Small-wavelength form error compensation during hydrodynamic polishing

This paper proposes a process control strategy for removing small-wavelength form error during hydrodynamic polishing, that is, by planning a tool dwelling time appropriate to accurately remove the form error. Volume removal analysis suggests that removal of an arbitrary error profile requires the tool to dwell at a given position for a period that is a linear function of the error profile. The dwelling-time distribution of the tool is solved by the non-negative least squares method. The residual error between the actual and desired profile is induced by this strategy. Residual error occurs mainly at the peaks and valleys of the profile, in addition to the boundaries of the machining area. Results indicate that the dominant factors in deciding residual error are the size of the machining zone, tool step, and wavelength and amplitude of the error profile. It is shown that larger residual error occurs in bands with wavelengths smaller than the machining zone, and vice versa. If the wavelength is sufficiently large, a small tool step effectively reduces the residual error. Furthermore, large variations in the amplitude of the error profile can be effectively reduced when the wavelength is large. Experimental results confirm that the proposed polishing strategy can remove an arbitrary profile and automatically reduce the small-wavelength errors. However, it is not effective when the wavelength of the error profile is near the size of the machining zone.