Computer aided design and optimization of hypoid gears

Abstract

Although hypoid gears provide smooth operation and high reduction ratios where compactness of design and maximum pinion strength are important, their efficiency is less than that of a similar set of spiral bevel gears. However, hypoid gears generally have greater tolerance to shock loading and can frequently be used at higher single stage ratios than spiral bevel gears. The objective of the present work is to develop a computer aided design (CAD) package for optimizing the design of hypoid gears. The CAD program calculates the gear set geometrical and strength performance variables such as the bending and contact safety factors. Strength calculations are based on ANSI/AGMA 2003-B97 standards. The CAD package allows the designer to select and change the design variables to satisfy any applied constraints. A genetic based optimization module manipulates the CAD package in a manner similar to the way that can be done by the designer but in an iterative and systematic way. The optimization module changes the design variables and compares the results to minimize the objective function subject to specified constraints. A minimum pinion volume objective function has been chosen in the present work. The main constraints are to equate the working bending and contact stresses to their respective allowable stresses. This would further make the best utilization of material and indirectly minimizes the volume. A numerical example is given to demonstrate the analysis procedure and the effectiveness of the optimization module. The results showed that the optimization procedure reduced the volume of a gear designed according to ANSI/AGMA 2003-B97 to 54% of its original volume. Further analysis was performed to study the effect of the design variables and the input parameters on the objective function.