Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Reciprocating Compressor Dynamics Modelling by a Bond Graph Approach

Journal of Vibration Testing and System Dynamics 5(2) (2021) 181--194 | DOI:10.5890/JVTSD.2021.06.006

Enaiyat Ghani Ovy , Qiao Sun

Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University DR NW, Calgary, AB, Canada

Download Full Text PDF



This research is dedicated to developing an analytical physics-based model of a reciprocating compressor based on a bond graph approach. At first, a mathematical model is developed for one-cylinder reciprocating compressor based on multi-body dynamics, particularly considering planar motion of the rigid bodies using body fixed reference frames. All the dynamical equations of motions are represented and linked altogether by the bond graph that simulates a complete system model. The model has unique capability to show forces at various joints, which enhances our understanding of complex system behavior. Moreover, the consequences of changing coefficients of those forces are accentuated. The utility of the model in fault diagnosis and condition monitoring are emphasized by highlighting the effects of a crack in a joint and a dent on cylinder wall. Nonlinear differential equations extracted from bond graph model are solved efficiently using a MATLAB stiff solver. Responses of the model parts are analyzed later by force analysis along with a comparison with a previous research to examine model validity.


Authors would like to acknowledge Alberta Innovates Technology Futures (AITF) and Mitacs Accelerate for the award to support the research work. Authors would also express their gratitude to Dr Mario Forcinito for his valuable insights and suggestions to accomplish the project.


  1. [1]  Schultheis, S.M., Lickteig, C.A., and Parchewsky, R. (2007), Reciprocating Compressor Condition Monitoring, Proceedings of the Thirty sixth Turbomachinery Symposium, 107-114.
  2. [2]  Mollasalehi, E., Jahromi, S.A.Z., Forcinito, M., Hu, W., and Sun, Q. (2012), Structural Fault Diagnosis of a Reciprocating Compressor using Bond Graph Approach, Proceedings of ASME International Design Engineering Technical Conferences {$\&$ Computers and Information in Engineering Conference}, 185-191.
  3. [3]  Viscomi, B.V., and Arye, R.S. (1971), Nonlinear Dynamic Response of Elastic Slider-Crank Mechanism, ASME Journal of Engineering for Industry, 93, 251--262.
  4. [4]  Lin, F.J., Fung, R.F., and Lin, Y.S. (1997), Adaptive Control of Slider-Crank Mechanism Motion: Simulation and Experiments, International Journal of System Science, 28(12), 1227--1238.
  5. [5]  Ha, J.L., Fung, R.F., Chen, K.Y., and Hsien, S.C. (2006), Dynamic Modelling and Identification of a Slider-Crank Mechanism, Journal of Sound and Vibration, 289, 1019--1044.
  6. [6]  Bos, A.M. and Tiernego, M.J.L. (1985), Formula Manipulation in the Bond Graph Modelling and Simulation of Large Mechanical Systems, Journal of the Franklin Institute, 319, 51-65.
  7. [7]  Engja, H. (1985), Bond Graph Model of Reciprocating Compressor, Journal of the Franklin Institute, 319(l/2), 115-124.
  8. [8]  Romero, G., F\{e}lez, J., Mart\{\i}nez, M. L., and Maroto, J. (2006), Kinematic Analysis of Mechanism by Using Bond Graph Language, Proceedings 20$^{th}$ European Conference on Modelling and Simulation.
  9. [9]  Jahromi, S.A.Z. and Mollasalehi, E. (2011), Modelling Vibration of a Reciprocating Compressor through Bond-Graph Technique, MITAC Report.
  10. [10]  Ovy, E.G. and Sun, Q. (2018), Wind turbine dynamics modelling by a bond graph approach, International Journal of Dynamics and Control, 6, 1523--1542.
  11. [11]  Paynter, H.M. (1961), Analysis and Design of Engineering Systems, MIT Press.
  12. [12]  Broenink, J.F. (1999), Introduction to Physical Systems Modelling with Bond Graphs, Technical report, University of Twente, Netherlands.
  13. [13]  Karnopp, D.C., Margolis, D.L., and Rosenberg, R.C. (2012), System Dynamics: Modelling and Simulation of Mechatronic Systems, Fifth Edition, John Wiley {$\&$ Sons, Inc}.
  14. [14]  CAMP-G (Computer Aided Modelling Program with Graphical Input) USERS MANUAL, Cadsim Engineering, Davis, Ca 95617 U.S.A., 2000-2007.
  15. [15]  Meriam, J.L. and Kraige, L.G. (2012), Engineering Mechanics: Dynamics, John Wiley {$\&$ Sons, Inc}.
  16. [16]  Hibbeler, R.C. (2010), Engineering Mechanics: Dynamics, Pearson Prentice Hall.
  17. [17]  Mahmood, S.L. and Rideout, G. (2011), Discrete Dynamic Modelling and Analysis of a Beam with a Nonlinear Fatigue Crack, Proceedings of the 23$^{rd}$ CANCAM.
  18. [18]  Ibrahim, A., Ismail, F., and Martin, H.R. (1987), Modelling of the Dynamics of a Continuous Beam including Nonlinear Fatigue Crack, J. Modal Analysis, 2(2), 76-82.
  19. [19]  Christides, S. and Barr, A. (1973), One dimensional theory of cracked Bernoulli-Euler beams, International Journal of Mechanical Sciences, 26(11/12), 639-648.
  20. [20]  Rahman, M. (2011), Applications of Fourier Transforms to Generalized Functions, WIT Press Southampton, Boston.
  21. [21]  Ovy, E.G., Forcinito, M., and Sun, Q. (2016), Bond Graph Model of Reciprocating Compressor for Machine Condition Monitoring, $40^{th}$ Vibration Institute Annual Training Conference, Asheville, North Carolina.
  22. [22]  Ovy, E.G. and Sun, Q. (2020), Ball-bearing dynamics modelling by a bond graph approach, International Journal of Modelling and Simulation.