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Answer :
a) The no-load speed of the AC servo-motor is 115/3 Vac.
b) The speed at which the motor will ruin is approximately 27 rpm.
To solve this problem, we need to apply the principles of torque and speed in an AC servo-motor system.
(a) Finding the no-load speed:
The no-load speed is the speed at which the motor operates when there is no external load attached to it.
In this case, the motor windings are excited with 115 Vac, and the stall torque is given as 3 lb. The no-load speed can be calculated using the following formula:
No-Load speed = Excitation Voltage / Stall Torque
Given:
Excitation voltage = 115 Vac
Stall torque = 3 lb
No-Load speed = 115/3 Vac
Therefore, the no-load speed of the AC servo-motor is 115/3 Vac.
(b) Finding the motor speed at which it will ruin:
To find the motor speed at which it will ruin, we need to consider the constant load, the coefficient of viscous friction, and the gear ratio.
The constant load is given as 0.9 lb ft, and the coefficient of viscous friction is given as 0.05 lb ft-sec. The gear ratio is 6.
First, we need to convert the constant load and the coefficient of viscous friction to lb units by multiplying them by a conversion factor of 12 to convert from ft to inches.
This gives:
Constant load = 0.9 lb ft × 12 in/ft = 10.8 lb in
Coefficient of viscous friction = 0.05 lb ft-sec × 12 in/ft = 0.6 lb in-sec
Next, we calculate the torque at the output of the gear system:
Torque at the output = Constant load × Gear ratio = 10.8 lb in × 6 = 64.8 lb in
Now, we can calculate the speed at which the motor will ruin.
The ruin speed occurs when the motor torque matches the sum of the load torque and the viscous friction torque.
Motor torque = Load torque + Viscous friction torque
Motor torque = 64.8 lb in + (0.6 lb in-sec × speed)
Given that the coefficient of viscous friction is 0.3 lb Ji-sec, we can assume Ji (moment of inertia) to be 1 for simplicity.
Now, we can rewrite the equation as:
Motor torque = 64.8 lb in + (0.6 lb in-sec × speed) = 3 lb × speed
Simplifying the equation:
64.8 + 0.6 × speed = 3 × speed
64.8 = 2.4 × speed
speed = 64.8 / 2.4
Therefore, the speed at which the motor will ruin is approximately 27 rpm.
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