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Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 1
Loudspeaker Parts
Measurement Seminar
Klippel GmbH
Stefan Irrgang
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 2
What does this seminar offer? • Overview on loudspeaker part measurements
o B-Field Testing o Temperature / Power Testing o Suspension Part Measurement
Low frequencies (lumped K(x)) Cone break up range (distributed)
o Material Parameter Measurement o RMA – Rocking Mode Analysis
• Relation to measurements at final loudspeaker
• Theory on measurement principles
• Available Industry Standards
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 3
Measurement of magnetic Flux density
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 4
Abstract
Measurement of magnetic Flux density (B Field Scanner)
The flux density B(phi,z) in the gap is automatically measured versus angle phi and height z by using a B-Field Probe and a mechanical scanning technique. This technique is the basis for predicting the force factor Bl(x) and for detecting problems in the design, assembling and magnetization causing rocking modes and voice coil rubbing.
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 5
Example: Static Measurement of B-field in the gap and force factor characteristic Bl(x)
hall sensor
z-axis
Turntable with r-axis and φ-axis
UH
I
b
d
Hall principle
B field
Hall voltage
Neubert, Lars
Master thesis 2010
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 6
Scanning Process
Cylindrical Coordinates
Vertical
position
z
Angle
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 7
Angle (degree) Vertical position z (mm)
30
20
10
B
(Tesla)
Magnetic
flux
density
Nk
NirzB
z
ki ,...,1
,...,1),,( 0
Magnetic Flux Density on the scanned surface
maximum Angle
Vertical
position z
minimum
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 8
Force Factor Nonlinearity Bl(x) Integration of the B field versus coil length l
l
l
lz drrBeBl )(
Angle
Angle
Radius r0
Rest Position
Height
Voice coil displacement
x
zr
Voice coil
z
2nd layer
Gap width
W
w
w
w
w
N
Ni
r
N
N
r
ziD
xBrm
rdzDxBmxBl
)2
(2
),2
()(
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 9
0 45 90 135 180 225 270 315 360 -10
-5
0
5
10
Angle f
%
VB()
Asymmetrical Field Distribution
0°
90°
180°
270°
maximum
minimum
%100)(
)(z
zz
B
B
BBV
Flux Density Variation
VBl(x=0,)
%100)(
)(),('2),(
xBl
xBlxBlxVBl
2
0
),(')( dxBlxBl
Variation of Force Factor Distribution
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 10
Asymmetries of the Magnetic Field
Additional magnet
Causes:
• Geometry is not axially symmetrical
• Position of the magnet
• Position of the pole piece
• Magnetization process
Consequences:
Tilting of the voice coil former
Rocking modes
Rubbing coil Higher-order distortion damage
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 11
Causes of Rocking Modes
Mass
Unbalances
Stiffness
asymmetries
Asymmetric acoustic loads…
B field
Asymmetries
Nk
NirzB
z
ki ,...,1
,...,1),,( 0
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 12
How to assess the Force Factor Nonlinearity ?
Magnetic System
STATIC
FEM
Geometry +
Material
Static
Flux Density
)0,( coill irBParameter
Identification
Transducer
Force Factor
Bl(x, icoil>0)
+ Stimulus
Voice Coil
Force Factor
Bl(x, icoil=0)
Integration over
Coil length
Geometry
+ Material
PrototypeHall Sensor
Scanningagreement ?
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 13
Temperature Monitoring (Power Test)
KLIPPEL
0
25
50
75
100
0,0
2,5
5,0
7,5
10,0
12,5
0 250 500 750 1000 1250 1500 1750 2000 2250
Increase of voice coil temperature Delta Tv (t) and electrical input power P (t)
Delta Tv [K]
P [W]
t [sec]
Delta Tv P real P Re
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 14
Static Temperature Tests Standards:
• ALMA TM-324 (Draft): Test Method for Voice Coil Maximum Operating
Temperature (TMO):
Find ratio (K) between hot and cold DCR for coil only (DC voltage)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 15
Conventional techniques:
Temperature Monitoring with DC source
Disadvantages:
• Requires additional hardware (large capacitor)
• Causes Offset in voice coil displacement
• Slow monitoring of voice coil temperature
• Fails in measuring drivers with crossover
• Limited in speed and AC-rejection
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 16
Temperature Measurement By Using a Steady-State Pilot Tone
Fourier
Transform
loudspeaker
system
current
sensor
U(t) I(t)
-
Stimulus
voltage
sensor
pow er
amplif ier
Pilot
Tone
Temperature
Calculation
Resistance of cold
speaker
Conductivity of Coil
Material
Increase of VC
Temperature
Transducer: 1- 4 Hz
Systems: 0.01 ... 3 kHz
Benefit of adding an additional tone:
• Quasi-dc measurement with ac-power amplifier possible (f < 4 Hz)
• High speed monitoring of variation of Re(t)
• Long term averaging using low amplitude • No external stimulus required • active during cooling phase (OFF-cylce) • Impedance measured at one frequency • power of pilot tone is negligible
KLIPPEL
5
10
15
20
25
30
35
40
45
50
2 5 10 20 50 100 200 500 1k 2k 5k 10k
Magnitude of electric impedance Z(f)
[Ohm
]
Frequency [Hz]
Measured
Most accurate measurement for
transducer
Not applicable for
temperature measurement
Impact of woofer, tweeter and crossover
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 17
Voice Coil Temperature Measured via Electrical Resistance Re (t)
• Based on voltage and current
measurement
• Re (t) corresponds with mean
value of the temperature
• Local temperature varies in
overhang coils
Better cooling of inner coil
windings (Heat radiation to
the pole tips, convection
cooling, high air velocity)
Indications of a thermal damage:
• loose windings voice coil rubbing
• shortcut of windings with pole gap reduced resistance
• open coil maximal resistance limited by instrument
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 18
Pilot Tone
DA2 or PM 8
Pilot tone
Dut 1
Speaker 1Amplifier 1Power Amplifier
Signal
Source
Input Signal +
Synchroneous
Pilot tone
OUT 1
IN 1
~Internal Pilot tone
OUT 2
Speaker 1Amplifier 1Power Amplifier
Passive
Filter
Active
Filter
DA2 or PM8
Dut 2
Dut 1
Speaker 2Amplifier 2
Passive
Filter
Active
FilterPower Amplifier
~
Signal
Source
Signal
Source
Asynchroneous
Pilot tone
External
Generator
~
Asynchroneous
Pilot toneExternal
Generator
DA2 or PM8
Dut 2Speaker 2Amplifier 2
Passive
Filter
Active
Filter
Power Amplifier
Signal
Source
Synchroneous
Pilot tone
Dut 1
Speaker 1Amplifier 1
Passive
Filter
Active
Filter
Power Amplifier
Signal
SourceInput Signal +
Synchroneous
Pilot tone
OUT 1
~
Pilot tone f1
OUT 2
Input Signal +
Synchroneous
Pilot tone
~
Pilot tone f1
MULTIPLEXER
External mixing of internal pilot tone
External mixing of external pilot tone
Internal mixing of the pilot tone
2Hz for woofer
2 Hz for subwoofer
20 Hz for tweeter
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 19
Assessing Maximal Power Handling
KLIPPEL
Increase of voice coil temperature Delta Tv (t) and electrical input power P (t)
DUT: 1 (01:35:54)
Delta
Tv [
K]
P [W]
t [sec]
0
50
100
150
200
250
300
0,0
2,5
5,0
7,5
10,0
12,5
15,0
17,5
20,0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500
Delta Tv P
failure
Permissable increase of VC temperature Pmax
190 K
13 W
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 20
Failure Detection („Death Report“)
• High sampling of state (X, Tv) and parameters
(Kms) period just before destruction
• Allows to investigate cause of failure
-10
0
10
20
30
40
50
60
70
80
90
100
0,00
0,25
0,50
0,75
1,00
1,25
1,50
1,75
0 2500 5000 7500 10000 12500
Increase of voice coil temperature Delta Tv (t) and electrical input power P (t)
DUT: 1 (04:04:40)
Del
ta T
v [K
]
P [W
]
t [sec]
Delta Tv P real P Re P con
25
50
75
100
125
150
175
0,25
0,50
0,75
1,00
1,25
1,50
1,75
14000 14100 14200 14300 14400 14500 14600
Increase of voice coil temperature Delta Tv (t) and electrical input power P (t)
DUT: 1 (04:04:40)
Del
ta T
v [K
]
P [W]
t [sec]
Delta Tv P real P Re P con
Regular Sampling
Fast Sampling
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 21
Suspension Part Measurement
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 22
Abstract
Linear Suspension Part Testing for QC (LST)
http://www.klippel.de/our-products/qc-system/additional-modules/linear-suspension-test.html
The QC LST is dedicated to the quality control of suspension parts (spiders, cones, surrounds) and passive radiators (drones). Linear mechanical parameters like resonance frequency, stiffness (LST Lite) or relative mass and stiffness deviation (LST Pro) are determined dynamically from the displacement frequency response. The device under test is stimulated pneumatically while displacement is measured by a cost effective triangulation laser.
Test objects with circular geometry are easily attached to the measurement bench without time consuming mounting effort by using a set of mounting parts (rings, cones). The fast loading mechanism is designed to change DUTs as fast as possible while ensuring stable and robust measurement conditions. For quality control limits can be calculated based on reference units to provide pass/fail verdicts.
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 23
Static Suspension Measurement
Tonwel:
Elasticity of Spider
Measurement System
based on EIA RS-438
http://www.tonwel.com/b-en-t05.php
Standards:
• ALMA TM-438 Measurement of the Stiffness of Loudspeaker
Driver Suspension Components
• EIA RS-438 (ANSI C83.116-1976)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 24
Method:
• Sample the working range
• Generate DC displacement xDC
• Measure associated state signals FDC
• Calculate instantaneous parameters
• Repeat the measurement at other working points
Quasi-Static Measurement of Kms(x)
F
x
secant
KMS(x)= FDC
xDC
Results depend on measurement time
Hysteresis has no importance for audio band
Dynamic measurement preferred
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 25
Practical Realization of Quasi-Static Method
Ringlstetter Harman Becker Straubing, Germany
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 26
Tonwell:
Compliance of Loudspeaker
Spider and Cone Test System
http://www.tonwel.com/b-en-t01.php
Quasi-Static non-linear
Measurement of Kms(x)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 27
Dr. Kurt Müller - R&D Tester -used for the development of any kind of suspensions during early design of components.
Hysteresis curves are basically used for interpretation or evaluation.
There are various opportunities to study the behaviour of suspension parts during their movement in a large range.
It’s an quasi static measurement and comparable with conventional tensile strength tests.
All samples have to be fixed during measurement at the neck (or inner diameter) and pressed down at the OD with pneumatic clamping force.
For analysis, the R&D-Tester has to be linked to a computer.
Weight Range: +/- 25 kg Precision: +/- 0.1 mm, +/- 1 mN Max Excursion: +/- 100mm
Quasi-Static non-linear
Measurement of Kms(x)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 28
Dynamic, Linear Suspension
Measurement
Tonwel:
The Test System for the
Resonance Frequency of
Loudspeaker Cones
http://www.tonwel.com/b-en-t03.php
Standards:
• IEC 62459/Ed.1
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 29
Linear Suspension Test (LST) Fast quality control of suspension parts and passive radiators
• Objective: check driver and system parts before assembly (spiders, cones,
domes, passive radiators) early quality control
• Software and optional hardware set for the QC System (Basic & Standard)
• Fast and easy mounting of DUT time efficient testing
• Fits a wide variety of DUT sizes
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 30
Mounting Suspension Parts
LST Bench
Variable Ring Set Mounting Cones Free air setup
Reflective
coverLaser beamCone
Spider
Ring set
Cone
B5 B4
BoltNutStandard
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 31
Processing of displacement response
KLIPPEL
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
101 2*101 3*101
Dis
pla
ce
me
nt x [
mm
]
Frequency [Hz]
Displacement Magnitude
f1 fr f2
-3dB
𝑄 =1
𝐷𝐹=
𝑓r
𝐵=
𝑓r
𝑓2 − 𝑓1
Simple processing, only based on displacement amplitude response (laser signal) Assumptions • Constant driving force • Constant moving mass m
(dominated by inner clamping)
𝑓r
=1
2𝜋 𝑘
eff
𝑚≙ arg max 𝑋 𝑓
Resonance Frequency
𝑘0 ≙ 𝑘eff 𝑥
peak, 𝑥
dc = 𝑚 2𝜋𝑓
r 2 for 𝑥peak
, 𝑥dc→ 0
Stiffness (small signal)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 32
Operator View
Control Panel
Displacement Response
Test Verdicts
Temperature/Humidity
Detailed Result Table
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 33
Testing in Operator Mode
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 34
Testing Passive Radiators
• Passive system element – difficult to test before loudspeaker assembly
• Most important parameter: moving mass
• Resonance frequency result of both suspension stiffness and moving mass
• Added mass method may be used to determine moving mass – inappropriate for QC
• Solution: monitoring relative deviation to „golden“ reference unit
KLIPPEL LST
Bench
Passive
Radiator
Fast clamper
Custom mounting
platform
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 35
Monitoring Mass & Stiffness Deviation using displacement response only
CMP
MMP
p CAB
qB qL
RAL
qqD
SPF
dx/dt
pD
ZD
RMP
Speaker Enclosure Passive Radiator
KLIPPEL
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,60
3*101 4*101 5*101 6*101 7*101 8*101 9*101
Dis
pla
ce
me
nt x [
mm
]
Frequency [Hz]
Displacement Magnitude Displacement Magnitude (Golden DUT)
Qf
fj
f
fabsfxf
Qf
fj
f
fabsfxf
fM
fM
ms
ms
11|)(|
11|)(|
)(
)(
0
2
0
2
2
0
0
2
0
2
2
0
Golden unit‘s
response
Tested unit‘s
response
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 36
Hardware Platforms
SPM Bench (RnD System)
• SPM Pro for linear and nonlinear testing
• SPM Lite for linear testing
LST Bench with internal laser
(QC System)
• Linear Suspension Test
LST Bench with external laser (RnD System)
• SPM Lite for linear testing
MSPM Bench (RnD System)
• MSPM Pro for linear and nonlinear testing
• MSPM Lite for linear testing
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 37
Non-linear Suspension Part Measurement
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 38
Abstract
Suspension Part Measurement (SPM)
http://www.klippel.de/our-products/rd-system/modules/suspension-part-measurement.html
Suspension Part Measurement features a dynamic identification of the small and large signal spider parameters (Force deflection curve, Stiffness curve, resonance, damping factor…) using an audio like ac-stimulus. This measurement can also be performed as an accelerated life test for separating fatigue from break-in and assessing the long term stability of the suspension.
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 39
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
10 1 10 2 10 3 10 4
[mm
/V]
f [Hz]
measured
• Different approaches to describe this effect
Magnitude o f Transfer Function X(f)/U(f)
estimated without creep
Problem: Suspension at Low Frequencies
Mmd Cmd(f) Rmd(f)-1
Bl
Re
V=dx/dt
i
Blv
Bli
U
ZL(f)
Kundsen and Jensen, JAES
1993
𝐶 𝑓 = 𝐶0 1 − 𝜆 log10𝑗𝑓
𝑓s
𝐶 𝑓 = 𝐶0
1 − 𝜅 log10
𝑗
𝑓𝑓min
𝑒−𝑗 tan −1
𝑓𝑓min
1 + 𝑓
𝑓min
22
Ritter, 2010
• compliance Cmd(f) and resistance
Rmd(f) increases to lower frequencies
below resonance f << fd
DC Audio Band
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 40
Static and Quasi-Static Measurement of Kms(x)
Disadvantages:
• Stiffness measured at very low frequencies is much smaller than the stiffness found in the audio band
• Static displacement of the suspension affects the rest position
• Creep, relaxation, hystereses only occur at low frequencies
• Time consuming
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 41
Method:
• Excite speaker with large AC-signal
• Measure a state variables XAC(t) and FAC(t)
• Estimate KMS(x) to describe relationship between input FAC and output XAC
Full dynamic Measurement F
x
secant
KMS(x)= F
X
FAC(t)
XAC(t)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 42
How to measure the Large Signal
Parameters of Suspension Parts
Advantages:
• dynamical method
• vertical operation
• robust, easy to use
• inexpensive Set up according to IEC Standard 62459
Example: SPM System
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 43
Dynamic Measurement of the Mechanical
Stiffness of Suspension Parts
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 44
Need for a Dynamic Measurement
of Suspension Parts
significant variation of Kms(x=0) at the rest position x=0
small variation of Kms(xpeak) at the maximal displacement Xpeak
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
displacement x [mm]
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
time
displacement x [mm]
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
time
displacement x [mm]
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
time
displacement x [mm]
Measurements in
15 min intervals
Kms(x)- versus time
Generation of a
dc component
by stiffness
asymmetry
Small variation at
maximal
excursion
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 45
Variation of Suspension Stiffness K(t)
versus Measurement Time t
Disadvantages of :
• measurement results depends on the properties of the stimulus
• assumes constant excitation during power test
• can not be transferred to other stimuli
• neglects the slope of the stiffness variation
1000 8060 12020 40 160140 180
K(t=1h)
K(t=100h)
K(t)
hourt
Speaker 2
Speaker 1
)h1(
)h100(h100
tK
tKR
break-in
fatigue
accumulated load
Stiffness ratio after 1 h and
100 h power testing
Idea:
Replacing time t by a quantity
describing the dosage of the
mechanical load
Performing a power test with
pink noise of constant
amplitude
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 46
Accumulated Load Model
Measurement Condition:
same stimulus of constant amplitude during the power test
0
K(W=0)
K(W)
WW90%W50%
K(W)
K
P=const.
N
i
wW
iieCWK
1
/1)(
)()0()(ˆ WKWKWK
Stiffness of loudspeaker suspension versus
accumulated work W
N=2 sufficient for most cases
loss of stiffness
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 47
Example: Poor Spider Suffering from Long-Term Fatigue
1,1
1,2
1,3
1,4
1,5
1,6
1,7
K(W)
[N/mm]
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 W [kWh]
measured
fitted
• 50% of initial stiffness
decay during life-cycle
• Only 50% of stiffness
decay during break in
• High fatigue ratio -
permanent but slow decay
of the stiffness
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 48
Measurement Technology Suspension Parts
Res
Laser
Sensor
Analyzer 2
suspension
loudspeaker
enclosure
inner clamping
System
Identification
K(x)
P
Fitting Algorihm
Parameters
of the Aging
Model
X(t)
Measurement of spiders, surrounds and passive
radiators using a laser sensor and system identification
dt
tdxtxxKtP
)()()()(
apparent mechanical power
nonlinear
system
identification
displacement
sensor
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 49
How to measure Micro Suspension Parts
Preparation
• Diaphragm glued or clamped in panel
• Diameter < 40mm
Measurement
• Passive excitation by pressure chamber below
• Laser measurement of displacement
• Microphone measurement of pressure
Laser Sensor
Microphone
Panel with DUT
Loudspeaker
Pressure
Chamber
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 50
Linear Parameter Identification
Calculation of Results
• Mass perturbation with known mass
• Fitting modelled Transfer function to the measurement
Measurement Signal
• Sweep Signal
• Measurement of Transfer function H(f) = X(f)/P(f)
KLIPPEL
0,00
0,01
0,02
0,03
0,04
10 2 10 3
Input Curves
Ma
gn
itu
de
Frequency [Hz]
Curve 1 without mass Curve 2 without mass
Curve 1 with mass Mean Fitted Curve Without Mass
Mean Fitted Curve With Mass Fitting Range
Added Mass
No Mass
H(f) = X(f)/P(f) 𝐻 =𝑋
𝑃=
𝑆𝐷𝐾
1 + 𝑠 ∗𝑅𝐾+ 𝑠2 ∗
𝑚𝐾
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 51
Nonlinear Parameter Identification
Calculation of Results
• Model Force FDUT from the measured Displacement
• Minimize error between measured Force (𝑃 ∗ 𝑆𝐷) and modelled Force
• Verification: Fitting Error <20%
Measurement Signal
• Low frequency Multitone signal
• Measurement of displacement
• Generated distortion results from nonlinear K(x)
KLIPPEL
-510
-410
-310
-210
10 2 10 3
Distortion in Frequency Domain
Fo
rce
[N
]
Frequency [Hz]
Fundamental (F_Stim) E_F(f) Distortion
KLIPPEL
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
-0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3
K(x) over Displacement
K(x
) [N
/mm
]
Displacement [mm]
K(x) Extrapolation K(x)
𝐹𝐷𝑈𝑇 = 𝑃 ∗ 𝑆𝐷 = 𝐾 𝑥 ∗ 𝑥 + 𝑅 ∗ 𝑥′ +𝑚 ∗ 𝑥′′
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 52
Comparing LSI vs. MSPM Results
Small differences possible
• Different time and temperature conditions – LSI: 5-10min
– MSPM: 2-5s
• Different application of force – LSI: at voice coil position
– MSPM: distributed over membrane area
diaphragm
backplate
magnet
pole plate
coil
Microspeaker
diaphragm
backplate
magnet
pole plate
coil
Force Force
Diaphragm
KLIPPEL
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
-0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2
K(x) over Displacement
K(x
) [N
/mm
]
Displacement [mm]
MSPM LSI
LSI Microspeaker
MSPM Diaphragm
Softer due to
temperature and time
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 53
Application
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 54
MSPM in Operation Laser positioning by clamping MSPM bench at
LST or SPM Bench
SCN - Scanning Vibrometer
Pro Driver Stand
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 55
Challenges in Suspension Design
Critical examples are flat and slim transducers used over the full audio
band (headphone, micro-speaker, TV-Speaker)
PROBLEMS:
1. Suspension centers the coil in the gap sufficient clearance to
avoid coil rubbing
2. Suspension determines the rest position of the coil in the gap coil
offset
3. No spider is used or distance between spider and surround is small
Rocking mode coil rubbing
4. Surround contributes significantly to the effective radiation area Sd
acoustical output
5. Suspension determines the peak displacement xmax required for bass
reproduction large geometry significant material deformation
6. Air pressure in the enclosure affect the stiffness of the suspension
7. Displacement (bass) affects modal vibration of the surround
strong intermodulation
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 56
Objectives of the Suspension
voice coil
former
diaphragm
frame
spider
diaphragm
backplate
magnet
pole plate
coil
microspeaker
Centering
Defining coil‘s
rest position
Suppressing tilting and rocking
Conclusion:
• Decreasing stiffness in the direction of intended
coil movement !
• Increasing stiffness in all other directions !
Solved by nonlinear
control with active
stabilization
Unsolved problem !
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 57
Suspension Characteristics for describing optimal properties in the particular application
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
-10,0 -7,5 -5,0 -2,5 0,0 2,5 5,0 7,5 10,0
Mechanical compliance Cms(X) vs displacement
Cm
s [m
m/N
]
Displacement X [mm]
more linear progressive
Compliance XC(x=0) at rest
position which is important for
resonance frequency fs
Maximal Excursion Xmech
which is important for
mechanical protection 25 %
Displacement limit XC
generating 10 % harmonics 75 %
Note: Symmetrical nonlinearities of the suspenion are usually beneficial
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 58
What is a Bad Suspension Part ? Properties which are not acceptable – k.o. criteria
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
displacement x [mm]
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
time
displacement x [mm]
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
time
displacement x [mm]
500
1000
1500
2000
2500
3000
3500
4000
4500
-15 -10 -5 0 5 10
[N/m]
time
displacement x [mm]
K(x=0)
Significant loss (> 30 %) of stiffness K(x=0,t) versus time after break-in
Ak Stiffness asymmetry Ak (> 20 %) measured at high excursion
Significant dc displacement generated dynamically by stiffness asymmetry
12 mm -17 mm
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 59
Bad Spider Suffering from Long-Term Fatigue
1,1
1,2
1,3
1,4
1,5
1,6
1,7
K(W)
[N/mm]
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 W [kWh]
measured
fitted
• 50% of initial stiffness
decay during life-cycle
• Only 50% of stiffness
decay during break in
• High fatigue ratio -
permanent but slow decay
of the stiffness
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 60
Spider - Weakest Part of the Loudspeaker
Research activity: Replacement of impregnated
fabric by new materials
Tupperware® gives lifetime warranty
KLIPPEL
0,0
0,5
1,0
1,5
2,0
2,5
3,0
-10 -5 0 5 10 15 20
Stiffness versus Displacement
Stif
fne
ss [N
/mm
]
Displacement x [mm]
Kms(x) after 10 min
Stability of a
Tupperware lid
over time
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 61
How to Specify the Suspension Part
R&D Measurement (e.g. SPM module)
• Vertical operation
• Clamping similar to final application
• Dynamic measurements
• Small and large signal domain
• Long-term Measurement (ageing, fatigue)
Important Characteristics
• Dynamic stiffness K(x=0) measured at small amplitudes
• Loss of stiffness K(x=0,t) versus time t
• Stiffness asymmetry Ak measured at high excursion
• DC-displacement generated dynamically
• Maximal peak displacement Xc giving decay of compliance to 75 %
More details in IEC Standard 62458 and 62459
QC
R&D
End-of-line Testing (QC System)
• Horizontal operation
• Minimal clamping
• Dynamical Measurement
• Small Signal Domain
• Fast measurement (< 1s)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 62
Material Parameter Measurement
2014
Stefan Irrgang
Klippel GmbH
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 63
Abstract
• Temperature Monitoring (Power Test)
• http://www.klippel.de/our-products/rd-system/modules/power-testing.html
• A fast and reliable measurement of the instantaneous voice coil temperature of woofer, tweeter, micro-speakers and active systems can be realized by using a small ac pilot tone added to the stimulus. This technique reveals the thermal dynamics (heating and cooling process) of voice coils with a small or large thermal capacity.
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 64
Measurement of Young‘s E-modulus and loss
factor of material samples
X/P [dB]
f [Hz]
- 3dB
0 dB
∆f
f 0
𝜂 =∆𝑓
𝑓0
𝐸 = 38.29𝑚𝑙3
𝑏𝑑3𝑓0
2
… mass
… width
… height
… length
m
b
d
l
Requirements: • Planar (flat) material samples
• Isotrophic material
• Constant thickness and density
Modal loss factor
Youngs E-modulus
Application: • Communication between driver and softpart manufacturer
• Checking production consistency
• Not applicable to FEM at high frequency
Method: • simple beam technique (Standard ASTM E 756-93)
• acoustical excitation (applicable to thin foils)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 65
Operation of the MPM Measurement hardware
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 66
Dustcap
Cone
Surround
Problem: • FEM requires accurate material material parameters for simulation • Compound materials are used in loudspeakers • Influence of glue and processing (variation of thickness and density) Table or standard values for materials are not applicable
• Material parameters are highly frequency dependent (factor 10 over audio band) The first prototype of the transducer is the best test measurement setup for
exciting the material and measurement the mechanical vibration at high frequencies.
Measurement of Youngs modulus and loss factor by
fitting FEM to Scanner
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 67
Vibration Data FEM
Calculation of modal Parameters FEM
Calculation of differences in modal Parameters
Calculation of modal Parameters SCN
Optimized material parameters
Parameter optimal?
No
Yes
Identification Process
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 68
KLIPPEL
100
105
110
115
6*10 2 8*10 2 10 3 2*10 3 4*10 3 6*10 3
AAL
AA
L/d
B
f/Hz
SCN FEMKLIPPEL
100
105
110
115
6*10 2 8*10 2 10 3 2*10 3 4*10 3 6*10 3
AAL
AA
L/d
B
f/Hz
SCN FEM
Iterations
Error
Optimal „fitting“ of the material
parameters by minimizing the error
between FEM and SCANNER
Iterative Parameter Identification
Residual modeling error
caused by
• Geometry (cone
thickness)
• Density variation
Optimal values of E-modulus
And modal loss factor
Mismatch between FEM
and scanner
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 69
Results
Frequency
E-Modulus
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 70
Scanning Vibrometer System
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 71
Abstract
Scanning Vibrometer System
http://www.klippel.de/our-products/rd-system/modules/scanning-vibrometer-system.html
The SCN Vibrometer measures the vibration and geometry of radiators, enclosures and mechanical structures used in loudspeakers, micro-speakers, headphones and other electro-acoustical or electro-mechanical transducers. The SCN Analysis Software performs visualization, animation and a modal analysis of the mechanical vibration using the scanned data which is provided by the vibrometer.
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 72
More Comprehensive Assessment
VibrationMotor Radiation
F
V
X(r)
F(r)
soundfield
u
near
field
far
fieldVoice
coil
Cone‘s
surface
Electrical
Measurement
Mechanical
Measurement
Lumped Parameters Distributed Parameters
electrical
Hx(f)=X(f)/U(f)
mechanical
Acoustical
Measurement
Cone Vibration
+ Geometry
mechanical acoustical
Far Field SPL
Response
Impedance
Ze(f)=U(f)/I(f)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 73
Cone Scanning Techniques
Doppler Interferometry
(Polytech, 1995)
Frankort 1978
Olson, 1950
Triangulation Laser Scanner
(Klippel, 2007)
geometry
displacement
Velocity destribution on the cone
intensity
Amplitude+ phase Amplitude Amplitude + phase
+ geometry
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 74
Triangulation Laser
Features: • measures reflected laser light
• provides displacement
• Also black, transparent surface
• 0 Hz ... 25 kHz (dc component !!!)
• robust
x
Vb Va
Vl
Target surface
transmitting point receiving
point
receiving point
transmitting point
LASER
LASER
Vd
PRO • cost effective alternative to the Doppler
Interferometry
• Accurate measurement of cone geometry
• dc component generated by driver nonlinearities
Cons • Short working distance • Needs robotics for scanning
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 75
Measurement of Cone Displacement ?!
KLIPPEL
-610
-510
-410
-310
-210
-110
500 1k 2k 5k 10k
[mm
/ V]
Frequency [Hz]
surround dust cap
-100 dB
Transfer function between electrical input voltage and displacement of a point on the diaphragm
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 76
How to measure displacement at 20 kHz ?
Sweep Shaping Averager
Amplifier Displacement
Sensortransducer
X(t)U(t)
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80
[V]
Time [ms]
Stimulus (t)KLIPPEL
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 80
[mm
][e-3
]
Time [ms]
Y2 (t)
Amplitude of displacement is almost constant (less than a micro meter)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 77
z
phi
r
SCN Scanning
System
Mechanical scanning system with one
rotational (φ) and two linear actuators (r, z)
Automatic Scanning Process
• Special control software
• Secure scanning of unknown
driver geometry
Start
Finish
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 78
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 79
Sd Scan (100 points)
Good for
measurement of
effective radiation
area and other
lumped parameters
Rectangular Scan (2000 points)
Good for TV and
microspeakers
Profile Scan (27 points)
Assuming
axial-symmetrical
vibration
Explore Scan
(226 points)
Good for vibration
analysis and sound
pressure prediction
of round speakers
Detailed Scan (2900 points)
Good for searching
for irregularities
Scanning Time
8 min 1 hour 8 hours
Resolution of the Scanning Grid
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 80
3D Animation Cross-sectional Cut
Amplitude Distribution
Visualization of Vibration Data
Phase Distribution
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 81
Sound-Pressure-Related Decomposition
generates sound reduces sound no sound
)()()()( cquadcanticinc vvvv rrrr
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 82
KLIPPEL
50
60
70
80
90
100
101 102 103
Sound Pressure SPL @ 1m, 1V Accumulated Acceleration (AAL)
Power Level +47 dB @ 1V
@ 0.4m
Three Important Responses
Power
On-axis
Example: woofer
Piston mode
AAL
Maximal possible
sound pressure
output
Acoustical
cancellation
Directivity
Index
Displacement is in-phase
Omni-directional behavior
(like a point source)
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 83
Practical Examples
discussed in Journal AES 2008
Woofer A with paper cone
Woofer B with magnesium cone
Woofer C with flat radiator
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 84
Smooth On-axis SPL Response ?
Woofer A with paper cone
KLIPPEL
40
45
50
55
60
65
70
75
80
10 2 10 3
SP
L [d
B]
f [Hz]
-30 degree
on -axis
+30 degree
Woofer B with magnesium cone
KLIPPEL
20
30
40
50
60
70
80
90
10 2 10 3 10 4
SP
L [d
B]
f [Hz]
-30 degree
on -axis
+30 degree
Woofer C with flat radiator
KLIPPEL
20
30
40
50
60
70
80
10 2 10 3 10 4
-30 degree
on -axis
+30 degree
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 85
Sufficient Cone Vibration ? KLIPPEL
50
55
60
65
70
75
80
10 2 10 3
SP
L [dB
]
f [Hz]
Total SPL
acceleration level
Woofer A with paper cone:
low Q factor of cone resonances
KLIPPEL
50
55
60
65
70
75
80
85
90
10 2 10 3 10 4
SP
L [d
B]
f [Hz]
Total SPL
acceleration level Woofer B with magnesium cone:
natural modes cause high peaks in SPL
KLIPPEL
30
40
50
60
70
80
90
10 2 10 3 10 4
SP
L [dB
]
f [Hz]
Total SPL
acceleration level
Woofer C with flat radiator
dips are not visible in AAL
AAL cause peak at 0.8 kHz
Compare SPL and AAL !
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 86
KLIPPEL
30
40
50
60
70
80
90
10 2 10 3 10 4
SP
L [dB
]
f [Hz]
Total SPL
acceleration level
Woofer C with flat radiator
What Causes Excessive Peaks ?
• low modal density reduce bending stiffness (cone thickness)
• low loss factor apply damping
• longitudinal mode increase longitudinal stiffness
Search for peaks in AAL !
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 87
Sufficient Damping of the Material ?
Woofer C with flat radiator
Increase loss factor of material
Read 3dB bandwidth in AAL !
1.0840
80)(
1
1111
f
fff
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 88
Where to apply additional damping ? Woofer C with flat radiator
820,3 Hz 12398,4 Hz
65
70
75
80
85
90
102 103 104
Total Acceleration Level
ACC
[d
B]
F re qu e nc y [H z ]
Find places of high deformation !
View the shape of the modes !
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 89
Where to apply additional damping ? Woofer B Magnesium cone
KLIPPEL
50
55
60
65
70
75
80
85
90
100 1000 10000
AA
L [dB
]
f [Hz]
Acceleration Level
10 5.01
01.02
11109,4 Hz
Rubber surround has sufficient losses Cone requires damping
0
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 90
replaced by
)(
),(
)(
coil
cc
S
Dv
dSv
S c
r
using mean voice coil velocity
2
),,(
)(
2
0
drv
v
coil
coil
)(q
),( cv r
Radiator‘s surface
coilr
)(q
)(DS
)(coilv
Rigid piston
The effective radiation area SD is an important lumped parameter describing the surface of a
rigid piston moving with the mean value of the voice coil velocity vcoil and generating the same
volume velocity q as the radiator‘s surface. The integration of the scanned velocity can cope
with rocking modes and other asymmetrical vibration profiles.
Effective Radiation Area SD Definition
)( 0DD SS Reading the absolute value at fundamental
resonance
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 91
0,5
1,0
1,5
2,0
2,5
3,0
cm2
1 10 Frequency [kHz]
)( 0DS
f0
Voice coil
)( 0DD SS
Reading the absolute value at
fundamental resonance gives
)(
),()(
,,
coil
icic
Dx
SrxS
Method:
1. Measurement of vibration and radiatior‘s geometry
2. Integration over surface and voice coil position
3. Calculation of effective radiation area SD()
4. Reading SD(s) at fundamental frequency s
Problems:
• Surface is covered by grill (surface is not visible for laser)
Effective Radiation Area
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 92
Benefits
• Measurement of geometry and mechanical vibration
• Visualization of vibration behavior
• Shows contribution to sound pressure output
• Directivity pattern
• Accurate Sd calculation
• Analysis of actively radiating cone regions
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 93
Vibration and Radiation Analysis Overview on Models, Parameters, Characteristics
3937,5 Hz
Radiator (cone, diaphragm, panel)
Drive Unit (woofer, tweeter, ...)
Geometry
Boundary
Element
Analysis
Finite
Element
Analysis
Sound Pressure •of total vibration
•of separated components
•on-axis
•directivity
Vibration
Material
Parameters
E,
Acceleration (accumulated level)
•of total vibration
•of separated components
enclosure,
horn, room
Modal &
Decomposition
Analysis
System (enclosure, horn, room)
Geometry
Shape of Components •natural modes
•radial/circumferential
•related with SPL output
•irregularities
Sound Power •of total vibration
•of separated components
3937,5 Hz
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 94
Root cause analysis of
Rocking modes
Scanning Vibrometer can make Rocking Modes visible
But it gives no clue on the root cause of the Rocking Mode
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 95 William Cardenas – Klippel GmbH
Imbalances?
KLIPPEL
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
100 200 500 1k 2k
Instantaneous crest higher order distortion (ICHD)
Sig
na
l a
t IN
1
[V]
Frequency [Hz]
-29
-27
-25
-23
-21
-19
-17
-15
-13
-11
-9
-7
-5
-3
-1
1
3
5
7
9
1112
13
35
40
45
50
55
60
65
70
75
102 103
Total Acceleration Level
AC
C [
dB
/ 1
V]
Frequency [Hz]
Total Acceleration Level Total Sound Pressure Level
PROBLEMS:
- Mechanical limit due to rub&buzz
- Reduction of the acoustic output
- Can be highly excited at large amplitudes
- Asymmetric radiation pattern
0°
330
300
270
240
210
180°
150°
120°
90°
60°
30°
-15 -10 -5
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 96
ER1,E
ER2,E
IRE
Root Causes Where are the asymmetries and Inbalances located? Example:
Dominant Stiffness Asymmetry is causing rocking mode
Direction of
Mode 1
Direction of
Mode 2
Klippel, Sound Quality of Audio Systems, Part 7 Measurement of Nonlinear Parameters, 97
• For more details on RMA, see separate presentation on ALMA 2016