15.1 INTRODUCTION

Involute gears, spur and helical ones, are widely used in reducers, planetary gear trains, transmissions, and many other industrial applications. The level of sophistication in the design and manufacture of such gears (by hobbing, shaping, and grinding) is impressive. The geometry, design, and manufacture of helical gears was the subject of research presented in the works of Litvin et al. [1995, 1999, 2001a, 2003], Stosic [1998], and Feng et al. [1999].

The advantage of involute gearing in comparison with cycloidal gearing is that the change of center distance does not cause transmission errors. However, the practice of design and the test of bearing contact and transmission errors show the need for modification of involute gearing, particularly of helical gears. Figure 15.1.1 shows a 3D model of a modified involute helical gear drive.

Figure 15.1.1: Modified involute helical gear drive.

The existing design and manufacture of involute helical gears provide instantaneous contact of tooth surfaces along a line. The instantaneous line of contact of conjugated tooth surfaces is a straight line L ₀ that is the tangent to the helix on the base cylinder (Fig. 15.1.2). The normals to the tooth surface at any point of line L ₀ are collinear and they intersect in the process of meshing with the instantaneous axis of relative motion that is the tangent to the pitch cylinders. The concept of pitch cylinders is discussed in Section 15.2.

Figure 15.1.2: Contact lines on an involute helical tooth surface.

The...