Research Article Vibration Transfer Path Analysis...

Research ArticleVibration Transfer Path Analysis and Path Ranking forNVH Optimization of a Vehicle Interior

B Sakhaei1 and M Durali2

1 Department of Mechanical Engineering Sharif University of Technology and NVH Department ofIran Khodro Powertrain Company (IPCO) Tehran 11365-11155 Iran

2Department of Mechanical Engineering Sharif University of Technology Tehran 11365-11155 Iran

Correspondence should be addressed to M Durali duralisharifedu

Received 19 October 2012 Accepted 19 November 2012 Published 17 June 2014

Academic Editor Hamid Ahmadian

Copyright copy 2014 B Sakhaei and M Durali This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

By new advancements in vehiclemanufacturing evaluation of vehicle quality assurance has got amore critical issue Today noise andvibration generated inside and outside the vehicles are more important factors for customers than before So far several researchershave focused on interior noise transfer path analysis and the results have been published in related papers but each method hasits own limitations In present work the vibration transfer path analysis and vibration path ranking of a car interior have beenperformed As interior vibration is a source of structural borne noise problem thus the results of this research can be used topresent the structural borne noise state in a vehicleThe proposedmethod in this paper does not need to disassemble the powertrainfrom the chassis The procedure shows a good ability of vibration path ranking in a vehicle and is an effective tool to diagnose thevibration problem inside the vehicle The simulated vibration spectrums in different speeds of the engine have a good compliancewith the tested results however some incompatibilities exist and have been discussed in detail The simulated results show thestrength of the method in engine mount optimization

1 Introduction

Noise and vibration which are perceived by passengers ina vehicle are important in the pleasantness of customersTransfer path analysis of noise in a vehicle is a subject thatmany researchers from the 90s up to now have worked onit to find the root cause of a noise problem in a vehicleBy taking help of these methods the paths of noise whichusually starts from engine mounts through body and endsto passenger compartment are investigated Transfer pathanalysis can find the weak points of every path of the vehiclethen the paths of high noise are identified and ranked AnNVH engineer then is able to find the problem and find adesign solution for making the transmission of noise better

The earliest work in this subject refers to Bendat andPiersol [1] in 1980 which used coherence analysis of the noisepaths to find various contributions In late 80s an alternatemethod was proposed which considers the system as asource-transfer function-receiver and assumes that the noise

in a vehicle compartment is a linear summation of differentpaths In this method the response in target point in vehiclecompartment is determined by multiplication of interfaceloading and transfer function from engine mount to thattarget point Then noise contributions are summed to get theoverall noise in the vehicle [2 3] As it is clear the mainchallenge in this method is measuring the interface loads [3]

Because of complexity in measuring the excitation forceson interfaces the indirect procedures were developed Inthese methods there is no need for direct measurementof interfacing forces Instead FRFs between all points ofsource and the FRFs between source and receiver (targets)are measured Then by inversing the FRF matrices andmultiplying it with the operational accelerations at the inputside the shares of each path from overall noise are calculated[4] Althoughmuch advancement has promoted thismethodand the accuracy of the results has been improved indirectmeasurements have the limitations of cost and time of testsIn 2008 a new method based on operational modal analysis

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 697450 5 pageshttpdxdoiorg1011552014697450

2 Shock and Vibration

was proposed This method named operational path analysis(OPA) which shortened the test time but it had accuracyproblem because excitation in one direction often has sideeffect responses in other directions and putting this methodinto effect needs high experience [5]

Multilevel TPA has the strength of indirect measurementbut can be done in a shorter time relative to indirect methodIt was first introduced in 2002 by Eisele et al [6] whichanalyzed the interior structural noise in a vehicle Howeverthe method is effective in prediction of the critical paths butless attention has been paid to it

Although almost all publications in interior noise transferpath analysis have focused on interior noise simulation thereis no work on the interior vibration simulation In this paperan interior vibration simulation of the vehicle for the first timewas done The method was based on multilevel TPA and theresults show that this method has the ability of TPA analysiseffectively It is a fast method which rarely has the problemof measurement noise interfering The results show thatvehicle interior vibration simulation has good potential ofengine mount optimization behaviour By this method alsovibration fault diagnosis is more effective than conventionalnoise path ranking methods

2 General Formulation

Vibrations in a vehicle mostly transfer from engine mountlocations through vibration transfer paths into the body ofthe car and finally receives to the target locations in passengercompartment Elements in vibration generation and transferinto the vehicle are divided into two major parts active andpassive elements IC engine is an active vibration source andthe engine mounts and body transfer functions from mountlocations to target points in the vehicle compartment arepassive elements

In passive part of vibration transfer each enginemount ineach vehicle principal coordinate comprises one path Thusfor a vehicle with 3 engine mounts there are 9 transfer pathsThese engine mount paths beside relative body and chassistransfer functions send vibration energy to the passengercompartment

Basic equation in transfer path analysis assumes thatthe total noise and vibration felt at passenger position aresuperposing the contribution of each path Equation (1)implies the relation [4] as follows

119910 (119891) =

119899

sum

1

119910119894(119891) (1)

where 119910(119891) = vibration at passenger location and 119910119894(119891) =

contribution of vibration from each pathThe system approach to the transfer path analysis explains

that the partial contribution 119910119894(119891) of the vibration in the

target point is a product of input force of the active part andthe transfer function between the interface and the receiverlike

119910119894(119891) = FRF

119894119896(119891) lowast 119865

119894(119891) (2)

By combining (1) and (2) general basic equation oftransfer path analysis is given by

119910 (119891) =

119899

sum

119894=1

FRF119894119896(119891) lowast 119865

119894(119891) (3)

As it is clear from (3) it is assumed that vibration transferpaths have linear behaviour Also it is obvious that transferpath analysis is performed in frequency region In thismethod as soon as any problem arises in overall amplitude ofvibration the different path contribution will be investigatedand the responsible path for that problem will be identifiedAs each contribution is equal to the product of the input forceand the transfer function then it is easier to locate the exactlocation of problem

Multilevel TPA is classified in fast TPA groups ofmethodsin which the contribution to a target response is a chain oflinked subsystems In this method few FRF measurementsare being performed and then bymultiplying the input signalto this chain the output will be the vibration share of eachpath at target location (4) Consider

119910119894(119891) = [119867

1] [1198672] [1198673] sdot sdot sdot 119865

119894(119891) (4)

where 119865119894(119891) = input forces at engine mount interface

By noting (4) the basic equation of multilevel TPA can bewritten as follows

119886interior = 119865119894 (119891) times119886interior119886body (119891)

997888rarr119886interior119865body (119891)

= 119886engine (119891) times119886body (119891)

119886engine (119891)times119865body (119891)

119886body (119891)

times119886interior (119891)

119865body (119891)

(5)

According to (5) for evaluation of 119886interior from each pathit is needed to measure three transfer functions of mounttransmissibility apparentmass and chassis transfer functionrespectively

3 Interior Vibration Simulation ofa Sedan Car

For evaluation of interior vibration in a sedan car com-partment a procedure of interior vibration simulation wasapplied based on multilevel TPA The vehicle was equippedwith a four-cylinder engine of 17 L The engine and gearboxwere installed on the chassis with three mounts two rubbermounts and one hydraulic mount The mounts are namedRH mount LH mount and Rear mount The RH mount wasa hydraulic mount and LH and Rear mounts were rubbermounts Figure 1 shows the transverse engine mountingsystem [7]

According to (5) two transfer functions of apparent massand bodyweremeasured by presence of engine on the vehicleIn some publications the transfer function was measuredwithout engine As it was tested (the results have not been

Shock and Vibration 3

LH mount

Roll axis

RH mount

Drive shafts axis

Rear mount

Figure 1 Transverse engine mounting system [7]

P1P2

P3

Figure 2 P1 hammer excitation P2 triaxial accelerometer for bodytransfer function and P3 triaxial accelerometer for chassis apparentmass [7]

reported) transfer functions without engine caused signifi-cant error in calculating the contributions

All of the measurements were performed with a BampK3570 data acquisition with 25Khz range FFT analyzer Thereare two 4524 BampK triaxial accelerometers and a piezoelectricimpact hammer of maximum 5KN force range The signalswere recorded with a 7Hz high pass filter to prevent doublehit error of impact hammer

First the body transfer function (119886interior(119891)119865body(119891))was measured by exciting the engine mount location with animpact hammer The impact was applied on the body side ofengine mount and the force was measured with piezoelectricelement of hammer Simultaneously a triaxial accelerometerwas installed on the vehicle compartment floor (point P2 inFigure 2) As it was mentioned the excitation was appliedat presence of engine and gearbox at original location Thefrequency span of the body transfer function was taken upto 800Hz because only the interior vibration of the vehiclewas importantThe frequency resolution of FFT analyzer was025Hz

Figure 3 shows the body transfer function between RHmount location and vehicle compartment on passenger footbottom at different principal directions

Apparent mass also was measured at engine mountlocations A triaxial accelerometer was installed on body nearthe engine mount location of the vehicle and the impacthammer applied the force beside the accelerometer position

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

40 140 240 340 440 540 640

Body transfer XBody transfer YBody transfer Z

Freq (Hz)

(m sminus

2N

dB)

Figure 3 Body transfer function of RH mount at different direc-tions

70

60

50

40

30

20

10

0

minus10

minus20

Apparent mass XApparent mass YApparent mass Z

40 140 240 340 440 540 640

Freq (Hz)

(Nm

sminus2

dB)

Figure 4 Apparent mass of RH mount region

(Figure 2) By calculating the ratio of 119865body(119891)119886body(119891) anapproximation of apparent mass could be got (Figure 4)

Mount transmissibility is the ratio of acceleration on bothsides of the mount on engine and body sides The mounttransmissibility was calculated by installing one accelerom-eter on engine side of each mount and another accelerometeron chassis side of mounts Input and output acceleration oneach enginemount were measured during a run-up of enginespeed on the chassis dynamometerThe 3rd gear was engagedduring the test and enginewas under full load condition (fullyopen throttle) Figure 5 shows the test setup to measure themount transmissibility on chassis dyno

The coherency spectrum of the mount transmissibilitysignal showed that only the main orders of the engine werecoherent Then only the transmissibility of these main orderswas taken into account

With a Matlab code the transmissibility of each mount ateach direction was calculated at different engine speeds

By multiplying the derived transfer functions with theinput acceleration on engine side and summing the vibrations


(a) (b)

Figure 5 Test setupmdash(a) accelerometer installation on both sides of engine mount (b) vehicle on chassis dyno

from different paths the interior acceleration at passengerfoot bottom could be simulated

For comparison between simulated and real vibration attarget point a triaxial accelerometer also mounted at thetarget point (Figure 2 P3) and simultaneously during therun-up test the vibration was measured The results of themeasurements are expressed in the next section

4 Results

Calculation of mount dynamic stiffness in real conditions ofmounts preload temperature and under engine operation isone valuable benefit of multilevel TPA while dynamicmountstiffness measurement in test lab by a power shaker usuallyhas large error

Mount dynamic stiffness will be in hand by multiplyingthe mount transmissibility and apparent mass at differentfrequencies (see (5))

Figure 6 shows themount dynamic stiffness of RHmountThemount dynamic stiffness decreases with frequency whichcomplies with conventional engine mounts [6]

Figure 7 shows the comparison between simulated andmeasured overall accelerations at target point There is acomplete accordance between the trends of simulated andreal signal but also still some differences exist

The differences between measured and simulated vibra-tion signal in the vehicle come from the damping of thematerials which covered the chassis of the vehicle on thefoot bottom region It was an asphalt layer The property ofdamping of asphalt in this region is nonlinear which dependson temperature As described earlier the linear transferfunction of body was taken into account in the analysis thenthe damping nonlinear behaviour of this layer cannot beconsidered in the analysis

The effect of damping also grows with the velocity ofexcitationTherefore at higher speeds themeasured vibrationcurve in Figure 7 was below the simulated results

These evidences show that the damping of body transferpaths has nonlinear frequency dependent behaviour and thisproperty should be studied with more care

40 140 240 340 440 540 640

Freq (Hz)

50

40

30

20

10

0

minus10

minus20

minus30

minus40

minus50Dyn

amic

mou

nt st

iffne

ss(N

m sminus

2dB

)

Kd119909Kd119910Kd119911

Figure 6 Dynamic mount stiffness derived by simulation

50

45

40

35

30

1200 2200 3200 4200 5200

Overall level test resultOverall level simulation result

Engine speed (rpm)

Ove

rall

vibr

atio

n(m

sminus2

dB)



1200 2200 3200 4200 5200

50

5

Overall amplitudeEngine mount

Gearbox mountTorque strut mount

Engine speed (rpm)

Am

plitu

de o

f vib

ratio

n(m

sminus2

dB)

Figure 8 Dynamic mount stiffness obtained by simulation

Figure 8 shows the contribution of each mount in overallvibration level The LH mount has higher share of vibrationin the compartment during engine run-up especially from1000 to 3500 rpm although RHmount behaviour in vibrationtransmission is desirable

This shows that LH mount needs to be modified Thensoftening of the LH mount can be a solution to this problemOf course the side effect of mount softening on rigid bodydisplacements of engine should be studied

5 Conclusion

Although there weremany advancements in the transfer pathanalysis of noise in the vehicle rare publications exist onvibration simulation of vehicle interior Interior vibrationof a vehicle can be taken as a representative of structuralborne noise Also vibration simulation of a vehicle interioris a powerful tool for engine mounts optimization Asit was proved one can give applicable modifications onengine mount system to make the vibration behaviour betterVibration TPA can realize the dynamic weak points of bodychassis

The results of vehicle interior vibration simulation andreal measurements of this quantity showed a good com-pliance The existing differences come from the nonlineardamping effect Because of the linear assumption of bodytransfer functions in this method these differences areinevitable

A complete study on damping ratio effect on the sim-ulated signal and also detailed mount optimization by thismethod will be performed in the next work Also furtherinvestigations are needed to be made on the effect of differentgears on the amount of vibration at target point

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the IPCO (Iran Khodro Power-train Company) for supporting this research

References

[1] J S Bendat and A G Piersol Engineering Applications of Corre-lation and Spectral Analysis JohnWiley amp Sons New York NYUSA 1980

[2] J Verheij Multipath sound transfer from resiliently mountedshipboard machinery [PhD thesis] Technische PhysischeDienst TNO-TH Delft The Netherlands 1986

[3] D de Vis W Hendricx and P van der Linden ldquoDevelopmentand integration of an advanced unified approach to structureborne noise analysisrdquo in Proceedings of the 2nd InternationalConference on Vehicle Comfort pp 465ndash473 ATA October1992

[4] K Janssens P Mas L Gielen P Gajdatsy and H van der Auw-eraer ldquoA novel transfer path analysis method delivering a fastand accurate noise contribution assessmentrdquo in Proceedings ofthe SAE Symposium on Ineternational Automotive TechnologySAE Paper no 2009-26-047 2009

[5] P Gajdatsy K Janssens W Desmet and H van der AuweraerldquoApplication of the transmissibility concept in transfer pathanalysisrdquoMechanical Systems and Signal Processing vol 24 no7 pp 1963ndash1976 2010

[6] N W Alt N Wiehagen and M W Schlitzer ldquoInterior noisesimulation for improved vehicle soundrdquo in Proceedings of theSAE Noise and Vibration Conference and Exposition SAE Paperno 2001-01-1539 2001

[7] J C Brown A J Robertson and S T Serpento MotorVehicle Structures Concepts and Fundamentals ButterworthHeinemann Oxford UK 2002

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Advances inOptoElectronics


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Navigation and Observation



DistributedSensor Networks



was proposed This method named operational path analysis(OPA) which shortened the test time but it had accuracyproblem because excitation in one direction often has sideeffect responses in other directions and putting this methodinto effect needs high experience [5]

Multilevel TPA has the strength of indirect measurementbut can be done in a shorter time relative to indirect methodIt was first introduced in 2002 by Eisele et al [6] whichanalyzed the interior structural noise in a vehicle Howeverthe method is effective in prediction of the critical paths butless attention has been paid to it

Although almost all publications in interior noise transferpath analysis have focused on interior noise simulation thereis no work on the interior vibration simulation In this paperan interior vibration simulation of the vehicle for the first timewas done The method was based on multilevel TPA and theresults show that this method has the ability of TPA analysiseffectively It is a fast method which rarely has the problemof measurement noise interfering The results show thatvehicle interior vibration simulation has good potential ofengine mount optimization behaviour By this method alsovibration fault diagnosis is more effective than conventionalnoise path ranking methods

2 General Formulation

Vibrations in a vehicle mostly transfer from engine mountlocations through vibration transfer paths into the body ofthe car and finally receives to the target locations in passengercompartment Elements in vibration generation and transferinto the vehicle are divided into two major parts active andpassive elements IC engine is an active vibration source andthe engine mounts and body transfer functions from mountlocations to target points in the vehicle compartment arepassive elements

In passive part of vibration transfer each enginemount ineach vehicle principal coordinate comprises one path Thusfor a vehicle with 3 engine mounts there are 9 transfer pathsThese engine mount paths beside relative body and chassistransfer functions send vibration energy to the passengercompartment

Basic equation in transfer path analysis assumes thatthe total noise and vibration felt at passenger position aresuperposing the contribution of each path Equation (1)implies the relation [4] as follows

119910 (119891) =

119899

sum

1

119910119894(119891) (1)

where 119910(119891) = vibration at passenger location and 119910119894(119891) =

contribution of vibration from each pathThe system approach to the transfer path analysis explains

that the partial contribution 119910119894(119891) of the vibration in the

target point is a product of input force of the active part andthe transfer function between the interface and the receiverlike

119910119894(119891) = FRF

119894119896(119891) lowast 119865

119894(119891) (2)

By combining (1) and (2) general basic equation oftransfer path analysis is given by

119910 (119891) =

119899

sum

119894=1

FRF119894119896(119891) lowast 119865

119894(119891) (3)

As it is clear from (3) it is assumed that vibration transferpaths have linear behaviour Also it is obvious that transferpath analysis is performed in frequency region In thismethod as soon as any problem arises in overall amplitude ofvibration the different path contribution will be investigatedand the responsible path for that problem will be identifiedAs each contribution is equal to the product of the input forceand the transfer function then it is easier to locate the exactlocation of problem

Multilevel TPA is classified in fast TPA groups ofmethodsin which the contribution to a target response is a chain oflinked subsystems In this method few FRF measurementsare being performed and then bymultiplying the input signalto this chain the output will be the vibration share of eachpath at target location (4) Consider

119910119894(119891) = [119867

1] [1198672] [1198673] sdot sdot sdot 119865

119894(119891) (4)

where 119865119894(119891) = input forces at engine mount interface

By noting (4) the basic equation of multilevel TPA can bewritten as follows

119886interior = 119865119894 (119891) times119886interior119886body (119891)

997888rarr119886interior119865body (119891)

= 119886engine (119891) times119886body (119891)

119886engine (119891)times119865body (119891)

119886body (119891)

times119886interior (119891)

119865body (119891)

(5)

According to (5) for evaluation of 119886interior from each pathit is needed to measure three transfer functions of mounttransmissibility apparentmass and chassis transfer functionrespectively

3 Interior Vibration Simulation ofa Sedan Car

For evaluation of interior vibration in a sedan car com-partment a procedure of interior vibration simulation wasapplied based on multilevel TPA The vehicle was equippedwith a four-cylinder engine of 17 L The engine and gearboxwere installed on the chassis with three mounts two rubbermounts and one hydraulic mount The mounts are namedRH mount LH mount and Rear mount The RH mount wasa hydraulic mount and LH and Rear mounts were rubbermounts Figure 1 shows the transverse engine mountingsystem [7]

According to (5) two transfer functions of apparent massand bodyweremeasured by presence of engine on the vehicleIn some publications the transfer function was measuredwithout engine As it was tested (the results have not been


LH mount

Roll axis

RH mount

Drive shafts axis

Rear mount


P1P2

P3







0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

40 140 240 340 440 540 640


Freq (Hz)

(m sminus

2N

dB)


70

60

50

40

30

20

10

0

minus10

minus20


40 140 240 340 440 540 640

Freq (Hz)

(Nm

sminus2

dB)








(a) (b)




4 Results








40 140 240 340 440 540 640

Freq (Hz)

50

40

30

20

10

0

minus10

minus20

minus30

minus40

minus50Dyn

amic

mou

nt st

iffne

ss(N

m sminus

2dB

)

Kd119909Kd119910Kd119911


50

45

40

35

30

1200 2200 3200 4200 5200


Engine speed (rpm)

Ove

rall

vibr

atio

n(m

sminus2

dB)



1200 2200 3200 4200 5200

50

5



Engine speed (rpm)

Am

plitu

de o

f vib

ratio

n(m

sminus2

dB)




5 Conclusion






Acknowledgment


References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










LH mount

Roll axis

RH mount

Drive shafts axis

Rear mount


P1P2

P3







0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

40 140 240 340 440 540 640


Freq (Hz)

(m sminus

2N

dB)


70

60

50

40

30

20

10

0

minus10

minus20


40 140 240 340 440 540 640

Freq (Hz)

(Nm

sminus2

dB)








(a) (b)




4 Results








40 140 240 340 440 540 640

Freq (Hz)

50

40

30

20

10

0

minus10

minus20

minus30

minus40

minus50Dyn

amic

mou

nt st

iffne

ss(N

m sminus

2dB

)

Kd119909Kd119910Kd119911


50

45

40

35

30

1200 2200 3200 4200 5200


Engine speed (rpm)

Ove

rall

vibr

atio

n(m

sminus2

dB)



1200 2200 3200 4200 5200

50

5



Engine speed (rpm)

Am

plitu

de o

f vib

ratio

n(m

sminus2

dB)




5 Conclusion






Acknowledgment


References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)




4 Results








40 140 240 340 440 540 640

Freq (Hz)

50

40

30

20

10

0

minus10

minus20

minus30

minus40

minus50Dyn

amic

mou

nt st

iffne

ss(N

m sminus

2dB

)

Kd119909Kd119910Kd119911


50

45

40

35

30

1200 2200 3200 4200 5200


Engine speed (rpm)

Ove

rall

vibr

atio

n(m

sminus2

dB)



1200 2200 3200 4200 5200

50

5



Engine speed (rpm)

Am

plitu

de o

f vib

ratio

n(m

sminus2

dB)




5 Conclusion






Acknowledgment


References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1200 2200 3200 4200 5200

50

5



Engine speed (rpm)

Am

plitu

de o

f vib

ratio

n(m

sminus2

dB)




5 Conclusion






Acknowledgment


References










RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Vibration Transfer Path Analysis...

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