them into another curve. Finally, we extend the engagement angle curve to make the peaks of the two curves meet.

After comparison of the two curves, we find that the changing trend of the engagement angle is very similar to the changing trend of the milling force. Therefore, we can use the engagement angle as a substitute for the milling force for analysis and calculation such as for large axial depths of cut and small radial depths of cut in cavity machining.

3. Control strategy for trochoidal milling

In high-speed cavity milling, a cutting mode with a large axial depth of cut and small radial depth of cut is often used. This is taken as the background; then, we will implement a serial of fundamental experiments (Fig. 9) and subsequently propose the control strategy for trochoidal machining.

(1) The milling force and tool wear increase with an increasing centre distance between neighbouring circles. An excessively large centre distance will increase the possibility of wear and damage to the cutting tool. The characteristics of the force change and tool wear are clearly indicated in Fig. 5 and Fig. 8.

(2) If the centre distance is set to equal the contour spacing of contour-parallel cutting, the milling force of trochoidal machining will be particularly high compared with contour-parallel cutting, which is more likely to make the tool fatigue and even become damaged.

However, the tool exhibits good heat dissipation in the trochoidal machining process; therefore, the ultimate tool wear tends to be low.

According to the above experiments on trochoidal machining, the main problem in trochoidal machining is the huge milling force, which tends to cause fatigue and breakage of the tool. Hence, the primary task of trochoidal machining control is to control the milling force.

The following control strategy for trochoidal milling will focus on the milling force. Moreover, the cavity geometry, tool wear, and milling efficiency will also be considered. The following will select the engagement angle as the auxiliary control parameter, not the spacing of the contour-parallel path. This is mainly because the spacing of the contour-parallel path is not an exact expression of milling force changes, but the engagement angle can provide for a very good expression (see 4.2).

3.2 Control strategy for trochoidal machining in cavity milling

If milling cavity is performed using the contour-parallel cutting method, the processing parameters, such as path spacing, cutting depth, and feedrate, are generally given by consulting a manual or by experience, which usually consider the bearing capacity of the cutting tool. Taking these basic parameters of contour-parallel cutting as a reference for trochoidal milling, and considering the above trochoidal machining features, a trochoidal machining control strategy is proposed as follows:

(1) According to the basic parameters of the contour-parallel cutting, such as the cutting tool radius (r) and path spacing (d), calculate the engagement angle (astr) or the milling force (Fstr) at the straight trajectory area of the contour-parallel cutting.

(2) According to the cavity geometry features, select an appropriate small circle, determine the area to insert the trochoid, and compute the location of the initial circle of the trochoidal path.

(3) Calculate a reasonable centre distance of neighbouring circles to meet the control requirements of the engagement angle or milling force.

Assuming that the mean engagement angle in trochoidal machining is atro ave and that

the maximum engagement angle is atro_max, calculate the following three parameters.