multiphysics of electrodynamic loudspeakers · nafems european multiphysics conference, 15 – 16...

Multiphysics of Electrodynamic Loudspeakers

Alfred J. Svobodnik, Tommaso NizzoliKonzept-X GmbH, Karlsruhe, Germany

NAFEMS EUROPEAN MULTIPHYSICS CONFERENCE, 15 – 16 NOVEMBER 2016, COPENHAGEN, DENMARK

• CAE is essential part to realize simulation driven engineering

• Recently, a very strong trend to move CAE upfront in the development process– “Frontloaded virtual product development”– Leads to significant increase in engineering efficiency

• Application of advanced modeling strategies for realistic simulations of loudspeakers is presented– “Frontloaded virtual product development” for audio

engineering

Introduction


Theory of Multiphysical Modeling of Loudspeakers• Since early 1970s multiphysical simulation of

loudspeakers published by the AES (Audio Engineering Society)

• 1D lumped parameter models– Highly useful, but limitations– Only pistonic motions covered– Applicable frequency

bandwidth limited due topartial vibrations at higherfrequencies


Voice Coil Electromagnetics

• Loudspeaker is driven by a time-harmonic voltage, V = V0

(iωt), applied to the voice coil which is immersed in the magnetic circuit where the driving force fe is generated:

• Jφ is the current density in the coil wire and Br is the magnetic radial flux density

coil

Vr

e dVBJf )(


Voice Coil Electromagnetics

• FEA mesh and Br


Structural Dynamics

• Governing equation for the mechanical vibrations in the frequency domain

• Km ... stiffness matrixDm … damping matrixMm … mass matrix

• um … vector of displacementsfm … vector of mechanical forces

mmmmm fuMDiK )( 2


Structural Dynamics

• Loudspeaker motion as a piston at low frequency (50 Hz, left), and “break-up” at 1.32 kHz


The Acoustical Domain

• Helmholtz equation discretized by means of finite elements describing the three-dimensional propagation of sound waves in the frequency domain:

• Ka, Ma and Da … acoustic stiffness, mass and damping matrix

• pa … vector of sound pressurefa … sound sources

aaaaa fpMDiK )( 2


The Acoustical Domain

• FEA mesh (left) and acoustic pressure front emission at 1.32 kHz (right)


The Coupled Multiphysical System• Governing equations of the coupled domains

(electrical, mechanical and acoustical domain):

• Cma and Cam are coupling matrices connecting the mechanical and acoustical domain

a

e

a

m

aaaam

mammm

ff

pu

MDiKCCMDiK

2

2


An Industrial Example for a Realistic Loudspeaker Simulation• Typical woofer loudspeaker for the

reproduction of low frequencies


An Industrial Example for a Realistic Loudspeaker Simulation• Comparison of simulation and measurement from 20 Hz up to 20 kHz


Major Challenges in each Physical Domain• Electromagnetics

– Nonlinearities at large excursions (at nominal power)• A significant portion of the voice coil moves

out of the main flux field, and thus less mechanical force is being induced

• Additional nonlinearities from inductance– Dependent on excursion and current

• Leads to unwanted audible distortions• Requires nonlinear modeling

– See specific papers from the authors


Major Challenges in each Physical Domain• Structural Dynamics

– Non-axisymmetric geometry or effects (e.g. rocking) require 3D models• Thin walled structures

– Shell finite elements

– Nonlinearities at largeexcursions (at nominalpower)• Nonlinear material behavior• Change in geometric stiffness (including instabilities)• Leads to unwanted audible distortions• Requires nonlinear modeling

– See specific papers from the authors


Major Challenges in each Physical Domain• Acoustical Domain

– Nonlinearities• For some applications, e.g. small transducers,

viscous effects of the air have to be accounted for– Sound energy is transformed to thermal energy

• Significant impact on vibrations and sound radiation

• Requires nonlinear modeling– See specific papers from the authors

multiphysics of electrodynamic loudspeakers · nafems european multiphysics conference, 15 – 16...

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