Nonlinear dynamics of electromechanical mechanisms

Research topic and my contribution

The NOMAD project investigated why finite-element predictions of a complex mechanism can change when its mesh, solver settings, or processor allocation changes. We isolated individual interactions to identify where that numerical sensitivity originates.

My primary focus in the NOMAD internship was the pawl-and-gear interaction in an electromechanical ratcheting mechanism. I worked on the idealized model and finite-element study, tracking how the hold pawl rotated as the ratchet wheel moved beneath it.

The central question was whether changes in the predicted motion came from the mechanism’s dynamics or from numerical choices in the simulation. I examined the pawl’s rotation history under shock and sustained vibration, comparing solver iterations, mesh density, and processor count.

Pawl and gear under shockFinite-element simulation of the pawl responding to an imposed shock displacement.

Pawl and gear under vibrationFinite-element simulation with sinusoidal displacement of the ratchet wheel.

Modeling the interaction

The ratchet wheel received a prescribed displacement. A pseudo-spring force seated the hold pawl against the gear, while the pawl’s support constrained its radial and axial motion and allowed rotation. Contact with the teeth determined the resulting rotation over time.

Finite-element mesh of the hold pawl and ratchet wheel — The pawl-and-gear submodel.

Detail of the contact between the hold pawl and ratchet teeth — The contact region between the pawl and gear teeth.

I also worked with an idealized representation using a rigid bar and a penalty spring. This provided a simpler way to examine rotation and contact alongside the finite-element response.

Rigid-bar and penalty-spring representation of the pawl interaction — Idealized model used to interpret the pawl’s motion.

Shock and vibration study

The finite-element simulations used Sierra/SolidMechanics. Holding the loading case fixed while changing numerical settings let me compare their effects on the same quantity: hold-pawl rotation over time.

Parameter	Cases compared
Momentum-balance iterations	1, 5, 10, 20, 50, 75, and 100
Mesh density	Fine, nominal, coarse, and very coarse
Processor count	64, 128, 192, 256, and 320
Loading	Haversine shock and sinusoidal vibration

Fine mesh near the pawl and gear contact — Fine contact-region mesh.

Very coarse mesh near the pawl and gear contact — Very coarse contact-region mesh.

What the comparisons showed

The pawl-and-gear response depended on both the numerical setting and the loading case. Under shock, several settings produced similar overall motion with differences near contact transitions. Under sustained vibration, changing iteration count or mesh density produced more pronounced differences in the rotation histories.

Iteration count

Pawl rotation under sinusoidal vibration for seven momentum-balance iteration settings — Pawl-and-gear rotation under sinusoidal vibration, comparing momentum-balance iteration settings.

Mesh density

Pawl rotation under shock for fine, nominal, coarse and very coarse meshes — Shock response across four mesh densities, with enlarged views of the differences.

Pawl rotation under sinusoidal vibration for four mesh densities — The corresponding mesh comparison under sustained vibration.

Processor count

In the pawl-and-gear cases studied, changing processor count gave closely overlapping rotation histories. This distinguished its response from other interactions in the larger ratcheting mechanism and helped identify which numerical choices needed closer attention.

Closely overlapping pawl rotation histories for five processor allocations — Pawl-and-gear vibration response across five processor allocations. The curves closely overlap.

Research team

I worked with Brennan Bahr and Shunsuke Winston on the broader NOMAD study. The team investigated three mechanism submodels: pin–spring–pawl, pin–pawl, and pawl–gear. The work shown above focuses on my primary pawl-and-gear assignment.

Quantifying the Effect of Non-Physical Parameters on the Nonlinear Dynamics of an Electromechanical Ratcheting Mechanism.
Brennan Bahr, Alan Pham, and Shunsuke Winston. Sandia NOMAD presentation, August 2025. SAND2025-09714PE.

The Sandia NOMAD internship group — The Sandia NOMAD group, summer 2025.

Mentors: Rob Flicek, Scott Grutzik, Rob Kuether, Chris Schumann, Aabhas Singh, and Kumar Vemaganti.