INTRODUCTION

The design of computer controlled machines extended the opportunity for the development of gears with a new topology of tooth surfaces. The new topology must provide the localization of the bearing contact, its stability even for misaligned gear drives, and the reduction of vibrations caused by transmission errors. The new topology of gear tooth surfaces can provide a predesigned function of transmission errors of a parabolic type that will be able to absorb piecewise linear functions of transmission errors caused by gear misalignment (see Section 9.2). The advantages of new surface topology can be achieved by application of generating tools of a simple enough shape just because the computer controlled machine is able to provide properly varied relations between the motions of the tool and the workpiece.

An additional advantage of application of a computer controlled machine is the possibility of increasing the precision of the installation of the machine-tool settings. In the most general case, a computer controlled machine for generation of gear tooth surfaces must have six degrees-of-freedom. Five of these degrees-of-freedom are necessary for the control of related motions of the tool and the workpiece. The sixth degree-of-freedom is required to provide the desired velocity of cutting (grinding) and is not related to the process of surface generation.

In the following sections of this chapter we consider three cases of generation of the workpiece surface Σp by the given tool surface Σt:

1. (i) Surfaces Σt and Σp are in continuous tangency and they contact each other at every instant at a point but not at a line.

2. […]