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Refer to the figure which shows a ship's propeller, drive train, engine, and flywheel. The diameter ratio of the gears is D1/D2=2/3. The inertias in kg-m2 of gear 1 and gear 2 are 100 and 500, respectively. The flywheel, engine, and propeller inertias are 104, 103, and 2500, respectively. The torsional stiffness of shaft 1 is 5x106 N-m/rad, and that of shaft 2 is 106 N-m/rad. Because the flywheel inertia is so much larger than the other inertias, a simpler model of the shaft vibrations can be obtained by assuming the flywheel does not rotate. In addition, because the shafts between the engine, gears and propeller are short, we will assume that they are very stiff compared to shaft 2. However, there are losses in the gear system which are represened by a damper with a damping coefficient of 300 Ns/rad. If we also disregard the shaft inertias, the resulting model consists of two inertias, one obtained by lumping the engine and gear inertias, and one for the propeller as seen in the figure below. kr2 ll a. Using these assumptions, what are the degrees of freedom of the system and what order do you expect the characteristic equation to be? b. Develop the system of dynamic equations for this engine / propeller. c. Find the characteristic equation using the Laplace transform method.

Refer to the figure which shows a ship's propeller, drive train, engine, and flywheel. The diameter ratio of the gears is D1/D2=2/3. The inertias in kg-m2 of gear 1 and gear 2 are 100 and 500, respectively. The flywheel, engine, and propeller inertias are 104, 103, and 2500, respectively. The torsional stiffness of shaft 1 is 5x106 N-m/rad, and that of shaft 2 is 106 N-m/rad. Because the flywheel inertia is so much larger than the other inertias, a simpler model of the shaft vibrations can be obtained by assuming the flywheel does not rotate. In addition, because the shafts between the engine, gears and propeller are short, we will assume that they are very stiff compared to shaft 2. However, there are losses in the gear system which are represened by a damper with a damping coefficient of 300 Ns/rad. If we also disregard the shaft inertias, the resulting model consists of two inertias, one obtained by lumping the engine and gear inertias, and one for the propeller as seen in the figure below. kr2 ll a. Using these assumptions, what are the degrees of freedom of the system and what order do you expect the characteristic equation to be? b. Develop the system of dynamic equations for this engine / propeller. c. Find the characteristic equation using the Laplace transform method.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Shaft 2 Engine D2 Flywheel Shaft 1 Propeller Refer to the figure which shows a ship's propeller, drive train, engine, and flywheel. The diameter ratio of the gears is D1/D2=2/3. The inertias in kg-m2 of gear 1 and gear 2 are 100 and 500, respectively. The flywheel, engine, and propeller inertias are 104, 103, and 2500, respectively. The torsional stiffness of shaft 1 is 5×106 N-m/rad, and that of shaft 2 is 106 N-m/rad. Because the flywheel inertia is so much larger than the other inertias, a simpler model of the shaft vibrations can be obtained by assuming the flywheel does not rotate. In addition, because the shafts between the engine, gears and propeller are short, we will assume that they are very stiff compared to shaft 2. However, there are losses in the gear system which are represened by a damper with a damping coefficient of 300 Ns/rad. If we also disregard the shaft inertias, the resulting model consists of two inertias, one obtained by lumping the engine and gear inertias, and one for the propeller as seen in the figure below. kr2 C1 a. Using these assumptions, what are the degrees of freedom of the system and what order do you expect the characteristic equation to be? b. Develop the system of dynamic equations for this engine / propeller. c. Find the characteristic equation using the Laplace transform method. d. Based on the roots of the CE, how will the propeller behave?
Transcribed Image Text:Shaft 2 Engine D2 Flywheel Shaft 1 Propeller Refer to the figure which shows a ship's propeller, drive train, engine, and flywheel. The diameter ratio of the gears is D1/D2=2/3. The inertias in kg-m2 of gear 1 and gear 2 are 100 and 500, respectively. The flywheel, engine, and propeller inertias are 104, 103, and 2500, respectively. The torsional stiffness of shaft 1 is 5×106 N-m/rad, and that of shaft 2 is 106 N-m/rad. Because the flywheel inertia is so much larger than the other inertias, a simpler model of the shaft vibrations can be obtained by assuming the flywheel does not rotate. In addition, because the shafts between the engine, gears and propeller are short, we will assume that they are very stiff compared to shaft 2. However, there are losses in the gear system which are represened by a damper with a damping coefficient of 300 Ns/rad. If we also disregard the shaft inertias, the resulting model consists of two inertias, one obtained by lumping the engine and gear inertias, and one for the propeller as seen in the figure below. kr2 C1 a. Using these assumptions, what are the degrees of freedom of the system and what order do you expect the characteristic equation to be? b. Develop the system of dynamic equations for this engine / propeller. c. Find the characteristic equation using the Laplace transform method. d. Based on the roots of the CE, how will the propeller behave?
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