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Acoustic Applications in Mechanical Engineering:

Structure-Borne Sound versus Air-Borne Sound

Marold Marold MoosrainerMoosrainerCADFEM GmbHCADFEM GmbH

2009 2009 JulyJuly 6th 6th

Acoustic Applications in Mechanical Engineering

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Agenda

§ Introduction into acoustics: common phrases, basic equation§Solving structural vibration problems with ANSYS§Solving structure-borne sound problems with ANSYS SBSOUND§Solving air-borne sound problems with ANSYS (FEM) §Solving air-borne sound problems with WAON (BEM)


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Introduction§machine acoustics§ speed of sound, wavelength, frequency§ basic concept of solving acoustic

problems by simulation


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Some phrases of machine acousticsdirect noise generation: flow acoustics (CFD + acou.)

indirect noise generation: vibroacoustics(FEM + acou.)

oscillating forces

transient flow

machine

machine structure

fluid, e.g. air

building structure

• structure-borne sound: a sound wave propagating in a solid medium• air-borne sound: a sound wave propagating in air


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Speed of sound – wavelength – frequency§Note that we solve the acoustic wave equation to model reflection,

scattering, absorption and thus we have to resolve each wave in its spatial pattern § important equation:

§ air: c≈340m/s, f=1000Hz → λ=0.34m§ water: c≈1500m/s, f=1000Hz → λ=1.5m

§ rule of thumb FEM, BEM: 6....10 linear elements per wavelength§ required elements for a domain of characteristic size a:

FEM (volume mesh): ~O(N3) BEM (surface mesh): ~O(N2)§ large acoustic FEM problem: 10M DOFs

large acoustic BEM problem: 20k DOFslarge acoustic FMBEM problem: 200k DOFs

fc λ=


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Basic concept of solving acoustic problems by simulation

Signal analysis (MBS, test, FFT)

StructureStructure--borne sound analysis borne sound analysis (FEM)(FEM)

AirAir--borne sound analysis borne sound analysis (FEM, BEM)(FEM, BEM)

Psycho acoustics (e.g. DIN 45631)

use Nuse N55 percentile values percentile values for transient noisefor transient noise


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Solving Structural Vibration Problems with ANSYS§modal analysis§ harmonic response analysis§ANSYS application example: train

wheel


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Solving structural vibration problems with ANSYS

§modal analysis: § standard procedure for the dynamic assessment of a structure§ compute the potential vibration shapes & resonance frequencies of a

structure without considering any excitation§ a library of specific solvers for special tasks:

§ standard: block Lanczos (LANB), § large problems: PCG Lanczos (LANPCG) § large problems, up to 10000 modes (SNODE) § rotordynamics: incl. gyroscopic effects (QRDAMP) § damped structures: incl. damping matrix (QRDAMP, DAMP) § break-squeal analysis: incl. friction (QRDAMP,UNSYM)§ FSI coupled systems: incl. fluid (UNSYM)

§ however: no amplitude results


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Modal analysis: mode shapes of a train wheel

1 2 3

654


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Solving structural vibration problems with ANSYS

§ harmonic response analysis§ now we introduce an excitation, for

instance a point force F=1N specified over a frequency range 0…2500 Hz§ only distinct modes will contribute to the

structural response, e.g. the modes having a nodal line at the excitation point will not be excited§ use “mode superposition” instead of

inverting “full” matrices whenever possible because of efficiency§ usually the response amplitude at some

points is postprocessed versus frequency


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Frequency response UY(f) at contact point


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Solving Structure-Borne Sound Problems with ANSYS SBSOUND§ basic equation of machinery acoustics§ANSYS application example: train

wheel


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Computation of structure-borne sound

§Acoustics is driven by velocity v=iΩu not by structural displacement u.§Acoustics assumes an ideal non-viscous fluid without shear layers. Thus

only the surface normal component of the structural vibration velocity is important.§Acoustics is not a local phenomenon like fatigue where we have to deal

with local notch stresses. Acoustics is a global phenomenon where the whole structure may contribute to sound radiation.§ thus let‘s try to get one integral quantity to describe the acoustic

fingerprint of a structure by simply averaging the normal surface velocities§For all this ideas apply the basic equation of machinery acoustics (cf.

textbooks)><= )(~)()(~ 2 fvAfcfP nσρ


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ANSYS macro library SBSOUND (structure-borne sound)

ü Perform normal projection of the displacement resultsü Compute surface averaged mean square velocity by integrationü Do all computations in modal subspace for higher efficiency and

extended postprocessing capabilities (modal contribution plot, panel contribution plot)

1 2 3

modal contributions show the influence of distinct modes


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Alternatively: bar chart of modal contributions for fixed f

§ total result (red bar) together with the (blue) modal contributions

§ the same figure is available for panel panel contributionscontributions if panels are defined before calling SBSOUND


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Sound radiation is not only a function of velocity amplitude!Sound pressure p for two plates vibrating in the same spatial pattern, both with equal velocity amplitude v0 but with different frequencies. There is, however, a big difference in the sound radiation! Radiation efficiency σ!

at 50 Hz and at 200 Hz

note the equal pressure scale


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Solving Air-Borne Sound Problems with ANSYS (FEM)§ interior frequency domain acoustic

FEM: living room§ exterior acoustics time domain FEM:

offshore hammer


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Interior acoustics: modal analysis by ANSYS FEM§ living room with defined absorbent

linings: mode 2 at 28 Hz (right) mode 50 at 152 Hz (left)


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Exterior acoustics: transient analysis by ANSYS FEM§Offshore hammer: for offshore applications a steel pipe has to be fixed

in shallow sea water. The pile has a length of 30m above sea ground, a radius of 2m, and a wall thickness of 50mm; half-sin force FY≈1E8N. § It’s partially immersed in water (water height 25m), where the speed of

sound c=1500m/s, and fluid density ρ=1000kg/m3, apply absorbent boundary condition at exterior surfaces

pipe

exterior fluid

interior fluid


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Results: animated displacement u and sound pressure p

Structural result§ pipe displacement§ radial component

important

Acoustic result§ sound pressure

animation§ sound pressure

signals at different microphone positions

PP


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Solving Air-Borne Sound Problems with WAON (BEM)§ features of BEM and FMBEM§FMBEM workflow for train wheel

example§ANSYS Workbench → WAON interface


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Computation of air-borne sound (typical BEM workflow)1. structural FE model

2. modal model (FEM): eigenfrequencies, mode shapes, modal damping

4. Acoustic BEM solves wave equation, no fluid volume mesh required. a) BEM result: sound pressure p, sound power P, radiation efficiency σb) field point mesh result (half sphere): sound pressure p, intensity I

3. Harmonic frequency (FEM) response results (structure-borne sound): surface displacements


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Compare FEM & BEM

§ before talking about the new development FMBEM let’s have a more general view on BEM

§BEM: divide only the surface.§ easy to create a mesh.

§The sound radiation problem can be handled completely§ no need for any particular

boundary condition like in FEM for exterior acoustic problems

FEMBEM

Interior Interior

Exterior Exterior


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Acoustics Software: &

WAON specialized acoustic software for efficient frequency domain sol.§ technology

§ based on Fast Multipole Bounday Element Method (FMBEM), a state of the art numerical technology

§ pro’s§ easy to learn (2-4 hours or even a seminar by WEBEX is sufficient) § easy to apply even if acoustics isn’t your every day business§ easy mesh operations – surface mesh of your radiating structure is sufficient§ low memory requirements, high performance, high frequencies (comp. to

BEM): e.g. automotive sensor applications at ultrasonic frequencies very efficient (park distance control, alarm)


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What is FMBEM

§ Conventional BEM

§ Calculation of interaction between all elements§ Memory requirement

§ O(N2)§ Solution time

§ O(N3) : direct solver§ O(N2) : iterative solver

§ Fast Multipole algorithm is applied to the boundary element method (BEM)§ The world's first commercial acoustic-analysis program with using FMBEM§ Accuracy is the same as conventional BEM

§ FMBEM

§ Calculation of interaction between cellsinstead of between elements (maths:clustering & multipole expansion)§ Solution time

§ O(N ～ N logN)§ Memory requirement

§ O(N ～ N logN)


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§ Available on larger structures and higher frequency at shorter times!§ Radiated noise from engine

§ Pressure or output power distribution around scooter engine.

§ 4.5 kHz analysis by 84,000DOF mesh.

§ Required memory(4.5kHz)§ Conventional BEM : 113 GB

§ FMBEM by WAON : 3 GB

Engine: Conventional BEM vs. FMBEM


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Compare FEM & BEMFEM acoustics BEM acousticslarge amount of data particularly for large distance results or scatter objects

reduced amount of data even for large distance results

volume meshes: prep/post efforts surface meshes: easy prep/post, less datadeveloper: easy math, user: more effort to handle

developer: complex math, user: more easy to handle

non-reflecting boundary conditions like FLUID130, perfectly matching layer (PML) for radiation problems

radiation problem solved very naturally because every boundary element “knows” about the radiation cond. analytically

strong in both frequency & time domain only strong in frequency domainmodal analysis available no modal analysis available

non-homogeneous acoustic media acoustic medium has to be homogeneous

porous media (foam) available (Biot theory) volome damping idealized by complex c

nonlinearities available (large amplitudes) confined to linear theory

convected wave eq. for flow eff. available quiescent acoustic medium


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ANSYS/WAON workflow: air-borne sound

§ train wheel example “reloaded”§Prepare WAON BEM

(surface) mesh in ANSYS and export it to CDB formatS

§ prepare WAON field point mesh (virtual microphones) in ANSYS and export it to CDB format


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Import BEM mesh & map ANSYS structural vibration results

WAON feature tree(max. 7 dialoguesto work throughintuitively)


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Import field point mesh (virtual microphones) &perform FMBEM harmonic response analysis (2-3 min.)


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Postprocess pressure amplitude & pressure level in dB & intensity vectors on field point mesh


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Compare air-borne power to structure-borne sound power§ blue curve: input power

(structure-borne sound power identical to SBSOUND result)§ due to radiation

efficiency σ this always is a very conservative estimate of the radiated active output power in red (air-borne sound power)§ good agreement at

higher frequencies above coincidence where we have radiation efficiency σ=1.


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ANSYS WorkbenchDeveloped by ANSYS, Inc.

Developed by CYBERNET SYSTEMS

WAON

Developed by CYBERNET SYSTEMS

WBtoWAON

Even more Easy to Use: Interface WBtoWAON


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WAON: some more solved acoustic applications

506070

8090100

110120

0 5 10 15 20

Frequency[kHz]

Sound Pressure Level[dB] Point1 Point2 Point3


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§ Structure: Single phasealternating currentelectric motor

§ Task: Simulate noisebehavior for silentoperation

§ Method: Coupledelectro-mechanic,structural-dynamic andacoustic analysis

Investigation of the Noise Behavior of an Electric Motor

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

f [Hz]

Sch

alll

eist

ung

speg

el [d

B]

Multiphysics: FEM/FEM/BEM application exampleelectromagneticselectromagnetics

struct. vibrationsstruct. vibrations

acousticsacoustics


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Conclusion

§ANSYS FEM for structural vibration analysis, multiphysics analysis (e.g. electro-magnetic excitation)§SBSOUND (ANSYS macro library provided by CADFEM) for a quick

rough structure-borne sound assessment§WAON for really doing fully-fledged acoustic simulations§FMBEM is a very comfortable technique particularly for the new user

because there is no need for volume meshing like in acoustic FEM§FMBEM technique overcomes the traditional drawback of

conventional BEM: matrix storage requirements & large CPU time due to direct solvers. High-speed iterative solvers available.§FMBEM by WAON allows the analysis of large scale models & high

frequencies§ acoustics is easy – acoustics is fun!

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