“An Isogeometric Analysis Approach to Kinematics of Spatial Rigid Multibody Systems with Imperfect Joints”
Authors: Remzija Cerimagic, Lisbeth Fajstrup, Torben Ole Andersen and Per Johansen,Affiliation: Aalborg University
Reference: 2020, Vol 41, No 1, pp. 29-40.
Keywords: Clearance joints, NURBS, Surface implicitization, Tribodynamics, Tribological kinematics, Isogeometric analysis
Abstract: This paper proposes a novel generic methodology for kinematics of spatial rigid-multibody systems with and without lubricated joints. In this method CAD surface representations in the form of non-uniform rational B-splines (NURBS) are used to address the interface kinematics. This eliminates the time and effort needed to manually parameterize the interface geometry, by enabling a direct use of the engineering designs encapsulated in CAD systems. Furthermore, the use of NURBS for surface representation allows integration of tribodynamics into an isogeometric analysis (IGA) setting. The kinematic formulation is based on a new implicit matrix approach for implicitization of CAD surfaces in three-dimensional space. The construction of such implicit matrices and their properties are explained, and explicit expressions for the gap height distance, velocity and relative velocities in a general clearance joint are provided.
PDF (632 Kb)
DOI: 10.4173/mic.2020.1.3DOI forward links to this article:
| [1] Ke Zhang, Caixia Guo, Yutao Li, Yuewen Su, Bodong Zhang and Peihu Gao (2023), doi:10.3390/coatings13122029 |
[1] Arora, J.S. (2012). Arora, J, S. Introduction to Optimum Design. Elsevier. .
[2] Askari, E. and Andersen, M.S. (2019). Askari, E, and Andersen, M.S. A modification on velocity terms of Reynolds equation in a spherical coordinate system. Tribology International. 131:15--23. doi:10.1016/j.triboint.2018.10.019
[3] Buse, L. (2014). Buse, L, Implicit matrix representations of rational bezier curves and surfaces. Computer-Aided Design. 46:14--24. doi:10.1016/j.cad.2013.08.014
[4] Cerimagic, R., Johansen, P., and Andersen, T.O. (2018). Cerimagic, R, , Johansen, P., and Andersen, T.O. Isogeometric tribodynamics of a radial piston fluid power motor. In I.Press, editor, Proc. of the 2018 Global Fluid Power Society PhD Symposium, GFPS 2018. pages 1--7. doi:10.1109/GFPS.2018.8472376
[5] Erkaya, S. and Uzmay, I. (2010). Erkaya, S, and Uzmay, I. Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst Dyn. 24:81--102. doi:10.1007/s11044-010-9192-0
[6] Flores, P., Ambrosio, J., Claro, J. C.P., and Lankarani, H.M. (2008). Flores, P, , Ambrosio, J., Claro, J. C.P., and Lankarani, H.M. Kinematics and dynamics of multibody systems with imperfect joints. Springer. .
[7] Flores, P. and Lankarani, H.M. (2010). Flores, P, and Lankarani, H.M. Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dynamics. 60(1--2):99--114. doi:10.1007/s11071-009-9583-z
[8] Hansen, A.H. and Pedersen, H.C. (2015). Hansen, A, H. and Pedersen, H.C. Energy cost of avoiding pressure oscillations in a discrete fluid power force system. In Proc. of the ASME/BATH 2015 Symposium on Fluid Power and Motion Control, FPMC, American Society of Mechanical Engineers. pages 1--10, 2015. doi:10.1115/FPMC2015-9581
[9] Hansen, A.H. and Pedersen, H.C. (2016). Hansen, A, H. and Pedersen, H.C. Optimal configuration of discrete fluid power force system utilised in the PTO for WECs. Ocean Engineering, 2016. 117(OE3694):88--98. doi:10.1016/j.oceaneng.2016.03.032
[10] Hansen, A.H. and Pedersen, H.C. (2016). Hansen, A, H. and Pedersen, H.C. Reducing pressure oscillations in discrete fluid power systems. In Proc. Part I: J. Syst. Control Eng., volume 230. pages 1093--1105, 2016. doi:10.1177/0959651815625015
[11] Hughes, T. J.R., Cottrell, J.A., and Bazilevs, Y. (2005). Hughes, T, J.R., Cottrell, J.A., and Bazilevs, Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering. 194(39--41):4135--4195. doi:10.1016/j.cma.2004.10.008
[12] Johansen, P., Roemer, D.B., Andersen, T.O., and Pedersen, H.C. (2015). Johansen, P, , Roemer, D.B., Andersen, T.O., and Pedersen, H.C. On the influence of piston and cylinder density in tribodynamics of a radial piston digital fluid power displacement motor. In Proc. of the ASME/BATH 2015 Symposium on Fluid Power and Motion Control, FPMC, American Society of Mechanical Engineers. pages 1--10, 2015. doi:10.1115/FPMC2015-9608
[13] Liu, W., Huang, Z., Liu, Q., and Zeng, J. (2016). Liu, W, , Huang, Z., Liu, Q., and Zeng, J. An isogeometric analysis approach for solving the reynolds equation in lubricated piston dynamics. Tribology International. 103:149--166. doi:10.1016/j.triboint.2016.06.030
[14] Machado, M., Costa, J., Seabra, E., and Flores, P. (2012). Machado, M, , Costa, J., Seabra, E., and Flores, P. The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems. Nonlinear Dynamics. 69:635--654. doi:10.1007/s11071-011-0293-y
[15] Murray, R.M., Li, Z., and Sastry, S.S. (1994). Murray, R, M., Li, Z., and Sastry, S.S. A mathematical introduction to robotic manipulation. CRC Press. .
[16] Pi, T. and Zhang, Y. (2019). Pi, T, and Zhang, Y. Modeling and simulation of revolute clearance joint with friction using the NURBS-based isogeometric analysis. Nonlinear Dyn. 95:195--215. doi:10.1007/s11071-018-4559-5
[17] Piegl, L. and Tiller, W. (1995). Piegl, L, and Tiller, W. The NURBS Book. Springer. .
[18] Piegl, L. and Tiller, W. (1998). Piegl, L, and Tiller, W. Computing the derivatives of NURBS with respect to a knot. Computer Aided Geometric Design. 15:925--934. doi:10.1016/S0167-8396(98)00028-4
[19] Stachowiak, G. and Batchelor, A. (2005). Stachowiak, G, and Batchelor, A. Engineering Tribology. Elsevier Butterworth-Heinemann. .
[20] Tian, Q., Flores, P., and Lankarani, H. (2018). Tian, Q, , Flores, P., and Lankarani, H. A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints. Mech. Mach. Theory. 122:1--57. doi:10.1016/j.mechmachtheory.2017.12.002
[21] Tian, Q., Liu, C., Machado, M., and Flores, P. (2011). Tian, Q, , Liu, C., Machado, M., and Flores, P. A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dynamics. 64(1--2):25--47. doi:10.1007/s11071-010-9843-y
[22] Tian, Q., Sun, Y., Liu, C., Hu, H., and Flores, P. (2013). Tian, Q, , Sun, Y., Liu, C., Hu, H., and Flores, P. Elastohydrodynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Computers and Structures. 114:106--120. doi:10.1016/j.compstruc.2012.10.019
[23] Tian, Q., Zhang, Y., Chen, L., and Flores, P. (2009). Tian, Q, , Zhang, Y., Chen, L., and Flores, P. Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Computers and Structures. 87(13--14):913--929. doi:10.1016/j.compstruc.2009.03.006
[24] Wall, W.A., Frenzel, M.A., and Cyron, C. (2008). Wall, W, A., Frenzel, M.A., and Cyron, C. Isogeometric structural shape optimization. Computer Methods in Applied Mechanics and Engineering. 197(33--40):2976--2988. doi:10.1016/j.cma.2008.01.025
[25] xin Xu, L. and gang Li, Y. (2012). xin Xu, L, and gang Li, Y. An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems. Nonlinear Dynamics. 70(3):2145--2161. doi:10.1007/s11071-012-0606-9
[26] Zhao, B., Zhou, K., and Xie, Y. (2016). Zhao, B, , Zhou, K., and Xie, Y. A new numerical method for planar multibody system with mixed lubricated revolute joint. International Journal of Mechanical Sciences. 113:105--119. doi:10.1016/j.ijmecsci.2016.04.016
BibTeX:
@article{MIC-2020-1-3,
title={{An Isogeometric Analysis Approach to Kinematics of Spatial Rigid Multibody Systems with Imperfect Joints}},
author={Cerimagic, Remzija and Fajstrup, Lisbeth and Andersen, Torben Ole and Johansen, Per},
journal={Modeling, Identification and Control},
volume={41},
number={1},
pages={29--40},
year={2020},
doi={10.4173/mic.2020.1.3},
publisher={Norwegian Society of Automatic Control}
};