Case of Missing Gear Mesh Frequency

Question:

“Why don’t we see the Gear Mesh Frequency (GMF) on the output side of a splash lubricated slow speed gear box?”

This is quite puzzling since common sense dictates that such peaks should be present.

My Answer:

The principles involved are the following:

1. Air, water and oil produce turbulence when worked on by machines like pumps, gears, fans, propellers etc.
2. Such turbulence creates damping force.
3. This is proportional to the square of the velocity.
4. But this damping force acts in quite a funny manner.
5. For slow speed machines (say below 750 rpm; slower the better) damping is positive that is it goes against the motion and so neutralizes the entropy as seen by the decrease in the vibration levels. Hence the gear mesh frequencies vanish. Coriolis Effect on the output side of the gear box also helps in attenuating the vibration.
6. But for high speed machines damping is negative. That is it goes in the direction of the motion and therefore enhances the entropy as seen by the increase in the vibration levels.
7. So, for low speed machines it goes against the motion and suppresses the GMF. In some cases it suppresses the fundamental peak as is found in the case of the vertical Cooling Water Pumps of Power Plants. GMF is produced when the fundamental frequency is superimposed onto the vibration generated through gear impacts.
8. It therefore follows that for high speed gear boxes it magnifies both fundamental and GMF peaks.

Missing peaks therefore indicate fluid turbulence, which might also be indicated by other peaks like vane pass frequencies. The condition monitoring of such gear boxes might best be done through Wear Debris Analysis/Ferrography.

So, this is the mystery of the missing GMF in splash lubricated slow speed gear boxes.

Therefore, splash lubrication for a low speed gear box is a good idea. It enhances the life of the gear box since it balances the entropy in the system.

But at the same time, with higher oil level in a splash lubricated high speed gear box the vibration level would increase, specially the fundamental and the GMF. That would spell trouble.

Similarly, it is better to have a turbulent air flow in low speed fans and blowers. It suppresses the vibrations and therefore enhances the life of bearings.

Nature also uses these principles of fluid turbulence and damping? Applications?

1. Bird’s nest are made up of loosely placed twigs and leaves usually not bound to each other. But these don’t break up or fall off in turbulent winds. Damping keeps them in place and provides the necessary security to birds.

2. Swift flowing rivers allow fishes to grow bigger and better.

3. Winds, storms etc neutralize the increase in entropy.

Design Ideas for Reliability & Sustainability?

1. Low speed gear boxes might best be lubricated by splash lubrication.
2. High speed gear boxes might best be lubricated by spray lubrication
3. Hotter and turbulent air might best be handled by low speed fans and blowers.

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Predicting Black Swans – Part II

In the earlier post we dealt with the concept of predicting a ‘black swan‘.

In this post, I intend to explore the concept a bit more: what exactly we monitor to notice a ‘black swan’ in time?

In doing so we would be forced to consider the natural response of a system.

The starting point of our exploration would be to understand how any system, as a whole, whether natural or engineered, would disturbed by a ‘black swan’.  A system is disturbed in three possible ways, which are as follows:

a) A system loses energy till it reaches a tipping point

b) A system gains more and more energy till it crosses the point of system resilience

c) A part of a system emits more energy than it is normally supposed to, that is going beyond the linear response of the part. 

So the natural way to watch a system to expect a ‘black swan’ in time, is to keep a tab on the ‘energy’ of a system in the following ways:

a) Monitor the entropy of a system. As a system functions the entropy of a system gradually rises till it hits a threshold limit indicating the appearance of a ‘black swan’ or an outlier. 

b) Monitor the energy gain of a system till it crosses the ‘resilience’ point to give birth to a ‘black swan’, outlier or a ‘wicked problem’. 

c) Monitor critical parts of a system for excess emission of energy till it goes beyond the linear response of a part. 

It is useful to remember that energy is transferred in ‘quanta‘ or in packets of energy. Therefore, it is natural to expect jumps of energy levels as we record by capturing the different manifestation of energy levels on monitoring trend charts. So when a ‘jump’ is big enough to cross a threshold limit or resilience point or linear response level indicated by its presence outside the Gaussian distribution range  we can be quite sure that a ‘black swan’ or an outlier or a ‘wicked problem’ would soon arrive on the scene. We call such an indicator as a signal.

Therefore, the central idea is to capture such signals in time, just before a ‘black swan’ makes it way to appear on the scene to dominate and change the system.

However, the question is how early can we detect that signal to effectively deal with the inherent ‘black swan’ in a system, which is yet to appear on the scene?

That would be explored in the next post.