An acoustic method to predict tooth surface failure of inservice gears

Umezawa, T. Ajima and H. Houjoh

A method is proposed for predicting tooth surface failure of gears in operation by automatic monitoring instead of relying on an operator's interpretation. It involves measuring frequency sideband variations around a dominant frequency component of the gear noise. Using the pitting fatigue test on three gear-pairs, the second harmonic of the meshing frequency was selected as the dominant frequency. As pitting fatigue increases, the sidebands around this frequency become stronger. Variations in the frequency spectrum are more marked than in the corresponding sound amplitude spectrum. The method is applicable to practical machinery.

Keywords: acoustic measurement, condition monitoring, gears, pitting fatigue, frequency components + sidebands

When a gearing unit begins to wear during operation, it is usually apparent by the particular noise it makes. It might be expected, then, that gear surface failures could be detected by analysing the sound emitted by the unit. But it is not easy to determine the operating condition of a machine and diagnose trouble simply by measuring its sound level with a meter because the power level is affected significantly by the surroundings. An alternative method is to analyse the frequency components to determine the quality of the sound.

Gear sounds are measured continuously when a pitting fatigue test is performed on spur gears. However, frequency analysis, which is the most usual method of examining the quality of sound, is no use for this purpose because it is difficult to detect changes in the detail of the spectrum. Consequently, we studied the frequency sideband variations about a dominant frequency component of the gear sound. The progress of pitting fatigue is indicated by a simple measure.

Experiments w i th gears

Specifications of the test gears and operating conditions for the pitting fatigue test are given in Table 1. The test gears were enclosed by 12 mm thick plastic plates and lubricated by feeding #180 turbine oil from the 'approach' side of the meshing.

After each 10 ~ revolutions of the pinion the sound was measured at a point 280 mm above the meshing point and the surface of the teeth examined. Pittings appeared on one or two pinion teeth surfaces after 4 x 106 revolutions of the pinion. The diameter of the largest pitting found was 0.5 mm and a few overlapping pittings were observed. The number of pittings increased in proportion to the number of

revolutions. When three or four pittings had appeared on each of the pinion teeth surfaces the test was complete.

Theory

In this study, frequency sidebands around a dominant frequency component of the gear sound are considered. If all tooth profiles are perfect and equal, and the gears mesh ideally, the radiated sound at fLxed speed rotation has the period of tooth meshing and line spectra given by the components of the meshing f requencyf and its harmonics (Figure 1). But, as real manufactured gears are not perfect, the radiated sound has the components of rotational frequency and its harmonics (Figure 2).

Table 1. Specifications of test gears and operating conditions

Module

Pressure angle

Number of teeth zl: Driver z2: Follower

Face width (mm)

Contact ratio

Speed (rpm)

Torque (N m)

Material Finishing

Zl z2

33 47

5 10

1.71

1400

167

4

20 °

Zl Z2 Zl Z2

32 48 27 53

5 10 5 10

1.71 1.70

1400 1270

142 1 57

$45C Hobbing JIS 4

0308-9126/83/040201-04 $03.00 © Butterworth & Co (Publishers) Ltd.

NDT INTERNATIONAL. VOL 16. NO 4. AUGUST 1983 201

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O3

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Frequency

Fig. 1 Power spectrum of an ideal gear sound (/n is the natural frequency for torsional vibration of gears; f is the tooth meshing frequency)

0

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o o3 b

27' I I I

f 2 f I I J I I

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l I I I 0 I 2 3 4 5

Frequency (kHz)

Sound power spectrum as a function of the number of load cycles: a - O; b - 5 x 105 load cycles; c - 14 x 105 load cycles. Gear ratio, zl: z 2 = 32:48

Frequency analysis The method of analysis used was essentially the same as that proposed in a previous reportM except for two features.

First, the signal around the dominant frequency component was extracted from the random noise with a bandpass filter (-3 dB, bandwidth + 50 Hz, 24 dB/ oct) and fed into a frequency-to-voltage (F/V) converter. The second harmonic (2f) was regarded as the dominant frequency (Figure 1).

Second, the AC signal level of the F/V converter output is measured with an AC RMS voltmeter (to be called the 'F/V output'). Operation of the F/V converter is illus- trated in Figure 3.

Simulation To simulate the gear sound the model we used was a sine wave modulated by white noise (Figure 4). The frequency of the carrier wave was 2f. An increase in the modulation input level, or white-noise level, corresponds to an increase in pitting fatigue (Figure 5).

Experimental results Both the actual gear sound and the simulated gear sound were analysed with the arrangement shown in Figure 6. The variation of the F/V output with the number of load cycles, ie increasing pitting fatigue, is shown in Figure 7. The F/V output increases almost monotonically for the three pairs of gears tested.

Figure 8 shows the variations in the spectra of the F/V converter output of the gear sound as a function of the number of load cycles, and the variations in the simulated signals as a function of the modulating signal level. Both sets of curves follow the same pattern, although the simulated signals are smoother than the actual signals. This difference is explained by

Input

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o ¢

I/

Time

q - ~ - \ - A - - ~ -~. Zero level

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Operation of the frequency-to-voltage converter

We considered the phases of the f -components and the harmonic components to be shifted by the existence of gear errors, ie these frequencies are modulated by gear errors. As a gear surface fails, the tooth profiles and spring constant (we regard the teeth as springs) change locally and more frequently. As the signal level gradually increases, the f -components and harmonics are modulated by a random signal.

(FM receiver) vco input

J Whffe-noise J _ ~ ,0u tpu , generator Oscil lator j =

Fig. 4 Block diagram of the gear-sound simulator

202 NDT INTERNATIONAL . AUGUST 1983

~ c

,>, . -IC ~x u ' -

a

Pitt ing

o p i t t ing

~ m

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I

b Fig. 5

/ • Modulating

/ / ~ x \ ~ ignal(vrm')

0 I 2 3 4 5

Frequency (kHz)

Power spectrum of the frequency-to-voltage converter input: a -- experiment; b--simulation

Oata recorder

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J o.mete, I J Frequency-to-

voltage converter J j - [ ~C

Fig. 6 Block diagram of the analysis procedure

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>= § 0.4

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0.2

=,

A

O O 0

I I O 5 IO

Number ~ load cycles (x IO s)

Fig. 7 F req~nc~t~v~ge converter output for large input signals. Gear ratios: A -z~: z 2 = 33:47; O -z~: z 2 = 32:48; [] - z l : z 2 = 27:53

our assumption that the frequency fluctuation of the gear sound is completely random.

Special behaviour of the frequency-to- voltage converter The F/V converter used in this study produced large negative pulses when the input signal was small. It was

insensitive to the input signal crossing the zero level (Figure 3). When the frequency fluctuation of the gear sound became strong and its frequency spectrum wider than the bandwidth of the bandpass filter, input to the F/V converter was small, and a large negative pulse appeared during the period after the first zero- level crossing.

The gear sound, set intentionally low to give a small signal input to the F/V converter was analysed with this system. Figure 9 shows the F/V output and Figure 10 shows the spectra. The F/V output is increased markedly by the large negative pulses. Both the F/V output and the spectra exhibit more marked fluctuations with the number of load cycles than the fluctuations obtained with large input (Figures 7 and

o~- ~ oL- vu -x~,~.

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a i

Number of 2 f load cycles (x IO s)

I I

"O

I 0 I

b

~ 0.4V

sional (Vrm) Y V 2f /

I I I 2 3 4 5

Frequency (kHz)

Fig. 8 Frequency-to-voltage output spectrum for lame input signals: a - experiment; b - simulation. Gear ratio, zl: z 2 == 33:47

0.8

0.6

t

® 0.4

, t -

' 0.2 g- c

A

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Q A O O

Fig. 9 ratios:A --zl: z 2 =, 33:47; O --zl: z 2 = 32:48; r-] -Z l : z 2 ,= 27:53

I I 5 IO 15

Number of load cycles (x IO s)

Frequenc~to-v~=ge converter output for small input signals. Gear

NDT INTERNATIONAL. AUGUST 1983 203

8). Figure 10 shows that the valleys at 2f and the harmonics become shallower as the number of load cycles increases. This is due to the regular occurrence of the large negative pulses and the increased fluctuation of the pulse width with the number of load cycles.

For the simulation, changes in the F/V output for several F/V input levels (carrier levels) are shown in Figure 11. When the carrier level is 0.12 VRMS, lbr example, the F/V output increases uniformly along OAB with increasing carrier level. The large negative pulses become apparent at B and the F/V output becomes steeper along BB' . With small F/V input, the amplitude variations have a greater influence on the F/V output than with large input (OC). The effects of changing the width of the bandpass filter are almost identical to the effects of changing the F/V input level (Figure 12). However, the bandwidth must be chosen such that only the dominant frequency component and the nearby components are extracted.

There are few differences between the correlation coefficients for the number of load cycles and the F/V output for large and small inputs (Table 2). The analysis using large input, then, is recommended for monitoring the progress of pitting fatigue because of the stability of the F/V output with regard to variations in the gear sound level.

Conc lus ion To diagnose the extent of pitting fatigue without relying on human judgement, a frequency fluctuation analysing method has been proposed and tested. A dominant frequency and the associated frequency

IO

c ~ ~I.i-

a

2f Number of 6 load cycles (x I05)

IO

2f

o"~ -6_e I > 4 - o o. 4 - 4 - " ~ 0

u. oo voltage output ~" (%m~)

i I 0 I 2 3 4 5

b Frequency (kHz) Fig. 10 Frequency-to-voltage output spectrum for small input signals: a - experiment; b - simulation. Gear ratio, zl: Z 2 = 33:47

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U(~ 0 5 I 0 115 . . . . 210

Modulating signal level (Vrms)

Fig. 11 Simulation frequency-to-voltage converter output against modulating signal level as a function of carrier level. Bandwidth is 4- 50 Hz

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Modulating signal l eve l ( V r r a l )

Fig. 12 Simulation frequency-to-voltage converter output against modulating signal level as a function of the bandpass filter. Carrier level is 0.11 VRM S

T a b l e 2 . C o r r e l a t i o n c o e f f i c i e n t s

zl 33 32 27 Gear pairs

z 2 47 48 53

Small input level 0.87 0.82 0.94

Large input level 0 .79 0.84 0.95

components of the gear sound, which are obtained through a bandpass filter, are analysed using an F/V converter. The second harmonic of meshing frequency was selected as the dominant frequency. The lbllowing results were obtained:

(1) As pitting fatigue increased, the fluctuation became stronger and the F/V output increased. This increase corelates with the number of load cycles.

(2) When the gear-sound signals are relatively small the action of the F/V converter is liable to be unstable to variations in the signal level and produces large negative pulses. However, in the output power spectrum, remarkably, the depths of the valleys at the dominant frequency and its harmonics decreased with an increase in the number of load cycles.

Reference I Umezawa, K. et ai, "On a prognosis of gear surface failure

using sound of gears', Bulletin of the Jpn Soc of Mech Eng. 25 No 203 (1982) pp 834-841

Authors Professor Umezawa, Mr Ajima and Mr Houjoh are at the Research Laboratory of Precision Machinery and Electronics, Tokyo Institute of Technology, Nagatsuta. Midori-ku, Yokohama 227, Japan.

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