Spindle configuration analysis and optimization considering the deformation in robotic machining applications

Robotic machining is an increasing application due to various advantages of robots such as flexibility, maneuverability and competitive cost. For robotic machining, the machining accuracy is the major concern of current researches. And particular attention is paid to the proper modeling of manipulator stiffness properties, the cutting force estimation and the robot posture optimization. However, through our research, the results demonstrate the spindle configuration largely affects the deformation of the robot end-effector (EE). And it may even account for approximately half of the total deformation for machining applications with the force acting perpendicular to the tool. Furthermore, the closer distance between the tool tip and the EE does not mean that the deformation tends to be smaller. Thus, it is reasonable to consider optimizing the spindle configuration based on the optimal robot posture, thereby exhausting advantages of the robot and further reducing machining errors. In this paper, a spindle configuration analysis and optimization method is presented, aiming at confirming the great influence of the spindle configuration on the deformation of the robot EE and minimizing it. First, a deformation model based on the spindle configuration (SC-based deformation model) is presented, which establishes a mapping between the spindle configuration and the deformation of the robot EE. And it confirms the large effect of the spindle configuration on the deformation of the EE. Then, a complementary stiffness evaluation index (CSEI) is proposed. And it adopts matrix norms to evaluate the influence of the spindle configuration on the complementary stiffness matrix in the SC-based deformation model. Using this index, the proposed SC-based deformation model is simplified for the ODG-JLRB20 robot adopted in this paper. Finally, a spindle configuration optimization model is derived to minimize the simplified SC-based deformation model using an iterative procedure. With this model, the optimal spindle configuration with respect to the EE can be obtained for a specific machining trajectory. Experimental results conducted on the ODG-JLRB20 robot demonstrate the correctness and effectiveness of the present method.