A Shaft Carries Several Out of Balance Masses in Planes A, B, C, D, and E: Solid Mechanics and Dynamics Assignment, NTU, Singapore

Question 1

A shaft carries several out of balance masses in planes A, B, C, D, and E.

1. If the shaft is to be supported by two bearings, the first bearing is located 80 mm from A and the other 125 mm from E, find the magnitude and direction of the bearing reactions when the shaft rotates at 300 rev/min.
2. If the shaft is to be balanced by two balancing masses with the eccentricity of 120 mm, one mass is to be located in a plane 100 mm from plane A, and the other 400 mm from plane A, find the mass and the angular position of these two balancing masses. The angular position is to be measured from plane A.

The mass and angular position of the unbalance mass E is obtained from the last 4 digits of the numerical code assigned.

The mass of E is represented by the last digit of the assigned number code (if the digit is 0, assumed 10)

The angular position (in degree) of mass E is represented by the number formed from the 3S, 4th, and 5th digits. If this angle is more than 360°, obtain its coterminal angle between 0 and 360°. The angle is measured CCW from A.

Question 2

A compound epic cyclic gear train is shown in Figure Q2. The power of 6 kW is supplied to shaft 6 which rotates with an angular velocity of 60 rad/s (CCW). Power is taken from shaft 2. The gear module is 1.5 mm

As an engineer, you are asked to select appropriate gear sizes such that the gear train provides output rotations in both CCW and CW directions depending on the configuration that you will recommend. Take note of the following requirements:

1. Three gear sizes are available from the last 6 digits of your number code.

Example:

Number code: 245860

Available gear teeth: 24, 58, 60 teeth

Number code: 702103

Available gear teeth: 70, 21, 10 (03) teeth (Any two-digit number less than 10, assume 10)

You may assign each of the above gear sizes to three gears either the sun or planet gears.

You are required to size up the remaining gears: Find the number of teeth for the ring gears and the remaining sun or planet gears. Ensure all gears fit appropriately in the gear train such that it can provide output speed in the CW and CCW directions by changing the configuration ie which gear is to be fixed and which are free to rotate.

Hint: You may need to do several iterations in selecting the gear teeth so that the gear train can provide both CW and CCW output directions. State clearly the configuration ie which gear component is to be fixed and which components are free to rotate in order to achieve CW and CCW rotations.

2. Once you have a gear set that complies to (a) above, calculate the following:

• The diameters of all the gears
• The output speeds of the CW and CCW rotations
• The fixing couple required on the fixed components when the output rotation in CW and CCW directions.

Question 3

Figure Q3 shows an 8m long I beam simply supported at A and D. The modulus of elasticity of the beam material is 10 GPa.

1. Calculate the second moment of area about a horizontal axis through the centroid of the I section.
2. Determine the slope and deflection equations of the beam including solving for the constant terms.
3. Find the slope and deflection at 2 m from A and 0.5 m from E
4. Find the maximum deflection of the beam. (At maximum deflection, slope = 0. You may need to do some research to learn the detail calculations)
5. Plot the deflection curve of the beam. An accurate graph is required such that deflections at any point along the beam can be ascertained from the graph. You may plot the graph manually or by any software, but the deflections at regular intervals of the beam must be shown.