1 Introduction and Motivation Hydraulic pumps convert mechanical to hydraulic power in the form of volume flow and pressure at the input side of hydraulic systems. This hydraulic power can then be used to generate linear movement by cylinders and rotational movement via motors at the output of the system. The principle of operation of hydraulic pumps and motors used in this process is identical. In centralized hydraulic systems, power is typically provided by a main pump operating at a constant speed, and the volume flows of the output drives are controlled by valves. The high dynamics achievable thereby are accompanied by throttling losses at the valves and supply pressures that are not attuned to the working pressures, resulting in Nachrichten 46 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 DOI 10.24053/ TuS-2023-0023 GfT-Förderpreis 2023 Experimental and Simulative Investigation of a Partially Hydrostatic Relieved Contact in Variable Speed Axial Piston Machines Felix Schlegel, Amos Merkel, Katharina Schmitz* Das Thema wurde für den GfT-Förderpreis 2023 in der Kategorie „Diplom- und Masterarbeiten“ im April eingereicht, die Auszeichnung findet im Rahmen der GfT-Tagung im September statt. In einigen tribologischen Kontakten hydraulischer Axialkolbenmaschinen wird der Schmierfilmdruck zum Teil durch Hydrodynamik und zum Teil durch eine lastabhängige hydrostatische Entlastung erzeugt. Die Abstimmung dieser Druckanteile stellt bei der Auslegung tribologischer Kontakte mit variabler Relativgeschwindigkeit und variabler Last eine Herausforderung dar. Besonders das Betriebs- und Verschleißverhalten des Gleitschuh-Schrägscheibe-Kontakts in drehzahlvariablen Axialkolbenmaschinen ist unter diesen Bedingungen aktuell nicht vollständig erforscht. In dieser Arbeit wird eine simulative und experimentelle Untersuchung des Gleitschuh-Schrägscheibe- Kontakts vorgestellt, mit dem Ziel, wesentliche Einflussfaktoren auf den Verschleiß bei Betriebspunktwechseln zu identifizieren. Schlüsselwörter Hydraulik, Axialkolbenmaschine, Gleitschuh-Schrägscheibe-Kontakt; EHD-Simulation, Modellversuch The lubrication film pressure of certain tribological contacts of hydraulic axial piston machines is generated partly by hydrodynamics and partly by a loaddependent hydrostatic relief. Matching these pressure components is a challenge in the design of tribological contacts with variable relative velocity and variable load. In particular, the operating and wear behavior of the slipper-swashplate-contact in axial piston machines has currently not been fully investigated under these conditions. Thus, in this work, a simulative and experimental investigation of the slipper-swashplate-contact is presented, to identify major factors influencing wear during operating point changes. Keywords hydraulic, axial piston machine, slipper-swashplatecontact, EHL-simulation, model experiment Kurzfassung Abstract * Felix Schlegel M.Sc. Amos Merkel M.Sc. Univ.-Prof. Dr.-Ing. Katharina Schmitz RWTH Aachen University, Institut für fluidtechnische Antriebe und Systeme (ifas), Campus-Boulevard 30, 52074 Aachen, Deutschland TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 46 Nachrichten 47 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 poor overall efficiencies / Fin15/ / Sch18/ . In distributed hydraulic system architectures, the output drives are independent of one another, which can increase efficiency and reliability depending on application / Fin15/ . One example is the electro-hydrostatic actuator (EHA), which consists of a self-sufficient cylinder supplied individually by a pump. An EHA with a bidirectional variable-speed pump can be controlled directly by the frequency converter of the drive motor / Fin15/ . This reduces piping and valves, consequently lowering the risk of leakage, as well as flowand throttling losses / All16/ . Due to the reversing operation, mixed friction occurs more frequently in these pumps than in constantly operated ones. Since EHA pumps only supply one drive, they are usually substantially smaller than pumps for centralized systems. It follows, that they must be operated at higher speeds if large volume flows are required for fast cylinder movements. Various pump types can be considered for use in EHA. Pumps in axial piston design are particularly suitable since they deliver high pressures at compact installation space, short response time, and high stiffness / Iva01/ . The basic structure of an axial piston machine in a swash plate design is shown in Figure 1. In axial piston machines, oil is displaced by an oscillating stroke movement of the working pistons. These pistons rotate with a cylinder block, which is connected to the drive shaft. The reciprocating motion of the pistons is created by the swivel angle of the swashplate. When operating as a pump, the delivery pressure is built up by the pistons being pushed into the cylinder block by the swashplate. The slippers thereby serve as axial bearings for the pistons. A stationary valve plate determines which piston chambers are connected to the highor low-pressure port, controlling the volume flow of the pump. Performance, efficiency, and service life of axial piston machines are essentially determined by three tribological contacts. These are the “cylinder block-valve plate” (a), the “piston-bushing” (b), and the “slipper-swashplate” (c) contact. The contact pressures acting there are generally too high to solely rely on a hydrodynamic bearing arrangement, to fully separate the surfaces of the contact partners / Koc97/ / Man13/ . Consequently, the three contacts are hydrostatically relieved, as shown in Figure 2. In the following, the slipper-swashplate contact is considered, since this can be classified as a critical failure point in some high-speed EHA pumps / Roe20/ . DOI 10.24053/ TuS-2023-0023 Figure 2: Principle of Hydrostatic Relief with Larger Scaled Gaps Figure 1: Structure of an Axial Piston Pump in Swashplate Design TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 47 Nachrichten 48 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 During hydrostatic relief, defined volume flows are guided from the piston chambers into the respective contacts. The hydrostatic pressure of the oil results in a force that reduces the load on the contact. The slipperswashplate contact is commonly designed to support approximately 95 % to 99 % of the contact load by the hydrostatic relief and the remaining 1 % to 5 % by the hydrodynamic pressure buildup due to the slipper’s movement / Iva01/ . In variable-speed pumps, a lower degree of hydrostatic relief is often selected to avoid floating at high speeds causing significantly increased leakage flows, decreasing the pump efficiency. Due to this coordination of the hydro-dynamic pressure build-up and the hydrostatic relief, the lubrication conditions of the slipper-swashplate contact depend on the speed and pressure of the pump. The mechanisms influencing wear in load and speed-variable operation have not been conclusively investigated / Roe20/ . In this publication, experimental and simulative investigations are presented showing effects that explain the increased wear of a partially hydrostatic relieved tribological contacts under variable relative velocity and variable load compared to constant operation. For this purpose, piston-slipper assemblies of an aviation-grade EHA pump for primary flight control were investigated. 2 Model Test Structure and Test Matrix The basic setup of the test rig used in this work is shown in Figure 3 and will be briefly explained below. It was also described in more detail in / Mer22/ with some parts of the subsequent shown experimental results. To reduce the complexity of the experiment, integrate measurement technology, and facilitate the isolation of individual effects, simplified kinematics are used in the test rig. There is no swivel angle, and the test rig is operated in inverse kinematics compared to the pump. Hence the rotor is driven, whilst the piston carrier is stationary. Consequently, no friction-induced rotation is imposed on the pistons and no centrifugal forces act on the slippers. Additionally, the piston carrier does not tilt, there is no reversal, and no piston stroke. Due to the lack of piston stroke, the slippers are instead supplied with pressure by a hydraulic unit. To measure the leakage volume flow of the hydro-static relief of the slippers, they are statically sealed, preventing oil from leaving the piston carrier through the piston-bushing contact. Three slippers can be tested at relative speeds of up to 12.56 m/ s and piston chamber pressures of up to 350 bar. The test rig allows continuous measurement of the leakage volume flow of the hydrostatic relief of the slippers, tempe- DOI 10.24053/ TuS-2023-0023 Figure 3: Test Rig Structure Table 1: Test Matrix TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 48 Nachrichten 49 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 rature and pressure in the piston chambers, the friction torque of the slippers as well as the speed of the running disk. Various test series were carried out to determine why increased wear occurs in axial piston pumps in variable load and speed operation. The characteristics of the friction torque and leakage of the slipper’s hydrostatic relief were recorded, and the wear, geometry, and surfaces of the slippers were continuously measured at discrete intervals during operating point changes. For this purpose, a sequence of three typical operating points (low, medium, high (frictional power)) shown in Table 1 was investigated. The sequence of operating point changes was selected to perform each change at least once. 3 Structure and Operation of the Simulation In this work, an elastohydrodynamic lubrication (EHL) simulation, based on the work of Wegner / Weg21/ and Lee / Lee20/ is used to obtain deeper insights into the behavior of the slipper-swashplate contact. The basic simulation setup is shown in Figure 4. The simulation is based upon a fluid-structure coupling. The macroscopic motion and load state of the slipper is determined via the pump kinematics (see / Sch14/ ) under the previously evaluated operating conditions and external loads. Using the finite element method (FEM), the deformation of the slipper is calculated with these loads and transferred to a calculation of the lubrication gap height. Subsequently, the lubrication gap height is determined with a numerical solution of the Reynolds equation (see / Bar10/ ) using the finite volume method (FVM). The average flow model of Patir and Cheng / Pat78/ is used to account for microhydrodynamics, and the model of Jakobsson, Floberg, and Olsson / Jak57/ is used to account for cavitation. With the help of the contact models according to Greenwood-Williamson / Gre66/ or Persson / Per06/ , the solid body contact pressure is then determined from the gap height. The calculated contact pressure is, depending on the gap height prorated consisting of the solid body and the fluid pressure. The calculated contact pressure is in turn coupled with the calculation of the deformation of the slipper. This numerical problem is solved iteratively using the Newton-Raphson method. The iteration is terminated once the force acting in the contact corresponds sufficiently accurately to the external load force, satisfying the force equilibrium at the slipper. Once the solution for the gap height has converged, the wear models according to Archard / Arc53/ and Fleischer / Fle80/ can be used to calculate local wear based on the solid contact pressure distribution. The wear coefficients required for this were previously determined on the model test rig. 4 Experimental Results Figure 5 shows the characteristic diagrams of the frictional force and the leakage volume flow of the hydrostatic relief of a slipper, as measured on the model test rig. The friction force shows the typical shape of a Stribeck curve. The release point, where the mixed friction area changes into the liquid friction area, shifts to higher relative velocities with increasing pressure. The leakage volume flow of the hydrostatic relief increases significantly with pressure. At low pressure, the leakage also DOI 10.24053/ TuS-2023-0023 Figure 4: Structure of the Elastohydrodynamic Lubrication (EHL) Simulation TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 49 Nachrichten 50 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 increases visibly with the relative velocity. At medium pressures, it is near constant while at high pressures the leakage decreases slightly with the relative velocity. The gravimetric wear of the three slippers measured during the tests shown in Table 1 is presented in Figure 6. For this purpose, the weight, the surface roughness, and the geometry of the slippers were measured at each marked point. The change in the weight of the slippers at each operating point change shows a hyperbolic curve, followed by a linear weight reduction. In the hyperbolic area of the curve, the slippers on average wear 10 times more than in the subsequent linear area of the curve, which is why a run-in process is assumed. The occurrence of the run-in process is also supported by the measurement of the surface roughness of the slippers. The measurements show pronounced roughness fluctuations during the hyperbolic areas in Figure 6, which are not found in the linear areas. The surface run-in process is more pronounced on the support land than on the sealing land. When changing to the “low” operating point, the surfaces of the slippers become rougher, while changing to the “high” operating point results in smoother slipper surfaces. In addition to the different operating behaviors, the slipper’s surfaces and wear patterns were also examined at the various operating points. These are shown in Figure 7. At the “low” operating point, the slippers wear evenly. At the “medium” operating point, the slippers wear locally towards one side of the slipper. With in- DOI 10.24053/ TuS-2023-0023 Figure 6: Gravimetric Slipper Wear during Test Campaign Figure 5: Slipper Friction Torque and Hydrostatic Relief Volume Flow Figure 7: Slipper Wear Depths at Different Operating Points TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 50 Nachrichten 51 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 creasing speed, the wear moves outwards to the support land. From the wear profiles of the “high” operating point, it can be seen that the circular sector primary affected by wear gets smaller at higher speeds. 5 Simulative Results Figure 8 shows a simulated map of the lubrication gap height distribution of the slipper at the investigated pressures and relative velocities. It can be seen that both the aver-age gap height and the qualitative shape of the gap, are distinctly depending on the operating point. The hydrostatic pressure from the pressure pocket of the slipper drops radially, with a logarithmic profile over the sealing land (SeL). This pressure curve causes the sealing land to be higher on the inside than on the outside. At high hydrostatic pressures, this deformation leads to a divergent lubrication gap forming along the sealing land on the leading edge (LE) of the slipper, preventing hydrodynamic pressure build-up. On the trailing edge (TE), the hydrodynamic pressure build-up is increased, creating a moment, tilting the slipper towards the leading edge. The result is a lower height difference along the support lands, causing lower hydrodynamic pressure build-up, that lowers the total gap height at high hydrostatic pressures. As simulations of Schenk / Sch14/ show, such behavior is not to be expected for a slipper without a support land. The highest surface deformation of a slipper without support lands is located at the outer edge of the sealing land. Therefore, the tilting of the slipper shown in Figure 8, results in a convergent lubrication gap. The support land has a stiffening effect on the slipper and prevents the outer edge of the sealing land from lifting. Due to the design of the chosen slipper, the support land is thus the main cause of its gap height decreasing with the hydrostatic pressure, causing higher wear at higher pump pressures. Based on the measured wear coefficients, wear simulations were carried out for the experimentally investigated operating points from Table 1, using the Persson contact model and the Archard wear model, on a digitized, DOI 10.24053/ TuS-2023-0023 Figure 9: Simulated and Measured Slipper Geometry after Wear at 6.28 m/ s and 150 bar Figure 8: Simulated Gap Height Distributions TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 51 Nachrichten 52 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 measured preworn slipper profile. As shown in Figure 9 for the operating point medium, the geometry simulated here is qualitatively in agreement with the measured geometry. It should be noted that the wear caused by individual scratches due to particle abrasion could not be represented in the simulation. The wear weight could be calculated at this operating point with a deviation of -3.8 % from the measured value. The greatest wear occurs directly at the pressure relief grooves at the outer edge of the sealing land and the inner edge of the support land. This is caused by buckling of the slipper at the pressure relief grooves under load. Simulations with an unworn ideal geometry show that the wear simulation reacts very sensitively to changes in the slipper edge geometries within the micrometer range. This is due to the low gap heights, since the calculated wear depths (Figure 9) after 5000 kJ applied frictional energy (dissipated energy in E4 run-in) are already about 8-14 % of the mean gap height. 6 Discussion of Simulation and Experiment Hereinafter the presented experimental and simulative results are interpreted and compared to derive predicates about the increased wear of variable-speed axial piston pumps with variable load compared to constant operation. As the pressure of the hydrostatic relief increases, the mean gap height decreases (Figure 8), and the leakage volume flow increases (Figure 5). Lower gap heights lead to increased solid friction, while higher leakage volume flows in smaller gaps lead to increasing shear gradients and thus to higher fluid friction. Therefore, in Figure 5, the friction force of the slippers increases with the pressure of the hydrostatic relief. With lower tilt, higher relative velocities are required to separate the surfaces by hydrodynamic pressure buildup. Since the slipper’s tilt decreases with increasing hydrostatic relief pressure (Figure 8), the release points of the Stribeck curves in Figure 5 are shifted to higher relative velocities with increasing pressure. The sealing effect of the gap under the slipper decreases with its increasing local height. Tilting of the slipper, therefore, leads to higher leakage. Due to high tilting at low pressure (Figure 8) the leakage volume flow increases with the relative velocity. At constant tilt, the leakage decreases with increasing relative velocity since fluid is dragged into the locally higher gap on the leading edge against the flow direction of the hydrostatic relief. Owing to lower tilting at high pressure (Figure 8) the leakage volume flow decreases because of the aforementioned effect with the relative velocity (Figure 5). The wear depth shift shown in Figure 7 can also be explained by Figure 8. With increasing pump pressure, the wear of the slipper shifts outwards, since the sealing land is raised more, especially at the inner edge. Due to its circular base, the tilting of the slipper also leads to a shift of the wear to the outside and a reduction of the affected circular sector. Both, the deformation of the slipper and the wear depths occurring during the run-in phase are of the same order of magnitude as the height difference caused by the tilting of the slipper. This is caused by the size of the slippers used in a very small EHA pump. Since the operating point-dependent adjustment and deformation, as well as the resulting wear, significantly change the hydrodynamics in the gap, the slipper microgeometry adapts to the new lubrication state after each operating point change. For this reason, the wear of the slipper investigated is significantly higher in load and speed variable operation compared to constant operation. 7 Summary and Outlook In this work, experiments and simulations were used to show how the operating point-dependent behavior of the partially hydrostatic relieved slipper-swashplate contact in axial piston machines influences its wear behavior. It is shown experimentally that the changing of operating points always results in a run-in process, during which wear is increased substantially. Based on measurements of the slippers’ frictional force, leakage, and wear, as well as with the aid of a simulation model of the lubrication gap height, it is shown that the reason for this are operating point-dependent changes in the lubrication state. The essential criterion for reducing the wear of partially hydrostatic relieved tribological contacts under variable relative velocity and load is therefore the constancy of the contact’s operating behavior. The lubrication gap height must be large enough to ensure that neither minor wear nor the deformation of the contact (slipper) significantly changes the lubrication conditions. Therefore, related to the axial piston machine, the slipper must be sufficiently stiff and the hydrostatic relief high enough. In addition, the geometry of the slipper should be designed so that the qualitative characteristics of the hydrodynamics do not change significantly under different loads. Especially, the use of support lands can, depending on their arrangement, have a negative effect on the wear behavior. 8 Acknowledgement This publication summarizes some of the results of the first author’s master thesis, which was awarded the 2023 promotional award of the German Society for Tribology (GfT). The first author would like to thank the GfT for DOI 10.24053/ TuS-2023-0023 TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 52 Nachrichten 53 Tribologie + Schmierungstechnik · 70. Jahrgang · 4-5/ 2023 the honor of this award, as well as Univ.-Prof. Dr.-Ing. Katharina Schmitz and Amos Merkel, who supervised this work and contributed significantly to the results. Furthermore, the authors would like to thank their project partner Liebherr-Aerospace Lindenberg GmbH, who provided the test objects used in this thesis as part of a research project of the German Federal Ministry of Economics and Climate Protection (BMWK), which was supervised by the DLR project management organization within the framework concept “LuFo VI-1”. References / All16/ Alle, N., Hiremath, S. S. et al. Review on electro hydrostatic actuator for flight control, International Journal of Fluid Power, Vol. 17, Issue 2, pp. 125-145, 2016, https: / / doi.org/ 1080/ 14399776.2016.1169743. / Arc53/ Archard, J. F. Contact and Rubbing of Flat Surfaces, Journal of Applied Physics, Vol. 24, Issue 8, pp. 981- 988, 1953, https: / / doi.org/ 10.1063/ 1.1721448. / Bar10/ Bartel, D. Simulation von Tribosystemen - Grundlagen und Anwendungen, 1st Ed., Viehweg + Teubner; GWM Fachverlage GmbH, Wiesbaden, 2010, https: / / doi.org/ 1007/ 978-3-8348-9656-8. / Fin15/ Findeisen, D., Helduser, S. Ölhydraulik - Handbuch der hydraulischen Antriebe und Steuerungen, 6 th Ed., Springer Vieweg, Berlin, 2015, https: / / doi.org/ 1007/ 978-3-642-54909-0. / Fle80/ Fleischer, G., Gröger, H. et al. Verschleiß und Zuverlässigkeit, 1st Ed., VEB Verlag Technik, Berlin, 1980, OCLC-Number: 1080904698. / Gre66/ Greenwood, J. A., Williamson, J. B. P. Contact of nominally flat surfaces, Proceedings of the Royal Society A Mathematical, Physical and Engineering Science, Vol. 295, Issue 1442, pp. 300-319, 1966, https: / / doi.org/ 1098/ rspa.1966.0242. / Iva01/ Ivantysyn, J., Ivantysynova, M. Hydrostatic Pumps and Motors, 1 st Ed., Akademia Books International, New Delhi, India, 2001, ISBN 9788188305087. / Jak57/ Jakobsson, B., Floberg, L. The finite journal bearing, considering vaporization: (Das Gleitlager von endlicher Breite mit Verdampfung). - Report no. 3 from the Institute of Machine Elements.; Chalmers Tekniska Högskolas Handlingar, Nr. 190. Avd. 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Contact mechanics for randomly rough surfaces, Surface Science Reports, Vol. 61, Issue 4, pp. 201-227, 2006, https: / / doi.org/ 10.1016/ j.surfrep.2006.04.001. / Roe20/ Röben, T., Viennet, E., Wider, H. Robustness of the Liebherr-Aerospace EHA Technology for future flight control application - 12th International Fluid Power Conference (12. IFK). Dresden, October 12 - 14, Vol. 2, pp. 233-24, 2020, https: / / doi.org/ 10.25368/ 2020.87. / Sch14/ Schenk, A. Predicting lubrication performance between the slipper and swashplate in axial piston hydraulic machines, Purdue University, West Lafayette, Indiana, 2014, https: / / docs.lib.purdue.edu/ open_ access_dissertations/ 359. / Sch18/ Schmitz, K., Murrenhoff, H. Grundlagen der Fluidtechnik Teil 1: Hydraulik, 5th Ed., Shaker Verlag, Aachen, 2018, ISBN 978-3-8440-6246-5. / Weg21/ Wegner, S. Experimental and simulative investigation of the cylinder block/ valve plate contact in axial piston machines, Aachen, RWTH Aachen University, 2021, DOI: 10.18154/ RWTH-2021-03796. DOI 10.24053/ TuS-2023-0023 TuS_4_2023.qxp_TuS_4_2023 20.09.23 09: 16 Seite 53