**Page description appears here**

“Comparison and Implementation of a Rigid and a Flexible Multibody Planetary Gearbox Model”

Authors: Martin Felix Jørgensen, Niels Leergaard Pedersen and Jens Nørkær Sørensen,
Affiliation: Technical University of Denmark
Reference: 2014, Vol 35, No 2, pp. 59-77.

     Valid XHTML 1.0 Strict

Keywords: multibody, gearbox, teeth, matlab

Abstract: We propose algorithms for developing (1) a rigid (constrained) and (2) a flexible planetary gearbox model. The two methods are compared against each other and advantages/disadvantages of each method are discussed. The rigid model (1) has gear tooth reaction forces expressed by Lagrange multipliers. The flexible approach (2) is being compared with the gear tooth forces from the rigid approach, first without damping and second the influence of damping is examined. Variable stiffness as a function of base circle arc length is implemented in the flexible approach such that it handles the realistic switch between one and two gear teeth in mesh. The final results are from modelling the planetary gearbox in a 500 kW wind turbine which we also described in Jørgensen et.al (2013).

PDF PDF (1042 Kb)        DOI: 10.4173/mic.2014.2.1

DOI forward links to this article:
  [1] Martin Felix Jørgensen, Niels Leergaard Pedersen and Jens Nørkær Sørensen (2014), doi:10.4173/mic.2014.2.4

[1] Amirouche, F. M.L. (2004). Fundamentals of multibody dynamics : theory and applications, Birkhauser. Includes bibliographical references and index.
[2] Ascher, U.M. and Petzold, L.R. (1998). Computer methods for ordinary differential equations and differential-algebraic equations, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. pages 3--305.
[3] Bae, D. and Haug, E. (1988). A recursive formulation for constrained mechanical system dynamics -- 2, closed-loop systems. Mechanics of structures and machines. 15(4):481--506.
[4] Ebrahimi, S. and Eberhard, P. (2006). Rigid-elastic modeling of meshing gear wheels in multibody systems, Multibody System Dynamics. 16(1):55--71. doi:10.1007/s11044-006-9021-7
[5] Gear, C. (1971). Simultaneous numerical solution of differential-algebraic equations, Circuit Theory, IEEE Transactions on. 18(1):89--95.
[6] Geradin, M. and Cardona, A. (2001). Flexible multibody dynamics: a finite element approach, John Wiley.
[7] Haastrup, M., Hansen, M.R., and Ebbesen, M.K. (2011). Modeling of wind turbine gearbox mounting, Modeling, Identification and Control. 32(4):141--149. doi:10.4173/mic.2011.4.2
[8] Hairer, E. and Wanner, G. (1996). Solving ordinary differential equations ii: Stiff and differential-algebraic problems second revised edition with 137 figures, Springer Series in Computational Mathematics. 14/2.
[9] Hansen, A.M., Rasmussen, F., and Larsen, T.J. (2011). Gearbox loads caused by double contact simulated with hawc2, Proceedings of EWEA Annual Event from Brussels, Belgium. page11.
[10] Haug, E.J. (1989). Computer Aided Kinematics and Dynamics of Mechanical Systems: Vol, I: Basic Methods. Allyn and Bacon.
[11] Huston, R.L. and Wang, Y. (1994). Flexibility effects in multibody systems, NATO ASI Series E Applied Sciences - Advanced Study Institute, 1994. 268:351.
[12] Jalon, J. G.d., Bayo, E., and Bahar, L.Y. (1995). Kinematic and dynamic simulation of multibody systems: The real time challenge, Applied Mechanics Reviews - Including Supplement. 48(1):B2.
[13] Jørgensen, M.F., Pedersen, N.L., Sørensen, J.N., and Paulsen, U.S. (2013). Rigid matlab drivetrain model of a 500 kw wind turbine for predicting maximum gear tooth stresses in a planetary gearbox using multibody gear constraints, Wind Energy.
[14] Klit, P., Casper, K., and Pedersen, N.L. (2009). Machine Elements - Analysis and Design, Polyteknisk Forlag.
[15] Multiphysics, C. (1998). www, comsol.se. 1998-2012.
[16] Nikravesh, P.E. (1988). Computer-Aided Analysis of Mechanical Systems, volume 186, Prentice Hall.
[17] Pedersen, N.L. and Jørgensen, M.F. (2014). On gear teeth stiffness evaluation, Computers and Structures, vol. 135, p. 109-117.
[18] Pedersen, N.L. and Pedersen, M.L. (1998). A direct derivation of the equations of motion for 3D-flexible mechanical systems, International Journal for Numerical Methods in Engineering, 1998. 41(4):697--719. doi:10.1002/(SICI)1097-0207(19980228)41:4<697::AID-NME306>3.0.CO;2-Y
[19] Peeters, J. L.M., Vandepitte, D., and Sas, P. (2006). Analysis of internal drive train dynamics in a wind turbine, Wind Energy. 9(1-2):141--161. http://dx.doi.org/10.1002/we.173, doi:10.1002/we.173
[20] Rasmussen, F., Hansen, A.M., and Larsen, T.J. (2012). Can transient loads occur internally in a planetary gearbox? Proceedings of EWEA 2012 - European Wind Energy Conference & Exhibition, http://orbit.dtu.dk/services/downloadRegister/10376650/Can_transient_loads.pdf.
[21] Shabana, A.A. (1989). Dynamics of Multibody Systems, Wiley & Sons.
[22] Shabana, A.A. (1997). Flexible multibody dynamics: Review of past and recent developments, Multibody System Dynamics. 1(2):189--222. doi:10.1023/A:1009773505418
[23] Øye, S. (2001). Various FLEX 5 documentation, DTU Mechanical Engineering.
[24] Ziegler, P., Eberhard, P., and Schweizer, B. (2006). Simulation of impacts in geartrains using different approaches, Archive of Applied Mechanics. 76(9-10):537--548.

  title={{Comparison and Implementation of a Rigid and a Flexible Multibody Planetary Gearbox Model}},
  author={Jørgensen, Martin Felix and Pedersen, Niels Leergaard and Sørensen, Jens Nørkær},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.

May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.