MATHEMATICAL MODEL OF TEETH  SURFACES OF DOUBLE INVOLUTES GEAR WITH LADDER SHAPE OF
TOOTH ON ANY ROTARY ANGLE

ZHANG Zhiqiang  XIA Zunfeng TANG Yong  LI Gang

(Department of Mechanical & Electrical Engineering, Changsha University, Changsha 410003)

Abstract: The outspread principle of involute and enveloping principle of curve is applied to build the model of double involutes gear contrate profile, the veracity is verified by the data. On the base of the mathematical model of double involutes gear contrate profile, the mathematical model of double involutes gear teeth surfaces is built, which is on any rotary angle. The 3D simulation pictures of double involutes gear of three typical cut tooth top’s circular arc radius and simulation of mesh are obtained by mathematical model of double involutes gear teeth surfaces, the correctness and feasibility of model is validated. The expression is very simple and coordinate is not translated by using, the any point of double involutes gear teeth surfaces is fast and truly described on any rotary angle, the simple and speedily new theory gist is offered for 3D numerical design, manufacture and the analysis of mesh, kinematics and dynamics of double involutes gears.

Key words: Double involutes gear  Involute outspread  Curve envelop  Contrate profile of gear  Mathematical model of gear teeth surfaces

CLC No: TH132

Received 20050418, received in revised form 20050910