# Time domain to angular domain approach

I have a rotating shaft where I need to move from the time domain to the angular domain to look for vibration faults. I have the data from a tachometer.

From another post I found these steps:

The steps involved for time domain --> Angle domain are:

1. Use the tachometer signal to obtain a speed signal. This is the inverse of the difference in time for each trigger point.
2. Depending upon the variability of the tachometer signal least squares cubic spline fitting is often used. Matlab spline library will work as will matlab central libraries. I use the fastBspline library.
3. Integrate the speed signal to obtain shaft angle position.
4. Determine the equal angle increments that you want to use. Keep the Nyquist theorum in mind, in other words there should be roughly the same number of points in the angle domain as in the time domain.
5. Switch the (time, angle) data to (angle, time). Resample the (angle, time) data to obtain uniform angle increments. Once this is done, do all the same processing you would have done, but now you are in the angle order domain.

Questions

In regards to step 2: What is returned if I integrate the speed signal (which is an array)? Surely that would not be a function or an array?

In regards to step 5: Why is it necessary to change from (time, angle) to (angle,time)? How is this plot related to the original vibration signal (time, acceleration)?

• I suggest you put some sample data to really illustrate what you are asking. For example, in (time, angle), which is the independent signal and which is dependent signal. – jithin Mar 24 '20 at 14:00
• For integrator, you can look for accumulator. The output is also an array. It gives the sum of inputs till that point. $y[n] = \sum_{k=0}^{k=n-1} x[k]$ – jithin Mar 24 '20 at 14:02