1 Introduction In large gear drives in heavy industry applications, wind turbines or in primary industry, gear stages of case-hardened pinions and through-hardened ring gears or internal gears can be in contact. Due to high gear ratios, a single tooth of the wheel is in gear mesh less frequently and thus, it can be designed from a softer material with a significant lower allowable contact stress compared to the case-hardened pinion. This offers economic advantages, but involves an increased risk of wear during its opera- Aus Wissenschaft und Forschung 24 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 Wear Calculation for Hard-Soft Gear Pairings Depending on Surface Hardness and Roughness Benedikt J. Siewerin, Johannes Schmelz, Karl J. Raddatz, Thomas Tobie, Karsten Stahl* Eingereicht: 22.8.2022 Nach Begutachtung angenommen: 23.2.2023 Dieser Beitrag wurde im Rahmen der 63. Tribologie-Fachtagung 2022 der Gesellschaft für Tribologie (GfT) eingereicht. In großen Zahnradgetrieben befinden sich in vielen Fällen vergütete Hohlräder oder Innenverzahnungen mit einsatzgehärteten Ritzeln im Eingriff. Das bietet wirtschaftliche Vorteile, birgt jedoch ein erhöhtes Risiko von Verschleiß im Betrieb. Es gibt verschiedene Testmethoden, um den zu erwartenden Verschleiß des verwendeten Zahnrad-Schmierstoff-Systems zu bewerten, allerdings werden dafür standardmäßig nur einsatzgehärtete Zahnräder verwendet. Eine direkte Übertragung der Testergebnisse auf die Praxisanwendung ist bisher nicht bekannt. In dieser Studie wurden die Einflüsse von unterschiedlichen Oberflächenhärten und -rauheiten sowie Schmierungszuständen systematisch auf dem FZG- Zahnrad-Verspannungsprüfstand untersucht. Die Ergebnisse zeigen ein erhöhtes Risiko für starken Verschleiß bei hart-weichen Zahnradpaarungen. Basierend auf diesen Ergebnissen wurde die Berechnungsmethode für die Verschleißlebensdauer von Zahnrädern erweitert, sodass eine Abschätzung der Verschleißlebensdauer von Zahnradpaarungen mit unterschiedlicher Oberflächenhärte auf der Grundlage von Standard-Verschleißtests möglich ist. Schlüsselwörter Maschinenelemente und Antriebsstrang, tribologische Systeme, Getriebe, langsamer Verschleiß, Wärmebehandlung In large gear drives, through-hardened ring gears or internal gears are often in contact with case-hardened pinions. This offers economic advantages, but involves an increased risk of wear during its operation. Various test methods exist to evaluate the expected wear of the used gear-lubricant-system, but typically with case-hardened gears only. A direct transfer of the test results to the application in field is not known so far. In this study, influences from different surface hardness and surface roughness values as well as lubricating conditions were systematically investigated on a FZG back-to-back test rig. The results prove a higher risk for strong wear for hard-soft gear pairings. Based on these results, a calculation method for the wear lifetime of gears was extended to allow an estimation of the wear lifetime of gear pairings with different surface hardness based on standard wear tests. Keywords Machine elements and drive train, tribological systems, gears, slow speed wear, heat treatment Kurzfassung Abstract * Dipl. Ing. Benedikt J. Siewerin (federführender Autor) Orcid-ID: https: / / orcid.org/ 0000-0001-9146-0368 Johannes Schmelz, B. Sc. Karl J. Raddatz, M. Sc. Orcid-ID: https: / / orcid.org/ 0000-0002-2007-4221 Dr. Ing. Thomas Tobie Orcid-ID: https: / / orcid.org/ 0000-0002-5565-6280 Prof. Dr. Ing. Karsten Stahl Orcid-ID: https: / / orcid.org/ 0000-0001-7177-5207 Gear Research Center (FZG) Technical University of Munich (TUM), Boltzmannstr. 15, 85748 Garching, Germany tion. For a safe operation of the machine, it is essential to know the wear life time already during the design process. In various test methods, the expected wear of gears in combination with the used gear lubricant can be evaluated. However, all standard test methods are regularly conducted with case-hardened gears only (e. g. [ASTM13, DGMK97]). The wear characteristics of these two types of gear sets are significantly different and inhibit a direct transfer of the tests results to the application in field, so far. Continuous or slow speed wear in the content of gear damages, describes the material that is continuously worn off of a gear during its whole runtime. It typically appears as scratches over the whole tooth flank. At the pitch diameter, where almost no wear occurs, a wear minimum can be observed (Figure 1), because the sliding speed is close to zero. Almost pure rolling prevails in the contact zone. Accordingly, wear shows characteristic profile form deviations at the addenda and dedenda of the tooth flanks [Sie19]. The evaluation of the wear risk for a gear box is not covered by a standardized procedure so far. Different test methods (e. g. [ASTM13, DGMK97]) in combination with calculation approaches enable the gear designer to predict the wear lifetime for a gear in field applications on basis of test results. Thus, the calculation method developed by Plewe [Win85] allows to estimate the amount of wear for a certain gear-lubricant-system under different conditions. The center of the calculation method is the so-called “Plewe diagram” with empirically determined wear curves. It relates the lubricant film thickness (calculated acc. to [Dow66]) with a linear wear coefficient c lT that is calculated from the measured loss in mass of the gear during a test run (see Figure 2a). Different values and characteristics of the wear coefficient are obtained for different material pairings and for lubricating oils and greases. Reference values have been de- Aus Wissenschaft und Forschung 25 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 Figure 1: Typical appearance of wear on a gear flank [Sie19] Figure 2: a Wear diagram acc. to Plewe [Win85] and b wear behavior of a hard-soft gear pairing (+) acc. to Joachim [Joa84] (displayed wear curves are assigned to gear pairings of following heat treatment: For oil lubrication: 1 - case-hardened/ through-hardened, 2 - case-hardened/ case-hardened, 3 - throughhardened/ through-hardened, 4 - gas-nitrided/ gas-nitrided and for grease lubrication: 5 - case-hardened/ case-hardened) a b significantly above a certain lubricant film thickness. If the lubrication regime tends toward mixed friction, the tooth flanks are separated more and more from each other by a lubricant film, which ensures adequate separation of the rolling partners in tooth contact even under more wear critical conditions. For this reason, the scattering range has already been extended for high lubricant film thicknesses and also includes significantly lower wear coefficients (curve 1, Figure 2). The investigations of this course will have a closer look on the behavior of gear stages with a combination of case-hardened (hard) and through-hardened (soft) gears. Based on the results, it aims to describe the wear behavior mathematically and thus, enables a transfer of the wear calculations between the two types of gear sets. 2 Experimental Investigations The experimental investigations have been executed on a FZG back-to-back test rig. “It utilizes a recirculating power loop principle, also known as a four-square configuration, to provide a fixed torque (load) to a pair of precision test gears […]. The slave gearbox and the test gearbox are connected through two torsional shafts [, one of which] […] contains a load coupling used to apply the torque through the use of known weights […] hung on the loading arm. The test gearbox contains heating elements to maintain and control the minimum temperature of the lubricant. A temperature sensor located in the side of the test gearbox is used to control the heating system as required by the test operating conditions” [ISO00]. A standard gear geometry, called “type C-PT” [FVA10] (see Table 1), is chosen as test gears. The main data of the gears are described in Table 1. The pinions are case- Aus Wissenschaft und Forschung 26 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 termined in extensive, experimental investigations with unalloyed mineral oils and fluid greases [Win85]. The linear wear coefficient c lT represents the mean linear amount of wear removed at each revolution of the gear. This makes it possible to compare different gear sizes and tooth geometries in terms of the amount of wear that occurs. Assuming continuous wear over time, the calculation also allows to compare the results of different test run times and speeds. However, the wear characteristics differ depending on the used lubricant as well as the material and heat treatment of the used gear set. Whereas the amount of wear is similar between the pinion and wheel of a gear pairing with similar surface hardness (following curve 2, Figure 2a), a gear pairing with differences in surface hardness ΔHV over 60 HV affects a significant increase of wear on the softer gear (following curve 1, Figure 2a) [Ple80]. Moreover, the amount of wear increases in general. A transfer of the wear coefficients between these two gear stage types is not possible at the moment. Additional investigations of Joachim [Joa84] with a material pairing of case-hardened pinions and throughhardened wheels at higher circumferential speeds and therefore, higher lubricant film thicknesses show, when plotted in the Plewe diagram (Figure 2b) that the wear coefficients are clearly below the expected range following the wear curve 1 for the investigated gear pairing. It can be seen that the through-hardened wheels also show low wear coefficient at lubricant film thicknesses above 0.5 µm. The wear calculation acc. to Plewe [Win85] would overestimate the expected amount of wear. Further investigations by Zornek [Zor14] with case-hardened pinions and softer, induction hardened internal gears confirm the observations of Joachim. Following these results, it can be assumed that the wear coefficients drop Figure 3: FZG back-to-back test rig [ISO00] hardened with a surface hardness of 719 HV1. The influence of the difference in surface hardness on the wear carrying capacity is investigated with four different wheel variants. A case-hardened wheel (HV ch = 770 HV) represents the state of the art from the standardized wear test acc. to DGMK 377-01 [DGMK97] as comparative variant. Moreover, three variants of through hardened wheels are tested. Their surface hardness is HV th1 = 257 HV, HV th2 = 280 HV and HV th3 = 322 HV. Another influence on the wear carrying capacity that is in the focus is the surface roughness of the harder pinion flank. The relevant parameter in gear applications is the arithmetic average roughness Ra that is a specification i. e. in technical drawings. The roughness is varied between a smooth surface of Ra s = 0.20 µm and a rough surface of Ra r = 0.51 µm. A third pinion surface condition of Ra m = 0.31 µm is tested that matches the standard requirements of the type C PT test gears. The surface roughness of all wheel flanks is Ra = 0.31 µm as well. As lubricant, the gear oil FVA 3 acc. to [FVA07] is chosen for all test runs. It is an ISO VG 100 mineral oil of API group I. It does not content any additives. Each test variant is examined in three different speed stages with three different lubricant film thicknesses (see Table 2). It allows to observe the evaluation of the wear coefficients acc. to [Win85] in relation to the lubricant film thickness. Wear is measured as loss in mass during a test run by weighting the test gears before and after a test run with an accuracy of 1 mg. The combinations of test gears (surface hardness and roughness) with the gear oil FVA 3 and the test parameters of Table 2 create the lubricant film thicknesses, listed in Table 3. The values are calculated acc. to [Dow66]. All variants have been conducted with pinions of the corresponding surface roughness and the wheels of surface hardness HV th2 = 280 HV1. For the variant with medium pinion roughness of Ra m = 0.31 µm, all wheel variants (one case-hardened and three through-hardened variants) were examined. Each test run was repeated to validate the result. 3 Test Results All test runs show clearly a significant higher amount of wear on the wheel compared to the pinion, when it is designed softer than the pinion. Moreover, the amount of wear on the harder pinion is minimal and therefore negligible. Contrary, the loss in mass is similar on pinion and wheel, when they are both casehardened. This is known from results of the standardized wear test. However, in all other variants with throughhardened wheels, the wear on the wheel accounts over 97 % of the total measured loss in mass for the gear pairing. Therefore, only the wear coefficients acc. to [Win85] of the through hardened wheels are necessary to consider in the evaluation of the test results. They are the life limiting partners of the hard-soft gear stage. For the comparative variant of a case-hardened gear pairing, pinion and wheel are considered in the wear evaluation. 3.1 Wear behavior of gear pairings with differences in their surface hardness As link to the slow-speed wear test acc. to DGMK 377-01 [DGMK97], the comparative variant contains of a pair of case-hardened test gears (similar surface hardness). The loss in mass is distributed equally between the pinion and the wheel. That wear behavior confirms the state of the art. The evaluated values of the coefficients are minimal higher than the wear coefficients of the plain mineral oil acc. to [Win85]. This can be a result of diffe- Aus Wissenschaft und Forschung 27 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 g ( yp [ ] Gear parameter Symbol Unit Value Shaft center distance a mm 91.5 Module m mm 4.5 Number of teeth z 1 / z 2 - 16/ 24 Face width b mm 14 Helix angle ° 0 Normal pressure angle ° 20 Profile mod. factor x 1 / x 2 - 0.1817/ 0.1715 Tip diameter d a1 / d a2 mm 82.46/ 118.36 Pitch diameter d w1 / d w2 mm 73.20/ 109.80 Table 1: Test gears (type C-PT acc. to [DGMK97]) Test parameter Stage 1 Stage 2 Stage 3 Oil Temperature 60 °C Torque (pinion) 132.5 Nm Nom. contact stress 1013 N/ mm 2 Rotational speed (pinion) 13 1/ min 133 1/ min 531 1/ min Circumferential speed 0.05 m/ s 0.5 m/ s 2.0 m/ s Test duration 20 h Number of load cycles (pinion) 15 600 159 600 637 200 Table 2: Test parameters ( g Speed stage Roughness Ra Lubricant film thickness h min* Relative film pinion wheel 1 0.20 μm 0.31 μm 0.0105 μm 0.0404 0.31 μm 0.0105 μm 0.0333 0.51 μm 0.0105 μm 0.0256 2 0.20 μm 0.31 μm 0.0493 μm 0.1860 0.31 μm 0.0492 μm 0.1587 0.51 μm 0.0489 μm 0.1207 3 0.20 μm 0.31 μm 0.1184 μm 0.4468 0.31 μm 0.1174 μm 0.3504 0.51 μm 0.1162 μm 0.2611 * calculated acc. to [Dow66] Table 3: Lubricant film thicknesses (values of flank roughness are mean value of measurements) the current test variant with a case-hardened pinion and a through-hardened wheel (Figure 4b). Therewith, all wear coefficients of the test variant of the wheel with hardness HV th2 = 280 HV follow the course of the curve within an allowable range. That approach does not conflict with the current state of the art. In theoretical consideration, a significant decrease of the wear coefficients should be expected as soon as sufficient lubricant conditions exist in the gear mesh. With higher lubricant film thicknesses, slow speed wear is no longer supposed to be the lifetime limiting damage mechanism, especially with entry in the area of mixed lubrication or full elastohydrodynamic lubrication. For this case, in [Win85] an extended range of the wear curve in the area of high lubricant films was already added (see Chapter 1). Moreover, other investigations by Joachim [Joa84] and Zornek [Zor14] have already shown a similar decrease of the wear coefficients under comparable test conditions for a hard-soft gear pairing. The horizontal translation of the wear curve that is now introduced describes that high amount of wear can even be expected for higher lubricant film thicknesses, when a hard-soft gear stage operates. For the variant ‘th2’, high wear is to be expected even at lubricant film thicknesses in the tooth contact that are 12-times higher compared to the variant with only case-hardened gears. However, the wear is reduced significantly, when a sufficient lubricant film thickness is reached. Aus Wissenschaft und Forschung 28 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 rent test conditions or equipment compared to the investigation of Plewe over 40 years ago. However, the course of the coefficients follows a translated wear curve acc. to [Win85] very closely (Figure 4a, solid lines). The wear coefficients of the through-hardened wheels from the variant HV th2 = 280 HV are compared to the belonging wear curve acc. to [Win85] (Figure 4, dashed lines). The corresponding reference wear curve is translated vertically along the ordinate until it passes through the wear coefficients of the test runs. Thereby, it describes the wear behavior of the gear-lubricant-system. It is noticeable that the results of the first two speed stages (at the lowest lubricant film thicknesses) follow the course of the shifted wear curve well. The wear coefficients of the third stage at the highest lubricant film thickness, however, are significantly below this curve. Therefore, the wear calculation severely underestimates the wear life time for this gearbox. This has been also observed by Joachim [Joa84] and Zornek [Zor14]. It confirms that even with a hard-soft gear pairing low wear coefficients can be reached, when higher lubricant film thicknesses occur. This behavior is also known from case-hardened gears. Therefore, in a first approximation, the reference wear curve for case-hardened gears acc. to [Win85] will be used to describe the wear behavior of a case-hardened/ through-hardened gear pairing as well. In contrast to the standardized procedure, the reference wear curve will be moved horizontally, along the abscissa, until it fits through the wear coefficients from Figure 4: Wear coefficients for the gear pairings of two case-hardened gears and a combination of a casehardened and a through-hardened gear calculated a acc. to the state of the art [Win85] and b only acc. to the wear curve of two case-hardened gears a b 3.2 Influence of a surface hardness difference In order to have a closer look on the influence of the surface hardness, further investigations have been conducted with two further through-hardened wheel variants of surface hardness HV th1 = 257 HV and HV th3 = 322 HV. The surface roughness is for all test gears Ra m = 0.31 µm. Analogous to the procedure in Chapter 3.1, the linear wear coefficients are calculated and inserted in the Plewe wear diagram. The wear curve for case-hardened gears acc. to [Win85] is translated until it has minimal deviations from the calculated wear coefficients of the respective test series (see Figure 5a). It represents the wear coefficients within a certain range very well in all cases. Moreover, a clear influence of the surface hardness difference can be seen. The tests with the softest wheel variant ‘th1’ show wear coefficients above the medium variant ‘th2’ at all speed stages. Based on the results, high wear is to be expected for this variant even for lubricant film thicknesses that are 15-times higher compared to the variant with only case-hardened gears. The wear coefficients in the wear tests with the harder through hardened wheels ‘th3’ are constantly below ‘th2’ and high wear is to be expected for lubricant film thicknesses that are 6-times higher compared to the variant with only case-hardened gears. This shows the clear trend that a higher difference in hardness between the meshing gears leads to higher wear. 3.3 Influence of a surface roughness of the harder gear In the second test series, the influence of the surface roughness of the harder gear (in this study the pinion) on the wear behavior has been investigated. The test runs are executed with through-hardened wheels (HV th2 = 280 HV) and harder, case-hardened pinions with the surface roughness of Ra s = 0.20 µm, Ra m = 0.31 µm and Ra r = 0.51 µm. In analogy to the previous test series, the linear wear coefficients are calculated and inserted in the Plewe wear diagram. The wear curve for case-hardened gears acc. to [Win85] is translated until it has minimal deviations from the calculated wear coefficients of the respective test series (see Figure 5b). The course of the translated wear curves describes the behavior in all cases in good approximation. This again supports the discussion from Chapter 3.1. The surface roughness and therefore, the lubrication condition has a clear influence on the wear behavior of a gear pairing, but in a different way compared to the influence of the surface hardness in Chapter 3.2. The wear coefficients are at a similar range in the slowest speed stage (at minimum lubricant film thicknesses). At higher circumferential speeds and therefore, higher lubricant film thickness, the wear coefficients of the different test runs show a bigger spread. The tests with the highest flank roughness of the pinion (Ra r ) show Aus Wissenschaft und Forschung 29 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 Figure 5: Wear coefficients for the test runs in dependence a of the difference in surface hardness and b of the surface roughness of the harder pinion a b of the wear curve are necessary. The relations for the two calculation factors are as shown in (4) and (5). (4) (5) The factor H R , like the factor H X , increases the calculated lubricant film thickness, but depending on the flank roughness Ra of the harder contact partner. The factor C R increases the linear wear coefficient for the softer contact partner. They are a function of the surface roughness of the harder contact partner (see Figure 6b and c). The equations are normalized for the standardized surface roughness of Ra = 0.3 µm of a type C-PT gear pairing. For the application in the wear calculation, the calculation procedure as shown in Equation (6) is recommended, while using the Plewe diagram: (6) = 0.1 1100 μ = 2.5 0.05 μ with Ra H as surface roughness of the harder rolling contact partner , = = , , = for > 60 HV Aus Wissenschaft und Forschung 30 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004 wear coefficients at all speed levels which are above the medium variant (Ra m ). It is noticeable that they are on a high wear level during the entire investigated range. Due to the unfavorable lubrication condition, the gear pairing stays in the area of high wear. The wear coefficients of the wear tests with the smoothest pinion flanks (Ra s ) are below the other two variants. 4 Introduction of an extended calculation approach With the results of the experimental investigations the wear carrying capacity of a case-hardened and throughhardened gear pairing can be described. Thereby, it is possible to integrate it as factors into the wear calculation. Since the wear coefficients of the hard-soft gear pairing also follow the course of the wear curve for casehardened gears acc. to [Win85], a conversion between the two gearbox types can be performed by shifting the wear curve by factors. The Equations (1) and (2) illustrate the basic procedure. It stands in analogy to the calculation of the surface durability or the tooth bending strength [ISO19a, ISO19b] that use a factor with index X to consider the influence of the surface hardness and a factor with index R for influences of the surface roughness. (1) (2) According to Chapter 3.2, the difference in surface hardness only has an effect on the horizontal translation of the wear curve. Therefore, only one factor H X for modification of the lubricant film thickness is necessary. The mathematical correlation results are displayed in Equation (3). The factor H X increases the calculated lubricant film thickness as a function of the difference in surface hardness ΔHV. (3) It should be noticed that the conversion does not change the lubricant film thickness in gear mesh, but moves the wear curve along the horizontal x axis. Thus, it changes the range of lubricant film thickness, in which wear or high wear is supposed to occur. The factor H X as a function of the surface hardness difference is shown in Figure 6a. Since the typical wear characteristics like significant higher wear coefficients for the softer gear in the gear mesh are to be expected for hardness differences ΔHV of more than 60 HV [Ple80], the factor is limited for ΔHV > 60 HV until further validation of the boundary conditions. For consideration of the influence of the lubrication condition in dependence from the surface roughness of the harder pinion, both horizontal and vertical translations , = , , = = 1.2 . Figure 6: Influence factors for wear calculation of a hard-soft gear pairing 5 Conclusion In this study, wear tests have been conducted on an FZG back-to-back test rig at three speed stages with a pairing of a case-hardened pinion and through-hardened wheel to investigate the wear characteristics of a hard-soft gear pairing. It is noticeable that significant higher wear occurs mainly on the softer wheel that can be designated as life limiting. Furthermore, the difference in surface hardness between pinion and wheel as well as the surface roughness of the harder contact partner (pinion) have been systematically varied to determine their effects on the wear carrying capacity. The wear coefficients from all test runs follow the wear curve acc. to Plewe [Win85] within a small range. For the hard-soft pairing, the wear curve can be translated in horizontal direction to describe the wear behavior. Therefore, higher wear is possible even at higher lubricant film thicknesses compared to a gear pairing of case-hardened gears. However, the wear coefficients decrease significantly above a certain lubricant film thickness and leave the region of high wear. The influences in dependence of the difference in surface hardness between pinion and wheel as well as in dependence of the surface roughness of the harder rolling contact partner have been quantified: With a larger difference in surface hardness or a rougher surface roughness of the harder gear, the wear carrying capacity decreases. A small hardness difference or finer surfaces have a positive effect on the wear resistance. In order to include these findings in the wear calculation, influence factors were introduced that are able to translate the wear curve acc. to Plewe [Win85] for the prevailing operating conditions. This enables the gear designer to make sufficient statements about the service life of a hard-soft gear stage under operating conditions from the results of a standardized wear test for gears. Acknowledgement The research project the test runs are part of were conducted with the support of the DGMK (German Society for Sustainable Energy Carriers, Mobility and Carbon Cycles e. V.) and FVA (Research Association for Drive Technology e. V.) research associations. The project was sponsored by the German Federal Ministry of Economic Affairs and Climate Action (BMWK) through the AiF (Arbeitsgemeinschaft industrieller Forschungsvereinigungen e. V.), project number 20679 N. References [ASTM13] D4998-13: Standard Test Method for Evaluating Wear Characteristics of Tractor Hydraulic Fluids (2013). [DGMK97] DGMK 377-01: Method to Assess the Wear Characteristics of Lubricants - FZG Test Method C/ 0,05/ 90: 120/ 12 (1997). [Dow66] Dowson, D.; Higginson, G. R.: Elasto-hydrodynamic Lubrication. Pergamon Press, Oxford (u.a.), 1 ed. (1966). [FVA07] FVA e.V. (Hrsg.): Referenzöle - Datensammlung, FVA-Heft 660, Research Association for Drive Technology e.V. (FVA), Frankfurt am Main (2007). [FVA10] FVA-Informationsblatt 2/ V: Pittingtest - Einfluss des Schmierstoffes auf die Grübchenlebensdauer einsatzgehärteter Zahnräder im Einstufen- und im Lastkollektivversuch (2010). [ISO00] ISO 14635-1: 2000: Gears - FZG test procedures - Part 1: FZG test method A/ 8,3/ 90 for relative scuffing load-carrying capacity of oils (2000). [ISO19a] ISO 6336-2: 2019(E): Calculation of load capacity of spur and helical gears - Part 2: Calculation of surface durability (pitting) (2019). [ISO19b] ISO 6336-3: 2019(E): Calculation of load capacity of spur and helical gears - Part 3: Calculation of tooth bending strength (2019). [Joa84] Joachim, F. J.: Untersuchungen zur Grübchenbildung an vergüteten und normalisierten Zahnrädern - Einfluß von Werkstoffpaarung, Oberflächen- und Eigenspannungszustand, Dissertation, Technical University Munich (1984). [Ple80] Plewe, H.-J.: Untersuchungen über den Abriebverschleiß von geschmierten, langsam laufenden Zahnrädern, Dissertation, Technical University Munich (1980). [Sie19] Siewerin, B. J.; Dobler, A.; Tobie, T.; Stahl, K.: Applicability of an Oil Based Calculation Approach for Wear Risk and Wear Lifetime to Grease Lubricated Gear Pairings. Proceedings of the ASME 2019 (2019). [Win85] Winter, H.; Plewe, H.-J.: Calculation of Slow Speed Wear of Lubricated Gears. Gear Technology 2. Heft: 6, S. 8-16 (1985). [Zor14] Zornek, B.; Tobie, T.; Stahl, K.: Flankentragfähigkeit gerad- und schrägverzahnter Innenverzahnungen unter Berücksichtigung anwendungsspezifischer Einflussgrößen, Research Project Nr. 482/ II (IGF-Nr. 16353), Report FVA-Heft Nr. 1086, Research Association for Drive Technology e.V. (FVA), Frankfurt am Main (2014). Aus Wissenschaft und Forschung 31 Tribologie + Schmierungstechnik · 70. Jahrgang · 1/ 2023 DOI 10.24053/ TuS-2023-0004