Thermal error prediction method for spindles in machine tools based on a hybrid model

Abstract

Thermal error is one of the major sources of machining inaccuracy. It becomes the dominant source of error and therefore should be predicted and compensated for. This article proposes a vector-angle-cosine hybrid model for thermal error prediction. The model combines the advantages of different constituent models and makes full use of the original measurement results. A multivariable linear regression model, a natural exponential model, and the finite element method are chosen as the three constituent models, and their advantages and disadvantages are demonstrated in detail. The combination weights of the three constituent models are determined by maximizing the cosine value of the angle between the vector-angle-cosine prediction vector and the actual thermal error vector. Experiments on spindle thermal errors are conducted to build and validate the proposed model. The performance comparison between the vector-angle-cosine hybrid model and the three constituent models indicates that the former has better accuracy and robustness under different working conditions. Some actual machining tests are conducted pre- and post compensation, and results show that the size errors are decreased by 60%.