Skip to main content
SpringerLink
Log in

Contact stiffness determination of high-speed double- locking toolholder-spindle joint based on a macro- micro scale hybrid method

  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

The stiffness of toolholder-spindle joint at high speeds plays an important role in the cutting efficiency and the machining accuracy. A double-locking toolholder (BTF type) is designed to improve the stiffness of joint. This paper presents a macro-micro scale hybrid method to determine the stiffness of double-locking toolholder-spindle joint at high speeds. In this method the finite element method and the three-dimensional fractal method are combined. It is assumed flat in macro-scale for the contact surfaces of joint. The finite element method is introduced to obtain the pressure distribution with the influence of centrifugal force at high speeds. In micro-scale, the contact surfaces are fractal featured and the three-dimensional fractal method is used to compute the stiffness based on the pressure. Experiments with BTF40-type toolholder are conducted to verify the efficiency of the proposed model in zero-speed case. The relationship between the stiffness and the technological parameters of the system can be derived based on the presented model. The upper limit of speed, the optimized range of each technological parameter are determined for obtaining the higher stiffness of joint. The results can provide theoretical basis for improving the cutting efficiency and the machining accuracy of high-speed machine tool.

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

Similar content being viewed by others

Abbreviations

a :

real contact area of a single asperity

al :

the real largest contact area of a single asperity

A r :

total real contact area

D :

three-dimensional fractal dimension

D s :

two-dimensional fractal dimension

E :

equivalent elastic modulus

E 1, E 2 :

elastic modulus of two surfaces

f :

normal load of a single asperity

F :

total normal load of contact surface

G :

fractal roughness parameter

G':

equivalent shear modulus

G 1, G 2 :

shear modulus of two surfaces

H :

hardness of the soft material

k :

coefficient related with the passion ratio

k n :

normal stiffness of a single asperity

k n :

total normal stiffness

k t :

total tangential stiffness

L :

sampling length

M :

asperity overlapping number of the joint surface topography

n :

frequency index

n max :

upper limit of frequency index

p :

normal load of a single asperity

r :

radius of the real contact region of a single asperity

R :

curvature radius

t :

tangential load of a single asperity

x, y :

planar Cartesian coordinates

Y :

yield stress of the soft material

δ:

normal deformation of a single asperity

δt :

tangential deformation of a single asperity

φm,n :

random phase

γ:

dimension parameter of the spectral density

v 1, v 2 :

Poisson ratio

µ:

static friction coefficient

τb :

shear strength of the soft material

ψ:

expand coefficient

':

truncated section of a single asperity

1c :

critical parameter demarcating the elastic and elastic-plastic regimes

2c :

critical parameter demarcating the elastic-plastic and plastic regimes

e :

parameter in the elastic regime

ep :

parameter in the elastic-plastic regime

p :

parameter in the plastic regime

References

  1. Schmitz, T. L. and Donalson, R. R., “Predicting High-Speed Machining Dynamics by Substructure Analysis,” CIRP Annals-Manufacturing Technology, Vol. 49, No. 1, pp. 303–308, 2000.

    Article  Google Scholar 

  2. Schmitz, T. L., Davies, M. A., and Kennedy, M. D., “Tool Point Frequency Response Prediction for High-Speed Machining by RCSA,” Journal of Manufacturing Science and Engineering, Vol. 123, No. 4, pp. 700–707, 2001.

    Article  Google Scholar 

  3. Ahmadian, H. and Nourmohammadi, M., “Tool Point Dynamics Prediction by a Three-Component Model Utilizing Distributed Joint Interfaces,” International Journal of Machine Tools and Manufacture, Vol. 50, No. 11, pp. 998–1005, 2010.

    Article  Google Scholar 

  4. Mayer, M. H. and Gaul, L., “Segment-to-Segment Contact Elements for Modelling Joint Interfaces in Finite Element Analysis,” Mechanical Systems and Signal Processing, Vol. 21, No. 2, pp. 724–734, 2007.

    Article  Google Scholar 

  5. Shen, Z. Y., Zhang, J. F., and Wu, Z. J., Feng, P. F., and Xu, C., “Modeling and Experimental Study on Static Characteristic of BT Tool Holder-Spindle Interface,” Advanced Materials Research, Vols. 311–313, pp. 726–731, 2011.

    Article  Google Scholar 

  6. Liu, X. Y., “The Identification Research and Application of High-Speed Double-Side Locking Tooholder-Spindle Joint,” M.Sc. Thesis, Department of Mechanical Engineering, Beijing University of Technology, 2012.

    Google Scholar 

  7. Qi, Z. J., “Research on Identification Method of Joint Parameters based on Finite-Difference and Residual Compensation,” M.Sc. Thesis, Department of Mechanical Engineering, Beijing University of Technology, 2013.

    Google Scholar 

  8. Tsutsumi, M., Anno, Y., and Ebata, N., “Static Characteristics of 7/ 24 Tapered Joint for Machining Center: 1st Report, Effects of Taper Size and Angle Error,” Bulletin of JSME, Vol. 26, No. 213, pp. 461–467, 1983.

    Article  Google Scholar 

  9. Shamine, D. M. and Shin, Y. C., “Analysis of No. 50 Taper Joint Stiffness Under Axial and Radial Loading,” Journal of Manufacturing Processes, Vol. 2, No. 3, pp. 167–173, 2000.

    Article  Google Scholar 

  10. Hanna, I. M., Agapiou, J. S., and Stephenson, D. A., “Modeling the HSK Toolholder-Spindle Interface,” Journal of Manufacturing Science and Engineering, Vol. 124, No. 3, pp. 734–744, 2002.

    Article  Google Scholar 

  11. Zhang, S., Ai, X., and Tang, W. X., “Performance of Spindle/ Toolholder Interfaces Under High Rotary Speed,” Journal of Shandong University of Technology, Vol. 33, No. 5, pp. 473–476, 2003.

    Google Scholar 

  12. Zhang, S., Ai, X., and Zhao, J., “FEM-based Parametric Optimum Design of Spindle/Toolholder Interfaces Under High Rotational Speed,” Chinese Journal of Mechanical Engineering, Vol. 40, No. 2, pp. 83–86, 2004.

    Article  Google Scholar 

  13. Wang, S. L., Lou, H., and Wang, Y. C., “Analysis on Torsional Rigidity Property of HSK Tooling System,” Machinery Design & Manufacture, No. 3, pp. 109–111, 2009.

    Google Scholar 

  14. Pu, H., “Reliability Analysis for Tapered Interference Joint of HSK Toolholder,” Tool Engineering, Vol. 39, No. 7, pp. 51–53, 2005.

    Google Scholar 

  15. Miao, X. and Huang, X., “A Complete Contact Model of a Fractal Rough Surface,” Wear, Vol. 309, No. 1, pp. 146–151, 2014.

    Article  Google Scholar 

  16. Majumdar, A. and Bhushan, B., “Fractal Model of Elastic-Plastic Contact between Rough Surfaces,” Journal of Tribology, Vol. 113, No. 1, pp. 1–11, 1991.

    Article  Google Scholar 

  17. Wang, S. and Komvopoulos, K., “A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part II-Multiple Domains, Elastoplastic Contacts and Applications,” Journal of Tribology, Vol. 116, No. 4, pp. 824–832, 1994.

    Article  Google Scholar 

  18. Wang, S. and Komvopoulos, K., “A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part I-Elastic Contact And Heat Transfer Analysis,” Journal of Tribology, Vol. 116, No. 4, pp. 812–822, 1994.

    Article  Google Scholar 

  19. Yan, W. and Komvopoulos, K., “Contact Analysis of Elastic-Plastic Fractal Surfaces,” Journal of Applied Physics, Vol. 84, No. 7, pp. 3617–3624, 1998.

    Article  Google Scholar 

  20. Zhang, X. L., Huang, Y. M., and Wen, S. H., “Fractal Model of Contact Stiffness of Joint Surfaces,” Transactions of the Chinese Society of Agricultural Machinery, Vol. 31, No. 4, pp. 89–92, 2000.

    Google Scholar 

  21. Wen, S. H., Zhang, X. L., Wen, X. G., Wang, P. Y., and Wu, M. X., “Fractal Model of Tangential Contact Stiffness of Joint Interfaces and Its Simulation,” Transactions of the Chinese Society for Agricultural Machinery, Vol. 40, No. 12, pp. 223–227, 2009.

    Google Scholar 

  22. Zhang, X. L. and Wen, S. H., “A Fractal Model of Tangential Contact Stiffness of Joint Surfaces based on the Contact Fractal Theory,” Transactions of the Chinese Society of Agricultural Machinery, Vol. 33, No. 3, pp. 91–97, 2002.

    Google Scholar 

  23. Zhao, Y., Song, X., Cai, L., Liu, Z., and Cheng, Q., “Surface Fractal Topography-based Contact Stiffness Determination of Spindle-Toolholder Joint,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, DOI No. 10.1177/0954406215578483, 2015.

    Google Scholar 

  24. Ausloos, M. and Berman, D., “A Multivariate Weierstrass-Mandelbrot Function,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 400, No. 1819, pp. 331–350, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  25. Kogut, L. and Etsion, I., “Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat,” Journal of Applied Mechanics, Vol. 69, No. 5, pp. 657–662, 2002.

    Article  MATH  Google Scholar 

  26. Liou, J. L., “The Theoretical Study for Microcontact Model with Variable Topography Parameters,” Ph.D. Thesis, Department of Mechanical Engineering, National Cheng Kung University, 2006.

    Google Scholar 

  27. Mandelbrot, B. B., “Self-Affine Fractals and Fractal Dimension,” Physica Scripta, Vol. 32, No. 4, pp. 257–260, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  28. Ji, C., Zhu, H., and Jiang, W., “Fractal Prediction Model of Thermal Contact Conductance of Rough Surfaces,” Chinese Journal of Mechanical Engineering, Vol. 26, No. 1, pp. 128–136, 2013.

    Article  Google Scholar 

  29. Zhang, X., Wang, N., Lan, G., Wen, S., and Chen, Y., “Tangential Damping and Its Dissipation Factor Models of Joint Interfaces based on Fractal Theory with Simulations,” Journal of Tribology, Vol. 136, No. 1, Paper No. 011704, 2014.

    Article  Google Scholar 

  30. Tian, H., Zhao, C., Fang, Z., Zhu, D., Li, X., and Mao, K., “Improved Model of Tangential Stiffness for Joint Interface using Anisotropic Fractal Theory,” Transactions of the Chinese Society of Agricultural Machinery, Vol. 44, No. 3, pp. 257–266, 2013.

    Google Scholar 

  31. Rongzhu, Z. and Bangwei, C., “Numerical Method of the Power Spectral Density,” High Power Laser and Particle Beams, Vol. 12, No. 6; pp. 664–668, 2000.

    Google Scholar 

  32. Zhang, S. and Ai, X., “Finite Element Analysis of HSK Spindle/ Toolholder Interface,” Mechanical Science and Technology, Vol. 23, No. 6, pp. 631–633, 2004.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing, 100124, China

    Yongsheng Zhao, Jingjing Xu, Ligang Cai, Zhifeng Liu & Qiang Cheng

  2. College of Computer Science, Beijing University of Technology, Beijing, 100124, China

    Weimin Shi

Authors
  1. Yongsheng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingjing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ligang Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weimin Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhifeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Qiang Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongsheng Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Y., Xu, J., Cai, L. et al. Contact stiffness determination of high-speed double- locking toolholder-spindle joint based on a macro- micro scale hybrid method. Int. J. Precis. Eng. Manuf. 17, 741–753 (2016). https://doi.org/10.1007/s12541-016-0092-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-016-0092-y

Keywords

Search

Navigation