How to Calculate Input Power for a Gear Train with Frictional Resistance?

[PizzaWizza]

Calculating the input power required for a drive gear in a train.

I have 4 gears, all in line. The driver shaft A rotates at 100 revs/min and the gear has a diameter of 40mm. 20 teeth with a module of 2mm

The output is to rotate at 400 revs/min and has a diameter of 160mm with 80 teeth and the same module of 2mm

The two idler gears are both 100mm each and have 50 teeth each

The output gear is working against a load of 200Nm

All shafts have a frictional resistance of 5Nm

I'm going to try work backwards from my output Torque to see if I can calculate the input.

How do I do this taking into account the frictional resistance.

If I call each gear A, B, C & D respectively with D being my output.

ωD x TD = 400x200 = 80000 W

I'm really not sure what I do to the power here to include the frictional resistance and work back over to calculate the power input required for each gear.

 

[tech99]

Calculating the input power required for a drive gear in a train.

I have 4 gears, all in line. The driver shaft A rotates at 100 revs/min and the gear has a diameter of 40mm. 20 teeth with a module of 2mm

The output is to rotate at 400 revs/min and has a diameter of 160mm with 80 teeth and the same module of 2mm

The two idler gears are both 100mm each and have 50 teeth each

The output gear is working against a load of 200Nm

All shafts have a frictional resistance of 5Nm

I'm going to try work backwards from my output Torque to see if I can calculate the input.

How do I do this taking into account the frictional resistance.

If I call each gear A, B, C & D respectively with D being my output.

ωD x TD = 400x200 = 80000 W

I'm really not sure what I do to the power here to include the frictional resistance and work back over to calculate the power input required for each gear.

Find the speed of each gear first, from the number of teeth.
Then multiply output torque by output speed to find output power.
The input power is output power plus losses, so for each wheel, calculate the speed times frictional torque, to find the power lost. Then add together the four values of power lost and the output power. This will give the input power.

 

[PizzaWizza]

Find the speed of each gear first, from the number of teeth.
Then multiply output torque by output speed to find output power.
The input power is output power plus losses, so for each wheel, calculate the speed times frictional torque, to find the power lost. Then add together the four values of power lost and the output power. This will give the input power.

Apologies, I've got my driver & driven the wrong way around. So driver gear rotates at 100rpm/min and has 80T and diameter of 160mm. The driven output shaft has 20T and a diameter of 40mm

I can find the rotational speed of gear C working back from Gear D via T1ω1 = T2ω2 ∴ 20x400 = 50xω2 = 160rpm/min for gear C which in turn means gear B is the same speed. So where do I find the torque for Gear C. It needs to overcome 200Nm to turn the output, do I multiply 205Nm by the angular velocity to achieve the power requirement in Watts?

 

[tech99]

Apologies, I've got my driver & driven the wrong way around. So driver gear rotates at 100rpm/min and has 80T and diameter of 160mm. The driven output shaft has 20T and a diameter of 40mm

I can find the rotational speed of gear C working back from Gear D via T1ω1 = T2ω2 ∴ 20x400 = 50xω2 = 160rpm/min for gear C which in turn means gear B is the same speed. So where do I find the torque for Gear C. It needs to overcome 200Nm to turn the output, do I multiply 205Nm by the angular velocity to achieve the power requirement in Watts?

I have drawn the diagram from your new description. You can find the speed of the four wheels from just the number of teeth.
Next find the output power from 2 pi x revs/sec x torque.
Now find the frictional power lost at each shaft from 2 x pi x revs/sec x frictional torque.
Now add the four frictional powers to the output power. This gives the input power.

 

[PizzaWizza]

I have drawn the diagram from your new description. You can find the speed of the four wheels from just the number of teeth.
Next find the output power from 2 pi x revs/sec x torque.
Now find the frictional power lost at each shaft from 2 x pi x revs/sec x frictional torque.
Now add the four frictional powers to the output power. This gives the input power.

Thanks very much. Makes sense