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# Torque required to rotate balanced structure

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## Torque required to rotate balanced structure

(OP)
Hello,

I need help to understand how to select a hydraulic motor to move a structure. Imagine a hinged beam with two concentrated loads on ends. The hinge is not in the center. The gravity is in negative Y direction. And the beam is stable in the XY plane, so the loads and moments are balanced. Now in the XZ plane, I want to rotate the beam about the hinge. How much torque would be required to do that?

### RE: Torque required to rotate balanced structure

How fast do you want it to rotate? What are the masses and forces?

Ted

### RE: Torque required to rotate balanced structure

The torque required for angular acceleration of the beam (to rotate it) has nothing to do with whether or not its balanced. It has to do with its rotary inertia. τ = mr2α. This equation is the rotational analog of Newton’s second law (F = ma) where torque is analogous to force, angular acceleration is analogous to translational acceleration, and mr2 is analogous to mass (or inertia).

Once you determine the required torque, selecting the motor will be easy.

### RE: Torque required to rotate balanced structure

(OP)
I found that one can follow these steps:

I = k^2*m

Where k = radius of gyration
I = mass moment of inertia

Then H = I.w (angular momentum)

and T = delta H/t (torque)

So T = I. alpha (alpha = angular acceleration)

This is ultimately the same formula mentioned by jboggs.

The linear velocity required in my case is 0.15m/sec. So I will use these equations and selecting an angular accelration I can get my torque.

### RE: Torque required to rotate balanced structure

you're not going to turn the forces into masses are you ? that'd be "wrong", no?

I don't think this problem is so much about mass.
I think you've got friction from the forces, or possibly some restraint.

As drawn the vertical forces do no work when they are rotated in the plane of the beam. If the forces are in "Y", then the plane is "X-Z" ... yes?
If these forces create a friction force, then this will do work in the X-Z plane. Each friction will sum for a torque about the center.

another day in paradise, or is paradise one day closer ?

### RE: Torque required to rotate balanced structure

Nashanas,

By "balanced", I interpret that you are not lifting anything. Your motor must accelerate your structure to speed in an acceptable period of time, and it must overcome bearing friction.

Questions:
1. Is this a production system that must run efficiently, or is it a one‑off that must run on the first try. Do you want an efficient motor, or one you are damn sure will work the first time?
2. Continuing with the question above, what are the consequences of the above motor being over powered?
3. How good are your bearings? Bearings for a large, cantilevered beam can be messy and complicated.
Have you thought them through carefully?

--
JHG

### RE: Torque required to rotate balanced structure

(OP)
Thank you for the responses. I will elaborate. This motor is supposed to be installed in a crane like structure. It is called a marine loading arm. It will be a fully operational machine and is supposed to last for decades. Imagine the horizontal arm of the crane and suppose that you have to rotate it. That is my problem. In the XY plane the loads have been balanced. But like you guys pointed out, friction is one of the loads, which I had overlooked. We will be using a hydraulic motor, so even if it is over powered, it can be controlled by pressure regulators, but that is the second phase. In the first phase I want to find a motor using mathematical equations. Our BOM already has a motor, but there is no technical explanation behind this selection. My company has recently assigned me this project and I am trying to understand as much as possible by myself.

The bearing is a large slew bearing, it is complicated yes. I will try to find the rating of the bearing.

### RE: Torque required to rotate balanced structure

are "A" and "B" loads or weights ?

the force to rotate a crane arm is usually very small, overcoming friction at the base.

The mass properties of the arm are a factor.

another day in paradise, or is paradise one day closer ?

### RE: Torque required to rotate balanced structure

Nashanas,

Will there be something hanging from your loading arm? It will have mass properties too.

--
JHG

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