Acoustic Applications in Mechanical Engineering: Structure-Borne Sound versus Air-Borne Sound

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1 Acoustic Applications in Mechanical Engineering: Structure-Borne Sound versus Air-Borne Sound Marold Moosrainer CADFEM GmbH 2009 July 6th

2 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) -1-

3 Introduction machine acoustics speed of sound, wavelength, frequency basic concept of solving acoustic problems by simulation -2-

4 Some phrases of machine acoustics machine fluid, e.g. air transient flow direct noise generation: flow acoustics (CFD + acou.) oscillating forces machine structure indirect noise generation: vibroacoustics (FEM + acou.) building structure structure-borne sound: a sound wave propagating in a solid medium air-borne sound: a sound wave propagating in air -3-

5 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: c = λ f air: c 340m/s, f=1000hz λ=0.34m water: c 1500m/s, f=1000hz λ=1.5m rule of thumb FEM, BEM: linear elements per wavelength required elements for a domain of characteristic size a: FEM (volume mesh): ~O(N 3 ) BEM (surface mesh): ~O(N 2 ) large acoustic FEM problem: 10M DOFs large acoustic BEM problem: 20k DOFs large acoustic FMBEM problem: 200k DOFs -4-

6 Basic concept of solving acoustic problems by simulation Signal analysis (MBS, test, FFT) Structure-borne sound analysis (FEM) Air-borne sound analysis (FEM, BEM) Psycho acoustics (e.g. DIN 45631) use N 5 percentile values for transient noise -5-

7 Solving Structural Vibration Problems with ANSYS modal analysis harmonic response analysis ANSYS application example: train wheel -6-

8 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 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 -7-

9 Modal analysis: mode shapes of a train wheel

10 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 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 postprocessedversus frequency -9-

11 Frequency response UY(f) at contact point -10 -

12 Solving Structure-Borne Sound Problems with ANSYS SBSOUND basic equation of machinery acoustics ANSYS application example: train wheel -11-

13 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) ~ f ) 2 n P( = ρ cσ ( f ) A< v~ ( f ) > -12 -

14 ANSYS macro library SBSOUND (structure-borne sound) Perform normal projection of the displacement results Compute surface averaged mean square velocity by integration Do all computations in modal subspace for higher efficiency and extended postprocessing capabilities (modal contribution plot, panel contribution plot) modal contributions show the influence of distinct modes

15 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 contributions if panels are defined before calling SBSOUND -14 -

16 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 v 0 but with different frequencies. There is, however, a big difference in the sound radiation! Radiation efficiency s! at 50 Hz and at 200 Hz note the equal pressure scale -15 -

17 Solving Air-Borne Sound Problems with ANSYS (FEM) interior frequency domain acoustic FEM: living room exterior acoustics time domain FEM: offshore hammer -16 -

18 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) -17 -

19 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/m 3, apply absorbent boundary condition at exterior surfaces pipe exterior fluid interior fluid -18 -

20 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 P -19 -

21 Solving Air-Borne Sound Problems with WAON (BEM) features of BEM and FMBEM FMBEM workflow for train wheel example ANSYS Workbench WAON interface -20 -

22 Computation of air-borne sound (typical BEM workflow) 1. structural FE model 2. modal model (FEM): eigenfrequencies, mode shapes, modal damping 3. Harmonic frequency (FEM) response results (structureborne sound): surface displacements 4. Acoustic BEM solves wave equation, no fluid volume mesh required. a) BEM result: sound pressure p, sound power P, radiation efficiency σ b) field point mesh result (half sphere): sound pressure p, intensity I -21 -

23 Compare FEM & BEM before talking about the new development FMBEM let s have a more general view on BEM BEM FEM 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 Interior Exterior Interior Exterior -22 -

24 Acoustics Software: & WAON specialized acoustic software for efficient frequency domain sol. technology based on Fast Multipole BoundayElement 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) -23 -

25 What is FMBEM 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 Conventional BEM FMBEM Calculation of interaction between all elements Memory requirement O(N 2 ) Solution time O(N 3 ) : direct solver O(N 2 ) : iterative solver Calculation of interaction between cells instead of between elements (maths: clustering&multipoleexpansion) Solution time O(N ~ N logn) Memory requirement O(N ~ N logn) -24 -

26 Engine: Conventional BEM vs. FMBEM 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 84,000 DOF mesh. Required memory(4.5khz) Conventional BEM : 113 GB FMBEM by WAON : 3 GB -25 -

27 Compare FEM & BEM FEM acoustics large amount of data particularly for large distance results or scatter objects volume meshes: prep/post efforts developer: easy math, user: more effort to handle non-reflecting boundary conditions like FLUID130, perfectly matching layer (PML) for radiation problems strong in both frequency & time domain modal analysis available non-homogeneous acoustic media porous media (foam) available (Biot theory) nonlinearities available (large amplitudes) convectedwave eq. for flow eff. available BEM acoustics reduced amount of data even for large distance results surface meshes: easy prep/post, less data developer: complex math, user: more easy to handle radiation problem solved very naturally because every boundary element knows about the radiation cond. analytically only strong in frequency domain no modal analysis available acoustic medium has to be homogeneous volomedamping idealized by complex c confined to linear theory quiescent acoustic medium -26 -

28 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 -27 -

29 Import BEM mesh & map ANSYS structural vibration results WAON feature tree (max. 7 dialogues to work through intuitively) -28 -

30 Import field point mesh (virtual microphones) & perform FMBEM harmonic response analysis (2-3 min.) -29 -

31 Postprocess pressure amplitude & pressure level in db & intensity vectors on field point mesh -30 -

32 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=

33 Even more Easy to Use: Interface WBtoWAON Developed by CYBERNET SYSTEMS WBtoWAON Developed by CYBERNET SYSTEMS WAON ANSYS Workbench Developed by ANSYS, Inc

34 WAON: some more solved acoustic applications Sound Pressure Level[dB] Point1 Point2 Point Frequency[kHz] -33 -

35 Multiphysics: FEM/FEM/BEM application example Investigation of the Noise Behavior of an Electric Motor electromagnetics struct. vibrations Structure: Single phase alternating current electric motor acoustics Task: Simulate noise behavior for silent operation Method: Coupled electro-mechanic, structural-dynamic and acoustic analysis Schallleistungspegel [db] f [Hz] -34 -

36 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! -35 -

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