Mathematical Model of the Tensioning in the Collet Clamping Mechanism with the Rotary Movable Input Link on Spindle Units | Journal of Engineering Sciences

Mathematical Model of the Tensioning in the Collet Clamping Mechanism with the Rotary Movable Input Link on Spindle Units

Author(s): Prydalnyi B. I.1*, Sulym H. T.2

Affiliation(s): 1 Lutsk National Technical University, 75 Lvivska street, 43018 Lutsk, Ukraine;
2 Bialystok University of Technology, 45C, Wiejska St., 15-351 Bialystok, Poland.

*Corresponding Author’s Address: [email protected]

Issue: Volume 8, Issue 1 (2021)

Received: March 30, 2021
The final version received: May 25, 2021
Accepted for publication: June 2, 2021

Prydalnyi B. I., Sulym H. T. (2021). Mathematical model of the tensioning in the collet clamping mechanism with the rotary movable input link on spindle units. Journal of Engineering Sciences, Vol. 8(1), pp. E23–E28, doi: 10.21272/jes.2021.8(1).e4

DOI: 10.21272/jes.2021.8(1).e4

Research Area:  MECHANICAL ENGINEERING: Computational Mechanics

Abstract. Increasing machining productivity causes the cutting forces acting on tools or workpieces to grow and requires extra clamping forces for their fixation reliably. In the research, a mathematical model of the operation of the clamping mechanism for fixating cylindrical objects on the spindle of machine tools at the stage of tension is presented. The presented design of the mechanism contains screw gear and provides self-braking. Based on the calculation model, mathematical dependencies are developed to describe the relationship among the movements of the parts of the mechanism when clamping forces are growing. The presented analytical dependencies allow considering the stage of growing clamping forces separately when the conservative type of forces are prevailing in the mechanism’s operation. That stage of work when both types of forces of dissipative and potential characters exist is considered. The developed dependencies describe the position of parts of the clamping mechanism depending on the generalized coordinate. The angle of rotation of the input rotating link is used as the generalized coordinate. This fact allows calculating the position of the elements of the clamping mechanism of this type depending on time. Results of the research enhance understanding the pattern of the change in the interaction of the elements and forces that act in the mechanism during the final stage of clamping. The obtained mathematical dependencies are a precondition for the development of design methodology for mechanisms of this type.

Keywords: machining, clamping drive, clamping forces, calculation model, screw gear.


  1. Szepesi, D., van’t Erve, A. H. (1984). Adaptive clamping control on high performance CNC lathes. Twenty-Fourth International Machine Tool Design and Research Conference. Palgrave, London, pp. 177–186, doi: 10.1007/978-1-349-81247-9_25.
  2. Denisenko, A. F., Yakimov, M. V. (2019). Dynamics of spindle assembly metal-cutting machine tool with anisotropic elastic support. The 4th International Conference on Industrial Engineering. Springer, Cham, pp. 1647–1655, doi: 10.1007/978-3-319-95630-5_176.
  3. Gasparov, E. S., Gasparova, L. B. (2020). Mathematical model of spindle unit bearing assembly. The 5th International Conference on Industrial Engineering. Springer, Cham. doi: 10.1007/978-3-030-22041-9_78.
  4. Liu, C. S., Chang, Y. H. (2017). Development of novel spindle motor with dual air gaps to improve output torque. Microsyst Technol, Vol. 23, pp. 371–379, doi: 10.1007/s00542-015-2685-2.
  5. Prydalnyi, B. (2021). The dynamic model of the automatic clamping mechanism with a rotating input link. Advances in Design, Simulation and Manufacturing IV. Springer, Cham, pp. 95–103, doi: 10.1007/978-3-030-77719-7_10.
  6. Thorenz, B., Westermann, H. -H., Kafara, M., Nuetzel, M., Steinhilper, R. (2018). Evaluation of the influence of different clamping chuck types on energy consumption, tool wear and surface qualities in milling operations. Procedia Manufacturing, Vol. 21, pp. 575–582, doi: 10.1016/j.promfg.2018.02.158.
  7. Hsieh, L-C., Chen, T-H., Lai, P-C. (2020). The kinematic design of mold clamping mechanism with minimal maximum acceleration. Advances in Mechanical Engineering, Feng Chia University, Po-Cheng Lai, Vol. 12(6), doi: 10.1177/1687814020926280.
  8. Song, B., Wang, H., Cui, W., Zhang, J., Liu, H. (2019). Dynamic simulation and optimization of clamping mechanism of online tension testing machine for wire ropes. Engineering Failure Analysis, Vol. 95, pp. 181–190, doi: 10.1016/j.engfailanal.2018.09.015.
  9. Soriano, E., Rubio, H., García-Prada, J.C. (2013). Analysis of the clamping mechanisms of collet-chucks holders for turning. New Trends in Mechanism and Machine Science, Springer, Dordrecht, Vol. 7, pp. 391–398, doi: 10.1007/978-94-007-4902-3_42.
  10. Sabirov, F., Suslov, D., Savinov, S. (2012) Diagnostics of spindle unit, model design and analysis. The International Journal of Advanced Manufacturing Technology, Vol. 62, pp. 861–865, doi: 10.1007/s00170-011-3848-7.
  11. Shitov, A. M., (2011) Complex examination of a spindle drive unit of a profile-grinding machine. Journal of Machinery Manufacture and Reliability, Vol. 40, doi: 10.3103/S1052618811010195.
  12. Murakami, H., Katsuki, A., Sajima, T., Uchiyama, K., Houda, K., Sugihara Y. (2021). Spindle with built-in acoustic emission sensor to realize contact detection. Precision Engineering, Vol. 70, pp. 26–33, doi: 10.1016/j.precisioneng.2021.01.017.
  13. Pozdîrcă, A. (2010). Design of a clamp mechanism. International Symposium on Science of Mechanisms and Machines. Springer, Dordrecht, pp. 687–698, doi: 10.1007/978-90-481-3522-6_58.
  14. Yadav, M. H., Mohite, S. S. (2018). Controlling deformations of thin-walled Al 6061-T6 components by adaptive clamping. Procedia Manufacturing, Vol. 20, pp. 509–516, doi: 10.1016/j.promfg.2018.02.076.
  15. Shaoke, W., Jun, H., Fei, D. (2019). Modelling and characteristic investigation of spindle-holder assembly under clamping and centrifugal forces. Journal of Mechanical Science and Technology, Vol. 33(5), pp. 2397–2405, doi: 10.1007/s12206-019-0438-3.
  16. Chao, Xu, Jianfu, Z., Pingfa, F. (2014). Characteristics of stiffness and contact stress distribution of a spindle-holder taper joint under clamping and centrifugal forces. International Journal of Machine Tools and Manufacture, Vol. 82-83, pp. 21–28, doi: 10.1016/j.ijmachtools.2014.03.006.
  17. Estrems, M., Arizmendi, M., Cumbicus, W.E., López, A. (2015). Measurement of clamping forces in a 3 jaw chuck through an instrumented aluminium ring. Procedia Engineering, Vol. 132, pp. 456–463, doi: 10.1016/j.proeng.2015.12.519.
  18. Alquraan, T., Kuznetsov, Yu., Tsvyd, T. (2016). High-speed clamping mechanism of the CNC lathe with compensation of centrifugal forces. Procedia engineering, Vol. 150, pp. 689–695, doi: 10.1016/j.proeng.2016.07.081.

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