increased the tool load. In the present work, a trochoidal model and a control strategy for controlling parameters are proposed and used to generate several kinds of pocket trochoidal paths.

Attempting to address the processing problems in milling narrow areas or corners in a pocket, this paper will present research on trochoidal machining. The milling forces, tool wear, tool path and cavity geometry will be comprehensively considered. The remainder of the paper is organized as follows. The modelling of the engagement angle and milling force in trochoidal machining is presented in Section 2. The control strategies for trochoidal machining are presented and analysed in Section 3. The realized methods of trochoidal machining in pockets are given in Section 4, followed by experimental identification in Section 5 and conclusions in Section 6.

2. Modelling of the engagement angle and force in trochoidal machining

2.1 Basic concepts

The engagement angle represents the contact geometrical relationship between the tool and the uncut material of the workpiece. As the tool travels along the tool path, the engagement angle continuously varies, as shown in Fig. 2. The engagement angle will reach its maximum value in the concave corner area. Accordingly, the amount of material to be cut will reach a maximum at the concave corner, similar to the milling force. As mentioned by Choy and Chan (2003), the cutter load is directly related to the cutter engage arc length or the engagement angle. Therefore, the engagement angle can be used to characterize the change trend of the milling force under certain conditions.

When the cutter mills the pocket in a contour-parallel cutting manner, the cutter load is very large at sharp corners, slots or other narrow areas. This is due to the large cutting engagement angle, which may even reach 180 degrees in the milling of a slot.

Trochoidal machining can decrease the engagement angle during processing because the material is gradually milled by a series of continuous circles. Therefore, the cutting load can be greatly reduced, and the cutter life can also be improved.

In the straight trajectory area as shown in Fig. 2, the engagement angle can be solved according to the tool path contour spacing d and the tool radius r, namely,

astr=arcos[(r-d)/r] (1)

In this paper, the value of astr will be taken as an important reference to control the trochoidal machining process. When we generate the cutting tool path for a mould pocket, the contour spacing d can be determined by experience or by consulting reference handbooks. Thereupon, the engagement angle astr can be easily determined.

2.2 Geometric modelling of engagement angle in trochoidal machining

The following is the geometric modelling of the engagement angle change process of the trochoidal trajectory, where the characteristics and rules are mastered and applied to a milling force control. The derivation process adopts a variable circle mode (Figs. 3a- c), and an isometric circle mode is regarded as a special case (Fig. 3d).

In Fig. 3a, the trochoidal paths are shown in dashed lines. The dashed-line circle (O2) and circle (O1) represent the current circle and the previous circle, respectively. To facilitate an analysis, each dashed-line circle is offset by a distance of r (tool radius) and is indicated by a solid line. The tool rolls along the dashed line circle, which is

equivalent to rolling on the inner side of the solid-line offset circle. One cycle of trochoid includes two sections: a connected curve (SE) and a circle (E-G-H-E).

A 3D coordinate system with the centre O1 of the previous offset circle as the origin (0, 0) is established. The distance between O1O2 is L. The tool centre C and the tangency point E1 are connected, C and O1 are connected, C and D are connected, and D and O1 are connected. Obviously, ∠DCE1 is the engagement angle.