Premise: the Transmission Error
The Transmission Error (Transmission Error, TE in short) of a gearbox originates from the difference between the effective instantaneous angular position of the output shaft and the theretical instantaneous angular position of the same shaft, given by the input shaft position reduced by the nominal geometrical transmission ratio.
Basically the TE can be expressed by following formula:
where:
τ=transmission ratio
ωout=output angular velocity
ωin=input angular velocity
The TE features, on average, always to be zero – since by definition the average input and output velocities are in a relationship defined by τ – but instantaneously it is not so, and it features the more ranging around zero the more inaccurate is the alignment among gears inside the gearbox.
The transmission error depends on the coupling imperfections and gear backlashes during energy transfer from the input to the output, so that it can be used as a parameter showing the efficiency of the gearbox.
The greater TE, the greater is the velocity oscillation of the gearbox output when input velocity is constant, and as a result:
- machine performance is reduced (i.e. if on the gearbox output depends the spindle machining, whose quality is negatively affected by motion irregularities)
- comfort is decreased (i.e. when the gearbox concerned is a lift winch that by means of ropes controls the motion of the liftcage, this last will move „in jerks“ instead of smoothly)
- greater impulsiveness in teeth contact > noise or vibration errors (i.e. a high gear teeth deflection at meshing could increase the transmission error and could generate a shaft resonance, or even induce to structural resonances of the box).
The main causes of the transmission error are:
- Abnormal meshing generated by gear eccentricity, or by faulty machining centre distance, or inconstant pitch or width, dented teeth or surface irregularities arising from machine processing, etc. These faults may be reduced thanks to a smart design of gears and improved due to a manufacturing process control.
- Local teeth deflections caused for example by high loads.
- Progressive wear during gearbox life (pitting on teeth sides, bearing backlash increase).
It can be stated that the transmission error is the most important index to evaluate the gear quality with regard to vibrational and acoustic features.
The application limit is characterised by a difficult performance of its measurement, even conceptually simple, because it requires the installation of two high-resolution encoders on input and ouput shafts, as shown in picture 1.
Therefore, the TE can be measured on a gearbox testing bench, where the application of high-resolution encoders is feasible, but it cannot be reliably measured at end-of-line or when working.
Application to gear test benches
The measurement of the TE may be evaluated not only in relation to the complete gearbox, but also to characterise the different stages of reduction, before the concerned gears are mounted inside the gearbox.
This is of particular interest especially for bevel gears, which due to their geometrically very complex shape are characterised by greater inaccuracy in contact, and consequently by a greater TE than in case of cylindrical gears: this worst contact causes noise and vibration troubles in the gearbox and in the final application, as we often experienced over the years during experimental campaigns performed with VMGears.
In view of this scenario, PEI VM has developed TRGears, a complete hardware + software system allowing to integrate even in most basic End-Of-Line test rigs a complex function as the measurement of Transmission Error, carrying out an analysis in few seconds, by storing the results of the test in a dedicated database (local and central) and by managing the acceptability thresholds manually or in self-learning mode.
TRGears proposes therefore on simple test benches an advanced analysis function until today present only on complex and expensive test rigs.
TRGears can be installed as an independent tool or together with VMGears (where a double and complete check of gear quality level is needed).
