23rd International Colloquium Tribology - January 2022 247 Design for Reliability of Gear Systems Concerning Wear Arshia Fatemi Robert Bosch Corporate Research, Renningen, Germany Corresponding author: Arshia.fatemi@de.bosch.com Poorna Satish Chowdary Maddukuri Freiberg University of Mining and Technology 1. Introduction Wear is one of the main damage mechanisms in gears operating at low speed. In the case of gears with a small module (smaller than one), wear also exists at higher rotational speeds and could be the main lifetime limiting damage mechanism [1]. In grease lubricated systems, wear might be the predominant damage mechanism due to starvation, channeling and absence of the lubricant [1]. Due to the uncertainties in wear models, it is difficult to predict the product life with confidence levels in tribological systems, while in structural mechanics (particularly fatigue), calculating lifetime distributions and failure probabilities are well established. This work shows that a lifetime distribution can be determined from tribological stresses and strength-related parame-ters considering scatterings. The reliability can then be determined as the probability of reaching the required service life. Since damage models and statistical ap-proaches are rarely used to predict reliability in wearing systems, therefore, the methodology of structural me-chanics is adopted to calculate a lifetime for wearing systems. 2. Methodology It can be shown that analogous to structural mechanics, a tribological system can also be described in terms of 1. Tribological Stress, 2. Tribological Strength 3. Damage Model and 4. Failure Criteria. Lifetime for a continuously wearing system is defined as the time, at which the wear reaches the maximum failure criteria or maximum allowable wear (Wmax) based on the extracted damage model. Figure 1 illustrates a generic form of the reliability concept in an “Archard-Like” wearing system. The Abscissa represents the stress (e.g., nor-mal force), whereas the slope of the curve can be under-stood as “strength” which amounts to various times reaching the allowable wear value (Wmax). The distribu-tion of this time is considered as lifetime distribution. Considering wear in lubricated gear systems, one of the most successful methods in literature is based on the seminal work of Plewe [2]. According to his work, the wear of the gear systems can be calculated utilizing a film thickness-dependent linear wear coefficient (CIT) acquired by a defined FZG back-to-back gear experi-ment. Figure 1: Lifetime distribution due to variability of wear curves in a linear wear system (Archard-like). For calculating wear in practical applications, a given scattering of input parameters is expected. There are mainly two sources of scatterings available in wearing systems. 1. Scattering of Stresses-related parameters (e.g., temperature, nominal contact stress, film thick-ness) 2. Scattering of Strength-related model parameters (e.g., linear wear coefficient as a result of slope and intercept of Plewe chart. Since the slope is as-sumed to be constant, the intercept will be the de-ciding value) The scattering of input variables propagating through the damage model leads to a lifetime distribution, expressed by a probability density function. This is possible if we can define the lifetime based on the damage model and failure criteria. The most common probability plots used in reliability analysis are normal, Weibull, and lognormal. Ideally, the scattering of model input parameters must be ob-tained by test programs with many repetitions. This might be a very timely procedure if the wear models are complicated and need more than one parameter. In reliability engineering, there are many ways and meth-ods to deal 248 23rd International Colloquium Tribology - January 2022 Design for Reliability of Gear Systems Concerning Wear with the scattering of input parameters. The most commonly used to derive the functional form of the lifetime distribution from the distributions of the involved parameters are Monte-Carlo Simulation and Latin Hypercube Sampling. Since there are few scatter-ing parameters in the Plewe wear model, the choice of sampling methods is not very essential. 3. Results and Discussion A Design for Reliability (DfR) methodology has been formulated for gear systems from the Plewe wear mod-el in OptiSLang. The considerably uncertain variables such as temperature and Plewe intercept to verify the influences on the lifetime of the pinion. The lifetime distributions are presented in the form of, e.g., L10 lifetime. Table 1: Statistical examples of the input parameters which scatter considerably Input Parameter Defined PDF Mean Standard deviation Temperature [°C] Norma1 115 15 Plewe Intercept [mm] Lognormal 2E-06 4.5E-07 The L10 lifetime (the time that 90 % of the gears will survive without failing by surface wear) could be achieved as the basis for calculating the gear lifetime and reliability. The statistical moments of lifetime distributions of the pinion are shown in Table 1. OptiSLang software provides a fitted distribution from the histogram of the responses. Plewe describes the damage model for Design for reliability (DfR) of gear systems is formulated. 4. Conclusion A Latin Hypercube sampling (LHS) has been adopted in order to handle several scattering model inputs in OptiS- Lang. For the reliability analysis, the input pa-rameters such as temperature and Plewe intercept are considered. It is observed that temperature significantly affects the wear life and is followed by Plewe intercept. Lifetime distributions of the pinion from the DfR implemented methodology on the gear damage mecha-nism and lifetime model in the form of L10 lifetime can be presented. References [1] A. Dobler; Risk and Avoidance of Wear in Small Gears Drives; GETLUB conference 2018 [2] H. Winter und J. Plewe, „Calculation of Slow Speed Wear of Lubricated Gears,“ AGMA Paper, Bd. November, pp. 9-18, 1982.