Establishment of Low-Cost and Stable Prediction Models Applied for Thermal Displacements in Three Axes

Thermal errors make a great impact on the machining accuracy of machine tools. In order to effectively reduce the thermal errors, the establishment of prediction models is needed to predict the thermal errors of the spindle based on the relationship between temperature and thermal deformation. In this study, a low-cost capturing device is used to collect temperature at multiple points and thermal displacements in three axes caused by thermal deformation. In addition to the establishment of prediction thermal displacement models in three axes, this research also studies the stability of the capturing device. A CNC lathe is used to measure temperature and displacement during a long period of the experiment, Feedforward Neural Network (FNN) and Support Vector Regression (SVR) are used to establish prediction thermal displacement models, and four indicators,
${R}^{2}$
,
RMSE
,
MSE
,
MAE
, are used to verify the predictive ability applied for thermal deformation. The experimental results show the best predictive ability found in the Fine Gaussian SVM in SVR, where
${R}^{2}$
is 0.93515. Finally, the verification experiment is carried out at the same rotational speed, and the actual values are compared and analyzed with the average thermal errors with simulated compensation. The experimental results show that the average of thermal errors on the Z-axis is within
$45.7356\mu \text{m}$
to
$- 2.4064\mu \text{m}$
, the average of thermal errors on the Y-axis is within
$- 6.4129\mu \text{m}$
to
$- 1.4436\mu \text{m}$
, and the average of thermal errors on the X-axis is within
$- 0.9863\mu \text{m}$
to
$0.1171\mu \text{m}$
, with thermal errors in three axes all effectively reduced.