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DOI: 10.1177/1077546312454321published online 18 September 2012Journal of Vibration and Control

Sivanandi Periyasamy and Thirunarayanaswamy AlwarsamyCombined effects of inertia and pressure on engine vibration

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Article

Combined effects of inertia and pressureon engine vibration

Sivanandi Periyasamy 1 and Thirunarayanaswamy Alwarsamy 2

AbstractThe present paper describes a methodology devised to study the engine block displacement of an internal combustionengine in the radial direction due to combustion force and inertia forces. The combustion force produced in in-cylinder isa substantial function of angular displacement and then correlated with pressure and temperature. Other than thesubstantial function, combustion force depends on chamber design, injection parameters, flow patterns and fuels. Butinertia is a function of angular displacement and a mass of reciprocating parts. Speed is directly related to combustion bymeans of indicated pressure and the indicated torque respectively. The engine was taken for an analysis along with speedand load as the design variables. The engine block displacement, time-domain frequency, wave form, side thrust andin-cylinder force were examined for the analysis. The results obtained provide the combined effect of combustion forceand inertia force induced displacement, uncertainty in combustion processes, nonlinear vibration of the engine block, andvibration spectra. This new approach in engine parameter design bestows insight with the combustion force and inertiainduced vibration and source of noise in the diesel engine.

KeywordsDisplacement, force, peak amplitude, side thrust, wave form

Received: 2 March 2012; accepted: 31 May 2012

1. IntroductionThe measurement of in-cylinder pressure has been anobject of study from the beginning of the internal com-bustion engine. A tremendous amount of useful infor-mation can be extracted from the cylinder pressuresignal for engine combustion control. However, thephysical cylinder pressure sensors are undesirablyexpensive and their health needs to be monitored for

fault diagnostic purposes (Junmin et al., 2005). Twoneural network-based independent cylinder pressuresrelated variable estimators were developed and veriedat steady state. The development of combustion indiesel engines is strictly dependent on combustionchamber and injection parameters. Thermo-acousticinstabilities in combustion chambers are the symbolof a serious threat to combustion chambers. It occursin the form of large amplitudes and low frequency pres-sure waves and heat release uctuations, which canlead to performance degradation as well as to relevantstructural damage. The vibration signal analysis and

mitigation of the amplitude of the vibration by usingdifferent methods and devices is an important task of the researcher since the eighteenth century. This type of work was carried out for all machinery and equipment.The impact of inlet, exhaust, and fuel injection param-eter has presented. The short term Fourier transform isused to identify different sources of internal combustionengine block vibration from single point accelerationmeasurements taken with a commercial knock sensor

(Vulli et al., 2009). The overall idea of single pointacceleration analysis for different prole tted enginesis presented (Periyasamy and Alwarsamy, 2012) forcombustion pressure only. Even a slight modicationor change in the engine parameter will induce vibration,

1 Government College of Technology, Coimbatore, India2 Department of Technical Education, Chennai, India

Corresponding author:S Periyasamy, Government College of Technology, Coimbatore 641013,India.Email: [email protected]

Journal of Vibration and Control0(0) 1–12! The Author(s) 2012Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/1077546312454321 jvc.sagepub.com








and abnormality such as knocking, combustion instabil-ity, thermo-acoustic vibration and squat performance.There is the possibility of using engine block vibrationas a mean diagnostic tool for the combustion modica-tions induced by injection parameters, and an acceler-ometer positioned at the engine block has been analyzed

(Carlucci et al., 2006). Piston slap is a cause of complextransient vibration response related to the impact exci-tation inside the engine, and the piston-slap impact withthe slap-induced vibration was correlated for enginedynamic behavior simulation and working conditionsmonitoring (Geng and Chen, 2005). Some origin of mechanically induced noise is caused by various forceswhich act on the moving parts of the engine to acceleratethem across their running clearances and thus causemechanical impacts. One of these sources is the pistonslap and dominates in high speed medium engines(Haddad and Pullen, 1974). An analytical treatmentwas conducted to investigate piston motion in a dieselengine and a computer program was written to predictoptimum designs for high mechanical efficiency and lownoise and vibration excitation due to offset settings of the crankshaft, piston-pin, and piston centre of gravity(Haddad and Kek-Tjen, 1995).

Excitation vibration of the engine due to piston slap,friction, speed, injection parameter, and load conditionare analyzed in various methodologies. One is that theimpact of excitations inside the engine are reasonablyanalyzed, based on an analytical model of the non-sta-tionary engine vibration. At this juncture time varyingtransfer properties were developed and discussed in

detail on their time-domain and time-frequencydomain characteristics (Zunmin Geng et al., 2003).Similarly an analytical tool has been proposed to dis-tinguish favourable oscillations from undesired thermo-acoustic combustion instabilities with the aid of movingaverage and exponentially weighted moving averagecharts (Fichera and Pagano, 2008). Different sourcesof vibration must be separated for detailed analysis.An attempt to separate the vibration sources by blindsource separation techniques and a combination of theblind least mean square algorithm with a deationmethod to separate several sources was proposed

(Xianhua Liu et al., 2008). In the same way a diagnosismethodology for internal combustion engines combus-tion was proposed by means of non-invasive measure-ments on the cylinder head, such as acoustic andvibration related to the internal indicated mean effect-ive pressure (Barelli et al., 2009). The internal variablesare studied using recurrence plots, recurrence quanti-cation analysis and continuous wavelet transform(Asok K.Sen et al., 2008). Similarly a practical applica-tion of nonlinear autoregressive moving average poly-nomial models with exogenous inputs technique wasproposed to model pressure dynamics inside the

cylinder of a direct injection compression ignitionengine (Olivier Grondin et al., 2005). In automotiveturbocharger the self-excited unstable region is identi-ed using vibration spectrum. It will be used for bear-ing design modications in oating ring journalbearings as well as custom design xed geometry bear-

ings (Gordon Kirk et al., 2010, 2011). In-cylinder pres-sure derivatives are also used to detect the combustionconditions. Sudden changes in the chamber pressurehave been amplied by the pressure derivative, andrelated to thermodynamic phenomena within the cylin-der (Jose M. Lujan et al., 2010). From the analysis of acoustic signals and vibration signals measurements, aninvestigation of the noise source identication in adiesel engine is presented, and the noise sources of anengine front were identied (Zhang and Han, 2005).The frequency and spectral of a new power splithybrid electric vehicle drive train’s vibrational behaviorare studied with the aid of a linear mechanical modeland proposed low frequency torsional analysis (Schulz,2005). The decision of the number of cycles to be mea-sured is performed on the basis of the cycle-to-cyclestandard deviation of the signal, and the spectrum ana-lysis allows the denition of cut-off frequency for thelter design. In general, a lower number of cyclesare needed in diesel engines due to their lower cycle-to-cycle dispersion (Payri et al., 2010). A detailed multi-body numerical nonlinear dynamic model of a singlecylinder internal combustion engine has formulated,and performed comprehensive noise, vibration, andharshness investigation of the engine (Boysal and

Rahnejat, 1997). The vibrational characteristics of aninternal combustion engine crankshaft have a vital rolefor cylinder health diagnostics. A rigid body model andexible body model are developed for predicting tor-sional vibrations of the crankshaft under differentengine powers, and natural frequencies and responseare calculated using the Holzer method, and the trans-fer method (Zhang and Yu, 2009).

A crank-angle domain numerical model of thecrankshaft dynamics for a six cylinder industrialdiesel engine is adopted to establish the effects of con-tinuous low-power production in individual cylinders

of a multi-cylinder engine (Mert Geveci et al., 2005).Vibration characteristics for the foundation type of anemergency diesel generator of a nuclear power plant isproposed and compared with the coil spring-viscousdamper system anchor bolt system (Kim et al., 2010).Constantly the suppression of vibration is done bychoosing absorber. An active, standalone vibrationabsorber utilizing the state feedback taken from theabsorber mass is proposed, and investigates the efficacyof an active vibration absorber in controlling resonantand transient vibrations of linear vibratory systems(Chatterjee, 2010). Wave propagation in in-cylinder is

2 Journal of Vibration and Control 0(0)








m 2 €x2 þ 2c3 _x2 þ ð c2 þ c1Þð_x2 À _x1Þ

þ ð k12 þ k2Þðx1 À x2Þ þ 2k 3x2 þ k11 ðx2 À x1Þ3

þ k12 Á ¼ 0 ð10Þ

If (x 1 – x2) is less than piston – cylinder assemblyclearance, use the linear approximation equations (11)and (12) for manipulating the displacements.

m 1 €x1 þ c2ð_x1 À _x2Þ þ k12 ðx1 À x2Þ ¼Py ð11Þ

m 2 €x2 þ 2c3x2 þ c2ð_x1 À _x2Þ þ 2k 3x2 þ k2ðx1 À x2Þ ¼ 0ð12Þ

The base stiffness k b and damping C b are not con-sidered, the inertia and radial impact parameters aretaken into account for analysis.

3. Experimental data acquisition andengine test

A single cylinder compression ignition engine was usedto generate the test data. This direct-injection four-stroke diesel engine was tted with xed valve timing

and speed control. The engine was coupled with amechanical dynamometer. A knock sensor is used tomeasure engine block vibrations. The engine specica-tions are tabulated in Table.1.

Two different sampling methods were available,namely: crank-angle-based sampling and time-basedsampling. Crank-based sampling is generally themost suitable for sampling engine test data. Mostcombustion events occur at different angular pos-itions of the crank shaft and therefore can easilybe located with crank-based sampling. However con-trol over the sampling frequency is not possible, thisis determined by the engine-crank speed and by thepulse per revolution of the encoder. Crank-baseddata sampling is therefore not readily suitable foridentifying xed-step discrete-time mathematicalmodels. Temporal sampling by contrast, involvesxed-time-step sampling controlled as usual by aninternal clock, such that the sampling rate is inde-pendent of the crank speed. Here constant time-sampling was used. For the experimental programthe engine was loaded using a dynamometer. Forno load condition the speed of the engine hasvaried from 1100 rpm to 1500 rpm in steps of 100 rpm. First the engine ran in normal mode and

the above design parameters were applied, thenusing Sendig 911-Vibrometer acceleration waspicked up through accelerometer vibration pick-upand stored in the data collector as shown Figure2. The accelerations were picked up around thecylinder block, and then MCME software was usedfor analyzing the collected data for variouscorrelations.

Figure 1. Engine model.

Table 1. Engine specifications

Engine parameters Value

No. of cylinder (n) OneBore D (mm) 85Stroke L (mm) 110Maximum speed N (rpm) 1500Connecting rod length (mm) 235Compression ratio 18:1Intake pressure (bar) 1Intake temperature (K) 300









4. Results and discussionExperimental values were taken, and analyzed for thepressure and inertia contribution. The in-cylinder com-bustion force was shown in Figure 3, the maximumforce occurred near the top dead centre. In the suction

stroke the pressure is equivalent to atmospheric pres-sure and the corresponding combustion force wasderived by multiplying pressure and piston area,which is very less than the maximum force. At lowspeed the fuel consumption was high, and part of thepower produced was exerting forces on side walls of thecylinder as shown in Figure 4. The side thrust is alter-natively acting towards and away from the cylindercentre since it is a function of the crank angle only.

The piston displacement and cylinder block werecalculated using equations (11) and (12) as shown inFigure 5. The piston displacement at suction stroke isin the opposite direction because up to 90 the vacuumcondition in the initial process is exerting force towardsthe centre of the cylinder. After 90 it is acting on thecylinder liner then on the engine block, in the same waynext 180 force stand-in against the piston, when dis-placement is in the inner side. But in the combustionstroke it exhibits maximum displacement because of combustion forces and subsequently varies in bothsides for the exhaust stroke. Equally the cylinder

block displacement also varies as shown in Figure 6.Every revolution piston and cylinder block displace-ment uctuates with speed. Side thrust force is chan-ging slowly, but displacement function changes quicklydue to the vibration phenomenon. The rst revolutionvariation is very smooth compared with the second

revolution. The quick changes later is represents thecombustion and hot gases behavior within the cylinder.High temperature gases have high momentum. Theautocorrelation function is used to detect a weak recur-ring signal which may be buried in a truly random noise(Rao and Gupta, 1984).

A hemispherical prole piston engine is normallyused in most of the internal combustion engine.Fourier transformed autocorrelation analysis wasshown in the Figure 7. However, the autocorrelationof this signal, which is a periodic function, predominatessince a truly random noise has its autocorrelation equalto zero. Values vary from the mean which represents theinstability in combustion and the consequent vibration.The main goal is to recover the information related tothe combustion phenomena from the engine blockvibration. The damping takes too much time for thecombustion cycle time of the diesel engine, because of the cycle-to-cycle variation in the combustion was dom-inating in the particular piston engine. At low load thecycle-to-cycle phenomena cause periodic behavior in

Figure 2. Engine experimental setup with Sendig.

Periyasamy and Alwarsamy 5








Figure 4. Side thrust force at different speed.

Figure 3. Theoretical combustion force.









Figure 5. Piston displacement at different speed.

Figure 6. Cylinder block displacement at different speed.









combustion timing; together with cylinder deviations.This is found responsible for decreasing the operatingregime (Persson et al., 2005). The combustion phenom-enon in the chamber is adverse to producing a con-structive pressure increase in the cylinder. But it isused to increase the unbalanced excess forces on the

kinematic chain, consequently it produces the vibrationand then the amplitude increased. An off-line time-frequency analysis of the cylinder pressure and theresulting knock signal determines the frequency rangewhere the information about the combustion can beextracted is shown in Figure 8. The high rst angular-frequency represents the pressure rise signal of combus-tion process within the same internal combustion engineworking cycle. The low frequency component may berelated to the auto ignition and appears a few crankangle degrees before the top dead centre for every com-bustion cycle. The spectrum has the lower amplitude

and is related to the slow increase of the cylinder pres-sure after the auto ignition. These effects are due to thecombustion pressure generated with the in-cylinder.

If the vibration velocity vector was in the oppositedirection, it will increase the rubbing action between thecylinder liner and compression rings. The energy

released by the combustion as the instantaneousenergy is the estimated source of vibration. This corres-ponds to the squared sum of Fourier coefficients. Thetheoretical displacement for various speeds is differentto each other, since inertia force is the function of theangular displacement and, in turn, the function of speed. The energy released in combustion was uniformand follows quasi-adiabatic heat release. This pressurebecomes the source of vibration and noise. Energyrelease and combustion phenomena are constantlyincreasing for the load as well as speed. The amplitudedepends on combustion, the unbalanced forces acting

Figure 7. Autocorrelation analysis at different speed.









on the reciprocating elements, kinematic chain androtary elements. Minimizing the maximum value of the frequency function of the primary system is veryimportant. The oscillation of the engine has a veryunstable motion over a long combustion cycle.Oscillation decay for a long period and growth for a

long period shows uncertainty of the combustion cycle.In the wave analysis is shown in Figure 9, the peakmode represents the high vibration point, and the com-bustion occurs at top dead centre. A random processwhose spectral density is constant over a very wide fre-quency range is called white noise. If the spectral densityof a process has a signicant value over a narrower rangeof frequencies, but is one which is nevertheless still widecompared with the centre frequency of the band, it istermed a wide-band process. If the frequency range isnarrow compared with the centre frequency it is termeda narrow-band process. Narrow-band processes

frequently occur in engineering practice because real sys-tems often respond strongly to specic exciting frequen-cies and thereby effectively act as a lter. The narrowband frequencies exist in the engine, and sudden loca-lized lower-intensity broad band responses caused bymotorized cylinder pressure. Theoretical values of dis-

placement and experimental values were slightly varied.All theoretical calculations are based on the ideal pres-sure developed in the cylinder, but the actual engineproducing part of the ideal pressure is the reason fordiverging values between the theoretical and experimen-tal displacement.The theoretical model of the engineproposed here was an idea to improve the experimentalvalidations. Deviation in this part is a function of damp-ing characteristics of lubricant used in between theengine block. Overall the displacement, forces, autocor-relation, waveforms and spectrum were useful to iden-tify the engine vibration and stability in combustion.

Figure 8. Amplitude spectrum analysis at different speed.









5. ConclusionsThe in-cylinder pressure induced displacement, Fouriertransformed autocorrelation function and time domainwave form have been used to recognize the uncertaintyof combustion from single point measurements averageengaged with vibration pick-up instruments. The auto-correlation of the engine is capable of spotting combus-

tion effectiveness in the cylinder. Time-domain waveform and the amplitude-spectrum analysis are suitablyaccompanied with the in-cylinder pressure induced dis-placement for identifying the combined effect of com-bustion and inertia forces. A time-domain wave form of rapidly decaying and growing responses for vibrationamplitude is an easy method to identify the instabilityin combustion and vibration knock. A new-fangledapproach is proposed to identify the cycle-to-cycle vari-ation of in-cylinder pressure along with inertia forces of an engine were correlated to combustion stability,vibration and other sources of noise.

FundingThe authors wish to acknowledge the government of Indiafor generous funds sanctioned through TEQIP scheme forpurchasing vibrometer and accelerometer, which is used tomeasure all the vibration parameters.

Notation

A’ Vibration constantC 1 Viscous damping between the piston assembly

and piston ring 0.013C 2 Viscous damping between the piston and cylin-

der wall 0.028C 3 Viscous damping between the cylinder wall and

engine casing 0.011C b Damping coefficient for base

Figure 9. Wave form analysis at different speed.









Á Piston clearance 0.5mmD Bore diameterE Young’s modulus

E[x2] Mean square value of random process underS(o )

k11 Contacting stiffness between piston and cylin-

der wallk2 Linear stiffness of the piston ring

k12 Linear stiffness between piston and cylinderwall

k3 Linear stiffness of cylinder wallkb Stiffness of baseL Stroke lengthl Length of connecting rod

N Speed of the engineP c Combustion pressureP i Inertia force of moving piston assemblyPy Side thrust forceP y Combustion pressure at y angle

r Radius of crankR( t ) Fourier transform of autocorrelation function

(FTAF)S(o ) Spectral density

u Amplitudexp Piston transverse displacementVy Volume at y angleo Natural frequency

o t Crank anglen Excited frequency

zr DisplacementDamping ratio

t Cycle time

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