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The trochoidal milling mode is widely used in high-speed machining, and due to good adaptability and flexible posture adjustment, ball-end milling cutters are conducive to complex surface machining with this mode. However, the processes of material removal and formation of machined micro surfaces are very difficult to describe as the profile of cutter teeth is complex and the trajectory direction changes continuously during the trochoidal milling process. A modeling method for the generation of micro surface topography of ball-end milling in the trochoidal milling mode is put forward. In this method, the locus equation of each cutter tooth is established based on the principle of homogeneous coordinate transformation, after which a Z-MAP algorithm is designed to simulate the micro surface topography. The Z-MAP algorithm can quickly obtain the part grid nodes potentially swept by the cutter tooth within a unit time step through the establishment of servo rectangular encirclement and instantaneous sweeping quadrilateral of the element of cutter teeth; the part grid nodes actually swept are further determined through an angle summation method, and the height coordinate is calculated with the method of linear interpolation according to Taylor’s formula of multivariate functions. Experiments showed that the micro surface topography resulting from ball-end milling in the trochoidal milling mode had high consistency with the simulation, which indicates that the proposed method can predict micro surface topography in practical manufacturing. In addition, a comparison of micro surface topography between trochoidal milling and ordinary straight-linear milling was conducted, and the results showed that the former was overall superior to the latter in resulting characteristics. Based on this conclusion, the influences of cutting parameters of ball-end trochoidal milling on surface characteristics, particularly amplitude and function, were analyzed according to the simulated micro surface topography data.

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The modeling of instantaneous rigid cutting force is the basis of physical simulation of milling. However, it is difficult to model due to the complex shape of the cutter teeth of ball-end milling cutter and the changeable posture during machining. Under the condition of considering the cutter posture adjustment, trajectory of cutter teeth is established based on the homogeneous coordinate transformation, an improved Z-MAP algorithm of recognition of instantaneous cutter and workpiece engagement area is proposed. By calculating the intersection point between the reference line of the cutter tooth and the boundary of the workpiece surface, or the one between the reference line and cutter teeth's sweeping surface, the instantaneous undeformed chip thickness is derived. And the cutting force coefficients are identified by non-linear regression method. On these bases, the calculation of the instantaneous cutting force model is established by using the infinitesimal integral method. In order to validate the reliability of the simulation model, vertical machining and inclined machining tests are carried out respectively. The results of experimental and simulated results are highly consistent, it is therefore indicated that the modeling simulation method is effective and could provide theoretical basis for the selection and optimization of parameters in actual machining.