Abstract

This thesis presents the dynamic response and optimal design of a lathe spindle under experimentally measured random cutting force excitations. The optimal design is based on minimizing the maximum mean square displacement response of the workpiece under the action of random cutting forces. The stochastic partial differential equation of motion characterizing the behavior of a lathe spindle-workpiece system is formulated based on the Euler-Bernoulli equation. A finite element method using beam elements is used for free vibration analysis to compute the undamped mode shapes and the natural frequencies of the spindle-workpiece system. The workpiece support at the running center has been modelled as hinged or fixed support and the theoretical results are compared with the laboratory experiments to classify the nature of the support condition. Based on the results, the end condition at the running center is classified as hinged. The effect of varying the spindle-bearing stiffness on the natural frequencies and mode shapes are also presented. The forced vibration of the spindle-workpiece system is studied by first investigating the nonstationary random response of a workpiece subjected to a constantly varying cutting tool contact in a turning operation. The results indicate that the workpiece response at the cutting tool is not significantly influenced by the tool feed rate for normal turning operations. A modal analysis in conjunction with the finite element technique is then used to calculate the mean square displacement of the workpiece. The experimentally calculated power spectral density of the cutting forces is used as the input excitation to the mathematical model. A parametric study of the effect of bearing stiffness and damping, bearing spacing, sectional rigidity, and external damper on the mean square displacement is presented. An optimal design of a lathe spindle using a direct search optimization technique with bearing stiffness and spacing, and spindle cross-sectional diameter as design variables, has been carried out. The effect of chuck diameter and workpiece slenderness ratio on the dynamic response of an optimized spindle is also studied. Finally, the influence of a third bearing in the spindle on an optimized system and the design of an external damper are also discussed