Calculating the probability of the failure-free operation of spur gear transmissions

The article presents an improved method for calculating the probability of failure-free operation of case-hardened spur gear transmissions. The existing methods for calculating the probability of failure-free operation of gear transmissions are analyzed. The failure tree for a case-hardened spur gear transmission is presented. The probability of failure-free operation of case-hardened cylindrical gear transmissions is presented as the product of the probabilities of failure-free operation of the gear and the wheel according to the following criteria (failure types): contact endurance (pitting), bending endurance (tooth breakage), and tooth interior fatigue fracture (deep contact chipping). An algorithm has been developed for calculating the probability of failure-free operation of case-hardened spur gear transmissions. To restore the torque distribution density function in the proposed method, nonparametric statistics methods are implemented. In the calculation of contact stresses, the skew angle is taken into account, which is the sum of two angles: the skew angle due to deformations of the transmission elements and the housing; the total angle of technological misalignment of wheel tooth surfaces, caused by errors in the manufacture of the teeth and mounting errors during the assembly of the transmission. An example of a test calculation of the probability of failure-free operation of a case-hardened spur gear transmission according to the presented method is given. Based on the work performed, conclusions are formulated.