Accurately solve the cutter–workpiece engagement (CWE) of ball-end milling has become a key problem for its mechanical behavior. In view of the limitations of the existent CWE solution methods of ball-end milling

such as low efficiency

poor universality and weak engineering applicability

a CWE solution method based on homogeneous transformation matrix is proposed to realize its prediction and analysis. Firstly

in light of the analysis of geometric characteristics in milling process

the analytical equations of vertical CWE are deduced; Then

from the perspective of multi-body system theory

the milling posture parameters of ball-end milling are characterized as coordinate matrix by homogeneous transformation method

and its analytical expression under any posture is derived. Besides

the milling process is discretized in time domain to analyze the effective milling edge and its evolution process in CWE. On this basis

the experiment for ball-end milling force is carried out to verify the reliability and accuracy of the solution method and milling force analysis. The results show that the proposed method can simplify the solution process of CWE

and the prediction of milling force is reliable and accurate; The increase of rake angle or roll angle will reduce the milling time of cutting edge and reduce the average milling force in the milling cycle; A larger milling force can be obtained with a smaller rake angle.