Mathematical modelling for prediction of surface roughness in Pneumatically Configurable Polishing process

Abstract

Pneumatically configurable polishing is a superfinishing process which can generate nano-meter level surface finish on workpiece surfaces. It utilizes pneumatic pressure for controlled inflation of a cup shaped elastomeric membrane which has a stretchable polishing film fixed to its bottom surface. A slurry containing abrasive particles, thoroughly mixed in a carrier medium is applied on the workpiece surface. When the inflated membrane is brought in contact with a rigid surface, it adheres to the profile of the workpiece being polished, which ensures the entrapment of abrasive particles between the membrane and the surface to be polished. The abrasive slurry is replenished at a fixed interval during the process. This flexibility of the membranous tool enables it to finish complex 3D surface profiles. The final surface characteristics generated are a function of process parameters as well as material properties. This study proposes a mathematical model for the prediction of surface roughness as a function of workpiece properties such as hardness, tool characteristics, and significant process parameters such as working gap, applied pneumatic pressure, spindle speed, concentration of abrasive slurry, abrasive mesh size and dwell time. The model uses Hertz contact theory of elastic surfaces for modelling of contact pressure between the inflated membranous tool and the workpiece surface. A single abrasive particle is modelled for its influence on the workpiece surface as a function of its radial distance from the tool centre. This model is used to estimate the combined effect of all the active abrasive particles, participating in the finishing process. The final penetration depth obtained at different radial coordinates is used to estimate the theoretical surface roughness on the workpiece surface. The normal, shear and friction forces acting on a single abrasive grain have been modelled to determine the process capability during material removal. The model is finally validated by performing experiments under different conditions of process parameters. The experimental findings and theoretical results are found to be within an error range of −16.5%–11.8%.