Modeling and experimental validation of transient surface roughness in magnetorheological finishing using 3-D magnetic flux density

Abstract

Mathematical modeling of finishing processes is a way of getting a scientific framework for understanding and controlling the process parameters that influence the result. It enables better optimization and predictability of outcomes like surface roughness, improving quality and efficiency. This paper presents a mathematical model for transient surface roughness in the magnetorheological finishing (MRF) process. The MRF fluid is the main component of this process, containing ferromagnetic and abrasive particles. It forms a cross-linked chain-like structure in the influence of magnetism. These chains are assumed to be similar to the HCP crystal structure. Each HCP chain’s position is calculated with respect to the central axis of the cylindrical permanent magnet. 3-D magnetic flux density is considered to estimate the accurate variation of it across the axial and radial direction of the magnet within the working gap of the MRF tool tip and workpiece. The modeled total magnetic flux density ($B_T$) is validated and found to be 3.93% less and 4.07% more than the total magnetic flux density using the Tesla meter and simulation, respectively. The axial magnetic force is calculated based on the axial magnetic flux density that acts on the abrasive particles through ferromagnetic particles. Hardness for nano-indentation is modeled and utilized in the transient material removal rate (MRR) model. Further modeling of transient surface roughness is formulated based on the MRR model. The formulated theoretical model of MRR and surface roughness are in close agreement with the experimental values with R-squared of 0.991 and 0.953, respectively.