1. Marine Engine Propeller Marine Engine Propeller ME 270 Dr. Granda Dong-Un Sul

2. Marine Engines Temporary engine N60ENTM40N60ENTM40: 400 HP An old marine engine manufactured by Gray Company

3. Problem Statement A marine engine connected to a propeller through gear is shown below. The mass moments of inertia of the flywheel, engine, gear 1 and 2 and the propeller (in kg-m^2) are 9000, 1000, 250, 150, and 2000, respectively.

4. Schematic

5. Objectives By using the Matlab, obtain the transfer functions and state form and run a test to draw reasonable outputs Build a bond graph of the system in CAMP-G Find natural frequency of the system Compare the results from Matlab with the ones in a reference book With another software, find the frequency of the model as well (i.e. Nastran4D)

6. 3D View For better understanding, this model was built in Solidworks. This model will transfer to Nastran4D to simulate.

8. Parts

9. Initial Bond Graph Two I-elements turn out in red which means that there are two derivative causalities in this system.

10. Bond Graph with derivative causality

11. Attaching C-element To eliminate derivative causality, C- elements are added into the system. As C-values get smaller, they can be negligible.

12. Differential Equations from Matlab Number of States 10 dP21=Q25/C25 dQ25=P11/I11*T13x14-P21/I21 dQ24=P11/I11-P23/I23 dP23=Q24/C24 dP19=Q17/C17 dQ17=P11/I11*T13x14-P19/I19 dQ4=SF1-P6/I6 dQ9=P6/I6-P11/I11 dP6=Q4/C4-Q9/C9 dP11=Q9/C9-Q17/C17*T13x14-Q25/C25*T13x14- Q24/C24

13. Simulink

14. State-Space function

15. Transfer function

16. Nastran4D Analysis

17. Frequency derived from Nastran4D Flywheel = 3.09E-5 Hz Gear1 = 2.39E-5 Hz Engine = 2.45E-5 Hz Propeller = 1.08E-5 Hz Gear2 = 1.09E-5 Hz

18. Conclusion Nastran4D will be helpful with accurate values in the system to find the frequency of it. However, I failed obtaining the appropriate frequency because the values were not given sufficiently. Plus, by using the Matlab, I couldn’t get the frequency of the system because determinant for A matrix became 0. I believed that to perform much more accurate analysis of the system more data should be provided.

19. Simple Model (Alternative approach) Schematic This is the schematic of the simple model which is equivalent to the system above with 5 mass moments of inertia. J1 can be obtained by summation of mass moment of inertia of the engine, gear1 and gear2. To get the torsional stiffnesses of shafts1 and 2, a shear modulus of 80 x 10^9 N/m^2 for steel is used to find the natural frequency of the system below.

20. Bond Graph

21. Differential Equations dP11=Q8/C8 dQ4=SF1-P10/I10 dQ8=P10/I10-P11/I11 dP10=Q4/C4-Q8/C8

22. Simulink Based on the differential equation, simulink was built in the Matlab.

23. A Matrix From the Matlab, A matrix was obtained like shown on the left side.

24. A Matrix with initial values

25. Calculation by hand

26. Solution from the book

27. Comparison (Natural Frequency) 1588.46 ± 1503.1483 (book) 1588.46 ±1503.147882 (Matlab)

28. Nastran4D

29. Frequency of the system from Nastran4D with initial values Mass1 = 7400.00 Kg Mass2 = 22222.22 Kg J1 = 2.8E-5 Hz J2 = 1.53E-5 Hz

30. Conclusion CAMP-G model helps find the natural frequency as it interfaces with Matlab, which generates A matrix. The natural frequency calculated by Matlab is very accurate. To get right results from Matlab, initial values should sufficiently be given like the second simple model. Due to errors taking place for the first model, complicated one, in some reasons, failure may be unavoidable. A bond graph will be a very useful tool once engineers understand how it works. It helps engineers to save their times and efforts without setting mathematical equations for the system that they want to work out. However, there is disadvantage of it. In other words, no one can guarantee whether the bond graph is correct or not. With the wrong bond graph, all analysis can be useless.

31. Enjoy your winter break!! Merry Christmas and Happy New Year!! Thank you very much!