A comprehensive model of wear, friction and contact temperaturein radial shaft seals$

D. Frölich n, B. Magyar, B. SauerInstitute of Machine Elements, Gears, and Transmissions (MEGT), University of Kaiserslautern-Gottlieb-Daimler-Straße 42, 67663 Kaiserslautern, Germany

a r t i c l e i n f o

Article history:Received 3 September 2013Received in revised form26 December 2013Accepted 31 December 2013Available online 9 January 2014

Keywords:Radial shaft seal ringContact temperatureWearFriction torqueFinite element simulation

a b s t r a c t

Radial shaft seals are used in a variety of applications, where rotating shafts in steady housings have to besealed. Typical examples are crankshafts, camshafts, differential gear or hydraulic pumps. In theoperating state the elastomeric seal ring and the shaft are separated by a lubrication film of just a fewmicrometers. Due to shear strain and fluid friction the contact area is subject to a higher temperaturethan the rest of the seal ring. The stiffness of the elastomeric material is intensely influenced by thistemperature and thus contact pressure, friction and wear also strongly depend on the contacttemperature. In order to simulate the contact behavior of elastomer seal rings it is essential to use acomprehensive approach which takes into consideration the interaction of temperature, friction andwear. Based on this idea a macroscopic simulation model has been developed at the MEGT. It combines afinite element approach for the simulation of contact pressure at different wear states, a semi-analyticalapproach for the calculation of contact temperature and an empirical approach for the calculation offriction. In this paper the model setup is presented, as well as simulation and experimental results.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

The field of applications for elastomeric radial shaft seals iswide and diverse. Automotive industry, washing machines, waterpumps or wind power plants are just four examples that empha-size how fundamentally different the applications and thus therequirements for seals can be. A typical radial shaft seal design isillustrated in Fig. 1.

In some applications, temperature is the critical factor. Espe-cially where large diameters and circumferential speeds areinvolved, the thermal properties of the elastomer need to be takeninto consideration. In other applications, the degree of efficiencyand the reduction of friction are significant. In all fields of use, theseal rings need to outlast the lifetime of the machine they areinstalled in. Thus ageing and wear must be reduced to a minimum.Due to this variety of applications and requirements, the choice ofan appropriate seal ring design and material is a challenge.

During the development process of new seal designs or newelastomer materials, test rigs are generally used to check the sealring under conditions that are close to the designated field of use.Experiments focusing on wear are especially time consuming. Thisis the reason why in recent years, simulation models have beenincreasingly used for preliminary tests of the seal ring behaviorand to reduce the experimental expense.

In a first section, this paper will give an overview of differentsimulation models for radial shaft seal rings that have beendeveloped in companies or research institutes in recent years.Then the model that has been developed at the Institute ofMachine Elements, Gears and Transmissions (MEGT) will beexplained. The structure of the model is introduced and acomparison with experimental results is given.

2. State of the art

Many researchers have developed simulation models to inves-tigate the behavior of seal rings in detail. Basically it can bedistinguished between macroscale and microscale modellingapproaches. The models making use of microscale approachestypically focus on a small section of the seal system that ismodelled physically detailed and very close to reality. Thesemodels can be used to extend the fundamental understanding ofthe functionality of radial shaft seal rings. Macroscale models areoften based on simplified empirical approaches, combined withhigher scale physical models. The focus of these macroscalemodels is on the function of the overall system.

Below the state of the art of these seal ring models is presented.Most of the macroscale models focus on just one aspect, that is,

on temperature, friction, or wear. By the use of an electro-thermalanalogy-model Upper [1] is able to determine the contact tem-perature in a seal ring as well as the temperature distribution.It can be shown that the wear of a seal ring and the associated

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Wear

0043-1648/$ - see front matter & 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.wear.2013.12.030

$This paper was presented at the 2013 World Tribology Congress.n Corresponding author. Tel.: þ49 631 205 3715.E-mail address: daniel.froelich@mv.uni-kl.de (D. Frölich).

Wear 311 (2014) 71–80

growing contact width have a significant influence on the tem-perature distribution within the seal ring. A high temperaturegradient within the seal ring volume is detected. Based on thesescientific findings, first finite element models that combine ther-mal and mechanical load steps are developed.

Stakenborg and Ostayen investigate the temperature-distri-bution in the contact zone of radial shaft seal rings [2] with thefinite element method and a thermal network. The authors demon-strate that the larger proportion of the heat generated in the contactarea dissipates through the shaft and a considerably smaller propor-tion dissipates through the seal ring.

Kang and Sadeghi use a microscale model to simulate thetemperature-distribution in the contact zone of seal rings [3].Making use of the elasto-hydrodynamic theory, they find that thecontact temperature on the surface of the seal ring is higher thanthe temperature on the shaft surface.

In [4], the temperature distribution due to friction heat in aradial shaft seal ring is simulated. The associated thermal defor-mation due to the friction power generated in the contact zone isstudied. It can be found that the influence of thermal deformationon the width of the contact zone and the resulting contactpressure is small. The elastomeric behavior is modelled usingconstant Mooney–Rivlin coefficients, independent of the currenttemperature distribution. In [5] and [6], the temperature distribu-tion within a radial shaft seal ring is calculated. The authorsconclude that the simulation of the friction torque in seal ringsrequires a combined thermal and mechanical model. First, thetemperature distribution is determined and then the mechanicalbehavior of the elastomeric material, taking into account itstemperature dependency, is simulated. Thereby, the contact pres-sure and the friction between seal and shaft can be simulatedmore accurately. A detailed insight in the contact temperature ofseal rings is given in [7]. A conjugated heat transfer simulation isconducted in order to study the influence of the contact friction,oil sump temperature and surrounding elements, e.g., shaft andhousing on the contact temperature. The comparison with experi-mental results using a thermographic camera shows a goodaccordance. An empirical approach to the temperature depen-dence of radial shaft seal friction is presented in [8]. Through theanalysis of test rig results a correlation of friction energy andcontact temperature is deduced. In an iterative calculation, bothdimensions can be determined. Dry friction and fluid friction makeup the resulting overall friction.

At the same time, the simulation of wear in seal rings isinvestigated. In [9], a finite element model for the simulation ofwear in a reciprocating elastomeric seal ring under different loadconditions is published. The occurring wear is modelled in theform of node-displacements of the finite element mesh. The effectof wear on the resulting pressure distribution can be analyzed.

Node displacement is the first of three common possibilities ofmodelling wear in FE-models. This strategy has been adopted inlater works of other authors. In [10], wear of radial shaft seal ringsand PTFE lip seals is simulated using a similar FE-approach in thesoftware ANSYS. The wear is not applied as a node displacement,but by deactivating elements. This method is called element-deathand represents the second basic possibility of modelling wear. Oneadvantage is that using this strategy a contortion of the mesh isavoided. With element death, a continuous wear progress cannotbe modelled. The accuracy is limited by the element size in thecontact zone. This can be regarded as a disadvantage. The softwareABAQUS offers a FORTRAN-Subroutine “umeshmotion” that can beused to move mesh-nodes independent of the underlying materialin an adaptive mesh region. This subroutine is used by [11] tomodel wear in a pin-on-disc tribometer. The authors compareexperimental tribometer results with simulation results, usingArchard's wear equation and find that the accuracy of thismodelling strategy is acceptable. A third possible modellingstrategy of wear in a FE-analysis is used by [12]. In this work,the seal is modelled as an axisymmetric component using thesoftware MSC.MARC. The application of wear is not accomplishedthrough mesh-modifications, but for each wear state, the geome-try, described by contour points along the contact zone, is updated.The current geometry is then meshed and used for furthersimulation steps. This strategy is particularly powerful for wearamounts larger than the elements in the FE-mesh.

The first microscale models for the simulation of the tribolo-gical behavior of radial shaft seal rings have been developedapproximately 25 years ago. In 1989, Gabelli develops a modelfor the simulation of the lubrication film thickness [13]. In hismodel, the film thickness formation combines micro-EHD action,based on interactions of surface asperities and hydrodynamicaction at the sealing interface, based on the solution of the generalReynolds' equation. The surface roughness of seal and shaft isdescribed with microundulations. Salant develops a simulationmethod for the estimation of the leakage rate [14], based on thesolution of the general Reynolds' equation, and taking into con-sideration the distortion of the seal surface undulations duringoperation, as described by [15]. In regions, where the localpressure falls below the cavitation pressure, the existence of both,liquid and gas are taken into consideration. This simulation modelis continuously refined and developed further by Salant. Otherscientists have taken up this simulation method in their ownsimulation models. Van Bavle et al. analyze different seal layoutsbased on the simulation method developed by Salant [16]. Theirdescription of the lubrication film is used in later research by otherscientists. In [17], the influence of the oil meniscus on the lip sealbehavior is simulated, demonstrating, that asperity contact occursin the seal interface if the meniscus moves too far to the liquidside. In [18], an extension of the model shown in [14] is presented.It can be applied for mixed lubrication, taking into considerationmicro-cavitation and micro-deformation of the surface undula-tions of the seal lip. With the simulation method presented in [19],the fluid mechanics of the lubrication film and the elastic lipdeformation are solved using the Reynolds' equation with flowfactors. This statistical approach improves the computationalefficiency. This approach is extended by [20], where the deforma-tion of the seal lip asperities is modelled, using a matrix ofelasticities that are predetermined with FE-simulations. In [21], athermal EHL-model of a seal ring is presented. The deformation isalso taken into account by using a matrix of elasticies. An artificialsurface is used to take into consideration the surface asperities.The system of equations is solved with the FE-method, instead ofthe wide spread finite difference method.

The above listed literature illustrates the difference betweenthe macroscale and microscale simulation approaches. In recent

Fig. 1. Schematic of radial shaft seal ring components.

D. Frölich et al. / Wear 311 (2014) 71–8072

years, many papers that treat the temperature distribution in sealrings, the friction torque between shaft and seal, or the wear ofseal rings separately on a macroscopic scale have been published.In [1] and [5], first approaches for a combined simulation of two ofthese factors are presented. An approach that combines the threeaspects of contact temperature, friction and wear of seal ring andshaft within one model is lacking so far.

Microscale models of the seal interface are typically used tosimulate lubrication film thickness, pumping rate and leakage,taking into consideration the influence of deformable surfaceundulations. Macroscopic modelling strategies are usually appliedfor the simulation of wear during the operation of seal rings.To reach acceptable computation times, the macroscale models ofthe seal interface must be described in less detail, using empiricalapproaches. The model presented in this paper falls within thecategory that use macro scale approaches.

3. Model setup

The basis of the presented simulation approach is a parametricaxisymmetric finite element model created in the softwareABAQUS. The model is developed using the ABAQUS Pythonscripting-interface. The seal geometry, its size as well as thermaland mechanical boundary conditions can easily be modified in thePython script. The definition of the simulation steps, the applica-tion of the boundary conditions and the wear application areperformed solely using Python scripting. The advantage of thePython script is that the FE-model can easily be combined withanalytical and empirical equations, e.g., for the calculation ofboundary conditions and loads. Hence the Fortran-subroutineumeshmotion is not used in the current model. The basic modelsetup is shown in Fig. 2.

Starting with the new seal ring, the wear of the model issimulated in a user defined number of time increments until therequested final wear state is reached. Within each wear increment,three simulation steps are conducted. The first simulation step is amechanical step. The seal ring geometry and the shaft geometryare updated according to Archard's wear equation by moving thecontact nodes in the direction of the contact normal, making useof the ALE Adaptive Mesh Constraint in ABAQUS. This displace-ments boundary condition on the contact nodes of seal (ds,i) andshaft (dw,i) is illustrated in Fig. 3. With the Adaptive MeshConstraint, the contact nodes can be moved independently ofthe underlying material. In addition, the mesh distortion in themodel areas, that are subject to wear are kept at a minimum andacceptable element aspect ratios are maintained. Additionalboundary conditions keep the outer nodes of the seal ring metalcase and the inner nodes of the hollow shaft fixed, making use ofthe encastre boundary condition.

The second simulation step is a coupled temperature-displace-ment-step. At the beginning, contact temperature and frictiontorque are calculated. It can be chosen between an empiricalapproach, according to [8], and a numerical approach developed atthe MEGT, based on [22,23]. The calculated contact temperature isapplied as a temperature boundary condition on the respectivenodes of shaft (ϑw,i) and seal (ϑs,i) (Fig. 4). In respect to the heattransition between the surfaces and the surrounding fluids, theheat transfer coefficients and the fluid temperatures are defined asboundary conditions (Table 1). Regarding the seal ring surface onthe oil side, fully-flooded conditions are assumed. The mechanicalboundary conditions of simulation step 1 are propagated to step 2.Subsequently, the temperature distribution in seal ring and shaft isdetermined.

In a last mechanical simulation step, the assembly of shaft andseal ring is simulated. The boundary conditions of the previous

steps are propagated. An axial displacement is applied on the shaft(Fig. 5). At the end of the simulation step, the refined mesh areasof seal and shaft are in contact (Fig. 5, right).

Resulting from this step is the contact pressure, taking intoaccount the current wear state and the current temperature. Thecontact pressure distribution of the last simulation step is the inputfor the wear calculation in the subsequent wear increment. Whenthe final sliding distance is reached, the simulation is aborted.

Fig. 2. Overview of simulation steps in the seal ring model.

Fig. 3. Boundary conditions on shaft and seal in simulation step 1 (wear step).

D. Frölich et al. / Wear 311 (2014) 71–80 73

3.1. Seal configuration

For the investigations presented in this paper, the followingseal configuration is chosen: The inner diameter of the radial shaftseal ring is 80 mm and the outer diameter is 100 mm (Table 2).

Simplifications of the geometry, e.g., the neglect of chamfers,were conducted in areas that are assumed to have no major effecton the simulation results. The elastomer material of the presentedseal ring consists of FKM, a fluoroelastomer. Its stress–strain-relation is strongly non-linear and temperature dependent. Forthe simulation of this hyper-elastic behavior, a temperaturedependent two parameter Mooney–Rivlin-model is chosen.As the model is exclusively applied for the simulation of steady-state problems, the visco-elastic behavior of the elastomer mate-rial is neglected. The input parameters of the Mooney–Rivlin-model have been determined by curve-fitting to uniaxial stressrelaxation test data of elastomeric samples at different tempera-tures between 0 1C and 140 1C (Table 3).

The oil used as lubricant in the development of the thermalmodel is a synthetic polyalphaolefin (ISO VG 1000).

3.2. Wear simulation

Generally, wear describes the removal of material from asurface, due to a mechanical load. It can be divided into fourcategories, according to the occurring wear mechanism.

Adhesive wear originates from physical bonding forces like vander Waals forces, hydrogen bridge bonds as well as metal, or ionicbonds. In contacting bodies, the peaks of rough surfaces cantemporarily fuse together, supported by friction heat and localpressure peaks. Due to sliding movements of the contactingbodies, these microbonds break up and in doing so change thesurfaces.

Abrasive wear usually occurs in pairs of one hard and one softcontact partner. The peaks of rough surfaces cut through the softermaterial and as a consequence, a groove develops. This movementis sometimes referred to as plowing. Abrasion can also be created

by hard particles between the interacting surfaces, e.g., inlubricants.

Erosive wear results from the interaction between a solidsurface and a fluid stream with a certain speed, which alsocontains abrasive particles. According to [24,25], this definitionincludes the impact of free-moving particles on a solid surface, too.

During the operation of machine elements such as seal rings,the wear progress of contact surfaces can basically be divided intothree major stages. At the beginning of the first stage, the contactsurfaces are in initial condition and subjected to a run-in. Surfacepeaks are flattened and in many cases friction is reduced. Often thewear gradient is high at the beginning and declines after a shortoperating time.

In the past, many scientists have investigated methods ofcalculating wear. The exact number of wear equations to be foundin literature is unknown, according to some estimates, however,there are several hundreds of them. Many of these equations canbe assigned to either a friction based approach or a contactpressure based approach. A wide spread approach, which fallsinto the second category, tracks back to Archard [26]. It is used bymany researchers for the calculation of seal wear [9,11,12].

V ¼ K 0QHs ð1Þ

In this equation, V is the volumetric amount of wear, K' is theempiric wear coefficient, Q is the contact normal force, H is thehardness of the softer body and s the sliding distance. A modifica-tion of this equation, where the hardness is put into relation to thewear coefficient is also very common [9,12,25]

V ¼ KQs ð2Þ

Here, V is the volumetric amount of wear, K is the empiric wearcoefficient, Q is the contact normal force and s the sliding distance.Eq. (2) is used for the calculation of wear in this paper. Thecoefficient K is determined experimentally for the elastomer in theseal lip and for the steal of the shaft.

In order to determine the empiric wear coefficient K, thecontour of the new seal ring and the contour of the worn sealring after a sliding distance of 5000 km on endurance test rigs areoverlaid (Fig. 6). The worn area between the contours is evaluatedusing a Matlab-script and converted into the wear volume throughmultiplication with the circumferential length of the seal.

By entering the known radial force of the seal ring and thesliding distance of the endurance run into Eq. (2), the empiric wearcoefficient K is determined. In an earlier research project at theMEGT institute, the influence of shaft velocity, oil temperature,contact pressure, and oil viscosity on the empiric wear coefficienthas been investigated experimentally [27]. A significant relation-ship between oil temperature and wear coefficient has beendetected. For that reason, a temperature-dependent wear coeffi-cient is used in the current simulation model (Table 4). For thetemperature range between 60 1C and 130 1C, the wear coefficientis linearly interpolated. The influence of shaft velocity, contactpressure and oil viscosity on the wear coefficient was found to beFig. 4. Boundary conditions on shaft and seal in simulation step 2 (thermal step).

Table 1Interaction properties of solid and fluid in the coupled temperature–displacement-step according to [1].

Heat transfer coefficients and fluid temperatures defined as interactions in simulation step 2

Heat-transfer coefficient air-steel [ Wm2K] αas 1.4

Heat-transfer coefficient oil-steel [ Wm2K] αos 14.3

Heat-transfer coefficient oil-elastomer [ Wm2K] αoe 81.4

Heat-transfer coefficient air-elastomer [ Wm2K] αae 8.1

Air temperature [1C] ϑa 20Oil sump temperature [1C] ϑo 70 (depending on operating conditions)

D. Frölich et al. / Wear 311 (2014) 71–8074

less strong in [27]. Thus it is neglected in the simulation. Experi-mental results of the current seal setup have shown no significantwear of the shaft. Therefore the empiric wear coefficient of theshaft is assumed as 0 mm3/N km. It must be noted that in sealring applications, where oil viscosity, elastomer material, or sealgeometry differ considerably from the presented setup, the empiric

wear coefficient will not be in accordance with the values presentedin Table 4.

For the application of wear in the FE-model, the definition ofadaptive mesh regions is necessary. The mesh needs to be refinedlocally and the structure needs to be strictly regular, as illustratedin Fig. 7.

3.3. Temperature calculation and friction torque

Due to solid friction between seal ring and shaft and due tofluid film friction, the temperature in the seal system has a localmaximum in the contact zone. This temperature maximum has astrong influence on the elastic properties of the elastomericmaterial. A simplified approach for the calculation of frictionpower in radial shaft seal rings is proposed by [28].

P ¼ f pvπdb ð3ÞHere P is the friction power, f is the coefficient of friction, P is thecontact pressure, v is the circumferential velocity of the shaft, d isthe shaft diameter, and b is the contact width.

In recent works, more complex and more accurate approachesfor the calculation of friction power and first approaches for thecalculation of contact temperature have been published.

In [8], an empiric approach is presented. Based on a largenumber of experiments, a friction model is developed. The friction

Fig. 5. Boundary conditions on shaft and seal in simulation step 3 (assembly step).

Table 2Configuration of the seal ring system.

Experimental seal system configuration

Inner seal diameter [mm] 80Outer seal diameter [mm] 100Seal material fluoroelastomerShaft material 1.7131Oil Polyalphaolefin, ISO VG 1000

Table 3Mooney–Rivlin-coefficients determined from uniaxial stress relaxation test dataat different temperatures.

Temperature(1C)

Mooney–Rivlin-coefficientC01 [MPa]

Mooney–Rivlin-coefficientC10 [MPa]

0 0.14 0.7320 0.12 0.6760 0.10 0.52

100 0.10 0.49140 0.09 0.48

Fig. 6. The worn area (gray) is measured by overlaying microscopic images of thenew seal ring contour and the contour of the worn seal after 5000 km slidingdistance on the test rig (schematic).

Table 4Empiric wear coefficients of the seal ring, determined experimentally at differentoil temperatures.

Oil temperature [1C] Empiric seal ring wear coefficient K mm3

N km

h i

60 3.3e-6130 4.5e-6

Fig. 7. Mesh of seal ring and shaft, refined in the contact zone.

D. Frölich et al. / Wear 311 (2014) 71–80 75

torque in this model is constituted of a non-viscous fraction at zerospeed and a velocity-dependent fraction.

T ¼ T0þTη ¼ μ0Frd2þηðϑÞ b

∑Rp

d2

� �3ð2πÞ260

n ð4Þ

Here T is the total friction torque, T0 is the initial friction torque,Tη is the viscous part of the friction torque, μ0 is the boundaryfriction coefficient, Fr is the radial force, d is the shaft diameter, η isthe dynamic fluid film viscosity, ϑ is the contact temperature, b isthe contact width, ∑Rp is the sum of the surface roughness Rp ofshaft and seal lip, and n is the rotational speed of the shaft.

The temperature in Eq. (4) can be calculated as the sum of oiltemperature ϑoil and over temperature ϑc in the contact area. Theover temperature is dependent on the friction power P per area A.As a result of measurements with different seal ring materials,radial forces and lubricants, [8] suggests an over temperature of16.5 K in the contact area for a friction power per area of 1 W/mm2.

ϑ¼ ϑoilþϑo; where ϑo ¼ fPA

� �ð5Þ

The model presented in this paper solves Eqs. (4) and (5) in arecursion. The resulting contact temperature ϑ is applied on thecontact nodes of shaft and seal lip as a boundary condition.

It should be noted that the experimental determination of theboundary friction coefficient μ0 is of great importance. The methodof determination is described in detail in [8]. In addition it isshown, that for a wide range of oils and elastomers, μ0 can beassumed as 0.3 in a good approximation. Therefore the valueμ0¼0.3 is used in the presented simulation model.

A second option for the contact temperature calculation in themodel, presented in this paper, is a numerical contact temperaturecalculation, based on [22,23]. The basis of this method is theenergy balance, taking into account the heat generated by internalfriction as well as the heat transport towards the wall. As a firststep, the equations for the surface temperatures of the contactingbodies can be written as a simplified form of Fourier's law for heatconduction [29,30]:

ciρiviλi

δϑiδx

� δ2ϑiδx2

þδ2ϑiδy2

� �¼ 0 ð6Þ

The energy equation implemented in the seal ring modelpresented in this paper has the following form:

�λc1δϑ1δy1

�λc2δϑ2δy2

þηðϑÞv2x

h0¼ 0 ð7Þ

In this equation λc1 and λc2 are the heat conductivity of thecontacting bodies, δϑ1=δy1 and δϑ2=δy2 are the temperaturegradient on the surface of the two contacting bodies, while η isthe dynamic fluid film viscosity and νx is the x-component of the

fluid velocity. For the calculation of the temperature profile of thelubricant, a parabolic distribution is assumed.

The pressure and temperature dependence of the fluid filmviscosity is determined by using the Rodermund equation [31]

lnηðϑ;pÞ

A

� �¼ BCþϑ

p�p0F

þ1� �ðDþEðB=CþϑÞÞ

ð8Þ

The oil-parameters that were used for the viscosity model arelisted in Table 5.

The mean viscosity ηm can be determined as the arithmeticmean of the viscosity η across the fluid film:

ηm ¼ 1hf ilm

Z hf ilm

0ηðϑ; pÞdy ð9Þ

As the oil in the contact zone between seal ring and shaft issubject to considerable shear, Eyring's material law [34] is used totake into account the non-Newtonian behavior

η¼ ηmτ=τEy

sin hðτ=τEyÞð10Þ

τ is the oil film shearing, and τEy is the Eyring shear stress, thatis the critical stress where Newtonian fluid behavior changes tonon-Newtonian.

4. Simulation results

Regarding the simulation results, it can be distinguishedbetween first, the analysis of the new seal ring in its initialcondition, second, the analysis of the seal system during endur-ance operation, and, third, the analysis of the worn seal ring andshaft after operation.

4.1. Initial condition of the seal system

Wear, friction and contact temperature are significantly influ-enced by the initial contact width and the initial contact pressurebetween shaft and seal lip. The lip contour in the FE-model needsto be modelled as close to the real seal lip as possible. Thereforethe seal is analyzed using a fringe projection microscope (Fig. 8).A cut across the seal lip reveals a seal lip radius of approximately215 mm. This radius is used to define the lip geometry of theFE-model.

In order to check the accuracy of elastomer stiffness and lipgeometry, preliminary tests of contact width and radial force areconducted. The contact width of seal ring and shaft is analyzed bymounting the seal ring on a hollow acrylic glass shaft. The contactarea is visualized using a microscope. In the FE-model, the contactwidth is determined by measuring the distance of the outermostnodes that show a positive contact pressure. It can be shown that

Table 5Parameters of PAO and reference oils according to [32,33].

Oil parameter PAO Ref. Oil1 Ref. Oil2 Ref. Oil3 Ref. Oil4

viscosity class ISO VG 1000 15 32 100 460Vogel parameter A [Pas] 5:588922� 10�5 8:22563� 10�5 7:0840� 10�5 2:84477� 10�5 1:37492� 10�5

Vogel parameter B [1C] 5715.756 693.2438 800.3 1235.573 1696.304Vogel parameter C [1C] 300 95 95 115 125Rodermund parameter D [–] 0.316144 0.6629436 0.8255 0.5490735 0.4977719Rodermund parameter E [–] �8:661369� 10�3 1:22344� 10�2 �2:31� 10�2 8:88301� 10�3 1:82924� 10�3

Rodermund parameter F [bar] 1400 2000 2000 2050 2000

D. Frölich et al. / Wear 311 (2014) 71–8076

experimental and simulated contact width are in good accordance(Fig. 9).

The radial force of seal ring and shaft is determined experi-mentally by using a test rig according to [35] (Fig. 10). The seal ringis mounted on a split shaft. One half of the shaft is fixed on a beamin bending. When mounted, the seal ring reduces the gap betweenthe two halves. This reduction is measured and converted into theradial force.

As the radial force is highly temperature dependent, the mea-surement is conducted at several temperatures over the anticipatedoperating conditions, from room temperature at 25 1C up to amaximum temperature of 190 1C. Fig. 10 shows that the accordanceof simulated and measured radial forces is very good.

4.2. Temperature and friction during operation

During endurance operations, the simulation model offers awide range of possibilities to analyze the contact temperature and

the temperature distribution of the seal system in different statesof wear. The following section demonstrates for a new seal ringthe resulting contact temperature at different working conditions.

At an oil sump temperature of 80 1C, the contact temperaturerises from 93 1C to 164 1C when the rotational speed of the shaft isincreased from 500 min�1 to 3000 min�1 (Fig. 11). For a seal ringdiameter of 80 mm, the corresponding range of surface velocitiesis 2.1 m/s to 12.6 m/s. The lubricant used is a synthetic poly-alphaolefine. The simulated contact temperature is in good accor-dance in the empirical and numerical simulation approach.

When the rotational speed is kept constant at 2000 min�1 andthe oil sump temperature is increased from 40 1C to 100 1C themaximum contact temperature rises from 110 1C to 150 1C (Fig. 12).

At a constant rotational speed of 2000 min�1 and an oil sumptemperature of 80 1C, the contact temperature shows a depen-dency on the oil viscosity (Fig. 13).

For lubricants with a lower viscosity (ref1, ref2, ref3), thecontact temperature amounts to 125 1C, while for lubricants witha higher viscosity, the contact temperature rises to approximately

Fig. 8. Fringe projection microscope picture of a FKM seal lip, with a lip radius of approximately 215 mm.

Fig. 9. Microscopic picture of the initial contact width of a seal ring on a hollow glass shaft (left), and the initial contact width in the finite element model (right).

Fig. 10. Schematic depiction of the shaft, divided in two halves for the measurement of radial force (left), comparison of initial radial force at different seal ring temperaturesin experiment and simulation (right).

D. Frölich et al. / Wear 311 (2014) 71–80 77

140 1C. Again, the empirical and numerical simulation approachesare in good accordance.

In addition to the maximum over temperature in the sealcontact, the numerical simulation approach provides the distribu-tion of the contact temperature along the contact width of the seallip (Fig. 14). It can be illustrated, that the contact temperaturedistribution is similar to the distribution of contact pressure.At higher rotational speed, the difference between the tempera-ture in the middle of the contact zone and the temperature at theedge of the contact zone becomes more distinctive.

4.3. Wear of the seal system during operation

During the operation of the seal system, an advancing materialremoval of the seal lip can be detected. Due to the removal and theconnected contour change of the seal lip, the tribological situationin the contact area changes permanently. The different aspects,which are affected by wear, can be analyzed with the presentedsimulation model in detail. The simulated change of the seal lipcontour up to a maximum sliding distance of 5000 km at arotational speed of 3000 min�1 is illustrated in Fig. 15.

Fig. 12. Contact temperature for different oil sump temperatures calculated withthe empiric and the numeric model.

Fig. 13. Contact temperature for different lubricants calculated with the empiricand the numeric model.

Fig. 14. Temperature distribution along the contact width on the seal ring surface,calculated with the numeric model.

Fig. 15. Simulated seal lip contour at different states of wear at a shaft rotationalspeed of 3000 min�1, starting with the new seal at 0 km and resulting in the wornseal at 5000 km.

Fig. 16. Asymmetric contact pressure distribution for different states of wear.

Fig. 11. Contact temperature for different rotational speeds of the shaft calculatedwith the empiric and the numeric model.

D. Frölich et al. / Wear 311 (2014) 71–8078

It can be seen that the initial contour of the seal lip is modelledas a radius. The asymmetric contact angles of the seal ringinfluence the position of the material removal. The contact angleon the air side is flatter than the angle on the oil side, which is whythe area of occurring wear is shifted to the air side. The change ofthe lip contour affects the contact pressure distribution in thesimulation (Fig. 16). The maximum contact pressure is reducedfrom 1.8 MPa at the beginning to 1.1 MPa at 5000 km.

The radial force as an integral of the contact pressure over thecontact area is illustrated in Fig. 17. It can be noted, that even thoughthe pressure distribution changes significantly during the operation of

the seal ring, the radial force is reduced by just 2%. Since the load inthe wear Eq. (2) does not change significantly during operation, thesimulated wear volume development during operation is approxi-mately linear in our simulation model (Fig. 17). In experiments thewear volumewill show a greater slope at the beginning that decreasestowards the end of the operation time. This running-in is not takeninto account due to the use of Archard's wear equation.

At the same time, the contact width grows from 100 mm toapproximately 180 mm at 5000 km (Fig. 18). The simulation resultsreveal an increase of the friction torque T during operation (Fig. 18).The cause for the increasing friction torque can be found in thesuperposition of two opposing effects. On the one hand, the radialforce decreases slightly, due to the material removal. The non-viscouscomponent of the friction T0 (Eq. (4)) decreases with the radial forceas well. On the other hand, a growing amount of lubricant is subjectto shear in the contact zone, due to the increasing contact width. Thisleads to an increase of the viscous component of the friction torqueTη (Eq. (4)). The influence of the growing contact width is dominantand the resulting overall friction torque T increases.

The development of friction torque during endurance seal ringoperations has also been investigated by [36]. For a comparableseal ring system at constant temperatures and a constant shaftvelocity, it could be found experimentally that the friction torqueincreases over operation time (Fig. 19) which confirms the simu-lated friction torque development in Fig. 18.

The increasing friction torque leads to an increase of thefriction power during the seal operation (Fig. 20). Due to theincrease of the contact width the resulting friction power percontact area decreases, as illustrated in Fig. 20.

Fig. 17. Simulation results for the development of wear volume and radial forceduring seal operation.

Fig. 18. Simulated friction torque and contact width development during the sealoperation.

Fig. 19. Friction torque development during seal operation, based on experimentalresults in [36].

Fig. 20. Simulated development of friction power and friction power per contactarea during the seal operation.

Fig. 21. Contact temperature distribution for different states of wear.

D. Frölich et al. / Wear 311 (2014) 71–80 79

The friction power per contact area is the significant dimensionthat influences the temperature in the contact zone of seal ring andshaft. The simulated temperature distribution correlates with thedecreasing friction power per area and has a distinct peak of 125 1C.Initially the contact temperature is distributed over a small contactwidth (Fig. 21). With progressing wear, the contact temperature isdistributed over a wider contact zone and shows a maximum contacttemperature of 113 1C at the end of the simulation.

For one spot in the center of the contact zone, the contacttemperature development shows a very good correlation whencomparing empirical and numerical simulation models (Fig. 22).

5. Conclusion

In this paper, a comprehensive simulation approach for radialshaft seal rings is presented. The model can be applied to analyzeseveral macroscopic aspects in the system of radial shaft seal rings.

Wear of radial shaft seal rings can be simulated with goodaccuracy as the temperature-dependent elastomer stiffness is takeninto consideration. The detailed insight into the contact temperaturedistribution helps to choose an appropriate elastomeric material.Especially the formation of oil carbon due to high contact tempera-tures can thus be avoided. Also the influence of wear on the frictiontorque can be analyzed. With the parametric model setup designoptimizations, e.g., minimizing the friction torque can be conducted.It must be noted, however, that the equations for the simulation ofwear and friction are based on empirical approaches. Thus the scopeof application of the listed friction and wear coefficients is limited toconditions similar to those presented in this paper. Moreover, it isimportant to note that the local distribution of temperature andpressure on a microscopic scale is influenced by surface asperities.With the presented simulation approach these local pressure andtemperature changes cannot be taken into account.

Acknowledgments

The authors would like to thank the German Research Founda-tion (DFG) for the support of the research within the CollaborativeResearch Centre 926 “Microscale Morphology of ComponentSurfaces (MICOS)”, sub-project C01.

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Fig. 22. Contact temperature development during seal operation, calculated withthe empiric and the numeric model.

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