INTRODUCTION

Generation of worms, screws, and helical gears by milling cutters or grinding wheels is considered. Two types of tools for this process are applied: (i) the finger-shaped tool, and (ii) the disk-shaped one. Figures 24.1.1(a) and 24.1.2 show the finger-shaped and disk-shaped milling cutters, respectively. There are two main problems of design when generation of helicoids is considered: (i) the tool surface Σc is given and surface Σp of the workpiece must be determined, and (ii) the inverse problem, when surface Σp is given and Σc is to be determined.

Henceforth, we use coordinate systems Sc, Sp, and Sf, which are rigidly connected to the tool, the workpiece, and the frame of the cutting machine, respectively. Figure 24.1.3 shows the installation of the disk-shaped tool. Here, rp is the pitch radius of the workpiece; rc is the cutter mean radius; Ec and γc are the shortest distance and the crossing angle between the axes of rotation of the tool and the workpiece. In the case of application of the finger-shaped cutter, coordinate systems Sc and Sf coincide, and the tool axis is xc [Fig. 24.1.1(b)].

The relative motion of the workpiece with respect to the tool is the screw one in both cases and is shown in Fig. 24.1.1(c); ψ and p are the angle of rotation and the screw parameter in the screw motion, respectively. Methods used for generation of helicoids, discussed in this chapter, have been developed by Litvin [1968].