A Linear Regression Thermal Displacement Lathe Spindle Model

Abstract

Thermal error is one of the main reasons for the loss of accuracy in lathe machining. In this study, a thermal deformation compensation model is presented that can reduce the influence of spindle thermal error on machining accuracy. The method used involves the collection of temperature data from the front and rear spindle bearings by means of embedded sensors in the bearing housings. Room temperature data were also collected as well as the thermal elongation of the main shaft. The data were used in a linear regression model to establish a robust model with strong predictive capability. Three methods were used: (1) Comsol was used for finite element analysis and the results were compared with actual measured temperatures. (2) This method involved the adjustment of the parameters of the linear regression model using the indicators of the coefficient of determination, root mean square error, mean square error, and mean absolute error, to find the best parameters for a spindle thermal displacement model. (3) The third method used system recognition to determine similarity to actual data by dividing the model into rise time and stable time. The rise time was controlled to explore the accuracy of prediction of the model at different intervals. The experimental results show that the actual measured temperatures were very close to those obtained in the Comsol analysis. The traditional model calculates prediction error values within single intervals, and so the model was divided to give rise time and stable time. The experimental results showed two error intervals, 19µm in the rise time and 15µm in the stable time, and these findings allowed the machining accuracy to be enhanced.

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Cooling of motor spindles—a review

“…Even displacements of up to several tenths of a millimeter can occur [35]. Research in which the influence of temperature rise on the spindle elongation is quantified can be found, for example, in [11,[36][37][38][39][40][41][42][43]. In general, the displacement of the TCP can be described by the superposition of the thermally induced displacements of the machine components within the thermo-mechanical effect chain.…”

“…Such corrective measures are often carried out for thermal stabilization of the entire machine or individual structural units (e.g., [51][52][53][54][55][56][57][58][59][60]). However, as motor spindles are usually the main sources of heat, there are a series of studies that deal with the modeling of spindles and their metrological investigation for the identification of correction values (e.g., [41,[61][62][63][64][65][66][67][68][69][70][71][72]). A review on this topic is given in [73].…”