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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As a result of the given above analysis, it can be concluded that the development of a methodology for assessing the reliability of hardened gears is currently an urgent task. The purpose of this paper is to improve the method of calculating the strength reliability of surface-hardened cylindrical gears, based on the probability determination of failure-free operation of the gear. Nomenclature ( ) the probability of fault-free operation for each possible failure of gear and wheel index of gear (k = 1) and wheel (k = 2) operating time twist angle due to deformations of transmission elements and case, radian the total angle of technological twist of the surfaces of the teeth of the wheels caused by errors in the manufacture of teeth and installation errors during the gear assembly, radian 1 i- е the value from the torque sample, Nm 1 nominal (average) torque value, Nm 1 twist angle of teeth in interlock caused by deformations of gear elements during 1 , radian 2 twist angle of teeth in interlock caused by deformations of transmission elements at maximum torque, radian 2. The procedure for the probability calculation of fault-free operation of toothed cylindrical gears Any type of gear failure is an independent event. Considering the gear mechanism as a technical system, authors can conclude that the probability of safe operation will be equal to the product of probability of safe operation for each of possible failures: ( ) = ∏ ( ) 6 =1 . (1) Figure 3 shows the algorithm for the probability calculation of failure-free operation of surface-hardened gears. In block 1 (Fig. 3), input data is performed, which is the same as for the check calculation of the gear mechanism. The necessity to select the torque distribution density function and its parameters or to load a sample of torque values will be the difference. Block 2 is a separate program that reconstructs the torque distribution density function using non-parametric statistics techniques. Blocks 3 and 4 perform parallel probability calculations of failure-free operation of gear and wheel by criterion of contact and bending endurance. Design formulas used in block 3 and 4 are taken from GOST 21354-87 (1989). Random number sensors are given: a coefficient that takes into account the load distribution between the teeth, the technological twist angles of surfaces of the teeth and the values of permissible contact and bending stresses. A distinctive feature of the proposed method is the calculation of the total twist angle, which is calculated as the sum of two angles, radian: = + . (2) The γ F angle depends on the amount of torque and is determined by the relationship, radian: =( 2 2 − 1 )( 1 1 ) 2 +(2 1 − 2 2 )( 1 1 ). (3) The probability calculation of failure-free operation of gear and gearwheel by the criterion of tooth interior fatigue fracture is performed in block 5. The detailed calculation is described in the paper of Lebedev at el. (2022). The calculation in block 5 requires a sampling of contact stresses, so the calculation is performed after block 3.