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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calculate the probability of fault-free performance of the automatic transmission, Ognjanovic (2013), the torque distribution function is specified by the Weibull distribution. The choice of the curve is justified by the recommendations of ISO 6336 (2019). In the paper of Rudenko et al. (2015) when calculating the reduction the gear of the motor-wheel of the mine truck, the distribution graph of the specific traction force on the wheel has the form that similar to the logarithmically normal distribution. According to Caichao et al. (2014) to assess the reliability of the wind-powered generator gear mechanism the torque sample shown in Figure 2 was applied. It appears from the image that it can be concluded that the torque distribution law has the form of a bimodal function.

Fig. 2. The statistic data of the torque at the intake shaft of the wind-powered generator gear

In references Syzrantsev et al. (2020) and Syzrantseva et al. (2017) the torque distribution density function is determined by methods of non-parametric statistics for which the results of experimental data are used. This approach makes the reliability assessment technique more flexible and versatile. Besides the indication of the density functions of the random variables distribution in the implementation of reliability calculations, it should be noted that the mathematical models of the working and permissible stresses of surface-hardened gears are also being improved. This is primarily due to the fact that an increase in the hardness of the surface layer of the tooth reduces its elastic properties, and this negatively affects the limit of bending endurance. Therefore, in Golofast (2004), when assessing the reliability of gears according to the bending endurance criterion, the parameters of the strengthened layer are taken into account. The influence of the microstructure of the tooth material is also taken into account. In an article by Brecher et al. (2017) the consideration of macro-and microcracks inside the gear body and the function of the hardness change of the strengthened layer in the calculation of bending strength made it possible to obtain results with an inaccuracy relatively to the experiment of less than 10%. The calculation of the fault-free performance probability according to the criterion of tooth interior fatigue fracture is the least developed: as a result of the analysis of domestic and foreign literature, not a single example of the method for determining the probability of fault-free performance was revealed - the calculations come down to the determination of the safety factor or transmission service life, Lebedev (2022). Firstly, there are differences in the methods used for calculating depth stresses due to various theoretical positions: the Guest-More hypothesis, reference book ed. Derzhavtsa (1985), a generalized Lebedev-Pisarenko limit state criterion for structurally heterogeneous material, Korotkin et al. (2021), Findlay test, Baydu et al. (2017), etc. Secondly, the hardness change function by the depth variation of the hardened layer is of great importance for the determination of the tooth interior fatigue fracture, which also has several equations, Houyi et al. (2020). Thirdly, when changing the torque value, the depth of the minimum safety margin inside the tooth body will also change, which requires determining the point from the depth of the hardened layer at which the probability of the safe operation according to tooth interior fatigue fracture criterion will be calculated.