Study On Mathematical Methods Of The Theory Of Chatter Stability In Milling Process

With the development of industrialization,the application of milling is becoming more and more extensive.However,the periodical change of cutting force in the process of machining excites flutter and shows flutter trace on the surface of machining.It reduces the quality of workpiece processing.Because of the complexity and difficulty of machining parts and materials in various fields.It is very important to study the flutter stability of milling.Thus,this paper mainly focuses on the mathematical method of the stability analysis of milling chatter.The main contents of this paper are as following:First,during milling,due to the limitation of some experimental conditions,the cutting force data can be measured by dynamometer,but the displacement experimental data can not be obtained because of the lack of displacement sensor.In this paper,the milling dynamics model with coupling effect and regeneration effect is considered.A mathematical method for judging the flutter stability of the system by cutting force data is proposed.First,the experimental data of cutting force are fitted by the least square support vector machine(LS-SVM)method.The optimal fitting parameters are obtained by analyzing the influence of parameters σ and γ on the fitting effect.Second,the fourth order Runge-Kutta method is used to solve the milling dynamic model and the displacement is obtained.The stability of the system is judged by chaos principle.Finally,the milling experiments of titanium alloy Ti6A14V are carried out.The method proposed in this paper is in accordance with the experimental phenomena.The results show that the method can effectively judge whether flutter occurs in a certain state.Second,because the above method can only determine whether a state of chatter in milling,and often need to get the spindle speed,axial cutting depth stability region.The paper improved the complete discretization scheme by the improved Euler formula of discrete differential processing of parts,and prove that the two order precision is the local discretization error that is more accurate than the original algorithm.Then,furthermore,in order to consider the effects of process damping,cutting thickness regeneration and coupling effect on milling machining,this paper studies the mechanical analysis of milling workpieces and cutters.A new mathematical model of process damping is established and its stability is predicted by the improved complete discretization scheme,and the stability boundary is obtained.Finally,since the predicted stability boundary is not conducive to the direct use of engineers in practical processing,a new mathematical model of process damping is considered.In this paper,a method of limit engineering of stability region based on extension correlation function is proposed.The stable limit boundary point is selected by using extension correlation function and the limit engineering function is fitted to obtain the limit boundary of stability region.For the engineer stable milling process to provide a strong support.