation piston is cylindrically mounted in the bushing carrier. A hydrostatically balanced lubrication gap between compensation piston face side and swivel plate (8) provides a low-friction guidance. The swivel plate (8) can be adjusted angularly to the housing (7), so that an inclination angle analogous to the angle inclined piston in the cylinder block can be adjusted. The hold-down device (5), which is guided on the swash plate (1) and slotted link (6), prevents the lifting of the slipper during the suction stroke in pumping operation. 4 Model preparation The part models are prepared for the following steps using a CAD program. In this case, design elements, such as radii or contours, which do not affect the rigidity of the component, are revised or removed. This is necessary in order to keep the number of elements and nodes of the discretized component model low and at the same time to keep the ratios of the element edge lengths within the limits, which are subsequently specified in the FE program by the modal calculation. In order to do so, the authors use the multi-body EHL simulation program enviroment FIRST. This software solves the Reynolds equation for the tribological contacts and couples them with Newton’s law of motion. Deformations caused by the fluid film pressure are calculated with a simplification of the FE model (modal reduction) to lower the above mentioned number of nodes and thereby the computing time. Discretization and preparation of the component models are carried out by means of Ansys ® Workbench and Ansys ® Classic. The processing includes the grouping of nodes depending on the functional area as well as the definition of master nodes (rigid body elements, RBE3 nodes) and their slave nodes for load introduction or clamping. Since the rigidity of the clamping is not negligible fixed bodies, for example the measuring plate (12), are not clamped in the centre of gravity as it is default setting, but at defined nodes using spring-damper elements. In FIRST the elastohydrodynamic calculation must be carried out on a two-dimensional mesh consisting exclusively of elements with a linear approach function. If necessary, the surface mesh of one of the two contact partners can be used. In this calculation all bodies are discretized by means of quadratic shape function. Hence a separate mesh is required. Thereby, the spatial resolution of the calculation results in the lubricated contacts can be varied independently of the component discretization. 5 Part reduction The component models would, in the present discretized manner in a dynamic multi-body simulation, create memory requirements and computation times that would be impractical. An adaptation of these models is done once Aus Wissenschaft und Forschung 11 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0028 Figure 3: Sectional view of the guiding unit TuS_6_2019.qxp_T+S_2018 28.11.19 14: 53 Seite 11 dition are coloured yellow, the red nodes illustrate the location and dimensions of the bearings with elastohydrodynamic coupling. In addition, the types of required boundary conditions and their origin differ. In model A the piston axial force, the lateral forces and the drive definitions like stroke and piston rotation are impressed via look-up tables. The axial force is calculated based on the experimentally determined cylinder pressure p dyn . Furthermore, the cylinder pressure is impressed on all surfaces that define the pressure-loaded volume (piston bore, rear bushing end face and outer cylindric piston surface), so that a realistic pressure-induced deformation set is achieved. The lateral piston forces acting in the centre of the piston ball can be determined experimentally or calculated from the piston axial force. In the models B and C, the piston stroke is given by the wobble plate. With sufficiently low suction pressure and high axial piston acceleration, the slipper can lift off the wobble plate. The hold-down device is represented by a spring system, which is situated in the sliding plane and rotates with the wobble plate. The normal force of the used spring is defined in the respective models by a lookup table. In Figure 6 the force is plotted along the spring stroke. Aus Wissenschaft und Forschung 12 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0028 by a combined, static and modal reduction. A comprehensive description of the procedure can be found at Gasch [Gas12, Lang Lan97 and Schönen Sch01]. The aim of this reduction is on the one hand to reduce the degrees of freedom of the body and thus to keep the calculation time to a practicable extent and on the other hand to correctly reflect the rigidity and the deformation especially of contact surfaces. The static reduction is based on the description of a mechanical problem using static approach vectors. These vectors are determined by a staticmechanical analysis using the finite element method (FEM). In the modal reduction, the mechanical problem is subjected to a natural vibration analysis. The number of modes to be calculated or the limit frequency f limit is specified by the user. As a result, high-frequency deformation components or modes, for example the z-shaped displacement of adjacent nodes, can be excluded from the solution. An abstracted and simplified representation of the two reduction principles is shown in Figure 4. 6 Simulation models Three different simulation models (see Figure 5) were set up, which differ in their complexity and the number of components. Nodes used to define the boundary con- Figure 4: Principle of the static and modal reduction, exemplified by means of the abstracted piston Figure 5: Simulation models, model A (left), model B (central), model C (right) TuS_6_2019.qxp_T+S_2018 28.11.19 14: 53 Seite 12 The force close to zero for z ≤ 30 μm represents the clearance between the slipper shoulder and the holddown device. By limiting the maximum force, the convergence of the calculation at the beginning of the simulation is improved, in the case of disadvantageous selected initial conditions of the piston - slipper assembly. Model B and especially model C are to be drafts. Section 7 gives reasons why the simulation results differ. The impact of increased model complexity on the required calculation time can be reliably estimated. 6.1 Model A Model A consists of the bodies piston and force measuring plate. The part force measuring plate consists of two CAD models, the force measuring plate itself and the bushing. During model preparation with ANSYS APDL, the outer mesh nodes of the bushing are connected to the mesh elements of the force plate by means of constraint equations. The separate model preparation of both components makes it possible to allocate different material characteristics to the bushing than to the force measuring plate. 6.2 Model B Compared to model A, model B is expanded by the swashplate and hence the contact slipper - swash plate. The piston lateral forces are impressed by the support of the assembly shoe and the piston on the swash plate. Added to this is the influence of the frictional force between the slipper and the swash plate, which, depending on the angular position φ, leads to an increase or decrease in the lateral force acting on the ball joint. Piston and slipper are connected with constraint equations. Thus, this model is only suitable for models in which for the inclination angle ψ = 0° applies. Otherwise, the varying difference angle between the wobble plate angle or swash plate angle and the slipper angle inevitably leads to high contact pressure at the edge of the non-freely movable slipper. Even at ψ = 0° this can occur by nonsynchronous rotation of the wobble plate and the elastically connected assembly slipper - piston, for example, caused by a high frictional torque in the piston - bushing contact. The consequence is edge wear on the flat sliding surface of the slipper. The stiffness of the employed rolling bearing is here, for lack of a linear model for description, considered idealized and more than two orders of magnitude higher than that of the force measuring plate. 6.3 Model C Model C is distinguished from model B by the additional degrees of freedom in the ball joint between piston and slipper. Both components are also connected to each other by means of an EHL-coupling. Therefore, this simulation model is also suitable for investigations at inclination angles ψ ≠ 0°. Furthermore, a relative movement in the ball joint about the axis of symmetry is possible. Because of the high friction torque caused by the high contact pressure in the ball joint this relative movement does not necessarily occur. Both analytical estimates and experimental data prove that the slide bearing piston - bushing is operated under mixed friction, in part with dominant solid friction fractions. This condition must be considered by suitable contact modelling, which is able to reproduce the high pressures and their high spatial gradients. The required relationship between contact pressure and gap height is made by the model of Greenwood and Tripp [Gre66, Gre70]. 7 Results Numerical methods are currently considered as a valid alternative to costly experiments and are increasingly used. The goal must therefore be to develop a realistic, self-contained model that does not require measurement data. One approach to assessing this goal is to discuss the results of the three different multi-body simulation models. With increasing model complexity, the required Aus Wissenschaft und Forschung 13 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0028 0,0 0,5 1,0 1,5 2,0 2,5 0 100 200 300 400 500 0,0 0,5 1,0 1,5 2,0 2,5 28 29 30 31 32 33 34 35 F hold in MN F hold in MN z in µm z in µm Figure 6: Characteristic curve of the hold-down device, detailed view on right side TuS_6_2019.qxp_T+S_2018 28.11.19 14: 53 Seite 13 In Figure 9, the leakage in the piston - bushing contact is plotted against the rotation angle, depending on the simulation model. There is no noticeable difference during the suction stroke. Differences during the pump stroke are due to slight differences in the radial and angular piston position in the sealing gap. Because of the cubic dependence, large dif- Aus Wissenschaft und Forschung 14 Tribologie + Schmierungstechnik · 66. Jahrgang · 6/ 2019 DOI 10.30419/ TuS-2019-0028 calculation times and the number of required parameters also increase. Model B requires about six and a half times the calculation time of model A. The calculation of Model C requires eight times compared to model A. Due to different assumptions and boundary conditions, different results can be expected in the simulation models. The main difference between the more complex models is the specification of the lateral force (see Figure 7). Compared with the measured data in model A, up to ten percent higher lateral forces are calculated for the models B and C, in particular during the pump stroke. The simplified calculation of the contact slipper - swash plate with constant pressure boundary conditions is identified as the cause for the deviating results of the slipper friction force. The measured slipper friction force, which results from the difference of the measured lateral force and the calculated kinematic lateral force is small and is not visible properly in the lateral force vibration of higher order. An indication for the high slipper friction force according to the simulation is provided by the pressure distribution at the contact surface between the slipper and swash plate and the ball joint. In model B, moderate pressures up to four times the high pressure p HD (desired pressure during pump stroke) always occur at the same position of the slipper outer edge. According to model C in the area of the inner bearing lands at a variable angular position contact pressures up to eighteen times of p HD occur. In model B a significant deformation and therefore high pressures on the bearing lands is prevented by the elastic coupling between the slipper and piston. However, the variation of the surface pressure and the slipper friction force does not provide a plausible reason for the frictional behaviour of the piston-bushing contact of the different models (Figure 8). Thus, in model B, there must be an unknown effect counteracting the lateral force increase, so that the result is almost identical to that of model A. Furthermore, the high-frequency vibrations of the test rig structure, as they were observed in the measured piston lateral forces, also do not occur in models B and C. φ in ° F lat,kin in kN A C B 0 1 2 3 0 90 180 270 360 Figure 7: Comparison of the simulated kinematic lateral piston forces using model A, model B and model C -50 0 50 100 150 0 5 10 15 20 25 |z| in mm F z,tot in N A C B Figure 8: Comparison of the simulated total axial friction force F z,tot using model A, model B and model C 0 0,05 0,1 0,15 0 90 180 270 360 φ in ° Q in l/ min A C B Figure 9: Comparison of simulation results concerning leakage Q using model A, model B and model C TuS_6_2019.qxp_T+S_2018 28.11.19 14: 53 Seite 14 ferences in the resulting pressure flow occur even with small changes, which may be caused by the different mechanical boundary conditions. Due to the lack of the correct slipper pressure (actually dependent on the gap height between slipper and wobble plate), both the models B and C are calculated with the geometrically predetermined, i.e. static, compensation ratio. The mean leakage flow in this contact according to model C is six times, according to model B, twelve times the leakage in the piston-bushing contact at the same operating point. This difference is caused by the elastic connection between the piston and the slipper, whereby the slipper glides angularly on the swash plate as a result of the piston friction torque. The leakage in the ball joint is according to simulation result three orders of magnitude below that of the piston-bushing contact. 8 Conclusion and outlook In this case, with focus on the piston-bushing contact, a relatively simple model is suitable. If only the consideration of the piston-bushing contact is relevant, computation time can be saved. The disadvantage of the dependence of measured data (in particular the pressure buildup) is the same for all models used here. This disadvantage can be prevented for purely qualitative examination, for example by using generic pressure build-up functions. A design study and study of the tribological behavior is also possible in this case. In addition, the simulation model can be used to determine quantities, which can be measured only with great effort in an experimental investigation. In some cases, influencing the tribological system is inevitable. Examples of this are the radial piston displacement and the pressure distribution in the contact. A significant error is made by assuming a constant temperature distribution in the piston-bushing contact. The thermo-elasto hydrodynamic modelling, especially considering the partial solid body contact, requires further research activity. 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