Knowing how to measure torsional vibration is of key importance in the area of vehicle development and refinement. The main contributory source is the engine where periodically occurring combustion cycles cause variation in the crankshaft rotary vibration. This vibration is transmitted to and modified further by other components in the powertrain such as the gearbox and by other equipment driven off the drive belt or chain. Additional torsional vibrations are also likely to appear downstream at the drive shafts and wheels.
The fundamental approach to analysing torsional vibration is to work in the angle domain rather than the time domain. This requires accurate measurement of the angular positions of shafts and gearwheels and involves instrumenting these components with tooth sensors, tachometers or laser sensors. Whichever type of instrumentation is used the fundamental output is the angular position of the rotating component as a function of time. In contrast to normal data acquisition applications where vibration signals are recorded at equispaced time intervals, for torsional applications the requirement is to measure the times of occurrence of equispaced angular positions.
Limitations of Conventional Data Acquisition Systems
Conventional data acquisition systems are limited in their precision by their maximum sampling rate – in some situations, they simply cannot sample fast enough to quantify an entity that is moving very quickly. The measurement of torsional vibration has two factors to take into consideration: the underlying circular motion and the rotary fluctuation superimposed on the circular motion. In fact, it is the fluctuation component that is usually of more importance to the vehicle analyst.
Consider the example of a signal from a shaft encoder that is outputting 1000 pulses per revolution at 6000 rpm. This is equivalent to
6000 * 1000 / 60 pulses /sec = 100,000 pulses /sec
Even with a system sampling at 400k samples/sec, this has an inherent positional error of 25% per pulse period. Increasing the sampling rate partially improves the situation but of course, this will also result in larger data sizes and unnecessary over-sampling at low pulse rates.
An improved method of Torsional Vibration measurement
A better approach to measuring pulse positions is to use a counter with a high-frequency clock to count the intervals between rising pulse edges. The equivalent sampling rate is now increased by approximately two orders of magnitude. The DATS Advanced Tachometer Module (Type 8×20) for Prosig’s DATS-tetrad and DATS-hyper12 systems operates at 240 MHz which gives an effective resolution of 4.167 nanoseconds (1 ns = 10-9 secs). In the context of the example above this now results in a positional error (of pulse duration) of less than 0.05%.
The differences between the Advanced Tacho measurement and a Standard Tacho measurement can be seen in the graph. The blue trace was from a signal sampled using a conventional equal-time based system and the red trace was the same signal sampled using a pulse-edge measurement system based on a high-frequency clock and counter. The input signal was a stepped-sine sweep whose discrete steps can clearly be seen in the red trace. The fluctuating nature of the blue trace indicates the degree of uncertainty and inaccuracy of the conventional method of capturing tacho signals.
Analysis methods for Torsional Vibration
One of the advantages of working in the angle domain is that spectral analysis of the pulse periods produces order waterfalls and order spectra directly without recourse to interpolated resampling.
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Adrian Lincoln is Signal Processing Technology Manager at Prosig Ltd and has responsibilities for signal processing applications, training and consultancy. He was formerly a Research Fellow at the Institute of Sound & Vibration Research (ISVR) at Southampton University. He is a Chartered Engineer and member of the British Computer Society and Institute of Mechanical Engineers.