Research On Static Stiffness,dynamic Characteristics And Milling Stability Of A Parallel Spindle Head

In this paper,the kinematics,statics,static stiffness,dynamic characteristics and milling stability of the 3-PRRU parallel spindle head are studied,and experiments are carried out on a 5-axis hybrid machine based on the 3-PRRU parallel spindle head to verify the correctness of the relevant theories.The kinematics and statics of the 3-PRRU parallel spindle head are analyzed,and the kinematic inverse solution and the internal forces of each hinge of this parallel mechanism are studied and obtained.For the kinematic analysis,the components in the branch chain are simplified,and the equations of motion and constraint equations are established through the vector ring of each moving branch chain,and then the kinematic inverse solution is obtained.The force and moment balance equations of the rod and the moving platform of each branch chain are established to complete the solution of the internal force of each hinge,and the solution results show that the internal force of the hinge changes with the change of the mechanism attitude.The kinematic inverse solution and the hydrostatic solution provide the theoretical basis for the static and dynamic characteristics analysis later.The static stiffness of the 3-PRRU parallel spindle head is studied,considering the influence of the hinge elasticity,calculating the hinge stiffness based on the Hertz contact theory,combining with the deformation coordination conditions,using the structural matrix method to establish the overall stiffness matrix,and further obtaining the dynamic platform stiffness,analyzing the change of linear stiffness in each direction with the dynamic platform attitude,in which the z-axis linear stiffness is better than the x-and ydirectional linear stiffness.Correspondingly,experimental stiffness measurement experiments in x,y and z directions are designed,and the experimental measurement results and simulation results show the same change trend,which verifies the correctness of the model.The dynamic characteristics of the 3-PRRU parallel spindle head are further investigated.The first and second order inherent frequencies of the parallel mechanism were obtained by simplifying the structure of the spindle head,treating each branch chain as a beam mechanism constrained by the spring structure,and establishing an overall elastic dynamic model of the mechanism,which showed that the inherent frequency of the mechanism was affected by the attitude of the moving platform and showed a certain symmetry with the change of the tilt angle.The experimental results show that the vibration patterns of each order show different vibration trends,and the amplitude changes of the frequency response curves in x and y directions are mainly concentrated around the second and first order inherent frequencies.Finally,the 3-PRRU parallel spindle head milling stability is studied.Based on the idea of differential method,the tool teeth are divided into several tiny teeth parallel to the axial direction,and the dynamic milling force model with two degrees of freedom of the tool in radial and tangential directions is established;the milling force model is solved by the first-order full discrete method in the time domain,and the milling stability leaflet diagram is drawn.Milling force coefficients and tool tip frequency response function identification experiments are designed,and finally the leaflet diagram verification experiments are carried out to verify the accuracy of the prediction results,which provide a reference for the selection of process parameters in milling processing.