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.