# AC universal motor calculations

#### valdorf

##### Newbie level 4
Hello,

First of all, sorry for my english, which is not my first language. I am currently making a design of AC universal motor (series motor) as a nutrunner (torque wrencher) for bolts wrenching at adjusted known torque. I would like to calculate a load torque using electric parameters such as current, speed. I know that there are an equation of torque T=P/w=IU/w. But there are also another equation T=k*I^2 (k - torque constant). So I am a bit confused which equation I really have to use. My controller will adjust desired torque (i.e. 500Nm) and controller will calculate torque from electrical parameters and run the motor until it reaches desired torque.

I have made a test, running motor for 5mins at no load and I have seen that motor temperature increases and a current decreases, and this means that my torque will drop depending on temperature. Also I observed that motor speed during this test was increased. My design at the moment has current and motor speed sensors, so I can track these two parameters. But I do not know if I really need to sense a voltage.

So my question would be: Could I create a relationship between motor current and motor speed to estimate desired load torque, or do I need to measure voltage in addition?

##### Super Moderator
Staff member
Do you plan to hold the unit? It will try to spin as soon as the fasteners make firm contact. To stop it from wrapping up its power cord you must grip the unit with the same force needed with an ordinary torque wrench. Be prepared or else it'll spin your arm.

I was just doing tests with my electric drill which runs on 120 VAC. Spinning freely it draws 2A. When stalled under power it draws 7A.
Somewhere between these two extremes you can take a reading and derive some idea of the load on the motor. I imagine you need to gear down the RPM so it takes a few seconds for the fastener to tighten to maximum. During that time window your circuit detects Ampere level. As soon as the reading rises to a desired spec, cut power.

I'm not sure a formula alone can provide a direct correlation. No doubt you have to run many tests on your project, and compare results to an ordinary torque wrench, and build a graph of Amperes versus torque.

#### KlausST

##### Super Moderator
Staff member
Hi.

P is only valid as long as the motor rotates.

You may use the current (I) information as torque information.
Then stop the motor as soon as the current is higher than the threshold.

Don't use high RPM, else the inertia of the moving mechanics (motor, gear...) will cause increase in torque.

Klaus

#### FvM

##### Super Moderator
Staff member
T=k*I^2 is valid also for stalled rotor in the first approximation. For a more accurate calculation, the stator B = f(H) saturation curve must be factored in.

#### valdorf

##### Newbie level 4
T=k*I^2 is valid also for stalled rotor in the first approximation. For a more accurate calculation, the stator B = f(H) saturation curve must be factored in.
Thanks. My tool which is under design has speed reduction with a gears. But I think not valid when winding temperature increases or decreases what causes changes in resistance. Let say I calibrate my tool using calibration equipment at 30*C i.e.:
I=5A, T=600Nm
I=6A, T=700Nm
...
My calibration became wrong when temperature increases to 50*C, because winding resistance changes.

Equation T=kI^2 is still correct and current is still proportional to torque? I dont think so.

#### FvM

##### Super Moderator
Staff member
My calibration became wrong when temperature increases to 50*C, because winding resistance changes.
Your post is rather vague. Are you reporting an observation or just guessing?

There are several reality factors that modifies the simplified I^2 torque relation. Winding resistance however doesn't affect it. I conclude from your post that you don't yet understand the physical background of the equation and neither its limitations.

In geared drive, gear friction will be a major source of torque variation, I'd expect that it's also temperature dependent to some extent.

Stator saturation occurs at higher currents will probably show a certain temperature depedency.

I guess that due to gear friction, it's hard to get better torque accuracy than 10 or 20 %.

#### valdorf

##### Newbie level 4
Your post is rather vague. Are you reporting an observation or just guessing?

There are several reality factors that modifies the simplified I^2 torque relation. Winding resistance however doesn't affect it. I conclude from your post that you don't yet understand the physical background of the equation and neither its limitations.

In geared drive, gear friction will be a major source of torque variation, I'd expect that it's also temperature dependent to some extent.

Stator saturation occurs at higher currents will probably show a certain temperature depedency.

I guess that due to gear friction, it's hard to get better torque accuracy than 10 or 20 %.
But it is very interesting, because I have analyzed two electric nutrunners tools (available on a market) on a torque testing equipment and they everytime wrenches at the same torque with an accuracy of 1-2%. They also have geared reductors and a circuit which measure current (Also temperature).

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#### FvM

##### Super Moderator
Staff member
Sure these tools are not implementing direct torque measurement by strain gauge?

I don't say it's impossible to achieve 2% accuracy with armature current measurement, but it probably involves a special gear design.

#### valdorf

##### Newbie level 4
Sure these tools are not implementing direct torque measurement by strain gauge?

I don't say it's impossible to achieve 2% accuracy with armature current measurement, but it probably involves a special gear design.
I am sure they do not have direct torque measurement. I think these tools are calibrated, depending on measured current, but also has a compensation curve which depends on motor voltage and/or speed. So when temperature of the windings rises, we could know that from measured voltage/speed and compensate torque value, i.e. T=(kI^2) + 'voltage-speed curve coef'. Am I wrong?

#### FvM

##### Super Moderator
Staff member
I suggest to make an empirical T = f(I) calibration curve with corrections for temperature and speed/voltage. The achieved torque accuracy depends on motor and gear quality.

Points: 2