KLIPPEL Tutorial on Cone Vibration and Radiation AES 2010

Loudspeakers and HeadphonesLoudspeakers and Headphonesa Tutorial on Cone Vibration and Sound Radiation Diagnosticsa Tutorial on Cone Vibration and Sound Radiation Diagnosticsgg

Wolfgang Klippel

Institute of Acoustics and Speech Communication, TU Dresden

www.klippel.de Tutorial: Cone Vibration and Radiation Diagnostics, AES London 2010, 1

p ,KLIPPEL GmbH

Our Topic TodayOur Topic Today

PERFORMANCEPERFORMANCE

70

80Total Sound Pressure Level

DESIGNDESIGN (geometry, material)(geometry, material)

conecone

0°330

300

270

240

210180°

150°

120°

90°

60°

30°

-20 -10

20

30

40

50

60

103 104

SPL

[dB]

Frequency [Hz]

Relationship ? spiderspider

Voice coilVoice coil

surroundsurround

Dust capDust cap


• What limits the usable frequency range ?• What causes peaks and dips in the SPL response after break-up ?• How to measure the mechanical vibration ?• Which mechanical modes are beneficial which are not ?• How to cope with vibration and radiation problems ?• How to get smooth responses, optimal directivity and low distortion ?

Simulation by Ulrik Skov Simulation by Ulrik Skov

Measurements Measurements for assessing small signal performancefor assessing small signal performance

Distance > 1 mDistance > 1 mDistance Distance ≈≈ 1 cm1 cmstimulusstimulus

Electrical Measurement

AcousticalMeasurement

60

70


dB]


Far Field SPL Response

Distributed Parameters acousticalacoustical

0°330

300

270

240

210180°

150°

120°

90°

60°

30°

-20 -10

20

30

40

50

103 104

SP

L [d

Frequency [Hz]

Lumped Parameters electricalelectrical

ImpedanceZe(f)=U(f)/I(f)

KLIPPEL

3

4

5

6

7

8

9

10

11

12

13

14

15

101 102 103

magnitude of electric impedance Z(f)

[Ohm

]

f [Hz]

measured estimated

Loudspeaker ModelLoudspeaker Model

Distance > 1 mDistance > 1 m

Distance Distance ≈≈ 1 cm1 cmstimulusstimulusVibrationMotor Radiation

F X(r) soundfield

near far

60

70


dB]


VibrationMotor Radiation

V F(r)u field field



0°330

300

270

240

210180°

150°

120°

90°

60°

30°

-20 -10

20

30

40

50

103 104

SP

L [d

Frequency [Hz] Far Field SPL Response

Distributed Parameters acousticalacoustical


Lumped Parameters electricalelectrical

KLIPPEL

3

4

5

6

7

8

9

10

11

12

13

14

15

101 102 103

magnitude of electric impedance Z(f)

[Ohm

]

f [Hz]

measured estimated

More Comprehensive AssessmentMore Comprehensive Assessment

VibrationMotor Radiation

F X(r) soundfield

near farVoice Cone‘s VibrationMotor Radiation

V F(r)u field fieldcoil surface


Mechanical Measurement



Lumped Parameters Distributed Parameters electricalelectrical

Hx(f)=X(f)/U(f)

mechanicalmechanical

Cone Vibration+ Geometry

mechanicalmechanical acousticalacoustical

Far Field SPL Response


Cone Scanning TechniquesCone Scanning Techniques

Amplitude+ phase Amplitude Amplitude + phase + geometry

Doppler Interferometry Doppler Interferometry (Polytech, 1995)(Polytech, 1995)

Triangulation Laser Scanner Triangulation Laser Scanner (Klippel, 2007)(Klippel, 2007)

geometry

Cladni FiguresCladni Figures(Cladni, 1787(Cladni, 1787

Corrington 1951)Corrington 1951)


Laser Intensity InterferometryLaser Intensity Interferometry(Frankort 1978)(Frankort 1978)

geometry

displacementVelocity destribution on the cone

intensity

Diagnostics on Cone Vibration and Radiation Diagnostics on Cone Vibration and Radiation

Sound Pressure•of total vibration •of separated components•on-axis

Improvements, New design choices

Drive Unit(woofer, tweeter, ...)

Geometryzzcc((ϕϕ,r,rcc))

VibrationHH ((jj rr ))

Acceleration(accumulated level)

Sound Power•of separated components •directivity index•coverage angle

on axis•Directivity (polar plot)

Vibration &RadiationAnalysis

3937,5 Hz

Selection of optimal drive


HHcc((jjωω,,ϕϕ,r,rcc)) •of total vibration•of separated components

•Components•modal analysis•radial/circumferential•contribution to SPL output•irregularities

optimal drive unit for loudspeaker system design

Prediction of Sound Pressure in the Far FieldPrediction of Sound Pressure in the Far Fieldusing Distributed Mechanical Parameters from Laser Scanningusing Distributed Mechanical Parameters from Laser Scanning

Rayleigh Integral Equation

jX )(2

• Fast prediction of sound pressure

• Based on measured geometry and

crrjk

S ca

ca dSe

rrrjXrjp ca

c

−−

∫ −=

),(2

),( 02 ωπρωω

( )dB

p

rjprSPL

o

aa

=

,log20),(

ωω


• Based on measured geometry anddisplacement x in z-direction

• Sufficiently accurate for shallow cones

• Could be improved by BEA

Practical ExamplesPractical Examplessee W. Klippel, et.al., “ Distributed Mechanical Parameters of Loudspeakers, Journal see W. Klippel, et.al., “ Distributed Mechanical Parameters of Loudspeakers, Journal

AES, Vol. 57, No. 7/8,9, 2009AES, Vol. 57, No. 7/8,9, 2009

Woofer A with paper cone

Woofer B with magnesium cone


Woofer C with flat radiator

Smooth SPL Response ?Smooth SPL Response ?


KLIPPEL

50

55

60

65

70

75

80

SPL

[dB] -30 degree

on -axis

+30 degree

40

45

102 103f [Hz]

Woofer B with magnesium cone

KLIPPEL

20

30

40

50

60

70

80

90

102 103 104

SPL

[dB]

f [Hz]

-30 degree

on -axis

+30 degree


Woofer C with flat radiator

KLIPPEL

20

30

40

50

60

70

80

102 103 104

-30 degree

on -axis

+30 degree

How to How to AAssess ssess TTotal otal CCone one VVibration ? ibration ?

),( crjX ω

Potential energydepends on bending

Kinetic Energydepends on


However, thickness of cone, Young‘s E Modulus, density are not known and can not be measured by laser scanner !!

p gstiffness

pmoving mass

Total mechanical energyNot practical !

Accumulated Acceleration LevelAccumulated Acceleration Level1078,1 Hz

),( crjX ω Weighted Sum of the absolute value of cone

l ti

KLIPPEL

80

90Acceleration Level

cS ca

caa dS

rr

rjXrja

c

∫ −=

),(

2),( 0

2 ω

πρωω

acceleration

),( crjX ω

Very similar to Rayleigh Integral for SPL prediction !!


Rigid body modes

30

40

50

60

70

80

100 1000 10000

ALL

[dB]

f [Hz]

dBprja

rAALo

aqa

=

),(log20),(

ωω

Reference sound pressure p0

Accumulated Acceleration Level (AAL)Accumulated Acceleration Level (AAL)

Acceleration levelKLIPPEL

70

80

90

Acceleration Level

Total sound Pressure levelRigid body modes

30

40

50

60

70

100 1000 10000

SPL

[dB]

f [Hz]

Total SPLRigid body modes

INTERPRETATION:


• AAL is comparable with SPL • AAL is identical with SPL for a rigid body mode• AAL is never smaller than SPL• AAL neglects acoustical cancellation• AAL has significantly less dips

• AAL describes total mechanical vibration

Sufficient Cone Vibration ?Sufficient Cone Vibration ?KLIPPEL

60

65

70

75

80

SP

L [d

B] Total SPL

acceleration level

Woofer A with paper cone:low Q factor of cone resonances

Compare SPL and AAL !

50

55

60

102 103f [Hz]

AAL is 5-8 dB higher than SPL

KLIPPEL

50

55

60

65

70

75

80

85

90

SPL

[dB]

Total SPL

acceleration level Woofer B with magnesium cone:natural modes cause high peaks in SPLAAL is 5-10 dB higher than SPL


102 103 104f [Hz]

KLIPPEL

30

40

50

60

70

80

90

102 103 104

SP

L [d

B]

f [Hz]

Total SPL

acceleration level

Woofer C with flat radiatordips are not visible in AALAAL cause peak at 0.8 kHzAAL is 10 – 30 dB higher than SPL

KLIPPEL90

Acceleration Level

Modal AnalysisModal AnalysisExpansion into a Series of Orthogonal ModesExpansion into a Series of Orthogonal Modes

::Accumulated Acceleration:Accumulated Acceleration:

30

40

50

60

70

80

100 1000 10000

SPL

[dB]

f [Hz]

Acceleration Level

Natural Functions describing mode shape

Frequency response for each mode

( )∑∞

=

=0

)(i

ii jHaja ωω

( )∑∞

=

=0

)(),(i

ciic rjHrjX ψωω

Displacement:Displacement:


NaturalNaturalFunctionFunction

NaturalNaturalfrequenciesfrequencies 840 Hz840 Hz 3,8 kHz3,8 kHz 8,1 kHz8,1 kHz70 Hz70 Hz 11,2 kHz11,2 kHz

Completely different mode shapes (orthogonal) !Completely different mode shapes (orthogonal) !

Frequency Response of a Single ModeFrequency Response of a Single ModeNatural Functions


Loss factor( )∑

∞

=

=0

)(),(i

ciic rjHrjX ψωω

Frequency response Natural Frequency

ωi

( ) ( )2//11

iiii

jjH

ωωωωηω

−+=

How to Specify the Radiator How to Specify the Radiator Cone, Diaphragm and SurroundCone, Diaphragm and Surround

KLIPPEL

70

80

90

Acceleration Level

Natural Functions

Total sound Pressure levelRigid body modes

30

40

50

60

70

100 1000 10000

SPL

[dB]

f [Hz]

Modal loss factor ηi of each mode ith-mode with

Natural frequency fi of the ith-mode with i 1 2

Natural Function Ψi (rc)of each mode ith-mode with i=1 2


i=1,2,... i=1,2,...

Geometry of the Radiator (shape, thickness, ..)

Young‘s E Modulus of the material

Loss factor of the material

i=1,2,...

92,5AAL [dB]

Sufficient Damping of the Material ?Sufficient Damping of the Material ?

3dB

0 dB

Read the bandwidth for 3dB decay in the accumulated acceleration level !!

Acceleration Level

77,5

80,0

82,5

85,0

87,5

6*102 7*102 8*102 9*102 103

f [Hz]

- 3dB

fI- fI+fi


i

iii f

ff −+ −=η

• Modal Loss Factor depends on frequency and temperature• describes the material used (independent of the geometry)• multiple parts (cone, surround, spider) may contribute to the modal loss factor

Where to apply additional damping ?Where to apply additional damping ?Woofer C with flat radiatorWoofer C with flat radiator

90

Total Acceleration Level

820,3 Hz 12398,4 Hz

65

70

75

80

85

90

102 103 104

AC

C [d

B]

Frequency [Hz]View the shape of the modes !


Find places of high deformation !

Where to apply additional damping ?Where to apply additional damping ?Woofer B Magnesium coneWoofer B Magnesium cone

KLIPPEL

85

90

50

55

60

65

70

75

80

85

100 1000 10000

AAL

[dB]

f [Hz]

Acceleration Level

10 >η 5.01 =η 01.02 <η

0ω


11109,4 Hz

Rubber surround has sufficient losses Magnesium requires damping

What Causes the Dips What Causes the Dips in the SPL Response of Woofer C ?in the SPL Response of Woofer C ?

1078,1 Hz q2

KLIPPEL

80

90

acceleration level q2

q130

40

50

60

70

102 103 104

SP

L [d

B]

f [Hz]

Total SPL

Significant difference between AAL and SPL !


PROBLEM: • There is sufficient mechanical vibration (no dip in AAL)• Node devides radiator in two areas each producing the same volume velocity in opposite phase

Acoustical cancellation q1+ q2=0

SoundSound--PressurePressure--Related DecompositionRelated Decomposition

Total displacement of Total displacement of woofer C at 1.4 kHzwoofer C at 1.4 kHz

generates sound Reduces sound no sound

ofoutantiintotal xxxx −++= quadrature


SPL ComponentsSPL ComponentsKLIPPEL

70

80

Total SPLIn-Phase Component

0

10

20

30

40

50

60

102 103

SPL

[dB]

f [Hz]

Anti-Phase ComponentRigid body mode

Quadrature component


f [Hz]

•In-phase component produces the highest SPL•Anti-phase component generates a small SPL below break-up•Quadrature component generates no SPL

r

The Secret of a Conventional Paper ConeThe Secret of a Conventional Paper Cone

rbrbrb• Cone break-up starts outside

O t i d t di t i ifi t d

1 kHz

rb

2 kHz

rb

4 kHz

rb

6 kHz

rb• Outer ring area does not radiate significant sound • Centre part radiates sound (in-phase component)• Effective radiation area decreases with frequency• A woofer converts into a tweeter at higher

frequencies


500 Hz 3 kHz 7 kHz

InIn--Phase Component contributing constructively to the soundPhase Component contributing constructively to the sound

Acoustical CancellationAcoustical CancellationKLIPPEL

80

90

0

10

20

30

40

50

60

70

80

2*102 4*102 6*102 8*102 103 2*103 4*103 6*103 8*103

SPL

[dB]

Total SPLIn-Phase Component

Anti-Phase Component


2 10 4 10 6 10 8 10 10 2 10 4 10 6 10 8 10f [Hz]

If the in-phase component equals the SPL of anti-phase component then a dip in the total SPL response is generated !!

Total Vibration Component

Components change the position at a Components change the position at a cancellation frequency cancellation frequency


anti-phase component


In-Phase Component

In-phase component

How to Avoid Dips in the Total SPL Response ?How to Avoid Dips in the Total SPL Response ?

KLIPPEL65 In-phase

2530354045

dB 5560

In phase

anti-phasetotal-phase

Keep anti-phase component 10 dB


10152025

200 1000 200 800Frequency [Hz]

Keep anti phase component 10 dB below in-phase component

Where is the sound radiated Where is the sound radiated in paper cone of Woofer A ?in paper cone of Woofer A ?

In phase component is dominant

KLIPPEL

70

80

In-Phase Component • In-phase component is dominant• No acoustical cancellation• In-phase component stays in the centre • radiation area shrinks with frequency

0

10

20

30

40

50

60

102 103

SPL

[dB]

f [Hz]

In-Phase Component



0.1 kHz 1 kHz0.7 kHz 10 kHz4 kHz1 kHz

In-Phase Component

Gradual BreakGradual Break--up of the Paper Coneup of the Paper Cone

qq3

q4

q1 is dominant and generates a dominant in-phase

Volumevelocity

q2

High bending stiffnesLow bendingstiffness

q1


pcomponent

frequency

Where is the sound radiated Where is the sound radiated in Woofer B: Magnesium Cone ?in Woofer B: Magnesium Cone ?

KLIPPEL

80

85

90

S

In-Phase Component Anti-Phase Component

• In-phase component is dominant

40

45

50

55

60

65

70

75

80

103 104

dB

- [V

] (

rms)

Frequency [Hz]

p p• No acoustical cancellation• In-phase component stays in the centre • radiation area shrinks with frequency


20 kHz12 kHz 15 kHz10 kHz7.5 kHz3 kHzIn-Phase Components

KLIPPEL

859095

(rm

s)

In-Phase Component Anti-Phase Component

Dominant InDominant In--Phase Component ? Phase Component ? Woofer C with flat radiatorWoofer C with flat radiator

Cancellation frequencies Check difference !

556065707580

103 104

dB

- [V

] (

Frequency [Hz]

in-phase

anti-phase


Localization of the in-phase component

•There is no dominant in-phase component which produces sound • Anti-phase component becomes equal to in-phase component• In-phase and anti-phase components change their location

How to Fix Acoustical Cancellation Problems ?How to Fix Acoustical Cancellation Problems ?

Area of in-phase component

INCREASE

o onode

Target: • Make in-phase component dominant• Suppress anti-phase component


Steps: 1. find location of in-phase component2. use FEA to simulate behavior3. increase bending stiffness at this area (thickness, curvature, rips)

Radiation into 3D SpaceRadiation into 3D Space

φ

9090oo

9090oo

ro

ϕ

--9090oo

--9090oo

180180oo

9090

Simulation by Ulrik Skov Simulation by Ulrik Skov


Pressure at the reference pointPressure at the reference point

Voltage at the terminalsVoltage at the terminals @ r@ r00= 1m and U= 1m and Uoo=2.83 V=2.83 V

SensitivitySensitivity

dBp

UrjHfLp

=

0

0010

),,,(log20),,(

φϕωφϕ

)(),,,(

),,,( 00 ω

φϕωφϕω

UrP

rjH =

Transfer Response H(jTransfer Response H(jωω,,ϕϕ,,φφ,r,roo))

Important Responses Describing Acoustical OutputImportant Responses Describing Acoustical Output

On-axisResponse

)0,0,()( fLfL pon =

ListeningWindow

Response

ϕ =0, ±10° , ±20° , ±30°φφ = = ±10°

∑=

=9

1

),,(91)(i

iiplW fLfL φϕ

EarlyReflectionResponse

ϕ =0, ±10° , ±20° , ±30° , ±40° , ±50° ±60° ±70° ±80° ±90° ±1800°

∑=

=I

iiiper fL

IfL

1

),,(1)( φϕ

Toole, 2007Toole, 2007SoundPower

Response

∫=ΠS

dSUrjHc

f 20

20 ),,,(1)( φϕω

ρ

Π

=)(log10)( ffL


φφ = = ±10 , ±60 , ±70 , ±80 , ±90 , ±1800φφ= = −−20°, −30°,− 40°, 40°, 50°, 60°

=Π0

10log10)(P

fL

With PWith P00=10=10--1212 WW

∫=

S

dSrjH

SrjHD2

0

20

),,,(

),0,0,(

φϕω

ω

Directivity

Directivity IndexDDI 10log10=

Sound Pressure SPL @ 1m, 1V Accumulated Acceleration (AAL)

Power Level +47 dB @ 1V

Three Important ResponsesThree Important Responses

KLIPPEL

60

70

80

90

100

AAL

Maximal possible sound pressure output

Acousticalcancellation


50

60

101 102 103 Power

On-axis

Example: woofer

Piston mode

DirectivityIndex

Displacement is inDisplacement is in--phasephaseOmniOmni--directional behaviordirectional behavior(like a point source)(like a point source)

Desired Directivity Index ?Desired Directivity Index ?

KLIPPEL

65

70

75

80

er

[dB

]

Sound Power Level SPL on-axis

power

SPL on-axis

KLIPPEL

-20

-10

0

10

20

30

Magnesium Cone

Flat Piston

Paper Cone40

45

50

55

60

102 103

Pow

e

f [Hz]


KLIPPEL

45

50

55

60

65

70

75

80

85

90

Pow

er

[dB

]


Woofer B with magnesium conepower

SPL on-axis

OmniOmni--directionaldirectional


-30

102 103 104

40

45

102 103 104

f [Hz]

KLIPPEL

30

35

40

45

50

55

60

65

70

75

80

85

90

102 103 104

Pow

er [

dB

]

f [Hz]


Woofer C with flat radiator power

SPL on-axis

Directivity Pattern in the Piston ModeDirectivity Pattern in the Piston Modera

Rayleigh Integral Equationcrrjkc

a dSerjXrjp ca −−

∫=),(

2),( 0

2 ωρωω

rc,1

rc,2Cone vibrates as a rigid Cone vibrates as a rigid bodybody


cS ca

arr

jpc

∫ −2)(

π

Phase shift generating by the difference in the distance between particular source point rc and reference point ra

Transition Frequency Transition Frequency ftfor a rigid pistonfor a rigid piston

0°330 30°

Polar plot

r

o

ot r

cfπ7.0

=

330

300

270

240

210180°

150°

120°

90°

60°

30

-15 -10 -5ro

r

r1

|r-r1|

r2

|r-r2|

λ/2


• At f= ft sound wavelength λ in air is approximately equal to the piston circumference

• At f > ft Sound power response decreases by 6 dB/oct.directivity index increases by 6 dB/oct. the beam becomes more directive

Cone CutCone Cut--off Frequency off Frequency fcfor rigid conefor rigid cone

cHH

Hcf o

c π=λ/2

0°330

300 60°

30°

Polar plot


f > fc many sound waves fit between cone top and base

attenuation on-axisgeneration of side lobes

270

240

210180°

150°

120°

90°-15 -10 -5

Rigid Piston and ConeRigid Piston and Cone

Sound Power

Lπ

Sound Pressure in axisLP

conecone

piston piston


fc fcft ft

ft transition frequency (above which piston has higher directivity)

fc cut-off frequency wavelength λ> 3H (cone height H)

ff

Directivity Pattern after BreakDirectivity Pattern after Break--upup

1078,1 Hz

ra

Rayleigh Integral Equationcrrjkc

a dSerjXrjp ca −−

∫=),(

2),( 0

2 ωρωω

rc,1

rc,2

Out of phase


cS ca

arr

jpc

∫ −2)(

π

2. Phase difference in the mechanical cone vibration of different source points rc

1. Phase shift generating by the difference in the distance between particular source point rc and reference point ra

Distance compensates for Phase of DisplacementDistance compensates for Phase of Displacement

0°

330

300 60°

30°

InIn--Phase Component Phase Component radiating the sound in 60 radiating the sound in 60 degree offdegree off--axis (woofer C)axis (woofer C)


270

240

210

180°

150°

120°

90°-15 -10 -5

Both geometry and vibration determine the directivity pattern !! Both geometry and vibration determine the directivity pattern !!

Headphone Headphone –– Vibration 2760 HzVibration 2760 Hz


Headphone Headphone –– Radiation 2760 HzRadiation 2760 Hz

0°

330

300 60°

30°

ϕTwo Circumferential Two Circumferential modes with modes with opposite phaseopposite phase


270

240

210

180°

150°

120°

90°-15 -10 -5

opposite phase opposite phase cause a beam cause a beam steering offsteering off--axisaxis + - + -

dipoledipole dipoledipole


20

30

40

50

60

70

103 104

SP

L [d

B]

Frequency [Hz]

How to Separate Circumferential Modes ?How to Separate Circumferential Modes ?

xxx +=

Decomposition technique for raditors with axialDecomposition technique for raditors with axial--symmetrical geometry:symmetrical geometry:

Total vibration mode

Circumferential vibration mode

circradtotal xxx +=

Radial vibration mode

Averaging over circumference radtotalcirc xxx −=


HigherHigher--order Circumferential Modesorder Circumferential ModesWoofer C with flat radiatorWoofer C with flat radiator

KLIPPEL90

Accumulated Acceleration Level

Total AAL Radial AAL Circumferential AAL


Above 4 kHz the AAL of the Above 4 kHz the AAL of the circumferential mode becomes circumferential mode becomes

comparable with the radial comparable with the radial componentcomponent

How much sound is generated How much sound is generated by the circumferential modes ? by the circumferential modes ?

50

55

60

65

70

75

80

85

90

102 103 104

SP

L [dB

]

f [Hz]

KLIPPEL

80

90

Total SPL

SPL Generated by Circumferential ModesSPL Generated by Circumferential Modesonon--axis response of woofer C axis response of woofer C

20

30

40

50

60

70

80

SPL

[dB]

Total SPL

Circular Component (Acceleration)

Circ lar Component (SPL)

on-axis


0

10

102 103 104

f [Hz]

Circular Component (SPL)

Circumferential component produces very low output on-axis

KLIPPEL

80

90

Total SPL

Sound Radiated in Other Directions ? Sound Radiated in Other Directions ?

20

30

40

50

60

70

SPL

[dB]

Circular Component (Acceleration)

Circular Component (SPL)

off-axis


10

102 103 104

f [Hz]

Circular component contibutes significantly to 60 degree off-axis

Power Generated by Circumferential ModesPower Generated by Circumferential Modeswoofer C Flat Pistonwoofer C Flat Piston

KLIPPEL90

power

KLIPPEL

50

60

70

80

Pow

er [d

B]

Total Power

Total AAL

Circular Component (Sound Power)


20

30

40

102 103 104

f [Hz]

How to Find Circumferential Modes How to Find Circumferential Modes on Radiators with Nonon Radiators with Non--axially Symmetrical Shape (e.g. Oval Speaker) ?axially Symmetrical Shape (e.g. Oval Speaker) ?

Cancellation effect in SPL on axis t i i d t

OnOn--axisaxis

TotalTotal KLIPPEL

65

70

Acceleration Level

Total Component Quadrature AccelerationQuadratureQuadrature

generates maxima in quadrature component of AAL (sound pressure related decomposition)


20

25

30

35

40

45

50

55

60

103 104

SP

L [d

B]

f [Hz]

1.3 kHz1.3 kHz

Is the Rocking Mode Too High ?Is the Rocking Mode Too High ?Woofer A with paper coneWoofer A with paper cone

Rocking is negliglible if d t t

60

70

80 Total AAL

-20 dB

voice coil rubbing


quadrature component is 20 dB below total component !

0

10

20

30

40

50

100 1000

[dB]

f [Hz]

Quadrature Component (AAL)

Anisotropy of the Cone MaterialAnisotropy of the Cone MaterialMidrange with KevlarMidrange with Kevlar

Fibrestructure

phase7 kHz7 kHz


amplitude

Nonlinear DistortionNonlinear Distortiongenerated bygenerated by significant deformation of the geometry

Shell segment σstress

High local displacementHigh local displacement

b

ξ

b<<ξstretch

ε

plastic deformation


18 inch wooferCompression driver

Influence of the Air Load Influence of the Air Load ??example headphone transducerexample headphone transducer

KLIPPEL

60

70

80

B] SPL free air

SPL vacuum

••Perform scans in air Perform scans in air

30

40

50

103 104

SP

L [d

B

f [Hz]

SPL free air

in airin air

3.8 kHz

and in vacuumand in vacuum••Compare mechanical Compare mechanical vibration (AAL) or vibration (AAL) or predicted sound predicted sound pressure output (SPL)pressure output (SPL)

in vacuumin vacuum


How to Optimize the Design ?How to Optimize the Design ?Coupled mechano-acoustical analysis

FEA BEAMagnetic

FEA

Mechanical System

(suspension,cone,

diaphragm)

Motor(coil,gap,

magnet)

Acoustical System

(enclosure,horn)

F X(rc)

F(rc)Far-Field

u Sound Propagation p(ra)

p(r)

v(r)

Pv

Tv

coilformer Radiator near field

FEAFEA


ThermalDynamics

Thermal

FEA

Providing Input Data for FEAProviding Input Data for FEARadiator

(cone, diaphragm, panel)

Material

E,ηFiniteElement

Drive Unit

MaterialParametersAnalysis

Predicted Víbration(accumulated level + shape)•of total vibration•of separated components

3937,5 Hz

Modal & DecompositionAnalysis

η



Geometry

Vibration

Measured Víbration(accumulated level + shape)•of total vibration•of separated components

3937,5 Hz

Modal & DecompositionAnalysis

AnalysisFitting

FEA Tools for Cone Design FEA Tools for Cone Design Progress:

• Processing time, handlingFineConeFineCone

By P. LarsenBy P. Larsen

by A. Svobodnikby A. SvobodnikNADworkNADwork

ocess g t e, a d g

• Asymmetries in the shape

• Geometrical nonlinearities (“variation of the geometry”)

• Acoustical-mechanical coupling

Problems:


ANSYSANSYS

ComsolComsol

• (Nonlinear) Material parameters

• visco-elastic properties (Hyperelasticity, creep, Relaxation)

PacsysPacsys

Optimal Design of the EnclosureOptimal Design of the Enclosure

Acoustical

Sound Pressure•on-axis•directivity


Geometry

enclosure,horn room

System(enclosure, horn, room)

Geometry

BEA+

FEA

Geometry

Vibration Sound Power

AdmittanceY(jω) at voice coil

3937,5 Hz

Linear Linear Lumped & Lumped & Distributed Distributed ParametersParameters


horn, roomGeometry

Velocity in the portVelocity in the port

Air NoiseAir Noise

Enclosure Enclosure and Horn and Horn DesignDesignusing FEA and BEA Toolsusing FEA and BEA Tools

NADwork ABECNADwork


PacSysPacSys

SummaryCheck List • Smooth SPL and power response (no dips and peaks) ?

S ffi i t ib ti f th di t ( d l d it ) ?• Sufficient vibration of the radiator (modal density) ?• Sufficient damping of the modal resonances (η > 0.03) ? • Gradual break-up replacing the piston mode ? • No acoustical cancellation (sharp dips in SPL)• Dominant in-phase component (AALin-phase > AALanti-phase) ?• In-phase component in the centre of the radiator ?• Shrinking size of area covered by in-phase component (Sd(f) 0) ? • Low quadrature component generating no sound (AALquad < AALtotal) ?


q p g g ( quad total)• Negligible rocking mode generating rub&buzz (AALcircular < AALtotal) ?• High local displacement causing nonlinear distortion ?• Desired directivity index ?• Higher-order circumferential modes contributing to power response ?

Many thanks !Many thanks !

Get a CD with the Analysis Software Get a CD with the Analysis Software

More detailed information please find in :More detailed information please find in :

W. Klippel, J. Schlechter, “Distributed Mechanical Parameters of LoudspeakersW. Klippel, J. Schlechter, “Distributed Mechanical Parameters of Loudspeakers Part 1:Part 1:


W. Klippel, J. Schlechter, Distributed Mechanical Parameters of Loudspeakers W. Klippel, J. Schlechter, Distributed Mechanical Parameters of Loudspeakers Part 1: Part 1: Measurement,“ J. Audio Eng. Society 57, No. 7/8, pp. 501 Measurement,“ J. Audio Eng. Society 57, No. 7/8, pp. 501 –– 511.511.

W. Klippel, J. Schlechter, “Distributed Mechanical Parameters of Loudspeakers W. Klippel, J. Schlechter, “Distributed Mechanical Parameters of Loudspeakers Part 2: Part 2: Diagnostics,“ J. Audio Eng. Society 57, No. 9, Diagnostics,“ J. Audio Eng. Society 57, No. 9,

Further ReferencesFurther References

F.J. M Frankort, „Vibration Patterns and Radiation Behavior of Loudspeaker Cones,“ J. of F.J. M Frankort, „Vibration Patterns and Radiation Behavior of Loudspeaker Cones,“ J. of Audio Eng. Soc., Sept. 1978, Vol.l 26. Pp. 609Audio Eng. Soc., Sept. 1978, Vol.l 26. Pp. 609--622622

Kaizer, A., “Calculation of the Sound Radiation of a Nonrigid Loudspeaker Diaphragm Kaizer, A., “Calculation of the Sound Radiation of a Nonrigid Loudspeaker Diaphragm Using the FiniteUsing the Finite--Element Method,”Element Method,” J. of Audio Eng. SocJ. of Audio Eng. Soc., ,Vol. 36 ,Nr. 7/8, pp. 539., ,Vol. 36 ,Nr. 7/8, pp. 539--551; 551; July 1988. July 1988.

L. Beranek, "Acoustics", L. Beranek, "Acoustics", published by the Acoustic Society of Americapublished by the Acoustic Society of America, New York (1996) , New York (1996)


Wright, J. R , “Automatic Vibration Analysis by Laser Interferometry,” Wright, J. R , “Automatic Vibration Analysis by Laser Interferometry,” presented at the presented at the 8888thth Convention of the Audio Eng. Soc.Convention of the Audio Eng. Soc., preprint 2889; (March 1990). , preprint 2889; (March 1990).

KLIPPEL Tutorial on Cone Vibration and Radiation AES 2010

Documents

Transcript of KLIPPEL Tutorial on Cone Vibration and Radiation AES 2010