Calibration

The balance is calibrated on its own roll spindle with known dead weights. Each bridge combination gets a statistically selected regression, and the fit ends with a pass/fail report.

6-component set-up: the roll housing hangs between new head plates on the bench stand; square sleeve on the balance, yoke at a load station, roll arm, drag and thrust pulleys.

Principle: roll the balance, not the weights

Weights always hang straight down. Because the spindle can roll the balance to any angle, the same yoke and weights load different components:

Roll	Hanger	Loads produced
0 / 180°	yoke on the top/bottom sleeve walls	normal force N and pitching moment m (both signs); rolling moment l from the roll arm
90 / 270°	the same yoke on the side walls	side force Y and yawing moment n (both signs)
45 / 135 / 315°	corner stirrup in V-notches	N and Y together (interaction terms)
0 / 90 / 180 / 270°	drag cable from the station pin, thrust from the front eyebolt	axial force A alone and combined with the other loads

Three of the roll cases: yoke + roll arm at 0°, corner stirrup at 45°, yoke on the side walls at 90°.

Bench mode needs roll −90..+180° (flight is ±90°). Leave a cable service loop at the spindle exit for 270° of twist, and give the control software a separate calibration roll limit.

Hardware

Square sleeve (1.85 in, 6061) bolts and dowels to the balance front face in place of the model puck. It has 1/4 in load holes in all four walls at x = −2, −1, 0, +1, +2 in on the balance axis, and V-notches across the corners at the same stations.
Roll arm slides over the sleeve at x = 0, held by dowels and set screws. Knife-edge notches at y = ±2 and ±4 in give up to 30 in-lbf of rolling moment.
Universal yoke on stub pins (its weight acts at the pin) and a 45° stirrup for the corner cases (a 90° V-seat with a knife-edge rib that drops into the corner groove at the station). Both hang in the lab frame.
Head plates v2: the roll housing pivots on its front cam-follower stud. The rear stud sits in a ±1.6° leveling slot, and a jack screw re-levels after every load. Drag and thrust pulleys are reused from the 3-component stand.
Collision check: clear at roll 0/45/90/135/180/270/315 with the hanger at x = −2, 0 and +2.

Head v2: housing on its own studs, leveling slot, jack-screw bridge.

Original bench stand (3-component balance): the pulleys and base design are reused.

Parts, drawings and CAD files

Drawing (PDF)	Part	STEP
WT-6C-300	Assembly, calibration (parts list)	assembly_calibration_6c_roll0.step
WT-6C-301	Sleeve, calibration	sleeve_6c_6061.step
WT-6C-302	Arm, roll calibration	roll_arm_6061.step
WT-6C-303	Stirrup, 45°	stirrup_45_6061.step
WT-6C-304	Yoke, calibration	yoke_6c_6061.step
WT-6C-305	Plate, head (qty 2)	head_plate_v2_6061.step
WT-6C-306-1	Bridge, jack	jack_bridge_v2_6061.step
WT-6C-306-2	Spacer, cross (qty 2)	cross_spacer_6061.step
WT-6C-307	Tube, base	base_tube_v2.step
WT-6C-308	Upright, pulley (qty 4)	drag_upright.step
WT-6C-309	Axle, pulley (qty 2)	thrust_axle.step
WT-6C-310	Pulley, cable, 2 in (qty 3, R5-2Z bearing)	pulley_2in.step

Method (after Ulbrich & Bader, NASA)

Six responses, each aligned with one load: PD = M2 − M1 → N, PS = M2 + M1 → m, YD = Y2 − Y1 → Y, YS = Y2 + Y1 → n, L → l, X → A.
Each response starts from its main term. An extra term from the 27-term set (6 linear, 6 squares, 15 products) is added only if |t| is significant (p < 0.001), every VIF < 5 and PRESS improves. A full quadratic overfits.
Applied loads are computed from the roll angle, the measured stand tilt, and the weights and CGs of the sleeve, yoke, stirrup and arm (from the CAD).
Zeros are taken with the balance alone at every roll angle and subtracted. This removes the balance's own weight, which changes with roll.
Schedule: 233 rows = 188 fit + 24 held-out check points + 21 zeros. Every point stays within full scale and the neck limits (|m| + 1.35|N| ≤ 48.75 in-lbf, |n| + 1.35|Y| ≤ 20.8 in-lbf).
Pass criteria: residual SD ≤ 0.25 % FS, no outliers, check-point errors ≤ 0.5 % FS (2σ), sensitivities within 15 % of theory.

Software check (synthetic 6-component balance)

The script was run end-to-end on synthetic data with deliberate errors built in: gauge sensitivities 2-5 % off, cross-talk into the axial, roll and yaw bridges, a self-weight zero that changes with roll, and 0.4 µV/V noise.

Built in	Recovered
Pitch necks +3 % / −2 %, yaw necks −3 % / +2 %	PD, PS, YD, YS within 0.1 % of the true values
Roll bridge +4 %, axial +5 %	0.04260 vs 0.04259; 0.35542 vs 0.35538 mV/V
Cross-talk: Y and N into L; N, m, Y, NA into X; m into the yaw bridges; n into the pitch bridges	all selected and recovered (e.g. X: 0.0040 N, −0.0030 m, 0.0019 Y, 0.00059 NA)
Neck spacing 2.70 in	2.701 (pitch), 2.700 (yaw) from the fitted coefficients
Check-point load error (2σ, % FS)	N 0.07, A 0.06, m 0.23, Y 0.10, n 0.12, l 0.08 - PASS

Limitation: Y and l are never applied together, so the Y·l interaction cannot be estimated. If the real data show it matters, add roll-arm points at roll 45°.

Files: balance_calibration_fit_6c.py (schedule / fit / apply / demo), calibration_schedule_6c.csv, calibration_6c_mass_properties.json; the 3-component version balance_calibration_fit.py; CAD in files; drawings WT-6C-301 to 307 on the Drawings page.