# Hydro Power Systems

• tamar

#### tamar

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 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.

• tamar
Not a homework question.

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 ag 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.

• • anorlunda, berkeman, Lnewqban and 1 other person