Abstract: Existing measurement and modeling methods for CNC machine tool rotational axis errors only considered the influences of multiple degrees of freedom(MDOF) static geometric errors or single degree of freedom thermal errors acting in isolation without accounting for the coupled effects, a simultaneous measurement and modeling for MDOF static/thermal errors in CNC machine tool rotational axes was proposed based on a double ball bar. Firstly, a model was developed to describe the variation in length of the double ball bar using homogeneous coordinate transformation. A static/thermal error identification model was constructed by solving a system of nonhomogeneous linear equations based on this model. Subsequently, to minimize the influences of thermal dissipation on the measurement results, a specific installation mode adapted to the simultaneous measurement of MDOF static/thermal errors was designed to reduce the installation time of the double ball bar. Additionally, a prediction model for MDOF static/thermal errors in rotational axis was established using a CNN-LSTM. Finally, experiments were conducted on the C-axis of a gear grinding machine to rapidly identify the rotational axis errors at various speeds. The accuracy of the prediction model was verified by utilizing the static/thermal error model to predict the errors of C-axis and the variation in length of the double ball bar. 

Key words: static/thermal error, error measurement, convolutional neural network long-short-term memory(CNN-LSTM), rotating axis, double ball bar

摘要： 针对现有的数控机床旋转轴误差测量与建模方法仅考虑多自由度静态几何误差或单自由度热误差单独作用的影响,未考虑几何误差和热误差耦合影响的问题,提出了一种基于球杆仪的数控机床旋转轴多自由度静/热误差同步测量与建模方法。首先基于齐次坐标变换建立球杆仪杆长变化模型,再基于该模型使用非齐次线性方程组建立静/热误差辨识模型;其次设计了适应多自由度静/热误差同步测量的球杆仪安装模式以缩短测量时间,减少热逸散对测量结果的影响;再次基于卷积长短期记忆神经网络（CNN-LSTM）建立旋转轴多自由度静/热误差预测模型;最后在数控蜗杆砂轮磨齿机的C轴上进行误差测量实验,对多种转速下的旋转轴多自由度误差进行快速辨识,并通过CNN-LSTM静/热误差预测模型对多自由度误差和球杆仪杆长变化进行预测，以验证所建模型的准确性。

关键词: 静/热误差, 误差测量, 卷积长短期记忆神经网络, 旋转轴, 球杆仪