# Friction Measurement of Rotating Equipment

1. Sep 12, 2012

### KLoux

Hello,

I have two questions that I have been pondering for some time without arriving at an acceptable explanation. The questions require a little bit of background information:

I work on rotating machinery that operate across a range of (relatively slow) speeds, and generally has a significant imbalance. Some of the things that are interesting to us are the distance from the CG to the axis of rotation, and friction. To determine CG offset and friction, we record the torque required to rotate the machine at a constant speed. By repeating this test at several speeds, we are able to create a friction model for the device that is a function of speed.

We can accurately measure the current through the motor driving the axis, and use this to estimate the torque (by multiplying by the torque constant). We simultaneously record speed and position data.

We assume that the torque vs. time curve for a constant speed test will be sinusoidal, due to the CG moving about the axis. This sinusoid will be offset from zero due to friction. We also assume that we know the frequency of the sinusoid, because we know the speed at which the machine is rotating. We can then fit a sinusoid to the torque data using linear regression techniques. For each speed at which we test, we get a friction torque (vertical offset of the sinusoid) and CG torque (amplitude of the sinusoid). The fits are visually very good, and generally have coefficient of determination above 0.99.

Currently, we average the CG torque values for all of the different speeds to arrive at our "accepted" CG torque (and then knowing the mass, we can compute the CG offset). This brings me to question #1: At higher speeds, the amplitude of the sine wave (CG offset) increases. From 15% of the top speed to 100% of the top speed, we generally see about a 15% increase in the amplitude. Can anyone offer an explanation for this? Our current model does not include this effect, so we are stuck with averaging, which gives us the correct torque value for only one speed.

For our friction model, we use a coulomb term (constant) and a viscous term (proportional to velocity). With the friction torque vs. speed data, we can fit a curve (straight line) to get these values. Generally the results are OK (coefficient of determination above 0.9 and visually some small errors in the model). If I include an aerodynamic term (proportional to the square of velocity), the results improve quite a bit, with r^2 generally above 0.98. The aerodynamic term is always small and negative. So the faster the machine rotates, the more the friction drops away from our predicted coulomb + viscous friction model. This is question #2: Any explanation for this phenomenon?