Modeling and application of workpiece stability based on the linear programming method

After being located on a machine bed or a fixture, a workpiece will be subject to gravity, cutting and inertial force during the machining operation. In order to keep the locating precision and the machining safety, it is necessary to maintain the workpiece stability during the entire machining process. A general framework is established to analyze the workpiece stability. Based on the linear approximation of the friction cone and variable transformation, a quantitive criterion is established to verify the workpiece stability. The linear programming method is employed to solve the problem. Results show that the proposed method, in addition to the verification of the workpiece stability, can be used to study the feasibility of the magnitude, placement of clamping forces and clamping sequence. The method is also suitable to the analysis of the robot hand grasp Stability.