Title: The Transient Magnetic Behaviour of Loudspeaker Motors' Mark Dodd
1The Transient Magnetic Behaviour of Loudspeaker
Motors.Mark Dodd
2Loudspeaker Basics
- Loudspeakers convert an electrical signal to a
mechanical signal and then to an acoustic signal.
- Moving coil linear actuator voltage -gt motion.
- Diaphragm motion -gt sound pressure.
3Loudspeaker Basics.
- Rigid body motion assumed.
- Mechanically loudspeaker is equivalent to a mass,
m mechanical resistance rmc and spring stiffness
k. -
- Equating forces gives Drive force F
4Loudspeaker Basics.
- The acoustic pressure P produced, at distance r
by a sinusoidal point source with volume velocity
U at angular frequency w is given by
- Where volume velocity U is produced by a
diaphragm with area S moving at velocity, dx/dt
is given by
5Pass Band Response.
- Motion mass-limited, decreasing amplitude with
frequency.
m
0.28m
0.21m
0.14m
70u
0
20
50
100
100
200
500
1k
1k
2k
5k
10k
10k
20k
20
20k
Frequency
Hz
6Pass Band Response.
- Velocity amplitude decreases above resonance
frequency.
-40
dB
-54
-68
-82
-96
-110
20
50
100
100
200
500
1k
1k
2k
5k
10k
10k
20k
20
20k
Frequency
Hz
7Pass Band Response.
- Radiation efficiency increases with increasing
frequency.
ohm
4.3k
3.3k
2.2k
1.2k
100
20
50
100
100
200
500
1k
1k
2k
5k
10k
10k
20
20k
Frequency
Hz
8Pass Band Response.
- Motional impedance is reflected in electrical
domain.
- Net result is an SPL response with a flat pass
band.
dB
110
80
dB
Uin2.83Vrms, Distance1m
100
64
90
48
80
32
70
16
60
0
20
50
100
100
200
500
1k
1k
2k
5k
10k
10k
20k
20
20k
Frequency
Hz
9Previous Approach
- Consider the static flux from permanent magnet
separately from flux produced by current flowing
through the coil.
- Use FEM to calculate static field calculate
Bl(x) for different coil displacements x.
- Calculate Flux through coil for an arbitrary
current.
10Polynomial method
- Assume that Lvc is a function of x but not i.
- Express force variation with current in terms of
coil inductance
FBl(x)I-Lvc(x)i2.
11Polynomial method
- Eddy Currents.
- AC signal through coil results in alternating
magnetic field. - EMF induced in any conductive loops round field.
- Current flow in skin depth.
12Polynomial method
- Eddy currents
- assumed to be confined to a cylindrical region
equal to skin depth adjacent to coil. - Permeability fixed at average static value.
- Constant current density in conductive region.
- Total Flux in gap now given by
- Flux from eddy currents used to derive Lvc as a
function of frequency and coil position Lvc(x,f).
13Polynomial method
- Runge Kutta method used to numerically solve
equations. - Spectrum of distorted sinusoidal waveform
produced is analysed with FFT.
14New Magnet Topology
15Flux2D Magneto-static FEM.
- Magneto-static solver uses static version of
Maxwell's equation.
- Force on a coil is calculated using
16Flux2D Magneto-static FEM Results.
- The force versus displacement may be calculated
for a range of coil displacements.
17Flux 2D Magneto-static FEM Results.
- Voice coil self Inductance may be calculated for
different coil positions and currents.
18Flux2D Magneto-dynamic FEM
- Linear steady state sinusoidal solution.
- No static magnetic field.
- Sinusoidal input to coil induces eddy-currents in
conductive regions. - Use of permeability from static solution would
give quick calculation of small signal dynamic
fields. - Could be used to generate Lvc(x,f) for parametric
model.
19Flux2D Transient Magnetic FEM
- Allows solution of stationary voice coil
permanent magnet with poles of non-linear steel
for time-varying currents fields. - Based on dynamic Maxwell's equation.
- Solution is made for 40-120 time-steps per period.
20Flux2D Transient Magnetic FEM
- Mesh uses quadrilateral elements to mesh skin
and give a fast solution time. - Mesh has frequency dependant spacing
perpendicular to metal surface.
21Flux2D Transient Magnetic FEM
- Sinusoidal voltage source input allows
calculation of blocked impedance of coil. - Voice coil is stranded conductor constant
current density. - Iron NdFeB are solid conductors with eddy
currents. - Hysteresis is neglected.
- Calculation may be for different coil positions
and voltage inputs.
22Flux2D Transient Magnetic FEM
23Flux2D Transient Magnetic FEM
24Flux2D Transient Magnetic FEM
- Power density currents at 80Hz various coil
displacements.
25Flux2D Transient Magnetic FEM
- Power density currents at 20Hz, 80Hz 240Hz.
26Flux2D Transient Magnetic FEM With Kinematics
- Mass, compliance and mechanical resistance
included in the model. - Acceleration is derived from driving force.
- Displacement mesh allows solution with coil
displaced axially. - Rigid body motion assumed.
- Compliance assumed to be linear.
- Iron BH curve and compliance force stiffness
curves do not include hysteresis.
27Kinematic Validation.
28Flux2D Transient Magnetic FEM with Kinematics
Results.
- Power density at 20Hz 40vrms input with coil
motion.
29Flux2D Transient Magnetic FEM with Kinematics
Results.
- magnetic field in gap plotted along contour, at
20Hz 40vrms input as a function of time.
30Flux2D Transient Magnetic FEM With Kinematics
Results.
- waveform and spectra of eddy currents in pole
31Flux2D Transient Magnetic FEM with Kinematics
Results.
- Acceleration waveform and spectra at 20Hz for
40vrms input.
32Flux2D Transient Magnetic FEM With Kinematics
Results.
- Relative Harmonic distortion of cone acceleration.
33Flux2D Transient Magnetic FEM With Kinematics
Results.
- Measured Versus FEM of SPL Magnitude of
impedance.
34Conclusion.
- Flux2D is able to predict loudspeaker motor
distortion from geometry and material properties. - FEM results contain a wealth of data including
some which cannot be readily measured. - Possible improvements are
- Include FEM derived Force versus Displacement
data for suspension. - Include magnetic Hysteresis of iron.
- Include mechanical Hysteresis of suspension.
- Better material property data required!