Question

A 40-pound motor is supported by four springs, each of a constant 225 psi. The motor is constrained to move vertically, and its amplitude of motion is observed to be 0.05 in. at a speed of 1200 rpm. Knowing that the weight of the rotor is 9 lb, determine the distance between the center of mass of the rotor and the axial axis of the rotating shaft.

Answer 1

To determine the distance between the center of mass of the rotor and the axial axis of the rotating shaft, we need to consider the forces acting on the system. By calculating the spring force using Hooke's law and setting the sum of the forces equal to zero, we can solve for the distance.

Step-by-step explanation:

To determine the distance between the center of mass of the rotor and the axial axis of the rotating shaft, we need to consider the forces acting on the system.

The weight of the motor and rotor creates a downward force, while the springs provide an upward force.

Using Hooke's law, we can calculate the spring force as the product of the spring constant and the displacement of the spring from its equilibrium position.

By setting the sum of the forces equal to zero, we can solve for the distance between the center of mass and the axial axis.

1. Calculate the total weight of the motor and rotor: 40 lb + 9 lb = 49 lb.
2. Convert the weight to Newtons: 49 lb × 4.448 N/lb ≈ 218.552 N.
3. Using the given amplitude of motion (0.05 in = 0.00127 m) and speed (1200 rpm = 125.66 rad/s), calculate the displacement at any given moment using the equation: displacement = amplitude × sin(angular speed × time).
4. Calculate the spring force using Hooke's law: spring force = spring constant × displacement.
5. Equate the sum of the forces to zero and solve for the distance between the center of mass and the axial axis