| Turning is a widely used machining technology,which plays an important role in the machinery manufacturing industry.The stability analysis on the turning system provides guidelines for the selection of cutting parameters,which may help to improve turning efficiency and precision,reduce tool wear,extend operational life of tools and give full play to performance of tools.This study focus on linear stability analysis of axial vibration of turning systems.The turning tool,modelled as a cantilevered bar,may undergo chatter due to the regenerative effect of cutting forces.The approximate undamped and damped turning tool models of single,two,three and nine degrees of freedom are established respectively.The equivalence between the approximate models and the continuous bar model is guaranteed by having the same first natural frequency and the same first modal damping ratio,which in this way determines spring stiffness,mass and damping.The delay differential equations of approximate undamped and damped turning tool models are obtained.The stability of the turning models is analyzed by using D-division method.The stability diagrams in the parameter of cutting width and spindle speed are obtained together with corresponding frequency curves.The characteristic root distributions of the equilibrium in different regions divided by the D-curves are investigated numerically,which is in good agreement with analytical results.The stability diagrams of the undamped models show that the stability region in the parameter plane of cutting width and spindle speed shrinks as the degree of freedom of models increases.When practical damping is considered,it can be seen from the stability diagrams of damped case that the stability results predicted by single-degree-of-freedom turning tool model are conservative in the relatively low speed region,but too large in the high speed region.While the stability region predicted by higher degree-of-freedom turning tool models is more accurate in the high speed region. |
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