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Interactive Involute Gear Analysis and Tooth Profile Generation using Working Model 2D

Abstract

Working Model 2D (WM 2D) is a powerful, easy to use planar multibody software that has been adopted by many instructors teaching Statics, Dynamics, Mechanisms, Machine Design, as well as by practicing engineers. Its programming and import-export capabilities facilitate simulating the motion of complex shape bodies subject to constraints. In this paper a number of WM 2D applications will be described that allow students to understand the basics properties of involute- gears and how they are manufactured. Other applications allow students to study the kinematics of planetary gears trains, which is known to be less intuitive than that of fix-axle transmissions.

Introduction

There are numerous reports on the use of Working Model 2D in teaching Mechanical Engineering disciplines, including Statics, Dynamics, Mechanisms, Vibrations, Controls and Machine Design1-9. Working Model 2D (WM 2D), currently available form Design Simulation Technologies10, is a planar multibody software, capable of performing kinematic and dynamic simulation of interconnected bodies subject to a variety of constraints. The versatility of the software is given by its geometry and data import/export capabilities, and scripting through formula and WM Basic language system. A number of textbooks11-15 include simulation examples generated with WM 2D, and some even provide a student version of the software on companion CDs12,14. In this paper several WM 2D applications will be described that allow students to understand the basics properties of involute gears, how they can be manufactured using rack or gear cutters, and what is the effect of addendum modification upon teeth geometry. Other WM 2D applications allow students to study the kinematics of two degree-of-freedom planetary gear trains, the motion of which is known to be less intuitive than that of fix-axle transmissions. In producing these applications, extensive use has been made of the interactive controls and scripting capabilities of the software.

The Involute Curve of a Circle

Gear Theory is a specialized topic that undergraduate students in Mechanical Engineering are exposed to in Kinematics and Dynamics of Machinery and/or Machine Design classes. It is known that involute gears are the most widely used in practice, being preferred over cycliodal and circular profile gears (like Wildhaber-Novikov), because of the following favorable properties16,17: the transmission ratio between two involute gears is not sensitive to the center distance modification; the same cutting tool can be used to manufacture gears with any number of teeth - the module (or diametral pitch) and whole depth of these gears will of course be the same;

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Simionescu, P. (2008, June), Interactive Involute Gear Analysis And Tooth Profile Generation Using Working Model 2 D Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--3796