The study of fixture stiffness part I: a finite element analysis for stiffness of fixture units

  • Y. Zheng
  • Y. RongEmail author
  • Z. Hou


This paper presents a systematic finite element model to predict the fixture unit stiffness by introducing nonlinear contact elements on the contact surface between fixture components. The contact element includes three independent springs: two in tangential directions and one in the normal direction of the contact surface. Strong nonlinearity is caused by possible separation and sliding between two fixture components. The problem is formulated by the penalty function method and is solved by the modified Newton--Raphson procedure. The model was validated by two cases of analysis of a linear cantilever beam and a simple fixture unit with two components. Results are in agreement with the corresponding analytical solution of beams and the previous experiment results for fixture in the literature.


Fixture Stiffness FEA Contact mechanics Friction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    An Z, Huang S, Li J, Rong Y, Jayaram S (1999) Development of automated fixture design systems with predefined fixture component types: part 1, basic design. Int J Flex Autom Integr Manuf g, Vol. 7, No. 3/4, pp.321–341Google Scholar
  2. 2.
    Aliabadi MH, Brebbia CA (1993) Computational methods in contact mechanics Computational Mechanics Publications/Elsevier Applied Science, Southhampton-BostonGoogle Scholar
  3. 3.
    Asada H, By A (1985) Kinematics analysis of workpart fixturing for flexible assembly with automatically reconfigurable fixtures. Proc IEEE Int Conf Robot Autom RA-1(2):86–93, 1985Google Scholar
  4. 4.
    Beards CF (1986) The damping of structural vibration by controlled inter-facial slip in joints. An ASME publication, 8 l-DET-86Google Scholar
  5. 5.
    Brost RC, Goldberg KY (1996) A complete algorithm for synthesizing modular fixtures for polygonal parts. IEEE Trans Robot Autom 12(1):31–46CrossRefGoogle Scholar
  6. 6.
    Chou YC Chandru V, Barash MM (1989) A mathematical approach to automatic configuration of machining fixtures: analysis and synthesis. J Eng Ind 111:299–306CrossRefGoogle Scholar
  7. 7.
    Chou YC (1993) Automated fixture design for concurrent manufacturing planning. Concurr Eng Res Appl 1:219–229CrossRefGoogle Scholar
  8. 8.
    Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis, 3rd edn. John Wiley & Sons, New YorkzbMATHGoogle Scholar
  9. 9.
    Fang B, DeVor RE, Kapoor SG (2002) Influence of friction damping on workpiece-fixture system dynamics and machining stability. J Manuf Sci Eng 124:226–233CrossRefGoogle Scholar
  10. 10.
    Fuh JYH, Nee AYC (1994) Verification and optimization of workholding scheme for fixture design. J Des Manuf (4):307–318Google Scholar
  11. 11.
    Grippo PM, Grandhi MV, Thompson BS (1987) The computer-aided design of modular fixturing systems. Int J Adv Manuf Technol 2(2):75–88CrossRefGoogle Scholar
  12. 12.
    Han H, Rong Y (2003) Development of a variation fixture design technique. Research Report, Worcester Polytechnic InstituteGoogle Scholar
  13. 13.
    Hurtado JF, Melkte SN (2002) Modeling and analysis of the effect of fixture-workpiece conformability on static stability. Trans ASME J Manuf Sci Eng 124:234–241, May 2002CrossRefGoogle Scholar
  14. 14.
    Kang Y, Rong Y, Yang J-C (2003) Computer-aided fixture design verification, part 1: the framework and modeling; part 2: tolerance analysis; part 3: stability analysis. Int J Adv Manuf Technol (to appear)Google Scholar
  15. 15.
    Kow TS, Kumar AS, Fuh JYH (1998) An integrated computer-aided modular fixture design system for interference free design. ASME IMECE, Anaheim, CA, Nov. 15–20. Manuf Sci Eng, MED-8:909–916Google Scholar
  16. 16.
    Kumar AS, Nee AYC (1995) A framework for a variant fixture design system using case-based reasoning technique. Computer-aided Tooling, ASME WAM, MED 2-1:763–775, 1995Google Scholar
  17. 17.
    Lee JD, Haynes LS (1987) Finite element analysis of flexible fixturing systems. J Eng Ind 109:134–139Google Scholar
  18. 18.
    Li B, Melkote SN (1999) An elastic contact model for prediction of workpiece-fixture contact forces in clamping. J Manuf Sci Eng 121:485–493CrossRefGoogle Scholar
  19. 19.
    Liao YG, Hu SJ (2001) An integrated model of a fixture-workpiece system for surface quality prediction. Int J Adv Manuf Technol 17:810–818CrossRefGoogle Scholar
  20. 20.
    Ma W, Lei Z, Rong Y (1998) FIX-DES: a computer-aided modular fixture configuration design system. Int J Adv Manuf Tech 14:21–32CrossRefGoogle Scholar
  21. 21.
    Ma W, Li J, Rong Y (1999) Development of automated fixture planning systems. Int J Adv Manuf Technol 15:171–181, 1999CrossRefGoogle Scholar
  22. 22.
    Marin RA, Ferreira PM (2002b) Optimal placement of fixture clamps: part 1, maintaining form closure and independent regions of form closure; part 2, minimizing the maximum clamping forces. J Manuf Sci Eng 124:676–694CrossRefGoogle Scholar
  23. 23.
    Markus A (1988) Strategies for the automated generation of modular fixtures. Proc Manuf Internal 97–103Google Scholar
  24. 24.
    Marsh ER, Yantek DS (1997) Experimental measurement of precision bearing dynamic stiffness. J Sound Vib 202(1):55–66CrossRefGoogle Scholar
  25. 25.
    Mazurkiewicz M, Ostachowicz W (1983) Theory of finite element method for elastic contact problems of solid bodies. Computer Structure 17:51–59zbMATHCrossRefGoogle Scholar
  26. 26.
    Nee AYC, Kumar AS (1991) A framework for an object/rule-based automated fixture design system. CIRP Ann 40(1):147–151CrossRefGoogle Scholar
  27. 27.
    Nnaji BO, Alladin S, Lyu P (1990) Rules for an expert fixturing system on a CAD screen using flexible fixtures. J Intelligent Manuf 1:31–48CrossRefGoogle Scholar
  28. 28.
    Pham DT, de Sam Lazaro A (1990) AUTOFIX-an expert CAD system for jigs and fixtures. Int J Mach Tools Manuf 30(3):403–411CrossRefGoogle Scholar
  29. 29.
    Rong Y, Zhu Y (1992) An application of group technology in computer-aided fixture design. Inter J Syst Autom Res Appl 2(4):395–405Google Scholar
  30. 30.
    Rong Y, Bai Y (1997) Automated generation of modular fixture configuration design. J Manuf Sci Eng 119:208–219CrossRefGoogle Scholar
  31. 31.
    Rong Y, Zhu Y (1999) Computer-aided fixture design. Dekker, New York, NYGoogle Scholar
  32. 32.
    Rong Y (2003) Four generations of computer-aided fixture design. Research Report, Worcester Polytechnic InsitituteGoogle Scholar
  33. 33.
    Roy U, Liao J (2002) Fixturing analysis for stability consideration in an automated fixture design system. J Manuf Sci Eng 124:98–104CrossRefGoogle Scholar
  34. 34.
    Sun SH, Chen JL (1995) A modular fixture design system based on case-based reasoning. Int J Adv Manuf Technol 10:389–395CrossRefGoogle Scholar
  35. 35.
    Trappey AJC, Su CS, Hou JL (1995) Computer-aided fixture analysis using finite element analysis and mathematical optimization modeling. ASME INECE, MED 2-1:777–787, Nov. 12–17, 1995Google Scholar
  36. 36.
    Tzou HS, Rong Y (1991) Contact dynamics of a spherical joint and a jointed truss-cell unit system: theory and stochastic simulation. AIAA J 29(1):81–88, 1991Google Scholar
  37. 37.
    Wang JH, Yang MJ (1999) Problems and solutions in the parameters of mechanical joints. In the 3rd International Conference in Inverse Problem in Engineering: theory and practice, June 13–18, Port Ludlow, WA, USA, ASME Paper No. ME 03Google Scholar
  38. 38.
    Wardak et al (2001) Optimal fixture design for drilling through deformable plate workpieces-part 1: model formulation. J Manuf Syst 20(1):21–23Google Scholar
  39. 39.
    Whitney DE, Mantripragada R, Adams JD, Rhee SJ (1999) Designing assemblies. Res Eng Des 11:229–253Google Scholar
  40. 40.
    Wu Y, Rong Y, Chu T (1997) Automated generation of dedicated fixture configuration. Int J Comput Appl Technol 10(3/4):213–235Google Scholar
  41. 41.
    Wu Y, Rong Y, Ma W, LeClair S (1998) Automated modular fixture design: part 1, geometric analysis; part 2, accuracy, clamping, and accessibility analysis. Robot Comput-Integr Manuf 14:1–26zbMATHCrossRefGoogle Scholar
  42. 42.
    Xiong C, Xiong Y (1998) Stability index and contact configuration planning for multifingered grasp. J Robot Syst 15(4):183–190zbMATHCrossRefGoogle Scholar
  43. 43.
    Yeh JH, Liou FW (1999) Contact condition modeling for machining fixture setup processes. Int J Mach Tools Manuf 39:787–803CrossRefGoogle Scholar
  44. 44.
    Zhu Y, Zhang S, Rong Y (1993) Experimental study on fixturing stiffness of T-slot based modular fixtures. NAMRI Transactions XXI, NAMRC, Stillwater, OK, May 19–21, pp 231–235Google Scholar

Copyright information

© Springer-Verlag London Limited 2007

Authors and Affiliations

  1. 1.Worcester Polytechnic InstituteWorcesterUSA

Personalised recommendations