# Mechanics (Statics) - Forces/Couples exerted by flexible bearings?

• vineroon
In summary: In order to do this, the shaft must be of a certain size so that the moment at the ends of the bearing span is the same as the moment of inertia of the bearings about the shaft. You can see this by considering the two beam problems: in the first, the ends of the beam are fixed and the shaft is rotating; in the second, the ends of the beam are fixed and the shaft is not rotating. In the second problem, the moment of inertia of the two bearings is the same about the shaft, so the moment at the ends of the beam is also the same. The shaft must be of the right size to make this happen.
vineroon
Problem Statement
A steel shaft 120 mm in diameter is supported in flexible bearings at its ends. Two pulleys, each 500 mm in diameter, are keyed to the shaft. The pulleys carry belts that produce the forces shown. Determine the internal forces on a vertical section through point A.

I've been trying to start this problem, but the one thing I cannot figure out are what sort of forces are exerted at the ends of the shaft by the flexible bearings.

Also, I'm not sure why the diameter of the shaft would be required since it asks you to calculate the shear and axial forces along with the moment at cross-section A.

Any help would be greatly appreciated.

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Hi vineroon,
If the bearings weren't "flexible" could you do this problem?

The only 'flexible' bearings I'm aware of won't change the forces because the loads still need to be resisted in full. So try the problem again without consideration for flexibility in the bearing area.

vineroon: Each pulley has a resultant force and torque that is applied at the shaft axial centerline. Can you compute the resultant force and torque of each pulley and apply these at the shaft axial centerline? Now you have a beam problem, right? Actually, two separate beam problems and a torsion problem, which you could work separately, right? Why do you think they tell you the bearings are flexible? Does that tell you anything about the rotational constraint at the ends of your two beam problems?

Good observation on your part; the shaft diameter is not required for the given question.

I think perhaps this is telling you that the bearings are not fixed ends, that is, they are like ball-in-socket bearings. Thus the bending moment at the ends of the bearing span must go to zero.

## 1. What is the purpose of flexible bearings in mechanics?

Flexible bearings are used to support and guide rotating or sliding parts in a mechanical system. They are designed to accommodate movements and misalignments between the parts, while still providing support and reducing friction.

## 2. How do flexible bearings exert forces and couples?

Flexible bearings exert forces and couples through the deformation of their material. As the rotating or sliding parts move, the bearings flex and bend, creating a reaction force and torque that helps to maintain the stability and alignment of the system.

## 3. Can flexible bearings handle high loads?

Yes, flexible bearings can be designed to handle high loads. The amount of load a flexible bearing can withstand depends on various factors such as the material used, the design of the bearing, and the operating conditions. It is important to carefully select and design flexible bearings to ensure they can handle the required loads.

## 4. What are the advantages of using flexible bearings?

One of the main advantages of using flexible bearings is their ability to accommodate movements and misalignments between parts. This reduces the stress and wear on the system, resulting in longer service life. Flexible bearings also help to reduce friction and noise, and can be designed to handle specific loads and operating conditions.

## 5. How do you determine the appropriate flexible bearing for a mechanical system?

The appropriate flexible bearing for a mechanical system depends on various factors such as the type of load, operating conditions, and required range of motion. It is important to consider these factors and consult with a bearing specialist to select the most suitable bearing for the specific application.

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