Effects of Input Speed on the Dynamic Response of Planar Multi-body Systems with Differently Located Frictionless Revolute Clearance Joints
This paper numerically investigates the effects of input
speed on the overall dynamic characteristics of a multi-body system
with differently located revolute clearance joints without friction. A
typical planar slider-crank mechanism is used as a demonstration case
in which the effects of the input speed on the dynamic performance
of the mechanism with a revolute clearance joint between the crank
and connecting rod, and between the connecting rod and slider are
separately investigated with comprehensive observations numerically
presented. It is observed that, changing the driving speed of a multibody
system makes the behavior of the system to change from
either periodic to chaotic, or chaotic to periodic depending on which
joint has clearance. The location of the clearance revolute joint and
the operating speed of a multi-body system play a crucial role in
predicting accurately the dynamic responses of the system. Therefore
the dynamic behavior of one clearance revolute joint cannot be used
as a general case for a mechanical system.
[1] Dubowsky, S. and Freudenstein, F., "Dynamic analysis of mechanical
systems with clearances, part 1: Formulation of dynamic model," Journal
of Engineering for Industry, vol. 93(1), pp. 305-309, 1971.
[2] Dubowsky, S. and Freudenstein, F., "Dynamic analysis of mechanical
systems with clearances, part 2: Dynamic response," Journal of Engineering
for Industry,, vol. 93(1), pp. 310-316, 1971.
[3] Dubowsky, S., Deck, J. F. and Costello, H., "The dynamic modeling of
flexible spatial machine systems with clearance connections," Journal of
Mechanisms, Transmissions and Automation in Design, vol. 109, pp. 87-
94, 1987.
[4] Earles, S.W.E. and Wu, C.L.S., "Motion analysis of a rigid link mechanism
with clearance at a bearing using lagrangian mechanics and digital
computation," Journal of Mechanisms, pp. 83-89, 1973.
[5] Wu, C.L.S. and Earles, S.W.E., "A determination of contact-loss at a
bearing of a linkage mechanism," Journal of Engineering for Industry,
vol. 99(2), pp. 375-380, 1977.
[6] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics
of four-bar linkage with clearances at turning pairs 1st report: General
theory using continuous contact model," JSME, vol. 21, pp. 518-523,
1978.
[7] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics of
four-bar linkage with clearances at turning pairs 2nd report: Analysis of
crank-lever mechanism with clearance at joint of crank coupler using
continuous contact model," JSME, vol. 21, pp. 1284-1291, 1978.
[8] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics of
four-bar linkage with clearances at turning pairs 3rd report: Analysis
of crank-lever mechanism with clearance at joint of coupler and lever
using continuous contact model," JSME, vol. 21, pp. 1292-1298, 1978.
[9] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics
of four-bar linkage with clearances at turning pairs 4th report: Forces
acting at joints of crank-lever mechanism," JSME, vol. 21, pp. 1292-
1298, 1978.
[10] Farahanchi, F. and Shaw, S. W., "Chaotic and periodic dynamics of a
slider-crank mechanism with slider clearance," Journal of Sound and
Vibration, vol. 177(3), pp. 307-324, 1994.
[11] Rhee, J. and Akay A., "Dynamic response of a revolute joint with
clearance," Journal of Mechanisms and Machine Theory, vol. 31(1),
pp. 121-134., 1996.
[12] Ravn, P., "A continuous analysis method for planar multibody systems
with joint clearance," Journal of Multibody System Dynamics, vol. 2,
pp. 1-24, 1998.
[13] Ravn, P., Shivaswamy, S., Alshaer, B. J. and Lankarani, H. M., "Joint
clearances with lubricated long bearings in multibody mechanical systems,"
Journal of Mechanical Design, vol. 122, pp. 484-488, 2000.
[14] Chunmei, J., Yang, Q., Ling, F. and Ling, Z., "The nonlinear dynamic
behavior of an elastic linkage mechanism with clearances," Journal of
Sound and Vibration, vol. 249(2), pp. 213-226, 2002.
[15] Chang, Z., "Nonlinear dynamics and analysis of four-bar linkage with
clearance," in In Proceedings of 12th IFToMM Congress, France, 2007.
[16] Schwab, A.L., Meijaard, J.P. and Meijers, P. , "A comparison of revolute
joint clearance models in the dynamic analysis of rigid and elastic
mechanical systems," vol. 37, pp. 895-913, 2002.
[17] Flores, P., Ambrosio, J., Claro, J.P., "Dynamic analysis for planar
multibody mechanical systems with lubricated joints," Journal of Multibody
Systems Dynamics, vol. 12, pp. 47-74, 2004.
[18] Flores, P., and Ambrosio, J., "Revolute joints with clearance in multibody
systems," Journal of Computers and Structures, vol. 82, pp. 1359-
1369, 2004.
[19] Erkaya, S., and Uzmay, I., "Experimental investigation of joint clearance
effects on the dynamics of a slider-crank mechanism," Journal of
Multibody System Dynamics, vol. 24, pp. 81-102, 2010.
[20] Shiau, T.N., Tsai, Y.J., Tsai, M.S., "Nonlinear dynamic analysis of
a parallel mechanism with consideration of joint effects," Journal of
Mechanism and Machine Theory, vol. 43, pp. 491-505, 2008.
[21] Erkaya, S. and Uzmay, I., "A neural-genetic (nn-ga) approach for
optimising mechanisms having joints with clearance," Journal of Multibody
Systems Dynamics, vol. 20, pp. 69-83, 2008.
[22] Erkaya, S., and Uzmay, I., "Determining link parameters using genetic
algorithm in mechanisms with joint clearance," Journal of Mechanisms
and Machine Theory, vol. 44, pp. 222-234, 2009.
[23] Erkaya, S., and Uzmay, I., "Optimization of transmission angle for
slider-crank mechanism with joint clearances," Journal of Structural
Multidiscipine Optimization, vol. 37, pp. 493-508, 2009.
[24] Khemili, I., and Romdhane, L., "Dynamic analysis of a flexible slidercrank
mechanism with clearance," European Journal of Mechanics,
Elsevier, vol. 27, pp. 882-898, 2008.
[25] Erkaya, S., and Uzmay, I., "Investigation on effect of joint clearance
on dynamics of four-bar mechanism," Journal of Nonlinear Dynamics,
vol. 58, pp. 179-198, 2009.
[26] Liu, T. S. and Lin, Y. S., "Dynamic analysis of flexible linkages with
lubricated joints," Journal of Sound and Vibration, vol. 141, pp. 193-
205, 1990.
[27] Ravn, P., Shivaswamy, S. and Lankarani, H. M., "Treatment of lubrication
in long bearings for joint clearances in multibody mechanical
systems," in Proceedings of the ASME Design Technical Conference,
Las Vegas, September 12-15 1999.
[28] Olivier, A. B. and Rodriguez, J., "Modeling of Joints with Clearance
in Flexible Multibody Systems," International Journal of Solids and
Structures, vol. 39, pp. 41-63, 2002.
[29] Kakizaki, T., Deck, J.F. and Dubowsky, S., "Modeling the spatial dynamics
of robotic manipulators with flexible links and joint clearances,"
Journal of Mechanical Design, vol. 115, pp. 839-847, 1993.
[30] Jia, X., Jin, D., Ji, L., and Zhang, J., "Investigation on the dynamic
performance of the tripod-ball sliding joint with clearance in a crankslider
mechanism. part 1. theoretical and experimental results.," Journal
of Sound and Vibrations, vol. 252(5), p. 919933, 2002.
[31] Bing, S. and Ye, J., "Dynamic analysis of the reheat-stop-valve mechanism
with revolute clearance joint in consideration of thermal effect.,"
Journal of Mechanisms and Machine Theory, vol. 43(12), pp. 1625-
1638, 2008.
[32] Flores, P., "Modeling and simulation of wear in revolute clearance joints
in multibody systems," Journal of Mechanisms and machine Theory,
vol. 44(6), pp. 1211-1222, 2009.
[33] Dupac, M. and Beale, D.G., "Dynamic analysis of a flexible linkage
mechanism with cracks and clearance." To be published in Journal of
Mechanisms and Machine Theory, 2010.
[34] Flores, P., Ambrsio, J., Claro, J.C.P., Lankarani, H.M. and Koshy, C.S.,
"Lubricated revolute joints in rigid multibody systems," Journal of
Nonlinear Dynamics, vol. 56(3), pp. 277-295, 2009.
[35] Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L., and Sawyer,
W.G., "Analysis of planar multibody systems with revolute joint wear,"
Journal of Wear, vol. 268, pp. 643-652, 2010.
[36] Flores, P., "A parametric study on the dynamic response of plnar
multibody systems with multiple clearance joints," Journal of Nonlinear
Dynamics, vol. 4, pp. 633-653, 2010.
[37] Dubowsky, S., and Moening, M.F., "An Experimental and Analytical
Study of Impact Forces in Elastic Mechanical Systems with Clearances,"
Journal of Mechanism and Machine Theory, vol. 13, pp. 451-465, 1978.
[38] Flores, P., Dynamic Analysis of Mechanical Systems with Imperfect
Kinematic Joints. PhD thesis, UNIVERSIDADE DO MINHO PARA,
2004.
[39] Cheriyan, S. K., Chracterization of Mechanical Systems with Real Joints
and Flexible Links. PhD thesis, Wichita State University, 2006.
[40] Nikravesh, P.E., Computer-Aided Analysis of Mechanical Systems,. Prentice
Hall, Englewood Cliffs, New Jersey, 1988.
[41] Baumgarte, J., "Stabilization of constraints and integrals of motion in
dynamical systems," Journal of Computer Methods in Applied Mechanics
and Engineering, vol. 1, pp. 1-16, 1972.
[42] Shabana, A. A., Computational Dynamics. John Wiley & Sons, New
York, 1994.
[43] Lankarani, H. M. and Nikravesh, P. E., "Continuous contact force
models for impact analysis in multibody systems," Journal of Nonlinear
Dynamics, pp. 194-207, 1994.
[44] Lankarani, H.M., and Nikravsh, P.E., "A contact force model with
hysteresis damping for impact analysis of multibody systems," Journal
of Mechanical Design, vol. 112, pp. 369-376, 1990.
[45] Love, A. E., A treatise on the Mathematical Theory of Elasticity. Dover
Publishers, 4th ed., 1944.
[1] Dubowsky, S. and Freudenstein, F., "Dynamic analysis of mechanical
systems with clearances, part 1: Formulation of dynamic model," Journal
of Engineering for Industry, vol. 93(1), pp. 305-309, 1971.
[2] Dubowsky, S. and Freudenstein, F., "Dynamic analysis of mechanical
systems with clearances, part 2: Dynamic response," Journal of Engineering
for Industry,, vol. 93(1), pp. 310-316, 1971.
[3] Dubowsky, S., Deck, J. F. and Costello, H., "The dynamic modeling of
flexible spatial machine systems with clearance connections," Journal of
Mechanisms, Transmissions and Automation in Design, vol. 109, pp. 87-
94, 1987.
[4] Earles, S.W.E. and Wu, C.L.S., "Motion analysis of a rigid link mechanism
with clearance at a bearing using lagrangian mechanics and digital
computation," Journal of Mechanisms, pp. 83-89, 1973.
[5] Wu, C.L.S. and Earles, S.W.E., "A determination of contact-loss at a
bearing of a linkage mechanism," Journal of Engineering for Industry,
vol. 99(2), pp. 375-380, 1977.
[6] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics
of four-bar linkage with clearances at turning pairs 1st report: General
theory using continuous contact model," JSME, vol. 21, pp. 518-523,
1978.
[7] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics of
four-bar linkage with clearances at turning pairs 2nd report: Analysis of
crank-lever mechanism with clearance at joint of crank coupler using
continuous contact model," JSME, vol. 21, pp. 1284-1291, 1978.
[8] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics of
four-bar linkage with clearances at turning pairs 3rd report: Analysis
of crank-lever mechanism with clearance at joint of coupler and lever
using continuous contact model," JSME, vol. 21, pp. 1292-1298, 1978.
[9] Furuhashi, T., Morita, N. and Matsuura, M., "Research on dynamics
of four-bar linkage with clearances at turning pairs 4th report: Forces
acting at joints of crank-lever mechanism," JSME, vol. 21, pp. 1292-
1298, 1978.
[10] Farahanchi, F. and Shaw, S. W., "Chaotic and periodic dynamics of a
slider-crank mechanism with slider clearance," Journal of Sound and
Vibration, vol. 177(3), pp. 307-324, 1994.
[11] Rhee, J. and Akay A., "Dynamic response of a revolute joint with
clearance," Journal of Mechanisms and Machine Theory, vol. 31(1),
pp. 121-134., 1996.
[12] Ravn, P., "A continuous analysis method for planar multibody systems
with joint clearance," Journal of Multibody System Dynamics, vol. 2,
pp. 1-24, 1998.
[13] Ravn, P., Shivaswamy, S., Alshaer, B. J. and Lankarani, H. M., "Joint
clearances with lubricated long bearings in multibody mechanical systems,"
Journal of Mechanical Design, vol. 122, pp. 484-488, 2000.
[14] Chunmei, J., Yang, Q., Ling, F. and Ling, Z., "The nonlinear dynamic
behavior of an elastic linkage mechanism with clearances," Journal of
Sound and Vibration, vol. 249(2), pp. 213-226, 2002.
[15] Chang, Z., "Nonlinear dynamics and analysis of four-bar linkage with
clearance," in In Proceedings of 12th IFToMM Congress, France, 2007.
[16] Schwab, A.L., Meijaard, J.P. and Meijers, P. , "A comparison of revolute
joint clearance models in the dynamic analysis of rigid and elastic
mechanical systems," vol. 37, pp. 895-913, 2002.
[17] Flores, P., Ambrosio, J., Claro, J.P., "Dynamic analysis for planar
multibody mechanical systems with lubricated joints," Journal of Multibody
Systems Dynamics, vol. 12, pp. 47-74, 2004.
[18] Flores, P., and Ambrosio, J., "Revolute joints with clearance in multibody
systems," Journal of Computers and Structures, vol. 82, pp. 1359-
1369, 2004.
[19] Erkaya, S., and Uzmay, I., "Experimental investigation of joint clearance
effects on the dynamics of a slider-crank mechanism," Journal of
Multibody System Dynamics, vol. 24, pp. 81-102, 2010.
[20] Shiau, T.N., Tsai, Y.J., Tsai, M.S., "Nonlinear dynamic analysis of
a parallel mechanism with consideration of joint effects," Journal of
Mechanism and Machine Theory, vol. 43, pp. 491-505, 2008.
[21] Erkaya, S. and Uzmay, I., "A neural-genetic (nn-ga) approach for
optimising mechanisms having joints with clearance," Journal of Multibody
Systems Dynamics, vol. 20, pp. 69-83, 2008.
[22] Erkaya, S., and Uzmay, I., "Determining link parameters using genetic
algorithm in mechanisms with joint clearance," Journal of Mechanisms
and Machine Theory, vol. 44, pp. 222-234, 2009.
[23] Erkaya, S., and Uzmay, I., "Optimization of transmission angle for
slider-crank mechanism with joint clearances," Journal of Structural
Multidiscipine Optimization, vol. 37, pp. 493-508, 2009.
[24] Khemili, I., and Romdhane, L., "Dynamic analysis of a flexible slidercrank
mechanism with clearance," European Journal of Mechanics,
Elsevier, vol. 27, pp. 882-898, 2008.
[25] Erkaya, S., and Uzmay, I., "Investigation on effect of joint clearance
on dynamics of four-bar mechanism," Journal of Nonlinear Dynamics,
vol. 58, pp. 179-198, 2009.
[26] Liu, T. S. and Lin, Y. S., "Dynamic analysis of flexible linkages with
lubricated joints," Journal of Sound and Vibration, vol. 141, pp. 193-
205, 1990.
[27] Ravn, P., Shivaswamy, S. and Lankarani, H. M., "Treatment of lubrication
in long bearings for joint clearances in multibody mechanical
systems," in Proceedings of the ASME Design Technical Conference,
Las Vegas, September 12-15 1999.
[28] Olivier, A. B. and Rodriguez, J., "Modeling of Joints with Clearance
in Flexible Multibody Systems," International Journal of Solids and
Structures, vol. 39, pp. 41-63, 2002.
[29] Kakizaki, T., Deck, J.F. and Dubowsky, S., "Modeling the spatial dynamics
of robotic manipulators with flexible links and joint clearances,"
Journal of Mechanical Design, vol. 115, pp. 839-847, 1993.
[30] Jia, X., Jin, D., Ji, L., and Zhang, J., "Investigation on the dynamic
performance of the tripod-ball sliding joint with clearance in a crankslider
mechanism. part 1. theoretical and experimental results.," Journal
of Sound and Vibrations, vol. 252(5), p. 919933, 2002.
[31] Bing, S. and Ye, J., "Dynamic analysis of the reheat-stop-valve mechanism
with revolute clearance joint in consideration of thermal effect.,"
Journal of Mechanisms and Machine Theory, vol. 43(12), pp. 1625-
1638, 2008.
[32] Flores, P., "Modeling and simulation of wear in revolute clearance joints
in multibody systems," Journal of Mechanisms and machine Theory,
vol. 44(6), pp. 1211-1222, 2009.
[33] Dupac, M. and Beale, D.G., "Dynamic analysis of a flexible linkage
mechanism with cracks and clearance." To be published in Journal of
Mechanisms and Machine Theory, 2010.
[34] Flores, P., Ambrsio, J., Claro, J.C.P., Lankarani, H.M. and Koshy, C.S.,
"Lubricated revolute joints in rigid multibody systems," Journal of
Nonlinear Dynamics, vol. 56(3), pp. 277-295, 2009.
[35] Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L., and Sawyer,
W.G., "Analysis of planar multibody systems with revolute joint wear,"
Journal of Wear, vol. 268, pp. 643-652, 2010.
[36] Flores, P., "A parametric study on the dynamic response of plnar
multibody systems with multiple clearance joints," Journal of Nonlinear
Dynamics, vol. 4, pp. 633-653, 2010.
[37] Dubowsky, S., and Moening, M.F., "An Experimental and Analytical
Study of Impact Forces in Elastic Mechanical Systems with Clearances,"
Journal of Mechanism and Machine Theory, vol. 13, pp. 451-465, 1978.
[38] Flores, P., Dynamic Analysis of Mechanical Systems with Imperfect
Kinematic Joints. PhD thesis, UNIVERSIDADE DO MINHO PARA,
2004.
[39] Cheriyan, S. K., Chracterization of Mechanical Systems with Real Joints
and Flexible Links. PhD thesis, Wichita State University, 2006.
[40] Nikravesh, P.E., Computer-Aided Analysis of Mechanical Systems,. Prentice
Hall, Englewood Cliffs, New Jersey, 1988.
[41] Baumgarte, J., "Stabilization of constraints and integrals of motion in
dynamical systems," Journal of Computer Methods in Applied Mechanics
and Engineering, vol. 1, pp. 1-16, 1972.
[42] Shabana, A. A., Computational Dynamics. John Wiley & Sons, New
York, 1994.
[43] Lankarani, H. M. and Nikravesh, P. E., "Continuous contact force
models for impact analysis in multibody systems," Journal of Nonlinear
Dynamics, pp. 194-207, 1994.
[44] Lankarani, H.M., and Nikravsh, P.E., "A contact force model with
hysteresis damping for impact analysis of multibody systems," Journal
of Mechanical Design, vol. 112, pp. 369-376, 1990.
[45] Love, A. E., A treatise on the Mathematical Theory of Elasticity. Dover
Publishers, 4th ed., 1944.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60493", author = "Onesmus Muvengei and John Kihiu and Bernard Ikua", title = "Effects of Input Speed on the Dynamic Response of Planar Multi-body Systems with Differently Located Frictionless Revolute Clearance Joints", abstract = "This paper numerically investigates the effects of input
speed on the overall dynamic characteristics of a multi-body system
with differently located revolute clearance joints without friction. A
typical planar slider-crank mechanism is used as a demonstration case
in which the effects of the input speed on the dynamic performance
of the mechanism with a revolute clearance joint between the crank
and connecting rod, and between the connecting rod and slider are
separately investigated with comprehensive observations numerically
presented. It is observed that, changing the driving speed of a multibody
system makes the behavior of the system to change from
either periodic to chaotic, or chaotic to periodic depending on which
joint has clearance. The location of the clearance revolute joint and
the operating speed of a multi-body system play a crucial role in
predicting accurately the dynamic responses of the system. Therefore
the dynamic behavior of one clearance revolute joint cannot be used
as a general case for a mechanical system.", keywords = "Chaotic behavior, Contact-impact forces, Dynamic response,Multi-body mechanical system, Periodic behavior, Poincare maps, Quasi-periodic behavior, Revolute clearance joint", volume = "5", number = "2", pages = "433-10", }
