Technical cutaway and architecture notes
Ghana scenario · The magnetic–piezo cutaway calculates one guided cartridge under imposed external motion. This separate study does not set the facility calculator’s power or efficiency.
CIPS (CuInP₂S₆) remains the research material. Its assembled-device stiffness, coupling and capacitance are not established here. Default mechanical values are editable design assumptions, not CIPS measurements; no CIPS electrical output is invented.
A · Magnetic–piezo research architecture
Calculating the first trajectory…
Initializing physics…
The driver path is imposed by an outside actuator; the cap moves according to calculated forces. The magnet pushes the guided cap, not bare CIPS. The drawing is not to scale: cap motion is exaggerated to ±12 drawing units at the entered travel limit. Exceeding travel or losing compression preload stops the calculation, rather than silently clamping motion. Replay restarts the same experiment from rest.
Edit the cartridge’s design assumptions
These values describe an idealized experiment, not supplier-approved hardware. Identical round magnets are held at fixed antiparallel axial orientations. Both faces of both disks are included. The 1.31 T starting point comes from Arnold’s N42SH grade table; uniform magnetization M ≈ Bᵣ/μ₀ is an additional approximation.
Leave this off while CIPS device data are missing. Off means a mechanical spring–damper model with no electrical branch, not a validated open-circuit CIPS cartridge. When on, entered coefficients are assumptions unless characterized for the actual device. The circuit is an AC resistor—not a rectifier, regulated bus or battery.
Energy balance, equations and published sources
With x positive into compression and y the driver’s vertical position: Fₓ = −∂Uₘ/∂x; m ẍ + c ẋ + kx − θV = Fₓ; Cₚ V̇ + V/R + θẋ = 0. The reciprocal θ terms include electrical reaction on motion. Preload is a balanced static bias: x = 0 is the mechanical equilibrium before magnetic loading, with an equal opposing fixture force. The calculation begins at rest with magnetic field energy already present. Off-axis force can become attractive; it is not clipped to repulsion.
Magnetic driver power is (∂Uₘ/∂y)ẏ, including negative power on return. Stored energy E = ½m ẋ² + ½kx² + ½CₚV² + Uₘ. Signed input work − resistor energy − damping heat − ΔE should approach zero as the time step is refined. Resistor energy is ∫V²/R dt, not separate peak voltage multiplied by peak current. Displayed means include startup and are not steady-state ratings.
This numerical face integral assumes hard, uniformly magnetized cylinders in nonmagnetic surroundings. A 36-patch-per-face model is spot-checked against 144 patches at 15 positions; differences above 3% block results. This checks resolution, not the true field or every point on the path. Demagnetization, eddy currents, hysteresis, guide friction, driver inertia/motor loss, nonlinear CIPS response, leakage, fatigue and temperature dependence are excluded. Returned work is ideal mechanical return, not guaranteed recovered electricity. Signed net work is not purchased drive energy. No electrical or facility efficiency is claimed.
- UT Austin: magnetic surface-density formulation — basis for the face integral.
- Vokoun et al. (2009): uniformly magnetized cylinders — finite-cylinder theory/experimental context, not validation of this discretization.
- Erturk & Inman (2008): coupled piezoelectric harvester modeling — reciprocal coupling, not CIPS coefficients.
- Io et al. (2022): CIPS nanogenerator — material research, not a complete cartridge parameter set.
- Arnold N42SH material table — magnet material starting point.
Research scaling architecture: annular banks of independently guided, preloaded piezo cartridges; an externally driven magnet rotor creates sequential force pulses. Each cartridge has local conditioning, then protected parallel connection to a shared electrical bus. This avoids putting raw, mismatched piezo outputs directly in parallel.
Scale cartridge area, stack geometry and the number of banks only after measuring absorbed work, thermal limits and fatigue. A stiffness-matching flexure may trade displacement for force; it cannot multiply work. No particular stack size or bulk rating is validated.
Inside the magnet
Educational illustrationA rotating machine and magnetization inside a material involve different kinds of motion. Explore local magnetization arrows, then compare them with the carousel’s magnetic force and torque study. These arrows are directions in a material, not tiny rotating generators.
Original geometric illustration, not a solved Landau–Lifshitz–Gilbert (LLG) model. Playback uses arbitrary visual time, deliberately slowed for explanation; it is not mechanical RPM or a calibrated spin frequency. This panel does not change watts or efficiency.
A traveling spin wave can be phase-coherent even though its magnetization varies with position.
Coherence and domains
A traveling spin wave can be phase-coherent; spatial variation alone does not make it incoherent. The dephased display is a separate teaching example. Domains and their walls require a spatial energy model; these twelve arrows do not predict a domain map.
What a material model needs
Micromagnetics balances exchange, anisotropy, demagnetizing and applied-field contributions. A quantitative model needs material-specific saturation magnetization Mₛ, exchange stiffness A, anisotropy K and axes, damping α, geometry, initial state, mesh resolution and the actual forcing timescale.
Two paths into a piezo
The cutaway above uses magnetic force on a guided cap. A magnetostrictive–piezoelectric composite instead transfers field-induced material strain through a bonded interface. That alternative needs its own materials, bond and loaded electrical characterization; it is not established for this CIPS cartridge.
Book context, modern sources and modeling limits
Ferromagnetism / Ferromagnetismus (H. P. J. Wijn, editor; Springer, 1966) provides historical context through Keffer’s spin waves, Carr’s secondary effects and Döring’s micromagnetics chapters. The review used accessible contents, chapter summaries and two-page previews, not a full-chapter derivation. This original diagram is a teaching construction informed by that context and the modern sources below; it does not reproduce a book figure or implement its full theory.
Historical Gaussian/CGS conventions require care before using formulas in an SI model: distinguish B from H and magnetization, and check the definition and units of every coefficient. The display above uses unitless directions. Its tilt decays with a chosen exponential envelope; no exchange equation, spin-wave dispersion, thermal noise or energy dissipation is solved.
A useful engineering next step is a bounded material model feeding the larger force, motion and load calculation. NIST distinguishes equilibrium minimization from time-dependent LLG evolution; its convenient default damping is not automatically appropriate for material dynamics. Neither a more detailed animation nor a published magnetoelectric voltage coefficient establishes device power, efficiency or net energy creation.
- Springer front matter and contents; Keffer: Spin Waves; Carr: Secondary Effects; Döring: Mikromagnetismus. Historical sources, not WegaWomb measurements.
- NIST OOMMF energy terms and time evolvers. Modern numerical methods and input definitions.
- Vansteenkiste et al., MuMax3 author manuscript (published DOI: 10.1063/1.4899186). Verified micromagnetic software; its material examples do not supply WegaWomb parameters.
- Zong et al., Cellulose-based magnetoelectric composites (DOI: 10.1038/s41467-017-00034-4). A bonded cellulose/Metglas laminate driven by applied alternating and static magnetic fields; measured voltage response with a lock-in amplifier. This is evidence for strain coupling, not loaded carousel output or CIPS device performance.
B · Generator-led hybrid architecture
The main generator uses moving permanent magnets and stationary coils. Magnet-assisted piezo modules act on identified vibration paths and monitor dynamic stress. The piezo energy share starts at zero until justified; it is never added on top of an unchanged generator output.
This is an established bulk-generation principle with an experimental piezo addition—not proof of Wegawomb’s performance. The animated geometry and efficiency assumptions are illustrative.