The reliability function of the case-hardened teeth of wheels of cylindrical gears

Abstract

BACKGROUND: Methods for calculating the load capacity and reliability of gears, accepted as standardized both at the national and international levels, are based on the laws of distribution of random variables, considered as the only possible ones, which is not entirely true. As a result, the developed gears have either overestimated or underestimated reliability, which leads to their low competitiveness. Therefore, the development of methods for assessing the reliability of the case-hardened gears, taking into account the actual laws of distribution of random variables, remains relevant, as it will make it possible to design competitive transmissions. AIM: Improvement of the current approach to calculating the reliability function of case-hardened gears according to their strength performance criteria. METHODS: The improved approach to calculating the reliability function is based on improved classical methods for testing the load capacity of cylindrical gears for contact and bending stresses (GOST 21354-87 and ISO 6336). The methodology for calculating the reliability function according to the criterion of deep contact durability is based on the Lebedev-Pisarenko criterion, the formulae of which have been modified for application to gears by V.I. Korotkin. The implementation of the proposed methods was carried out in MathCAD software. RESULTS: The methods for calculating the reliability function of the case-hardened gears according to the criteria of contact and bending durability, which take into account the variable value of the misalignment in the gearing caused by the deformation of the shafts, the bearing rings and the housing (force misalignment), are proposed. In addition, the dependence of the calculation results of the reliability function of cylindrical gears on the method of setting the force misalignment in the gearing of teeth (constant or variable value) is shown. Validation of the improved approach was carried out using the data available in the scientific and technical literature on failures of the case-hardened gears. The scientific novelty of the research lies in the proposed method for calculating the reliability function of the case-hardened gears according to the criterion of deep contact durability, which performs the calculation under an unknown law of distribution of effective stresses using the Parzen-Rosenblatt method (the method is also used in methods for contact and bending durability criteria), as well as in taking into account the variable value of the force misalignment in the meshing. CONCLUSION: The practical significance of the research lies in the ability of probabilistic determination of the cause of gear failure according to six criteria (pitting, tooth breakage, tooth interior flank fracture of both the pinion and the wheel), which makes it possible to adjust the design, the manufacturing technology, and the operating requirements in order to ensure the required gear performance during its design.