Research on Thermo-Mechanical Coupling Deformation for the Ball Screw of Machine Tool Spindle Feed System

  • Wenhua YeEmail author
  • Yunxia Guo
  • Ruijun Liang
  • Jianhua Xu



A spindle feed system is continuously subjected to cutting forces, cutting heat and frictional heat during machining processes, which interact to form a complex, nonlinear and thermal-force coupling field. The coupling field causes deformations and vibrations of the mechanism that affect the machining accuracy. Therefore, determining the thermal-force coupling dynamic characteristics of the mechanism is beneficial, as it lays the theoretical foundations for accurate error compensation and the design and optimization of the spindle feed system.


The deformation of the spindle feed system in actual working processes is approached by modeling, simulation and verification. Based on the theory of mechanics and heat transfer, the models for the transient milling force and the temperature field are established to obtain the real-time, dynamic cutting force and the associated heat values. A thermo-mechanical coupling model is also deduced, and the deformations generated by the cutting force and heat are simulated using the finite element method. Moreover, the thermo-mechanical coupling deformations of the system are emulated. The above deformation results are tested and confirmed.


This paper establishes the deformation rules under the cutting force and cutting heat as well as their associated coupling effects. When studying thermo-mechanical coupling, the initial deformations of the ball screw are dominated by the cutting forces. The effects of heat on the X-direction deformations gradually exceed the effects of the cutting forces. The Y-direction deformations are primarily caused by the forces, with little influence from the heat. The Z-direction deformations are mainly caused by the heat, with negligible influence from the forces.


Thermo-mechanical coupling Ball screw Spindle feed system Deformation 



This work is financially supported by the National Natural Science Foundation of China (Nos. 51575272, 51775277).


  1. 1.
    Hu S et al (2015) Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools. Int J Mach Tools Manuf 97:60–71CrossRefGoogle Scholar
  2. 2.
    Altintas Y, Verl A, Brecher C et al (2011) Machine tool feed drives. CIRP Ann Manuf Technol 60:779–796CrossRefGoogle Scholar
  3. 3.
    Yun WS, Kim SK, Dong WC (1999) Thermal error analysis for a CNC lathe feed drive system. Int J Mach Tools Manuf 39:1087–1101CrossRefGoogle Scholar
  4. 4.
    Wu CH, Kung YT (2003) Thermal analysis for the feed drive system of a CNC machine centre. Int J Mach Tools Manuf 43:1521–1528CrossRefGoogle Scholar
  5. 5.
    Mayr J, Jedrzejewski J, Uhlmann E et al (2012) Thermal issues in machine tools. CIRP Ann Manuf Technol 61:771–791CrossRefGoogle Scholar
  6. 6.
    Xu ZZ, Liu XJ (2014) Study on thermal behavior analysis of nut/shaft air cooling ball screw for high precision feed drive. Int J Precis Eng Manuf 15:123–128CrossRefGoogle Scholar
  7. 7.
    Huang SC (1995) Analysis of a model to forecast thermal deformation of ball screw feed drive systems. Int J Mach Tools Manuf 35:1099–1104CrossRefGoogle Scholar
  8. 8.
    Min X, Jiang S (2011) A thermal model of a ball screw feed drive system for a machine tool. Proc Inst Mech Eng 225:186–193Google Scholar
  9. 9.
    Horejs O (2007) Thermo-mechanical model of ball screw with non-steady heat sources. In: Proceedings of the international conference on thermal issues in emerging technologies: theory and applicationGoogle Scholar
  10. 10.
    Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools. Int J Mach Tools Manuf 40:1235–1256CrossRefGoogle Scholar
  11. 11.
    Altintas Y, Eynian M, Onozuka H (2008) Identification of dynamic cutting force coefficients and chatter stability with process damping. CIRP Ann Manuf Technol 57:371–374CrossRefGoogle Scholar
  12. 12.
    Powałka B (2008) Roundness error prediction in valve seat machining based on cutting force model and machine tool system dynamics. CES Manuf Sci Technol 32:45–57Google Scholar
  13. 13.
    Kaymakci M, Kilic ZM, Altintas Y (2012) Unified cutting force model for turning, boring, drilling and milling operations. Int J Mach Tools Manuf 54:34–45CrossRefGoogle Scholar
  14. 14.
    Tan L, Zhang DH et al (2015) Influence of tool geometrical parameters on milling force and surface integrity in milling titanium alloy. China Mech Eng 26:737–742Google Scholar
  15. 15.
    Budak E (2006) Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity. Int J Mach Tools Manuf 46:1478–1488CrossRefGoogle Scholar
  16. 16.
    Chen W, Xue J, Tang D et al (2009) Deformation prediction and error compensation in multilayer milling processes for thin-walled parts. Int J Mach Tools Manuf 49:859–864CrossRefGoogle Scholar
  17. 17.
    Yang JG, Fan KG, Du ZC (2013) Technique of real-time error compensation on NC machine tools. China Machine Press, BeijingGoogle Scholar
  18. 18.
    Fan KG, Li HL, Yang JG (2015) Traceability analysis and coupling compensation for guide way-induced errors in large CNC gantry guide way grinder. Int J Adv Manuf Technol 80:907–919CrossRefGoogle Scholar
  19. 19.
    Li LG, Wang AM et al (2014) Finite element analysis of 3D milling of side and face milling cutter based on the mechanical–thermal coupling field. Manuf Autom 16:45–49Google Scholar
  20. 20.
    Zhang DJ (2008) Thermo-mechanical coupling modeling and experimental study of cutting processing. Shanghai Jiao Tong University, ShanghaiGoogle Scholar
  21. 21.
    Ma C, Yang J et al (2017) Dynamic thermal-structure coupling analysis and experimental study on ball screw feed drive system of precision machine tools. Appl Mech Mater 868:124–135CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.College of Mechanical and Electrical EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

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