Third-order Runge-Kutta Based Chatter Stability Solution Method For Milling Process And Its Application

As an advanced manufacturing technology,high performance milling is widely used in manufacturing such as aerospace,orbit transportation,automobile,etc.By means of dynamic modeling for milling process and predicting the corresponding physical parameters,the chatter free high performance milling can be achieved by cutting conditions optimization,in which the prediction of chatter stability is the key factor.Usually,the regenerative effect of cutting thickness is considered as the major cause of chatter.After deeply studying on cutting mechanism,carefully analyzing the stress situation of the cutting tool,the dynamic model is built and use the appropriate algorithm is used to obtain the stability lobes diagram.This paper is focused on finding a new solution algorithm for the existing dynamic model and the application of this algorithm.The main research contents of this paper are as follows:Firstly,as the analytical method is difficult to deal with the nonlinear stability problems and the computation efficiency of the semi-discretization method is too low,this paper proposed a third-order Runge-Kutta based semi-analytical method for solving the stability of milling process drawing lessons from the semi-discretization method.In order to improve the prediction efficiency,the dichotomy was used instead of the sequential search for obtaining the critical axial depth of cut.On the platform of Matlab the corresponding simulation program was developed and fast prediction of stability lobes diagram was implemented.Secondly,on the basis of the developed third-order Runge-Kutta based simulation program for solving the chatter stability,the chatter stability lobes of variable spindle speed milling process was predicted,in which a sinusoidal variation of spindle speed was used.Comparing the stability lobe diagram of variable spindle speed with that of constant spindle speed,the application of variable spindle speed can effectively suppress chatter.Lastly,both the cutting force coefficient identification test and the hammer test are conducted to obtain the required parameters for chatter stability simulation.The chatter verification tests are also performed tovalidate the correctness of the proposed solution method and the corresponding simulation program.