One of the new and widely used polishing processes for the surfaces of cylindrical parts is the Magnetic Rotary Abrasive Polishing Process (MRAF). This process is done using magnetic force and rotational speed simultaneously and oppositely. In this process, the forces required for machining and surface polishing are applied to the surface of the workpiece through magnetic and rotational force. One of the capabilities of this process is the ability to finish the internal and external surfaces of various parts with a special geometric shape and axial symmetry. The purpose of this article is to investigate the mathematical model of the chip removal mechanism and surface roughness changes, as well as applied forces in the process, for an abrasive particle. In order to model and optimize process parameters, response surface method and analysis of variance have been used. Based on the presented mathematical model, it was observed that the parameters of rotation speed (S), working distance (w) and the dimensions of the abrasive particle (A) have a significant effect on the quality of the surface (Ra). Based on the surface response method, the lowest surface roughness value was obtained through a rotation speed of 700 rpm, a working distance of 1.5 mm and an abrasive particle with dimensions of 18 micrometers, which is equal to 43.64 nm and with the experimental value obtained from the tests, That is, 43 nm had an acceptable match and had a desirability level of 0.9959. The obtained results were in good agreement with each other in theoretical and experimental modes.