Aspherical Magnetorheological Polishing Algorithm And Experimental Study

Magneto-rheological Finishing (MRF) is a deterministic polishing technology. Aspheric MRF algorithm, related to several machining process, plays a significant role in the surface figures'controlling process. The effectiveness of the algorithm determines the final result of aspheric finishing process and its efficiency hereby. In this dissertation, the aspheric MRF algorithm is explored and studied thoroughly, hence providing the base technology and support for conducting aspheric MRF process and possessing related technological capabilities.A new evaluation method for aspheric MRF process is proposed. The method is procured by analyzing the formation mechanism of aspheric MRF removal function. The analysis indicates that the removal function is determined by geometry and non-geometry parameters, which are decoupled afterwards. Therefore, the major geometry factor in the process-the immersion depth's influences on the removal function is learned and hence building the influence law. Further the method of removal function's evolving from plane to curve is proposed. The evolving process involves two type's evolving, which are removal function's reciprocal evolving on plane with respect to immersion depth, and removal function's evolving with respect to various curve radii.Lower Body Array (LBA) and Homogeneous Matrix Transformation (HTM) are applied to solve the required displacement for each aspheric MRF machine joints, hereby the universal displacement algorithm is found. The displacement algorithm mainly adopts the advantages of LBA, which performs well in expressing complicated topological structure mathematically. The work in this chapter also provides a theoretical basis for constructing universal displacement calculating software for aspheric MRF process. Besides, the nonlinear error's evaluation method is studied for aspheric interpolation process, which is utilized to aid the controlling the joints'motion in case of extreme nonlinear motion error.The path planning algorithm and dwell time algorithm is proposed for aspheric MRF process. For aspheric surface, not like plane, the figure error is difficult to be expressed in orthogonal space. Therefore, this dissertation found the method for aspheric surface, which involves planning the figuring process in arc space. Moreover, as aspheric MRF process is mainly conducted in meridian slice and hence the different dwell time algorithm with plane, this dissertation procure the aspheric dwell time algorithm by compensating the rotation of removal function into its influence matrix. Furthermore, a figuring method is proposed for aspheric surface which is located unexpectedly, and verified its effectiveness by simulation.Therefore, the aspheric MRF algorithm is obtained and experimentally validated. The deterministic property requires the algorithm is capable of controlling the process in each step with limited tolerance. The higher efficiency, more deterministic process controlling and better precision has been always the focus of aspheric MRF algorithm, regardless of any MRF process, like extraction and evaluation of removal function, displacement controlling, path planning and dwell time solving. This dissertation is preliminarily effected in aspheric figure convergence, and sure to be enhanced further.