Aus Wissenschaft und Forschung 20 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 Introduction The properties of the lubricant have a significant influence on the tribological behavior of a sealing system. In many applications, sealing contacts are lubricated by oil which can be modeled sufficiently accurate with Newtonian behavior. However, in grease lubricated sealing systems, such as within pneumatic valves, the lubricant shows significantly non-Newtonian behavior. In that case, more detailed measurements have to be performed in order to accurately describe the lubricant and ultimately calculate the friction. This paper presents measurements of several rheological properties of a grease used in a pneumatic spool valve. Based on these measurements, the Herschel-Bulkley and Palacios-Palacios model are parametrized and implemented into an elasto-hydrodynamic lubrication (EHL) simulation of the sealing contact. The resulting friction forces are compared qualitatively for two different temperatures. In addition, the difference between the two non-Newtonian viscosity models and a Newtonian approximation of the fluid is discussed with respect to an application in the EHL simulation of seals in pneumatic spool valves. Rheological Characterization and EHL Simulation of a Grease in a Lubricated Sealing Contact Niklas Bauer, Susanne Hahn, Simon Feldmeth, Frank Bauer, Katharina Schmitz* Eingereicht: 31.8.2021 Nach Begutachtung angenommen: 18.1.2022 Dieser Beitrag wurde im Rahmen der 62. Tribologie-Fachtagung 2021 der Gesellschaft für Tribologie (GfT) eingereicht. Diese Arbeit gibt Einblicke in das tribologische Verhalten fettgeschmierter Kontakte in pneumatischen Schieberventilen. Aufgrund des stark nicht-newtonschen Fließverhaltens des Fettes wurden verschiedene rheologische Messungen durchgeführt, um die beiden Materialmodelle nach Herschel-Bulkley und Palacios-Palacios zu parametrieren. Diese beiden Materialmodelle wurden in eine EHD Simulation des Dichtkontakts integriert und für zwei Temperaturen qualitativ verglichen. Für das Dichtsystem ist die Reibkraft nahezu unabhängig von der Wahl des Materialmodells. Außerdem konnten mit einer newtonschen Näherung des Fließverhaltens qualitativ vergleichbare Reibkräfte mit etwa 10 % Abweichung gegenüber den nicht-newtonschen Modellen erzielt werden. Schlüsselwörter Dichtung, Elasto-Hydrodynamik (EHD), Pneumatik, Reibung, Rheologie, Schmierfett, Simulation, Ventil This contribution provides an insight into the tribological behavior of grease-lubricated contacts in pneumatic spool valves. As the properties of the grease are strongly non-Newtonian, multiple measurements were performed to parameterize two viscosity models, the Herschel-Bulkley and the Palacios-Palacios model. These models are integrated into an EHL simulation of the sealing contact and qualitatively compared for two temperatures. For that system, the total friction force is rather unaffected by the choice of the viscosity model. In addition, qualitatively similar results with about 10 % deviation from the non-Newtonian behavior could be obtained using a Newtonian approximation of the lubricant. Keywords Elasto-hydrodynamic lubrication (EHL), Friction, Grease, Pneumatics, Rheology, Seal, Simulation, Valve Kurzfassung Abstract * Niklas Bauer 1 Orcid-ID: https: / / orcid.org/ 0000-0002-5520-0611 Susanne Hahn 2 Orcid-ID: https: / / orcid.org/ 0000-0002-1891-0286 Simon Feldmeth 2 Orcid-ID: https: / / orcid.org/ 0000-0003-0018-0710 PD Dr.-Ing. Frank Bauer 2 Orcid-ID: https: / / orcid.org/ 0000-0001-7799-7628 Univ.-Prof. Dr.-Ing. Katharina Schmitz 1 Orcid-ID: https: / / orcid.org/ 0000-0002-1454-8267 1 RWTH Aachen University, Institute for Fluid Power Drives and Systems (ifas), Campus-Boulevard 30, 52074 Aachen, Germany 2 University of Stuttgart, Institute of Machine Components (IMA), Pfaffenwaldring 9, 70569 Stuttgart, Germany TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 20 Pneumatic spool valves Pneumatic spool valves are used to control the air flow between components of a pneumatic system. They consist of a spool within a housing with several ports as shown in Figure 1. The spool is actuated either pneumatically or with a solenoid by the pilot valve. The connection between these ports is opened or blocked depending on the position of the spool. Subject of this contribution is a valve as shown in Figure 1 where the seals are placed on the spool and move relative to the housing. There are two types of seals in this kind of valve. In this work, only the inner seals (1) used to block or connect the ports are analyzed. During operation, these seals make and lose contact to the housing depending on the position of the spool. This discontinuity is not considered within this work, as its focus is on the influence of the lubricant. Grease Both, the simulation and the measurement were conducted on a grease with perfluorpolyether base oils (PFPE). The grease is rated NLGI 1 grade. Its temperature range extends from well below 0 °C to far above 100 °C. The base oil viscosity at 40 °C is given as about 40 mm 2 / s. Non-Newtonian fluid As non-Newtonian viscoelastic fluids, greases show a complex rheology that depends on a variety of influences / Lug13/ , / Mez20/ , / Bau21a/ . The approaches to describe the flow behavior mathematically are accordingly numerous. The simulation presented in this paper bases on the widely used Herschel-Bulkley model / Her26/ , which describes the shear stress τ in dependence on the shear rate using the yield stress τ 0 , and the factors K and n: (1) With Newton’s law of viscosity M = M N + OṖ - Ṗ (2) eq. (1) can be expressed in terms of shear viscosity: (3) As the shear viscosity in eq. (3) would tend to zero for very high shear rates, Palacios and Palacios added a term to the Herschel-Bulkley model to limit the shear viscosity at high shear rates to the base oil viscosity η b / Pal84/ : (4) Shear viscosity An MCR 302 rheometer of the Anton Paar Germany GmbH was used to measure the shear viscosity. The measurements were conducted using a cone-plate system with a diameter of 25 mm and an angle of 1.0° / DIN17a/ . The grease is applied at room temperature and trimmed at a gap height of 0.062 mm before the final measuring gap height of 0.052 mm is adjusted. The height of 0.052 mm corresponds to the imaginary height of the removed cone apex. Then, the sample is tempered with a heating rate of 2 K/ min to the measuring temperature (ϑ 1 = 25 °C, ϑ 2 = 50 °C), which is maintained for 10 min, before the actual measurement starts. The shear viscosity is measured with a linearly increased shear rate from 0 1/ s to 17,500 1/ s in two different test durations: t 1 = 300 s and t 2 = 3600 s. For each shear acceleration, three measurements were conducted. Figure 2 shows the shear viscosity measured at ϑ 1 = 25 °C (left) and ϑ 2 = 50 °C (right). While the viscosity rapidly decreases at the beginning of the shearing, the curve flattens as the shear rate increases. In between a shear rate of 10,000 1/ s and 15,000 1/ s all curves show a more or less sudden strong drop of the viscosity indicating grease being ejected from the gap. From this moment on, the gap is no more completely filled, and the later values must be discarded. M = Q ⋅ Ṗ Q = M N Ṗ + OṖ -63 M = M N + OṖ - + Q S Ṗ Aus Wissenschaft und Forschung 21 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 Figure 1: Pneumatic spool valve. Picture provided by courtesy of Festo / Fes18 TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 21 The temperature was modified in steps of 1 K, with each temperature step being adjusted for 5 min before measuring the viscosity. Figure 3 shows the viscosity of the bled oil of both measurements. At the boundary between the measurements 1 and 2, the curves blend into each other, so that both a good repeatability and a negligible effect of the separated measurement can be assumed. The viscosity of the bled oil decreases sharply with increasing temperature, especially in the low temperature range, while the viscosity decrease is less pronounced at the higher temperatures of measurement 2. The measurement results in a dynamic viscosity of the bled oil of η b,25 °C = 94.78 mPa s at 25 °C respectively η b,50 °C = 50.95 mPa s for 50 °C. Yield stress according to DIN 51810-2 There are numerous definitions and thus also different methods for determining the yield stress τ 0 of viscoelastic materials. Therefore, the values of τ 0 can vary significantly, as compared e.g. by Dinkgreve et al. / Din16/ . DIN 51810-2 / DIN17b/ specifies two definitions, which base on an oscillatory test with amplitude sweep: The yield point τ yield , as the limit of the linearviscoelastic-range, and the flow point τ flow at the intersection of the storage modulus G' with the loss modulus G’’. The measured values are shown in Table 1 for 25 °C and 50 °C. Aus Wissenschaft und Forschung 22 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 The grease shows an influence of the temperature: At 50 °C the viscosity is about 20 % lower than at 25 °C. The influence of the measuring durations is much lower: At 25 °C the longer sheared samples show a slightly lower viscosity whereas at 50 °C there is no discernible difference between the test durations. Viscosity of bled oil The viscosity of bled oil was measured with the same rheometer as the shear viscosity, using a parallel-plate system with a diameter of 25 mm, a gap height of 0.5 mm and a shear rate of 100 1/ s. To reduce the influence of condensing water at decreasing temperatures and also to keep the test gap completely filled over all temperatures, the viscosity was measured in two separate measurements: • Measurement 1: temperature decrease from ϑ = 25 °C to ϑ = -5 °C • Measurement 2: temperature increase from ϑ = 25 °C to ϑ = 130 °C Figure 2: Shear viscosity of the grease with linearly increased shear rate from 0 to 17500 1/ s in t 1 = 300 s and t 2 = 3600 s for ϑ 1 = 25 °C (left) and ϑ 2 = 50 °C (right) Figure 3: Dynamic viscosity of the bled oil η b for different temperatures Temperature [ ] [ ] [ ] 25 32.7 300.4 50 64.7 303.8 Table 1: Yield point τ yield and flow point τ flow according to DIN 51810-2 for ϑ 1 = 25 °C and ϑ 2 = 50 °C TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 22 Simulation model For modeling the pneumatic seal in the spool valve, the simulation model ifas-DDS / Ang20/ is used. As shown in Figure 4, it combines the commercial FEM-software Abaqus / Das21/ with a finite difference solution of the Reynolds equation to account for both the macroscopic deformation of the seal as well as the hydrodynamic pressure build-up within the sealing contact. The coupling of the FEM and the Reynolds equation is implemented monolithically with the Abaqus User Subroutine UEL. Originally developed for the simulation of friction of reciprocating hydraulic seals / Ang17/ , it is also capable of calculating the macroscopic wear geometry / Ang19/ . For taking into account cavitation phenomena, the ifas-DDS contains the Jakobsson-Floberg-Olsson cavitation model / Jak57/ , / Ols65/ using the implementation according to Woloszynski / Wol15/ . Further details of the implementation are given in / Bau21b/ . The total friction force is calculated as the sum of the solid and the fluid friction force. The solid friction is calculated assuming a constant shear stress in the real area of contact. The real area of contact depends on the local gap height and is implemented using a lookup table which has been calculated in advance. The fluid friction force is given by the shear stress of the fluid in the contact. Further details of the implementation are given in / Ang20/ . Implementation of non-Newtonian lubricant behavior For including Herschel-Bulkley behavior in the EHL-simulation it is possible to use a generalized Reynolds equation as described by Dowson / Dow62/ , Booker / Boo89/ or Yang / Pei90/ . However, these equations introduce additional integrals over the gap height direction z, which typically have to be solved numerically. In order to avoid the additional effort of the numerical integration over the gap height, an alternative approach is pursued. Instead of taking into account the variation of the shear rate along the gap height, the shear rate avg is calculat- Ṗ Ṗ ed for each node by averaging over the height coordinate. Based on avg , the locally averaged viscosity η avg is calculated for each node according to the respective viscosity model. The advantage of this simplification is the reduction of computational effort both regarding execution and implementation time. Validity and accuracy of this simplification largely depend on how closely the averaged shear rate matches the actual shear rates within the contact. For calculating the average shear rate, as a first step, the flow of a Newtonian fluid is considered. Its linear relation between shear rate and shear stress leads to a parabolic flow profile within a lubricated contact. For one moving and one fixed surface, the shear rate can be derived by a force equilibrium at an infinitesimal fluid element: (5) It can be seen, that the shear rate consists of two terms: the first term is caused by the Couette or shear flow due to the relative movement of the two surfaces. The second term is caused by the Poisseuille or pressure flow, caused by axial pressure gradients within the contact. It can be seen that, for Newtonian fluids, the average of the shear rate caused by the pressure flow along the gap height is always zero, as it is a linear function assuming opposite values at the top and bottom of the gap. Therefore, the average shear rate avg is simply given by the term corresponding to the shear flow. In this contribution, the same relation is assumed for the investigated non-Newtonian models as well, even though no clear distinction between shear and pressure flow can be made due to the nonlinearities of the model. This assumption is made for two reasons: First, it is expected, that the contributions of the pressure flow still lead to positive shear rates close to one surface and negative shear rates close to the other surface. Therefore, when averaging in height direction, most of the shear Ṗ TUV "- (W) = X #U ℎ + ℎ 2Q Z[ Z\ ⋅ ]2 ⋅ W ℎ − 1^ Ṗ Ṗ Aus Wissenschaft und Forschung 23 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 Figure 4: Structure of the dynamic sealing simulation ifas-DDS TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 23 both models the three parameters n, K and τ 0 are found via optimization. The residual to be minimized by finding the optimal set of parameters of the Herschel-Bulkley or Palacios-Palacios model for all data points i is given as: (9) The optimization of the logarithm was chosen, because the values of both shear rate and viscosity vary by multiple orders of magnitude. This ensures an equal weighting of both high and low viscosities when calculating the residual. Without the logarithm, the high viscosities at low shear rates are overweighed, leading to an overall worse fit at the more relevant higher shear rates. Figure 5 shows a comparison of the measurement results and the fits for both 25 °C and 50 °C in a log-log plot. For the following evaluation, only the measurements with a duration of 3600 s are considered, since there are more data points available. As the shear rates occurring in the simulation model can be higher than in the measurements, an extrapolation of the measurement results to higher shear rates based on the models is shown as well. As mentioned earlier, all results obtained after the ejection of the grease from the gap were neglected during the fitting. The parameters and the coefficient of determination R 2 are given in Table 2. It can be seen that both viscosity models are able to accurately represent the measurement data, recognizable both by the similarity of the curves and the equally good coefficients of determination. The coefficient is slightly lower for the fits at 50 °C due to the higher deviation of measurement data. Regarding the behavior of the two models, there is no visible difference for shear rates where measured data are present. However, the extrapolation of both models provides different results as the term with the base oil viscosity of the Palacios-Palacios model gains more importance for higher shear rates leading to _`log`Q aU/ b,c d − log`Q(log Ṗ c , e, O, M N [, Q S ])dd c Aus Wissenschaft und Forschung 24 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 rate corresponding to the pressure flow will cancel itself out. Secondly, the small gap heights and high relative velocities within the investigated tribosystem result in a high quotient of v rel / h, so that the shear flow is much higher for most operating conditions than even the maximum contribution of the pressure flow. Thus, the locally averaged shear rate is calculated as follows: (6) Based on this assumption, the viscosity is calculated as: (7) Combining the described approach with the Reynolds equation in the form given in / Bau21b/ results in equation (8). This form of the Reynolds equation considers variations of the viscosity along the axial direction x, but assumes a constant viscosity in height direction z in order to reduce computational effort. It is expected that the error introduced by this simplification will increase for higher gradients of hydrodynamic pressure, since the shear caused by pressure flow is not considered. The size of the error and the scope of validity of these assumptions are currently investigated and will be published in another paper. Obtaining the model parameters In order to find the optimal material parameters of the Herschel-Bulkley (HB) or Palacios-Palacios (PP) model, a curve fitting was performed using the non-linear least squares method. For the latter model, the bled oil viscosity η b is obtained from the measurements so that for Ṗ / ij = 1 ℎ ⋅ k Ṗ (W)mW N ≈ 1 ℎ ⋅ k Ṗ TUV "- (W)mW N = X #U ℎ Q / ij = O ⋅ Ṗ / ij -63 + M N ⋅ Ṗ / ij 63 + Q S X #U 2 Z Z\ p(1 − 1)qℎ + (1 − 1)q r Φ t u − Z Z\ v (1 − 1)qℎ E 12Q / ij Φ w Z[ Z\ x + ⋯ + Z Zz [(1 − 1)qℎ] = 0 (8) Figure 5: Comparison of measured viscosity (before ejection) and least squares fits with the Herschel-Bulkley (HB) and Palacios-Palacios (PP) model for 25 °C (left) and 50 °C (right) TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 24 an overall higher viscosity compared to the extrapolation with the Herschel-Bulkley model. The impact of this difference on the friction force is discussed later. It is worth noting that for both viscosity models the fitting results of the parameter τ 0 are considerably higher than both yield and flow point obtained by the measurements according to DIN 51810-2. Major differences between different estimation methods for the yield stress are a common issue, e.g. discussed in / Cyr15/ , and origin in the varying definitions and measuring methods of the yield stress. Since the aim of the used viscosity models is the best possible resemblance of the shear viscosity measurements, the values obtained from the curve fitting are used in the Herschel-Bulkley or Palacios-Palacios model instead of the yield or flow point measured according to DIN 51810-2. Simulation setup The sealing system was modeled as axisymmetric. Geometry and mesh of the simulation model are shown in Figure 6. The model consists of the three parts seal, housing and spool. The inner and outer radius of the seal in assembled condition are about 1.4 mm and 3 mm with a length of about 0.72 mm in axial direction. The geometry of the spool has been adjusted so that there is no axial clearance between seal and spool in order to prevent axial movement between seal and spool after assembly. The seal is meshed with 6066 nodes and 5800 first order axisymmetric hybrid elements. The number of elements for which the Reynolds equation is solved is 200. The simulation has been repeated with a finer mesh with 400 nodes for solving the fluid domain. The calculated friction forces obtained with the two different resolutions have been compared. Since the difference was barely visible in direct comparison, it was concluded that the current mesh provides sufficient accuracy. The housing and the spool are modeled as analytical rigid surfaces. As mentioned earlier, the different diameters within the housing are neglected, so that it can be represented by a cylindrical surface. The seal is modeled as an incompressible hyperelastic Mooney-Rivlin material with C 10 = 0 MPa and C 01 = 1.78 MPa. Outside the seal, atmospheric pressure was assumed. Cavitation was assumed to occur at a relative pressure of -0.1 MPa. Due to the singularity of both viscosity models at = 0, the local viscosity in contact was limited to η max = 10 Pa s in order to prevent infinite values. Since the properties of the contact between seal and housing within the valve have not yet been evaluated, the characteristics of a dummy surface are chosen for the calculation of the solid contact stresses and the flow factors. The values used were obtained for an isotropic surface with an RMS roughness of about 2 µm as presented in / Sca18/ . In reality, the surface is expected to be anisotropic, so that the results presented here have to be interpreted qualitatively. For the tangential stresses, a constant shear stress acting on the real area of contact of τ cont = 1.5 MPa was assumed. The contact between spool and seal was modeled using the exponential contact behavior in Abaqus with a constant coefficient of friction of µ = 0.2. Ṗ Aus Wissenschaft und Forschung 25 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 Figure 6: Left: Mesh of the seal and measurements (mm) of the assembled seal. Right: Stresses after assembly of spool and housing (spool and housing are shown as lines on the right part of the figure) Temperature Model | } ~  €  : ‚ [ °ƒ ] [ − ] [ − ] [ „… † ‡ ] [ „… ] [ ˆ 6‰ „… † ] [ % ] 25 HB 0.7262 3.9985 555.04 - 99.53 25 PP 0.6327 6.7823 530.96 94.779 99.53 50 HB 0.6641 4.4314 793.79 - 98.15 50 PP 0.5089 14.5919 697.26 50.954 98.19 Table 2: Parameters of the best fits of the Herschel-Bulkley (HB) and Palacios-Palacios (PP) model for 25 °C and 50 °C for t 2 = 3600 s TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 25 especially around v rel = 0. With increasing temperature, the total friction force slightly increases. This can be attributed to the lowering of the viscosity for higher temperatures. On the one hand, this leads to lower fluid shear stresses and thus lower fluid friction. On the other hand, as shown in Figure 8, the lower viscosity also leads to a decreased gap height. As the separation of the two contact partners gets smaller, the real area of contact increases, which causes higher solid friction. Overall, the total friction becomes slightly higher for higher temperatures. The choice of the viscosity model has a lower impact than the temperature, even though shear rates of up to 5 · 10 5 1/ s occur locally in the contact at high speeds. As seen earlier, the Palacios-Palacios model predicts higher viscosities at those shear rates. Similar to the effect of the temperature, this increase in viscosity causes larger values of the gap height, see Figure 8. This, in turn, leads to a decrease in solid friction. However, the higher viscosity also leads to an increase in fluid friction. Eventually, these two effects nearly cancel each other out, so that the total friction force is nearly independent of the choice of viscosity model. This is especially true for high relative velocities at 50 °C where the difference between the two curves is barely visible. Figure 9 (left) shows the arithmetic average of the local viscosity of all nodes in contact for each relative velocity. It can be seen, that the average viscosity appears to be approaching a constant value for high relative velocities. It shall be checked whether the behavior of a greaselubricated system at high velocities can be approximated with a Newtonian fluid with a constant viscosity. For that, the average value of the viscosities for high velocities at 25 °C is calculated (η Newton,25 °C ≈ 0.145 Pa s) and used for a simulation with a Newtonian fluid. The result is shown in Figure 9 (right). The solid friction is in extremely good correlation for velocities over 200 mm/ s. However, there is a noticeable difference in the behavior Aus Wissenschaft und Forschung 26 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 As for initial and boundary conditions, spool and housing are placed in radial distance from the seal so that no contact occurs. During the first step of the simulation, the system is assembled by moving the analytical rigids into their final positions prestressing the sealing contact, see Figure 6 (right). In the next step, the spool faces are accelerated with a constant acceleration up to a velocity of 700 mm/ s within 1.5 ms. Immediately after reaching the maximum velocity, the acceleration is inverted until the seal reaches a velocity of -700 mm/ s in the opposite direction. This process is repeated until the friction force reaches a steady-state oscillation. During the first acceleration and deceleration period much higher friction forces occur than during the rest of the simulation. This is because the lubricant film needs some time to build up. Before that, a high amount of solid friction occurs as due to the assembly in the simulation, no lubricant is present in the contact at the start of the simulation. It is expected, that this effect is a lot less severe in reality, since the contact is never completely dry even after long standstill periods. For that reason, the friction is not evaluated during the first acceleration and deceleration period. Results Figure 7 shows a comparison of the fluid (dotted lines), solid (dash-dotted lines) and total friction forces (solid lines) for the two investigated temperatures and models. Since the real contact properties have not yet been obtained, only a qualitative comparison of the measurements against each other is possible. Therefore, all friction forces have been normalized by division with the constant F max,25 , which is the maximum of the total friction force of the simulation with the Herschel-Bulkley model at 25 °C. The gap height at the maximum velocity is shown in Figure 8. It can be seen that the qualitative behavior is similar for both models and temperatures. A hysteresis is visible, Figure 7: Calculated total friction (solid lines), solid friction (dash-dotted lines) and fluid friction (dotted lines) for the Herschel-Bulkley (HB) and Palacios-Palacios (PP) parameters for 25 °C (left) and 50 °C (right) TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 26 of the fluid friction. For the Newtonian fluid, the friction force resembles a straight line. In contrast, for both the Herschel-Bulkley and the Palacios-Palacios model the curve describes an S-shape close to the center, see also Figure 7. This shape can be attributed to the high viscosities at low shear rates. The Newtonian approximation cannot resemble this behavior. Thus, it predicts too low fluid friction at low relative velocities. Conversely, at higher shear rates, the lack of shear thinning of the Newtonian fluid causes higher friction forces than the grease models. Conclusion This contribution provides an insight to the properties of grease-lubricated contacts in pneumatic spool valves. First, the lubricant properties such as shear viscosity, yield stress and bled oil viscosity were measured. As a second step, the measured data were fit and extrapolated using two different viscosity models, namely the Herschel-Bulkley and the Palacios-Palacios model. Finally, the model parameters were integrated into an EHL simulation of a sealing contact in order to study the influence of the temperature and the impact of the choice of the viscosity model. The comparison was based on a dummy surface, so that the focus of the comparison was on the qualitative comparison of the friction force and its components. It can be concluded that the total friction force is rather unaffected by the choice of the viscosity model for the investigated system. In addition, it was found that qualitatively similar results can be obtained with a Newtonian lubricant if the viscosity is chosen correctly and if deviations of about 10 % in terms of the total friction force are acceptable. However, in order to obtain the correct Newtonian viscosity for the approximation a simulation with non-Newtonian properties is still necessary. Thus, an experimental determination of the shear viscosity cannot be avoided if precise results are required. Aus Wissenschaft und Forschung 27 Tribologie + Schmierungstechnik · 68. Jahrgang · 6/ 2021 DOI 10.24053/ TuS-2021-0034 Figure 8: Calculated gap height at v rel = 700 mm/ s for the Herschel-Bulkley (HB) and Palacios-Palacios (PP) parameters for 25 °C (left) and 50 °C (right) Figure 9: Left: Average viscosity in contact for the Herschel-Bulkley model as a function of the velocity. Right: Comparison of Herschel-Bulkley model and Newtonian approximation regarding total friction (solid line), solid friction (dash-dotted line) and fluid friction for 25 °C. TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 27 / Din16/ Dinkgreve, M., Paredes, J., Denn, M. M., Bonn, D. On different ways of measuring “the” yield stress, Journal of Non-Newtonian Fluid Mechanics, Vol. 238, S. 233-241, 2016. DOI: 10.1016/ j.jnnfm.2016.11.001. / Dow62/ Dowson, D. A generalized Reynolds equation for fluid-film lubrication, International Journal of Mechanical Sciences, Vol. 4, Nr. 2, S. 159-170, 1962. DOI: 10.1016/ S0020-7403(62)80038-1. / Fes18/ Festo SE & Co. 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DOI: 10.1080/ 10402004.2015.1035414. / Das21/ Dassault Systems: Abaqus 2021 Documentation, 2021. / DIN17a/ DIN: 51810-1 - Prüfung von Schmierstoffen - Prüfung der rheologischen Eigenschaften von Schmierfetten - Teil 1: Bestimmung der Scherviskosität mit dem Rotationsviskosimeter und dem Messsystem Kegel/ Platte, 4/ 2017. / DIN17b/ DIN: 51810-2 - Prüfung von Schmierstoffen - Prüfung der rheologischen Eigenschaften von Schmierfetten - Teil 2: Bestimmung der Fließgrenze mit dem Oszillationsrheometer und dem Messsystem Platte/ Platte, 4/ 2017. TuS_6_2021.qxp_TuS_Muster_2021 02.02.22 17: 17 Seite 28