Dynamic Modeling, Simulation And Optimization Of High Speed Milling Under Complicated Cutting Conditions

With high speed milling under complicated cutting conditions as the research object of this paper, several problems corresponding to dynamic modeling and simulation of end milling are investigated. The dynamic cutting force model and the analytical chatter stability model for both circular corner milling and tee slot milling are setup. The receptance coupling model of a spindle-holder with a cutting tool is presented. With the result of dynamic simulation, the cutting parameters of milling process are optimizated. Based on the related researches and achievements, several functional modules are developed which are verified by cutting experiments and have some successful applications in practical engineering.As for the further research of dynamic modeling and simulation of end milling, the time domain simulation is inplemented by applying the numerical integration algorithm to solve the dynamic differential equations, and as a result, the chatter stability lobes in the time domain are otained by applying some chatter detection criteria synthetically to the simulated data. With the traditional analytical solution for the stability limits, the influence of modal parameters, i.e frequency, damping ratio and stiffness, on the chatter stability lobes are discussed, and a general method for modal simplification is achieved.With receptance coupling model, the end point receptances of the tool obtained by an analytical model, and the frequency response function of the spindle-holder assembly obtained by hammer tests, the receptance of spindle-holder and tool assembly is achieved. Futher more, the effects of cutter's diameter and the overhange length on the chatter limits of the machining system have been investigated according to the developed functional module.By applying the orthogonal polynomial global estimation approach to the FRF of the tool tip, the modal parameters of a machining system are obtained, which are indispensable to the simulation of dynamic cutting force and the chatter stability in the time domain.As for the dynamic modeling and simulation of a milling process under complicated cutting condition, firstly, when the approach of cutting force modeling and simulation of flat end mill is used as reference and the discretiztion approach is applied to the cutting edges of a bull nose end mill, the cutting force model and the cutting force coefficients identification expressions for a bull nose end mill are obtained.Secondly, based on the geometrical modeling for the cutting edges of a tee slot end mill, the dynamic differential equations are set up, in which the regenerative effect is taken into account. When the numerical integration approach is used for solving of these equations, the dynamic cutting forces of tee slot milling are achieved. On the basis of the above achievements, the stability lobes in terms of axial depth of cut under a given radial depth of cut and the stability lobes in terms of radial depth of cut under a given axial depth of cut are both created to meet the requirements of practical applications. The cutting experiments for both dynamic cutting forces and chatter stability of tee slot milling have approved the validation of the related simulation model and algorithm.Lastly, when a typical geometrical model of circular corner milling is constructed and the circular cutting path is discretized, the engagement angles between the tool and the workpiece at each discretized positions are first calculated, and then the overall cutting forces acting on the cutter are obtained. As a result, the cutting forces, the power and the torque during the whole process of the circular corner milling are predicated. The dynamic equations for circular corner milling are set up, in which the regenerative effect is taken into account. When the average directional coefficients are obtained by numerical intergration, the analytical determination of chatter limits used for linear milling can be adopted for circular corner milling, the precondition is that the maximal radial engagement angle instead of the nominal radial engagement angle should be used. The expressions of the maximal radial engagement angle for circular corner milling with both uniform and non-uniform radial depth of cut are derived by the geometrical relationship between the cutter and the workpiece. The cutting force and the chatter stability models were verified by cutting experiments.With the result of the dynamic modeling and simulation of a milling process, the optimization of the milling process is further studied. The optimization variables include the spindle speed n, the axial depth of cut ap, the radial depth of cut ae and the feedrate per flute ft. The minimal cutting time is selected as the target of the optimization and the result of dynamic simulation is selected as the constraint condition of the optimization. It is convenient to obtain the optimized cutting parameters when the complicated optimization problem is divided into several relative simple conditional extremum problems. The constraint condition of chatter stability is introduced into the optimization of the milling process. As a result, the dynamics of high speed milling can further be reflected and the optimization of cutting parameters is more scientific and effective. The verification tests conducted for the cutting parameters optimization of both pocket milling and tee slot milling have approved that when the approach of dynamic simulation and optimization presented in this paper are used the machining efficient can be improved remarkably. Meanwhile, several successful engineering applications have also revealed the significant applied value of dynamic simulation and cutting parameters optimization.