Abstract
A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intrajoint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed, and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.
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Nikravesh, P.E.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs (1988)
Haug, E.J.: Computer-Aided Kinematics and Dynamics of Mechanical Systems, vol. I. Allyn and Bacon, Boston (1989)
Shabana, A.A.: Dynamics of Multibody Systems,. Wiley, New York (1989)
Nikravesh, P.E.: Planar Multibody Dynamics: Formulation, Programming, and Applications. CRC, London (2008)
McCarthy, J.M.: Geometric Design of Linkages: Systems and Controls. Springer, New York (2000)
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies. Lecture Notes in Applied and Computational Mechanics, vol. 34. Springer, Berlin (2008)
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamics of multibody systems with spherical clearance joints. J. Comput. Nonlinear Dyn. 1(3), 240–247 (2006)
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S.: Lubricated revolute joints in rigid multibody systems. Nonlinear Dyn. 56(3), 277–295 (2009)
Ambrósio, J., Veríssimo, P.: Sensitivity of a vehicle ride to the suspension bushing characteristics. J. Mech. Sci. Technol. 23, 1075–1082 (2009)
Park, J., Nikravesh, P.E.: Effect of steering-housing rubber bushings on the handling of a vehicle. SAE Paper 970103, SAE, Warrendale, Pennsylvania (1997)
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S.: A study on dynamics of mechanical systems including joints with clearance and lubrication. Mech. Mach. Theory 41(3), 247–261 (2006)
Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112, 369–376 (1990)
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contact-impact force model on the dynamic response of multibody systems. Proc. Inst. Mech. Eng. K, J. Multibody Dyn. 220, 21–34 (2006)
Ambrósio, J., Verissimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. 22, 341–365 (2009)
Flores, P., Lankarani, H.M.: Spatial rigid-multi-body systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. (2009). doi:10.1007/s11071-009-9583-z
Dubowsky, S., Freudenstein, F.: Dynamic analysis of mechanical systems with clearances, Part 1: Formulation of dynamic model. J. Eng. Ind. 93(1), 305–309 (1971)
Dubowsky, S., Freudenstein, F.: Dynamic analysis of mechanical systems with clearances, Part 2: Dynamic response. J. Eng. Ind., Ser. B 93(1), 310–316 (1971)
Dubowsky, S., Gardner, T.N.: Design and analysis of multilink flexible mechanism with multiple clearance connections. J. Eng. Ind. 99(1), 88–96 (1977)
Kakizaki, T., Deck, J.F., Dubowsky, S.: Modeling the spatial dynamics of robotic manipulators with flexible links and joint clearances. J. Mech. Des. 115, 839–847 (1993)
Bengisu, M.T., Hidayetoglu, T., Akay, A.: A theoretical and experimental investigation of contact loss in the clearances of a four-bar mechanism. J. Mech. Transm. Autom. Des. 108, 237–244 (1986)
Bauchau, O.A., Rodriguez, J.: Modelling of joints with clearance in flexible multibody systems. Int. J. Solids Struct. 39, 41–63 (2002)
Innocenti, C.: Kinematic clearance sensitivity analysis of spatial structures with revolute joints. J. Mech. Des. 124, 52–57 (2002)
Wu, W., Rao, S.S.: Interval approach for the modeling of tolerances and clearances in mechanism analysis. J. Mech. Des. 126, 581–592 (2004)
Farahanchi, F., Shaw, S.: Chaotic and periodic dynamics of a slider-crank mechanism with slider clearance. J. Sound Vib. 177(3), 307–324 (1994)
Rhee, J., Akay, A.: Dynamic response of a revolute joint with clearance. Mech. Mach. Theory 31(1), 121–124 (1996)
Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behaviour of planar rigid multibody systems including revolute joints with clearance. Proc. Inst. Mech. Eng. K, J. Multibody Dyn. 221(2), 161–174 (2007)
Ryan, R.R.: ADAMS-Multibody System Analysis Software, Multibody Systems Handbook. Springer, Berlin (1990)
Smith, R.C., Haug, E.J.: DADS-Dynamic Analysis and Design System, Multibody Systems Handbook. Springer, Berlin (1990)
Gilardi, G., Sharf, I.: Literature survey of contact dynamics modeling. Mech. Mach. Theory 37(10), 1213–1239 (2002)
Flores, P., Leine, R., Glocker, R.: Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach. Multibody Syst. Dyn. 23(2), 165–190 (2010)
Flores, P., Ambrósio, J., Claro, J.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12, 47–74 (2004)
Flores, P., Ambrósio, J.: On the contact detection for contact analysis in multibody systems. In: XXII ICTAM, 22nd International Congress of Theoretical and Applied Mechanics, Adelaide Convention Centre, Adelaide, Australia, August 25–29, 2 p. (2008)
Flores, P.: Contact-impact analysis in multibody systems based on the nonsmooth dynamics approach. Post Doctoral Report, ETH-Zurich, Switzerland (2009)
Pfeifer, F., Glocker, C.: Multibody Dynamics with Unilateral Constraints. Wiley, New York (1996)
Anitescu, M., Potra, F.A., Stewart, D.E.: Time-stepping for three-dimensional rigid body dynamics. Comput. Methods Appl. Mech. Eng. 177(3), 183–197 (1999)
Pang, J.-S., Stewart, D.E.: Differential variational inequalities. Math. Program. 113, 345–424 (2008)
Tasora, A., Negrut, D., Anitescu, A.: Large-scale parallel multi-body dynamics with frictional contact on the graphical processing unit. Proc. Inst. Mech. Eng. K, J. Multibody Dyn. 222, 315–326 (2008)
Glocker, C., Studer, C.: Formulation and preparation for numerical evaluation of linear complementary systems in dynamics. Multibody Syst. Dyn. 13, 447–463 (2005)
Förg, M., Pfeiffer, F., Ulbrich, H.: Simulation of unilateral constrained systems with many bodies. Multibody Syst. Dyn. 14(2), 137–154 (2005)
Pfeiffer, F., Foerg, M., Ulbrich, H.: Numerical aspects of non-smooth multibody dynamics. Comput. Methods Appl. Mech. Eng. 195(50–51), 6891–6908 (2006)
Brogliato, B., Ten Dam, A.A., Paoli, L., Genot, F., Abadie, M.: Numerical simulations of finite dimensional multibody nonsmooth mechanical systems. Appl. Mech. 55, 107–150 (2002)
Glocker, C., Pfeiffer, F.: Complementarity problems in multibody systems with planar friction. Arch. Appl. Mech. 63(7), 452–463 (1993)
Pang, J., Trinkle, J.C.: Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction. Math. Program. 73(2), 199–226 (1996)
Trinkle, J.C., Tzitzouris, J.A., Pang, J.S.: Dynamic multi-rigid-body systems with concurrent distributed contacts. Philos. Trans. Math. Phys. Eng. Sci. 359(1789), 2575–2593 (2001)
Pfeiffer, F.: The idea of complementarity in multibody dynamics. Arch. Appl. Mech. 72(11–12), 807–816 (2003)
Signorini, A.: Sopra alcune questioni di elastostatica. Atti della Societa Italian per il Progresso della Scienza (1933)
Moreau, J.J.: Application of convex analysis to some problems of dry friction. In: Zorski, H. (ed.): Trends in Applications of Pure Mathematics to Mechanics, vol. 2, pp. 263–280. Pitman, London (1979)
Panagiotopoulos, P.D.: Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functionals. Birkhäuser, Basel (1985)
Kwak, B.M.: Complementarity problem formulation of three-dimensional frictional contact. J. Appl. Mech. 58, 134–140 (1991)
Anitescu, M., Potra, F.A.: Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dyn. 14(3), 231–247 (1997)
Brogliato, B.: Some perspectives on the analysis and control of complementarity systems. IEEE Trans. Autom. Control 48(6), 918–935 (2003)
Leine, R.I., Nijmeijer, H.: Dynamics and Bifurcations of Non-smooth Mechanical Systems. Lecture Notes in Applied and Computational Mechanics, vol. 18. Springer, Berlin (2004)
Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw Hill, New York (1970)
Hertz, H.: On the contact of solids—On the contact of rigid elastic solids and on hardness, pp. 146–183. MacMillan, London (1896). Miscellaneous Papers. (Translated by D.E. Jones and G.A. Schott)
Mansour, W.M., Townsend, M.A.: Impact spectra and intensities for high-speed mechanisms. J. Eng. Ind. 97(2), 347–353 (1975)
Miedema, B., Mansour, W.M.: Mechanical joints with clearance: a three mode model. J. Eng. Ind. 98(4), 1319–1323 (1976)
Haines, R.S.: Survey: 2-Dimensional motion and impact at revolute joints. Mech. Mach. Theory 15, 361–370 (1980)
Flores, P.: Dynamic analysis of mechanical systems with imperfect kinematic joints. Ph.D. Dissertation, Mechanical Engineering Department, University of Minho, Guimarães, Portugal (2005)
Srivastava, N., Haque, I.: Clearance and friction-induced dynamics of chain CVT drives. Multibody Syst. Dyn. 19(3), 255–280 (2008)
Erkaya, S., Uzmay, I.: A neural-genetic (NN–GA) approach for optimising mechanisms having joints with clearance. Multibody Syst. Dyn. 20(1), 69–83 (2008)
Erkaya, S., Uzmay, I.: Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn. 58(1–2), 179–198 (2009)
Zukas, J.A., Nicholas, T., Greszczuk, L.B., Curran, D.R.: Impact Dynamics. Wiley, New York (1982)
Goldsmith, W.: Impact—The Theory and Physical Behaviour of Colliding Solids. Edward, London (1960)
Greenwood, D.T.: Principles of Dynamics. Prentice Hall, Englewood Cliffs (1965)
Nikravesh, P.E.: Initial condition correction in multibody dynamics. Multibody Syst. Dyn. 18, 107–115 (2007)
Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1, 1–16 (1972)
Gear, W.W.: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs (1971)
ANSY, Y14.5M-1994, Dimensional and Tolerancing. ASME, New York (1994)
Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York (1990)
Flores, P.: MUBODYNA – A FORTRAN Program for Dynamic Analysis of Planar Multibody Systems. University of Minho, Guimarães (2010)
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Flores, P. A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn 61, 633–653 (2010). https://doi.org/10.1007/s11071-010-9676-8
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DOI: https://doi.org/10.1007/s11071-010-9676-8