Temperature integration model and measurement point selection for thermally induced machine tool errors

Abstract This paper proposes a new method to characterize and predict thermally induced errors in machine tools. The thermal error model predicts positioning errors between the tool and workpiece that are caused by deformations in the machine structure due to heat flow from both internal and external sources. These thermally induced errors can account for as much as 70% of the dimensional errors on a machined workpiece. If thermal errors can be predicted, they can be removed in real time by the machine controller. The success of performing the prediction relies on the thermal error model being both accurate and easy to implement. In this paper, a new thermal error model is presented which capitalizes on the notion that thermally induced errors are related to the integral of the temperature field and captures that integral via the Gaussian integration technique. This approach therefore creates a simple linear model with analytical foundations, where the number and location of the sensors are selected as the Gaussian integration points along an assumed polynomial temperature profile. Advantages to this approach over many of the alternative approaches include the fact that warm-up and cool-down situations can be represented by the same model as steady-state conditions. Also, since the model is based on the analytical solution for thermally induced errors, less training data are required than other methods. Furthermore, the optimum number and location of temperature measurements are predetermined and do not require additional measurements, while some alternative approaches require a large number of measurements from many sensors to determine the subset of optimum sensor locations. Test results on a spindle show that between 93–96% of the thermally induced axial errors are predicted for a variety of spindle duty cycles.