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 Gear Drive Systems - Basic Equations
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ron_o
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1052 Posts

Posted - June 16 2014 :  15:48:26  Show Profile Send ron_o a Private Message  Reply with Quote
Gear Box Drive Theory... part 1

The gear box drive ratio is defined as :-

Drive ratio = input speed / output speed

Example 1400 rpm input , output 200 rpm

Drive ratio = 1400 / 200 = 7 : 1 requction

Gear box drives are used to either increase or decrease the input drive speed.

If the output speed is reduced then the output torque is increased and likewise if the output speed is increased then the available output torque is reduced.

In the real world losses due to friction within the gear box drive result in a reduction in actual output power .

The efficiency of the gear box is usually expressed as :-

Efficiency = power output / power input

Efficiency = output speed x output torque / input speed x input torque

On a practical application another force has to be taken into account , this force is called the Holding Torque.
The Holding Torque is the force required to prevent the gearbox itself turning.

ron

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ron_o
Moderator



United Kingdom
1052 Posts

Posted - June 16 2014 :  17:32:15  Show Profile Send ron_o a Private Message  Reply with Quote
Gear Box Drive Theory ... continued part 2

Holding Torque.. continued.

If we assign the variables T1 to be the input torque , T2 to be the output torque and finally T3 to be the holding torque then the sum of these three variables must always be equal to zero.

To assist in the calculation we can assign a positive and negative rotational value to the direction of rotation.

lets say that clockwise is positive and anticlockwise is negative

We now only require one further equation

Power input = 2 x Pi x rpm(input) x Torque(input) / 60

this can be re arranged to :-

Torque(input) = 60 x Power(input) / 2 x Pi x rpm(input)

Where:-
Power input is in Watts
Torque is in Nm ( Newton metres )
rpm = revolutions per minute
Pi = 3.14159

ron

Edited by - ron_o on June 16 2014 17:38:52
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ron_o
Moderator



United Kingdom
1052 Posts

Posted - June 16 2014 :  17:46:06  Show Profile Send ron_o a Private Message  Reply with Quote
Gear Box Drive Theory ... continued part 3

Example

Using the values used in part 1

Input 1400 rpm , clockwise rotation ( so positive sign ) , 5 Kw
Output 200 rpm , anticlockwise rotation ( so negative sign )

First step is to calculate the input torque

input torque ( Nm ) = 60 x 5000 watts / 2 x Pi x 1400 rpm

input torque (Nm ) = 300000 / 8796.46 = 34.104 Nm

Lets assume that he gearbox is 80% efficient ( ie 20% energy is lost within the gearbox )

Efficiency = output power / input power

So :-

output power = efficiency x input power = 80 x 5000 / 100 = 4000 watts

output torque = 60 x 4000 watts / 2 x Pi x 200 = 600 / Pi = 190.98 Nm

NOTE
remember the direction of the output shaft in this example is anticlockwise so is given a negative sign

The Holding Torque ( Torque 3 ) can now be calculated

Torque 1 + Torque 2 + Torque 3 = 0

( +34.104 ) + ( - 190.98 ) + ( Torque 3 ) = 0

Torque 3 = 190.98 - 34.104 = + 156.876 Nm ( clockwise rotation )

ron




Edited by - ron_o on June 17 2014 15:55:24
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