A loading rig for six-axis load-cell error characterization

The problem

Load cells in experimental aerodynamics turn the forces and moments on a wind-tunnel model into strain-gauge signals. Like any instrument they drift: hysteresis between loading and unloading, creep under a constant load, thermal drift as tunnel flow changes the gauges’ temperature, and possibly a dependence on orientation. To quantify those errors you need to apply loads you already know, precisely, and hold them.

The sensor was an Interface 6A40: a cylinder 2.4 in across and 1.6 in tall that measures force and moment on all three axes. Its limits set the design envelope: 50 N transverse and 200 N axial force, 5 N·m about each axis.

Design

First concept, rejected

The first concept hung the springs from an outer MDF box around a printed inner stand. Cutting and joining MDF would stack tolerance errors into the applied load, and a single M6 bolt to the orientation stand would have been an unstable mount.

Redesign: a truss instead of a box

The redesign replaced the box with a truss of 6 mm stainless tubes and resin-printed joints on a 4 × 4 in base: more compact, stiffer and with far fewer joints to get wrong. Several final dimensions were still unknown, so I modeled the whole assembly parametrically in SolidWorks against a set of reference planes. Changing one dimension rebuilt the rest. The angled tube connectors came from surface operations, the one part of the model that needed manual repair after large changes.

Knowing the applied load

Each spring hangs from an eyebolt in a 10-24 thread. Turning the knob draws the eyebolt up, and notches every 15° on the knob and its mount count the turns. One notch stretches the spring by a known amount:

$$\Delta F = k\,p\,\frac{\theta}{360^\circ} = 85\ \tfrac{\text{lbf}}{\text{in}} \times \tfrac{1}{24}\ \text{in} \times \frac{15^\circ}{360^\circ} \approx 0.148\ \text{lbf per notch}$$

where k is the catalog spring rate and p the thread pitch. The geometry stops each spring at 0.3 in of extension, before it yields, which caps the load at 25.5 lbf (113 N), inside the 200 N axial limit. The side spring’s line of action sits one inch above the cell’s moment plane, so its moment in lbf·in equals its force in lbf.

Small features carry the rest. A cross-shaped key in each mount stops the eyebolt from turning, so all of the knob’s rotation becomes extension. Flats on the knob take a ¾ in wrench if a hand can’t turn it, and a lip under the knob cuts its contact area and friction.

The loading piece

The loading piece couples both springs to the load cell. If it broke, the shock could damage the sensor, so it is deliberately overbuilt: Formlabs Tough 2000 resin, filleted hoops to avoid stress concentrations, and a predicted stretch at 30 lbf too small to matter.

Build and proof test

Load-bearing joints are resin printed; the base plate is FDM. I bonded the steel tubes into the printed joints with J-B Weld while holding the structure at its maximum compressive load, so the cured joints carry no slack. Tight fits were toleranced at 0.01 in and loose ones at 0.02 in.

To check the loading piece I hung a 30 lbf weight from it for more than a minute; no deformation was visible.

The test plan it was built for

The user guide hands the rig to the next student with these steps, logged through a LabJack:

1. Zero point. From the loosest setting, tighten until the reading just moves; that notch is zero, and each notch after it adds about 0.15 lbf.
2. Creep. Hold a constant load and record over a set period.
3. Hysteresis. Load and unload in steps with the knob.
4. Thermal drift. Record while tunnel flow speed changes the temperature.
5. Orientation. Repeat the above with the rig turned on the orientation stand.

What I took from it

This project pushed my CAD further than anything before it: parametric modeling, surface features and configurations, and a better order of operations so early guesses could change without breaking the model. It also taught me resin printing properly: orientation and curing decide whether a part reaches its rated strength. I presented the rig at the aerospace department’s Brown Bag seminar on November 11, 2022.