The dynamic analysis of an elastically supported lathe spindle-workpiece system subjected to random cutting forces is presented. The stochastic partial differential equation characterizing the behavior of the system was formulated from the Euler-Bernouli equation. Based on free vibration analysis and experimental verification of the natural frequencies, the hinged boundary condition was considered for the running center. A finite element technique in conjunction with the modal analysis method were used to calculate the mean square displacement of the workpiece. The experimentally calculated power spectral density of the cutting forces was used as the input excitation to the mathematical model. The effect of bearing stiffness and damping, and bearing spacing on the mean square displacement were studied. A direct search optimization technique was carried out to select optimal bearing stiffness and the bearing spacing. Results are presented in the form of plots and tables.

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