Statistical analysis and suppression of vibration frequency bifurcation in diamond turning of Al 6061 mirror

In diamond turning of metal mirrors, the reflectivity heavily relies on the mirror surface roughness, and the vibration of machine tool is one of the crucial factors affecting the mirror surface roughness. Previous articles mostly focused on the vibration of the spindle, but in the process of spherical surface machining, the influence of Z-direction moving parts can not be ignored. In this work, by using the transfer matrix and prediction-correction method, a dynamics model is developed to determine the different order vibration frequencies for Z-direction moving parts. The vibration patterns are further revealed in terms of the state vector of each order component with consideration of the external forces, e.g. dynamic cutting forces and linear motor thrust harmonics. As the machining parameters increase, the vibration tends to become instability, and the bifurcation of vibration frequency appears. The sensitivity analysis results firstly show that the cutting depth and workpiece surface slope are the most important factors influencing the vibration frequency bifurcation phenomenon. The probability density distribution of the vibration frequency bifurcation is firstly established as a function of the workpiece shape by stochastic big data simulations, and an adaptive optimization algorithm of interpolation point position is established. Finally, the correctness of the model is verified by experiments, and the relative error is kept below 10%. Through the new interpolation point planning algorithm, the vibration is reduced by more than 50%. Our findings are of significant importance for improving the spherical/aspherical surface reflectivity of metal mirrors.