Geometric accuracy allocation for multi-axis CNC machine tools based on sensitivity analysis and reliability theory

Machining accuracy of a machine tool is influenced by geometric errors produced by each part and component. Different errors have varying influence on the machining accuracy of a tool. The aim of this study is to optimize errors to get a desired performance for a numerical control machine tool. Applying multi-body system theory, a volumetric error model was constructed to track and compensate effects of errors during operation of the machine, and to relate the functional specifications on volumetric accuracy to the permissible errors on the joints and links of the machine. Error sensitivity analysis was used to identify the influence of different errors (especially the errors which have large influences) on volumetric error. Based on First Order and Second Moment theory, an error allocation approach was developed to optimize allocation of manufacturing and assembly tolerances along with specifying the operating conditions to determine the optimal level of these errors so that the cost of controlling them and the cost of failure to meet the specifications is minimized. The approach developed was implemented in software and an example of the geometric errors budgeting for a five-axis machine was discussed. It is identified that the different optimal standard deviations reflect the cost-weighted influences of the respective parameters in the equations of the functional requirements. This study suggests that it is possible to determine the coupling relationships between these errors and optimize the allowable error budgeting between these sources.