Marine Engine Marine Engine PropellerPropeller

Marine Engine Marine Engine PropellerPropeller

ME 270 ME 270

Dr. GrandaDr. Granda

Dong-Un Sul Dong-Un Sul

Marine Engines

Temporary engine

N60ENTM40: 400 HP

An old marine engine manufactured by

Gray Company

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.

Schematic

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)

3D View

• For better understanding, this model was built in Solidworks.

• This model will transfer to Nastran4D to simulate.

Parts

Initial Bond Graph• Two I-elements

turn out in red which means that there are two derivative causalities in this system.

Bond Graph with derivative causality

Attaching C-element• To eliminate

derivative causality, C-elements are added into the system.

• As C-values get smaller, they can be negligible.

Differential Equationsfrom 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

Simulink

State-Space function

Transfer function

Nastran4D Analysis

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

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.

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.

Bond Graph

Differential Equations

• dP11=Q8/C8• dQ4=SF1-P10/I10• dQ8=P10/I10-P11/I11• dP10=Q4/C4-Q8/C8

Simulink

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

A Matrix

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

A Matrix with initial values

Calculation by hand

Solution from the book

Comparison(Natural Frequency)

• 1588.46 ± 1503.1483 (book)

• 1588.46 ±1503.147882 (Matlab)

Nastran4D

Nastran4D• 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

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.

Enjoy your winter break!! Merry Christmas and Happy

New Year!!

Thank you very much!