finalc.sol.fall2010

finalc.sol.fall2010 - ME 352 Machine Design I Fall Semester...

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1 ME 352 - Machine Design I Name of Student___________________________ Fall Semester 2010 Lab. Div. Number__________________________ FINAL EXAM. OPEN BOOK AND CLOSED NOTES. Wednesday, December 15th, 2010. Use the blank paper provided for your solutions. Write on one side of the paper only. Where necessary, use the given figures to show vectors. Any work that cannot be followed is assumed to be in error. Staple each problem separately and attach your crib sheet to the end of Problem 1. Problem 1 (25 Points) . For the mechanism in the position shown in Figure 1, the constant angular velocity of the input link 2 is 2 3krad/s ω= with a torque 12 T1 . 5 k N - m =− acting at bearing 2 O. The length of link 2 is 2 OA 0 .12m , = 22 O G 0.045 m, = 23 O G 0.09 m, = and the free length of the spring attached between ground pin O 1 and pin A is 0.5 m. A viscous damper is attached between pin O and link 3. There is a horizontal force P acting at pin A, gravity is acting vertically downward, and the effects of friction in the mechanism can be neglected. The known data (where 23 R is the vector from bearing O 2 to the mass center 3 G and 3 R is the vector from the ground pin O to the mass center 3 G ) is: 23 R 3 R 23 R ′′ 3 R 2 m 3 m 2 G I 3 G I K C m/rad m/rad m/rad 2 m/rad 2 kg kg kg.m 2 kg.m 2 N/m Ns/m + 0.052 + 0.104 + 0.150 + 0.120 7 12 0.75 2.25 15 75 Determine: (i) the first-order kinematic coefficients of the linear spring and the viscous damper. (ii) the potential energy of the spring. (iii) the equivalent mass moment of inertia of the mechanism. (iv) the magnitude and direction of the external force P. Figure 1. A planar mechanism.
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2 ME 352 - Machine Design I Name of Student _____________________________ Fall Semester 2010 Lab . Div. Number ____________________________ Problem 2 (25 Points). Part A. A rotating shaft is simply supported by two bearings at A and B as shown in Figure 2. Gears 1, 2, and 3 are rigidly attached to the shaft at locations C, D, and E, respectively. Gear 1 at location C weighs 165 N, gear 2 at location D weighs 255 N, gear 3 at location E weighs 90 N, and the weight of the shaft can be neglected. If the first critical speeds of the shaft with each gear attached separately are 11 ω 190 rad/s, = 22 ω 105 rad/s, = and 33 ω 280 rad/s, = respectively, then determine: (i) The first critical speed of the shaft with all three gears using the Dunkerley approximation. (ii) Numerical values for the influence coefficients 11 22 a,a, and 33 a. (iii) If gear 2 is now moved to location E and gear 3 is moved to location D, then determine the first critical speed of the new system using the Dunkerley approximation. Figure 2. A rotating shaft with three gears rigidly attached. Part B. The weights of three flywheels rigidly attached to a shaft rotating with a constant angular velocity are 1 W4 5 0 N = , 2 W 325 N, = and 3 W7 6 0 N . = The nine influence coefficients of the shaft are: 6 11 a2 . 2 5 x 1 0 m / N = , 6 22 a1 . 6 2 5 x 1 0 m / N = , 6 33 . 5 x 1 0 m / N = , 6 12 21 a a 0.95 x 10 m/N == , 6 13 31 aa0 . 6 5 x 1 0 m / N , and 6 23 32 . 8 5 x 1 0 m / N . Determine: (i) The deflections of the shaft at each flywheel.
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finalc.sol.fall2010 - ME 352 Machine Design I Fall Semester...

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