Milling Dynamics High Efficiency Analysis Method And Its Application In Five-Axis Machining

One of the important premises for realizing high-end manufacturing is to solve the vibration problems in the machining process.In many types of cutting vibration,the chatter caused by the improper combination of cutting parameters(spindle speed and cutting depth)is the most harmful to the machining system,because it will not only affect the quality and surface accuracy of the workpiece,but also aggravate tool wear and breakage,reduce the service life of the machine tool,and stimulate the fatigue of the operator for the strong noise caused by chatter.From the view of milling dynamics,the important way to avoid chatter is to construct the functional relationship between the critical stable depth of cut and spindle speed,namely the stability lobe diagram(SLD),to optimize the process parameters.Therefore,the key to accurately obtaining stability machining parameters is to develop high efficiency and high accuracy milling dynamics analysis.Ball-end mill is one of the most widely used tools,and five-axis NC machining is a typical high-flexible processing technique.It is of great significance to achieve chatter-free for five-axis ball-end milling.Taking the milling dynamics analysis as a principal line,this paper focuses on the synchronous prediction of machining stability&surface location error(SLE),and the dynamic modeling of five-axis ball-end milling.This research mainly includes the following several aspects:Firstly,the analysis method of machining stability based on Newton polynomial(NP)is proposed.According to compare the computational performance of different order methods,the best NP prediction method is determined.Only sixth orders local discretization error make it have obviously higher prediction accuracy in comparison with first-order full discretization method(FDM),second-order FDM,third-order FDM,semi-discretization method,complete discretization scheme with Euler's method,and Runge-Kutta-based complete discretization method.Meanwhile,quite a few coupling terms existing in the state transition matrix save considerable computing time,and make the proposed method achieve both high efficiency and high accuracy.Secondly,the Newton polynomial prediction method is extended into SLE prediction to construct the steady state coefficient matrix which is only relation with spindle speed and not affected by the change of time.The calculation time is reduced greatly,and the goal of synchronized and efficient prediction of stability&SLE is realized.Thirdly,a novel identification method considering the variation of radial cutting depth is presented to calculate cutting force coefficients of five-axis ball-end milling.The force coefficient identification model suitable in the non-groove cutting of five axis ball end milling is developed at first.Afterwards,the effect of the radial cutting depth on the force coefficients are discussed,and the phenomenon that the force coefficient calculated from a certain radial cutting depth can not be applied to all working conditions is revealed.Based on this fact,the high order polynomial functions between force coefficients and radial cutting depth are presented to realize accurate calibration of cutting force coefficients at any radial cutting depth.At last,a new prediction method based on the analytical model of cutter-workpiece engagement(CWE)is proposed to compute the chatter stability of five axis ball end milling.According to the optimal Newton polynomial prediction method,the transition matrix representing the machining state of five axis ball end milling is established in each combination of spindle speed and cutting depth,which has a mapping relationship with the ultimate axial angles of the dynamic cutting segment in a cutting cycle.Drawing support from the geometric relation between the ball-end mill and workpiece,CWE in five-axis ball end milling is extracted,and the axial angles of upper and lower limits of cutting edge involving dynamic cutting are determinated.They are connected with the reserved "interface" of the state transition matrix to predict the chatter stability of five axis ball end milling,which is verified by the cutting experiments.In summary,the work done in this paper on the modeling and analysis of milling dynamics can provide theoretical supports and application guidances for high performance machining.