ACTA TECHNICA CORVINIENSIS - Bulletin of Engineering

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ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGtested toothed gear, closing gear and stretchingclutch. The electric engine with a power of 15[kW] with the use of belt transmission poweredthe closing gear. The gear load was regulated bythe levers with weights, stretching clutch andtorsional shafts. The work speed of the gear wasset with the use of frequency converter steeringthe work of the electric engine. The tested gearand the closing gear had the same transmissionratio and the same wheel base.TestedgearboxTensionclutchClosinggearboxBelttransmissionElectricalengineFig. 1 Scheme of the circulating power test rigIn fig.1 the tested toothed gear is presentedworking in the rotating power system.The toothed gear with straight teeth was tested,where the number of teeth in the pinion and thewheel equalled 16 and 24 respectively. In thetests the toothed wheels made of 20H2N4A wereused, which were carburizated and hardened tothe hardness equalling 60-62 HRC.THE EXPERIMENT DESCRIPTIONThe aim of the experiment was an attempt toclassify the type and stage of teeth damages ingear wheels with the use of artificial neuralnetworks [5-9,12-14,16].In the experiments it was decided to use thediagnostic information about the objectcondition included in the vibration signal. Onthe basis of literature [2-6,9-11,13-15,17] thesignal assumed as the information carriercorrectly reflecting the damages of toothed gearwas the transverse vibration speed signal of thewheel shaft. The measures were taken in thedirection of inter-teeth force interaction.The measurement system consisted of angularposition sensors of shafts, a logic unit, a laservibrometer, the signal analyser and a computer.The measurement of the transverse vibrations ofthe gear wheel was conducted with the use oflaser vibrometer Ometron VH300+. The logicunit with two angular position sensors of shaftsenabled the precise definition of the connectionmoment of the same pair of teeth. The registeredvibration speed signal and the reference signalfrom the logic unit were processed in the signalanalyser DSPT SigLab. The measured signalswere sampled with frequency of 25600 [Hz] andregistered on a PC computer.In order to check the functioning correctness ofthe neural classifiers in the task of defect stageidentification of the toothed gear, a series oftransverse vibrations measurements wasconducted of the wheel shaft in an undamagedgear and in a gear with modelled damages:• cracks at the tooth base (1 and 3 [mm]),• crumblings on the tooth tip (0,75 and 1,5 and2 [mm]).The measurements were conducted for atoothed gear working at two rotational speeds ofthe wheel shaft (900 and 1800[obr/min]) and withtwo loads (138 and 206 [Nm]).The result of the conducted process of signalregistration was the achievement of the matrixconsisting of 971 transverse vibrations speedsignals of the wheel shaft.The vibration signals registered on FZG standwere put under the influence of five filters.Filters number 1 and 2 were low-pass filters withthe range of 6 and 12 kHz. Next filters enabledgetting the residual signals (filter number 3) andthe differential signals (filter number 4). The lastfilter enabled getting the signal of meshingfrequency range from 0.5-1.5 [5,6,9-11].Signal in time domain, known as residual signalwas achieved by the removal from the spectrumof bands including the rotational constituents ofthe wheel shafts and their harmonics and theconstituents of the meshing frequencies andtheir harmonics, and next by the use of theinverse Fourier transform. The differential signalwas achieved similarly to the residual signal, butin this case the removed bands around themeshing frequency and their harmonics werewider and included the sidebands connectedwith the rotational frequencies of the toothedwheels.In the next stage of tooth damage modelscreation the vibration signals achieved with theuse of five filters were put under the influence ofcontinuous wavelet transform (CWT) [1,4-6,8,13,15].162010/Fascicule 2/AprilJune /Tome III
ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGIn the next stage of tooth damage modelscreation the vibration signals achieved with theuse of five filters were put under the influence ofcontinuous wavelet transform (CWT).Wavelet analysis consists of signaldecomposition and presenting it in the form oflinear combination of basic functions, calledwavelets. The feature which distinguishes thismethod of signal analysis from other methods isthe multi-stage signal decomposition, variableresolution in time and frequency domain andpossibility to use basic functions other thanharmonic functions. Continuous wavelettransform is defined as follows:1+∞⎛ t − b ⎞CWT(a,b) = ∫ ψ⎜⎟⋅xa −∞ ⎝ a ⎠where:ψ t – the analyzing wavelet,a, b()()dt t(1)a – the scale parameter, a ∈ R , a ≠ 0 ,b – the time parameter, b ∈ R .Wavelet frequency is regulated by the parameterof scale a, whereas using parameter b one cantest the local properties of the time runs.This method, due to the possibility of adjustmentof the window width to the analysed frequencyrange enables testing the non-stationary signals.For the long-term variation runs the windowexpands in time domain, whereas with highfrequencies it narrows preserving a constantsurface area. The authors in paper [8] states thatthe proper choice of the basic wavelet and thearray of the scale value determine thecorrectness of the diagnosis process of theobject technical condition with the use ofwavelet analysis.In the preliminary test the usefulness of 83 basicwavelets was checked, which belonged to series:haar, daubechies, biorthogonal, coiflets, symlets,morlet, mexican hat, meyer, reversebiorthogonal, gaussian, complex gaussian,shannon, frequency b-spline, complex morlet,discrete approximation of meyer.In order to describe the change character of thesignal amplitude under the influence of CWT for20 scale analyses, chosen in preliminary stage, ameasure was marked. This measure describedthe change course of the amplitude CWTdistribution in time domain. In the tests theusefulness of 35 diagnostic measures commonlyused in literature was checked (variationcoefficient, peak coefficient, clearance+coefficient, shape coefficient, impulsing andasymmetry coefficient, quarter and averagedeviation; arithmetic, geometric and harmonicaverages; quartiles, non-dimensionaldiscriminants, central moments, cumulants,signal energy, efficiency values, inter-peakvalues, maximum and minimum, variance,positional variation coefficient) [5,6].As a result of tests 14525 sets of models werebuilt. Each set of models had the size of 971x20.This size reflected the number of cases (numberof measured on FZG stand vibration signals) andthe number of network inputs (number of scales,in which the measure was marked). Each optionof model sets was divided into halves and it thisway teaching and testing data were achieved.In preliminary investigations were chosenfollowing wavelets [5,6]:• Daubechies Wavelet 9 (wavelet no. = 9),• Morlet Wavelet (wavelet no. = 37),• Reverse Biorthogonal Wavelet 3.7 (waveletno. = 50),and estimators [5,6]:• impulse ratio (estimator no. = 5),• root mean square (estimator no. = 14),• value of range between maximum andminimum (estimator no. = 25).In the tests performed in order to build adiagnostic classifier the artificial neural networksof multilayer perceptron type (MLP) were used.In case of application of such neural networks,one needs to define the architecture, the methodof network teaching and the type of neuronsused in hidden layers of the network [7,12,16]. Itshould be remembered, however, that the stagesshould not be divided, because they are directlyconnected. At the same time literature shows thelack of rules connected with the choice of theparameters and points out the necessity of theirsetting with the use of experimental method –trial and-error method [7,12,16].In the conducted experiments for each set ofmodels the best option of network architecturewas chosen. By the selection of networkarchitecture the usefulness of classifiers build ofone and of two hidden layers was checked. Onthe basis of preliminary tests [5,6] it was assumedthat for each hidden layer there is a possibility ofexisting of 5, 10, 15, 20, 25 and 30 neurons.Simultaneously, an attempt was made to check,if for an analysed diagnostic task an optimumarchitecture can be defined, independently fromthe way models are built.2010/Fascicule 2/AprilJune /Tome III 17
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ACTA TECHNICA CORVINIENSIS - Bulletin of Engineering

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