This paper focuses on the friction behavior of jour- nal bearings operating from hydrodynamic to mixed lubrication regime where severe metal-metal contact occurs. Therefore, friction tests with two diﬀerent static loads are carried out on the journal bear- ing test-rig from KS Gleitlager. The test results in form of Stribeck curves provide a solid base to proof the isothermal elastohydrodynamic simulation approach. The simulation approach solves the av- eraged Reynolds equation introduced by Patir and Cheng and considers metal-metal contact by using the Greenwood and Tripp contact model. All nec- essary surface parameters are derived from surface scans. No less essential in this approach are the experimentally identiﬁed lubricant properties under high pressure and high shear rate. The calculated friction torque matches the mea- surement results within the measurement uncertainty for a wide range of operation conditions. With the validated simulation approach the inﬂuence of surface smoothing due to metal-metal contact is discussed. Additionally, the limits of a constant boundary coef- ﬁcient are identiﬁed and the eﬀects of ﬂow factors are presented. ∗VIRTUAL VEHICLE Research Center, Austria †VIRTUAL VEHICLE Research Center, Austria ‡VIRTUAL VEHICLE Research Center, Austria §KS Gleitlager GmbH, Am Bahnhof 14, 68789 St. Leon- Rot, Germany ¶KS Gleitlager GmbH, Am Bahnhof 14, 68789 St. Leon- Rot, Germany1 Introduction The mixed lubrication regime describes the transition between the pure hydrodynamic lubrication regime, where a ﬂuid separates the contacting surfaces and the boundary lubrication regime, where metal-metal contact is leading. Characteristically for the mixed lubrication regime is that the ﬂuid ﬁlm cannot com- pletely separate the adjacent surfaces and single as- perities interact. Hence, the friction in mixed lu- brication regime (mixed friction) is characterized by the co-existence of hydrodynamic and asperity fric- tion [1]. The friction coeﬃcient ﬁnds its minimum between the pure hydrodynamic lubrication and the mixed lubrication. In terms of friction reduction and eﬃciency it is beneﬁcial to operate lubricated con- tacts in this condition. Unfortunately, wear occurs as asperities are in contact and durability problems can occur. Especially in the automotive sector a trend to cut fuel consumption and emissions has been established which is driven by emission regulations and customer satisfaction. Downscaled turbocharged combustion engines with high power density are an achievement in modern engine development for performance im- provement. The high power and small dimensions of engine components lead to highly loaded lubri- cated contacts such as journal bearings. Another ef- ﬁciency beneﬁt is pledged to friction reduction with low-viscous lubricants. These advancements lead to a decreasing oil ﬁlm thickness in lubricated contacts. This means that journal bearings, which formerly mainly ran in pure hydrodynamic lubrication regime to ensure a long lifetime, may partly expose metal- 1 metal contact during the dynamic operation [2, 3, 4]. Figure 1: Sketch of a Stribeck curve with diﬀerent lubrication regimes For lubricated contacts, and particularly for jour- nal bearings the Stribeck curve (see ﬁgure 1), named after Richard Stribeck [5, 6], has became a common tool to assess friction beneﬁts. A static load is ap- plied to the journal bearing and the friction torque is measured for a wide speed range. With such a test conﬁguration the diﬀerent lubrication regimes can be identiﬁed. Bovington [7] describes the importance of the Stribeck curve in bearing design and discusses the eﬀect of low-viscosity lubricant and oil additives. He conducted several tests with various engine oils which were formulated diﬀerently. More recently, the inﬂuence of surface dimple eﬀects on journal bearing friction are experimentally studied [8] by evaluating the Stribeck curve. In the present study, a similar test setup is used for the measurements. The exper- imental results in form of Stribeck curves provide a solid base to validate the simulation approach. Predictive simulation approaches to describe lubri- cated contacts in journal bearings are broadly dis- cussed in literature and diﬀer in their level of de- tail. An overview of elastohydrodynamic lubrication analysis of conformal contacts without metal-metal contact is given by Booker et al. [9]. The exten- sive review focuses on the 2D Reynolds equation and discusses, among other things, bearing deformation, mass-conservative cavitation and pressure-viscosity eﬀects. Also, the eﬀect of surface roughness on bear-ing performance in elastohydrodynamic lubrication is discussed. Dobrica et al. [10] compare stochastic and deterministic models in more detail and conclude that the stochastic model correctly anticipate the trends of the deterministic models for the investigated sur- faces. Both studies don’t consider slip boundary con- ditions which is recently reviewed and discussed by Jao et al. [11]. Beyond the scope of this study is the 3D consideration of the ﬂuid ﬁlm using a com- putational ﬂuid dynamics (CFD) approach [12]. Re- cently, Shahmohamadi et al. [13] present a thermo- hydrodynamic analysis using CFD approach includ- ing a vapour transport equation to consider cavita- tion. Both, temperature and pressure distribution agree well with experimental data. However, the interaction of single asperities be- tween the contacting surfaces occur in mixed lubri- cation regime and have an impact on journal bearing performance. Simulation approaches considering the asperity contact in journal bearings are covered in many text books, for instance [14, 15, 16]. There- fore, an extensive reference list is not replicated here. Notably, only a minor number of publications dis- cuss journal bearing friction in severe mixed lubri- cation and verify the calculated results with mea- surement results. Bartel et al. [17] present an ana- lytical model considering metal-metal contact by us- ing an energy approach. The calculated results were compared to measured Stribeck curves. The authors conclude that the viscosity-pressure behavior has a huge inﬂuence on the results and should not be ne- glected. Further, macro-deformation of shaft and bearing need to be considered for realistic friction prediction. Lu et al. [18] present a simple theoretical analysis for friction prediction in mixed and bound- ary lubrication regime and veriﬁed the analysis for diﬀerent loads and temperatures. The tool is also used to investigate the eﬀect of surface pattern and asperity orientation on Stribeck curves [19]. Wang et al. [20] present an analytical method to derive Stribeck curves and discuss the inﬂuence of roughness, elasticity, and thermoelasticity on friction. Especially the elastic deformation has a strong inﬂu- ence on the friction behavior. The inﬂuence of sur- face adaption caused by running-in wear on friction in dynamically loaded bearings is discussed by Bar- 2 tel et al. [21]. Beside the change of surface roughness an adaption of the bearing geometry is calculated. A clear reduction of maximum contact pressure and friction is identiﬁed for the worn bearing. The inﬂu- ence of a worn geometry on journal bearing perfor- mance is also discussed by investigating misaligned bearings [22] and bearings subjected to numerous starts and stops [23]. Both papers conclude that a worn bearing geometry decreases the bearing temper- atures. Sun et al. [24] calculate the eﬀect of surface roughness change on misaligned journal bearings and highlights the importance of elastically deformation of the contacting bodies. However, no contact model is implemented to discuss friction due to asperity in- teraction. The present study focuses on friction losses in jour- nal bearings operating in severe mixed lubrication regime. The analytical investigation uses an isother- mal mixed elastohydrodynamic simulation approach which considers the elastic deformation of shaft and bearing structure. Although the temperature is as- sumed to be constant within the bearing, the varia- tion between diﬀerent loads and shaft speeds is con- sidered with introducing an equivalent bearing tem- perature. The equivalent bearing temperature is de- rived from temperature measurements at the back of the bearing shells. Additionally, the piezoviscous and non-Newtonian behavior of the lubricant are in- cluded in the approach. The equation describing the lubricant viscosity is dependent on temperature, pressure and shear rate and was previously derived by measurement. The detailed derivation of the vis- cosity equation was published in [25] and validated for dynamically loaded journal bearings operating in mainly hydrodynamic regime. The inﬂuence of asperities on hydrodynamic fric- tion is included by using the ﬂow factors according to Patir and Cheng [26, 27]. Friction due to metal- metal contact is considered by the Greenwood and Tripp contact model [28]. To derive the parame- ters for both, ﬂow factors and contact model, bearing shell surface and shaft surface were scanned by white light interferometry. From the surface scans rough- ness parameters and asperity orientation are estab- lished. The boundary friction coeﬃcient is the re- maining unknown parameter which is chosen to beconstant in this work. Primary aim of this study is the validation of the simulation approach to calculate journal bearing fric- tion in severe mixed lubrication regime. Further, the practicability and limits of the simple elastic Greenwood-Tripp contact model in combination with a constant boundary friction coeﬃcient is discussed. For a secondary aim, the inﬂuence of surface smoothing due to running-in on friction in mixed lubrication is discussed. Therefore, a ran-in jour- nal bearing surface is analyzed and a second contact model is derived. The inﬂuence on metal-metal con- tact pressure, minimum radial clearance and friction is analyzed. Further, the exclusion of the ﬂow factors from the simulation and its eﬀect on journal bearing friction is discussed. Moreover, the presented study complements previ- ous research by the authors which focused on journal bearing friction excited by dynamic loads. Allmaier et al. [29, 30] presented a simulation approach using an isothermal bearing assumption. He included the viscosity-pressure relation for diﬀerent single-grade lubricants and validated the friction losses over a wide range of operation conditions. Metal-metal con- tact was identiﬁed by simulation and also by mea- suring the contact voltage [31]. Later, the isothermal model was extended to a thermo-elastohydrodynamic model [32] which is able to predict the measured tem- peratures at the bearing shell. The results also justi- ﬁed the usage of an isothermal simulation approach in terms of friction prediction. Sander et al. [25] in- cluded the non-Newtonian behavior of modern multi- grade engine oils into the isothermal simulation ap- proach. Again, the simulation results were validated for a variety of shaft speeds and dynamic loads up to 100 MPa speciﬁc load in the test bearing. After the test procedure worn areas on the bearing surface were identiﬁed which was caused by metal-metal con- tact. Metal-metal contact was also identiﬁed by sim- ulation. As a consequence research on the running in process of journal bearings was conducted [33, 34]. Complementary, the presented results are obtained from the same simulation approach yet discuss fric- tion in severe mixed lubrication regime. 3 2 Lubricant properties The lubricant’s viscosity is directly related to the fric- tion in hydrodynamic lubrication regime. In mixed lubrication regime the lubrication additives modiﬁes the frictional behavior of the contacting surfaces. It is thus important to explicitly describe the lubricant. In this work a fully formulated low viscous 0W20 hydrocarbon engine oil is used as it is available on the automotive market. The main properties of the mod- ern lubricant including the density and the viscosity at various conditions are given in table 1. Table 1: Basic properties of the tested 0W20 lubri- cant Density at 40◦C 832.5 kg/m3 Dyn. viscosity 40◦C 37.5 mPas Dyn. viscosity 100◦C 6.8 mPas HTHS-viscosity12.7 mPas Additionally to the temperature dependency of the rheological properties, the viscosity is strongly de- pendent on pressure and shear rate. Therefore, the piezoviscous and the non-Newtonian behavior of the lubricant were analyzed. In previous publication by the authors [25] the parameters (see table 2) for the empirical viscosity equation according to Vogel [35], Barus [36] and Cross [37] were derived from experi- mental data: η(T, p, ˙γ) =A·eB (T+C)+α·p·( r+1−r 1 + (K·˙γ)m) (1) In the simulation the viscosity is represented by equation (1). The corresponding values are listed in table 2. 3 Testing The journal bearing test-rig at KS Gleitlager was used to perform the experimental friction measure- ment. The test-rig is sketched in ﬁgure 2. 1The HTHS-viscosity is deﬁned as the viscosity at high tem- perature (150◦C) and high shear rate (1061/s).Table 2: Parameters for Eqs. (1) derived from exper- imental data [25] A 0.0516 mPas B 1127.6◦C C 130.7◦C α0.00095 1/bar r 0.53 - m 0.79 - K 7.9 e-8 s Figure 2: Journal bearing test-rig at KS Gleitlager 4 It consists of a rotating straight shaft which rests on two supporting journal bearings in support brack- ets. The shaft is driven by an elastically clutched electric motor. A test connecting rod is placed in between the two support brackets. An external load is applied onto the test connecting rod and on to the test journal bearing. The test journal bearing has a diameter of 47.8 mm and a width of 17.2 mm and corresponds to a typical big-end bearing used in modern combustion engine. The preconditioned oil is supplied through a hole in the lower bearing shell which. Both support journal bearings have a diameter of 54 mm and a width of 25 mm. It has an 180◦oil supply grove all along the top shell. All three bearings are made of a steel-aluminum compos- ite material. The test rig is equipped with a torque transducer, a Manner Sensortelemetrie 50 N m with an accuracy of±0.15 N m. The transducer is placed between the electric motor and the shaft to measure the friction torque generated by all three bearings. The bearing temperatures were monitored during the test. There- fore, PT100 elements were placed at the back of the bearing shells. The elements have an accuracy of ±0.5◦C. 3.1 Test conditions For the investigation of friction in mixed lubrication regime a static load is applied to the test connecting rod. Hence, only the top shell of the test bearing and the bottom shell of the support bearings are stressed. Further the oil is supplied via the unloaded bearing shells. Two load cases are investigated, the ﬁrst with 8 kN load and the second with a 4 kN load which correspond to 10 MPa speciﬁc load in the test bear- ing and 5 MPa, respectively. In the beginning of each test new bearing shells are placed into the test con- necting rod and the support brackets. One test run consists of a constant speed-up to 6000 rpm followed by a constant speed-down until the shaft stops to rotate. One test run lasts for 12 min. The second half in other words, the speed-down is recorded and evaluated. The shaft speed during the speed-down is plotted in ﬁgure 3 over time (dashed black line). The lubricant which is supplied to all three bear- Figure 3: Shaft speed (black dashed curve) and oil supply temperature (black and grey solid curve) over time ings is preconditioned during the entire test proce- dure. Hence, the lubricant supply temperature stays stable between 91◦C and 92◦C during the test run and is similar for both load cases. The black solid curve in ﬁgure 3 shows the supply temperature for 10 MPa load and the grey solid curve represents the supply temperature for 5 MPa load. 3.2 Test results The measured overall friction torque is shown in ﬁg- ure 4 over the shaft speed for both load cases. The black curve represents the measured friction torque under the speciﬁc static load of 10 MPa. At a shaft speed of 6000 rpm the friction torque is 1.6 N m. By reducing the shaft speed the friction moment de- creases to a minimum of 0.5 N m at around 400 rpm. Below 400 rpm the friction moment abruptly in- creases. At high speed the bearing operates in hydro- dynamic lubrication regime. The rise of the friction torque below 400 rpm is attributed to metal-metal contact between the shaft and bearing shell. The grey curve shows the friction torque measured with an ap- plied load of 5 MPa. Compared to the 10 MPa load case, a lower friction torque can be identiﬁed all over the investigated speed range. In the hydrodynamic 5 Figure 4: Friction torque over shaft speed for 10 MPa static load (black) and 5 MPa static load (grey) regime the friction torque is reduced by around 15 %. 4 Simulation For the simulation the KS Gleitlager test rig is mod- eled within the ﬂexible multi-body solver AVL Ex- cite Power Unit2[38, 39]. The test shaft, the test connecting rod and the two support brackets are rep- resented as mathematical condensed ﬁnite element structures which can deform elastically [40]. The lu- bricated journal bearings which connect the compo- nents are calculated by solving the Reynolds equa- tion by ﬁnite volume approach [38]. The discretiza- tion points of the lubrication regime are equally dis- tributed along the axial and circumferential direc- tion. In the presented model 25 points in axial di- rection are chosen for all bearings. In circumferen- tial direction the test bearing has 200 points and the support bearing has 176 points. Every second point is directly coupled to a point on the solid structure. The displacement of the points in between are inter- polated. The coupling method is described in [41]. When the distance between the facing surfaces de- creases their surface roughness will aﬀect the oil ﬂow. 2Version 2014.1, AVL List GmbH, Advanced Simula- tion Technology, Hans-List-Platz 1, 8020 Graz Austria, www.avl.comPatir and Cheng [26, 27] introduced ﬂow factors to the Reynolds equation taking this inﬂuence into ac- count: −∂ ∂x( ϕxh3 12η∂p ∂x) −∂ ∂y( ϕyh3 12η∂p ∂y) + +∂ ∂x( hu1+u2 2) +∂ ∂x( ϕsu1+u2 2σs) +∂h ∂t= 0, (2) where x,ydenote the circumferential and the axial direction, respectively. pis the hydrodynamic pres- sure and hthe oil ﬁlm thickness which is dependent onxandy. Further, u1andu2denote the sliding speeds of the facing surfaces. The inﬂuence of surface roughness is considered by the pressure ﬂow factors ϕx,ϕyand the shear ﬂow factor ϕs. The oil viscosity ηis considered temperature, pressure and shear rate dependent in this paper (see equation 1). The consideration of the asperity contact itself is described below (see section 4.2). The cavitation model is based on the JFO approach [42, 41]. How- ever, the non-linear model is solved in time domain. Therefore, each simulation runs until a stable quasi- static condition is achieved. 4.1 Friction Moment The friction torque acting on the bearing surface considers both, hydrodynamic losses and losses due to asperity contact. Therefore, the friction torque MFriction can be calculated by integrating the shear stresses over the bearing surface: MFriction =r∫∫ A(τh+τa)dxdy, (3) where Adenotes the bearing surface and ris the nominal shell radius. τhis the hydrodynamic shear stress. It is calculated by τh=η·u1−u2 h(ϕf±ϕfs)±ϕfph 2·∂p ∂x,(4) where + and −refer to the shell surface and the journal surface, respectively. ϕf,ϕfsandϕfpare the shear stress factors according to Patir and Cheng. 6 The shear stress in case of asperity contact τabe- tween the shell surface and the journal surface is cal- culated by τa=µBound·pa, (5) where µBound is the boundary friction coeﬃcient andpadenotes the asperity contact pressure. 4.2 Asperity contact pressure The asperity contact pressure is calculated using the Greenwood and Tripp approach [43, 28]. The the- ory of Greenwood and Tripp is based on the contact of two nominally ﬂat, random rough surfaces. The asperity contact pressure can be written as pa=KE∗F5 2(Hs), (6) where E∗is the composite elastic modulus, E∗= (1−ν2 1 E1+1−ν2 2 E2)−1, where νiandEiare the Poisson ratio and Young’s modulus of the adjacent surfaces, andF5 2(Hs) is the form function, which is deﬁned as F5 2(Hs) ={ 4.4086·10−5(4−Hs)6.804,ifHs<4 0, ifHs≥4 (7) Hsis a dimensionless clearance parameter, deﬁned asHs= (h−δs)/σs), with σsbeing the combined asperity summit roughness, which is calculated ac- cording to σs=√ σ2 s,J+σ2 s,S (8) andδsbeing the combined mean summit height, δs=δs,J+δs,S. The form factor F5 2(Hs) becomes zero for a dimensionless clearance parameter beyond four which further means no asperity contact occurs. Finally, the elastic factor Kis deﬁned as K=16·√ 2·π 15·(σs·βs·ηs)2·√σs βs, (9) where βsis the mean summit radius and ηsis the summit density.4.3 Bearing temperatures The lubricant temperature within the journal bearing varies according to the local position. For the simula- tion, an equivalent bearing temperature is introduced to consider the temperature as constant in the lubri- cation gap. For each speed the equivalent temper- ature is calculated from the measured bearing back temperatures. The approach is described in [25]. For completeness the equivalent temperatures are listed in table 3 for a speciﬁc load of 10 MPa and in table 4 for 5 MPa, respectively. TTBrepresents the equivalent temperature of the test bearing. TSB1andTSB2is the temperature for the support bearings. The maximum temperature diﬀerence between the test bearing and the two sup- port bearings is around 2◦C. At 3000 rpm a maxi- mum temperature of 108◦C for 10 MPa speciﬁc load is reached. At shaft speeds below 500 rpm the tem- perature remains similar within 0.6◦C for each bear- ing. Hence, an extensive heating due to asperity con- tact was not observed. 4.4 Surface roughness and contact pairs The surfaces of bearing shell and shaft were scanned by a white light interferometer to determine the ﬂow factors and the surface parameters for the contact pairs. Therefore measurement spots of a size of 1 mm by 1 mm were analyzed. The bearing shell was mea- sured before the test run and for comparison a worn bearing shell was scanned. In combination with the shaft surface two contact pairs are generated (see ta- ble 5). The ”new” contact pair combines the new bearing shell surface with the shaft surface. The ”worn” contact pair represents the worn bearing shell surface. The hardened steel shaft is not subjected to any surface changes during the test. Therefore, the shaft surface parameters remain unchanged. The arithmetic average Raof the bearing shell surface drops from 0.27 µm to 0.22 µm. The root mean square Rqdecreases from 0.34 µm to 0.26 µm. Ta- ble 5 summarizes the parameters of the ”new” and ”worn” contact pair. Speciﬁed are the arithmetic average of the surface 7 Table 3: Equivalent bearing temperatures at 10 MPa load Speed [rpm] 150 200 250 300 400 500 1000 3000 TTB[◦C] 101.0 101.0 101.1 101.2 101.4 101.6 102.8 108.0 TSB1[◦C] 102.4 102.5 102.5 102.6 102.8 103.0 104.3 108.0 TSB2[◦C] 102.7 102.8 102.9 103.0 103.2 103.3 104.5 108.2 Table 4: Equivalent bearing temperatures at 5 MPa load Speed [rpm] 150 200 250 300 400 500 1000 3000 TTB[◦C] 99.1 99.2 99.2 99.3 99.4 99.6 100.6 105.6 TSB1[◦C] 101.1 101.1 101.2 101.2 101.3 101.4 102.3 105.6 TSB2[◦C] 101.4 101.4 101.5 101.5 101.6 101.6 102.5 106.1 Table 5: Surface roughness and simulation input pa- rameters for the test bearing shell and the shaft Contact pair New Worn Surface Shell Shaft Shell Shaft Ra[µm] 0.27 0.14 0.22 0.14 Rq[µm] 0.34 0.20 0.26 0.20 σ[µm] 0.28 0.13 0.23 0.13 δ[µm] 0.39 0.21 0.19 0.21 K[-] 0.001 0.002 E∗[GPa] 53.3 53.3 µBound [-] 0.02 0.02 Γ [-] 12 4 12 4 proﬁle Ra, the root mean square of the proﬁle Rq as well as the asperity summit roughness (root mean squared) σand the mean summit height δwhich both are relevant for the contact model in the simulation. The combined Young’s modulus E∗and the elastic factor Kare calculated according to section 4.2. A boundary friction coeﬃcient µBound of 0.02 is deﬁned. Γ identiﬁes the orientation of the asperities for each surface by the deﬁnition from Peklenik [44] which is used by Patir and Cheng: Γ =λ0.5x λ0.5y, (10) where λ0.5xandλ0.5yrepresents the autocorrela- tion length in circumferential and axial direction. If Γ is greater than one, as in the present case, the as-perities are align with the circumferential direction. Figure 5: Calculated contact pressure according to equation 6 over oil ﬁlm thickness for both contact pairs Figure 5 shows the asperity contact pressure over the oil ﬁlm thickness. The solid line represents the ”new” contact pair which shows no contact until a lubrication gap below 1.2 µm. The contact pressure strongly increases with a further reduction of oil ﬁlm thickness. The ”worn” contact pair is shown as dash- dotted line. First asperity contact pressure can be identiﬁed around 1 µm. The increase of contact pres- sure is slightly steeper compared to the ”new” contact pair because of the higher elastic factor K. 8 Figure 6: Pressure ﬂow factors according to Patir and Cheng over oil ﬁlm thickness for both contact pairs The pressure ﬂow factors in circumferential (x) and axial (z) direction for the two contact pairs are shown in ﬁgure 6. Both curves show an equal characteris- tics as the asperity orientation of the surfaces does not change but the curve of the ”new” contact pair is slightly shifted to a higher lubrication gap hcom- pared to the ”worn” contact pair. The characteristic curves of the shear ﬂow factor ϕsand the shear stress factors ϕf,ϕfsandϕfpare shown in A. 5 Simulation results and vali- dation This section starts with a comparison between mea- surement and simulation and continues with a de- tailed discussion of the simulation results. The dashed black curve in ﬁgure 7 shows the fric- tion torque obtained from the measurement with a static load of 10 MPa. The grey area represents the uncertainty band of the torque and speed mea- surement. The other black lines represent the calcu- lated friction torque, where the solid line refers to the ”new” contact pair and the dash-dotted line to the ”worn” contact pair. For both contact pairs the cal- culated friction torque at 1000 rpm and 3000 rpm are equal where all three bearings mainly operate Figure 7: Comparison between calculated friction torque and measured friction torque over shaft speed at a load of 10 MPa. in hydrodynamic regime. At 500 rpm and below, a higher friction torque is calculated for the ”new” con- tact pair. However, both calculated friction curves lie within the measurement uncertainty. Regarding the position of minimum friction torque, the ”worn” con- tact pair shows a good match to the measurement. The minimum friction torque occurs at 400 rpm. Figure 8 shows the comparison between measure- ment and simulation similarly to previous the ﬁgure yet for a static load of 5 MPa. The beginning of pure hydrodynamic lubrication is shifted to a lower shaft speed at around 500 rpm. Again, the calcu- lated friction torque is equal for both contact pairs in the hydrodynamic regime and matches the measured torque. As asperity contact occurs below 500 rpm the calculated friction torque diﬀers between the two contact pairs. Obviously, the rougher ”new” contact pair shows a higher friction torque compared to the ”worn” contact pair. While the calculation results with the ”new” contact pair lie within the measure- ment uncertainty for all speeds, the friction torque is slightly underestimated with the ”worn” contact pair at low speed. The calculated friction torque agrees with the mea- sured friction torque for 5 MPa and 10 MPa over a wide range of operation. Hence, it can be concluded, 9 Figure 8: Comparison between calculated friction torque and measured friction torque over shaft speed at a load of 5 MPa. that the presented method is suitable for lubricated journal bearings operating with intense asperity con- tact. Subsequently, the calculated results are further analyzed to discuss the inﬂuence of surface roughness on asperity contact pressure and friction losses. The case with a static load of 10 MPa is therefore exem- pliﬁed. First, the contributions of each bearing to the over- all friction torque are of interest. Figure 9(a) shows the friction shares with the ”new” contact pair ap- plied. Correspondingly, ﬁgure 9(b) shows the results calculated with the ”worn” contact pair. In the pure hydrodynamic lubrication regime, between 1000 rpm and 3000 rpm, the overall friction torque is equally distributed between all three bearings. By reducing the shaft speed, it can be identiﬁed, that asperity contact occurs primarily at the test bearing followed by the two support bearings. The bearing load per projected area is roughly three times higher at test bearing compared to the support bearings. As a re- sult, the increase of friction moment with reducing shaft speed is mainly credited by the test bearing. Hence, the test bearing is mainly responsible for the sharp increase of the overall friction losses at lower speed. By regarding the results of the two contact pairsit can be seen that the roughness inﬂuence is most notable at the higher stressed test bearing. Thus, the test bearing is further analyzed (see ﬁgure 10). Figure 10(a) and ﬁgure 10(b) show the share of hy- drodynamic friction torque and friction torque caused by asperity contact for the ”new” and ”worn” contact pair. The hydrodynamic friction torque decreases monotonically with decreasing shaft speed and is sim- ilar for both cases. Hence, the torque diﬀerence at shaft speeds at 500 rpm and below can be traced back to the friction caused by asperity contact only. The ”new” contact pair shows a notable asperity friction torque at 500 rpm while it almost completely van- ished for the ”worn” contact pair. With a further speed reduction the torque caused by asperity con- tact steeply rises up to 1.25 Nm for the ”new” contact pair at 150 rpm. In comparison the calculated maxi- mum asperity friction torque for the ”worn” contact pair reaches 0.6 Nm. Additionally, the maximum hydrodynamic pres- sure and maximum asperity contact pressure which occurs in the lubrication gap are displayed as grey lines. The solid grey line represents the maximum hydrodynamic pressure. It nearly stays constant over the engine speed except at very low speed when it drops drastically, but ﬁrst asperity contact pressure already occurs at higher shaft speed before the hy- drodynamic pressure decreases. Therefore, the hy- drodynamic pressure drop is not directly dependent to the occurrence of asperity contact. The maxi- mum asperity contact pressure itself raises poten- tially with decreasing shaft speed. The deviation of maximum asperity contact pressure between the ”new” and ”worn” contact pair at the same speed is roughly 5 MPa. This deviation stays constant over the shaft speed. The increase of friction moment in mixed lubrica- tion is also dependent on the size of the area where asperity contact occurs. Figure 10(c) and ﬁgure 10(d) show the formation of asperity contact area for the ”new” and ”worn” contact pairs at three diﬀerent shaft speeds. At 500 rpm (bottom ﬁgure) the asper- ity contact concentrates on the bearing edges only. This edge loading is caused by the elastic bending of the shaft for the presented case. However, a smaller size of contact area can be identiﬁed for the ”worn” 10 contact pair. The results of the ”new” contact pair at 250 rpm shows a contact area which spreads all along the bearing width. At the same speed, the contact area calculated with the ”worn” contact model is still concentrated on the edges. At 150 rpm both con- tact pairs show asperity contact all along the bearing width. Regarding to the above discussed maximum hydro- dynamic pressure, the beginning of the pressure drop correlates to the speed where asperity contact pres- sure spreads over the whole bearing width for the ﬁrst time. This is the case for both contact pairs. The maximum asperity contact pressure remains at the bearing edge regardless of the shaft speed. It can also be identiﬁed that the circumferential position of the maximum asperity pressure moves towards the top position of the bearing with lower shaft speed. This behavior is best visible in ﬁgure 11 which shows the minimum radial distance between shaft and bear- ing shell and its corresponding circumferential posi- tion. At a shaft speed of 3000 rpm the minimum radial displacement between shaft and bearing shell is 2 µm. The minimum distance occurs at 30◦from the top po- sition in other words, the shaft is shifted in circum- ferential direction with reference to the bearing shell. The minimum radial distance decreases with a drop in shaft speed. With ﬁgure 5 in mind asperity con- tact begins at around 1.2 µm for the ”new” contact pair and 1.0 µm for the ”worn” contact pair, respec- tively. The minimum radial distance as well as its circumferential position is exactly the same, as long as the bearing operates in hydrodynamic lubrication regime. Below 1 µm the radial distance distinguishes for the two contact pairs but the circumferential posi- tion remains similar. At 150 rpm the minimum radial distance, calculated with the ”new” contact pair, is 0.7µm. Using The ”worn” contact pair results to a minimum radial distance of 0.6 µm. At 150 rpm the shaft has moved towards the top position of the bearing and stays at 10◦.6 Discussion The simulation results match the measured Stribeck curve for the presented load cases. Especially at a speciﬁc load of 10 MPa, the results calculated with both contact pairs lie within the measurement un- certainty. Although, the calculated results with the ”worn” contact pair show a clearly reduced friction torque in the mixed lubrication regime compared to the ”new” contact pair. The detailed bearing results from previous section additionally estimate a reduced contact pressure, reduced size of contact area and a reduced minimum distance between shaft and bear- ing shell. Also the transition between hydrodynamic and mixed lubrication regime moves to a lower speed. Regarding the transition speed, the ”worn” contact pair appears to be more suitable at a speciﬁc load of 10 MPa. At 5 MPa the results with the ”new” contact pair match the transition speed. It can be expected that an adaption of the surface roughness occur in the beginning of bearing operation. In the presented measurement procedure a speed up was performed before the Stribeck curve was determined. During the speed up metal-metal contact already occurs and a smoothing of the surface takes place. At higher speciﬁc load obviously higher metal-metal contact pressure develops and a quicker adaption of surface roughness can be expected. The quicker adaption at 10 MPa load eventually explains the good match of measurement and simulation with the ”worn” surface roughness. Nevertheless, the calculated friction beneﬁt in mixed lubrication regime only considers the adap- tion of surface roughness due to running in. Beside the change of surface roughness, an adaption of the surface geometry occurs and eﬀects the load carrying capacity of the ﬂuid ﬁlm. Additionally, a decrease in boundary friction coeﬃcient with the running in progress can be expected which will further increase the friction beneﬁt [45]. 6.1 Boundary friction coeﬃcient A constant boundary friction coeﬃcient µBound is chosen for this model, although more complex mod- els with a variable boundary friction coeﬃcient ex- 11 ist [39]. The simpliﬁcation bears the advantage that only a single variable has to be deﬁned for a spe- ciﬁc combination of bearing/shaft material and lu- bricant. The comparison between measurement and simulation show that the constant friction coeﬃcient is suitable to predict friction in mixed lubrication regime where metal-metal contact is dominant in the high loaded region of the bearing. The results show a maximum asperity contact pressure of up to 20 MPa. Disadvantage of a single friction coeﬃcient is the re- striction to the mixed lubrication regime. In bound- ary lubrication regime, for instance the shaft starts to rotate, the friction torque is underestimated. A change of µBound does neither aﬀect the friction losses in hydrodynamic regime nor impact the magni- tude of asperity contact pressure. In fact it ampliﬁes or reduces the friction torque caused by asperity con- tact (see equation 5). The transition speed between hydrodynamic and mixed lubrication stays exactly the same. Nevertheless, friction in mixed lubrication is strongly dependent on ﬁlm forming additives (fric- tion modiﬁer) added to the lubricant. The focus in the present work does not lie on the speciﬁcation of lubricant additives but their inﬂuence should be mentioned as further research in this ﬁeld is of inter- est. Spikes [46] identiﬁed three separate mechanisms in which lubricant additives can inﬂuence friction in mixed lubrication: (a) formation of a layer to reduce boundary friction at asperity contacts (b) formation of a thin ﬁlm of high viscosity on the surface and (c) a change (reduction or increase) of eﬀective surface roughness. Hence, for the friction prediction with dif- ferent formulated engine oil an exclusively change of µBound will may not provide satisfying result. Film forming additives in journal bearing application also enable a shift of the transition between hydrodynamic and mixed lubrication. 6.2 Inﬂuence of ﬂow factors on fric- tion torque The presented results in previous section are calcu- lated using the averaged Reynolds equation which considers the ﬂow factors according to Patir and Cheng (see equation 2). The inﬂuence of neglect-ing the ﬂow factors on the calculated friction torque is shown in ﬁgure 12. The grey lines correspond to the calculated fric- tion torque without considering the ﬂow factors. The black lines include the ﬂow factors in the calcula- tion. The friction torque in pure hydrodynamic lu- brication regime, above 1000 rpm, is not aﬀected by the ﬂow factors. By lowering the shaft speed and hence reducing the lubrication gap two changes when neglecting the ﬂow factors can be identiﬁed. First the calculated friction torque in mixed lubrica- tion regime increases notable without taking the ﬂow factors into account. Second the transition between hydrodynamic and mixed lubrication moves slightly to a higher speed. However, the simulation results with the ”worn” contact pair and without ﬂow fac- tors match the measurement over the observed speed range. The ”new” contact pair overestimates the fric- tion torque at low shaft speed. 7 Conclusion This paper discusses journal bearing friction in mixed lubrication regime. For discussion purposes, mea- surements on a journal bearing test rig at KS Gleit- lager were performed with two diﬀerent static loads acting on the bearings. The measurement results provide a sound basis to validate the presented sim- ulation approach. A detailed viscosity speciﬁcation of the lubricant, dependent on temperature, pressure and shear rate, is included in the simulation model. The oil model has previously been validated for dy- namic loads and a wide range of operation condi- tions [25]. The surface texture of the journal bearings have a major inﬂuence on friction in mixed lubrica- tion regime. Hence, the surface of the state-of-the- art journal bearings are scanned and furthermore the ﬂow factors, introduced by Patir and Cheng and pa- rameters for the Greenwood and Tripp contact model are established. The comparison of the friction torque between measurement and simulation show a good agreement in the hydrodynamic and mixed lubrication regime. Hence, the presented input data are suitable for the friction prediction in journal bearings operation un- 12 der severe conditions. The chosen constant boundary friction coeﬃcient of µBound = 0.02 is appropriate for the presented combination of lubricant and bear- ing/shaft material. Both lubricant and material are current state of the art components used in modern combustion engines. Furthermore, the simulation results are analyzed to discuss the inﬂuence of surface roughness on as- perity contact and friction moment. A run-in surface roughness shows a lower maximum contact pressure and a reduced area of asperity contact compared to the roughness of a new bearing shell. A lower tran- sition speed between hydrodynamic and mixed lubri- cation is identiﬁed. The run-in surface also predicts a smaller minimum distance between shaft and bearing shell. 8 Acknowledgment We would like to express our gratitude to our sup- porting industrial and scientiﬁc project partners, namely KS Gleitlager, AVL and the Institute of Tri- bology of the TU Clausthal. The authors would like to acknowledge the ﬁnan- cial support of the ”COMET - Competence Cen- ters for Excellent Technologies Programme” of the Austrian Federal Ministry for Transport, Innovation and Technology (bmvit), the Austrian Federal Min- istry of Science, Research and Economy (bmwfw), the Austrian Research Promotion Agency (FFG), the Province of Styria and the Styrian Business Promo- tion Agency (SFG). Furthermore, we acknowledge the partial ﬁnan- cial support of the Austrian Science Fund (FWF): P27806-N30. 9