Journal of Central South University

, Volume 26, Issue 1, pp 168–183 | Cite as

Modeling and application of thermal contact resistance of ball screws

  • Xiang-sheng Gao (高相胜)Email author
  • Min Wang (王民)
  • Xue-bin Liu (刘学滨)


Aiming at determining the thermal contact resistance of ball screws, a new analytical method combining the minimum excess principle with the MB fractal theory is proposed to estimate thermal contact resistance of ball screws considering microscopic fractal characteristics of contact surfaces. The minimum excess principle is employed for normal stress analysis. Moreover, the MB fractal theory is adopted for thermal contact resistance. The effectiveness of the proposed method is validated by self-designed experiment. The comparison between theoretical and experimental results demonstrates that thermal contact resistance of ball screws can be obtained by the proposed method. On this basis, effects of fractal parameters on thermal contact resistance of ball screws are discussed. Moreover, effects of the axial load on thermal contact resistance of ball screws are also analyzed. The conclusion can be drawn that the thermal contact resistance decreases along with the fractal dimension D increase and it increases along with the scale parameter G increase, and thermal contact resistance of ball screws is retained almost constant along with axial load increase before the preload of the right nut turns into zero in value. The application of the proposed method is also conducted and validated by the temperature measurement on a self-designed test bed.

Key words

ball screw fractal theory thermal contact resistance contact stress preload 



为了求解滚珠丝杠副的接触热阻,提出了一种基于最小余能原理和MB 分形理论的解析方法。 该方法在求解接触热阻时可考虑接触面的微观分形特征。采用最小余能原理求解法向应力分布,进而 采用MB 分形理论求解接触热阻。通过自行设计实验验证了该方法的有效性。理论和实验的结果对比 说明,该方法可准确获得滚珠丝杠副接触热阻。在此基础上,讨论了分形参数对滚珠丝杠副接触热阻 的影响,分析了螺母轴向载荷对滚珠丝杠副的接触热阻的影响。结果表明,接触热阻随着分形参数D 的增加而减小,随着尺度参数G 的增加而增加。在右螺母预紧力变为零之前,滚珠丝杠副接触热阻随 着轴向载荷的增加几乎保持不变。最后,开展了该建模方法在自行设计试验台的应用,开展了相应的 温度测试,进一步验证了该方法的有效性。


滚珠丝杠副 分形理论 接触热阻 接触应力 预紧力 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    ZHANG Hui-jie, ZHANG Jun, LIU Hui, LIANG Tao, ZHAO Wan-hua. Dynamic modeling and analysis of the high-speed ball screw feed system [J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2015, 229(5): 870–877.Google Scholar
  2. [2]
    ZHANG Jun, LI Bo, ZHOU Chang-xing, ZHAO Wan-hua. Positioning error prediction and compensation of ball screw feed drive system with different mounting conditions [J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2016, 230(12): 2307–2311.Google Scholar
  3. [3]
    ATTIA M H, KOPS L. On the role of fixed joints in thermal deformation of machine tool structures [J]. Annals of the CIRP, 1978, 27(1): 305–310.Google Scholar
  4. [4]
    LI Fu-ping, LI Ying, LIU Zhi-feng, HU Qiu-shi, LIU Jian-yong, LI Yan. Thermodynamic performance analysis and improvement for cross-saddle type slide of electric discharge machine [J]. Vibroengineering Procedia, 2015, 5: 9–14.Google Scholar
  5. [5]
    MIN X, JIANG S. A thermal model of a ball screw feed drive system for a machine tool [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011, 225(1): 186–193.Google Scholar
  6. [6]
    BOSSMANNS B, TU J F. A thermal model for high speed motorized spindles [J]. International Journal of Machine Tools & Manufacture, 1999, 39(9): 1345–1366.Google Scholar
  7. [7]
    JIN Chao, WU Bo, HU You-min, YI Peng-xing, CHENG Yao. Thermal characteristics of a CNC feed system under varying operating conditions [J]. Precision Engineering, 2015, 42(4): 151–164.Google Scholar
  8. [8]
    JIANG S, ZHENG Y. An analytical model of thermal contact resistance based on the Weierstrass-Mandelbrot fractal function [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2010, 224(4): 959–967.Google Scholar
  9. [9]
    XU Rui-ping, XU Lie, ZHAO Lan-ping. Fractal description of thermal contact resistance between rough surfaces [J]. Journal of Shanghai Jiao Tong University, 2004, 38(10): 1609–1612. (in Chinese)Google Scholar
  10. [10]
    ZOU Ming-qing, YU Bo-ming, CAI Jian-chao, XU Peng. Fractal model for thermal contact conductance [J]. Journal of Heat Transfer, 2008, 130(10): 101301.Google Scholar
  11. [11]
    LIU Zhi-feng, PAN Ming-hui, ZHANG Ai-ping, ZHAO Yong-sheng, YANG Yong, MA Cheng-yu. Thermal characteristic analysis of high-speed motorized spindle system based on thermal contact resistance and thermalconduction resistance [J]. International Journal of Advanced Manufacturing Technology, 2015, 76(9–12): 1913–1926.Google Scholar
  12. [12]
    CUI Ling-li, HUANG Jin-feng, ZHANG Fei-bin. Quantitative and localization diagnosis of a defective ball bearing based on vertical-horizontal synchronization signal analysis [J]. IEEE Transactions on Industrial Electronics, 2017, 64(11): 8695–8705.Google Scholar
  13. [13]
    WEN Shu-tao, TAN Yi, SHI Shuang, DONG Wei, JIANG Da-chuan, LIAO Jiao, ZHU Zhi. Thermal contact resistance between the surfaces of silicon and copper crucible during electron beam melting [J]. International Journal of Thermal Sciences, 2013, 74(6): 37–43.Google Scholar
  14. [14]
    SALGON J, ROBBE-VALLOIRE F, BLOUET J, BRANSIER J. A mechanical and geometrical approach to thermal contact resistance [J]. International Journal of Heat and Mass Transfer, 1997, 40(5): 1121–1129.zbMATHGoogle Scholar
  15. [15]
    SADEGHIFAR H, DJILALI N, BAHRAMI M. A new model for thermal contact resistance between fuel cell gas diffusion layers and bipolar plates [J]. Journal of Power Sources, 2014, 266: 51–59.Google Scholar
  16. [16]
    SADEGHIFAR H, DJILALI N, BAHRAMI M. Counter-intuitive reduction of thermal contact resistance with porosity: A case study of polymer electrolyte membrane fuel cells [J]. International Journal of Hydrogen Energy, 2016, 41(16): 6833–6841.Google Scholar
  17. [17]
    TANG Qing-yun, ZHANG Wei-fang. The effect of pressure on thermal contact conductance of superalloys under high temperature [J]. International Journal of Heat and Mass Transfer, 2016, 103: 1208–1213.Google Scholar
  18. [18]
    MO Jing-wen, BAN Heng. Measurements and theoretical modeling of effective thermal conductivity of particle beds under compression in air and vacuum [J]. Case Studies in Thermal Engineering, 2017, 10: 423–433.Google Scholar
  19. [19]
    ZHANG Guo-dong, ALBERDI R, KHANDELWAL K. Analysis of three-dimensional curved beams using isogeometric approach [J]. Engineering Structures, 2016, 117(15): 560–574.Google Scholar
  20. [20]
    CHERN S S, CHEN W H, LAM K S. Lectures on differential geometry [M]. Singapore: World Scientific, 2000.Google Scholar
  21. [21]
    CONDE B, DROSOPOULOS G A, STAVROULAKIS G E, RIVEIRO B, STAVROULAKI M E. Inverse analysis of masonry arch bridges for damaged condition investigation: Application on Kakodiki bridge [J]. Engineering Structures, 2016, 127(15): 388–401.Google Scholar
  22. [22]
    POLONSKY I A, KEER L M. A numerical method for solving rough contact problems based on multi-level multi-summation and conjugate gradient techniques [J]. Wear, 1999, 231(2): 206–219.Google Scholar
  23. [23]
    JOHNSON K L. Contact mechanics [M]. London: Cambridge University Press, 1985.Google Scholar
  24. [24]
    LIU Shuang-biao, WANG Qian. Study contact stress fields caused by surface tractions with a discrete convolution and fast Fourier transform algorithm [J]. ASME Journal of Tribology, 2002, 124(1): 36–45.Google Scholar
  25. [25]
    TIAN Xue-feng, BHUSHAN B. A numerical threedimensional model for the contact of rough surfaces by variational principle [J]. ASME Journal of Tribology, 1996, 118(1): 33–42.Google Scholar
  26. [26]
    STANLEY H M, KATO T. An FFT-based method for rough surface contact [J]. ASME Journal of Tribology, 1997, 119(3): 481–485.Google Scholar
  27. [27]
    NOCEDAL J, WIGHT S. Numerical optimization [M]. Beijing: Science Press, 2006.Google Scholar
  28. [28]
    ZHANG Xue-liang, HUANG Yu-mei, HAN Ying. Fractal model of the normal contact stiffness of machine joint surfaces based on the fractal contact theory [J]. China Mechanical Engineering, 2000, 11(7): 727–729. (in Chinese)Google Scholar
  29. [29]
    WANG S, KOMVOPOULOS K. A fractal theory of the interfacial temperature distribution in the slow sliding regime: part II—multiple domains, elastoplastic contacts and applications [J]. ASME Journal of Tribology, 1994, 116(4): 824–832.Google Scholar
  30. [30]
    MAJUMDAR A, BHUSHAN B. Fractal model of elastic–plastic contact between rough surfaces [J]. ASME Journal of Tribology, 1991, 113(1): 1–11.Google Scholar
  31. [31]
    GE Shi-rong, ZHU Hua. Fractal theory in tribology [M]. Beijing: China Machine Press, 2005. (in Chinese)Google Scholar
  32. [32]
    HU Jian-zhong. Study on the accuracy degradation mechanism of the ball screw mechanism [D]. Beijing: Beijing University of Technology, 2014. (in Chinese)Google Scholar
  33. [33]
    WEI Chung-chin, LIN Jen-fin, HORNG Jeng-haur. Analysis of a ball screw with a preload and lubrication [J]. Tribology International, 2009, 42(11, 12): 1816–1831.Google Scholar
  34. [34]
    OYANGUREN A, LARRANAGA J, ULACIA I. Thermomechanical modelling of ball screw preload force variation in different working conditions [J]. The International Journal of Advanced Manufacturing Technology, 2018, 97(1–4): 723–739.Google Scholar
  35. [35]
    GAO Xiang-sheng. Research on dynamic and thermal characteristics of high-speed machining centers and their key components [D]. Beijing: Beihang University, 2013. (in Chinese)Google Scholar
  36. [36]
    SHI Hu, ZHANG Dong-sheng, YANG Jun, MA Chi, MEI Xue-song, GONG Guo-fang. Experiment-based thermal error modeling method for dual ball screw feed system of precision machine tool [J]. The International Journal of Advanced Manufacturing Technology, 2016, 82(9–12): 1693–1705.Google Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Advanced Manufacturing Technology, College of Mechanical Engineering and Applied Electronics TechnologyBeijing University of TechnologyBeijingChina
  2. 2.Beijing Key Laboratory of Electrical Discharge Machining TechnologyBeijingChina

Personalised recommendations