# Constant velocity => 0 Torque?

1. Jun 24, 2014

### cristian

Hello guys!

I'm trying to model a simple model of a driving shaft connected to a rear axle. The axles are connected to each other by a pinion and crown gear. However this isn't any problem to model.

My problem is that I want the driving shaft to rotate at a constant angular speed and then also apply torque to it. Is this even possible?

The formula: Torque = (Inertia)*(Angular velocity)

says that Torque = 0 when Angular velocity = 0.

My idea was to use a brake (or motor) at the rear axle to be able to create torque on the driving shaft.

I've been stuck with this for 2 days now, any help is appreciated :)

2. Jun 24, 2014

### cristian

I just found out that the "total torque" will be 0 due to the constant angular velocities. There will however be an internal torque. This internal torque is generated from two motors (connected to the two shafts) working against each other.

But I still don't know which extra formula to use.

- T1*w1 = T2*w2; T is torque and w is angular velocity
- T = J*a; J is moment of inertia and a is the angular acceleration
- n = w1/w2; n is the gear ratio and is given

I think there should be some useful formula handling the internal torque. Do you guys have any idea which? My mechanical skills are not that good as you can see, so any tip would make me happy.

3. Jun 24, 2014

### Baluncore

Constant angular velocity does not always imply zero torque.
Power = energy flow rate = RPM * Torque.
You must consider the energy flow through the system.

4. Jun 24, 2014

### tygerdawg

Yes, you can drive something at constant speed with greater than zero torque.

You've got a fundamental problem in that your equation is in error.
Torque = MassMomentOfInertia X AngularAcceleration (not AngularVelocity)

AngularAcceleration = "alpha" is approximately deltaVelocity/deltaTime

If deltaVelocity = zero then yes, of course alpha = zero.

In most physical situations (other than the vacuum of space) you will encounter resistance to motion (gravity encountered in slopes, various frictions, wind resistance, etc.), so torque must be applied to keep something moving at constant velocity.

(a rose by any other name) "Total Torque" may be called "Peak Torque" which is the maximum torque to get a body moving from rest through all the accumulated resistances to motion and up to desired speed in the desired amount of time. Steady State Torque used to maintain that desired speed is usually much less.

Analysis of motion requires you account for all loads, inertias, and resistances.

5. Jun 25, 2014

### cristian

Thank you guys, now I understand better! Appreciate it a lot! :)