Research On Milling Force Modeling For Ball End Milling Of Curved Surface

In the process of curved surface machining,the posture and feed direction of cutter always change constantly,which results in the constant change of cutter workpiece engagement(CWE).Therefore,it is essential for the milling force modeling to obtain the CWE and the instantaneous engage section of cutting edge in curved surface machining.In the ball end milling of curved surface,it is necessary for the milling force research to obtain instantaneous milling contact situation and establish milling force model.The main work is as follows:(1)Based on the comprehensive analysis of the changes in cutter posture and feed direction during curved surface machining,the instantaneous milling coordinate system and instantaneous cutter coordinate system are defined to describe the relative posture and contact relationship between cutter and workpiece quantitatively.By analyzing the forming principle of the CWE,the boundary of the CWE is divided into three spatial curves.Then,the curves can be solved by means of analytical and numerical methods.(2)Considering the arbitrary changes in the direction of cutter axis,the difference of cutter rotation reference frame between the independent instantaneous cutter coordinate system at each cutter location point is analyzed and quantified as an angle to compensate.Based on the static cutting edge model of ball end mill,the cutter rotation increment angle is defined to convert the static model into a dynamic model,and the instantaneous space posture of the cutting edge is obtained.Then,the mathematical description of cutter rotation in curved surface machining with arbitrary changes in the direction of cutter axis is completed.Finally,the instantaneous engage section of cutting edge is solved by the method of projection dimension reduction.(3)Based on the classic oblique cutting theory,a milling force model is established,and the shearing effect and ploughing effect were taken into consideration.And the calculation method of the undeformed chip thickness is improved,which is suitable for the curved surface machining with arbitrary changes in the direction of cutter axis and feed.Finally,the validity verification of the milling force model is completed through the milling experiments.