To System Optimization of Spur Gears

Abstract

In the present work mathematical modeling is performed for one of important blocks of the system optimization of the tooth geometric shape by the stress-strain state which is connected with the gear reliability. The optimization function based on the system method is stated. The study of the stress state is carried out; it is shown that the strength of the tooth is provided mainly by the bending and contact strength in the area of the tooth dedendum. Optimization of the tooth geometry is considered individually for the bending and contact stresses. The optimal contour of the tooth in the root part depending on the action of forces in meshing that provide the fatigue strength in bending, is determined. Optimization by contact stresses is carried out; the formula for the length of contact is obtained. The analysis showed that in order to calculate the tooth strength, there is no more need to solve the flat problem of the elasticity theory; the beam theory and the Hertz formula with account of friction are sufficient. For the transition curve with the ratio of the smallest radius of curvature to half the width of the tooth less than 0.6, it is necessary to clarify the method of the instant warping theory of elasticity. The contour of the tooth is represented by a composite function in the form of a spline. Positive and negative effects of different tooth profiles (involute, parabola and transition curve) are noted.