Calculating Force on Shaft Bearings - Hydro Power Systems

In summary, the conversation discusses the calculation of forces on a shaft bearing based on the moment of inertia, rotating speed, and allowable vibration. The forces can be axial or radial and are affected by the machine's condition and vibration specification. A simplified model of a rotating machine is presented, and it is noted that bearing forces cannot always be accurately calculated from vibration measurements. A two-plane dynamic balance can be done to reduce unbalance forces and accurately calculate hydrodynamic forces.
  • #1
tamar
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TL;DR Summary
Force calculation
I know the moment of inertia and the rotating speed of a shaft, and the allowable vibration is 2mm/sec. How is the force calculated? What is the formula to calculate the force on the shaft bearings which are a know distance from centre of gravity?
Thanks
 
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  • #2
:welcome:

Which forces, axial or radial? What does vibration have to do with it?

Is this a homework question? If so, we can move it to a homework forum, and you are required to post your attempt at the answer before getting help.
 
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  • #3
Not a homework question.

Both axial and radial.
Vibration means it is the limit allowable as an unbalanced load for vibration hence this will exert extra load on bearings which I need to calculate.
 
  • #4
School notes I have pulled out from the garage from 30yrs ago:)
 
  • #5
It would depend very much on the type of hydro turbine, and its condition. I don't know of any simple formula. Perhaps others here can help, such as @jrmichler
 
  • #6
A vibration specification of 2 mm/sec can be translated into acceleration and displacement if it is at a single frequency. This is only rarely the case.

A simplified model of a simple rotating machine, such as a simple hydro turbine is as follows:
A lumped mass representing the rotor
A spring representing the shaft
A spring representing the bearing
A lumped mass representing the bearing housing
A spring representing the machine frame
A lumped mass representing the machine frame
A spring representing the machine foundation

Vibration measurements are typically made on bearing housings, and sometimes on machine frames. Given all of the springs and masses in a simplified model, calculating bearing forces from a measurement made on the bearing housing is only rarely possible.

If you have an unusually simple machine where all stiffnesses are "large", and there is a known unbalance, then bearing forces can be calculated from the unbalance moment and speed. This would be the case in, for example, a one cylinder engine or reciprocating air compressor.

The real world solution is to do a two plane dynamic balance, then calculate the hydrodynamic forces. If it is properly balanced, the unbalance forces will be small compared to the hydrodynamic forces. Note that hydrodynamic forces can vary at the blade passing frequency, which is a cause of vibration.
 
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1. What is the purpose of calculating force on shaft bearings in hydro power systems?

The purpose of calculating force on shaft bearings in hydro power systems is to determine the amount of force that is being exerted on the bearings due to the weight of the rotating shaft and any additional forces, such as water pressure, acting on the system. This information is important for designing and selecting bearings that can withstand the forces and ensure the safe and efficient operation of the system.

2. How is the force on shaft bearings calculated?

The force on shaft bearings is calculated by summing up all the forces acting on the shaft, including the weight of the shaft, the weight of the rotating parts, and any external forces such as water pressure. This total force is then divided by the number of bearings supporting the shaft to determine the force acting on each bearing.

3. What factors can affect the force on shaft bearings?

The force on shaft bearings can be affected by a variety of factors, including the weight and speed of the rotating shaft, the weight and distribution of the rotating parts, the direction and magnitude of any external forces, and the design and placement of the bearings. Changes in any of these factors can result in a different force being exerted on the bearings.

4. How does the force on shaft bearings impact the design of hydro power systems?

The force on shaft bearings is a critical factor in the design of hydro power systems as it determines the size, type, and placement of bearings needed to support the rotating shaft. If the force on the bearings is too high, it can lead to premature wear and failure of the bearings, resulting in costly repairs and downtime. Therefore, accurate calculation of the force on shaft bearings is essential for ensuring the safe and efficient operation of hydro power systems.

5. Are there any precautions that should be taken when calculating the force on shaft bearings?

Yes, there are several precautions that should be taken when calculating the force on shaft bearings. These include accurately determining the weight and distribution of the rotating parts, accounting for any external forces, and using appropriate safety factors to ensure the bearings can withstand the calculated force. It is also important to regularly monitor and adjust the force on the bearings as needed to prevent excessive wear and potential failure.

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