Force modeling and deflection compensation of miniature ball end mills

by Clayton, Stuart Harold.

Clayton, Stuart Harold. Force Modeling and Deflection Compensation of Miniature Ball End Mills. (Under the direction of Thomas A. Dow) The primary objective of this research is to increase the quality and productivity of precision milling operations. More specifically, increased accuracies and reduced costs are desired for die fabrication of injection molds when small flexible tools are required. The problem with miniature tools is their radial compliance. Typical machining forces in die materials such as hardened steels can cause significant tool deflection. When features on the order of 100 µm are desired, tool deflections can cause form errors exceeding 20% of the desired geometry. There were two main goals of this research: 1) to develop an accurate cutting force model and 2) to design and implement a spindle actuation system utilizing real-time forcefeedback machining. The first goal was to gain knowledge and understanding of the machining process by predicting cutting forces for miniature tools. The second goal involved the design of a closed loop actuated spindle system that can manipulate a tool path in one dimension. A precision actuated spindle allows real-time implementation of deflection compensation algorithms to reduce geometric form errors from tool deflection. The results from this research indicate that machining forces for miniature ball end mills are both predictable and repeatable. Experimental tests were conducted using a variety of two-flute ball end mills, workpiece materials, chip areas, upfeeds, and tool tilts. It was shown that the cutting force model provides a complete dynamic understanding of the machining forces and paves the way for the actuation system that was built into the tool spindle. Two different control algorithms were tested and proven successful as feature errors were reduced with each technique. The first algorithm involved an open loop technique where the force model was used to create an altered tool path that compensated for tool deflection. This was accomplished by predicting the machining forces, dividing by the appropriate tool stiffness to obtain deflection, and superimposing the deflection onto the original tool path. The second algorithm entailed closed loop control with forcefeedback machining using a newly designed PZT actuated spindle. The machining forces, which were used to predict tool deflection, were measured with a force transducer. The tool was moved in response to the deflection using a PID controller that regulated the voltage to a pair of PZT actuators. Errors produced from tool deflection were reduced with both control techniques. Experimental results showed that both control techniques, open and closed loop, reduced errors. The open loop compensation methods reduced error by approximately 65%, while the closed loop compensation methods reduced errors by 80%.