Theoretic analysis on and application of behaviors of machine tool joints

Abstract

Theoretic analysis on the behaviors of mechanical structure joints is presented.Starting from a basic dynamics equation, the relationship between the static displacement and the load on the joint of a single plane is derived,which is further converted into an expression of the static rigidity.And the expression of damp at the joint of a single plane is derived on the basis of the concept that the input energy is equal to the damp consumption in some direction in a vibration cycle.A rotary structure is equivalent to a multi-plane solid by regarding the multiple joints in a mechanical structure as the combination of joints of multiple single planes.The equivalent joining rigidity and damp at the joint of a machine tool with given structural form and defined load thus can be calculated. Compatibility equations for rigid and flexible joining are given to integrate the behaviors of joints in the overall dynamics modeling of a machine tool.The overall modeling and calculation of the XK712B vertical boring and milling machine as well as the comparison with the test results show that the absolute relative error of comprehensive rigidity is less than 5% and the absolute relative error of natural frequency is less than 9%.By integrating the behavior of joints into the complete machine model,the comprehensive static and dynamic behaviors of the machine as a whole can be predicted more accurately.