Vibration Noise Engine Test

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<ul><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 1/7</p><p>3 Vibration and noise</p><p>Introduction</p><p>Vibration is considered in this chapter with particular reference to the design and oper-ation of engine test facilities, engine mountings and the isolation of engine-induceddisturbances. Torsional vibration is covered as a separate subject in Chapter 9, Cou-pling the engine to the dynamometer.</p><p>The theory of noise generation and control is briefly considered and a brief accountgiven of the particular problems involved in the design of anechoic cells.</p><p>Vibration and noise</p><p>Almost always the engine itself is the only significant source of vibration and noisein the engine test cell.15 Secondary sources such as the ventilation system, pumpsand circulation systems or the dynamometer are usually swamped by the effects ofthe engine.</p><p>There are several aspects to this problem:</p><p> The engine must be mounted in such a way that neither it nor connections to itcan be damaged by excessive movement or excessive constraint.</p><p> Transmission of engine-induced vibration to the cell structure or to other buildingsmust be controlled.</p><p> Excessive noise levels in the cell should be avoided or contained as far as possibleand the design of alarm signals should take in-cell noise levels into account.</p><p>Fundamentals: sources of vibration</p><p>Since the vast majority of engines likely to be encountered are single- or multi-cylinder in-line vertical engines, we shall concentrate on this configuration.</p><p>An engine may be regarded as having six degrees of freedom of vibration about</p><p>orthogonal axes through its centre of gravity: linear vibrations along each axis androtations about each axis (see Fig. 3.1).</p></li><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 2/7</p><p>22 Engine Testing</p><p>Z</p><p>Z</p><p>X</p><p>X</p><p>Y</p><p>Y</p><p>Figure 3.1 Internal combustion engine: principle axes and degrees of freedom</p><p>In practice, only three of these modes are usually of importance:</p><p> vertical oscillations on the X axis due to unbalanced vertical forces; rotation about the Y axis due to cyclic variations in torque; rotation about the Z axis due to unbalanced vertical forces in different transverse</p><p>planes.</p><p>Torque variations will be considered later. In general, the rotating masses are carefullybalanced but periodic forces due to the reciprocating masses cannot be avoided. The</p><p>crank, connecting rod and piston assembly shown in Fig. 3.2 is subject to a periodicforce in the line of action of the piston given approximately by:</p><p>f=mp2crcos+</p><p>mp2crcos 2</p><p>n where n= l/r (1)</p><p>m</p><p>f</p><p>I</p><p>r</p><p>c</p><p>Figure 3.2 Connecting rod crank mechanism: unbalanced forces</p></li><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 3/7</p><p>Vibration and noise 23</p><p>Here mp represents the sum of the mass of the piston plus, by convention, one-thirdof the mass of the connecting rod (the remaining two-thirds is usually regarded asbeing concentrated at the crankpin centre).</p><p>The first term of eq. (1) represents the first-order inertia force. It is equivalentto the component of centrifugal force on the line of action generated by a mass mpconcentrated at the crankpin and rotating at engine speed. The second term arisesfrom the obliquity of the connecting rod and is equivalent to the component of forcein the line of action generated by a mass m/4nat the crankpin radius, but rotating attwice engine speed.</p><p>Inertia forces of higher order (3, 4, etc., crankshaft speed) are also generatedbut may usually be ignored.</p><p>It is possible to balance any desired proportion of the first-order inertia forceby balance weights on the crankshaft, but these then give rise to an equivalent</p><p>reciprocating force on the Z axis, which may be even more objectionable.Inertia forces may be represented by vectors rotating at crankshaft speed and twice</p><p>crankshaft speed. Table 3.1 shows the first- and second-order vectors for engineshaving from one to six cylinders.</p><p>Table 3.1 First- and second-order forces, multicylinder engines</p><p>Firstorderforces</p><p>1</p><p>1 1 1 1 1 1</p><p>1 1</p><p>1</p><p>1</p><p>1 1 1 1 1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>22</p><p>2 2 2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>2</p><p>33 3 3</p><p>3</p><p>3</p><p>3</p><p>5</p><p>5</p><p>5</p><p>5</p><p>5</p><p>6</p><p>6</p><p>6</p><p>6</p><p>5</p><p>5</p><p>5</p><p>33</p><p>3</p><p>3</p><p>3</p><p>3</p><p>3</p><p>2 2 2 2</p><p>2</p><p>3 3 3 3</p><p>44 4</p><p>55</p><p>6</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>4</p><p>2</p><p>2</p><p>2</p><p>Secondorderforces</p><p>Firstordercouples</p><p>Secondordercouples</p></li><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 4/7</p><p>24 Engine Testing</p><p>Note the following features:</p><p> In a single cylinder engine, both first- and second-order forces are unbalanced.</p><p> For larger numbers of cylinders, first-order forces are balanced. For two and four cylinder engines, the second-order forces are unbalanced andadditive.</p><p>This last feature is an undesirable characteristic of a four cylinder engine and in somecases has been eliminated by counter-rotating weights driven at twice crankshaftspeed.</p><p>The other consequence of reciprocating unbalance is the generation of rockingcouples about the transverse or Z axis and these are also shown in Fig. 3.1.</p><p> There are no couples in a single cylinder engine. In a two cylinder engine, there is a first-order couple. In a three cylinder engine, there are first- and second-order couples. Four and six cylinder engines are fully balanced. In a five cylinder engine, there is a small first-order and a larger second-order</p><p>couple.</p><p>Six cylinder engines, which are well known for smooth running, are balanced in allmodes.</p><p>Variations in engine turning moment are discussed in Chapter 9, coupling theengine to the dynamometer. These variations give rise to equal and opposite reactions</p><p>on the engine, which tend to cause rotation of the whole engine about the crankshaftaxis. The order of these disturbances, i.e. the ratio of the frequency of the disturbanceto the engine speed, is a function of the engine cycle and the number of cylinders.For a four-stroke engine, the lowest order is equal to half the number of cylinders:in a single cylinder there is a disturbing couple at half engine speed while in a sixcylinder engine the lowest disturbing frequency is at three times engine speed. In atwo-stroke engine, the lowest order is equal to the number of cylinders.</p><p>The design of engine mountings and test bed foundationsThe main problem in engine mounting design is that of ensuring that the motionsof the engine and the forces transmitted to the surroundings as a result of theunavoidable forces and couples briefly described above are kept to manageablelevels. In the case of vehicle engines it is sometimes the practice to make use of thesame flexible mounts and the same location points as in the vehicle; this does not,however, guarantee a satisfactory solution. In the vehicle, the mountings are carriedon a comparatively light structure, while in the test cell they may be attached to amassive pallet or even to a seismic block. Also in the test cell the engine may be</p><p>fitted with additional equipment and various service connections. All of these factorsalter the dynamics of the system when compared with the situation of the engine in</p></li><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 5/7</p><p>Vibration and noise 25</p><p>service and can give rise to fatigue failures of both the engine support brackets andthose of auxiliary devices, such as the alternator.</p><p>Truck diesel engines usually present less of a problem than small automotive</p><p>engines, as they generally have fairly massive and well-spaced supports at the fly-wheel end. Stationary engines will in most cases be carried on four or more flexiblemountings in a single plane below the engine and the design of a suitable system isa comparatively simple matter.</p><p>We shall consider the simplest case, an engine of mass m kg carried on undamped</p><p>mountings of combined stiffness kN/m (Fig. 3.3). The differential equation definingthe motion of the mass equates the force exerted by the mounting springs with theacceleration of the mass:</p><p>md2x</p><p>dt2 +</p><p>kx=</p><p>0 (2)</p><p>a solution is</p><p>x= cons tan t sin</p><p>k</p><p>m t</p><p>k</p><p>m= 20 natural frequency = 0 =</p><p>02</p><p> =1</p><p>2</p><p>k</p><p>m (3)</p><p>the static deflection under the force of gravity=mg/kwhich leads to a very convenientexpression for the natural frequency of vibration:</p><p>0 =1</p><p>2</p><p> g</p><p>static deflection (4a)</p><p>C of G</p><p>Figure 3.3 Engine carried on four flexible mountings</p></li><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 6/7</p><p>26 Engine Testing</p><p>or, if static deflection is in millimetres:</p><p>0 =1576</p><p>static deflection(4b)</p><p>This relationship is plotted in Fig. 3.4Next, consider the case where the mass m is subjected to an exciting force of</p><p>amplitudefand frequency /2. The equation of motion now reads:</p><p>md2x</p><p>dt2+ kx= fsint</p><p>the solution includes a transient element; for the steady state condition amplitude ofoscillation is given by:</p><p>x= f/k12/20</p><p> (5)</p><p>here f / k is the static deflection of the mountings under an applied load f. Thisexpression is plotted in Fig. 3.5 in terms of the amplitude ratio xdivided by staticdeflection. It has the well-known feature that the amplitude becomes theoreticallyinfinite at resonance, = 0.</p><p>If the mountings combine springs with an element of viscous damping, the equa-tion of motion becomes:</p><p>md2x</p><p>dt2+ cdx</p><p>dt+ kx= fsint</p><p>40</p><p>30</p><p>20</p><p>10</p><p>54</p><p>3</p><p>2</p><p>10.2</p><p>Naturalfrequency</p><p>(Hz)</p><p>0.5 1 2 5</p><p>Static deflection (mm)</p><p>10 20 50 100 300</p><p>Figure 3.4 Relationship between static deflection and natural frequency</p></li><li><p>8/13/2019 Vibration Noise Engine Test</p><p> 7/7</p><p>Vibration and noise 27</p><p>6</p><p>4</p><p>2</p><p>0</p><p>0</p><p>Amplituderatio</p><p>1 2Frequency ratio</p><p>0</p><p>Figure 3.5 Relationship between frequency and amplitude ratio (transmissibil-ity) undamped vibration</p><p>wherecis a damping coefficient. The steady state solution is:</p><p>x= f/k1 </p><p>2</p><p>20</p><p>2+ </p><p>2</p><p>c2</p><p>mk20</p><p>sintA (6a)</p><p>If we define a dimensionless damping ratio:</p><p>C2 = c2</p><p>4mk</p><p>this equation may be written:</p><p>x=f/k</p><p>1 2</p><p>20</p><p>2+4C2 </p><p>2</p><p>20</p><p>sintA (6b)</p><p>(ifC= 1 we have the condition of critical damping when, if the mass is displacedand released, it will return eventually to its original position without overshoot).</p><p>The amplitude of the oscillation is given by the first part of this expression:</p><p>amplitude= f/k</p><p>1</p><p>2</p><p>20</p><p>2+4C2 220</p></li></ul>


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