A fusion algorithm of corrected J-T model and DBN network for precision prediction of spindle assembly

The high-speed winding machine spindle is the core component of the entire winding machine, and its assembly precision directly determines the working performance and service life of the entire machine. However, its assembly process is complex, and there are many sources of errors, which makes it difficult to predict the assembly precision. This article aims to propose a new method to solve this problem. This article adopts a mechanism-data fusion approach. On one hand, a corrected Jacobian-Torsor (J-T) model, based on Jacobian torsor theory, is established to describe the spindle shaft assembly error transfer mechanism under parallel relationships, correcting the range of variation of its spin volume. On the other hand, the mechanism model is used as a basis to expand the measured data, solving the small sample problem of the data model. Simultaneously, the data model compensates for the mechanism model. A prediction model combining deep belief neural networks and a two-layer BP neural network is introduced. The mechanism model is further adjusted based on the measured data, taking into account the influence of non-geometric feature elements on assembly error propagation. Comparing with the measured assembly data of a certain type of spindle, the results show that, in terms of prediction accuracy, the average error of the prediction method in this paper is 0.016 mm compared to 0.0985 mm for the conventional J-T model, which indicates a reduction in the average error by about 83.75%. In terms of data model comparison, compared with the BP neural network and DBN-SVR models, the model in this paper reduces the average prediction error by about 76.27% and 70.89%, respectively, which validates the effectiveness of the proposed method. This fusion-based approach shows more promise in predicting assembly accuracy with higher precision, providing a more reliable tool for high-speed winder spindle assembly.