Static contact mechanism between compliant tool and sculptured surface in blade belt grinding

Belt grinding significantly enhances the manufacturing precision and surface quality of blades, thereby improving the dynamic performance and service life of aero-engines. However, the current technology has not yet achieved deterministic polishing, resulting in limited improvement in surface quality of blades. One of the primary reasons is that the flexible contact between complex curved surfaces is influenced by the workpiece curvature, tool size, and feed direction, resulting in a conforming contact. This contradicts the non-conforming contact assumption in traditional contact theory. In response to the contradiction and these influencing factors, this study proposed an analytical model to predict the contact conditions between the grinding tool and free-form surfaces. Based on integral method, the three-dimensional contact is reduced to a series of two-dimensional contact conditions between flexible and rigid circles with varying upper and lower limits of integration. Therefore, the limitation of non-conforming contact has been broken through. These upper and lower limits take into account the influence of tool size and curvature variation on the contact, and these contact conditions are further categorized into convex and concave contact to achieve the goal of predicting the contact force, contact area and pressure distribution. Experimental results show that traditional models are only applicable for the contact conditions where the feed direction is at 0°or convex contact conditions with a small press depth, becoming invalid as the press depth increases. In contrast, the model proposed in this study is applicable to all contact conditions, the predicting accuracy of contact force, contact area and max pressure is 7%, 16.4% and 13.1% respectively, while the error of the traditional method is 27.6%, 23.5% and 19.4%. Therefore, the comparison results prove the effectiveness and correctness of the proposed model. Consequently, the proposed model can more accurately predict the contact conditions in flexible belt grinding, thus improving the prediction accuracy of material removal rate and surface roughness in the subsequent grinding, and ultimately providing theoretical guidance for enhancing the manufacturing accuracy and surface quality of complex blades.