27.1 INTRODUCTION

Indirect determination of gear tooth thickness by overwire (ball) measurement has found broad application. This topic has been the subject of research by many scientists. The earliest publications dealing with such measurement of worms and spatial gears are Litvin s papers and books. Detailed references regarding the history of the performed research are given in Litvin [1968].

The application of computers and subroutines for the solution of systems of nonlinear equations is a significant step forward in this area that was accomplished by Litvin et al. [1998b]. This chapter covers the following topics:

1. Algorithms for determination of location of a wire or a ball placed into the space of a workpiece with symmetric and nonsymmetric location of tooth surfaces

2. Relation between the tooth thickness and overwire measurement this relation enables us to use the developed algorithms for a workpiece with various tolerances.

The developed theory was applied for measurement of tooth thickness of worms, screws, and involute helical gears. Computer programs for this purpose have been developed.

27.2 PROBLEM DESCRIPTION

Consider that a ball (a wire) is placed into the space of a workpiece (a worm, screw, or gear). The surfaces of the ball and the workpiece are in tangency at two points whose location depends on the geometry of the surfaces of the workpiece, the width of the space, and the diameter of the ball. The surface geometry of the workpiece is represented analytically and the width of the space and the ball (wire)...