Analysis and Modeling of Angular Errors in Precision Sliding Motion with Application to Machine Tools
 
 

Cecil M. Daniel | PhD | 1998

There is a continuous requirement for higher levels of accuracy in machined components. A major contributor to errors in machined workpieces is the inaccuracies inherent to the machine tool itself. The objective of this work is to analyze and model roll, pitch and yaw errors in precision sliding motion occurring in a machine tool slideway. These angular errors are significant in determining the accuracy behavior of a slideway but are also the least studied among the machine tool error types, and difficult to detect and compensate for.

An experimental setup built around a SETCO SHL-12 slideway is used for designed experiments aimed at identifying key factors affecting pitch and yaw errors. The role of guide surface form error, and elastic contact deformation at the joint interface, on slideway angular errors are then established. A technique for determining contact coefficients of the elastic foundation model is then developed. The effect of heat source application on the slideway is modeled using finite difference and finite element techniques. Further, the role of manufacturing and assembly deviations on slideway accuracy is modeled using coordinate transformation.

Predictive models based on surface form error and joint contact deformation are then developed for estimation of angular errors along the travel of the slide. An iterative numerical algorithm is used to compute joint surface inclinations that achieve a force and moment equilibrium. Inputs to the model include the geometry of the slideway and the measured surface form error on the guide rails. Further, a 3-D model for prediction of slideway pitch and roll errors is developed based on a perfect plane supported on two splines representing the surface form errors of the two guide rails.

Pitch and yaw errors predicted by the models were validated against autocollimator readings. Good correlation between the model predictions and experimental data is observed. The models provide the foundation for a design level estimate of slideway accuracy. Applications for the models include slideway error budgeting, tolerance sensitivity analysis and design optimization to achieve required levels of accuracy.

If you have any comments or suggestions please e-mail jwsuther@mtu.edu.