Optimal Motor Location for the Reduction of Residual Vibrations in Mode-Coupled Ultra-Precision Manufacturing Machines

Ultra-precision manufacturing (UPM) machines are used to fabricate and measure complex parts having micrometer-level features and nanometer-level tolerances/surface finishes. Therefore, low-frequency residual vibrations that occur during the motion of the machines’ axes must be minimized. Recent research by the authors has revealed that coupling the vibration modes of passively-isolated machines by properly selecting the location of the vibration isolators could lead to a drastic reduction in residual vibrations. However, the effect of motor location on the residual vibrations of mode-coupled UPM machines has not been rigorously analyzed. In this paper, an objective function which minimizes residual vibration energy with respect to motor location is defined and analyzed. It is shown to have a guaranteed global minimum irrespective of the parameters of the UPM machine. Conditions that ensure that the global minimum is located in a practically feasible design space are explored. Finally, the merits of optimal motor placement on residual vibration reduction are demonstrated using simulations conducted on a 5-axis ultra-precision machine tool.