Abstract
As various errors result from manufacture and assembly processes or wear effect, clearance joint widely exists in mechanical system as a base component. The coupling analysis of tribology and dynamics of clearance joint is important to the reliability of mechanical system. A nonlinear contact pressure distribution mode (NLCP) is proposed to combine dynamics analysis with wear calculation together in this paper. The discrete thought of Winkler model is adopted to deal with contact problem with a high conformal rate. The contact relationship in a local microcontact area can be regarded as the contact between cylinder and plane. And the local contact pressure is acquired based on Hertz contact theory. The NLCP model has not only described the nonlinear relationship between contact pressure and penetration depth, but also avoided the complexity in contact pressure computation. The performance of NLCP model is demonstrated in comparison with asymmetric Winkler model, revealing that NLCP model has enhanced the calculation accuracy with a good efficiency. A comprehensive experimental study on the wear calculation of a slider–crank mechanism with clearance joint is presented and discussed to provide an experimental verification for NLCP model. The paper’s work has solved the contact problem with a high conformal rate and has described the nonlinear relationship between contact pressure and penetration depth. It has great value to the wear analysis of clearance joint.
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Erkaya, S., Uzmay, I.: Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn. 58(1), 179–198 (2009)
Flores, P., Leine, R., Glocker, C.: Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Syst. Dyn. 23(23), 165–190 (2010)
Flores, P., Koshy, C.S., Lankarani, H.M., et al.: Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn. 65(4), 383–398 (2011)
Askari, E., Flores, P., Dabirrahmani, D., et al.: Nonlinear vibration and dynamics of ceramic on ceramic artificial hip joints: a spatial multibody modeling. Nonlinear Dyn. 76(2), 1–13 (2014)
Tian, Q., Liu, C., Machado, M., et al.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64(1), 25–47 (2011)
Erkaya, S., Uzmay, I.: Effects of balancing and link flexibility on dynamics of a planar mechanism having joint clearance. Sci. Iran. 19(3), 483–490 (2012)
Pereira, C.M., Ramalho, A.L., Ambrosio, J.A.: An enhanced cylindrical contact force model. Multibody Syst. Dyn. 35(3), 277–298 (2015)
Askari, E., Flores, P., Dabirrahmani, D., et al.: Dynamic modeling and analysis of wear in spatial hard-on-hard couple hip replacements using multibody systems methodologies. Nonlinear Dyn. 82(1–2), 1039–1058 (2015)
Yaqubi, S., Dardel, M., Daniali, H.M., et al.: Modeling and control of crank-slider mechanism with multiple clearance joints. Multibody Syst. Dyn. 36(2), 1–25 (2015)
Varedi-Koulaei, S.M., Daniali, H.M., Farajtabar, M., et al.: Reducing the undesirable effects of joints clearance on the behavior of the planar 3-RRR parallel manipulators. Nonlinear Dyn. 86(2), 1–16 (2016)
Askari, E., Flores, P., Dabirrahmani, D., et al.: A computational analysis of squeaking hip prostheses. J. Comput. Nonlinear Dyn. 10(2), 024502 (2014)
Johnson, K.L., Johnsonm, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)
Machado, M., Moreira, P., Flores, P., et al.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012)
Ma, J., Qian, L., Chen, G.: Parameter estimation of the Lankarani–Nikravesh contact force model using a new modified linear method. In: IEEE International Conference on Advanced Intelligent Mechatronics. IEEE (2015)
Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42(2), 440–445 (1975)
Herbert, R.G., Mcwhannell, D.C.: Shape and frequency composition of pulses from an impact pair. J. Eng. Ind. 99(3), 663–671 (1977)
Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112(3), 369–376 (1990)
Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5(2), 193–207 (1994)
Bai, Z., Zhao, Y.: A hybrid contact force model of revolute joint with clearance for planar mechanical systems. Int. J. Non Linear Mech. 48(48), 15–36 (2013)
Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints. Nonlinear Dyn. 73(1–2), 259–273 (2013)
Zhang, X., Zhang, X., Chen, Z.: Dynamic analysis of a 3-RRR parallel mechanism with multiple clearance joints. Mech. Mach. Theory 78(78), 105–115 (2014)
Pereira, C.M., Ramalho, A.L., Ambrósio, J.A.: A critical overview of internal and external cylinder contact force models. Nonlinear Dyn. 63(4), 681–697 (2011)
Flodin, A., Andersson, S.: Simulation of mild wear in spur gears. Wear 207(1–2), 16–23 (1997)
Põdra, P., Andersson, S.: Wear simulation with the Winkler surface model. Wear 207(1), 79–85 (1997)
Liu, C.S., Zhang, K., Yang, R.: The FEM analysis and approximate model for cylindrical joints with clearances. Mech. Mach. Theory 42(2), 183–197 (2007)
Su, Y., Chen, W., Guo, C.: Wear prediction of clearance revolute joints using winkler surface model. Mocaxue Xuebao/Tribology 32(4), 320–324 (2012). http://www.tribology.com.cn/ch/reader/create_pdf.aspx?file_no=20120402&year_id=2012&quarter_id=4&falg=1
Li, P., Chen, W., Zhu, A.: An improved practical model for wear prediction of revolute clearance joints in crank slider mechanisms. Sci. China Technol. Sci. 56(12), 2953–2963 (2013)
Flores, P., Sio, J., Claro, J., et al.: Influence of the contact-impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng. Part K J. Multibody Dyn. 220(1), 21–34 (2006)
Hertz, H.: On the contact of solids—on the contact of rigid elastic solids and on hardness (Translated by DE Jones and GA Schott). Miscellaneous Papers (1896)
Goldsmith, W., Frasier, J.T.: Impact: the theory and physical behavior of colliding solids. J. Appl. Mech. 28, 639 (1961)
Bai, Z.F., Zhao, Y., Chen, J.: Dynamics analysis of planar mechanical system considering revolute clearance joint wear. Tribol. Int. 64(3), 85–95 (2013)
Flores, P.: Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44(6), 1211–1222 (2009)
Shen, X., Cao, L., Li, R.: Numerical simulation of sliding wear based on Archard model. In: International Conference on Mechanic Automation and Control Engineering, pp. 325–329 (2010). doi:10.1109/MACE.2010.5535855
Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24(8), 981–988 (1953)
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The authors would like to acknowledge the financial support of National Natural Science Foundation of China (NSFC, No: 51175409).
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Zhu, A., He, S., Zhao, J. et al. A nonlinear contact pressure distribution model for wear calculation of planar revolute joint with clearance. Nonlinear Dyn 88, 315–328 (2017). https://doi.org/10.1007/s11071-016-3244-9
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DOI: https://doi.org/10.1007/s11071-016-3244-9