1 Introduction Wind energy production is a cornerstone in the transition from fossil energy to renewable energy. With a share of over 30 % in the year 2023 wind energy has already become the most important renewable energy source in Germany [1]. To further increase the energy production from wind and maintain its competitiveness wind turbines are designed with increased rotor diameters and thus higher power ratings [2]. Larger rotor diameters lead to an increase in weight of the rotor and to increased torque as well as non-torque loads that the drivetrain has to bear. Thus, the main bearing, the gearbox and the adjacent structure need to increase in size to carry the loads. The gearbox is one of the major contributors to the weight of a wind turbine drivetrain. The ring gear of the first planetary stage massively contributes to the gearbox weight and size. Thus, the size of the planetary stage needs to be decreased to increase the power density of the drivetrain. The use of journal bearings as planetary bearings instead of conventional rolling bearings is a recent driver of a decrease in weight of wind turbine gearboxes [3]. Journal bearings have a smaller installation space compared to rolling bearings since there are no rollers. In addition, journal bearings have an infinite lifetime and are remarkably reliable when designed and operated correctly. Special load cases, e.g. strong deformation due to overload, can eventually lead to mixed friction and thus abrasive wear in the journal bearings resulting in a change in contour and roughness of the sliding surface. For a re- Science and Research 29 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 Model uncertainty of a multiscale, elasto-hydrodynamic simulation method for the prediction of abrasive wear in journal bearings Thomas Decker, Georg Jacobs, Carsten Graeske, Pascal Bußkamp, Julian Röder, Tim Schröder* submitted: 20.09.2024 accepted: 11.01.2025 (peer review) Presented at GfT Conference 2024 Journal bearings have a potentially unlimited service life. In combination with the increased power density compared to rolling bearings journal bearings are attractive for the use in wind energy gearboxes. The reliability of journal bearings is significantly influenced by their wear behavior. Journal bearings are typically designed using elasto-hydrodynamic (EHD) simulations. The abrasive wear behavior of a journal bearing can be calculated with a wear algorithm which is coupled to the EHD-simulation. This approach is commonly used to simulate the abrasive material removal and smoothing of the surface roughness. State of the art wear calculation methods contain a large number of parameters and are prone to calculation errors due to parameter uncertainty. Therefore, the aim of this work is a quantified maximum model error (deviation of simulation results due to uncertainties in the parameterization) of a simulation tool for the calculation of abrasive wear in hydrodynamic journal bearings based on the wear model according to Fleischer. First, the influence of individual input parameters on the elasto-hydrodynamic simulation and the accumulated wear volume and wear depth is analyzed by means of a sensitivity analysis. The parameters with a relevant influence are identified and discussed on the basis of the sensitivity analysis. From the experimental work on a journal bearing test rig measurement uncertainties in terms of wear volume are derived and their influence on the wear coefficient and the overall model error are examined. The overall accuracy of the wear simulation model is then evaluated with regard to the selected input parameters in terms of a worst-case scenario analysis. Keywords Wear simulation, Journal bearings, Abrasion, EHDsimulation, Sensitivity analysis Abstract * Thomas Decker, M.Sc. Prof. Dr.-Ing. Georg Jacobs Carsten Graeske, M.Sc. Pascal Bußkamp, M.Sc. Julian Röder, M.Sc. Chair for Wind Power Drives (RWTH Aachen University), Campus-Boulevard 61, 52074 Aachen Dr.-Ing. Tim Schröder Vestas Nacelles Deutschland GmbH, Martin-Schmeißer-Weg 18, 44227 Dortmund 3 Method This work addresses the wear simulation method presented in [9] with the aim to quantify the maximum calculation uncertainty by means of a worst-case scenario analysis. The study is carried out using an EHD model of a journal bearing component test rig. The test specimens are specified in section 4.3 and more details about the test rig can be found in [9,11]. The calculation uncertainty is defined as the difference between a maximum and a minimum wear calculation result depending on two different sets of input parameters: one for a minimum and one for a maximum wear rate. Both extreme parameter sets consist of the most influential parameters at their lower and upper boundaries of a determined range based on literature. The most influential parameters in terms of wear behavior are identified using a sensitivity analysis. The sensitivity analysis is performed according to M ORRIS [12] . The wear simulation method was checked for plausibility in [9] by comparing it with experimentally determined wear depth values after tests on the journal bearing test rig. The applied wear simulation method can be divided into three parts (see also Figure 1). First, the EHD simulation model (1) calculates the asperity contact pressure p a,i,j for each node (i,j) considering the contact model according to G REENWOOD AND T RIPP [13] and taking additionally micro-hydrodynamic phenomena according to P ATIR AND C HENG [14] into account. The EHD model also considers general properties of the tribological contact (e.g. clearance S, lubricant viscosity) and operating conditions (specific pressure p̅ and sliding speed v S ). Secondly, based on the calculated asperity contact pressure distribution p a,i,j the wear model (2) calculates the wear depth per node h W,i,j according to Fleischer [10] considering a local coefficient of friction μ a,i,j according to O FFNER AND K NAUS [15]. Thirdly, the surface roughness model (3) calculates the surface smoothing according to D ECKER AND K ÖNIG [9,8]. Additionally, adjustments of the bearing surface profile lead to changes in the roughness. The updated roughness parameter R and the wear depth per node h W,i,j are used as input for the next iteration step until the simulation end time is reached. Figure 1 summarizes the wear simulation method as a flow chart, illustrates the models used in each section of the method and lists the parameters analysed within the sensitivity analysis. Table 1 gives an overview of the analyzed model parameters and the defined ranges based on literature, supplemented by measurements. For the roughness orientation Γ and elastic factor K recommended values from literature are used [17,16,7,19]. The deviation of the surface roughness R was determined by means of tactile surface measurements of the specimen before the experiment. This measurement study showed a variation in surface roughness of ± 10 % (see section 4.2). The deviation in the bearing temperature T stems from different friction intensities during the running-in process, which results in a decay of the temperature towards a steady state. More details about the ther- Science and Research 30 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 liable design of journal bearings simulations can be applied to assess the abrasive wear behaviour early in the design process without the need for expensive prototype testing. The major downside of state-of-the-art wear simulations is the high number of input parameters which makes the results prone to measurement and parameterization imprecisions. This work addresses the uncertainty of a given wear simulation method and suggests an approach to quantify the maximum calculation error. The first step is to identify the most influential parameters by means of a sensitivity analysis. The most important parameter is then determined metrologically using wear experiments on a journal bearing test rig and parameter inaccuracies due to measurement errors are also identified. The final result of this work is a worst-case quantification for the uncertainty in the wear simulation results. 2 State of the art for the simulation of abrasive wear Wear simulations have been subject to numerous research efforts in the past. P RÖLß [4] simulated the abrasive running-in wear behaviour of journal bearings in planetary gearboxes to analyse changes in contour and roughness. H AGEMANN ET. AL. [5] developed a wear calculation method for journal bearings of planetary gears considering elastic deformations and abrasive wear and D ING ET. AL. [6] presented a validation of their journal bearing simulation tool. K ÖNIG ET. AL. [7] demonstrated that abrasive wear on hydrodynamic journal bearings can be calculated reliably for constant and transient operating conditions (e.g. start-stop). Validation of this approach was achieved from experiments on a component test rig [8]. D ECKER ET. AL. [9] presented a multi-scale wear simulation method suitable for the simulation of abrasive wear in wind turbine journal bearings as an adaption of the work by K ÖNIG . The method consists of an iterative loop between an elasto-hydrodynamic (EHD) model of a journal bearing and a software tool simulating abrasive wear in terms of material removal and smoothing of the surface roughness. F LEISCHER’S wear law [10] is used for in this approach and supplemented by the smoothing of surface roughness. A validation of the method on a component test rig showed a good agreement between measurement and simulation [9]. Transferability of the wear simulation tool to different EHD models (e.g. planetary journal bearings in wind turbine application) was also demonstrated. L EHMANN ET AL. [11] evaluated different wear models for the wear calculation on journal bearings. All the aforementioned wear calculation approaches have in common that they have a high number of input parameters. This results in a high parameterization effort and the risk of calculation errors due to inaccuracies in the parameterization. There is a lack of studies investigating these inaccuracies. mo-hydrodynamic behavior of journal bearings can be found in [18]. Since the presented wear calculation method in this work assumes isothermal behavior of the bearing over time a constant bearing temperature is assumed. The sensitivity analysis examines the maximum and minimum measured temperature value during the experiments. Analogous, the bearing clearance S is kept constant and is assumed to have a range of uncertainty of ± 10 μm due to thermal expansion effects and deviations in the manufacturing process. The coefficient of friction is examined in a range typical for journal bearings [7]. The friction energy density e R of F LEISCHER’S wear law is examined in a range according to comparable experimental studies [17,16,19]. The parameter range for b, c and L S of the O FFNER AND K NAUS model is based on literature values [17,16]. The sensitivity analysis in this work is based on a factorial sampling plan according to M ORRIS [12] to rank the influence of the analyzed parameters on the outputs of the wear simulation method. Compared to other sensitivity analysis methods, M OR- RIS’ approach requires a comparably low number of simulations to analyze a high number (n = 10) of parameters [20]. The interpretation of the results is based on the mean μ *EE and the standard deviation σ EE of the so-called elementary effects (EE) of the parameters on the model output [12]. The quality of the results depends on the number of repetitions r which are required to calculate μ *EE and σ EE . S ALTELLI ET AL . [20] recommend r min = 4 as lower boundary to achieve sufficient results. M ORRIS ’ sampling method is based on one-factor-at-a-time randomization and restricted to analysis of elementary effects. Further details about designing the sampling matrices are given in [12]. Typically, the influence of the parameters on an output are interpreted graphically by plotting the standard deviation of the elementary effects σ EE over the mean elementary effects μ *EE . High mean values indicate a high influence of the corresponding parameter. Thus, analyzing the mean elementary effects enables a ranking of the parameter influence. High standard deviation values indicate a nonlinear effect [12]. 4 Results First, in section 4.1 the results of the sensitivity analysis are presented. The most influential parameters according to the resulting ranking are varied to calculate the worst- Science and Research 31 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 MBS/ EHD Simulation 1 Extended Reynolds equation to consider microhydrodynamics according to [Patir&Cheng] = Roughness orientation Contact model according to [Greenwood&Tripp] = . , K Elastic factor Roughness parameter General simulation parameter T Temperature Bearing clearance Coefficient of friction Wear model Wear model according to [Fleischer] 2 e R Friction energy density Local coefficient of friction according to [Offner&Knaus] , , = + , , , + , , , , , , with , , = , , b Model coefficient Model coefficient Reference length Surface model Surface smoothing per patch according to [König] 3 Asperity contact pressure , , Asperity contact ratio , , Wear depth , , Roughness Figure 1: Flow chart of the wear simulation method according to [9] Parameter Unit Lower boundary Upper boundary Reference Roughness orientation - 1 100 [17,16] Elastic factor - 0.0003 0.003 [17,7] Roughness parameter 10 % + 10 % measurements Temperature ° 55 70 measurements bearing clearance 0.14 0.16 measurements Coefficient of friction - 0.05 0.2 [17,7] Friction energy density 1 10 13 1 10 16 [17,16,19] Model coefficient (O&K) - 1,000 10,000 [17,16] Model coefficient (O&K) - 50 1,000 [17,16] Reference length 1 10 -6 2 10 -6 [17,16] Table 1: Parameter range for sensitivity analysis the typical representation of σ EE over μ *EE for each objective. The high μ *EE values of the friction energy density e R indicate the highest sensitivity of wear depth h W , wear volume V W , hydrodynamic pressure p h,e and asperity contact pressure p a,e at simulation end to the friction energy density e R . However, the friction energy density e R shows less significant influence on the hydrodynamic pressure p h,s and asperity contact pressure p a,s at the beginning of the simulation. The graphical determination of the parameters with the second and third largest influence on the wear behavior is not possible without further ado. To perform a rank-based evaluation, the parameters are ranked based on their μ *EE values for each objective. Subsequently, the mean rank regarding the objectives h W , V W , p h,e , p a,e is determined to evaluate the influence of the parameters on the wear and the pressure distributions at simulation end (Table 2). According to the determined mean ranks of the grouped objectives, the elastic factor K from the contact model by G REEN- WOOD AND T RIPP [13] is one of the two most influential parameters. The other second most influential parameter b and the following highest ranked parameters c and L S are coefficients of the local friction model according to O FFNER AND K NAUS [15]. The results show a significant influence of the parametrization of the contact model and the local friction model compared to the remaining parameters. Science and Research 32 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 case uncertainty of the wear simulation method. The friction energy density e R is the most significant parameter regarding wear. Due to high deviations (three orders of magnitude) of e R in the literature the parameter range is determined based on in-house experiments to increase the accuracy of the worst-case uncertainty calculation. The determination of e R is based on the measured wear in the experiments. Hence, in section 4.2 the wear volume measurement method and the determination of its uncertainty is presented. Section 4.3 explains the determination of e R for different test procedures. 4.1 Sensitivity analysis The Sampling for the sensitivity analysis is based on r = 5 repetitions to vary the parameters given in Table 1 on p = 4 levels. Thus, N = (n + 1) · r = 55 wear simulations are performed to analyze the sensitivity of the aforementioned parameters according to M ORRIS . The influence of the variation of the ten parameters on six objectives is evaluated. The considered objectives are the wear depth h W , wear volume V W , hydrodynamic pressure p h,s at simulation start, hydrodynamic pressure p h,e at simulation end, asperity contact pressure p a,s at simulation start and asperity contact pressure p a,e at simulation end. For each objective, the normalized mean μ *EE and the standard deviation σ EE of the elementary effects of the ten parameters on the model output is calculated. Figure 2 illustrates the results of the sensitivity analysis with Figure 2: Graphical results of the sensitivity analysis according to Morris for selected objectives Overall rank 1 2 2 4 5 6 6 8 9 10 Mean rank ( , , , , , ) 1.0 3.3 3.3 3.8 5.3 6.0 6.0 8.0 8.5 10.0 Parameter Table 2: Mean ranks of the parameters regarding wear and pressure distribution at simulation end As the friction energy density e R has the highest influence on the resulting wear volume V W and the wear depth h W , it is important to determine e R precisely. Since the values for the friction energy density e R are not known a priori, experimental investigations provide a good starting point for determining the relevant range of e R values for the operating points to be simulated. After the experimental determination of the parameter range for the conditions on the test bench, the influence of the uncertainty of the friction energy density e R on the wear behavior can be investigated. 4.2 Wear volume measurement uncertainty This work addresses the calculation uncertainty of the wear simulation method presented in [9]. However, the experimental measurement of the wear volume V W shows uncertainties too. The measured wear volume V W is used to determine the range of the friction energy density e R for the worst-case scenario analysis of the test rig wear simulations. Thus, the wear volume measurement uncertainty influences the determination of e R . The determination of the wear volume measurement uncertainty allows the precise identification of the possible range of e R . The wear volume V W is determined by a comparison of the contour before and after the experiment. The contour is determined using a tactile measurement in axial direction at seven angular measurement points ϕ i t [90°; 135°; 160°; 180°; 200°; 225°; 270°] of the journal bearing. Due to their availability and the low technical complexity tactile measurements are preferred in this work over other measurement approaches (e.g. optical 3d-contour measurements as suggested in [16]). In addition, in this work the friction energy density e R is determined directly on the basis of test bench tests, whereas in comparable work it was determined on tribometers [16]. The seven measurement positions ϕ i are depicted in Figure 3 (a) and the used measurement system is shown in Figure 3 (b). The measurement length in axial direction is l m = 29.7 mm. The contour at each angular position ϕ i is measured discretely and the distance between the measurement points is Δl = 0.5 μm. Thus, 59.400 measurement points are evaluated in axial direction. In general, the wear depth h W over the bearing width W is calculated by evaluating the difference between the contours before and after the experiment. At the angular measurement point ϕ i the wear depth h W (w j , ϕ i ) is determined for each axial measurement point w j with j t [0; 1; …; 59,400]. In Figure 3 (a) the wear depth at the front side of a journal bearing h W (w j = 0 mm, ϕ = 135°) is depicted. The planimetric wear (1) at the measurement point ϕ i can be approximated by summing up the products of the wear depth values h W (w j , ϕ i ) and the discrete axial measurement distance over the bearing width W. To approximate the wear volume (2) at the measurement point ϕ i the wear area A W (ϕ i ) is multiplied with the corresponding arc length Δϕ (ϕ i ). The arc length Δϕ (ϕ i ) starts at the middle angular position between the measurement point ϕ i and the previous measurement point ϕ i-1 . The arc length Δϕ (ϕ i ) ends at the middle angular position between ϕ i and the following measurement point ϕ i+1 . The arc length Δϕ (180°) is shown in Figure 3 (a). The total wear volume (3) is defined as the sum of the wear volume V W (ϕ i ) at each measurement point ϕ i . The calculation of the wear area A W is illustrated in Figure 4 (a) for the measurement ( ) = , , ( ) = ( ) ( ) = ( ) Science and Research 33 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 (a) (b) 1 measurement prism 2 journal bearing 3 probe arm 4 mearement system 1 2 3 4 90° 200° 270° 225° 180° 160° 135° arc length (180°) bearing width W ( = 0 , = 135°) axial measurement direction Figure 3: Specification of the journal bearing test specimen (a) and the measurement system (b) e R for different operating conditions two operating points (A and B) are defined. The specific pressure p̅ ̅ , sliding speed v s and target temperature T t of both operating points are listed in Table 3. Two test specimen combinations are tested for both operating points each. The two test specimen combinations are defined as i and ii. Thus, in total four test runs (A.i, A.ii, B.i, B.ii) are performed on the test rig. The measurement parameters and the results are summarized in Table 3. The total wear volume V W and the mean wear depth h W ¯¯ over the bearing width at the lowest angular position (ϕ = 180°) of the bearing are evaluated. Each test run takes 20 h and is divided into two sections with 10 h each. Wear volume V W and mean wear depth h W ¯¯ are measured after 10 h and after 20 h of testing. The results are plausible, as the test runs A with higher pressure compared to B lead to more wear. Additionally, less wear is measured in the second part of each test run compared to the first one due to running-in processes [9]. The test results can also be used to determine the friction energy density e R experimentally. F LEISCHER [10] defines (4) as the quotient of friction work W F and wear volume V W . The friction work = Science and Research 34 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 point ϕ i = 180° of an exemplary bearing. Figure 4 (b) visualizes the approximation of the wear volume V W (ϕ i ) based on the arc length Δϕ (ϕ i ) at ϕ i = 180°. In order to determine the wear volume measurement uncertainty, the measurement is performed three times for the same test specimen under the same conditions. The mean measurement error range of the wear volume yields ΔV W,error = 0.61 mm 3 . Therefore, the uncertainty of the wear volume measurement is quantified with ΔV W =± 0.3 mm 3 . Possible reasons for measurement errors may be imprecisions in adjusting the angular position (Δϕ = ± 1°) or the starting point of the axial contour measurement (Δl start = ± 0.1 mm). The same procedure for a tactile roughness measuring device leads to the uncertainty of the roughness measurement of ΔR = ± 10 %, which was also applied for the sensitivity analysis (Table 1). 4.3 Calculation of the friction energy density based on experimental results The test series is performed on the same component test rig that was used and described in [9,11]. The tested journal bearings are made from a copper-tin alloy CuSn12Ni2-C (produced in a continuous casting process), the nominal bearing diameter is D = 120 mm and the nominal bearing width is W = 30 mm. To determine contour [ μm] [mm] W (180°) time t=0h time t=10h wear depth W (a) W (180°) W (180°) arc length (180°) (b) Figure 4: Determination of the wear area (a) and approximation of the wear volume (b) Operating point A B Specific pressure [ ] 35 25 Sliding speed [ / ] 0.1 0.1 Target temperature [° ] 55 55 Test specimen i ii i Ii Bearing diameter [ ] 120.02 120.03 119.98 119.99 Shaft diameter [ ] 119.89 119.92 119.91 119.86 Bearing clearance [ ] 0.130 0.110 0.070 0.135 Surface roughness [ ] 0.34 2.28 2.75 2.72 Surface roughness [ ] 0.56 0.48 0.61 0.60 Measurement results A.i A.ii B.i B.ii = 10 [ ] 4.82 4.78 0.72 0.45 = 20 [ ] 0.14 0.73 0.21 0.17 = 10 [ ] 14.0 14.0 2.1 1.3 = 20 [ ] 0.9 1.4 0.8 0.7 Table 3: Test parameter for the experiments (5) is calculated based on normal force F N , sliding speed v S and time integration of the coefficient of friction μ(t). Normal force F N and sliding speed v S are known from the defined operating conditions for the wear experiments on the test rig. The coefficient of friction over time μ(t) can be calculated using C OULOMB ’s law of friction. The normal force F N is known and the friction force F F (t) can be determined by dividing the measured friction moment M F by the known bearing radius. The wear volume V W is measured according to section 4.2. However, the measurement of wear volume V W shows an uncertainty of ΔV W = ± 0.3 mm 3 (see section 4.2). The uncertainty of the wear volume measurements leads to an uncertainty in the calculation of e R . The experimentally quantified values of the friction energy density e R are shown in Figure 5 (a) for each test run. The uncertainty in the calculation of the friction energy density Δe R due to the wear volume measurement uncertainty is represented by error antennas. Considering the uncertainty of the friction energy Δe R density due to measurement uncertainties of the wear volume, a range from 1.2 · 10 15 J · m -3 to 3.1 · 10 16 J · m -3 can be measured for both operating points A and B. Alternatively, the range can be determined using the F LEISCHER diagram by evaluating e R depending on the friction shear stress τ R and the linear wear intensity I h [10]. The asperity friction shear stress (6) can be calculated by multiplying the applied asperity contact pressure p a by the coefficient of friction μ. The linear wear intensity (7) = ( ) = = is defined as quotient of the wear depth h W and the sliding distance s R . The sliding distance is known for a given sliding speed v s considering the test time t. The wear depth h W can be measured. The mean wear depth h W ¯¯ at the angular measurement point ϕ = 180° is used for the calculation. The resulting e R values for each test run according to the F LEISCHER diagram are depicted in Figure 5 (b). The maximum uncertainty Δe r in the F LEISCHER diagram ranges from 1.0 · 10 15 J · m -3 to 3.5 · 10 16 J · m -3 . The dimension of the range is comparable to the determination method based on the measurement uncertainties of the wear volume. The neglect of the local distribution of wear by analyzing the mean wear depth at a single angular measurement point instead of the total wear volume may be a cause of the slightly greater scatter. The relative distribution of the e r values between the individual test runs is qualitatively equal. As both methods of calculating the friction energy density e R are comparable, in terms of a worst-case scenario the larger range is used to determine the uncertainty of the wear simulation method. Thus, the friction energy range shown in Table 1 is updated to the new range of e R,min = 1.0 · 10 15 J · m -3 and e R,max = 3.5 · 10 16 J · m -3 . 4.4 Wear calculation uncertainty Due to uncertainties in the determination of model parameters the calculation of the wear volume using the presented wear simulation method is subject to uncertainties. This section presents the resulting uncertainty of the wear simulation method itself. The wear calculation uncertainty is quantified based on the maximum calculation error in terms of the wear volume and depth. To simulate maximum wear, the five most influential parameters according to the sensitivity analysis in section 4.1 Science and Research 35 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 Figure 5: resulting uncertainty in the calculation of the friction energy density Δe R due to the wear volume measurement uncertainty (a) and range of e R based on the Fleischer diagram (b) (a) (b) Taking Figure 6 into account, the maximum relative wear volume uncertainty for the considered operating points is quantified with ΔV W,rel < ± 49 %. The maximum relative wear depth uncertainty is Δh W,rel < ± 48 %. This very high uncertainty can be attributed to the high parameterization inaccuracy in the wear parameter. In reality it can be expected that the actual calculation error will be smaller, as this is a worst-case scenario. 5 Summary Unlike rolling-element bearings, journal bearings have a theoretically unlimited fatigue lifetime and are therefore particularly reliable when designed and operated correctly. However, external load conditions can lead to wear that might lead to seizure of the bearing. Thus, wear simulations are used to optimize the journal bearing design. Currently, wear simulations are used to predict the wear behavior. In order to determine the accuracy of the used method, the worst-case scenario calculation was performed in this work. First, the most significant parameters of the wear model were identified by applying a sensitivity analysis according to M ORRIS [12]. The highest influence was shown for the friction energy density e R . Thus, a precise determination of e R is required. However, the value is unknown a priori and dependent on the operating point. In addition, the parameter range from lite- Science and Research 36 Tribologie + Schmierungstechnik · volume 71 · issue 5-6/ 2024 DOI 10.24053/ TuS-2024-0036 are configurated to generate maximum wear. The configuration is based on the lower and upper parameter boundaries of the sensitivity analysis. In contrast to the one-factor-at-a-time approach, all parameters take the extreme value here. The remaining parameters are kept constant in the medium value range. Since the sensitivity analysis showed the greatest influence of e R on the wear volume, the minimum and maximum values from the experimental determination (section 4.3) are used instead of the boundary values from the literature to increase the accuracy. The parameter values for maximum and minimum wear simulations are summarized in Table 4. Each operating point with p̅ t [10 MPa; 15 MPa] and v s t [0.1 m · s -1 ; 0.2 m · s -1 ] is simulated for minimum and maximum wear for a duration of 10 h. The absolute uncertainty is defined as the difference between the minimum and maximum wear metric at the simulation end. Minimum wear volume V W,min , maximum wear volume V W,max and the absolute uncertainty of the wear volume ΔV W,abs for each operating point are shown in Figure 6 (a). Analogous, Figure 6 (b) visualizes the wear depth values h W and the uncertainties of the wear depth Δh W,abs . The absolute wear uncertainties increase for operating points with higher wear intensity. Thus, the absolute uncertainties of both wear metrics depend on the operating point. Both metrics show a comparable relative uncertainty, regardless of the operating point. Parameter (variated) Unit Max. wear Min. wear Parameter (constant) Unit Med. wear Elastic factor - 0.003 0.0003 Roughness orientation - 50 Friction energy density 1.0 10 15 3.5 10 16 Roughness parameter ± 0 % Model coefficient (O&K) - 1,000 10,000 Temperature ° 55 Model coefficient (O&K) - 1,000 50 Bearing clearance 0.15 Reference length 2 10 -6 1 10 -6 Coefficient of friction - 0.1 Table 4: Parameter values for maximum and minimum wear Figure 6: Quantified uncertainty of the wear calculation with regard to wear volume (a) and wear depth (b) (a) (b) rature is large. To realistically limit the parameter range, experimental tests were conducted on the component test rig. The minimum e R,min = 1.0 · 10 15 J · m -3 and maximum e R,max = 3.5 · 10 16 J · m -3 were determined for the considered operating points. The resulting absolute wear uncertainties ΔV W,abs and Δh W,abs are dependent on the operating point and increase for higher wear intensity. The relative wear uncertainties ΔV W,rel and Δh W,rel are similar and show a limit of < 49 % for the worst-case scenario. A more realistic uncertainty due to the imprecise determination of the model parameters may be significantly lower than this value. Also validation experiments of the presented method show, that valid wear simulation results can be achieved through precise parameter adjustments, when the real system behavior is well known [9]. The uncertainty identified in this work poses a challenge for the wear calculation, especially if no experimental confirmation tests can be carried out. 6 Outlook In this work it was demonstrated that the high measurement uncertainty in the determination of the wear volume V W jeopardizes the parameterization of the wear coefficient e R . To improve on the parameterization the determination of the wear volume should be further investigated in future work. In addition, for the two different phases of the wear experiments (test runs 1 and 2) and the two tested operating points different values for the wear coefficient e R were determined. To improve the parameterization of the wear model a time dependent wear coefficient could be introduced using the approach by L IJESH [21] as suggested by L EHMANN ET. AL. in [11]. Lastly, the used wear simulation model should be extended to include thermal effects. This has the potential to further increase the model fidelity and reduce deviations to the real-world wear behavior. References [1] Statistisches Bundesamt. 2024, “Stromerzeugung 2023: 56 % aus erneuerbaren Energieträgern,” https: / / www.destatis.de/ DE/ Presse/ Pressemitteilungen/ 20 24/ 03/ PD24_087_43312.html, accessed April 23, 2024 [2] Deutsche WindGuard. 2023, “Status of Onshore Wind Energy Development in Germany: Year 2023” [3] T. Thys and W. Smet. 2023, Selective assembly of planetary gear stages to improve load sharing [4] M. 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