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