Is the following method correct? In order to find the health of a dc motor, we apply nominal current on the excitement and nominal voltage on the rotor. After that, we compare the final rpm with the nominal. If they are the same then the motor is healthy. If not, it is unhealthy. Can someone explain if there is mathematical equation behind this ?

 

Is the following method correct? In order to find the health of a dc motor, we apply nominal current on the excitement and nominal voltage on the rotor. After that, we compare the final rpm with the nominal. If they are the same then the motor is healthy. If not, it is unhealthy. Can someone explain if there is mathematical equation behind this ?

That is not a test I have ever done, but I don't see how it could hurt. What I do is take the motor apart and inspect it. Check:
Bearings (might as well replace while apart)
Commutator
Brushes
Windings

Check continuity between opposite sides on Commutator.

Put it back together and run it at nameplate parameters for a while, make sure it doesn't overheat.

 

Certainly the steps in post #1 are the initial evaluation check for a motor, except that running current should also be measured.
But the very first check should be a resistance check of the winding resistance, both across each winding and then between each winding and the motor frame.
A total evaluation will require running the motor to drive a load at the rated output speed and torque, and verify that the input current is close to the specified values. This is usually done using a dynamometer.

 

There are two things that are most likely to cause problems in the performance of a DC motor. They are brushes and bearings.They are both relatively easy to inspect and maintain. Brushes are an easy component of a motor to access and should be replaced if they are worn or damaged. Bearings should be cleaned and lubricated regularly. They should be replaced if they become stiff or worn.
Running tests should be performed after the physical maintenance has been completed.

 

The commutator should be examined for any wear, and if necessary, skimmed in a lathe, and then undercut, if it is an older style, new versions do not require undercutting..
It sounds like you may have a wound field motor, if this is a wound shunt field motor, it is rare these days as most have been P.M. field for some decades now..

 

I have had many little DC brushed motors fail with burnt out brushes. But all my DC brushless motors last forever.

 

It all comes down to how complete a verification of motor health is required, and how much effort would be spent. The resistance checks could be completed in a minute or two, adding a measurement of the terminal resistance while slowly rotating the motor will add a few more minutes, but as the bearings can be felt at the same time, it is a good addition. It the correct power supply is available then certainly a running check will provide added information as to the condition, even better if the supply is metered and adjustable..
So the question becomes "what is the purpose of the evaluation?" That affects the amount of effort to be expended quite a lot.