机床主轴轴向热误差一阶自回归建模方法

First-order autoregressive modeling method for axial thermal error of machine tool spindle

摘要:

针对机床主轴热误差经验建模法缺乏物理意义,建模精度和鲁棒性受热变形伪滞后效应影响较大的问题,从理论角度推导出一种具有明确物理意义且不受伪滞后效应影响的主轴热误差建模方法。 将主轴简化为一维杆件,考虑主轴圆柱面与空气的对流散热,利用传热学得到一维杆在单端热源条件下温度场和热变形的解析表达式；对热变形表达式进行形式变换,推导得到一维杆在单端固定热源条件下热变形的一阶自回归表述形式；推导验证在变化热源条件下,一维杆热变形一阶自回归模型的有效性,并指出自回归模型系数与主轴物理特性、自回归时间间隔、热源条件的关系；进行有限元仿真,并在海德曼T65车床上进行实验验证。 仿真结果表明,一阶自回归模型可有效估计一维杆在变化热源条件下的热变形,不受伪滞后效应影响。 在T65车床上的实验结果表明,与多元线性回归模型相比,一阶自回归模型的鲁棒性更高且具有明确的物理意义。

Abstract:

To solve the problem that the empirical modeling for thermal error of machine tool spindle lacks physical significance, and the modeling accuracy and robustness are greatly affected by pseudo-hysteresis effect of thermal deformation, a modeling method for thermal error of machine tool spindle which has clear physical meaning and is not affected by pseudo-hysteresis effect is derived from theoretical perspective. Firstly, the spindle is simplified as a one-dimensional rod. Taking into account the convection between cylinder surface and air, the analytical solutions of temperature field and thermal deformation of the rod under the condition of single-end heat source are obtained by using heat transfer theory. Then the thermal deformation expression is transformed, and the first-order autoregressive model for the rod under the condition of single-end fixed heat source is derived. After that, the validity of the first-order autoregressive model for the thermal deformation of the rod under the condition of variable heat source is verified, and the relationship between the coefficients of the autoregressive model and the physical characteristics of the spindle, the time interval of the autoregressive model and the heat source is pointed out. Finally, finite element simulation is carried out, and the experimental verification is performed on Headman T65 lathe. The simulation results show that the first-order autoregressive model can effectively estimate the thermal deformation of the one-dimensional rod under the condition of variable heat source and is not affected by the pseudo-hysteresis effect. The experimental results on the T65 lathe show that, compared with multiple linear regression model, the first-order autoregressive model is more robust and has clear physical significance.