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 DC Permanent Magnet Motor Calculations
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ron_o
Moderator


United Kingdom
1052 Posts

Posted - June 01 2014 :  17:31:06  Show Profile Send ron_o a Private Message  Reply with Quote
I recently "found" an old DC permanent magnet motor from a 12 volt cordless drill in my junk box. Which i wanted to test to see if it was suitable to power a small device

Back EMF of a permanent magnet DC motor.

1) measure the no load speed of the motor at it's stated working voltage

2) measure the DC resistance of the motor

results were 8500 rpm and 0.55 ohms , stated working voltage 12 volts

Pi = 3.14159

3) convert rpm to radians per second

w = rpm x 2 x Pi / 60 = 8500 x 2 x Pi / 60 = 53407 / 60 = 890 rads/s

Under no load conditions V = E so E = 12 volts

w = E / Kt0

Note Kt0 is a constant for this motor only

so Kt0 = E / w = 12 / 890 = 0.01348

Stall Torque.... since the motor is not rotating no BEMF is being generated so the current limiting factor is the DC resistance of the winding and brush contacts resistance

I = V / R so stall current is 12 / 0.55 = 21.8181 amps

The Stall Torque = Kt0 x I(amps) = 0.01348 x 21.8181 amps = 0.2941Nm

To calculate the speed of the motor when it is loaded by a torque of
0.15 Nm ( the purpose of this calculation )

I(load current) = Torque / Kt0 = 0.15 / 0.01348 = 11.1275 amps

E(bemf) = V - ( I(load current ) x R( motor resistance )

E(bemf) = 12 - ( 11.1275 x 0.55 ) = 12 - 6.120 ) = 5.88 volts

Convert E(bemf) to rads/s

w = e(bemf) / Kt0 = 5.88 / 0.01348 = 436.2 rads/s

Convert rads/s to rpm

rpm = 60 x 436.2 / 2 x Pi = 4165 rpm

Which when actually tested gave a reading of 4152 rpm

ron

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olddawgsrule
Advanced Member



USA
1434 Posts

Posted - June 02 2014 :  16:37:36  Show Profile  Visit olddawgsrule's Homepage Send olddawgsrule a Private Message  Reply with Quote
Two questions;

"To calculate the speed of the motor when it is loaded by a torque of
0.15 Nm (the purpose of this calculation)"

Nm stands for?

Where did the .15Nm come from?

Old in age, not in mind, so
'Teach me something new'!

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ron_o
Moderator



United Kingdom
1052 Posts

Posted - June 02 2014 :  18:30:41  Show Profile Send ron_o a Private Message  Reply with Quote
Hi ODR

Nm stands for Newton metre and the 0.15 Nm figure was a torque load that the unit i wanted to drive required to turn it.

The calculation was performed to see if the small DC motor was strong enough , rather than make up a mounting plate etc only to find the motor was not up to the task.

ron
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olddawgsrule
Advanced Member



USA
1434 Posts

Posted - June 03 2014 :  15:42:00  Show Profile  Visit olddawgsrule's Homepage Send olddawgsrule a Private Message  Reply with Quote
I'll have to add this to my spreadsheet collection for further reference.

I also learn as I build the sheet.
Gives me a chance to break it down part by part.

Can you do this in reverse?
Looking to figure footpounds (?) of water required to turn the motor.


Old in age, not in mind, so
'Teach me something new'!

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ron_o
Moderator



United Kingdom
1052 Posts

Posted - June 03 2014 :  17:00:10  Show Profile Send ron_o a Private Message  Reply with Quote
Hi ODR

The Nm value can be readily converted into foot/pounds :-

Inch Pounds ( in/lbs ) = Nm x 8.85

Foot Pounds ( ft/lbs ) = Nm x 0.7376

hope that helps

ron
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ron_o
Moderator



United Kingdom
1052 Posts

Posted - June 03 2014 :  17:06:00  Show Profile Send ron_o a Private Message  Reply with Quote
Hi again ODR

Are you trying to work out the amount of force / torque required to turn a generator to provide a required amount of electrical energy ?

ron
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olddawgsrule
Advanced Member



USA
1434 Posts

Posted - June 06 2014 :  17:33:14  Show Profile  Visit olddawgsrule's Homepage Send olddawgsrule a Private Message  Reply with Quote
Yes that's what I'm up to.

I'm about to meet up with my Cousin and pass along 3 DC motors I've collected.
I still don't believe they'd be good for a wind genie application, but his Hydro project I do believe they'd fit in nicely.

It would be nice to calculate the force required as you've done here with your situation, before going into the build.

I hesitate to ask, you do so much..
If you have time
If your so willing

He has a beaver pond uphill of the house. I'm heading up to help survey the area and attempt to determine the possibilities. It's in the new plot he bought, uphill from his and hear it's 2 acre plus.
Sounds like it has possibilities.






Old in age, not in mind, so
'Teach me something new'!


Edited by - olddawgsrule on June 06 2014 17:54:40
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ron_o
Moderator



United Kingdom
1052 Posts

Posted - June 07 2014 :  17:48:41  Show Profile Send ron_o a Private Message  Reply with Quote
Hi ODR

Well it sounds like a worthwhile project ( so no need to hesitate to ask ) so lets see what we can do.

I will need the details of the three motors ( volts and amps + rpm ).

By beaver pond am i right to assume a dam and that a head of water exists .... if so what is the difference in height between the two water levels ?

It will also be necessary ( at some point ) to establish the volume of water flow per unit time. This information will allow gearing and wheel bucket dimensions to be calculated.

I will start a new topic in the "WATER POWER" section of the forum

ron
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