Mechatronics of a ball screw drive using an N degrees of freedom dynamic model



High-performance position control in machine tools can only be achieved modeling the dynamic behavior of the mechatronic system composed by the motor, transmission and control during the design stage. In this work, a complex analytical model of a ball screw drive is presented and integrated in a mechatronic model of the actuator to predict the dynamic behavior and analyze the impact of each component of the transmission. First, a simple 2-dof model is presented, and its analysis sets the basis for the development of a more complex model of several degrees of freedom, whose resulting fundamental transfer functions are represented using natural and modal coordinates. The modeling in modal coordinates carries a reduction of the transfer function that reduces computational work. The two models are compared and experimentally validated in time and frequency domains by means of experimental tests carried out on a specifically developed ball screw drive test bench.


Ball screw drive Machine tool dynamics Mechatronics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Magnani G, Rocco P (2010) Mechatronic analysis of a complex transmission chain for performance optimization in a machine tool. Mechatronics 20(1):85–101CrossRefGoogle Scholar
  2. 2.
    Feng G-H, Pan Y-L (2012) Investigation of ball screw preload variation based on dynamic modeling of a preload adjustable feed-drive system and spectrum analysis of ball-nuts sensed vibration signals. Int J Mach Tools Manuf 52(1):85–96CrossRefGoogle Scholar
  3. 3.
    Wu S-T, Lian S-H, Chen S-H (2015) Vibration control of a flexible beam driven by a ball-screw stage with adaptive notch filters and a line enhancer. J Sound Vib 348:71–87CrossRefGoogle Scholar
  4. 4.
    Feng B, Zhang D, Mei X, Mu E, Huang X (2015) Investigation of the controller parameter optimisation for a servomechanism. Proc Inst Mech Eng B J Eng Manuf 229(1 Suppl):98–110CrossRefGoogle Scholar
  5. 5.
    B. Fernandez-Gauna, I. Ansoategui, I. Etxeberria-Agiriano, M. Graña, ReinforcemenEng Appl Artif Intellt learning of ball screw feed drive controllers, , vol. 30, pp. 107–117 2014.Google Scholar
  6. 6.
    Fujita T, Matsubara A, Kono D, Yamaji I (2010) Dynamic characteristics and dual control of a ball screw drive with integrated piezoelectric actuator. Precis Eng 34(1):34–42CrossRefGoogle Scholar
  7. 7.
    Zhang J, Zhang H, Du C, Zhao W (2016) Research on the dynamics of ball screw feed system with high acceleration. Int J Mach Tools Manuf 111:9–16CrossRefGoogle Scholar
  8. 8.
    J.-S. Chen, Y.-K. Huang, C.-C. Cheng (2004) Mechanical model and contouring analysis of high-speed ball-screw drive systems with compliance effect, Int J Adv Manuf Technol, 24, no 3–4Google Scholar
  9. 9.
    Vicente DA, Hecker RL, Villegas FJ, Flores GM (2011) Modeling and vibration mode analysis of a ball screw drive. Int J Adv Manuf Technol 58(1–4):257–265Google Scholar
  10. 10.
    Zhang L, Wang T, Tian S, Wang Y (2016) Analytical modeling of a ball screw feed drive for vibration prediction of feeding carriage of a spindle. Math Probl Eng 2016:1–8Google Scholar
  11. 11.
    Dong L, Tang WC (2014) Adaptive backstepping sliding mode control of flexible ball screw drives with time-varying parametric uncertainties and disturbances. ISA Trans 53(1):110–116MathSciNetCrossRefGoogle Scholar
  12. 12.
    Yamazaki T (2008) Mathematical model for feed drive system in microscopic motion area. Arch Mater Sci Eng 33:35–38Google Scholar
  13. 13.
    Vesely J (2009) Complex model of machine structure with feed drive. Int J Nat Sci Eng 2(4):193–199Google Scholar
  14. 14.
    Altintas Y, Verl A, Brecher C, Uriarte L, Pritschow G (2011) Machine tool feed drives. CIRP Ann Manuf Technol 60(2):779–796CrossRefGoogle Scholar
  15. 15.
    Zulaika JJ, Campa FJ, Lopez de Lacalle LN (2011) An integrated process–machine approach for designing productive and lightweight milling machines. Int J Mach Tools Manuf 51(7–8):591–604CrossRefGoogle Scholar
  16. 16.
    Ouyang H, Zhang J (2015) Passive modifications for partial assignment of natural frequencies of mass–spring systems. Mech Syst Signal Process 50–51:214–226CrossRefGoogle Scholar
  17. 17.
    Yang T, Lin C-S (2004) Identifying the stiffness and damping parameters of a linear servomechanism. Mech Based Des Struct Mach 32(3):283–304CrossRefGoogle Scholar
  18. 18.
    Zulaika, Juan José; Ander Altamira Jon, Diseño mecatrónico de servomecanismos de alta dinámica, Automática e instrumentación, p. (362): 59–64, 5 Ref, 2005.Google Scholar
  19. 19.
    George Ellis (2004)Control system design guide., 3rd Edition. Elsevier Academic PressGoogle Scholar
  20. 20.
    GroB, H., Hamann, J., Wiegärtner, G., Electical feed drives in automation. Publicis-MCD, 2001.Google Scholar
  21. 21.
    Caracciolo R, Richiedei D (2014) Optimal design of ball-screw driven servomechanisms through an integrated mechatronic approach. Mechatronics 24(7):819–832CrossRefGoogle Scholar
  22. 22.
    Lee J, Hyun J, Wang S, Ki S (2015) Development procedure for a vibration transmission element using a reversed design optimization method. J Sound Vib 345:72–85CrossRefGoogle Scholar
  23. 23.
    Chen CL, Jang MJ, Lin KC (2004) Modeling and high-precision control of a ball-screw-driven stage. Precis Eng 28(4):483–495CrossRefGoogle Scholar
  24. 24.
    Sun Y-H, Chen T, Wu CQ, Shafai C (2016) A comprehensive experimental setup for identification of friction model parameters. Mech Mach Theory 100:338–357CrossRefGoogle Scholar
  25. 25.
    I. Ansoategui, F. J. Campa, C. López M. Díez, (2016) Influence of the machine tool compliance on the dynamic performance of the servo drives, The International Journal of Advanced Manufacturing Technology, OctGoogle Scholar

Copyright information

© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentUniversity College of Engineering Vitoria-Gasteiz, University of the Basque Country UPV/EHULeioaSpain
  2. 2.Mechanical Engineering Department, Bilbao Faculty of EngineeringUniversity of the Basque Country UPV/EHULeioaSpain

Personalised recommendations