DC Motor Specifications and Gear Ratio Calculation for Model Boat Propeller"

In summary, a small DC motor with an operating voltage of 4.5V and a stall torque of 6.6*10^-3 Nm has the capability to power a propeller with 0.1 Nm of torque at 200 rpm. The power required for the propeller is 2.09W, while the motor produces 2.14W at its maximum load point, making it suitable for the task. A gear ratio of 85 would be suitable, considering the maximum and minimum gear ratios allowed. The calculations were done using the maximum load values and a later amendment to the question specified 'maximum efficiency' instead.
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Homework Statement



A small dc motor has the following specifications and is being considered for powering the propeller of a model boat. The propeller has the intended capability of supplying 0.1Nm of torque at 200rpm.

Operating voltage = 4.5V
Stall torque = 6.6*10^-3 Nm
Stall current = 6.26 A
No load speed = 21 000 rpm
No load current = 0.29 A
Maximum load torque = 1.2*10^-3 rpm
Maximum load speed = 17 000 rpm

Show that this motor does have the power to meet this capability, and determine an approximate gear ratio with which it should be used in order to supply the required combination of torque and speed.

Homework Equations



Power = torque * angular speed

The Attempt at a Solution



Okay so the power required for the propeller is

=0.1 Nm * 200 rpm
=0.1 Nm * (200*2pi)/60 rad s^-1
=2.09W

The power produced by the motor at maximum load (low power point?) is
=1.2*10^-3 Nm * 17000 rpm
=1.2*10^-3 Nm * (17000 *2pi)/60 rad s^-1
=2.14W

Does this mean that since at its low power point the motor produces more than sufficient power to power the propeller that it is suitable?

As for the gear ratio:

17 000 rpm/ 200rpm = 85, so this would be the maximum gear ratio allowed
0.1 Nm/1.2*10^-3 Nm = 83.3, so this would be the minimum gear ratio allowed

Therefore a gear ratio of 85 would be suitable? (These margins seem rather close, especially because there will be power losses in any real system.)

Also: I've done all these calculations using the maximum load figures and ignored the rest. Is this correct? This is the only question for this data and I don't feel that the rest are likely be so superfluous.
 
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I was given an amendment to the question. It was 'maximum efficiency' not 'maximum load' values. Have hence sorted the problem. Thanks to everyone who took a look at it.
 

What is the difference between brushed and brushless DC motors?

Brushed DC motors have a physical commutator and brushes that deliver power to the rotor, while brushless DC motors use electronic commutation to deliver power to the stator. Brushless DC motors are typically more efficient, have longer lifespans, and require less maintenance than brushed DC motors.

What is the relationship between voltage, current, and torque in a DC motor?

In a DC motor, the torque produced is directly proportional to the current flowing through the motor's windings and the strength of the magnetic field. The voltage applied to the motor determines the speed at which the motor rotates, as well as the amount of current flowing through it.

What is the significance of the "kv" rating in DC motor specifications?

The "kv" rating, or voltage constant, is a measure of the motor's speed constant. It is the ratio of the motor's speed in revolutions per minute (rpm) to the voltage applied to the motor. This rating is important for determining the motor's speed and torque capabilities.

What is the difference between rated and maximum current in a DC motor?

The rated current is the maximum current that a motor can continuously handle without overheating. The maximum current, on the other hand, is the absolute maximum current that a motor can handle for a short period of time, typically a few seconds, before overheating. Exceeding the maximum current can damage the motor.

How do I determine the power rating of a DC motor?

The power rating of a DC motor is typically determined by multiplying the rated voltage by the rated current. This will give you the maximum power that the motor can continuously output. However, the actual power output of a motor may vary depending on the load and other factors.

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