I am having a difficuilt time understanding if there is a parameter that defines the amount of time it would take to get to any given speed (rpm) from a DC brush motor. Can some help explain to me if there is a speed constant of some sort, and how would you go about measuring this, or if there is an equation for this?

I've search on the internet, and the only thing close I found is "Mechanical time constant". This term was defined as "the time required for the motor's speed to attain 63.2% of its final value for a fixed voltage level."

Is the mechanical time constant what I am looking for?

 

Well, it is a bit more complicated than that.

You have to go back to physics and mechanics. Your motor will be connected to something which will have a given inertia, in addition to its own internal inertia. Your motor will also be able to apply a maximum continuous tourque, and a peak torque (higher current for a limited time).

So, motor makers publish motor inertia, peak torque, and continuous torque. The torque values are related to current.

So using this data, and depending on your mechanical system coupled to it, you can use the F=MA equation and its derivatives (I think its just Tourque = inertia * radial accelleration for rotating systems, but I'd check the books if it were me.) Of course, inertia units are a pain, but there are conversion charts available.

Of course, once you get the accelleration, and know the max speed of the motor, you can guess roughly when it will come up to full speed.

Hope this helps,
~Ken

 

Troll Master,

I have a document that explains the Drive Motor Equations for dc and bldc motors. In the document there is equation 17 that gives the equation for the dc motor response in speed that is dependent on the mechanical and electrical time constant. For a step input in voltage you can calculate the motor speed for a 63.2% response of its final value. This document can be emailed to you if you give me your email address.

George W. Younkin, PE, IEEE Fellow
Staff Engineer
Industrial Controls Consulting
A division of Bull's Eye Research, Inc.
N7614 HWY 149
Fond du Lac, WI 54935
Ph: 920: 929-6544
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E-mail: [email protected]

 

With qualification,

The mechanical time constant is what you need With no friction, applying a voltage to a motor results in a exponential rise in RPM verses time Five time constants are required to get to (almost) full speed

Assuming a low electrical time constant for the motor winding (t=L/R), when a voltage is appled to a motor the motor will pull a current equal to

I=V/R where R is the armature resistance.

The mtor wuill then start accelerating based on the motor's torque constant and the total rotor and load inertia. The current will continuously decrease with time as the RPM rises due to the BEMF of the motor.

The formula for the motor time constant is

t = RJ/KtKe

where t = seconds
R = Ohms
J = Kg-m^2
Ke = Rad/sec/volt
Kt = N-m/amp

However, if the applied voltage is too high the iron in the motor will magnetically saturate or magnets will demagnatize so there is a maximum initial voltage that can be applied to a motor. For this condition some form of current limiting must be used.

 

Yes, the mechanical time constant is the most important factor. It is essentially intertia. Other factors include what the final speed value is. This depends on the load and the voltage.

Robert Scott
Real-Time Specialties
Embedded Systems Consulting