TL.
Laboratorium voor Scheopshydromocha ArchiefMeketweg 2,2828 CD Deft
- -F 016 -18WSimulation of the Noise Radiated from an Operating Diesel Engine
Nickolas Viahopoulos
Depanment of Naval Architecture
and Marine Engineering
University of Michigan
2600 Draper Road, 214 NA&ME Bldg.
Ann Arbor, MI 48109-2145
Abstract
Numerical methods can be used to compute the vibration of powertrain systems or components and the corresponding radiated noise. Specifically, the finite element method can be utilized in computing the structural vibration[l-31. The
strucan-al response constitutes the boundary conditions for the acoustic analysis. The boundary element method is utilized in computing the radiated noise[4-6]. In order to achieve reliable noise predictions it is important to have accurate information for the structural vibration since it is the source of the noise. In this work a methodology for applying the loads on the structure is presented. k allows to exert as excitation a combination of
measured accelerations, and foces or pressures. It is utilized in
simulating the noise radiated from a running engine and
determining the effects of design changes. Numencal results for
the radiated noise are compared to test data for a baseline
design. The effect of two structural design modifications on the
radiated noise is computed, ai-id conclusions are deducted.
L Introduction
The objective of this work was to simulate numerically the noise radiated from a running engine, and identify tbe impact of
design changes to the emitted noise. A finite element model, including the cylinder bhxk, the cylinder head, the flywheel
housing, the gearcase, and the crankshaft was constructed. lt
was utilized
in computing the structural vibration underoperating load.
Two major sources of excitation wereRichard D. Stark 1111
Automated Analysis Corporation
2805 S. Industrial, Suite 100
Ann Arbor, MI 48104
NCA-Vol. 24, Proceedings of the ASME
Noise Controland Acoustics Division ASME 1997
Yury Kalish
Detroit Diesel Corporation
13400 Outer Drive, West
Detroit, MI 48239-4001
considered; the gas forces and che inertia loads. The gas forces were applied as pressure loads on the cylinder walls and the
cylinder head. The inertia loads were applied as measured iriaxial acceleration at the beanng caps. The necessity of
prescribing the structural vibration at points oc the structure, other than the support locations led to the development of an
"equivalent force" method. In a general purpose finite element software[8] the large mass method is recommended in enforcing the desired motion at the locations of interest[9]. A concentrated mass, at least lO times the structural mass must be attached to
each individual degree of freedom where the motion must be
enforced. Then a force equal to the large mass times the desired acceleration must be applied in that particular degree of freedom as excitation. This methodology works very well for base excitation where the enforced motion is specified at the support
location of the structure. However, this is not applicable to the problem of interest, if the large mass method is used in
enforcing the accelerations at the beanng caps, the structural
normal modes of the engine will be altered and the natural
frequencies will be shifted. An initial attempt to utilize this approach resulted in normal modes for the engine block which did not correlate with the available test data. Therefore, the necessity to perform this analysis led to the development of an
"equivalent force" method[ 141. A methodology was developed which computes an equivalent force
for each one of the
prescribed degrees of freedom. Those equivalent forces when applied on the structural finite element model as excitation,
result in the desired vibration at the measurement locations. In
attached to the location of enforced displacement. Therefore.
the modal basis of the structure is ao altered. In addition the computation of the structural vibration by the equivalentforce method was inteerated within the acoustic boundary element
analysis process. Thus, vibration test data, structural finite element analysis, and acoustic boundary element noise computations were combined into a single numencal process. The dynamic characteristics of the structure are represented in terms of the normal modes and the natural frequencies. This information comprises part of the input to the combined analysis process. The measured accelerations and the pressure
combustion loads are also parts of the input. The equivalent
force method computes the structural vibration based on: The norma] modes and natural frequencies of the structure. The prescribed acceleration and pressure loads.
The structural damping.
The vibration results on the outer surface of the structure are utilized as boundary conditions for the acoustic analysis. Since the equivalent force method has been integrated within thenoise pedictiori software, there is no need for an external transfer of
data. The computed vibration, the discretization of the structural model, and the discretization of the rristic boundary element model are utilized in computing the emitted noise. A
brief technical background, the application, and the validation of
this approach in simulating the noise radiated fiuui the block of
an operating diesel engine are presented.
II. Mathematical Formulation and Numerical Implementation
¡1.1. Euivalenz Force Method
In order to physically present how the large mass method operates. and in order to demonstrate the error which is introduced in the modal basis, a simple simply supported beam
structure can be used (Figure 1). In this example thevibration
along the y-direction in the middle of the beani is considered to be prescribed. The large mass is attached to the corresponding degree of freedom. Then artificial nodes are generated in the
normal modes of the system. In the equivalent force method a mechanical load is applied instead along the prescribed degree of freedom (d.o.f.) (Figure 2) which will result in the desired motion. The process is similar to an algorithm utilized in enforcing constraints in a non-linear static and dynamic structural response process[ll-121.
Figure 1.1 .arge Mass Method for a Simply Supported Beam
Feq
Figure 2. Equivalent Force Method for a Simply Supported Beam
The values for the equivalent forces can be derived from information associated with the behavior of the structure under a
unit load applied at each location where the accelerations are measured[l4). For simplicity acceleration will be considered to
be measured along two degrees of freedom (d.o.f.) in the systerit
1thand j. By applymg a unit load on each one independenth.
information about the corresponding vibration induced at the two Uil1 JU(j
and i
4jiJ t.Uij displacements at the ith andj d.o.f. due to the ori the ith and th do.f. respectively. Then the can be derived[14]:
feil
fUmi.f
ffUin1li
fd Jd J
fejJ
=1,iJ - i.in
where
f
= equivalent forces applied on the i and j do.f., , = measured vibration. If mechanical loads arepart of the excitation in addition to the accelerations, then Um,
= vibration induced by the mechanical loads only. The equivalent forces can be combined with the external mechanical loads and comprise the excitation in the finite element system of equations:
[w2[MJiw[C1+[K]]{u}= {f}
(2)where [MI=mass matrix, (CI=damping matrix, [KJ=stiffness matrix, {u} =displacement of vibration, (f) = force exritatii
and o =frequency of analysis x 2it.
11.2. miei ration with Acousric Boundary Elemenjts
The structural vibration computed through the equivalent force method comprises the boundary conditions for the noise
analysis. The boundary element method is used for acoustic computations[lO). It is based on the principle that the vibration
is the source for the generation of noise. Through an integral
locations cari be extracted.
L
[Uil
are the d)naniic unit led applied equivalent forces
equation it associates the radiated noise to the vibration on the
surface of the structure which generates the noise.
pdr
1(F)
(3)
Sa
where 6p, &ip = primary acoustic variables on the surface of the
vibrating structure, the former is related to the acoustic pressure and the latter is associated with the vibration velocity, and = position vectors associated with a point on the surface of the structure and the data recovery point where the noiselevel is
being computed. and G = Green's function. The primary vanables are computed first in the boundary element
methodology. A linear system of equations is generated and all the primary variables are computed from the vibration
information. Then Equation 3 is utilizedto compute the acoustic
response at any point in space.
A simple representation of how vibration and acoustic c*xnputations are linked can be demonstrated by two single
degree of freedom systems, one representing the structure, and
another representing the acoustic medium. Fs
Xs
Figure 3. Single Degree of Freedom System Representingthe Structure
Ka
Xs Xa
Figure 4. Single Degree of Freedom System Representing the Acoustic Medium
In Figures 3 and 4. Ks = stiffness of structure. Ms = mass of
structure, Xs = structural vibration, Fs = structural excitation.
Ka = stiffness of acoustic
system. Ma = mass of acoustic stiffness, Xa = response of acoustic system, representing the radiated noise. The finite element method is used to model the structural system. The equivalent force method provides the excitation, and the structural vibration (Xs) is computed first. Then it is applied as excitation to the acoustic system. and theboundary element method is employed in computing the acoustic
response (Xa) (i.e. noise).
The equivalent force method has been integrated with the acoustic prediction software. Since a structural finite element library s not available within the acoustic code, instead of
assembling or importing the structural matrices, the normal
modes and natural frequencies are imported and represent the
structural system. Once the vibration is computed (using
Equations I and 2), the acoustic velocitiesare generated on the surface of the boundary element model using the relationship:
Mode % Diff 3.5 2 5.5 3 -08 4 -0.6 5
02
6 -0.3Table I. Correlation Tables between Test and Nuniencal Normal Modes
The results show good correlation between test and finite
element analysis. The largest differences were observed at
Mode 7 8 9 10 Il 12
% Diff 4.3 5.8 4.8 -0.2 0.1 1.6
u =nu (4)
a st
where ua = acoustic velocity. , = unit normal, and ¿ =
st
structural velocity. The structural and the acoustic models do
not require equivalent discretization or coinciding nodes. A mapping technique is used in generating the acousticvelocities
from the structural vibration. Then the boundary element
method can compute the radiated noise. Since the engine
constitutes a stiff structure compared to the surrounding medium (air). the structural and the acoustic problems are dc-coupled.
III. Application, Validation
'rhe equivalent force method was utilized inperforming the structural vibration and the acoustic analysis for an engine block
of an inline six cylinder diesel engine. The measured triaxial
acceleration at the bearing caps, and the combustion pressure loads applied on the cylinder head and the cylinder walls comprised the excitation. The equivalent force method has been incorporated into a boundary element acoustic prediction
scheme. The normai modes and the natural frequencies of the structure are imported into the acoustic prediction software from
a structural finite element modal analysis. The test data for the
acceleration, and other force data are alsopart of the input. The computed radiated acoustic power was compared successfully to test data. The effect on the radiated noise of two design changes introduced to the engine assembly was computed and the information was utilized in making decisions with respect to the design.
A structural finite element model including the cylinder
block, the cylinder head, the flywheel housing, the gearcase. and the cramkshaft was constructed. A modal analysis was performed initially to determine the natural frequencies and the mode shapes. Table I presents a comparison summary for the percentage of difference in the natural frequencies between the first thirteen measured and the computed normal modes.
nodes dominated by total block motion. The skirt modes demonstrated very good correlation. The modal basis was computed up to a frequency of 2500Hz. and sixty six normal
modes were extracted. The modal infoqm,ation was imported into the acoustical analysis code. The combination of measured tnaxial data at the bearing caps. and combustion pressure loads
at the cylinder walls and the cylinder head comprised the excitation. The equivalent force method wa.s utilized in
computing the vibration of the block between O - 2,500Hz at 5Hz increments. The vibration of the outer surface of the block was
mapped on the acoustic boundary element model. This process was also automated and there was no need for external exchange
of data. The acoustic boundary element model represents the
geometry of the outer surface of the block. Two data recovery
planes were defined at one meter distance from the block. They
were positioned ax its left side and in front of it. The data recovery planes represent the microphone locations in the
numerical simulation. Figure 5 presents the acoustic boundary element model and the two data recovery planes. The entire analysis was performed for two load cases representing two
combinations of RPM and engine load (1950RPM al 50% load. and 2100RPM for 100% load).
Figure 5. Acoustic Boundary Element Model and Data Recovery Planes
Test data were available for the latter, and ail the results
presented here concern the latter case. Figure 6 presents results for the sound pressure level ata single point in the front of the
engine. The results demonstrate similar trends and similar absolute values for the sound pressure level. The correlation is
better for lower frequencies (below 1600Hz). This is expected
because although the analysis was performed up to 2,500 Hz the modal information was extracted only up to the saine frequency. Therefore, a modal truncation error was introduced in the high
frequency range of the analysis. In addition, the test data
included noise from engine accessories which were not present
Ar
Figure 7. Additional Ribbing on the Block
Figure 8. Ladder Frame Stiffener
ed r,o
n g
e O w,-
n c e e
r.rs r. (1)
Figure 6. Numerical and Test Data for the Acoustic SPLat
in the numerical model. Thecorrelation of the acoustic response between analysis and test datawas considered very satisfactory.
The effect of two design changes ori the radiated noise was
jetermined through numerical simulations.
Specifically, the
effect of additional ribbing on the block (Figure 7) and the influence of a ladder frame (Figure 8) were analyzed.
The
veraJi radiated sound power did no
change significantly
between the baseline and the two modified designs.
The changes altered the radiated power by +0.5dB and -02dB. The
change in the sound power per 1/3 octave frequency band is presented in Figure 9. IBI inc L § §
Figure 9. Radiated Sound
Power per 1/3 Octave Frequency Band
for Three Desirns
,7.
ma na ¡nra
4t.
gI
II a ,ii. aaa
a ir,a .xFigure II. Change
in the Acoustic Response at the LefiSide of the Engine
In addition the change in the sound pressure level
between the
baseline and the two mcx±fled
designs is presented for the two
points located in the front and the left side of the engine (Figures10 and Il respectively). 1V. Conclusions
The integration of the equivalent force method with ari acoustic boundary element formulation was utilized in computing acoustic results for the noise radiated from an
operating six cylinder Diesel engine.
A combination of measured acceleration and combustion pressures was providing the excitation. Numerical results were successfullycompared to test data. The effect of design changes on the radiated noise was
also computed. This application
demonstrates how the equivalent force method can be utilized to integratetest data into numerical analysis. In addition, it identifies how the structural finite element method can be combined with acousticboundary elements in perfirtirg
a structural-acoustics simulation. The correlation to test data validatesthe numerical process. Finally. by computing numerically the effect of design changes
cm the
radiated noise, the power of the numerical simulations was
demonstrated. lt allows to identify the impact of modifications
1 s,, J 4 -is
a
"la
a wi,a I, Ga
nia a WT7 a Bi7* a
Q_ pREFERENCES
1.
N. Lalor and M. Petvt. "Modes of Eneine Structure
Vibration as a Source of Noise," SAE Paper 750833, Milwaukee, 1975.N. Labor and M. Petyt, "Noise Assessment of Eneine
Structure Designs by Finite Element Techniques," Engine Noise, Excitation, Vibration and Radiation, Edited by R.
Hickling and M.M. Kamal, Plenum Press, 1982.
MG. Milsted, T. ang, RA. Hall, "A Numerical Method for Noise Optimization of Engine Structures," Journal of
Automobile Engineering. Vol. 207, pp. 135-143.
S.M. Kirkup and R.J. Tyrrell, "Computer-Aided Analysis of
Engine Noise," International Journal of Vehicle Design. Vol. 13, No.4. 1992, pp. 388-402.
G.H. Koopman and H. Benner, "Method for Computing the
Sound Power of Machines Based on
the Helmholtz Integral." The Journal of the Acoustical Society of America, Vol. 7d, No. 1, pp. 78-89.M. Hazel, C. Norrey, H. Kikuchi, and D. Tres, "Using
Predictive Acoustic Analysis to Evaluate Noise Issues in
Under Hood Applications," SAE Paper 960145,
International Congress & Exposition, Detroit, Michigan,
February 1996.
K. Ochiai, "Dynamic Behavior of Engine Structure Vibrations," Engine Noise, Excitation. Vibration, and
Radianon, Edited by R. Hickling and M.M. Kamal. Plenum Press, 1982.
"MSCINASTRAN, Handbook for Dynamic Analysis." M.A. Gockel, Editor, June 1983, The MacNeal . Schwendier Corporation.
"MSC/NASTRAN Dynamics Seminar Notes," October 1992. The MacNeal-Schwcndler Corporation.
IO. "COMET/Acoustics User's Manual," Version 3.0, October
1995, Automated Analysis Corporation.
II.
M. M. Bernitsas, N. Viahopoulos. 'Three-Dimensional Nonlinear Static of Pipelaying Using Condensation in an Incremental Finite Element Algorithm,' Computers andStructures, Vol. 35, No. 3, pp. 195 . 214, 1990.
M. M. Bemitsas, N. Vlahopoulos, 'Static Non-Linear Three-Dimensional Analysis of a Riser Bundle by a Substructuririg and Incremental Finite Element Algonthni, International Journal for Numerical Methods in Engineering, Vol. 28, 1989, pp. 2517 - 2540.
K. J. Bathe, "Finite Element Procedures in Engineering
Analysis,' Prentice - Hall, Inc. 1982.
V1ahculos, R. D. Stark HI, W. Kargus 1V, "A New
Methodo1og' of Applying Measured Acceleration and Forces as Excitation on Powertrain Models for noiseon the performance of a system without the need to construct any Prediction." Symposium on Complexity in Acoustics, 19% prototype. It can therefore reduce the design cycle and lead to A.SME International Mechanical Engineering Confere
