Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools

• Effects of different heat transfer modes on thermal behavior of ball screw system are compared quantitatively.
• Thermal expansion coefficient is modeled as a temperature dependent parameter.
• Relationship is established to describe the thermal error transfer and transformation.
• Critical temperatures are proposed to embrace the thermal effect of screw shaft.
• Thermal expansion and error are formulated into a nonlinear function of position and working time.

In order to investigate the effect of thermal expansion on the ball screw feed drive system of a precision boring machine tool, theoretical modeling of and experimental study on thermally induced error along with heat generation characteristics are focused in this paper. A series of thermal experiments are conducted on the machine tool to measure and collect the thermodynamic data with the feed drive system operating at different speeds. Based on the heat generation and transfer analysis of ball screw system, thermal expansion of screw shaft in the axial direction is modeled mathematically. Relationships between the thermal error and axial elongation are established to characterize the thermal error distribution considering the thermal expansion coefficient as a temperature-variant parameter. It turns out that the thermal error varies with different working positions through the ball screw length and working time nonlinearly, and there definitely exists certain transform from the thermal expansion to the thermal error obtained by measurement. In addition, regression analysis is employed to carry out the theoretical modeling of thermal error with the temperature data of the critical heat generation points. The relations between temperature rise and thermal error are formulated directly while taking the thermal expansion as an implicit variable. Experiments under a different condition are preformed and the proposed methods for thermal error modeling prove to be effective and accurate enough to be used in the machining process as well.

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