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The Transient Magnetic Behaviour of Loudspeaker Motors. Mark Dodd

The Transient Magnetic Behaviour of Loudspeaker Motors. Mark Dodd. Loudspeaker Basics. Loudspeakers convert an electrical signal to a mechanical signal and then to an acoustic signal. Moving coil linear actuator: voltage -> motion. Diaphragm: motion -> sound pressure. Loudspeaker Basics.

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The Transient Magnetic Behaviour of Loudspeaker Motors. Mark Dodd

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  1. The Transient Magnetic Behaviour of Loudspeaker Motors.Mark Dodd FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  2. Loudspeaker Basics • Loudspeakers convert an electrical signal to a mechanical signal and then to an acoustic signal. • Moving coil linear actuator:voltage -> motion. • Diaphragm:motion -> sound pressure. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  3. Loudspeaker 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: • For a small current i: FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  4. Loudspeaker 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: FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  5. Pass Band Response. • Motion mass-limited, decreasing amplitude with frequency. m 0.28m 0.21m 0.14m 70u 0 20 20 50 100 100 200 500 1k 1k 2k 5k 10k 10k 20k 20k Frequency Hz FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  6. Pass Band Response. • Velocity amplitude decreases above resonance frequency. -40 dB -54 -68 -82 -96 -110 20 20 50 100 100 200 500 1k 1k 2k 5k 10k 10k 20k 20k Frequency Hz FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  7. Pass Band Response. • Radiation efficiency increases with increasing frequency. ohm 4.3k 3.3k 2.2k 1.2k 100 20 20 50 100 100 200 500 1k 1k 2k 5k 10k 10k 20k Frequency Hz FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  8. Pass Band Response. • Motional impedance is reflected in electrical domain. • Net result is an SPL response with a flat pass band. dB 110 80 dB Uin=2.83Vrms, Distance=1m 100 64 90 48 80 32 70 16 60 0 20 20 50 100 100 200 500 1k 1k 2k 5k 10k 10k 20k 20k Frequency Hz FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  9. Previous Approach • Use FEM to calculate static field & calculate Bl(x) for different coil displacements x. • Consider the ‘static’ flux from permanent magnet separately from flux produced by current flowing through the coil. • Calculate Flux through coil for an arbitrary current. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  10. Polynomial method • Assume that Lvcis a function of x but not i. • Express force variation with current in terms of coil inductance: F=Bl(x)I-Lvc(x)i2. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  11. Polynomial 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. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  12. Polynomial 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). FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  13. Polynomial method • Equating forces. • Equating voltages. • Runge Kutta method used to numerically solve equations. • Spectrum of distorted sinusoidal waveform produced is analysed with FFT. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  14. New Magnet Topology FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  15. Flux2D Magneto-static FEM. • Magneto-static solver uses static version of Maxwell's equation. • Force on a coil is calculated using FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  16. Flux2D Magneto-static FEM Results. • The force versus displacement may be calculated for a range of coil displacements. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  17. Flux 2D Magneto-static FEM Results. • Voice coil self Inductance may be calculated for different coil positions and currents. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  18. Flux2D 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. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  19. Flux2D 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. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  20. Flux2D 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. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  21. Flux2D 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. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  22. Flux2D Transient Magnetic FEM • Flux at 80Hz. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  23. Flux2D Transient Magnetic FEM • Permeability at 80Hz. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  24. Flux2D Transient Magnetic FEM • Power density currents at 80Hz various coil displacements. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  25. Flux2D Transient Magnetic FEM • Power density currents at 20Hz, 80Hz & 240Hz. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  26. Flux2D 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. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  27. Kinematic Validation. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  28. Flux2D Transient Magnetic FEM with Kinematics Results. • Power density at 20Hz 40vrms input with coil motion. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  29. Flux2D Transient Magnetic FEM with Kinematics Results. • magnetic field in gap plotted along contour, at 20Hz 40vrms input as a function of time. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  30. Flux2D Transient Magnetic FEM With Kinematics Results. • waveform and spectra of eddy currents in pole FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  31. Flux2D Transient Magnetic FEM with Kinematics Results. • Acceleration waveform and spectra at 20Hz for 40vrms input. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  32. Flux2D Transient Magnetic FEM With Kinematics Results. • Relative Harmonic distortion of cone acceleration. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  33. Flux2D Transient Magnetic FEM With Kinematics Results. • Measured Versus FEM of SPL & Magnitude of impedance. FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

  34. Conclusion. • 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! FLUX Users Club 2001 - Aix en Provence - 27, 28 September 2001

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