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Residual learning of the dynamics model for feeding system modelling based on dynamic nonlinear correlate factor analysis

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Abstract

Feeding system modelling is the foundation for control strategy optimization, contour error compensation, etc., to improve the productivity and quality of a part. This paper proposes a novel residual learning approach for fitting the simulation error of the dynamics model of a machine tool feeding system. Then, the feeding system model consisting of the dynamics model and the residual model is constructed by integrating prior knowledge with statistical learning knowledge. The residual model is trained by using the training dataset generated from the dynamics model instead of using only the input and output data (i.e., the end-to-end data). In addition, a dynamic nonlinear correlate factor extraction method is proposed to extract the training dataset from the dynamics model and the reference data. Compared to the end-to-end data, the training dataset knows very well about the system’s nonlinear features owing to the internal prior knowledge of the dynamics model. Experiments conducted on a vertical milling centre confirm the effectiveness of the feeding system model in dynamic response prediction. Compared to the existing dynamics or data-driven modelling method, the proposed method can achieve higher prediction accuracy in nonlinear motion processes, such as the reverse process, and can obtain stable performance with respect to different feedrates owing to the residual learning approach.

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Acknowledgements

This research was supported by the National Science and Technology Major Project [grant number 2018ZX04035002-002] and the National Natural Science Foundation of China [grant numbers 51575210 and 51675204].

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Authors and Affiliations

  1. National Numerical Control System Engineering Research Center, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yakun Jiang, Jihong Chen, Huicheng Zhou, Jianzhong Yang & Guangda Xu

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  1. Yakun Jiang
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  2. Jihong Chen
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  3. Huicheng Zhou
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Correspondence to Huicheng Zhou.

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Appendices

Appendix 1. Machine tool feeding system

Based on a part program, the CNC system decomposes the contour to each single-axis reference position, u, which is fed to the machine tool feeding system. As illustrated in Appendix Fig. 20, the feeding system, as the core component of a machine tool, consists of mechanical transmission elements, a servo motor and its controller. Compared to the output position,w′, detected by the rotary encoder, the actual position,w, representing the position of the worktable, can reflect the true size of a part because of the errors caused by the mechanical transmission elements [13] are included.

Fig. 20
figure 20

The structure of the machine tool feeding system

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In the work described here, the model of the feeding system is used to predict the actual position, w. To build an accurate model of the feeding system, the key challenges are decreasing the contour error in the nonlinear motion process and achieving stable prediction performance with different feedrates.

Appendix 2. Parameters and their identification results

Owing to the residual model for modelling the simulation error of the dynamics model, the parameters of the dynamics model do not need to be accurately identified. Therefore, the models for the servo drive and servo motor were built based on their design parameters. The main parameters of the mechanical transmission elements identified by using the least squares estimation (LSE) method [33] for the X- and Y-axis are given in Appendix Tables 4 and 5, respectively. Otherwise, the other parameters were set up by using the default values.

Table 4 Parameters and their identification results for the X-axis
Full size table
Table 5 Parameters and their identification results for the Y-axis
Full size table

Appendix 3. Associated parameters of the NURBS curves

Heart contour: Order: k = 4, knot vector: {0, 0, 0, 0.15, 0.5, 0.5, 0.85, 1, 1, 1}; control points (x, y): {(0.0, 0.0), (−20.0, 50.0), (40.0, 20.0), (75.0, 0.0), (40.0, 20.0), (−20.0, 50.0), (0.0, 0.0)}; weights: {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0}.

Goggles contour: Order: k = 4, knot vector: {0, 0, 0, 0.15, 0.3, 0.45, 0.6, 0.75, 0.9,1,1, 1}; control points (x, y): {(0.0, 0.0), (10.0, −40.0), (40.0, −10.0), (70.0, −40.0), (80.0, 0.0), (70.0, 10.0), (40.0, 20.0), (10.0,10.0), (0.0, 0.0)}; weights: {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0}.

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Jiang, Y., Chen, J., Zhou, H. et al. Residual learning of the dynamics model for feeding system modelling based on dynamic nonlinear correlate factor analysis. Appl Intell 51, 5067–5080 (2021). https://doi.org/10.1007/s10489-020-02096-2

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