Force/Position Coupling Control In Polishing Optical Free-form Surface

The application of ultra-precision optical components is being widely used in moderncutting-edge technology, such as aerospace, national defense, space telemetering, militaryreconnaissance, and scientific instrument. The optical system including optical free-formsurface is superior to the traditional optical system, because of the special surface structureand the design of multi-degree of freedom. Due to the irregular geometric features, thepolishing precision and the quality of optical free-form surface is difficult to guarantee.Polishing is to improve the surface roughness of the workpiece without destroying theexisting geometry. The polishing pressure between the tool and the surface is the main factorto decide the polishing quality. In order to maximize the polishing precision and realize thecertainty of polishing, it is necessary to real-time control the polishing force between the tooland the surface. In this paper, the automatic polishing processing is on the self-developedultra-precision polishing experimental platform. The polishing force for polishing of opticalfree-form surface is real-time controlled by controlling the pose of the polishing tool, so as toensure the high surface quality.The material removal theory and the contact characteristics between the tool and thesurface are analyzed. And the material removal rate model and the polishing force model areestablished. The influence factors of the models are analyzed respectively, and the polishingparameters are planned and set reasonably. According to the coupling relationship, thepolishing force is converted to the normal displacement compensation on the cutter path.The inverse kinematics model of the ultra-precision polishing machine is established byusing the method of D-H homogeneous coordinate transformation, and the inversekinematics solutions are solved. According to the cutter path, the motion forms of thefour-axis CNC machine are calculated by MATLAB. The motion simulation is conducted by ADAMS, and the accuracy of the inverse kinematics model is verified.The model of the polishing force control system is built in MATLAB/Simulink by usingposition based on impedance control. It is composed of the inner position loop and the outerforce loop. And the velocity jacobian matrix and the force jacobian matrix are derived.According to the force/position coupling relationship and the inverse kinematics model, thepolishing force control is realized by the position control of the four axes.The simulation experiments of the position control and the force control are carried outrespectively. The simulation results show that the position tracking effect and the forcetracking effect are very satisfactory. The union simulation experiments show that theforce/position coupling control system is able to track input force signals quickly andaccurately. And the force tracking error is within0.01N. The simulation results prove that theforce control system with position based on impedance control has good effect on trackingthe desired force for polishing of optical free-form surface.The polishing force control based on force-position coupling provides the theoreticalfoundation for the force control for ultra-precision polishing of optical free-form surface.