On the frequency content of the surface vibration of a diesel engine

Journal of Sound and Vibration ( 1977) 52(3), 365-386

ON

THE

FREQUENCY VIBRATION

CONTENT OF

OF THE

SURFACE

A DIESEL ENGINE

V. MARPLES Department of’EttgineerinR, Utticwrsityof Warwick. Cooetttty. England (Recekd

12 July 1976, and itz twised jbrm 30 January 1977)

The results of an experimental investigation into the narrow band frequency content of the surface vibration of a particular four cylinder, water-cooled, indirect injection diesel engine are described. The long term objective. of which the work reported here is a part, is the reduction of noise emission at source. Noise is radiated from the engine as a result of surface vibration. The characteristics of surface vibration are described and an explanation is given of why the discrete frequency response of the engine has hitherto appeared to be broad band in nature. The relationship of the pure tone response to the combustion pressure spectrum is also described. The vibration of the engine side wall has the greatest amplitude in the frequency band 2.9-3.8 kHz, irrespective of engine speed and load, which could be a result of piston slap. The vibration of the crankcase skirt. in contrast, is more or less uniform throughout the frequency range O-5 kHz. reflecting the great difficulty in achieving a significant reduction in the overall level at this location. The low frequency pressure spectrum is shown to have roughly a 47 dB/decade decline in amplitude with frequency below 800 Hz, in comparison with an oft-quoted figure of 30 dB!decade. Significant differences between no load and half load pressure spectra are shown to exist.

1. INTRODUCTION

Diesel engines and diesel engined vehicles are renowned for their relatively high noise levels. It is reasonably well established [I] that in a diesel power plant, the engine itself is the only remaining source for which a satisfactory technique for reduction at source has not yet been discovered and developed. In contrast to the petrol engine, the noise output of a diesel engine has been shown [2] to be virtually independent of load on the engine and to increase with engine speed at a rate of 30 dB(A)/decade. This figure represents to some extent an extrapolation since the normal working speed range of many engines is little over one octave and that of relatively few exceeds 21_octaves. The “A” weighting scale is used because this, as compared to an unweighted sound pressure level, reflects more nearly the human subjective response and because, by attenuating the prominent, low frequency harmonics of engine rotational speed, some inconsistent variation in sound pressure level with speed is eliminated [3]. The 30 dB(A)/decade of engine speed is supposed to be associated with, and a result of, a corresponding 30 dB(A)/decade fall with frequency in the amplitudes of the harmonics of the cylinder pressure. Such a belief is based on the assumption that the noise level is more or less proportional to the pressure, being the major source of excitation in the engine and that, as engine speed increases, the pressure spectrum simply translates to higher frequencies. On the subject of load dependency, while most authors agree that diesel engine noise is largely load independent, Kaye and Ungar [4] report an 8 dB(A) increase in noise from no load to full load at an engine speed of 1500 rev/min. In trying to understand the origins and causes of engine noise and its characteristics it appears to be helpful to look at the problem under three headings : the effect of the combustion 365

366

V. MARPLES

process, the influence of mechanical impacts which can occur because of the need for working clearances (e.g., piston slap) and the nature of the dynamic response of the engine structure. Priede [5] studied the cylinder pressure characteristics closely. He found very large stroketo-stroke variations (of the order of 30 dB) and later, with Grover and Lalor [6] showed that noise impulses due to firing of different cylinders were also widely different. In determining the pressure spectra the low frequency region was dominated by 210 dB (re 2 x 10m5 N/m’) integral harmonics of the firing frequency but, as the harmonics became more closely packed in each 3 octave band it became impossible to separate them and the spectral level began to fall, acquiring a constant slope of -30 dB/decade by a frequency of about 100 Hz. Since the harmonic frequencies are proportional to engine speed, and the whole of the pressure spectrum levels, being dictated by the pressure-time diagram which is considered to be independent of speed, are also speed independent, the spectrum is assumed to shift bodily towards higher frequencies as the engine speed increases. The spectral components above 100 Hz thereby increase at the rate of 30 dB/speed decade and it is this effect which is considered to be the determining factor in giving engine noise a 30 dB(A)/decade dependency on engine speed. It was shown that the intensity of the low frequency harmonics is dependent on peak cylinder pressure and on the relative width of the pressure-time diagram while the mid-frequency components are related to the steepness of the diagram : that is, to the severity of the almost instantaneous increase of pressure. With injection advance, the ignition is delayed and both the peak pressure and the rate of pressure rise are much higher. Advances of between 10” and 30’ give rise to increases of noise of 5 dB. Both gradual injection of the fuel and retarding the injection are measures which help to produce a smooth pressure increase and so keep the noise to a minimum. But retardation can have significant disadvantages as far as power output, fuel economy and exhaust emission are concerned. Automatic injection retard with load shedding is a feature of the distributor injection pump and results in as much as 10 dB difference in noise level between full and no load conditions. a difference not found with fixed injection timing. This variation in behaviour could well account for differences of opinion about the load-dependency of diesel engine noise. The fall off at mid-frequencies of the cylinder pressure spectrum is arrested by the development of a peak in the spectral envelope at either 2-3 kHz or at 5-8 kHz by standing wave effects in the combustion space. The higher frequency is associated with the smaller overall distances in the direct injection combustion space as compared with the indirect injection space. If it is accepted that cylinder pressure spectral level is directly related to noise then there are advantages in delaying the spectral peak to a higher frequency (corresponding to a region in which the ear is less sensitive) whereby the direct injection engine is considered to be the more desirable. Tiede and Kabele [7] found that the location and size of the 5-8 kHz peak was related to pressure fluctuations occurring in the vicinity of peak cylinder pressure but with considerable cycle-to-cycle variation. But they concluded that the effect was not significant as far as the overall engine noise is concerned. And yet a reduction of 15 dB in the size of the spectral peak, by changing from a dished combustion chamber to a toroidal chamber brought with it a reduction of 3 dB(A) in engine noise. In broad terms there is a clear relationship of engine noise to both speed and load but these relationships are the averaged responses of a number of engines and therefore should not be applied to individual engines without further specific evidence. Although a number of guide lines relating to combustion space construction and control of the combustion process to minimize noise have become available it is unlikely that more than a few dB(A) can be trimmed from the overall noise levels by these measures. Piston slap is the type of mechanical impact, possibly influencing the noise output of an engine, which has been the subject of most investigation. This sudden movement of the piston across the clearance space usually takes place four times per cycle, close to, but not necessarily

SURFACE

VIBRATION

OF A DIESEL ENGINE

367

at the top and bottom dead centre positions. The resulting impact force on the cylinder liners is thought to be transmitted to the remainder of the engine structure, exciting it to vibration. The external surfaces of the engine, being coupled to the surrounding air, thereby emanate noise. Griffiths and Skorecki [8], in attempting to determine the extent of the piston slap effect, concluded that it predominated in the frequency range 2-4 kHz while the experimental results of Fielding and Skorecki [9] indicate that the effects extend to 10 kHz. Ungar and Ross [IO] developed a theoretical description of piston slap which not only enabled the crank angles at which piston slap occurs to be determined but also endeavoured to predict the acoustic energy emission starting from the assumption that all the lateral kinetic energy of the piston was imparted to the block as vibratory energy. But so far it has not been possible to establish a correlation between impact velocity and surface vibration, much less one between piston slap and noise emission. Concerning the responsiveness of the engine structure, Priede, Grover and Lalor [6] seemed to conclude, along with several other investigators (e.g., Russell [1 1]and Thien [I?]) that reduction of the ability of the structure to respond to excitation is the only possible way of obtaining any significant reduction at source. Priede, Austen and Grover [13], by fitting 19G aluminium covers with + inch of sprayed damping material and $ inch of 5 lb/ftl fibreglass to the inside, the whole being supported by bonded rubber mounts, were able to achieve 10 dB loss through the panels and thus, by selective removal, were able to show that the worst sources of noise were the crank case walls and the timing drive cover. These, taken together, accounted for most of the noise in the l--3 kHz region. The oil pan was prominent as a noise source around 1 kHz and the bell housing in the range 2-4 kHz. The cylinder head was found to contribute very little. Surprisingly the front pulley was found to be a prominent source being responsible for up to 15 dB in the range 1-2 kHz. It was discovered later that crankshaft vibration due to periodic loading from the combustion gave rise to an amplitude of vibration of the pulley normal to its plane of something of the order of 0.003 inch. Various techniques have been developed for reducing the emission from these sources. They include a combination of vibration isolation and damping techniques and can result. when all areas are treated, in a reduction of the engine noise of about 5 dB(A). To determine more about ways in which the main structure of the engine could be altered advantageously, many investigations of vibration characteristics have been undertaken. There is always the tacit assumption that noise and vibration go hand in hand. Although we imagine this to be largely true, and indeed there is some evidence to support it, it cannot yet be said that there is any correspondence in detail and that a reduction of surface vibration will result in a pro rafa reduction of engine noise. The best that we can say is that, as reported by Chan and Anderton [14], overall similarities do exist between near field, 4 octave. “A” weighted sound pressure level and either mean square surface velocity or acceleration (depending on frequency range). In order to proceed beyond such generalizations, it is necessary to enter the realm of vibration testing and narrow band analysis. Such tests show large numbers of modes in the most important frequency regions. of the order of thirty per thousand Hertz, and yet Waters, Lalor and Priede [15] assert that the noise is determined principally by the horizontal bending mode of vibration and Jenkins, Lalor and Grover [I61 that there are only two major noise-radiating modes of an in-line engine: horizontal bending and a conical mode. The vibration technique, involving the measurement of vibration levels in + octave bands is also responsible for the conclusion that engine block vibration is dominated by panel modes with nodes at the heavier sections in the vicinity of the main bearing supports. Frequencies of panel modes have been calculated on the assumption that they exist and occur quite densely in the vicinity of 2.5 kHz. It is therefore concluded that panel vibration is a

368

V. MARPLES

significant contributor to overall engine noise, which must be suppressed by structural change. Stiffening of the external walls has produced a reduction in the relative vibration level between the panel centre and edge of from 10 to 3 dB [12]. In an attempt to reduce the modal density of an engine structure Priede and his co-workers were led to design a number of research engines. The first one consisted of a main structural frame with underslung crankshaft and crankcase of damped panels bridging the structural members. Covers and crankshaft pulley were also damped and isolated. The projected 25 dB improvement turned out to be 10-l 1 dB. The failure to approach the projected figure more closely is presumably an indication that the basic assumption, that the majority of noise is emitted by panel vibration, is incorrect. This engine was found to have greater 3 octave levels of vibration than the normal engine at the sump face and so a modified version was produced featuring a skirted crankcase and tunnelled crankshaft location, the object being to give greater structural stiffness and greater support to the main bearings and reduce the degree of excitation at the sump flange. The overall noise level was reduced by a further 2 dB as compared with the previous engine. This is not a clear indication of a desirable design trend because tests on existing production blocks show quite clearly that whereas engine side wall vibration is very similar for underslung crankshaft and skirted crankcase engines above crankshaft level, the vibration at the sump flange of the skirted crankcase engine is much greater, particularly in the vicinity of 1 kHz. This has resulted in the suggestion that the skirt should be removed and a deeper oil pan used, connected directly to the lower deck of the block. The whole of this problem stems from the very large, rapidly varying forces which are applied to the crankshaft, and via the main bearings to the lower part of the block. The conventional engine structure is too flexible in torsion because the oil pan, even when cast, is not sufficiently rigid to give adequate support. Some “feel” for the relative orders of magnitude of the required rigidity can be obtained by realizing that, other things being equal, a wet liner engine exhibits more side wall vibration than a dry liner engine. It was therefore proposed by Thien [ 121 to use a stiffening plate at the oil pan flange and by Priede, Grover and Lalor [6] to connect the main bearings together to give them mutual support by using a bearing cap beam. The latter was so effective in reducing wall vibration that a wet liner engine with the beam had less vibration than a dry liner engine. But no appreciable reduction in noise resulted [16]. A subsequent modification to a four cylinder, in-line engine abolished the conventional crankcase walls. The crankshaft was supported by an integral structural framework to which was attached damped panels for the crankcase [6]. The noise generated by this engine had octave band levels 8-19 dB lower than a similar conventional engine at frequencies above 500 Hz. A second approach results in casting an engine block in magnesium. While never considered to have any commercial viability it was aimed at proving a point. If the noise is in some way proportional to vibration then, if the natural frequencies of a structure can be shifted beyond the range of the frequencies of the existing forces, one can expect a considerable reduction in the noise level. The purpose of the magnesium engine was to increase the structural natural frequencies by at least an order of magnitude, and was cast with much thicker walls than the conventional engine block in order to keep the overall weight the same. The natural frequencies of the magnesium block should then be nearly four times greater than those of the cast iron block and therefore, if apro rata relationship holds, the noise could be expected to be reduced by about 25 dB. Noise reductions of only the same order as with the other research engines were obtained. At least a part of the failure must be attributed to the concept. For a structure with high modal density a shift of frequency of four times is not sufficient to effect a large reduction in response. On a basis of all modes being equally excited

SURFACE VIBRATION OF A DIESEL ENGINE

369

a reduction of only 6 dB would occur. But the six-fold increase in thickness goes beyond the region of simple proportionality and additional modes can be expected, tending to increase the modal density back towards its original value. Thus, while it has been shown that vibration of the engine structure, particularly the side walls and crankcase, contributes significantly to the noise level of diesel engines, all the techniques so far attempted to suppress this vibration in conventional structures have failed. In general the attempts have been made on the basis of some hypothesis relating to the nature of the vibration response or as a result of considering the structure to be analogous to a simple vibrating system. There seems to be no understanding in depth of the characteristic of the surface vibration or of the near field noise.

0

25

50

100 f

Figure

1. l/3 Octave spectrum

200

-Octave

500

‘k

centrefreouency

of diesel engine noise. --,

Zk

Ok

Hk

IGk

(Hz)

Unweighted;

----,

“A” weighted. Engine

speed = 2000 rev/min.

It would appear therefore that there is a need to be able to explain why the f octave noise spectra have their characteristic form (see Figure 1). The unweighted spectrum is dominated by a component at forcing frequency and by its harmonics. When “A” weighted this dominance is replaced by that of the broad, featureless spectrum between about 500 Hz and 3 kHz. Since the 3 octave bands are so wide, relatively speaking, at these frequencies it is impossible to say what characteristics of the engine play a part in producing this broad spectrum. This can be discovered only by the use of narrow band analysis, often a timeconsuming business. And to understand the role of surface vibration in generating noise, analyses must be performed of not only the far field noise but also the near field noise and of the engine vibration. This report deals with the results of some analyses of the latter. 2. OBJECTIVES

The purpose of the investigation was to look, in detail, at the relationship of the engine surface vibration to exciting sources within the engine. Whereas the purpose was to draw conclusions relating to the noise output of a diesel engine, it was recognized at the start that the relationship between mechanical vibration of a surface and the noise emitted by the surface is a very complex one, the details of which are only incompletely understood. For this reason it was desirable, for the current investigation, to eliminate the structure-borne to air-borne transition by measuring only surface vibration and not air-borne noise. Furthermore, the existing environment of the engine test cell was quite unsuited to obtaining useful noise measurements. However, it is well known that both the surface vibration and the noise, when subject to constant percentage bandwidth analysis, exhibit harmonics offiring frequency

370

V. MARPLES

up to about 600 Hz, the fourth and eighth harmonics being by far the most prominent, and from about 500 Hz a high, broad band response, falling off from about 4000 Hz. Although the levels of the low frequency harmonics often exceed that of the broad band region, if the levels are “A” weighted, which is necessary to arrive at a representation of the probable subjective response to the noise, the low frequency harmonics then become less significant. The intention therefore was to study the composition of the broad band response in the vicinity of 1 kHz.

3. INSTRUMENTATION The instrumentation used for the investigation is shown in schematic form in Figure 2. The pressure transducer was mounted in no. 2 cylinder and the accelerometers used for

counter

i~llOl

losrnpe

rroce IOSCII

Figure 2. Schematic of instrumentation.

measuring the vibration were attached to various points on the engine surface either via the standard Briiel and Kjaer magnet or via mounting studs bonded to the surface. In either case the accelerometer was screwed on only sufficiently tightly to hold it in place and with an interface of grease, thereby assuring adequate response to 5 kHz [I 71. A tape recorder speed of 15 in/s was used throughout in order to achieve a bandwidth to 5 kHz while conserving tape as far as possible. All signals were analysed in overlapping bands of 500 Hz from 50 Hz to 5 kHz. The harmonic levels vary, sometimes appreciably, with time and so do the harmonic frequencies because the rotational speed of the engine fluctuates with time. These variations result in averaged spectra losing discriminability. The real time analyser presents 250 data points in its display. Where the spectral band is 500 Hz wide the discrimination is therefore 2 Hz. This is not the equivalent filter bandwidth however. That bandwidth can be determined by analysing a pure tone fed to the instrument. Doing so reveals that the 3 dB bandwidth is 5 Hz while at 30 dB down the bandwidth is 18 HZ. The filter characteristic is very important for two reasons. The first is that no spectrum generated by the analyser will display a narrower peak than that of the characteristic and that therefore, with peaks such as this can be associated the presence of a pure tone in the incoming signal. The second reason is that where tones occur in the incoming complex signal which are separated by less than about 8 Hz, and unless the difference in their levels is less than about 10 dB, it is probable that the presence of the lower intensity component will not be detectable with any degree of certainty.

SURFACE

VIBRATION

OF A DIESEL

371

t:NCilhl-

If the spectral band of the display is anything other than 500 Hz the discriminability wili be one two hundred and fiftieth of the spectral bandwidth and the filter 3 dB bandwidth will be 1 l’o of the spectral bandwidth. Similar limits apply to the detection of close frequent) components as those described for the case of a 500 Hz spectral band.

3. ANALYSER

4.1.

FREQWNCY

PERFORMANCE

WITH

ENGINE

VIBRATION

SIGNALS

CONSIDERATIONS

Due to normal fluctuation of engine speed under nominally constant conditions. signals representing vibration or noise of a reciprocating internal combustion engine present some difficulties in interpretation when subject to very narrow band analysis. The vibration of an engine structure in service is comprised ofharmonic response at frequencies integrally related to the engine combustion cycle frequency (which is equivalent to half engine speed for an engine employing a four stroke cycle) and of inharmonic. constant frequency response due to excitation of the structure at its natural frequencies. In theory the former can be investigated most easily by slaving the filter centre frequency to the engine rotational speed. a spectrum in terms of harmonic order rather than frequency resulting, while the latter is most easily investigated with filter centre frequency independent of engine speed. In practice such an idealized theoretical approach is found to be inadequate. Apart from the difficulties of sensing the rotational speed sufficiently rapidly and sufficiently accurately for the purpose the harmonic and inharmonic components of the overall response are not just two separate part\ of the whole. They are intimately related because it is often the harmonic excitation which initiates the inharmonic response, which then decays as the excitation frequency changes only to build up again as the excitation frequency drifss back toward the (inharmonic) resonant frequency of the structure. Thus the vibration is more transient in nature than steady state, being comprised of a confusing array of time-dependent harmonic and inharmonic responses. This is the type of signal with which the real time, or any other, type of analyser has to deal. Results can be averaged over extended periods of time but in the presence of frequency cycling and transient build-up and decay. excessive averaging merely gives rise to loss of discrimination. On the other hand a lower limit is set to the record length to be averaged by the sampling rate of the instrument (intimately associated with the highest frequency in the desired spectrum) and by the data storage capacity of the instrument. For the instrument used for the investigation renorted here, when a 500 Hz band spectrum is required the minimum record length which must be taken into store is 3 second real time, equivalent to between 8 and 30 engine revolutions at 1000-3600 rev/min, respectively. Fluctuations within this record length are therefore not detectable and, in fact, themselves give rise to loss of frequency accuracy and detectability. The only way to reduce the extent of this influence is to reduce the real time equivalent of the store size by increasing the sampling rate. This increases the upper frequency of the spectral band and also the bandwidth of the detected spectrum which also brings an increase in the equivalent filter bandwidth and hence a loss of discrimination. The particular analysis bandwidth selected will therefore always have a lower discrimination than ideal and will be a compromise between narrow filter bandwidth on the one hand and near instantaneous analysis on the other. In order to detect any periodic fluctuation in vibration due to cyclic engine speed variation, idealiy the real time equivalent of the store capacity should be not greater than about 3 milliseconds (equivalent to { of the cycle time at the maximum engine speed of 4750 rev/min). But also, since the harmonics of combustion cycle frequency at 1000 rev/min are only 8 Hz apart, the filter 3 dB bandwidth should be not greater than about 5 Hz. With the instrument

372

V. MARPLES

available the former requirement is unattainable, the closest approach being 12.5 milliseconds with which is associated a spectrum bandwidth of O-20 kHz and a filter 3 dB bandwidth of 200 Hz! This bandwidth is clearly unacceptable for the detection of multiple components which might have a separation as low as 10 Hz and where the intention is to look at individual sources and modes. So it is better to satisfy the filter bandwidth criterion, being alive to the possibility of error and confusion due to the effects of engine speed fluctuation. 4.2. OVERALL CHARACTERISTICS In order to understand the discussion in subsequent sections, the significance of the results presented and the reasoning behind the course of the investigation, it is necessary to have an overall picture of the more general characteristics of the vibration response of the engine surface. Figure 3 shows a O-5 kHz spectrum (50 Hz filter bandwidth) of the surface vibration

Frequency

(Hz i

Figure 3. O-5 kHz acceleration spectrum at 1870 rev/min, no load, averaged over 16 seconds.

at a particular position on the side wall with the engine running at no load at 1870 rev/min. Although the associated 3 dB bandwidth of 50 Hz is too large to permit detection of individual harmonics and modes it does reveal the broader features of the overall spectrum and can direct attention to the major frequencies of significance. The spectrum of Figure 3 is plotted on a linear frequency scale and not as a function of logarithm of frequency as is so often the case. The standard 3 octave band limits are drawn on the diagram to aid comparison with the logarithmically related 3 octave spectra. The extent of the increase of bandwidth from low to high frequency is clear. It is evident that, even with the + octave bands centred on 2.5 kHz and 3.16 kHz broken down into a succession of 50 Hz bands, the amplitude levels are still greater in this vicinity than elsewhere in the spectrum. The most prominent components appear to lie between 2500 and 3160 Hz and this is even in the absence of “A” weighting to reduce the intensity of the low frequency components which, in other circumstances, often predominate. Other points of interest revealed by the spectrum of Figure 3 are the presence of surprisingly high levels in the 3 octave band centred at 800 Hz, the maximum at the centre of the 1600 Hz band and the singular peak at 3420 Hz. It should be noted that the peak in the 125 Hz band is probably the actual level of the eighth harmonic of combustion cycle frequency (the second harmonic of firing frequency for a four cylinder engine). The highest peak in the 800 Hz, f octave band is indicative of the 56th harmonic of cycle frequency while that at 3420 Hz is very close to the 219th but could, in fact, be representative of a fixed frequency response of the structure rather than of a harmonically related response. It is worth noting that, without narrow band analysis, the spectral peaks at 3420 and 4250 Hz would go undetected and that, when the engine speed is increased so that the levels around the 56th harmonic are distributed

SURFACE VIBRATION OF A DIESEL ENGINE

373

between the adjacent 800 and 1000 Hz f octave bands, the nature of the associated peak would be lost. The main conclusion to come from this preliminary result is that, if there were a near I : I relationship between engine wall vibration and emanated noise, the components in the region 2.5 kHz-3.1 kHz would be almost totally responsible for the overall level. Even without the I : 1 relationship the same frequency range is still very important. 4.3. RELIABILITY OF FREQUENCY DETECTION Figure 4 shows the results of two analyses in the band 2-2.5 kHz with 5 Hz filter bandwidth. The analyses were made some minutes apart with the engine running under nominally constant conditions at no load and at 2330 rev/min. A detailed comparison of the curves shows that virtually all the same discrete frequency components are present in both spectra,

Figure 4. 2-2.5 kHz acceleration spectra at 2330 rev/min, no load; spectra relate to operation of engine under nominally constant conditions at instants 2 minutes apart.

corresponding frequency values differing by not more than 3 Hz, but corresponding amplitudes bearing no apparent relationship. In some places the evidence for the presence of a particular component is limited (e.g., at 2148 Hz in the lower curve of Figure 4) and sometimes the presence has to be inferred largely by compariosn (e.g., in the lower curve of Figure 4 at 2369 Hz by comparing with the upper curve where the presence is obvious). So it seems that the engine speed fluctuations which occur from one half-second storage period of the analyser to another, several periods later, is sufficient to account for an uncertainty in the frequency values of the peaks of the response of only about i 2 Hz in the vicinity of 2.2 kHz which, when extrapolated, can be expected to be of the order of? 4 Hz at 5 kHz. (Since the analyser detects spectrum level at only 250 points within any 500 Hz band there is also a rt 1 Hz uncertainty in the determination of any particular frequency value.) But the engine speed fluctuation does give rise to considerable uncertainty in the amplitude levels. At low frequencies, particularly for every fourth harmonic of combustion cycle frequency, (which are the harmonics of firing frequency) the uncertainty in both the harmonic frequency, and, to a lesser extent, the amplitude is relatively small. But for other order harmonics there is much less consistency (I Ti and 7 dB respectively), and at higher frequencies apparently none at all. At least some of this is due to fluctuations in the frequencies of the exciting forces (harmonic components of the summated cylinder pressures) giving rise to transient vibration at sum and difference frequencies of the excitation and structural resonant frequencies. To obtain useful frequency information the signals must be subject to a near instantaneous spectral analysis followed by the application of a systematic technique for the identification of harmonically related components.

374 4.4.

V. MARPLES

RELIABILITY

OF AMPLITUDE

DATA

By recording the vibration signals and replaying them an attempt was made to make repeated analyses at more or less the same position in time by using a manual triggering procedure. Although not adequate to ensure repeated analysis of exactly the same _5second of recorded data it was possible to perform analyses of data batches within a few seconds of each other as opposed to the analyses which yielded the 1”;; and 7 dB figures quoted above which the spread over a period of about 10 minutes. Even so, there was insufficient for useful comparative data to be extracted and tabulated. Number of spectra averaged

Frequency

(kHz)

Figure 5. Display of O--.5kHz acceleration spectra relating to operation at 2000 rev/min, no load, showing effect of averaging different numbers of successive spectra (50 Hz filter bandwidth).

To do this therefore, it is necessary to average over a period of time by taking a simple average of the several spectra relating to contiguous half-second periods. The results of averaging over 4, 32 and 256 successive 5 kHz band spectra (22, 24, 28) are shown in Figure 5 and are compared with a single, unaveraged spectrum from the same period of time. The immediate loss of discrimination upon starting to average is evident and the curves indicate that averaging more than four spectra will probably give so much “smoothing” that it will then not be possible to draw conclusions relating to individual modes and harmonics. Now the spectral analyses are really required in 500 Hz bands to enable discrete frequency components to be detected, which is an order of magnitude increase in discrimination as compared with the 5 kHz band of Figure 5. But, the sampling rate being an order of magnitude slower for a 500 Hz band than for a 5 kHz band, a greater signal length is already employed in producing a single 500 Hz spectrum. These two effects can be expected to cancel out, more or less, and again averaging over four spectra gives some measure of amplitude reliability without too much loss of discrimination. It can be seen that averaging of spectra of signals containing components where frequencies are subject to small periodic variations is tantamount to employing a filter with reduced selectivity. The 3 dB bandwidths of the prominent peaks of the unaveraged spectrum is 5 Hz while that of the peaks of the spectrum resulting from averaging 32 spectra is St Hz.

SURFACE VIBRATION OF A I)IFSEL ENCXNF

5. DESCRIPTION

375

OF TESTS

tests the transducer signals were recorded on For all except a small number of preliminary magnetic tape for subsequent analysis. In the case of pressure signals, the level of the spectrum peaks, falling off by some 40 dB before 500 Hz, soon traverses the whole 48 dB of the tape recorder dynamic range, thus rendering the higher frequency components undetectable without high pass filtering. The batches of tests conducted were as follows. (i) The engine was operated under nominally constant conditions at nominal speeds of 1500, 1800,2000,2300,2800 and 3 100 rev/min at no load, cylinder pressure and acceleration at one point of the engine side wall being recorded so that preliminary ideas about spectral content could be formulated. The speeds were chosen to encompass the most frequently used part ofthe speed range and in a manner to avoid a simple relation between the harmonic components of the several different speeds. (ii) The engine was operated under constant conditions at nominal speeds of 1500,2300,3 100 rev/min at half load, cylinder pressure and acceleration at the same point on the engine side wall as in (i) above being recorded. This was to determine if the fact that the engine was working under load produced a significant and repeatable effect on the spectrum. (Several investigators have concluded that load is not an important factor in affecting the noise output of a diesel engine, a conclusion based largely on measurements of “A” weighted sound pressure level.) (iii) The engine was operated under constant conditions at nominal speeds of 1500,2300,3 100 rev/min at no load, recordings of the engine surface vibration being made at several locations. 6. DISCUSSION

OF RESULTS

6.1. PRE.SSURE SIGNALS It is quite clear from the O--500 Hz spectra of the unfiltered pressure signal for no load on the engine that, at low frequencies, all harmonics of the combustion cycle frequency are present: in fact this is true up to at least the 35th. Starting from a maximum spectra1 level of about 400 lb/in’ for the first and second orders of cycle frequency, the harmonic amplitude soon falls rapidly and does so at a rate of about 2 dB per harmonic component up to about the 18th harmonic. This uniform rate of decrease cannot be associated with a uniform rate per multiple of engine harmonic frequency which has sometimes been used as a basis for explaining the 30 dB(A)/decade rise in noise with engine speed. For this explanation to be valid not only would the pressure spectrum need to fall at 30 dB/frequency decade but increasing engine speed would have to result in a simple translation of the pressure spectrum along the frequency axis. This does not happen at low frequencies. though it may at higher frequencies. The hlope of the spectrum alters with engine speed at no load is shown in Figure 6, from which it can be seen that the harmonic amplitudes fall consistently by about 1.75 dB per harmonic at engine speeds above 2000 revymin but below that speed the fall-off increases. reaching about 2t_ dB per harmonic at 1500 rev/min. At these lovv frequencies the contribution of the corresponding noise to the “A” weighted sound pressure level is small. Beyond the 18th harmonic the amplitude levels and the relationship between consecutive levels seems to be less predictable. Up to about the twelfth harmonic of cycle frequency the harmonic amplitude appears to be independent of time for given nominal load and speed settings. However, beyond the twelfth harmonic the amplitudes vary considerably with time, the variation ranging from 3 dB to about 9 dB in some cases.

376

V. MARPLES

Figure 6. Slope of low frequency, no load pressure spectrum envelope uerslcsengine speed. -, , theoretical -2 dB/harmonic.

Empirical;

With the engine under load the low frequency linear relationship between harmonic amplitude and harmonic order no longer seems to apply. The level of the fundamental component is much the same as under no load but the envelope of the spectral peaks [see the lower curve in Figure 7) seems to be more akin to the classic function (sinx)/x, which is the envelope of the spectrum of a narrow, constant level pulse, though it does not correspond exactly of course. This is to be expected because the pressure-time diagram of a diesel engine is not a sharp edged pulse but, exhibiting very rapid pressure rise in the vicinity of top dead centre, particularly when the engine is under load, and occupying not more than a quarter of the cycle time, it is not devoid of similarity. It is interesting to observe that, in comparing the spectrum envelope with the graph of (sinx)/x, the width of the pulse which would be roughly equivalent to the pressure diagram would be equal to only 40” of crank rotation: that is, corresponding to less than a half of the engine working stroke. The no load (upper) and full load spectra to 1 kHz at an engine speed of 3 135 rev/min are shown together for comparison in Figure 7 plotted versus log frequency. Above 250 Hz a straight line can be fitted across the spectral peaks at no load but such a line shows a fall off in amplitude of 47 dB per frequency decade. It is not possible to fit such a line to the full load curve.

Frequency

I H L)

Figure 7. Cylinder pressure spectra WKWSlog, frequency for both no load (upper) and full load (lower) at 3135 rev/min. (Since the spectra are generated by logarithmic conversion of a constant bandwidth analysis the increasing width of the peaks towards low frequency is not significant.)

SURFACE VIBRATION

Figure

8. Envelopes

of low frequency

pressure

spectra

OF A DIESEL ENGINE

at various

engine speeds.

(a) No load;

(h) half load,

Figure 8, displaying envelopes of pressure spectra for the frequency range O-l kHz, reveals the effects of both speed and load on the source of excitation in the engine. 6.2 VIBRATION SIGNALS 6.2.1. Orerall response In beginning to assess the vibration characteristics of an engine it is helpful to look first of all at the wide band response in order to assess such matters as repeatability, relative significance within the spectrum and the gross effects of such influences as speed and load. With the engine operating without load the O-5 kHz spectra (50 Hz filter bandwidth) for the different speeds are essentially similar consisting of some low frequency peaks at engine speed-related harmonic frequencies, a broad band of responsiveness around 1400 Hz, and a much broader, more intense and, in view of the logarithmic amplitude scale, much more significant region between about 2.9 and 3.8 kHz. Within this band some component at a frequency just over 3 kHz appears to predominate, the peak becoming more pronounced, and becoming unquestionably the highest intensity component, as the engine speed increases. Also, as the engine speed increases towards the maximum, subsidiary peaks at about 3550 and 4050 Hz develop. The maximum level of the spectrum rises by about IO dB between 1570 and 3 115 revimin under no load conditions, an increase corresponding approximately to 34 dB/decade. The half load maximum spectrum level significantly exceeds the no load maximum spectrum level only at the higher engine speeds, and then by only about 2 dB which is associated with an increase in maximum level under full load of about 37 dB/decade (11 dB/octave). Analysis with the narrow, 5 Hz bandwidth and averaging over only four consecutive spectra serves to reveal the very dense discrete frequency nature of the response (Figure 9). The prominence of low frequency harmonics of engine speed is apparent. Comparison of the nature of the low and high frequency parts of the spectra indicate that engine speed fluctuation causes the variation in frequency ofhigh order harmonics to exceed 5 Hz(the filter bandwidth).

378

V.MARPLES

c,

:

3

Frequency

4

(k&l

Figure 9. O-5 kHz spectra (5 Hz filter bandwidth) of engine side wall vibration for various values of engine speed while operating at no load. (a) 2330 rev/min; (b) 2030 rev/min.

The development of the intense level of vibration at a frequency just above 3 kHz as the engine speed is increased is evident. Close examination of the spectra in this vicinity shows that it is not just one frequency component which gives rise to the high level, nor even always the same components. There appear to be at least four components within the vicinity of 3020 Hz and many more between 3000 and 3400 Hz. Under half load conditions the response in the vicinity of 4 kHz is rapidly becoming the second most important contributor to the overall vibration level. 6.2.2. Frequency content Narrow band analyses in overlapping 500 Hz bands yields much more information about the frequency content of the acceleration signals than do the O-5 kHz spectra. A typical selection of 500 Hz band spectra is shown in Figure 10. For each 500 Hz band the fundamental (combustion cycle) frequency is determined, followed by the frequencies of the several harmonics. Other peaks in the spectrum are then located and their frequencies determined. These are assumed to be due either to resonance in the structure, indicative of a natural frequency, or to response to inharmonic excitation, perhaps arising from belt-driven accessories whose rotational speeds will not be exactly or predictably related to engine speed. In locating such inharmonic components it must be recognized that

(9

in order to reduce the plotting time associated with the real time analyser read-out the x-axis scan rate is made so fast (relatively) that some smoothing of the displayed spectrum occurs, thereby eliminating some peaks from the hard copy as compared with the built-in oscilloscope display (it also results in a 1 dB reduction of the plotted height of a pure tone

peak) ; (ii) even a temporary arrest in the rate of rise or fall of the flank of a spectrum peak indicates the presence of a subsidiary peak adjacent to, but of lower amplitude than the main peak (e.g., spectrum at 2849 Hz in Figure 10); (iii) an almost insignificant widening of the peak, as compared with that of the filter characteristic can also indicate the presence of one or more adjacent, low-intensity peaks. A comparison of the narrow band spectra for several speed and load combinations of the engine enables common response frequencies to be identified and tabulated. The tabulation

SURFACE

VIBRATION

Hormonlcs

L-_--

I-_

OF A DIESEL ENGIN

of combustion

cycle

I

379

fWuenCy

.1--.

_~~_.~_

.-..

3.;

3.8

3.9

i.,

i.,

:.’

;.

FT.2

2.3

I’.*

1.5

,.&

Frequency Figure engine

(kcir)

10. 500 Hz band spectra of engine side wall vibration operating at I.570 rev/min, no load.

covering

the frequency

range O-5 kHz for the

reveals those frequencies at which harmonic response at one speed coincides with inharmonic response at another, serving to emphasize how impossible is the task of separating excitation frequencies from natural response frequencies by the classical techniques of mass and stiffness change while still retaining basically the same type of engine structure. Such a table also shows the extent to which a particular frequency, whether the result of forced or natural response, occurs in all records. Yet also, because of rapid temporal ampli-

380

V. MARPLES

tude variation, it shows how difficult it is to get complete overall correspondence without analysing large amounts of data and large numbers of spectra, a prohibitive task without on-line data reduction of the real time analyser output. An assessment of the data indicates that the modal density of the structure increases with frequency. For example, in the band 2.9 kHz-3.4 kHz there are something of the order of 30-5 I natural modes of vibration, 39-54 in the band 3.3-3.8 kHz and 42-57 in the band 3.74.2 kHz. Taking a certain, rather arbitrary degree of corroboration of the universal presence of a particular frequency as proof, it is probable that there are not less than 37 modes in the first band mentioned above, not less than 43 in the second and not less than 44 in the third. In round figures this means that the modal density is about one every 10 Hz, a figure which agrees with results of vibration tests of engine blocks generally. In the light of the high density of pure tone components in the high frequency spectrum and in the fluctuation in narrow band amplitude levels described in section 4.3 it is possible to hypothesize about the reasons why the high frequency spectrum of the surface vibration, and of the noise emanated by the engine of a diesel engine power unit has hitherto appeared to be broad band in nature, with energy distributed continuously throughout the frequency range, whereas very rapid narrow band analysis suggests a discrete spectrum. In order to understand the hypothesis it is necessary to bear in mind that within the most significant part of the frequency range, 2.9-4.1 kHz, the engine speed-related harmonics, which are separated by only some 8 to 30 Hz depending on the actual value of engine speed are about of the IOOth-200th order of combustion cycle frequency. The harmonic separation is of the same order of magnitude as the average natural frequency separation of the structure, 10 Hz. Now the engine speed fluctuates with time even under nominally constant conditions. The fluctuation is not less than about 0.2 ‘1;;which is a variation of about 8 Hz in the frequency range of interest which, again, is of the same order of magnitude as the natural frequency separation. Thus, in normal operation the excitation of any particular mode can be thought of as being a sinusoidal function of a periodically varying quantity. That is, it is dependent on sin(nwt) where w. the radian frequency of engine rotation, is approximated to by w = o0 + dwsin LV, in which 52 is the frequency of cyclical engine speed variation of magnitude Aw. Thus, as the rotational speed of the engine changes, the frequency of the appropriate harmonic swings through the corresponding natural frequency. Because of the close proximity of natural frequencies any harmonic will, towards the upper extremity of its frequency deviation, excite an adjacent mode of vibration while the initial mode finds itself re-excited by the next lower harmonic force component. There are, in fact, two distinct mechanisms at play, both of which lead not only to fluctuation of the amplitude of the vibration but which, because of the variation of exciting frequency, cause fairly rapid alternation of the frequencies of what would otherwise be recognisable as pure tone components of the response. This fluctuation, together with the high density within the spectrum of such behaviour helps to hide the basic character of the vibration, an occurrence which is possible only where the natural frequency separation, the excitation harmonic spacing and the excitation frequency variation are of the same order of magnitude. The two mechanisms are illustrated by the graphs of Figures 11 and 12. The former shows the vibration of a very lightly damped single degree of freedom system which is excited by a force whose frequency is 5 ()i lower than the system natural frequency. The phenomenon of “beating”, due to the interaction of “free” and “forced” components of the vibration, is clearly demonstrated in which the system vibrates at the mean (half the sum) of the excitation and natural frequencies, the amplitude being modulated at the rate of half the difference of the excitation and natural frequencies. For the example of the engine structure, the “instantaneous” excitation frequency might be only 0.2j’,‘, (4-6 Hz) different from the natural frequency. The fluctuation in amplitude occurring at 2-3 Hz is of the same order as the

SURFACE VIBRATION

Figure frequency

I I. “Beating”

of very lightly damped is 5 “/, lower than the natural frequency.

381

OF A DIESEL ENGINF

single

degree

of freedom

system

excited

by force

whose

Figure 12. Transient vibration of a lightly damped single degree of freedom system. excited by a force of constant magnitude whose frequency increases fairly rapidly from IO “,, below to 10”;above the system natural frequency. n/w2 = 10-j.

382

V. MARPLES

fluctuations observed and the vibration, taking place 2-3 Hz removed from the system natural frequency, will tend to confuse the process of identification of normal mode behaviour. Figure I2 shows the nature of the vibration of a single degree of freedom system where damping is of the same order as that to be found in engine structures and which is excited by a force, the frequency of which increases uniformly with time. The curveshows the presence of a starting transient, a steady build-up of vibration amplitude to a maximum which occurs at a frequency higher than the system natural frequency, followed by a fairly rapid collapse and a final decaying transient. Where the excitation frequency decreases uniformly through the system natural frequency the vibration exhibits similar characteristics, the maximum amplitude now occurring at a frequency lower than the natural frequency. The parameters of the diesel engine situation are that the excitation frequency sweep begins from a value of o/o,, of the order of 0.997 and the sweep rate parameter, a/w,?, is of the order of 5 x IOe4. The effect of the former will be that the starting transient will not be dissipated by the time that the maximum response due to sweeping through the natural frequency has been reached and the slower rate of sweep will give rise to a greater maximum vibration level and to a reduced shift of frequency of this maximum level from the natural frequency. Even so the shift will be of the order of several Hz. The overall picture is further confused by the fact that, whereas Figures 1 I and I2 represent the vibration subsequent to an initial steady state, in practice a steady state condition, in terms of vibration behaviour, never exists and so each change of stimulus produces a new transient response on top of a previously existing transient vibration. All that drawing analogies with simple transient vibration theory tells us is that we can expect (i) the detected frequencies of inharmonic vibration response due to normal mode behaviour to fluctuate by several Hz as between consecutive analyses, and (ii) the amplitudes of vibration as detected by narrow band analysis to be continually varying, sometimes between wide limits. 6.2.3. Amplitude

levels

Examples of the best records displaying amplitude information of the vibration spectra of the engine surface are shown in Figure 9. These are O-5 kHz spectra, of 5 Hz filter bandwidth, obtained by analysing the same portion of signal repeatedly in contiguous 500 Hz bands and scaling down the frequency span of the plot so that all ten analyses for the band O-5 kHz can be plotted as a continuous spectrum. Figure 9 refers to the side wall vibration at no load. At low frequencies, less than 500 Hz, the spectra are dominated by a component at firing frequency (equal to combustion cycle frequency times number of cylinders) and its second or third harmonic at low or high engine speeds, respectively. There is also an obvious rise in spectral level below 1 kHz. In finding which harmonics have the greatest amplitude around this frequency it is discovered that it varies from the 28th harmonic of rotational frequency at low engine speed to the 15th at high speed. And in fact the maximum level always occurs in the region of 750-800 Hz. Thus the higher levels in this vicinity are due primarily to responsiveness of the structure rather than to intensity of the excitation, although the latter can be seen to be playing a part when one looks at the values of the levels as a function of engine speed and recalls the way in which the pressure spectrum varies with engine speed. A similar increase in spectral level occurs in the vicinity of l-41.5 kHz. Depending on engine speed, the largest component can variously be associated with from the 30th harmonic of firing frequency (120th of combustion cycle frequency) to the 59th of cycle frequency. Since the latter is not one of the more prominent firing frequency harmonics one can expect its effects to be a little less pronounced than those of the others.

SURFACE

VIBRATION

OF A I)ltSEL

ENGINI:

383

A further increase in the level of the spectrum occurs around 262.7 kHz where the level is equal to or greater than either of the previous two. At these frequencies the ascribing of a harmonic number is a little less certain than at low frequencies due to engine speed variation. In view of the previous conclusions about the predominant effect being the engine block susceptibility it is not necessary to continue to determine harmonic order. The highest levels for all the spectra occur within the band 3-3.4 kHz, this part of the spectra dominating the overall, or indeed the “A” weighted, response. This is therefore the most important frequency region as far as the side walls are concerned. A pure tone, or a pail of pure tone components. exists at about 3010 Hz which often rises to 4 dB in excess of an) other single component. The presence of similar tones is also noticeable at 4020 and 4OSO Hz throughout the speed range investigated. The absolute values of the vibration levels of these spectra are not very significant, partly because no obvious detailed correlation exists between surface vibration and emanated noise and partly because the absolute levels are affected both by the averaging process and by the frequency shift due to engine speed fluctuation. The spectra, however, do confirm the influence of multi-modal response of the structure and point up the most important frequency range. Vibration tests would provide corroboration of this and near field noise measurements would yield confirmation of the importance of this region to the overall noise spectrum. The spectra of the vibration with the engine under load show essentially the same features as the no load spectra. The only localized difference of any note is the increase in the mean spectrum level between 2.6 and 3 kHz. In addition, it is quite clear that the no load spectra are a few dB lower, at all engine speeds. up to 3%3?; kHz but thereafter are a few dB higher. In the spectra of the vibration of the crankcase skirt close to the region of attachment of the oil pan, low frequency harmonics of firing frequency are clearly evident and so also is the component at 4020 Hz, particularly as engine speed increases to higher values. Apart from these the spectrum is depressingly flat, showing how extremely difficult it would be to effect a significant reduction in the overall vibration level at this location. The vibration spectra for the longitudinal direction was detected at the rear of the cyjlinder head and the vertical vibration on the top of the rocker cover for one engine speed only. Their very obvious difference from each other and from the previous spectra serves to emphasize that no direct relationship between the far fieldnoise spectrum of the engine and the vibration spectrum relating to any one point on the engine surface can be expected.

7. CONCLUSIONS 7.1.

PRESSURE SIGNALS

(1) The pressure spectrum of the engine exhibits. as far as can be detected up to 1000 Hz. all harmonics of the combustion cycle frequency. The amplitudes of the harmonics fall progressively from a maximum at the fundamental frequency, as other investigators have shown. (2) With the engine running light the harmonic amplitudes fali regularly by about 2 dB per component which, to about 800 Hz, can be approximated to by about 47 dB/decade (see Figure 8). (Figures between 30 and 48 dB have been suggested by other research workers, the lower figures usually corresponding to the no load condition.) (3) As the engine speed increases the spectrum envelope does not translate in frequency (as has been implied previously) but takes on a shallower slope (see Figure 7) down from a fundamental component of virtually constant amplitude, the higher harmonics thereby becoming more significant. (Components beyond 1000 Hz or at levels more than 45 dB below the fundamental have not been investigated.)

384

V. MARPLES

(4) The pressure spectrum under load is quite different (see Figures 7 and 8(b)), signifying a much more steeply rising pressure-time diagram than with the engine running light. No part of the spectral envelope reveals even an approximately straight line portion with either linear or logarithmic frequency. (5) With the engine operating under nominally constant conditions the intensity and frequency of low order components of the pressure spectrum are virtually time-independent. Fluctuations commence at about the 15th harmonic and, at frequencies less than 500 Hz amount to about 3 dB in amplitude, k I Hz in frequency. At higher frequencies both forms of variation can be expected to be much larger. 7.2.

VIBRATION

ACCELERATION

SIGNALS

Apparently the near instantaneous vibration spectra exhibit no repeatability. (2) On closer investigation spectra for nominally identical situations exhibit largely the same frequency components but the amplitudes are unrelated. (3) Whereas at low frequencies only combustion cycle harmonics appear in the acceleration spectrum, at high frequencies there are additionally many other inharmonic components. (4) In large measure the inharmonic components appear in all spectra irrespective of engine load and speed. It is concluded therefore that these represent the natural response of the engine structure, the modal density in the vicinity of 2-4 kHz being about 100 per 1000 Hz. (5) The nature of the vibration as exhibited by the time-dependent spectra appears to be due to the interplay of dense, excitation harmonics due to the cylinder pressure, whose frequencies vary periodically as the engine speed fluctuates and of equally dense modes of vibration of the engine structure, characterized by fixed frequencies. At a particular instant of time a certain pressure harmonic, its frequency being coincident with that of a mode of the structure will excite that mode. Subsequently the vibration at that frequency will decay as the harmonic frequency increases (say) but will build up again as the next lower pressure harmonic, increasing in frequency, begins to excite that mode. This is not a steady state process, even in the presence of uniform variations. Starting transients at every change will occur and these will overlap giving rise to the total lack of repeatability and the need for averaging. (6) It is therefore impossible to look for a significant reduction in engine surface vibration by the separation of excitation and natural response frequencies by the classical techniques of mass and stiffness change. Only radical innovation can hope to succeed. (7) The apparently broad band vibration spectrum in the region 500-5000 Hz has been shown to be composed of many, closely spaced, pure tone components. This spectrum, and the noise spectrum, have hitherto been viewed as broad band because of a combination of the following three factors. (1)

(a) Many of the pure tone components are harmonics of cycle frequency. But under normal, nominally steady, operating conditions, the engine speed, and hence cycle frequency, will fluctuate by about O-6 %. Harmonics in the vicinity of 3 kHz therefore vary in frequency by about 18 Hz over a period of a few sceonds. The frequency separation of such harmonics is between 8 and 30 Hz. (b) The inharmonic pure tone components are due to structural resonance effects. The modal density is such that modes are separated, on average, by about 10 Hz, a value which is the same order of magnitude as the excitation harmonic spacing. (c) Interaction of varying frequency excitation forces with fixed frequency natural responses, the density of both being much the same, leads to a complex pattern of response, highly temporally dependent, which, over a short period of time, will exhibit pronounced response at all frequencies.

SURFACEVIBRATIONOF A I)IESELENGINE

385

(8) For the indirect injection, four cylinder engine used in these tests, the most important frequencies governing the overall level of the side wall vibration are between 2.9 and 3.8 kHz. This range lies within the range 2-4 kHz suggested by Griffiths and Skorecki [8] as the most significant for piston slap. (The side wall vibration was transduced along and within the line of piston stroke). (9) Single, or double, very prominent components at 3010 and 4020 Hz could be due to cavity resonance effects in the combustion space. There is no evidence as yet either for or against this. (IO) In broad terms the O-5 kHz spectrum of side wall vibration is similar in shape for all speeds and loads. The maximum level increases by about 4 dB/octave (13 dB/decade) with engine speed. There is relatively little additional increase with load. the change manifesting itself more by shift of energy from high frequency (greater than 3.5 kHz) to lower frequency. ( I I ) Determination of some spectra for the crankcase skirt, cylinder head and rocker cover serve to show that, within the area investigated. the 2.9 to 3.8 kHz high level is characteristic of the side wall movement. The skirt shows more or less uniform response over the whole frequency range. There would therefore be great difficulty in reducing significantly the overall level of vibration in this region. The tests reported here have shown the nature of the surface vibration of the engine block and, by implication, of the noise spectrum. They have also shown something of the dependencies of the surface vibration. But before really valuable conclusions about the relationship of engine structure to noise emanation can be made a more extensive programme of work is required encompassing vibration tests to determine dynamic characteristics on the one hand and near field noise evaluation and its relationship to surface vibration on the other.

ACKNOWLEDGMENT I am grateful to Carleton University, Ottawa, Canada, for making facilities available this research project and to the Ford Motor Company of Canada for finance.

for

REFERENCES 1. V. MARPLE~1975 Department

of Mechanical and Aeronautical Engineering, Carleton Unirersit)), 75-2. Diesel-engined vehicle noise. 2. A. E. W. AUSTENand T. PRIEDE1958 Institution ofMechanical Engineers Symposium on Engine Noise and Noise Suppression, pp. 19-53. Origins of diesel engine noise. 3. N. A. GRAHAMand V. MARPLES1971 Journal of Agricultural Engineering Research 6. 394-398. Ottawa, Report No. ME/A

A method of rating some acoustic characteristics of agricultural tractor cabs. 4. M. C. KAYE and E. E. UNGAR 1973 U.S. DOT-TST-74-2. Truck noise IIIB-Acoustic and performance test comparison of initial quieted truck with contemporary production truck. 5. T. PRIEDE1960-61 Proceedings of the Institution of Mechanical Engineers (Automotive Diri.yion) 1, 63-77. Relation between form of cylinder pressure diagram and noise in diesel engines. 6. T. PRIEDE,E. C. GROVERand N. LALOR1969 Society of Automotive Engineers Paper No. 690452. Relation between noise and basic structural vibration of diesel engines. 7. D. D. TIEDE and D. F. KABELE1973 Society of Automotive Engineers Paper No. 730245. Diesel engine noise reduction by combustion and structural modifications. 8. W. J. GRIFFITHSand J. SKORECKI1964 Journal of Soundand Vibration 1. 345-364. Some aspects of vibration of a single cylinder diesel engine. A. Effects of cooling water on cylinder pressure and surface vibration. B. Mechanics of piston slap. 9. B. J. FIELDINGand J. SKORECKI1969-70 Proceedings of the Institution qf Mechanical Engineers 184,859-874. Identification of mechanical sources of noise in a diesel engine: sound originating from piston slap. 10. E. E. UNGAR and D. ROSS 1965 Journal of Soundand Vibration 2, 132-146. Vibrations and noise due to piston-slap in reciprocating machinery.

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V. MARPLES

11. M. F. RUSSELL1972 Society of Automotive Engineers Paper No. 720135. Reduction of noise emissions from diesel engine surfaces. 12. G. E. THIEN 1973 Society of Automotive Engineers Paper No. 730244. Use of specially designed covers and shields to reduce diesel engine noise. 13. T. PRIEDE, A. E. W. AUSTEN and E. C. GROVER 1964-65 Proceedings of the Institution of Mechanical Engineers 179, 113-143. Effect of engine structure on noise of diesel engines. 14. C. M. P. CHAN and D. ANDERTON1972 Proceedings of’the International Conl&ence OII Noise Control Engineering 261-266. The correlation of machine structure surface vibration and radiated noise. 15. P. E. WATERS,N. LALORand T. PRIEDE 1969-70 Proceedings of the Institution of Mechanical Engineers 184,63-72. The diesel engine as a source of commercial vehicle noise. 16. S. H. JENKINS,N. LALORand E. C. GROVER1973 Society qf Authomotive Engineers Paper No. 730246. Design aspects of low-noise diesel engines. 17. V. MARPLESand N. A. GRAHAMI973 Journal of the Society ofEnuironmenta1 Engineers 12,19-20.