Calculating Power Needed for Torque & Revolutions

[uselesspotus]

Homework Statement

Lets say I am tightening a screw and I have multiple torque values with their respective number of revolution. How should I go on about calculating the power required?

Also let's assume we know the time it takes to tighten the screw.

2. The attempt at a solution
I know Power = T*dθ/dt = Tω = 2*pi*n*T, where T = torque, ω = angular velocity, n = number of revolution/sec
Since the torque is not constant I am not sure how to approach this problem. Is there any other information i need in order to calculate the power?

 

[gneill]

Hi uselesspotus, Welcome to Physics Forums.

Power is measure of the rate at which energy is being delivered (Watts, or Joules per second). So either you want the instantaneous power at some instant in time, or perhaps the average power delivered over the entire operation.

If the former, then you have your P = Tω formula. If it's the average power you want then if you have the torque as a function of θ, T(θ), you can integrate the torque over the angle and divide by the total time.
$$P_{avg} = \frac{1}{\Delta t} \int_{\theta_i}^{\theta_f} T(\theta) d \theta$$

 

[uselesspotus]

Hi uselesspotus, Welcome to Physics Forums.

Power is measure of the rate at which energy is being delivered (Watts, or Joules per second). So either you want the instantaneous power at some instant in time, or perhaps the average power delivered over the entire operation.

If the former, then you have your P = Tω formula. If it's the average power you want then if you have the torque as a function of θ, T(θ), you can integrate the torque over the angle and divide by the total time.
$$P_{avg} = \frac{1}{\Delta t} \int_{\theta_i}^{\theta_f} T(\theta) d \theta$$

Thnx I get it now. Also does torque depend on how fast you rotate something? I would think it does not since it only depends on force. For example, using a hand instead of a machine.

This means work would just be Work = T_f*θ_f (assume initial torque was zero in previous power calculation) since work is ∫Pdt

 

[gneill]

Thnx I get it now. Also does torque depend on how fast you rotate something? I would think it does not since it only depends on force. For example, using a hand instead of a machine.

Just look at how torque is calculated. No mention of speed in there. What it is that applies the force is irrelevant too.

This means work would just be Work = T_f*θ_f (assume initial torque was zero in previous power calculation) since work is ∫Pdt

Sure, if the torque has a constant value for all values of θ.

 

[uselesspotus]

Sure, if the torque has a constant value for all values of θ.

How would the equation change if the torque wasn't constant? Wouldn't the work still be, after integrating, W = P*t_f-P*t_i And because the initial time = 0 W = P*t_f where P is Pavg (the equation u provided in earlier post)...I believe I am thinking of this wrong way.

Going back to the Pavg equation, I would have to do numerical integration if I just have the data set not the function itself right?

 

[gneill]

How would the equation change if the torque wasn't constant? Wouldn't the work still be, after integrating, W = P*t_f-P*t_i And because the initial time = 0 W = P*t_f where P is Pavg (the equation u provided in earlier post)...I believe I am thinking of this wrong way.

Going back to the Pavg equation, I would have to do numerical integration if I just have the data set not the function itself right?

If you have a data set with constant torque values that cover a number of revolutions each then you can break the problem up accordingly; Presumably you'll have time intervals to correspond with torques and angular displacements. On the other hand, if you have torque as some function of the angle then you can integrate symbolically and plug in the limits.

 

[OldYat47]

I'd have to ask why you need to know the power "required"? In any case, as mentioned, torque does not depend on speed or velocity of any kind, power does. For example, if you are twisting at constant torque and varying speed then the power will vary linearly with the rotational velocity.
power = work X time; work = force X distance; power = force X distance / time, power = force X (distance / time), so power = force X velocity

 

[CWatters]

Power = torque * angular velocity

If neither torque or angular velocity are constant you need to plot a graph of the product and find where it's a maximum. That will give you the max peak power.