Computer Aided Design and Optimization of Hypoid Gears Alaa Mohamed * , T.A. Osman ** , A.Khattab ** , Mostafa. Shazly *** * Mechanical Engineering Department, Akhbar El Yom Academy, Giza, Egypt. ** Mechanical Design &Production Engineering Department, Faculty of Engineering, Cairo University, Giza, Egypt. *** Mechanical Engineering Department, The British University in Egypt, Cairo, Egypt. 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. Keywords: Genetic algorithms, hypoid gears, volume optimization. I. INTRODUCTION Hypoid gears are used in various automotive, rotorcraft and industrial applications to transmit power between two perpendicular shafts having a certain amount of offset. Hypoid gears are similar to spiral bevel gears except that the shaft center lines do not intersect. The shaft offset introduces several advantages to hypoid gears such as larger pinion size with less number of teeth, higher contact ratio, and lower contact stresses. However, higher relative sliding velocity between contacting surfaces results in high power losses and wear rates are among the common problems found in hypoid gears. chung-yunn lin [1] Created CAM package for optimum design of spiral bevel and hypoid gear by applying optimization techniques stresses. An optimization procedure for finding corrective machine tool settings is then proposed to minimize surface deviations of real cut pinion and gear-tooth surfaces. The results reveal that surface deviations of real cut gear-tooth surfaces with respect to the ideal ones can be reduced to only a few microns. Therefore, the proposed method for obtaining corrective machine tool settings can improve the conventional development process and can also be applied to different manufacturing machines and methods for spiral bevel and hypoid gear generation. chung-yunn lin [2] Created CAM package for optimum design of Spiral Bevel and hypoid gear with minimum surface deviation. Based on the Gleason hypoid gear generator, a mathematical model of the tooth surface is proposed. Applying the proposed mathematical model, the sensitivities of tooth surface due to the variations of machine- tool setting are also investigated. The corrective machine-tool settings, calculated by using the sensitivity matrix and the linear regression method, are used to minimize the tooth- surface deviations. The minimization problem was solved by using the singular value decomposition (SVD) method. II. COMPUTER AIDED DESIGN OF HYPOID GEARS Visual basic program has been developed to help the design of hypoid gears. The programs are subdivided into three main parts, design procedure for strength, design procedure for gear geometry and design procedure for force analysis. The developed package allows the designer to design Gleason hypoid, Klingelnberg hypoid, and Oerlikon hypoid gears using AGMA standards for steel, cast iron, aluminum alloy, bronze, or any other material of known mechanical properties. It also has the options for obtaining pinion and gear geometry, and evaluating pinion and gear forces. The output for pinion and gear geometry includes: pitch diameter, mean pitch radius, offset angle, pitch angle, spiral angle, mean cone distance, pressure angle on concave side, pressure angle on convex side, outer cone distance, mean addendum, mean dedendum, dedendum angle, addendum angle, outer dedendum, outer addendum, whole depth, root angle, face angle, outside diameter, pitch cone apex, root apex, face apex, mean pitch diameter, mean normal circular tooth thickness, and mean normal chordal tooth thickness. The output for pinion and gear system includes: gear ratio, shaft angle, hypoid dimension factor, limit pressure angle, 978-1-4673-4810-2/12/$31.00 ©2012 IEEE