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Verification of the Back-EMF Method for Piston Velocity Measurements



Ray Radebaugh, Michael A. Lewis, Peter E. Bradley


Linear compressors are used to drive pulse tube or Stirling cryocoolers, and they can be used as expanders in place of inertance tubes when inertance tubes cannot provide sufficient phase shifts between flow and pressure. Commercial linear compressors rarely incorporate position sensors, so PV power, flow rates, and flow-pressure phase at the piston are usually unknown. Use of the back EMF in linear motors to measure piston velocity was previously proposed. A comparison of this derived velocity with that determined from an accelerometer attached to the piston showed good qualitative agreement. However, no measurements have been reported on its accuracy or on comparisons with position sensors. We report here on a comparison of piston velocity measurements determined from the back-EMF method with that from a linear variable displacement transducer (LVDT) attached to a piston of a commercial linear compressor. Comparisons using a second compressor with a laser position sensor are also discussed. The back EMF is the complex voltage difference between normal operation and that where the pistons are locked to prevent movement for the same current. The velocity is simply the back EMF divided by the force constant of the motor. Measurements were made at 16 Hz, 30 Hz, and 60 Hz in both compressors. Our results show that the velocity amplitudes determined from the back-EMF method and the LVDT agree within 7 %. The laser position sensor showed abnormal behavior (20 % to 30 % deviations) for strokes less than about 20 % of full stroke. Agreement was within about 5 % at higher strokes.


cryogenics, cryocoolers, linear compressor, linear expander, linear motor, position, velocity


Radebaugh, R. , Lewis, M. and Bradley, P. (2012), Verification of the Back-EMF Method for Piston Velocity Measurements, Cryocoolers, [online], (Accessed May 23, 2024)


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Created July 10, 2012, Updated February 19, 2017