24.1 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 ? _c is given and surface ? _p of the workpiece must be determined, and (ii) the inverse problem, when surface ? _p is given and ? _c is to be determined.

Figure 24.1.1: Generation by finger-shaped milling cutter: (a) illustration of cutter; (b) illustration of tool installment; (c) illustration of screw motion of coordinate system S _p.

Figure 24.1.2: Disk-shaped milling cutter.

Henceforth, we use coordinate systems S _c, S _p, and S _f , 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, r _p is the pitch radius of the workpiece; r _c is the cutter mean radius; E _c and ? _c 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 S _c and S _f coincide, and the tool axis is x _c [Fig. 24.1.1(b)].

Figure 24.1.3: