Prosig Signal Processing Blog

By Dr Colin Mercer, Technical Director, Prosig

The measurement of the twist angle between two points along a shaft or through a gear train may be derived from a pair of tacho signals, one at each end of the shaft. Typically the tacho signals would be derived from gear teeth giving a known number of pulses/revolution. For example one end of a shaft could have a gear wheel with say 60 teeth giving 60 pulses/revolutions when measured with say an inductive or eddy current probe.
If there is a gearbox between the two measurement points then it is necessary to know the overall gear ratio and also whether the input and output shaft are rotating in the same or opposite directions. Gearbox ratios when expressed as one value are often inaccurate. Thus in DATS the numerator and denominator are requested as integers so that the ratio is known exactly.

The following examples show one case of a crankshaft where the rear end had a gear with 60 teeth giving 60 pulses/rev and the front end had a 20 tooth gear giving 20 pulses/rev. Data was collected over 30 seconds at 100000 samples/second giving some 3 million data points per signal. The engine concerned was a high performance engine with an operation speed in the range 6000 to 12000 rpm.

The first two signals below are the two tacho signals. Figure 3 is an expanded view of the front tacho and Figure 4 is the speed deduced from the tacho signals.

Figure 1: Front Tacho Pulse stream
Figure 2: Rear Tacho Pulse stream
Figure 3: Expanded View of Front Tacho Pulse stream
Figure 4: Speed from Front Tacho Pulse stream Determination of the angular vibration used the TWIST module. In the example below the front signal was used as reference and the rear as the target.
Figure 6 Angular Shaft Vibration Rear relative Front Initially there is a mean twist of around -2.3º with a vibration amplitude of about ±0.15º crank angle. However after 22 seconds, which corresponds to a speed of about 10000 rpm, it would appear that the shaft has some form of resonance at this speed. Figure 7 below shows the angular vibration plotted versus speed.
Figure 7 Angular Vibration Versus Speed The second example involves a compound gear which had some degree of inbuilt damping. This was intended to remove the larger vibrations. The compound gear has a gear ratio of 41/17 and the output signal had 17 points per rev. This compound gear was attached to the front of the crankshaft. Again the front crank was used as reference and this time the compound gear was used as the target. Figure 9 shows the result.
Figure 8 Compound Gear Tacho signal
Figure 9 Compound Gear Twist relative to Front Crank The initial twist is approximately 0.9º with a vibration level of around ±0.2º but at high speeds the vibration level increases quite significantly. At around 11000 rpm the average twist amplitude is approximately ±0.8º.There are a whole variety of analysis tools which may now be applied. As a simple example the frequency content as a function of time is shown in the waterfall below.
Figure 10 Compound Angle Frequency versus Time The are many observations which may be made. Clearly there is order related information and a waterfall versus speed would be the next analysis, initially using the crank tacho.
Figure 11 Compound Gear Orders It is clear that the vibration is, as expected, related directly to the crank shaft. However the presence of half orders was not originally expected.