the contact are largely affected by the interference between seal and counter surface. In practice, seal and counter-surface are subject to manufacturing tolerances ultimately leading to deviations from the designed geometry. For example, deviations in the bore diameter of a pneumatic valve can strongly affect the normal stresses in the contact and thus the behavior of the valve. Therefore, an intricate and timeconsuming design process is necessary to define the geometry and tolerances which strike the optimal balance between tightness, low friction and manufacturing cost. In addition to the macroscopic geometry deviations, the manufacturing process also introduces roughness on the micro-scale. The roughness, in turn, affects the frictional Aus Wissenschaft und Forschung 62 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 Introduction The behavior of seals depends on various parameters. Besides the operating conditions and the properties of the sealing-material and the lubricant, the stresses within the sealing contact play an important role. To achieve tightness, the normal contact pressure between seal and counter surface needs to be sufficiently high. However, higher contact pressures lead to an undesired increase in friction and ultimately wear. These normal stresses in Influence of Manufacturing Tolerances on the Behavior of Pneumatic Seals using EHL Simulations Niklas Bauer, Katharina Schmitz* Eingereicht: 6.9.2022 Nach Begutachtung angenommen: 26.1.2023 Dieser Beitrag wurde im Rahmen der 63. Tribologie-Fachtagung 2022 der Gesellschaft für Tribologie (GfT) eingereicht. Die Dichtungsreibung in pneumatischen Schieberventilen hängt von einer Vielzahl von Einflussgrößen ab. Dazu zählen beispielsweise die Schmierstoff- und Dichtungswerkstoffeigenschaften, die Oberflächen der Kontaktpartner sowie auch die Geometrie. In der Praxis unterliegen Oberflächenrauheit und Geometrie Fertigungstoleranzen. Diese Veröffentlichung stellt eine simulative Untersuchung vor, wie sich diese Toleranzen auf den Dichtkontakt auswirken. Dazu werden Reibkraft und Leckage für verschiedene Bohrungsdurchmesser und Oberflächenrauheiten berechnet. Eine Vergrößerung des Bohrungsdurchmessers führt zu einer fast linearen Abnahme der Reibung und einer Zunahme der erwarteten Leckage. Höhere Amplituden der Oberflächenrauheit erhöhen sowohl die Reibung als auch die erwartete Leckage. Schlüsselwörter EHD-Simulation, Pneumatikventil, Reibung, Toleranz, Translatorische Dichtung, Transiente Simulation The sealing friction in pneumatic spool valves is influenced by several factors, like the lubricant and sealing material properties, the topography of the contacting surfaces and the geometry. In practice, surface roughness and geometry are subject to manufacturing tolerances. This publication presents a simulative investigation on how these tolerances affect the sealing contact. For that, friction force and leakage are calculated for different bore diameters and surface roughness. An increase in bore diameter leads to an almost linear decrease in friction and an increase in expected leakage. Higher surface roughness amplitudes are predicted to increase both friction and expected leakage. Keywords EHL Simulation, Friction, Pneumatic Valve, Reciprocating Seal, Tolerance, Transient Simulation Kurzfassung Abstract *Niklas Bauer Orcid-ID: https: / / orcid.org/ 0000-0002-5520-0611 Univ.-Prof. Dr.-Ing. Katharina Schmitz Orcid-ID: https: / / orcid.org/ 0000-0002-1454-8267 RWTH Aachen University, Institute for Fluid Power Drives and Systems (ifas), Campus-Boulevard 30, 52074 Aachen TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 62 behavior of the valve, too, since both solid contact mechanics and lubricant flow are affected by height and structure of the roughness. Extending an elasto-hydrodynamic lubrication (EHL) simulation tool developed for calculating the friction in reciprocating sealing contacts, this contribution presents an estimation of how manufacturing tolerances of surface roughness and macroscopic geometrical deviation affect the tribological behavior of a sealing contact using the example of a pneumatic spool valve. It is investigated, to what extend deviations of inner diameter and roughness affect the sealing contact by comparing the predictions of the simulation model. It shall be answered, how friction force and leakage are affected by the two investigated parameters and how strong the respective influence of the two parameters is. Pneumatic Spool Valve The investigated spool valve is shown in Figure 1. Its purpose is to guide the flow of pressurized air in a pneumatic system. The valve consists of a housing with five ports and a spool which is pneumatically moved in axial direction by a pilot valve. Depending on the position of the spool within the housing, the ports are connected to or disconnected from each other. In order to prevent losses by leakage, two kinds of seals are used in the valve. The inner seals (1) prevent unwanted airflow between disconnected ports. They make or lose contact with the counter surface when the valve is switched by moving over a chamfer (control edge). The outer seals are used to prevent leakage to the environment. Simulation Model The dynamic sealing simulation model ifas-DDS was originally developed to describe the dynamic friction behavior of reciprocating seals in hydraulic systems / Ang20/ . The EHL simulation model considers the deformation of the seal using the commercial FEM-software Abaqus / Das21/ and extends the calculation by contact mechanics and surface structure / Ang17/ as well as the Reynolds equation to describe the hydrodynamic pressure buildup. The structure of the simulation model is shown in Figure 2. Aus Wissenschaft und Forschung 63 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 Figure 2: Structure of the dynamic sealing simulation ifas-DDS. Figure 1: Pneumatic spool valve. Picture provided by courtesy of Festo / Fes18/ . TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 63 constant velocity, the counter face is decelerated using the same acceleration followed by the same pattern in opposite direction. This cycle is repeated multiple times. The total distance between both end points is s max . Influence of Inner Diameter With decreasing bore diameter, higher interference and thus higher normal stresses are expected to occur in the contact. For small deviations of inner diameter, a linear relation of friction force and bore diameter is expected. Therefore, the investigated tolerances were purposefully chosen with a value considerably larger than in the actual application to check if the expected linear tendency also occurs for large deviations of the bore diameter. The investigated values for the diameter deviation Δd i were chosen in a range from -40 µm to +40 µm. According to the standard DIN EN ISO 286-1, this range of diameter values is within the tolerance designation JS11 for the bore diameter of more than 6 mm / DIN19/ . Figure 4 (left) shows the results for the friction force for one stroke plotted against the position of the spool s using different bore diameters. All forces have been normalized Aus Wissenschaft und Forschung 64 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 Simulation Setup For this contribution, the inner seal ring is investigated. To eliminate effects caused by moving over the control edge, a countersurface with a constant diameter is considered. The geometry of the seal and the housing matches the geometry in the real valve. Since the exact geometry provided by the manufacturer is confidential, a simplified geometry of comparable size and with similar geometric features is shown in Figure 3 for illustration purposes. Figure 3 (right) shows a threedimensional graphic of the seal. This only serves illustration purposes, since the simulation was conducted as a two dimensional axisymmetric model. The model was built as a nonlinear axisymmetric model in Abaqus, using incompressible hyperelastic material properties for the seal. The non-Newtonian fluid behavior of the grease was obtained as described in / Bau21/ . The contact mechanics parameters such as normal contact pressure, real area of contact and the flow factors as introduced by Patir and Cheng / Pat78/ , / Pat79/ were calculated using the commercially available software TriboX / Tri21/ . The values used for the calculation in this contribution are presented in / Bau23/ . For determining the influence of deviations of the bore diameter Δd i , the simulation was conducted with five different constant inner diameters. In addition, nine different values for the surface roughness were investigated. The influence of surface roughness was only considered for the contact properties and the hydrodynamic pressure buildup. The influence of large scale roughness whose magnitude is so high that it affects the macroscopic shape of the counter surface was not considered. Thus, the shape of the counter surface was ideally cylindrical in the FEM model for all investigated values of surface roughness. The other parameters were chosen in accordance with the study presented in / Bau22/ and are presented in Table 1. A constant solid shear stress of τ c was assumed to act on the real area of contact. The counter face moves in a reciprocating pattern, in which the seal is accelerated with constant acceleration a const until the constant velocity v max is reached. After a phase of Parameter Symbol Unit Value Acceleration ! "# $ %% & ' * -/ 3 Mooney-Rivlin Coefficient 4 56 7 89: ; 3 Mooney-Rivlin Coefficient 4 65 7 89: ; <>/ ? Consistency Index (Viscosity model) @ AA 7 9: B& " CC ; -<>/ DE Number of Nodes for the Reynolds eq. F GHI 7 J ; DD- Number of FEM-Elements F KLKMK" # 7 J ; E3 - Number of FEM-Nodes F "! NK# 7 J ; E3>O Flow Index (Viscosity model) F AA 7 J ; 3<-ED> Total Distance of Spool Movement P MQR 7 %% ; </ Maximum Velocity of Spool movement S MQR B$ %% & * EO Base Oil Viscosity (Viscosity model) T U AA 7 9: B& ; VO<>>V W 3 XY Friction Coefficient (Seal - Spool) Z [KQLX[\! ! L 7 J ; 3< ? Density of Seal Material ] #KQL ^ _ %% Y ` <D W 3 Xa Yield Stress (Viscosity model) b 6 AA 7 9: ; ? E3<V- Solid Shear Stress b 789: ; <? Table 1: Parameters used for the simulation runs presented in this publication Figure 3: Simplified geometry for illustration purposes. The interference before assembly is indicated on the left part of the figure. TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 64 by the maximum value of the friction force for the case without geometrical deviations F 0,max . The qualitative behavior is very similar for all investigated bore diameters despite the comparably large quantitative deviations. Figure 4 (right) shows the maximum of friction and normal force as well. In addition, the minimum peak values of the contact pressure during operation (cont. pressure) as well as the contact pressure during static conditions, i.e., without any lubrication (stat. pressure) are depicted. When comparing the respective maximum values of the friction force for different diameter deviations, an almost linear tendency can be observed. The maximum friction and normal force follow the same decreasing tendency. The same can also be observed for the maximum value of the static solid contact pressure without lubrication. However, the influence of diameter deviation on the maximum of the solid contact pressure during operation is considerably smaller than on the other compared values. This can be explained by the influence of hydrodynamics. Figure 5 shows the solid contact pressure plotted against the axial coordinate x in the sealing gap. All values have been normalized to the maximum of the static solid contact pressure of the reference case p c,0 . The left part of the figure shows the distribution of solid contact pressure during static conditions without hydrodynamics. All curves have a similar shape and decrease with increasing bore diameter. This can be attributed to a reduced interference. The right part of the figure shows the solid contact pressure during movement with the maximum velocity. With increasing interference, mainly the contact width rather than the peak value increases. This explains Aus Wissenschaft und Forschung 65 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 Figure 4: Friction force and refence force (green) depending on the axial position for different diameter deviations (left). Maximum of friction force, normal force, dynamic and static contact pressure depending on the diameter deviation Δd i (right). Figure 5: Contact pressure for different deviations of inner diameter Δd i without hydrodynamic (left) and during movement with v rel = 34 mm/ s (right). TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 65 surface roughness has an almost negligible effect on both height and shape of the solid contact pressure distribution in this case. The only change is that the area where stresses occur becomes slightly wider. This, in turn, leads to a slightly lower maximum value as already shown in Figure 6. In contrast to the static case, when moving with the maximum relative velocity the solid contact pressure is strongly affected by the surface roughness which is depicted in Figure 7 (right). A higher surface roughness leads to an overall higher value of the solid contact pressure during movement. The reason for the different influence of the surface roughness on the solid contact pressure is caused by the presence or absence of hydrodynamic. If there is no relative velocity and thus no hydrodynamics, the solid contact pressure entirely depends on the macroscopic deformation of the seal. When the magnitude of surface roughness changes, the deformation of the seal is also affected in an order of magnitude similar to the roughness. The roughness assumed in this publication is, as typical for most technical surfaces, in the micrometer range. Since the deformation of the seal is in the order of magnitude of millimeter, the macroscopic deformation of the seal as well as the resulting distribution of solid contact pressure is almost unaffected by roughness changes even by factor 2, as shown in Figure 7 (left). However, during movement, hydrodynamic effects occur, which change the influence of roughness on the contact pressure. The hydrodynamic pressure acts in the same direction as the normal contact pressure and thus increases the separation between seal and counter surface. This, in turn, leads to overall lower solid contact pressures. When the magnitude of roughness increases, more separation is necessary to reduce the solid contact Aus Wissenschaft und Forschung 66 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 why the normal force changes more drastically than the peak value of the solid contact pressure as shown in Figure 4 (right). Influence of Surface Roughness For investigating the impact of different surface topographies, it was assumed that the qualitative shape of the counter surface roughness does not change with changing roughness magnitude. For that, the values of contact pressure, real area of contact and flow factors as determined in / Bau23/ were adjusted for different values of the arithmetic average roughness R a . Since these parameters are given as functions of the ratio h/ R a , i.e., the ratio of mean separation h and R a , the adjustment to different values of R a corresponds to a rescaling of the contact pressure curve. The investigated values of R a range from 0.5 · R a,0 to 2 · R a,0 , where R a,0 denotes the arithmetic average roughness of the measured counter surface. Since all wavelengths of roughness are assumed to change proportional to one another, the other roughness parameters such as R z and R q change by the same factor. The results of the simulation are depicted in Figure 6. Similar to the previously discussed diameter deviation, the relation between roughness amplitude and friction force is also almost linear and shows the same qualitative behavior at each spool position s. Again, friction and normal force increase by roughly the same factor. In contrast to the diameter variation, the static contact pressure is almost constant, whereas the other three considered quantities, friction, normal force and maximum of solid contact pressure vary almost similarly. Figure 7 (left) shows the distribution of solid contact pressure in the static case. It can be seen that increasing Figure 6: Friction force and refence force (green) depending on the axial position for different values of surface roughness R a (left). Maximum of friction force, normal force, dynamic and static contact pressure depending on surface roughness R a (right). TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 66 pressure of the larger asperities by the same amount. For that, a higher hydrodynamic force would be necessary. However, the hydrodynamic pressure does not increase for higher values of surface roughness. Therefore, the hydrodynamic pressure is not high enough to sufficiently separate the seal from the increased surface roughness so that the contact pressure during movement increases, as shown in Figure 7 (right). Expected Effect on Leakage The effect of bore diameter and surface roughness on the leakage has been assessed by comparing the pressure flow at the narrowest gap according to / Fis20/ . Since the minimal separation changes during operation due to hydrodynamic effects, the maximum of the minimal separation has been chosen for comparison. This ensures that the most critical operating conditions in terms of leakage are compared. For estimating the leakage Q˙ leak , the following formula has been used: Q˙ leak [ h min 3 · Φ p (h min ) (1) The estimated leakage Q˙ leak is given as a function of the narrowest gap height h min and the pressure flow factor at this position Φ p (h min ). It must be noted that this approximation does not consider the effects of starved lubrication or the complex phenomena of air leakage through a grease-lubricated sealing contact. Thus, this estimation is merely meant to give a rough comparison of the likelihood of leakage to occur during operation. The results are presented in Figure 8. Aus Wissenschaft und Forschung 67 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 Figure 8: Change of estimated leakage and highest minimal separation both with respect to the reference case for different bore diameter deviations Δd i (left) and different values of roughness R a (right). Figure 7: Contact pressure for different values of surface roughness R a without hydrodynamic (left) and during movement with v rel = 34 mm/ s (right). TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 67 that both friction and expected leakage increase with increasing surface roughness. However, the simplified generation of surface characteristics does not take into account that the frictional solid shear stress acting on the real area of contact is affected by the surface topography / Per01/ . In addition, the applied scaling of the surface parameters might not correspond to actual surfaces with different values of R a . This is because the different length scales of surface roughness might each be affected in a different way when another manufacturing process is used for producing a rougher or smoother surface. If the found relations stay valid for starved conditions or applications where the seal is affected by air pressure will be subject of future investigations. Especially for starved conditions with limited lubricant supply it is expected that the surface roughness strongly affects the available amount of lubricant and thus the friction force and separation. Acknowledgement The authors thank the Fluid Power Research Fund of the VDMA for its financial support (grant: FKM No. 7049620). Literature / Ang17/ Angerhausen, J., Murrenhoff, H., Dorogin, J., Persson, B. N. J., Scaraggi, M. The Influence of Temperature and Surface Structure on the Friction of Dynamic Hydraulic Seals - Numerical and Experimental Investigations, The 10th JFPS International Symposium on Fluid Power, 2017. / Ang20/ Angerhausen, J. Physikalisch motivierte, transiente Modellierung translatorischer Hydraulikdichtungen - Dissertation, Reihe Fluidtechnik: D 102, Shaker Verlag, Düren, 2020. ISBN: 978-3-8440-7502-1. / Bau21/ Bauer, N., Hahn, S., Feldmeth, S., Bauer, F., Schmitz, K. Rheological Characterization and EHL Simulation of a Grease in a Lubricated Sealing Contact, Tribologie und Schmierungstechnik, Vol. 68, Nr. 6, S. 20-28, 2021. DOI: 10.24053/ TuS-2021-0034. / Bau22/ Bauer, N., Bekgulyan, S., Feldmeth, S., Bauer, F., Schmitz, K. Experimental determination and EHL simulation of transient friction of pneumatic seals in spool valves, Proceedings of the 21 st International Sealing Conference (ISC), Stuttgart, Germany, 2022. / Bau23/ Bauer, N., Baumann, M., Feldmeth, S., Bauer, F., Schmitz, K. Elastohydrodynamic Simulation of Pneumatic Sealing Friction Considering 3D Surface Topography, Chemical Engineering & Technology, Vol. 46, Nr. 1, S. 167-174, 2023. DOI: 10.1002/ ceat.202200471. / Das21/ Dassault Systems: Abaqus 2021 Documentation, 2021. / DIN19/ DIN German Institute for Standardization: DIN EN ISO 286-1 Geometrical product specifications (GPS) - ISO code system for tolerances on linear sizes - Part 1: Basis of tolerances, deviations and fits, 2019. Aus Wissenschaft und Forschung 68 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 For the case of the varying surface diameter, it can be seen, that even though only comparatively small changes of the highest minimal separation h min occur, the estimated leakage increases drastically for higher bore diameters. This can be attributed to the proportionality of the leak rate Q˙ leak and the third power of minimal separation h min 3 . As for the variation of roughness, the changes of both quantities are even more drastic, with the leakage probability being almost proportional to the roughness. However, the change of the estimated leakage compared to the highest minimal separation is still rather small given the aforementioned proportionality. This can be explained by the change of the flow factor Φ p which is also affected by the change of roughness. Here, a higher surface roughness hampers the flow stronger for higher gap heights, ultimately causing a less steep increase in estimated leakage. The leak rate in static conditions cannot be assessed this way, because the flow factors were not calculated for the small gap heights occurring in static conditions. To qualitatively compare the leakage during static conditions, the static solid contact pressure as depicted in Figure 4 and Figure 6 can be used. For the case of varying diameter, the static contact pressure sharply decreases for increasing bore diameter. Thus, the minimal separation and also the leakage are expected to increase for higher bore diameters. As for the changing roughness, the static distribution of solid contact pressure is almost similar. Since the solid contact pressure p c is given as a function of the ratio of separation and average roughness h/ R a , the separation h increases with an increasing value of R a . Again, given the proportionality of the leak rate Q˙ leak and the third power of minimal separation h min 3 , the probability for leakage to occur is expected to be considerably higher for higher surface roughness. Conclusion The two parameter sensitivity studies presented in this contribution aim to bring a better understanding of how friction force and leakage in pneumatic spool valves are affected by a variation of the bore diameter and the surface roughness. It has been found that the EHL simulation model predicts lower friction and higher leakage for an increasing bore diameter. This is in line with the expectations, since with decreasing interference, lower normal contact stresses occur. Interestingly, the increase in friction force follows an almost linear tendency, even for comparatively high deviations from the original diameter. Thus, the impact of diameter deviations on the friction of the investigated sealing contact can be simply taken into account by scaling the resulting friction force. For a diameter deviation of +20 µm a change in friction force of about 15 % is expected to occur. Care should be taken with the interpretation of the presented results for surface roughness. It has been found, TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 68 / Fes18/ Festo SE & Co. KG: Info Valve and valve terminal series VG, https: / / www.festo.com/ net/ SupportPortal/ Files/ 381028/ PSIplus_VTUG_en_V05_M.pdf, 2018. / Fis20/ Fischer, F. J., Schmitz, K., Tiwari, A., Persson, B. N. J. Fluid Leakage in Metallic Seals, Tribology Letters, Vol. 68, Nr. 4, 2020. DOI: 10.1007/ s11249-020- 01358-x. / Pat78/ Patir, N., Cheng, H. S. An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication, Journal of Lubrication Technology, Vol. 100, Nr. 1, S. 12-17, 1978. DOI: 10.1115/ 1.3453103. / Pat79/ Patir, N., Cheng, H. S. Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces, Journal of Lubrication Technology, Vol. 101, Nr. 2, S. 220-229, 1979. DOI: 10.1115/ 1.3453329. / Per01/ Persson, B. N. J. Theory of rubber friction and contact mechanics, The Journal of chemical physics, Vol. 115, Nr. 8, S. 3840-3861, 2001. DOI: 10.1063/ 1.1388626. / Tri21/ Tribo Technologies: Tribo-X, https: / / www.tribotechnologies.com/ de/ tribo-x, 2021. Aus Wissenschaft und Forschung 69 Tribologie + Schmierungstechnik · 69. Jahrgang · 5-6/ 2022 DOI 10.24053/ TuS-2022-0046 TuS_5_6_2022.qxp_TuS_5_6_2022 09.02.23 16: 31 Seite 69