How to find req'd. motor power to lift counter weight at given speed and acceleration?

[MrMohr]

Hello all! Greetings from the structural engineer's forum. As a structural guy I always get a little nervous around problems with objects not in "equilibrium"

I have a simple counter weight / motor problem. I've done some home work (old posts, my old dynamics book, etc...) and I've come up with a solution but since I've never really solved a problem like this I would love some feedback.

The problem:
I've attached a sketch with the problem and my solution.

Basically there is a object attached to a cable that is pullied over to a counter weight object of roughly equivalent weight. There is a drive cable from the counter weight to a winch. The simple question is what is the power required of the winch to move the counter weight and original object?

My solution:
I drew a free body of the counter weight and determined the tension in the drive line using ΣFy = m * a
Then I used P = T * v to solve for the power required to draw the cable at the given speed.
I came up with P = (CounterWeight / g * a)* v (see my sketch)

Additional questions:
How do the blocks effect the solution? with a given diameter I assume you can add some factor in the lines for inefficiencies.
How does the cable (weight and elasticity) effect the solution?
Does the drum diameter gear ratio etc. effect the power required? It seems to me they only effect the speed and torque.
How do differences in weight between the object and the counter weight effect the system?
I'm looking for max power required, so I assumed this is at max acceleration. How doe the power requirement change after acceleration finishes and it is running at the given speed?

anything else I am overlooking?

Like I said I am a little new to these types of problems but I am very much interested in learning. Any comments or suggestions would be greatly appreciated.

Thanks!

 

[MikeHalloran]

You've buggered up the problem by drawing it with snatch blocks.
You need to effectively put all the pulleys on a common shaft, which is in turn driven by the motor.

Search on "Atwood's Machine" for derivations and videos.



Mike Halloran
Pembroke Pines, FL, USA

 

[MrMohr]

Opps, they are not "snatch blocks" even though they are drawn from a single line. The location of the block is fixed.

I'm looking into the atwood's machine now...

 

[PersonalProfile]

I am struggling with the understanding the practicalities etc, though if neglecting this and inertia (and delta of rope mass and "sheave" friction) of the left hand side, to me the system is balanced and you deductions appear correct.

1. Assuming these are standard blocks (sheaves?) there are established values for friction etc, which you could use to check your balance / the impact on motor power. "Typically" this is negligible.
2. "Typically" this is negligible.
3. "Typically" this is negligible.
4. Adjust your FBD and you will have your answer.
5. For your current model: nil. In real life it will be some number, refer 1 and 4.

"Typically" is "typical" industrial applications, though given the focus this appears to be receiving, this may not be the case.

Regards,
Lyle

 

[SceneryDriver]

Easy formula for determining needed motor horsepower:
Hp = FS/550t

Where:
F = force in pounds
S = distance in feet
t = time in seconds

For your sheaves' bearings, a good standard assumption is:
Plain bearing: add 10% for friction (per block)
Ball bearing: add 5% for friction (per block)
Well-adjusted and lubed tapered roller bearing: 3% (per block)

Assuming you're dealing with 7x19 wire rope:
D:d ratio, where:
D = tread diameter of the sheave
d = diameter of the cable

In the entertainment industry, minimum D:d ratio should be 8:1 That's for static wire ropes. Running wire rope is usually put on sheaves with a 25:1 D:d ratio or so, to minimize fatigue damage from sharp bending. Larger ratio is better and keeps the wire rope happy. 25:1 is also a good ratio for drums as well.

You will have a small efficiency loss in the motor's gearbox, typically ~2%, depending on the type of gearing. Worms are less efficient than helical gears, for instance. This is rarely a factor.


SceneryDriver

 

[dvd]

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