Dynamics Analysis And Optimization Of Fixturing Layout

Fixturing is the problem must be faced firstly in the machining process because different fixturing layout directly can influence the position of the workpiece offset, and then affecting the machining accuracy of the workpiece. The reasonable planning of the fixturing layout is crucial to guarantee the machining quality and safety manufacturing. Therefore, the prediction and control method is systematically proposed for the workpiece position error.The static and dynamic methods were used in this paper to analyze the workpiece during workpiece position offset relationship changes over time. And with friction or not was considerd. In dynamic approach analysis, whether the influence of damping on problem was taken into account. And these results were compared together. In which,the method of dynamic analysis is firstly transforming the contacts between the workpiece and fixture into the linear spring-damp system, and the vibration differential equation of the workpiece, which can determine the position movement of the workpiece in the fixturing layout, is concluded to obtain the workpiece position deviation according to the theory of kinematics and elastic mechanics. Based on the fact that the contacts between the workpiece and fixture are unidirectional, the hook law is used to formulate the constraint conditions of the workpiece position deviation. According to coordinate transformation method, the modal analysis solution technology of the vibration differential equation is proposed to predict the workpiece position error. A numerical test is demonstrated to validate the prediction results are in good agreement with the experimental data in the reference. And then, in order to minimize the workpiece position deviation, the optimal model with the objective of minimizing the 2-norm of the workpiece position deviation is proposed for the fixturing layout. According to the workpiece position deviation in the reasonable fixturing layout, the individual fitness is defined by taking its 2-norm as independent variable. Thus, the genetic algorithm can be skillfully developed to solve the optimal model of fixturing layout. The presented prediction and control method of workpiece position error can avoid the solution of the optimal model under the condition of the workpiece in unstable fixturing. It can provide a basic theory of fixturing layout design for the complex workpiece.Besides, in this paper, the workpiece was assumed flexible, fixture rigid, spring-damper elements were used to replace the contact portions. By calculating the first six natural frequencies of the fixture-workpiece system, the corresponding amplitudes of the frequency to the six orders have been acquired. By adjusting the clamping fixturing layout, the square of the corresponding amplitudes of the frequency of six orders were sumed up togeher, which was regarded as the objective function to be optimised. When the minimal objective function is achieved, then the optimal fixturing layout has been reached, which also means the smallest deformation of the fixturing.Therefore, machining accuracy of the workpiece can be improved from this aspect.The several methods mentioned above can be effectively to predict the actual machining position offset, and some of the factors that affect machining accuracy can be avoided. Finally, the processing efficiency and accuracy can be effectively improved.