Nonlinear Dynamic Analysis Of The Feed System Of CNC Machine Tools

The feed system of machine tool has complex nonlinear dynamic behavior in the process of machining,which makes the machining accuracy of parts affected.Through the establishment of mechanical model and mathematical model,the influence of nonlinear factors on the mechanical characteristics of the feed system is analyzed theoretically,which will provide theoretical basis for improving the feed system of machine tool.Firstly,the nonlinear dynamics of feed system with viscoelastic damping material is studied.When modeling,the numerical control table can be considered as a vibrator,and the additional viscoelastic material can be represented by fractional differential terms.The forced vibration of a single degree of freedom gap vibrator with fractional micro terms is studied.The approximate analytical solution of the system is obtained by Krylov-Bogoliubov-Mitropoisky method.The primary resonance of piecewise linear system is analyzed,and a unified expression of the fractional-order differential term is obtained,here the fractional order is restricted between 0 and 2.It is found that the fractional differential term affects the dynamic characteristics of the system in the form of equivalent linear damping and equivalent linear stiffness,while the clearance affects the dynamic characteristics of the system in the form of equivalent nonlinear stiffness.The expression of the amplitude frequency response of the main resonance is obtained,and the stability condition of the system is obtained.It is verified by power series method.The influence of fractional order and clearance on the amplitude frequency response of the system is analyzed in detail.Secondly,the physical model and mathematical model of the feed system with friction and clearance are established,and the main resonance of worktable with clearance and friction under harmonic excitation is studied.According to the segment condition of the clearance and the segment condition under the friction model,the upper and lower limits of the integration are determined,and the approximate analytical solution of the main resonance is obtained by the average method,which lays a foundation for the subsequent analytical solution and the mechanical model with friction in clearance.For the integer order mathematical model,Runge Kutta method is used to verify the approximate analytical solution,which is proved to be correct,and the stability condition of the steady-state solution is given.It is found that the friction affects the vibration of the system in the form of equivalent nonlinear damping.The phase diagram method is used to analyze the phenomenon of stick slip vibration when the feed speed is small.Then,the mechanical model of the feed system with two degrees of freedom including clearance and friction is established.According to the average method,the approximate analytical solution of the feed system of the two degrees of freedom machine tool is solved and verified by the numerical solution.It is found that the numerical solution has a high degree of fitting with the analytical solution.According to the Lyapunov stability analysis,the curves of the maximum real part of the eigenvalue and the excitation frequency are obtained to judge the stability of the system.It is found that when the friction force increases in a certain range,the amplitude of the system decreases and the resonance frequency does not change.When the clearance increases,the resonance frequency shifts to the left.When the lead of the ball screw increases,the resonance frequency shifts to the right.The clearance and lead of ball screw are related to the equivalent stiffness,which affects the vibration of worktable.Finally,the mechanical model of five degrees of freedom is established for the feed system of the machine tool,and the numerical simulation analysis is carried out for the system.It is found that when the feed speed is low,due to the negative slope characteristics of the Stribeck friction model,and the displacement of the worktable crawls.The coupling effect of clearance and friction makes the feed system prone to creep at low speed.