By Alan Friedman & Glenn White
This is Part 1 of a two-part series adapted from the original paper “Mobility: A New Approach to Measuring Actual Forces in Machinery” by Alan Friedman & Glenn White. In this post, we’ll explore why vibration levels can be misleading, introduce the concept of mobility, and lay out the basic equations behind it.
When most of us began learning about vibration analysis in the context of machinery fault diagnosis, we learned about how the various faults appeared in the vibration spectra. Perhaps we were given some guidelines on what vibration amplitudes were acceptable and which were excessive for certain types of machines. We most likely were left with the impression that when it comes to vibration in machinery, less is better and more is worse. Unfortunately, it is not as simple as it seems.
For example, in Figure 1 are two identical vertical machines with an equal amount of imbalance on the fans at the top. Looking at just the horizontal direction, we would expect to see the same vibration levels at 1x, or the running speed of the machine.
Now, if we take one of these machines and firmly attach it to a wall as shown at the left in the figure, what happens to its vibration levels at 1x (the shaft rate)? The assumption would be that it would go down. As the machine is now less free to vibrate one would expect it would vibrate less. Then let’s say that the machine that is not attached to the wall has vibration levels at 1x that exceed an “industry standard” and the one attached to the wall now has levels low enough to not exceed that alarm level. Which one will we balance?
Well, obviously the one that exceeds the alarm. But realistically, which machine is going to fail first? We know from the way we set up this scenario that both machines contain the same amount of imbalance even though we can’t tell that now from the vibration data! You see; it’s not as simple as it seems!
Lets think about it. In the machine not attached to the wall, the forces of imbalance are causing it to vibrate – generating motion. The machine that is attached to the wall is now less free to vibrate; in other words, it is less flexible or stiffer. So where are those forces of imbalance going? The force from the imbalance must be borne by the bearings on its way to the wall. Because there are more forces on the bearings in the attached machine, this one will fail first. Our instinct to repair the machine with higher vibration levels would have been misguided!
In a second example, we have a horizontal machine with an imbalance and we take vibration measure- ments in the vertical and horizontal directions. You might think that we should have the same ampli- tude in both vertical and horizontal axes at 1x since the imbalance force should be the same in these two axes. In reality, the two peaks will most likely not be of the same amplitude! Which peak do we cite when we want to tell someone the machine needs to be balanced; the bigger one? Do we tell them it is only imbalanced in the horizontal direction? The real question is why will we see different vibration levels in these two axes?
The Concept of Mobility
If a machine is less free to vibrate, this would increase the force in the bearings. When we are talking about “freedom to vibrate” what we are really talking about is “stiffness”… a way of describing a structure’s freedom to vibrate or freedom to move. What I would like to suggest is that if we do not know a machine’s stiffness, we don’t know all the forces it is experiencing… and we don’t have informa- tion about the damage being done. If we don’t know anything about the damage being done to the ma- chine, why are we bothering to collect vibration data? Isn’t that the whole purpose of vibration analy- sis? Mobility is defined as the inverse of stiffness. If stiffness is the reluctance of a structure to respond to a force, mobility is the ease with which a structure responds to a force. High mobility means easy to move, and high stiffness means hard to move. I like to use mobility because it turns out that it is easier to measure in practice.