Probability of no-failure operation of cylindrical gears: tooth interior fatigue fracture

The reliability of a technical system is determined by its storageability, maintainability, durability and reliability. Probability of failure-free operation, as a quantitative assessment of failure-free operation, is an important parameter of gear reliability. The calculation of the probability of failure-free operation is carried out according to various criteria - possible types of gear failure. For case-hardened spur gears, such failures are: gear tooth failure (bending fatigue), pitting (rolling-contact fatigue), deep fatigue failure (tooth interior fatigue fracture). The purpose of the article is to develop a methodology for calculating the probability of failure-free operation of case-hardened cylindrical gears according to the tooth interior fatigue fracture. The object of research is case-hardened spur and helical gears. The article analyzes the existing methods for assessing the reliability of cylindrical gears according to the tooth interior fatigue fracture. An algorithm is developed and calculation formulas are presented for determining the probability of failure-free operation of a spur gear according to the tooth interior fatigue fracture. To determine the acting stresses inside the tooth body, formulas are used based on the generalized Lebedev-Pisarenko limit state criterion for a structurally inhomogeneous material. To determine the contact stress distribution density function, the methodology implements nonparametric statistics tools. The implementation of the developed methodology and comparison of the calculation results with the values of the probability of failure-free operation of the calculated gear according to the criteria of rolling-contact fatigue and bending endurance showed that with an increase in the maximum torque, the limiting criterion for the failure-free transmission becomes tooth interior fatigue fracture. The developed technique can serve as a part of the methodology for the verification calculation of spur gears based on numerical simulation methods.