This blog was originally published by Michael Stanley, systems/algorithms team manager in the Sensors Solution Division at Freescale, on the Embedded Beat.

Freescale’s made a big push in recent years in the realm of sensor fusion.  We are very proud of those accomplishments, and today we’re still the only major sensor vendor to take our solution fully open source.  But you can do a whole lot more with sensors than simply modelling motion.  In another blog post, Ian Chen introduced the concept of Sensor Data Analytics.  Essentially, this boils down to looking for patterns in raw sensor data, and their relationship to everyday activities and events. The starting point for this is often raw vibration data from an accelerometer.  The machine condition monitoring industry has been utilizing vibration data for many years to predict machine failure before it occurs.  If you’re looking online, you’ll find the industry has a number of aliases:


All refer to essentially the same thing.  For cost reasons, machine monitoring was historically used only for very expensive machines that cannot tolerate unscheduled downtime.  MEMS technology has now reduced the sensor cost to negligible levels, and the only thing standing in the way of further adoption is expertise and software availability.  And things are changing there too.

Centrifugal Pump (source:

Figure 1: Centrifugal Pump (source:

Let’s look at some examples.  The figure above shows a “classic” industrial application.  A rotary motor is coupled mechanically to a centrifugal pump.  The motor, coupling and pump are all subject to various physical problems.  These include things like:

  • shaft misalignment
  • bearing failures
  • load imbalance
  • looseness
  • gearbox faults
  • drive belt failures
  • resonance

Interestingly, ALL of these problems manifest themselves as changes in the vibration signature(s) of the system.

Shaft Misalignment

Figure 2: Shaft Misalignment

Figure 2 shows variations in shaft alignment between the motor and pump.  These can cause a 2X rotation frequency term to show up in Fast Fourier Transform results run on vibration sensor outputs.

Figure 3: Effects of Bearing DefectsFigure 3: Effects of Bearing Defects


Figure 3 is a simplified view of a bearing, with inner trace, outer trace and roller balls between the two.  Defects in any of these three will again manifest themselves in the vibration data FFT.  The changes in frequency content are well understood as a function of the bearing geometry, and are shown n the figure.  The variables in these equations include:

  • Pd  = pitch diameter
  • Bd  = ball diameter
  • Nb  = number of balls
  • S  = speed (revolutions/sec)
  • q  = contact angle
  • BSF  = Ball Spin Frequency
  • BPFO  = Ball Pass Frequency of Outer Trace
  • BPFI  = Ball Pass Frequency of Inner Trace


In coming posts, I’m going to explore other patterns.  Some are deterministic (like those shown above).  Others are purely statistical.  My colleagues and I will also give you a peak at the tools and workflow we’re using to collect and analyze data.  This includes advanced machine learning techniques, which is an area of science that didn’t even exist when I went to school.  We’re having a lot of fun using it to look for patterns.  You can too.

In the meantime, if you are intrigued by the examples shown above, pick up a copy of the Harris’ Shock and Vibration Handbook (Sixth Edition).  Chapter 16 gives a great overview of “Condition Monitoring of Machinery”.