基于热弹性理论与温度场积分中值定理的电主轴热误差研究

Study on thermal error of motorized spindle based on thermoelastic theory and mean-value theorem of integral of temperature field

电主轴热误差的精确建模较困难,且大多数仅关注轴向热误差而忽略径向热误差。因此,提出了基于热弹性理论与温度场积分中值定理的热误差建模方法。用热弹性理论建立了电主轴轴承温度—热变形模型,将积分中值定理运用在轴向热误差建模中,得到了关键点温度—轴向热变形的线性模型,仅需一个传感器测量关键点温度就可得到主轴末端伸长量。分析电主轴径向和轴向误差机理,得到耦合热误差模型。设计了利用球杆仪快速测量电主轴热误差的新方法,将误差理论建模数据与实际测量数据作对比,验证了其可行性,并将热误差模型导入自主开发的外挂式误差补偿器中,实验表明加工孔径热误差降低了73.5%左右,证明该方法合理、有效。

It is difficult to model the thermal error of motorized spindle accurately,and most researches just focus on the axial thermal error and ignore the radial thermal error.Therefore,a method for establishing the model of thermal error is proposed by using thermoelastic theory and mean-value theorem of integral of temperature field.The bearing temperature-thermal deformation model of the motorized spindle is formulated by using the thermoelastic theory.Then,the mean-value theorem of integral is used in the axial thermal error modeling.Therefore,a linear model of spindle temperature and axial thermal deformation is obtained,and the elongation of the end of the spindle could be achieved only by measuring the temperature of key points.The mechanism of radial and axial errors generation of the motorized spindle is analyzed to get the coupled thermal error model.A novel method for measuring thermal error of the motorized spindle by using a ballbar is presented.The feasibility is evaluated by comparing the error theoretical modeling data with the actual measurement data and the error model is imported into the developed independently external-hanging error compensator.Experimental results show that the thermal error of machining the hole’s radial-error is reduced by about 73.5%,which shows that the method is reasonable and effective.