Skip to main content
SpringerLink
Log in

A novel approach to the thermal-deformation coupling calculation of the high-speed spindle-bearing system

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

It has a positive impact on the machining accuracy to predict precisely the thermal error caused by the temperature change for the high-speed spindle-bearing system. In this paper, the dual reciprocity method (DRM) based on compactly supported radial basis functions (CSRBFs) and the line integration boundary element method (LIM-BEM) are presented for the thermal-deformation coupling calculation. The essential idea of this method is building the thermal-deformation coupling model only by the boundary information and obtaining results by line integrals. In this process, the boundary element model discretized by the discontinuous iso-parametric quadratic boundary element is established. Then, the transient temperature is calculated by the CSRBFs-DRM, and the thermo-elastic deformation is done by the LIM-BEM, under the exact calculation of the heat generation and the thermal contact resistance. To validate the effectiveness, thermal-deformation coupling experiments are conducted. The proposed method is compared with experimental data and the finite element method. The result shows that the proposed model is more appropriate for the thermal-deformation coupling calculation for the satisfactory universality and accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

The datasets generated during the current study are not publicly available but are available from the corresponding author on reasonable request.

References

  • An, Z., Yu, T., Bui, T.Q., Wang, C., Trinh, N.A.: Implementation of isogeometric boundary element method for 2-D steady heat transfer analysis. Adv. Eng. Softw. 116, 36–49 (2018)

    Article  Google Scholar 

  • Baranoglu, B., Mengi, Y.: The use of dual reciprocity boundary element method in coupled thermoviscoelasticity. Comput. Methods Appl. Mech. Eng. 196(1–3), 379–392 (2006)

    Article  MATH  Google Scholar 

  • Bossmanns, B., Tu, J.F.: A thermal model for high speed motorized spindles. Int. J. Mach. Tools Manuf. 39(9), 1345–1366 (1999)

    Article  Google Scholar 

  • Chen, C.S., Brebbia, C.A., Power, H.: Dual reciprocity method using compactly supported radial basis functions. Commun. Numer. Methods Eng. 15, 137 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, X.-W., Yuan, Z.-C., Peng, H.-F., Cui, M., Yang, K.: Isoparametric closure elements in boundary element method. Comput. Struct. 168, 1–15 (2016)

    Article  Google Scholar 

  • Gnitko, V., Degtyariov, K., Karaiev, A., Strelnikova, E.: Multi-domain boundary element method for axisymmetric problems in potential theory and linear isotropic elasticity. WIT Trans. Eng. Sci. 122, 13–25 (2019)

    MathSciNet  MATH  Google Scholar 

  • Grujicic, M., Zhao, C.L., Dusel, E.C.: The effect of thermal contact resistance on heat management in the electronic packaging. Appl. Surf. Sci. 246(1–3), 290–302 (2005). https://doi.org/10.1016/j.apsusc.2004.11.030

    Article  Google Scholar 

  • Hamzehei Javaran, S., Khaji, N.: Dynamic analysis of plane elasticity with new complex Fourier radial basis functions in the dual reciprocity boundary element method. Appl. Math. Model. 38(14), 3641–3651 (2014). https://doi.org/10.1016/j.apm.2013.12.010

    Article  MathSciNet  MATH  Google Scholar 

  • Khan, S., Khan, M.R., Alqahtani, A.M., Shah, H.H., Issakhov, A., Shah, Q., et al.: A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation. AIMS Math. 6(11), 12560–12582 (2021). https://doi.org/10.3934/math.2021724

    Article  MathSciNet  MATH  Google Scholar 

  • Khanbabazadeh, H., Iyisan, R., Ozaslan, B.: 2D seismic response of shallow sandy basins subjected to obliquely incident waves. Soil Dyn. Earthq. Eng. 153, 107080 (2022)

    Article  Google Scholar 

  • Lei, J., Yun, L., Zhang, C.: An interaction integral and a modified crack closure integral for evaluating piezoelectric crack-tip fracture parameters in BEM. Eng. Anal. Boundary Elem. 79, 88–97 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Li, H., Shin, Y.C.: integrated dynamic thermo-mechanical modeling of high speed spindles, part 1: model development. J. Manuf. Sci. Eng. 126(1), 148–158 (2004a). https://doi.org/10.1115/1.1644545

    Article  Google Scholar 

  • Li, H., Shin, Y.C.: Integrated dynamic thermo-mechanical modeling of high speed spindles, part 2: solution procedure and validations. J. Manuf. Sci. Eng. 126(1), 159–168 (2004b). https://doi.org/10.1115/1.1644546

    Article  Google Scholar 

  • Li, X., Li, H., Hong, J., Zhang, Y.: Heat analysis of ball bearing under nonuniform preload based on five degrees of freedom quasi-static model. Proc. Inst. Mech. Eng. Part j J. Eng. Tribol. 230(6), 709–728 (2015). https://doi.org/10.1177/1350650115611155

    Article  Google Scholar 

  • Li, X., Liu, J., Li, C., Hong, J., Wang, D.: Research on the influence of air-gap eccentricity on the temperature field of a motorized spindle. Mech. Sci. 12(1), 109–122 (2021a)

    Article  Google Scholar 

  • Li, Y., Zhang, Y., Zhao, Y., Shi, X.: Thermal-mechanical coupling calculation method for deformation error of motorized spindle of machine tool. Eng. Fail. Anal. 128, 105597 (2021b). https://doi.org/10.1016/j.engfailanal.2021b.105597

    Article  Google Scholar 

  • Liu, J., Ma, C., Wang, S., Wang, S., Yang, B., Shi, H.: Thermal-structure interaction characteristics of a high-speed spindle- bearing system. Int. J. Mach. Tools Manuf. 137, 42–57 (2019). https://doi.org/10.1016/j.ijmachtools.2018.10.004

    Article  Google Scholar 

  • Liu, W., Bornassi, S., Shen, Y., Ghalandari, M., Haddadpour, H., Firouzabadi, R.D., et al.: Investigation on behaviors of acoustoelastic cavities using a novel reduced finite element–dual reciprocity boundary element formulation. Eng. Appl. Comput. Fluid Mech. 15(1), 1885–1901 (2021)

    Google Scholar 

  • Ma, C., Mei, X., Yang, J., Zhao, L., Shi, H.: Thermal characteristics analysis and experimental study on the high-speed spindle system. Int. J. Adv. Manuf. Technol. 79(1–4), 469–489 (2015a). https://doi.org/10.1007/s00170-015-6821-z

    Article  Google Scholar 

  • Ma, C., Yang, J., Zhao, L., Mei, X., Shi, H.: Simulation and experimental study on the thermally induced deformations of high-speed spindle system. Appl. Therm. Eng. 86, 251–268 (2015b)

    Article  Google Scholar 

  • Makarov, S.N., Noetscher, G.M., Raij, T., Nummenmaa, A.: A quasi-static boundary element approach with fast multipole acceleration for high-resolution bioelectromagnetic models. IEEE Trans. Biomed. Eng. 65(12), 2675–2683 (2018)

    Article  Google Scholar 

  • Ostanin, I.A., Mogilevskaya, S.G., Labuz, J.F., Napier, J.: Complex variables boundary element method for elasticity problems with constant body force. Eng. Anal. Boundary Elem. 35(4), 623–630 (2011). https://doi.org/10.1016/j.enganabound.2010.11.008

    Article  MathSciNet  MATH  Google Scholar 

  • Ping, P., Peng, R., Kong, D., Chen, G., Wen, J.: Investigation on thermal management performance of PCM-fin structure for Li-ion battery module in high-temperature environment. Energy Convers. Manag. 176, 131–146 (2018)

    Article  Google Scholar 

  • Sutradhar, A., Paulino, G.H., Gray, L.J.: Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method. Eng. Anal. Boundary Elem. (2002). https://doi.org/10.1016/S0955-7997(01)00090-X

    Article  MATH  Google Scholar 

  • Than, V.-T., Wang, C.-C., Ngo, T.-T., Huang, J.H.: Estimating time-varying heat sources in a high speed spindle based on two measurement temperatures. Int. J. Therm. Sci. 111, 50–65 (2017). https://doi.org/10.1016/j.ijthermalsci.2016.08.004

    Article  Google Scholar 

  • Wang, Q., Zhou, W., Cheng, Y., Ma, G., Chang, X.: Line integration method for treatment of domain integrals in 3D boundary element method for potential and elasticity problems. Eng. Anal. Boundary Elem. 75, 1–11 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, Q., Zhou, W., Cheng, Y., Ma, G., Chang, X.: NURBS-enhanced line integration boundary element method for 2D elasticity problems with body forces. Comput. Math. Appl. 77(7), 2006–2028 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Yan, K., Hong, J., Zhang, J., Mi, W., Wu, W.: Thermal-deformation coupling in thermal network for transient analysis of spindle-bearing system. Int. J. Therm. Sci. 104, 1–12 (2016)

    Article  Google Scholar 

  • Yang, Y., Du, Z., Feng, X., Yang, J.: Real-time thermal modelling approach of a machine tool spindle based on bond graph method. Int. J. Adv. Manuf. Technol. 113(1–2), 99–115 (2021). https://doi.org/10.1007/s00170-021-06611-8

    Article  Google Scholar 

  • Yu, B., Cao, G., Huo, W., Zhou, H., Atroshchenko, E.: Isogeometric dual reciprocity boundary element method for solving transient heat conduction problems with heat sources. J. Comput. Appl. Math. 385, 113197 (2021). https://doi.org/10.1016/j.cam.2020.113197

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng, D.-X., Chen, W.F.: Effect of structure and assembly constraints on temperature of high-speed angular contact ball bearings with thermal network method. Mech. Syst. Signal Process. (2020). https://doi.org/10.1016/j.ymssp.2020.106929

    Article  Google Scholar 

  • Zhou, W., Yue, Q., Wang, Q., Feng, Y.T., Chang, X.: The boundary element method for elasticity problems with concentrated loads based on displacement singular elements. Eng. Anal. Boundary Elem. 99, 195–205 (2019). https://doi.org/10.1016/j.enganabound.2018.11.016

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou, C., Qu, Z., Hu, B., Li, S.: Thermal network model and experimental validation for a motorized spindle including thermal–mechanical coupling effect. Int. J. Adv. Manuf. Technol. (2021). https://doi.org/10.21203/rs.3.rs-159145/v1

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R&D Program of China (No. 2021YFB2011000), the National Natural Science Foundation of China under Grant (Nos. 52205281 and 52075248), Natural Science Foundation of Shaanxi Province under Grant (No. 2021JZ-02), Two-chain Fusion high-end machine tool projects of Shaanxi Province under Grant (2021LLRh-01-02), Major Science and technology projects of Shaanxi Province of China (No. 2018zdzx01-02-01HZ01). The authors express their gratitude for their support.

Author information

Authors and Affiliations

  1. Key Laboratory of Education Ministry for Modern Design & Rotor-Bearing System, Xi’an Jiaotong University, Xi’an, China

    Ziquan Zhan, Bin Fang, Shaoke Wan, Yu Bai, Jun Hong & Xiaohu Li

  2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, China

    Ziquan Zhan, Bin Fang, Shaoke Wan, Yu Bai, Jun Hong & Xiaohu Li

Authors
  1. Ziquan Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shaoke Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jun Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiaohu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Bin Fang or Xiaohu Li.

Ethics declarations

Conflict of interest

No conflict of interest exits in the submission of this manuscript.

Consent for publication

The manuscript is entitled “A novel approach to the thermal-deformation coupling calculation of the high-speed spindle-bearing system”. The manuscript has not been published elsewhere, and it has not been submitted simultaneously for publication elsewhere.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhan, Z., Fang, B., Wan, S. et al. A novel approach to the thermal-deformation coupling calculation of the high-speed spindle-bearing system. Int J Mech Mater Des 19, 391–406 (2023). https://doi.org/10.1007/s10999-022-09634-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-022-09634-5

Keywords

Search

Navigation