Calculating Force on Shaft Bearings - Hydro Power Systems

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Discussion Overview

The discussion revolves around calculating the force on shaft bearings in hydro power systems, particularly in relation to vibration limits and the types of forces involved. Participants explore the complexities of the problem, including the influence of axial and radial forces, and the implications of vibration specifications on bearing loads.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the formula for calculating the force on shaft bearings given the moment of inertia, rotating speed, and allowable vibration.
  • Another participant questions whether the forces in question are axial or radial and how vibration relates to the calculation.
  • A participant clarifies that both axial and radial forces are relevant and that vibration indicates the allowable unbalanced load affecting the bearings.
  • One participant suggests that the calculation depends significantly on the type and condition of the hydro turbine, indicating a lack of a simple formula.
  • A detailed model of a simple rotating machine is proposed, including various components like lumped masses and springs, highlighting the complexity of calculating bearing forces from vibration measurements.
  • It is mentioned that in simpler machines with known unbalance, bearing forces can be calculated from the unbalance moment and speed, but this is not common in more complex systems.
  • A real-world solution involving dynamic balancing and hydrodynamic forces is suggested, noting that properly balanced systems will have smaller unbalance forces compared to hydrodynamic forces.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of formulas and the complexity of the calculations involved. There is no consensus on a specific method or formula for calculating the forces on the bearings, indicating ongoing debate and exploration of the topic.

Contextual Notes

The discussion highlights limitations in the applicability of simplified models to real-world scenarios, as well as the dependence on specific machine conditions and configurations. The relationship between vibration measurements and bearing forces remains unresolved.

tamar
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TL;DR
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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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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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.
 
School notes I have pulled out from the garage from 30yrs ago:)
 
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
 
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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