A workpiece stability-based iterative planning of clamping forces for fixturing layout specification of a complex workpiece

Abstract

When a workpiece is reasonably located on a machine bed, it will be subject to gravity and cutting forces in the machining process. In order to prevent them from causing the position variation and the production accident, it is important to determine clamping forces for workpiece stability. In this paper, the workpiece stability is categorized into the force existence for the unknown clamping forces and the force feasibility for the given clamping forces. A linear programming technology is suggested to verify the force existence and the force feasibility at the corresponding clamping point. And then, the clamping surface is discretized into a node set for one clamping force. At every node with the force existence, the magnitude of clamping force can be obtained by the “1-clamping force” iterative planning algorithm in which the step will generally decrease with the difference of the force existences between two adjacent clamping forces until it is no more than the threshold value. Moreover, the workpiece is frequently hold by n clamping forces which can equivalently be described as a function of one polar radius and n-1 polar angles. Thus, “n-clamping force” iterative planning algorithm can be established to solve the polar radius by calling the 1-clamping force iterative planning algorithm. Finally, the n-clamping force iterative planning algorithm is used to obtain double clamping forces. The maximum relative errors of placements and magnitudes are 0.145% and 0.151% in comparison with the results of the analytic method, respectively. Again, a third typical fixturing layout is used to validated 1-clamping force iterative planning algorithm with the relative errors within 0.770%. Because the proposed method transforms the continuous design problem of clamping forces into the discrete analysis problem of workpiece stability, it can not only apply to the complex workpiece but also benefit the development of automated fixture design.