Skip to main content
SpringerLink
Log in

Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Interference fits are widely used for connecting impeller and shaft assembly that are forced together slowly by pressing. The interference fit design ensures stable balance behavior and allows for positive contact between the impeller and shaft assembly throughout the range of operating speeds. In addition to maintaining radial contact, sufficient net radial interface pressure must remain in order to transmit torque when the rotational speed is very high. Therefore, the interference fit between the impeller and the shaft assembly is one of the most important factors influencing the performance of the turbo unit in the design of turbocharger compressor. A suitable fit tolerance needs to be considered in the structural design.

A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference fit loading is used for the analysis. The finite-element (FE) parametric quadratic programming (PQP) method developed based on the parametric variational principle (PVP) is used for the analysis of the stress distribution in the three-dimensional (3D) contact problem of impeller. The advantages of the parametric programming method compared with conventional approaches are that the penalty factors can be canceled and that solutions can be obtained directly without tedious iterative procedures such as the general incremental iterative method. To save time in the computation, a~multi-substructure technique is adopted for structural modeling. This not only simplifies the calculation, but also provides a convenient service for process computer-aided design (CAD) by means of FE simulation. The effects of the fit tolerance, coefficient of friction and rotational speed (centrifugal force), wall thickness of the shaft sleeve and the contact stress on the interference-fitting surfaces are studied in detail in the numerical computation. It is found that a nonuniform initial amount of interference in the structural design avoids the relative displacement generated and ensures uniformity of the contact stress. To assure quality of press-fitting, the amount of interference between the shaft sleeve and shaft should be strictly controlled to avoid the rapid increase of the contact stress. The numerical results demonstrate the high accuracy and good convergence of the algorithm presented here, which provides an effective approach that achieves more-reliable interference-fitted connections and more-precise assembly accuracy with lower manufacturing cost in the structural design.

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

References

  1. Hearn E.J. (1977). Mechanics of Materials. Pergamon, Oxford, 194–223

    Google Scholar 

  2. Φyvind B. (1989). Computer-Aided Tolerancing. ASME, New York, 79–82

    Google Scholar 

  3. Shigley J.E. and Mischke C.R. (1988). Standard Handbook of Machine Design. McGraw–Hill, New York, 8–13

    Google Scholar 

  4. Zhang Y., McClain B. and Fang X.D. (2000). Design of interference fits via finite element method. Int. J. Mech. Sci. 42: 1835–1850

    Article  MATH  Google Scholar 

  5. Sen S. and Aksakal B. (2004). Stress analysis of interference fitted shaft–hub system under transient heat transfer conditions. J. Mater. Des. 25: 407–417

    Google Scholar 

  6. Chang M.Z. and Yong J. (1994). The solution of frictional contact problems using a finite element mathematical programming method. J. Compos. Struct. 52(1): 149–155

    Article  Google Scholar 

  7. Daniel W.J.T (1982). Flywheel design by the finite element method. Mech. Eng. Trans. Inst. Eng. 7: 75–79

    MathSciNet  Google Scholar 

  8. Prasad N.S., Sashikant P. and Ramamurti V. (1994). Stress distribution in interference joints. J. Compos. Struct. 51(5): 535–540

    Article  MATH  Google Scholar 

  9. Parson Wilson, E.A.: A method for determining the surface contact stresses resulting from interference fits. J. Eng. Ind. Trans. 208–218 (1970)

  10. Tsuta T. and Yamaji S. (1973). Finite Element Analysis of Contact Problem: Theory and Practice in Finite Element Structural Analysis. University of Tokyo Press, Tokyo, 177–194

    Google Scholar 

  11. Ohte N. (1972). Analysis of elastic contact stress by using finite element method. (in Japanese). Trans. Jpn. Soc. Mech. Eng. 38: 2210–2216

    Google Scholar 

  12. Okomoto N. and Nakazawa N. (1979). Finite element contact analysis. Int. J. Numer. Methods Eng. 14: 337–357

    Article  Google Scholar 

  13. Satish Kumar K. (1996). Analysis of a cracked lug loaded by a interference fit pin. Int. J. Mech. Sci. 38(8–19): 967–979

    Article  Google Scholar 

  14. Zhao H. (1997). Numerical analysis of the interference fitting stresses between wheel and shaft. Int. J. Mater. Prod. Technol. 12(4–6): 514–526

    Google Scholar 

  15. Chen X., Balendra R. and Qin Y. (2004). A new approach for the optimization of the shrink-fitting of cold-forging dies. J. Mater. Process Technol. 145: 215–223

    Article  Google Scholar 

  16. Hur K.D., Choi Y. and Yeo H.T. (2003). A design method for cold backward extrusion using FE analysis. Finite Elements Anal. Des. 40: 173–185

    Article  Google Scholar 

  17. Castagnetti D. and Dragoni E. (2005). Optimal aspect ratio of interference fits for maximum load transfer capacity. J. Strain Anal. 40(2): 177–181

    Article  Google Scholar 

  18. Zhang H.W., Zhong W.X. and Gu Y.X. (1998). A combined parametric quadratic programming and iteration method for 3D elastic-plastic frictional contact problem analysis. Comput. Methods Appl. Mech. Eng. 155: 307–324

    Article  MATH  Google Scholar 

  19. Zhang H.W. and Schrefler B.A. (2000). Global constitutive behaviour of periodic assemblies of inelastic bodies in contact. Mech. Compo. Mater. Struct. 7(4): 355–382

    Article  Google Scholar 

  20. Zhang H.W., He S.Y., Li X.S. and Wriggers P. (2004). A new algorithm for numerical solution of 3D elastoplastic contact problems with orthotropic friction law. Comput. Mech. 34(1): 1–14

    Article  MATH  Google Scholar 

  21. Zhang, H.W., Zhong, W.X.: Quadratic Programming Method for Numerical Modeling of Elastoplastic Contact Problems: Theory, Software, Applications. In: part 1, pp. 65–72. Advances in Engineering Plasticity and its Applications. Trans Tech, Switzerland, (2004)

  22. Okamoto N. and Nakazawa M. (1979). Finite element incremental contact analysis with various frictional conditions. Int. J. Numer. Methods Eng. 14: 337–359

    Article  MATH  Google Scholar 

  23. Klarbring A. (1986). A mathmatical programming approach to three dimensional contact problems with friction. Comput. Methods Appl. Mech. Eng. 58: 175–200

    Article  MATH  MathSciNet  Google Scholar 

  24. Sage A.P. and White C.C. (1977). Optimum System Control. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  25. Billups S.C. (2000). Murty KG. Complementarity problems. J. Comput. Appl. Math. 124: 303–318

    Article  MATH  MathSciNet  Google Scholar 

  26. Wright S.J. (1997). Primal–Dual Interior-Point Methods. SIAM, Philadelphia

    MATH  Google Scholar 

  27. Meyer D.W., Plesha M.E. and Cooper R.F. (1992). A contact friction algorithm including nonlinear viscoelasticity and a singular yield surface provision [J]. Comput. Struct. 42(6): 913–925

    Article  Google Scholar 

  28. Zhang H.W., Zhong W.X. and Gu Y.X. (1995). A combined programming and iteration algorithm for finite element analysis of three-dimensional elastic contact problems [J]. Acta Mech. Sinica - English 11(4): 318–326

    Article  Google Scholar 

  29. Subramani D.A., Ramamurti V. and Sridhara K. (1997). Numerical analysis and experimental verification of the radial growth of a turbocharger centrifugal compressor impeller. J. Strain Anal. 2(32): 119–121

    Article  Google Scholar 

  30. Turner A.B., Davies S.J. and Childs P.R. (2002). Development of a novel gas turbine driven centrifugal compressor. Proc Inst. Mech. Eng. 214(A): 423–437

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

    H. W. Zhang, A. H. Liao & C. H. Wu

Authors
  1. H. W. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. H. Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. H. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. H. Liao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, H.W., Liao, A.H. & Wu, C.H. Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method. Arch Appl Mech 77, 421–437 (2007). https://doi.org/10.1007/s00419-006-0099-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-006-0099-4

Keywords

Search

Navigation