Following Load Lines to your Working Points, and Reluctance to Optimize: Coercing the Most Out of Your Magnets. Dr.

Transcription

1 The Association of Loudspeaker Manufacturers & Acoustics International presents Following Load Lines to your Working Points, and Reluctance to Optimize: Coercing the Most Out of Your Magnets Dr. David Hyre, CTO

2 Outline Driver and magnetic-circuit background Permanent-magnet properties Load Lines and Working Points origin, influences, intuition Examples with different materials and environments

3 Too Much of a Good Thing? Costs materials and shipping Complexity Physical constraints depth, torque Does it provide any benefits?

4 Driver and Magnetic Circuit Magnetic circuit akin to electrical: MMF ~ EMF Φ ~ I R ~ R MMF = Φ * R Major difference: air & vacuum carry flux, not current

5 Permanent Magnets 1 Intrinsic Magnetization J J 0 = M sat B r = µ 0 M sat H ci H c Intrinsic magnetization J (dashed) & internal field B (solid) curves for Dexter HF050 ceramic magnet Y-intercepts are J 0 & B r, magnetization & H=0 X-intercepts are H ci & H c, coercivity, field for J or B =0

6 Permanent Magnets 2 N N N Working Point H d µ 0 M µ 0 M µ 0 H d B S S S If reluctance is non-zero, it causes a coercive force in reverse direction, H d, that opposes B and reduces it below B r Working point is where magnet operates in circuit

7 Relations 1 Flux Φ like current : Φ out = Φ in Φ = B m A m = k 1 B g A g Flux from magnet face Flux through gap k 1 = leakage factor ( > 1 ) Flux from magnet scales with area of face Flux density in gap scales inversely with gap-face area

8 Relations 2 MMF like EMF (voltage) : MMF = 0 H m l m + k 2 H g l g = 0 (=Ni if VC driven) k 2 = loss factor ( > 1 ) from reluctance > 0 Losses can be compensated by increasing l m

9 Relations 3 Flux density in gap created by H g B g = µ 0 H g Combine 3 equations & rearrange to find slope of line describing magnet in circuit

10 Load-Line Equation B m / µ 0 H m = -(k 1 /k 2 ) (A g l m ) / (A m l g ) Aside from leakage & loss factors, characteristic line is dependent only on physical dimensions of components. Incr. Slope : Thicker magnet, taller gap face Decr. Slope : Wider gap, larger magnet face

11 Determining Load Line Working Point B op H op = H d Load Line can be determined by FEA: sample B,H inside magnet Load Line runs from 0,0 through sampled point

12 Using the Load Line B m / µ 0 H m = -(k 1 /k 2 ) (A g l m ) / (A m l g ) (k 1 /k 2 ) can be estimated this way Slope = Permeance Coefficient (PC) = 1/Reluctance + Slope : Thicker magnet, taller gap face - Slope : Wider gap, larger magnet face Many magnet catalogs marked with PC

13 Reading a Catalog Dexter HF050 ceramic, straight from catalog + Slope : Thicker magnet, taller gap face - Slope : Wider gap, larger magnet face

14 Load-Line Graph Working Point ΔH ΔH = µ 0 Ni / l m Current in voice coil creates its own field and shifts load line.

15 Different PM Materials Load Line at operating current Different PM materials will have different margins of safety (ceramics shown).

16 High Temperature Apparently stable with wide margin at room temperature but not at high temp (NdFeB shown).

17 Low Temperature Safe at high temp! However, a surprise awaits during the next cold snap (ceramic shown) Will stabilize at lower B r

18 Modeling in MōTIV Morph from closed circuit to real driver (Wiggins tutorial) Load line moves with physical dimensions and current Effect of saturation by increasing only magnet OD Combined effects of o C & i Case study: unauthorized swap of magnet material in proto

19 Simplified Too Much? Complex Simple Real driver compared to simplified version with same critical dimensions Modeled in Ansoft Maxwell and in MōTIV Similar results despite differences

20 Conclusions Working with magnets can be intuitive Simple relations govern their behavior Simple models can remain valid & relevant Temperature and voice-coil currents can have a strong effect Extensive saturation de-rates magnet A load-line study gives a wealth of information, and allows changes to be estimated even before FEA Case study / cautionary tale

21 Thank you for attending. A free demo version of MōTIV software is available from DYNE Analytics, for exploring the topics presented.

22 Modeling in MōTIV Morph from closed circuit to real driver (Wiggins tutorial) Load line moves with physical dimensions and current Effect of saturation by increasing only magnet OD Case study: unkown swap of magnet material Combined effects of o C & i Intuitive conclusions (take-home intuitions)