circle centre is (xoi,yoi), the next trochoid circle centre (xoj,yoj) on the curve Up should satisfy the following relation:

(xOi

 xOj

)2 ( y

 yOj

)2  L2

(26)

In certain cases, the selected trochoid circle is small (rh<rh1), and residual material may remain after trochoidal machining. Thus, we must use several trochoid circles that gradually diminish to finish the transition, and then, we must use the isometric circles for milling, as shown in Fig. 14 b.

4.2.3 Machining adopting perforative corner trochoid along medial axis

This type of trochoidal method mainly adopts the mode of isometric circles. The medial axis can be calculated using the method of Voronoi diagrams according to the contour curves of the cavity. Obviously, the calculation efficiency and accuracy of the medial axis are critical factors. Ibaraki et al. (2010) presented an algorithm of trochoidal tool path by using medial axis and validated model efficiency through experiments. A corresponding computation method can be obtained by referring to the algorithm and controlling the engagement angle.

4.3 Trochoidal machining for narrow areas

Narrow areas, such as slots, often occur in cavity machining. The width of the narrowest area can be defined as h=k*d (such as k=3~5, where d is the cutter diameter). Trochoidal machining remains a very good method for the machining of narrow areas because it helps reduce the cutting load. However, if the actual width exceeds this value, the contour-parallel cutting approach is preferred for removing the material from the narrow area.

There are mainly two types of treatment for the narrow area: (1) calculating the bisector or medial axis of the narrow area and using the trochoidal method with variable circles to mill materials (Fig. 15a) and (2) calculating the bisector or medial axis of the narrow area and using the trochoidal method with isometric circles to first mill the materials; then, the trajectory of contour-parallel cutting is used to remove the residual material (Fig. 15b). The corresponding calculation method is similar to that in 4.2.

5. Experiment

5.1 Test platform

The test platform consists of a high-speed machining centre (DMC-60T), a tool workpiece system, and a cutting force measuring system. The force measuring system includes a force platform, a charge amplifier, and data acquisition software. The force measuring device is a Kistler9265B dynamic piezoelectric dynamometer with the sensitivity of 0.05 N. The charge amplifier is a Kistler5019. The test results for the milling force include three component forces: Fx, Fy, and Fz. Their synthesized   force

can be calculated using the formula   F   .

5.2 Comparative experiment

Fig. 16 shows a cavity model by the factory. The sizes of the cavity are 100*70mm. There is a 40 degree corner in B area of the model, and a slot in C area. The material of workpiece is P20, and its hardness is HRC36. The tool path generated from CAM software. Use this tool path for direct machining of workpieces without any auxiliary processing. See Fig. 16b for relevant process parameters and machined cavities. After the machining of 14 workpieces, the tool wear reaches the wear-out failure criterion

(VB > 0.3 mm). Test the milling force of a tool path loop and obtain the result (Fig. 16c). Large loads often change abruptly at corners. Check the tool edge, and tipping (Fig. 16d) may be found, which indicates the loads on the tool are very large.