PSI - Issue 50

S.Yu. Lebedev et al. / Procedia Structural Integrity 50 (2023) 155–162 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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The probability of safe operation of the gear mechanism is estimated by different failure modes. Thus, for surface-hardened gears, possible failures during operation will be not only the loss of contact or bending strength, but also the exfoliation of the hardened surface layer caused by the loss of depth contact strength. Figure 1 presents the fault tree of the surface-hardened gear mechanism. The probability events generating the transmission failure are contact pitting tooth strippage and deep contact painting (exfoliation of the hardened layer), and the probability of the same event for the wheel and wheel gear may differ due to the distinction in geometry, material and type of thermal treatment. The authors note that there is no abrasive wear in the tree, since it is practically absent in case hardened gears, according to the published literature: Reshchikov (1975) and Kogaev et al. (1991).

Fig. 1. The fault tree of the case-hardened gear

To calculate the probability of fault-free performance according to the contact and bending endurance criterion, it is necessary to have density functions of distribution of two random variables: actual and permissible stresses. Both functions are mathematical models, the equations of which are presented in standard transmission calculation methods: ISO 6336 (2019) and GOST 21354-87 (1989). Some of the parameters of mathematical models are random numbers (torque, twist angle, contact surface hardness, etc.), therefore, when calculating, these parameters are set by samples of random numbers taken from experimental data, Vikas Sharma et al. (2016), or use random number (DST) sensors with given distribution parameters by YuanTao et al. (2017). The parameters associated with any technological factors (assembly and manufacture defects) are usually given by the DST with a logarithmically normal distribution law, Prushak et al. (2018). The law of torque distribution may have different equations depending on the operating conditions. So according to Reshetov (1988), the operation of the gear mechanism is divided into light, medium and heavy modes, for each of which the function of the torque distribution density is determined. The specific applications of different torque density curves to assess the transmission reliability of any technical system are considered in the paper. According to Ying et al. (2010) torque access to calculate the probability of fault-free performance of the gear drive of the lifting mechanism is an order statistics with a logarithmically normal distribution density function dependent on four forces affecting on the ship: unbalanced weight, wind load, friction forces and inertia forces. To