GitHub - rmit-wgbowley/Isopod: IsoPod | Axial Shake Generator (0.45 W @ 8.81 Hz)

Axial Shake Powered Pill System – Electromechanical Design of the IsoPod by William Bowley

The Hercules Challenge is a co-design consortium challenge available to first-semester, first-year engineers through the mandatory introductory class, "Introduction to Professional Engineering."

TLDR: Designed, simulated, manufactured, and experimentally validated a human-powered axial electromagnetic generator producing 0.43–0.47 W from hand shaking using custom FEA and physical prototype testing

Overview

The IsoPod is a pill system that reminds users when to take their medication through an e-ink display on the cylindrical face of the device, providing a simple visual reminder.

This repository focuses on the design, simulation, construction, and validation of the axial shake generator (ASG) at the device's core. The generator converts intentional shaking motion into electrical energy via magnetic induction, which charges the IsoPod's Li-Po battery. This extends battery life, or with enough motion, can enable complete self-reliance.

Why generate electrical?

In humanitarian contexts, reliable grid power isn't guaranteed, nor are reliable supply chains for expendable batteries. The ASG decouples the IsoPod from external infrastructure by converting user motion into electrical energy.

Table of Contents

• Overview
• Why generate electrical?
• Axial Shake Generator
  • Electromagnetics
  • Design & Topology
  • Numerical Model
  • Simulation Results
• Construction
• Results
• Validation
  • New Mechanical Model
  • Simulation Results
• Conclusion
• Bibtex Citation

The generator consists of an armature (greyish-olive) made of poles (magnets), a stator (minty aqua) made of slots (coils), and restoring magnets (light yellow-green) which act as magnetic springs that allow the armature to build velocity from the user shaking the device with their forearm muscles.

Electromagnetics

An ASG produces electricity via the interaction between a slot and a pole. When a pole moves axially through a slot, it produces an induced voltage within that slot due to the changing magnetic field generating a changing electric field. The induced electric field opposes the change in magnetic flux that produced it, a consequence of Lenz's law. These ideas come together to form Faraday's Law of Induction:

$$V = -N\frac{d\Phi}{dt} \implies -\frac{d\lambda}{dt}$$

where $λ = N\Phi$ is the flux linkage between the slot and pole. Flux linkage can be thought of as the magnitude of how strongly the magnetic field links with the winding (turns in a slot). Higher linkage generally means the system can produce a larger induced voltage for the same change in armature position.

Luckily, using related rates, the two main parameters appear:

$$V_{\text{induced}} = -\frac{d\lambda}{dt} \implies -\frac{d\lambda}{dz} \cdot \frac{dz}{dt}$$

The first term is the derivative of flux linkage over the z-axis (magnetic design), and the second term is the z-axis velocity (mechanical input). These can be analytically approximated as:

$$\frac{dz}{dt} = A \omega \cos(\omega t + \phi)$$ $$\frac{d\lambda}{dz} = \frac{d}{dz} (B \cos(kz)) \implies -\mu H k \sin(kz)$$

where k = 2π / pitch is the spatial frequency.

These two derivatives expose the important mechanics of the system. Increasing acceleration A and frequency ω may increase induced voltage, but these are constrained by the user's physical abilities. Whereas the permeability μ and H may increase the induced voltage while generally not being constrained by the user's physical abilities.

Once induced voltage is established, the usable electrical power is determined by the generator's internal resistance:

$$P = \frac{V_{\text{rms}}^2}{R_{\text{internal}}}$$

This relationship drives one of the main trade-offs: increasing turns raises induced voltage but also increases resistance due to longer wire length. The optimal design maximizes V/R, not just peak voltage.

Design & Topology

The high-level topology in figure 2 was selected to enable oscillatory motion through magnetic restoring forces. The end poles act as magnetic springs, creating a restoring force when the armature approaches the limits of travel.

The alternating pole arrangement (N-S|S-N) was selected because the transition between opposing poles creates a rapid change in magnetic field along the z-axis, increasing the spatial rate of change of flux linkage:

$$V \propto \frac{d\lambda}{dz}$$

A pole pitch of 10 mm was selected, matching the pole length and maintaining direct magnetic coupling between adjacent opposing poles. The topology uses four stator slots interacting with four active armature poles, with two additional poles placed on each end of the armature to increase usable travel distance. This allows approximately 20 mm of positive and negative armature displacement while maintaining magnetic coupling between the armature and stator.

Maintaining slot overlap throughout the motion range produces a more consistent induced voltage waveform, where the primary amplitude is dominated by the mechanical velocity term:

$$V \propto \frac{dz}{dt}$$

The symmetric pole arrangement also reduces unwanted harmonic content compared with asymmetric topologies. Finally, no high-permeability materials were introduced into the armature or stator structure. The stator consists of copper windings, while the magnetic poles use N52 Neodymium permanent magnets.

Given the 4 slots within the stator and the 8 poles within the armature, the measured frequency relationship suggests:

$$f_{\text{electrical}} \approx 4 \times f_{\text{mechanical}}$$

This is consistent with the pole pitch and the number of magnetic cycles encountered per mechanical oscillation.

Numerical Model

The ASG was modelled using FemmMagneticRender (FEMM) with shapely for translating PYFEA CSG (constructive solid geometry) to FEMM native primitives. An axially symmetric coordinate system (z-r) was used due to the generator's rotational symmetry around its z-axis. A Dirichlet boundary condition was applied, with the radial boundary at 2× the slot outer radius and the axial boundary at 1.2× the stator tube length. The armature motion relative to the origin was simulated using:

$$ z = \text{travel} \cdot \sin(2\pi f t) $$

The resistance was obtained from FemmMagneticSolver during an initial configuration solve, and then the flux linkage was obtained per solve. Using the simulation time-step, the induced voltage was calculated using finite difference:

$$V_{\text{induced}} = -\frac{\lambda_{\text{new}} - \lambda_{\text{old}}}{t_{\text{step}}}$$

This was then used to calculate the RMS voltage, and using the generator's internal resistance, the expected power output was obtained. This method represents a quasi-transient method due to its use of asymptotic field conditions ($t=\infty$) per time step. This is reasonable due to the absence of highly magnetically permeable materials and the low operating frequency of the generator.

Simulation Results

The parameter file can be found here, written in .uiv (unit-informed values). The simulation files can be found here, written in Python using the pyfea solver-adapter engine. Solver assumptions can be found here.

Construction

The generator was printed out of ABS on a Voron 2.4. The armature consisted of a carbon fibre rod with 8 x N52 poles inserted into it in the pattern described above, using superglue to secure the end poles.

The stator consisted of 4 coils with 180 turns per coil of 0.2 mm enameled copper wire, with each coil wound in the opposite direction to the last as described above. The coils were secured in place with 10 mm and 5 mm thick Kapton tape, with the first and last layers of the coil being wrapped.

The restoring magnets were flat 12 mm x 3 mm neodymium magnets. The generator stator was split into two pieces: the main piece, which housed the coils and one restoring magnet, and the cap, which held the other restoring magnet and was attached via 3 x M3 x 20 mm bolts. The two outputs of the generator were secured to the side and then extended with ~1.25 mm stranded copper wire.

Results

The completed generator was tested by hand-shaking at a measured fundamental mechanical frequency of 8.81 Hz with an electrical frequency of 35.2 Hz (the 4 coils produce 4 cycles per mechanical oscillation). The open-circuit voltage was recorded using an oscilloscope:

The measured waveform shown in Figure 6 has a similar shape to the predicted waveform in Figure 4 but seems less periodic and more jerky. Another observation is that the negative recovery appears stretched while still being a similar amplitude. This is most likely attributed to degradation of the prototype due to its usage as a demo item.

Validation

The simulated power output was 0.323 W whereas the measured power was 0.43-0.47 W, which is 25-45% lower than the measured value. The peak voltages are much higher and the slew rate was significantly different, leading to the possible source being the idealized motion of the armature versus the realized motion.

The simulation used the same mechanical frequency but produced lower peak voltages. If the prototype's armature acceleration was much higher than expected, the armature was likely slamming into the end-caps due to the repulsion force not being high enough. The maximum velocity was most likely higher and hence:

$$V \propto \frac{d\lambda}{dz}$$

New Mechanical Model

Given this, a new model for the motion could be proposed that takes into consideration the magnetic repulsion force and the likely much higher mechanical acceleration but lower frequency, using an oscillating force function:

$$F_{\text{magnetic}} = -\frac{dU}{dz}$$ $$F_{\text{shaking}} = am\sin(\omega t + \phi)$$

One approach would be to model the armature velocity as:

$$\frac{dz}{dt} = \int \frac{F_{\text{magnetic}} + F_{\text{shaking}}}{m} \ dt$$

However, given the ability of FemmMagneticSolver to calculate the Maxwell stress tensor, the $F_{\text{magnetic}}$ term was obtained directly from the solver rather than using finite difference of the magnetic energy density over the z-axis. This decouples the solution from the displacement output, removing dynamic step sizes and leading to a potentially more stable solution.

Simulation Results

The parameter file can be found here, written in .uiv (unit-informed values). The simulation files can be found here, written in Python using the pyfea solver-adapter engine. Solver assumptions can be found here.

Conclusion

The axial shake generator successfully produced 0.43-0.47 W of usable power from human motion at a mechanical frequency of 8.8 Hz (electrical 35.2 Hz) with an unknown acceleration function. The simulation with the new mechanical model predicted 0.526 W, within 12-22% of measured values. The differences in slew rates between the simulation and measured results can be attributed to no-load electrical dynamics versus the oscilloscope probe loading.

The generator design demonstrated the feasibility of powering low-energy devices in humanitarian contexts where grid power is unreliable, depending on load factors. However, it may be more viable as a battery supplementary system, depending on the trade-offs between battery size and generator duty cycle.

Bibtex Citation:

@misc{Bowley_2024,
  author = {Bowley, William},
  title = {{IsoPod: Axial Shake Generator}},
  url = {https://github.com/rmit-wgbowley/isopod-generator},
  year = {2024},
  note = {
    GitHub repository,
    Electromagnetic Subsystem Of The Isopod
  },
  license = {MIT}
}