Numerical Analysis of a Low-Cost Spherical Air Bearing for CubeSat ADCS Testing

TL;DR: To reduce friction and parasitic torques in ground-based CubeSat ADCS verification, I numerically evaluated a low-cost, machinable, flat-orifice (straight/unpocketed) spherical air bearing with multi-supply (13 inlets) using ANSYS Fluent.

Problem

On-orbit, satellites operate close to a torque-free environment. On the ground, however, ADCS validation is often distorted by:

• mechanical contact and friction,
• parasitic external torques,
• gravity torque due to CoM–CR (Center of Mass–Center of Rotation) offset.

A near-frictionless support is therefore crucial for meaningful ADCS testing.

Why a Spherical Air Bearing?

Spherical air bearings provide a low-friction, microgravity-like support for satellite simulators.

In this project, the design choices prioritized cost and manufacturability:

• Orifice-restricted instead of porous-restricted, and
• Unpocketed (straight) orifices instead of pocketed geometries to improve dynamic stability.

Unpocketed designs are generally less prone to pneumatic hammer instabilities associated with trapped pocket volumes.

Design: Multi-Supply Architecture (13 Inlets)

The socket geometry is fed by 13 inlets: 1 central plus 12 peripheral.

Geometry & Supply Conditions

Method: ANSYS Fluent CFD Setup

The simulations were performed in Fluent assuming compressible ideal gas and laminar flow.

Solver & Models

• Solver: Pressure-based, steady, absolute
• Viscous model: Laminar
• Density: Ideal gas
• Viscosity: Sutherland (three-coefficient)
• Energy equation: Enabled
• Pressure–velocity coupling: Coupled
• Pressure discretization: PRESTO!
• Momentum/Density/Energy: Second Order Upwind
• Convergence aid: Pseudo-time stepping

Mesh — Local Refinements

Thin-film regions require strong local refinement near inlet–film junctions due to steep gradients.

Performance Metrics

Two main performance metrics were used:

1. Net load capacity (W)
2. Static stiffness (K)

Definitions:

W = ∫ (p − Patm) * cos(θ) dA
K = − dW/dh

With multiple inlets, the pressure field varies with azimuth (φ), so the general (angular) formulation is considered.

Results (Key Findings)

1) Net Load Capacity (h = 100 µm)

On wall_sphere (lift direction 0, −1, 0) in Fluent:

The viscous contribution is negligible compared to pressure; load capacity is dominated by the pressure field.

2) Static Stiffness (95–100 µm interval)

Using a secant approximation:

• K ≈ 1.2 N/µm
• (approximately 1.2 × 10⁶ N/m)

This indicates a meaningful restoring response to small changes in film thickness.

3) Pressure & Flow Field Observations

• Pressure peaks around the inlets and decays toward the outlet.

• Reported gauge pressure range (approx.):

  • pg,max ≈ 1 × 10⁵ Pa
  • pg,min ≈ 2.54 × 10⁴ Pa

In the flow field, local acceleration appears near inlet regions:

Local Linear Model for W(h)

A local linear approximation around 100 µm:

W(h) ≈ W100 + K(100 − h)
W100 = 279.18848 N,  K ≈ 1.2 N/µm
(h in µm)

Design Decisions & Trade-offs

Unpocketed (straight) orifice choice

• ✅ Improved dynamic stability (more resistant to pneumatic hammer)
• ⚠️ Single-orifice load may be limited → mitigated via multi-orifice supply

Multi-supply (13 inlets)

• ✅ Potentially higher load capacity and stiffness through a more favorable pressure profile
• ✅ More distributed support, which can help produce a restoring moment under tilt conditions

Limitations

• Results are reported for a single supply architecture and around a limited film-thickness neighborhood.
• A broader parametric sweep (h, supply pressure, orifice diameter) and tighter solution verification are left for future work.

Next Steps

• Quantitative comparison with a single-orifice reference geometry
• Parametric scan over h, supply pressure, and orifice diameter → W(h), K(h) curves
• Time-dependent studies on dynamic stability (pneumatic hammer) and sensitivity to tilt / CoM–CR offset
• Experimental validation of the CFD model