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Technical Briefs

# Tooth Surface Generation and Geometric Properties of Straight Noncircular Bevel Gears

[+] Author and Article Information
Lin Jing

School of Information, Mechanical and Electronic Engineering,  Shanghai Normal University, Shanghai 201418, P. R. C.

J. Mech. Des 134(8), 084503 (Jul 23, 2012) (6 pages) doi:10.1115/1.4006998 History: Received May 15, 2011; Accepted June 03, 2012; Published July 23, 2012; Online July 23, 2012

## Abstract

A general mathematical model is established to describe the geometries and geometric characteristics of tooth surfaces of straight noncircular bevel gears. One of the direction angles of the normal vector of the tooth surfaces is taken as a function of the angular position of its origin, called the direction angle function (DAF). The normal vector and DAF are introduced to characterize this model. The normal vector including its direction angles and modulus is solved first and then the corresponding tooth surfaces and their geometric properties, such as major curvatures and slide coefficients, could be generated and calculated directly, logically and systematically by using this model and defining various DAFs. This method is applicable to many types of straight noncircular bevel gears with different tooth surfaces including tooth surfaces cut by the crown rack cutter or others. In addition, by using this method, it is relatively easy to realize the desired geometrical and mechanical properties into the design.

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Topics: Gears

## Figures

Figure 1

Tooth surface in Sm

Figure 2

Transformation from Sm to S

Figure 3

Angular velocity vectors of bevel gears

Figure 4

Direction angle

Figure 5

Bevel gear cut by crown rack cutter

Figure 6

Geometric properties of elliptical bevel gear cut by crown rack cutter

Figure 7

Elliptical bevel gears with polynomial DAFs

Figure 8

Maximum curvatures with polynomial DAFs

Figure 9

Slide coefficients with polynomial DAFs

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