A MATHEMATICAL MODEL OF OPTIMIZATION FOR GEARS WITH INCREASED CONTACT RATIO

Abstract

Reducing the mass and dimensions of gears is an actual task of modern mechanical engineering. One of the perspective ways to solve for involute spur gears it is the use of gearing with an increased working tooth depth and profile contact ratio εα ≥ 2. The study is devoted to the development of mathematical optimization model for such gears. Optimality criteria is formulated as follows: the contact stresses in the pitch point must take a minimum value when all constructive, geometric, kinematic, and technological constraints are met, first, when the profile contact ratio εα ≥ 2 is ensured. The equations that make up the mathematical optimization model are written. Variables planning are defined. These are addendum coefficients of the basic racks tooth for pinion and wheel h*a1, h*a2; profile angle of the basic rack α; addendum modification coefficient of the pinion x1. Formed a system of constraints for the variables planning: the main functional constraint of the minimum value of the profile contact ratio: εα ≥ 2; constraint for the addendum coefficients of the basic racks tooth for pinion and wheel h*a1, h*a2; constraint for profile angle of the basic rack α; constraint for addendum modification coefficients x1, x2; absence of the cutter interference for tooth dedendum; absence of the sharpening for tooth addendum; absence of the mesh interference; ensuring the bending strength of pinion and wheel teeth. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned to develop of methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results.

Key words: gear, profile contact ratio, contact stress, optimization, objective function, variables planning, constraints of the variables planning.