A Study on Prediction of Stability Lobe Diagram in End Milling Process Considering Thermal and Rotation Effects of Spindle-Bearing System

Abstract

In metal cutting, performance of machine tools and productivity are critical issues to be enhanced through various solutions since manufacturing automation is accelerated with state-of-the-art technologies. Especially, chatter vibration induced by excessive machining conditions is investigated until recently by many researchers to improve the performance of machine tools. Due to the complexity of spindle system, many solutions including nonlinear parameters were suggested, which show that dominant aspects for the spindle system are composed of rotation and thermal effects caused by bearings. In general, support bearings inside the spindle should be analyzed correctly to predict chatter occurrence during spindle operation, and enable to depict the characteristic changes of spindle-bearing assembly. Hence, this research is motivated by the rotation and thermal effects of bearings induced by cutting process, which could become better solution to predict chatter stability analysis close to actual circumstances. In analytical approach part, conventional method using Hertzian contact theory of rolling elements was used to define local contact stiffness with deformation of contact area. Next, in order to calculate stiffness of bearing, contact angle between balls and raceways is derived from the geometrical interference induced by preload or initial assembly condition. To realize rotation status of spindle-bearing system, centrifugal force and gyroscopic moment are added in the deformation calculation process in accordance with spindle rotation speed. At the same time, heat generation generated by friction of ball bearing causes thermal expansion, which changes contact angle starting from center point of the rolling ball to the raceway groove. At last, final geometric change derived by the elastic deformation of bearing inside shows contact angle changes, which is related to the stiffness change of whole spindle-bearing system. In characterization chapter, refined impact hammer method is suggested to investigate both effects of actual spindle system using dummy tool. Conventional test only indicates static status of the system, but refined one enables to realize rotation and thermal effects. Impact force is exerted on the tool end during rotation with a capacitance sensor as non-contact sensor, also same test with pre-operation time was conducted to reveal thermal effect on spindle characteristic. It was clearly found that the rotation of spindle-bearing system is affecting the coherence of frequency response analysis, hence coherence check was conducted in accordance with important factors having a great influence on coherence changes. In addition, to compare test results with analytical solutions, Finite Element Model (FEM) was designed based on it for accurate temperature distribution and stiffness curve results. Those conclude that FEM simulation and analytical solutions were successfully agreed with experimental approaches, even if simplification of nonlinear parameters is applied to this method. In dynamic modeling of spindle-bearing system, lumped model for a bond graph was proposed using dynamic equation of the spindle-bearing model. Movement of each mechanical element was set as proceeding with cutting forces at the tool end, while tool, tool holder, bearings, and shaft including interfaces of each one were represented as simplified spring-damper single element. FEM simulation results were entered into model as input parameters, in order to derive frequency response of system for comparison. As a result, frequency response follows the trend of frequency shift induced by rotation or thermal effect. In addition, maximum error was less than 3% on average, which obviously shows that the lumped model was helpful to realize dynamic spindle-bearing system. In the chapter for stability lobe diagram evaluation, characterization results were applied to draw stability machining conditions of end milling system based on cutting conditions. Already it was found that the specific features affect the system, rotation effect gives lower stable axial depth of cut than reference diagram while the thermal effect produce the increase of stable area. When compared with the result of applying the lumped model, a difference caused by the abrupt peak was observed in specific areas, but the mean error converges to less than 7%, indicating that it has the similar shape. Based on the stability lobe diagrams, each experimental condition is selected at the determined spindle rotation speed, and actual cutting tests and the stability region derived from the diagram are evaluated through experiments where axial depth is continuously changed.