Transmission error (TE) has long been thought to be a major contributor to gear vibration and noise, but insufficient consideration has been given to the different types of TE and how they generate vibrations. TE is defined as the difference in torsional vibration of two meshing gears, scaled so as to represent linear motion along the line of action, this being common to the two gears, as opposed to the corresponding variations in angular displacement, inversely proportional to the pitch radii. There are three distinct types of TE, with different origins and properties: 1) Geometric TE (GTE) given by deviations of the (combined) tooth profiles from ideal involute 2) Static TE (STE) including elastic deformation of the teeth and therefore being load dependent 3) Dynamic TE (DTE) where the loads on the teeth depend on the dynamics of the system, and thus include inertial as well as stiffness effects, so that they vary with speed for frequencies above the lowest resonance. It has long been recognized that TE can be measured very accurately by phase demodulation of the signals of shaft encoders rigidly attached to each of the gears in mesh. The encoders can be mounted on the free ends of the gear shafts (the section not transmitting torque).

It has recently been realized that all three types can be measured; GTE at low speed and low load, STE at low speed and higher load, and DTE at higher speed and higher load, as long as the machine can be operated over a range of speeds and loads. Compared with measurements of the actual angular motions from which the TEs can be calculated, the TEs are much more repeatable, because the two gears follow the same small speed variations, which cancel out in the TE.

Measurements have been made on a single stage gearbox, with hardened and ground spur gears, over an input gear speed range from 2 – 20 Hz, and input shaft torque range from 0 – 20 Nm. Heidenhain ROD426 shaft encoders were used, with 1000 pulses per rev, as well as a one per rev tacho pulse as a phase marker. A simulated tooth root crack has been inserted in one tooth on the input pinion. One of the four bearings had an inner race fault, but in this case that can be considered as part of the background noise. Other projects involve diagnosing the gear and bearing faults separately when both are present at the same time.

A previous paper [1] was made with the same basic test rig (though with a different gear set and naturally developing pitting over an operating period of many hours). Unfortunately, the encoders used at that time (actually included in slip rings) had a low torsional resonance frequency, which precluded making measurements at higher than 2 Hz shaft speed, so only GTE and STE could be estimated, the latter only at zero and 20 Nm load. The results were promising, but could not show dynamic effects.

The results of the current tests show that the measured GTE, STE, and DTE behave as might be expected, and correspond well with a lumped parameter simulation model of the test rig, for both TE and acceleration responses. The indications are that TE has several advantages over vibration acceleration (or even the raw torsional vibrations) as a diagnostic parameter, being close to the source (the gearmesh) and with “common mode rejection” from the two gears, thus being much less sensitive to operating conditions and rig parameters, including the much greater number of transfer paths, modulations, and resonances in the casing vibration measurements.