Process modeling and correction of dynamic errors in diamond turning

Diamond turning is a machining process utilizing a high precision lathe and a diamond tool, which produces parts to tolerances measured in terms of nanometers. An essential ingredient to achieving such accuracy is the ability to control the relative position of the tool and the workpiece. The existence of dynamic motion errors contributes to surface finishes being often an order of magnitude greater than the theoretical finish of an ideally controlled process. Piezoelectric fast tool servos have demonstrated the necessary range and bandwidth to correct for these errors. However, the dynamic and non-repeatable nature of these errors requires that they be measured in-process to provide the desired fast tool servo command input. Two approaches to this measurement are investigated. The first involves position sensing of the most prominent errors. The second involves sensing the dynamic variations in forces at the tool workpiece interface, and from them inferring the relative motion. This force based approach is advantageous because it uses fewer sensors, requires less setup, and does not neglect any errors. It does however require an accurate model of the relationship between the dynamic variations in tool forces and the dynamic motion errors. For this purpose, a model of the cutting process is developed which relates dynamic errors to force variations while giving consideration to the cutting geometry, errors in previous cuts, machining parameters, state of tool wear, and material properties. Experimental verification of the model indicates that it is suitable to be used for position determination by means of tool force measurement.