Abstract
To address the thermal deformation of machine tool components, a thermal error prediction model based on the ROA-LSSVM network was proposed. First of all, the heat transfer mechanism of the linear feed system was analyzed. By analyzing temperature distribution characteristics during the heat transfer process, the best temperature measurement point position was determined to ensure that the thermal error could be accurately predicted. Secondly, in order to build a prediction model with high accuracy and strong robustness, Raccoon optimization algorithm (ROA) was proposed to optimize the hyperparameters of the least square support vector machine (LSSVM) network model, which was difficult to determine the kernel function and penalty function. Finally, the experiment was measured on a VDL-600A machining center, and the accuracy and practicability of the proposed thermal error prediction model were verified by the thermal deformation in the measurement process. The experimental results show that The ROA-LSSVM model reduces the RMSE by 42% compared with the LSSVM network and 45% compared with the SVM network.
You have full access to this open access chapter, Download conference paper PDF
Keywords
- Machining centers
- Heat conduction mechanism
- Thermal error of linear shaft
- ROA-LSSVM model
- Prediction of thermal error
1 Introduction
CNC machine tools are known as “industrial mother-machines”, which significantly impact manufacturing advancement [1]. Many studies have shown that the influence of thermal error on the machining accuracy of machine tools is as high as 40–70% [2]. Therefore, it is important to reduce the influence of thermal error on the machining accuracy of the machine tool.
Researchers [3,4,5,6] at home and abroad have conducted in-depth research on thermal error compensation technology. To effectively implement thermal error compensation, it is crucial to establish a precise thermal error model. Scholars [7,8,9,10] generally use neural networks, support vector machines, multiple regression and grey theory to establish thermal error models. however, a substantial number of temperature sensors must be strategically positioned during testing, and the subsequent sncreeing of heat sensitive points should be carried out.
However, there are many problems in the selection of conventional temperature measurement points, more sensor wiring and collinearity between measurement points, therefore, to address these issues, this study examines the heat source of the linear feed system using the heat transfer mechanism and identifies the optimal thermal sensitive point to enhance the precision of the thermal error model. Moreover, A new algorithm (ROA) combined with the thermal error prediction model of least square support vector Machine (LSSVM) is proposed to optimize the kernel function, penalty function and relaxation variables of the network. Finally, thermal error measurement tests are carried out on a VDL-600A vertical machining center to verify the reliability of the proposed method.
2 Temperature Field Analysis of Feed System Based on Heat Conduction Mechanism
2.1 Temperature Field Analysis of the Feed System
As depicted in Fig. 1, the ball screw is dispersed into m lead screw units Si (i = 1 2… m), each segment length is S, the length of the non-moving end of the lead screw motor end is S0, and the length of the non-moving end of the other side is SM. the heat transfer mode is shown in Fig. 2.
Take Δs within the travel range of the lead screw, and the energy conservation relationship within Δt time is:
where, ΔU represents the change of internal energy in the range of Δs; Qf (s,t) represents the friction heat generated by the nut; Qcd(s,t) represents the heat conduction of the micro end of the lead screw Δs to the adjacent sides; Qcv(s,t) represents the heat pair flow between the lead screw and the surrounding air in the state of motion; Qr(s,t) represents the amount of thermal radiation between Δs and the surrounding air.
Take a Si segment of the lead screw for analysis, and the change in internal energy of the lead screw between time (t−Δt, t) is::
where, c is the specific heat capacity and the value is 460 J/kg · ℃; ρ indicates the density of the lead screw, the value is 7850 (kg/m3); R is the screw diameter value of 40 mm, Qf (s, t) calculation formula is as follows:
where, qf(s,t) represents the average heat generated within the travel of the lead screw, and its value is 42 W.
The calculation for heat conductivity Qcd (s, t) is as follows:
where, k value is 71.568 (W/m · ℃), The formula for Qr is:
where, Ta(t) represents the ambient temperature around the lead screw at time t. the value of cr is 5.667 × 10–8 W/(m2 · K4). The calculation formula of Qcv(s,t) is as follows:
where, hcv value is 60.47 (W/m · ℃). after calculation and analysis, considering the influence of heat source on bearing seat with fixed end, T(0, t) = TS0−τj is required; considering the influence of free end bearing seat, T(L, t) = TSM−τj, and Ta(t) = Ta−τj should be guaranteed.
3 Thermal Error Measurement Experiment of Feed Shaft
3.1 Measurement of Thermal Error of Linear Feed Shaft
This paper takes the X-axis of machining center of VDL-600A vertical milling machine as the research object to measure the thermal positioning error of linear feed shaft of machine tool. field measurement is shown in Fig. 3, the location of the temperature sensor is shown in Fig. 4.
In the process of experimental measurement, the NI-5910 temperature acquisition system was used for temperature collection, and the XL-80 laser interferometer was used for displacement collection.
The specific test process is as follows:
-
(1)
First, the positioning error of the X-axis in the initial state was measured. The test method is reciprocating measurement, each measurement point stays for 2 s, the reverse overstep is 5 mm, and the reverse gap was eliminated.
-
(2)
Make the X-axis reciprocate in the range of 50– 550 mm at a speed of 10000mm/min for 20 min;
-
(3)
The X-axis stops moving to test the positioning error of the X-axis;
-
(4)
Repeat steps (2) and (3) until the X-axis reaches thermal equilibrium.
In this experiment, three kinds of experiments at different constant speed are designed to investigate the impact of temperature on the thermal error of the feed system at various speeds.
Table 1 displayed the test conditions in detail.
3.2 Results of Thermal Error Measurement
Taking a measurement result as an example, The collected data includes temperature values and corresponding thermal error values as follows.
As can be seen from Fig. 5, With the increase of time, the temperature change of the bearing seat at the fixed end increases the most, reaching a maximum of 33.6 ℃, while the temperature rise of the free end changes little. and finally becomes stable after 220 min. It can be seen from Fig. 6 that the displacement curve and temperature change rule of the machine tool are basically the same during operation. With the passage of time, the thermal positioning error increases gradually. The displacement caused by heat tends to be stable after 200 min and reaches a maximum of 70 μm.
4 Heat Error Modeling with Raccoon-Optimized LSSVM
LSSVM is more sensitive to noise during model training, and the processing of noise is relatively poor. This may cause the training results to be affected by noise and the generalization performance is poor. Therefore, this paper uses raccoon optimization algorithm (ROA) to address the aforementioned challenges, Through the iterative process, the algorithm can search the optimal parameter combination of the least squares support vector machine model, thus improving the accuracy and generalization ability of the model.
5 Model Prediction and Evaluation
With the temperature variable and position of the best thermal sensitive points were determined as the input, and the established ROA-LSSVM model, LSSVM model and SVM neural network model were used to predict the thermal positioning error of the X feed axis. Thermal errors of X axis in 60 and 240 min predicted results and residual errors of each network model are shown in Fig. 7:
As Fig. 7 illustrates, it is evident that the predicted residual value of SVM network model is 10.9 μm at most. The maximum residual predicted by LSSVM model is 8.6 μm. After adjusting the LSSVM model using ROA algorithm, the fluctuation becomes significantly smaller, and the maximum residual is 1.9 μm.
The model’s goodness of fit was assessed according to the root-mean-square error RMSE, fitting coefficient R2, mean absolute error MAE and mean deviation MBE. The goodness of fit of each model is shown in Table 2.
As indicated in Table 2, Compared with SVM network, the RMSE of ROA-LSSVM model is reduced by 45%. Compared with the LSSVM network, the RMSE of the ROA-LSSVM model is reduced by 42%. It is proved that the thermal error prediction model of CNC machine tool linear axis based on ROA-LSSVM network has higher prediction accuracy.
6 Conclusions
-
(1)
In view of the difficulty in determining the thermal sensitive points, heat transfer analysis of the feed system is carried out using the heat conduction theory to simulate the heat transfer process more accurately, so that the modeling results are more close to the actual situation.
-
(2)
The thermal error prediction model based on ROA-LSSVM is established, and the least square support vector machine is improved by using ROA algorithm to iteratively refine the LSSVM prediction model parameters, which is difficult to determine parameters, easy to fall into overfitting and low prediction accuracy.
-
(3)
After the thermal error measurement experiment of VDL-600A vertical machining center, the heat transfer theory adopted provides a strong support for determining the thermal sensitive points of the linear feed system, and greatly enhances the accuracy of the network model. In addition, the ROA-LSSVM model avoids the random error caused by the empirical setting parameters, and the goodness of fit indexes are better than the traditional LSSVM model and SVM model. It has achieved a great breakthrough in forecasting accuracy.
References
Yang JG (2012) Current situation and prospect of error compensation technology for CNC machine tools. Aeronaut Manufact Technol 05:40–45. https://doi.org/10.16080/j.issn1671-833-x.2012.05.003
Guo SJ, Yang J, Qiao G et al (2022) Assembly deviation modelling to predict and trace the geometric accuracy of the precision motion system of a CNC machine tool. Mech Mach Theory 169. https://doi.org/10.1016/J.MECHMACHTHEORY.2021.104687
Fu GQ, Zheng Y, Zhou LF et al (2023) Look-ahead prediction of spindle thermal errors with on-machine measurement and the cubic exponential smoothing-unscented Kalman filtering-based temperature prediction model of the machine tools. Measurement 210. https://doi.org/10.1016/J.MEASUREMENT.2023.112536
Chen J, Fang H (2018) Research on thermal error compensation technology of CNC machine tools. Mech Des Manufact 2018(10):142–145. https://doi.org/10.19356/j.cnki.1001-3997.2018.10.037
Li K (2023) Accuracy detection and error compensation of CNC machine tools. Equipment Manag Maintenance 1:107–109. https://doi.org/10.16621/j.cnki.issn1001-0599.2023.01.41
Liu K, Song L, Han W et al (2022) Time-varying error prediction and compensation for movement axis of CNC machine tool based on digital twin. IEEE Trans Industr Inf 18(01):109–118. https://doi.org/10.1109/TII.2021.3073649
Fujishima M, Narimatsu K, Irino N et al (2018) Thermal displacement reduction and compensation of a turning center. CIRP J Manuf Sci Technol 22:111–115. https://doi.org/10.1016/j.cirpj.2018.04.003
Liu J, Ma C, Gui H et al (2023) Intelligent digital-twin prediction and reverse control system architecture for thermal errors enabled by deep learning and cloud-edge computing. Expert Syst Appl 225:120122. https://doi.org/10.1016/J.ESWA.2023.120122
Mayr J, Jedrzejewski J, Uhlmann E et al (2012) Thermal issues in machine tools. CIRP Ann 61(2):771–791. https://doi.org/10.1016/j.cirp.2012.05.008
Ma C, Zhao L, Mei XS et al (2016) Thermal error modeling of machine tool spindle based on particle swarm optimization and BP network. J Shanghai Jiaotong Univ (Chin Ed) 50(5):686–695. https://doi.org/10.16183/j.cnki.jsjtu.2016.05.007
Acknowledgements
Foundation Project: National Natural Science Foundation of China (52065053); Basic Research Funds for Universities directly under the Inner Mongolia Autonomous Region (ZTY2023005).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2024 The Author(s)
About this paper
Cite this paper
Ding, Q., Guo, S., Chen, G., Tang, S. (2024). Thermal Error Modeling Method of Machining Center Linear Axis for Heat Conduction Mechanism. In: Halgamuge, S.K., Zhang, H., Zhao, D., Bian, Y. (eds) The 8th International Conference on Advances in Construction Machinery and Vehicle Engineering. ICACMVE 2023. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-97-1876-4_99
Download citation
DOI: https://doi.org/10.1007/978-981-97-1876-4_99
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-97-1875-7
Online ISBN: 978-981-97-1876-4
eBook Packages: EngineeringEngineering (R0)