# DC Motor / Current Control and Torque/Speed Relationship

#### samsharp99

Hello,

First time posting here as I havn't been able to find a suitable answer to my question to help me understand some issues I am having with DC motors. I am trying to calculate the maximum speed and acceleration of a dc motor being driven by a current source with a known inertia.

I have a DC motor connected to a load (a mass of known inertia) through a harmonic drive and belt drive. The motor is connected to a servo amplifier that's operating in torque mode i.e. it provides a current to the motor proportional to the voltage input. The current is limited to 2A.

I understand that the torque output of the motor is proportional to the output via torque = current * torque constant.

So if I apply the maximum current (2A) to the motor, this generates a torque which causes the motor/load to accelerate.

I also understand that the motor produces a back emf, proportional to the speed of the motor.

Am I correct in saying that the motor will continue to accelerate until the back EMF is equal to the maximum voltage that the servo amplifier can supply? If this is the case, how can I calculate the maximum speed of the motor with the known inertia load?

I also understand that there are a number of friction effects (static + velocity dependent) that will also effect the maximum speed by removing torque from the system, but I'm not sure how they fit into the equation?

I am trying to understand the relationship between the current input to the motor and the acceleration, torque and speed produced.

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#### Baluncore

See what happens when you pay in advance. I am sure you have worked out the answer by now, so I will provide an answer for those who find this more than 8 years after you posed the original question.

Am I correct in saying that the motor will continue to accelerate until the back EMF is equal to the maximum voltage that the servo amplifier can supply? If this is the case, how can I calculate the maximum speed of the motor with the known inertia load?
The critical thing is that the constant motor current produces a constant torque. Along with inertia, that determines the initial acceleration, but it does not decide the maximum RPM.

Although the maximum RPM may be limited by the imperfect output voltage compliance of the motor current controller, the theoretical speed limit will be when the sum of torques due to frictional losses, windage and output shaft load are equal to the motor torque.

The controlled current that flows through the motor will develop a voltage drop due to the (hopefully constant) winding resistance. The generated back EMF is proportional to the RPM and will be added to the resistive drop to give the motor terminal voltage. That terminal voltage will only be about twice the rated motor voltage and needs to be sourced by the motor controller.

"DC Motor / Current Control and Torque/Speed Relationship"

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