# External Six-Component Strain Gauge Balance for Low Speed Wind Tunnels (2014) Samardzic, Anastasijevic, Marinkovski, Curcic (Military Technical Institute VTI, Belgrade), Isakovic. *Scientific Technical Review*, 2014, Vol. 64, No. 3, pp. 40-46. 7 PDF pages. Page refs below: "p.N" = PDF page N (journal page = N + 39). ## 1. Summary The paper describes a **platform-type external 6-component balance** for small low-speed tunnels (test section 0.4-0.6 m x 0.4-0.6 m, up to 50 m/s; p.1-2). The model sits on two struts (main + tail) that are fixed to a triangular platform. The platform is held by six rods with elastic pivot flexures, and each rod loads one single-force strain-gauge load cell: 3 vertical and 3 horizontal. The cells sit under the test-section floor. A pitch/yaw positioning system is built in. All six cells use the same gauged closed-frame flexure ("binocular" style), made from PH 13-8 Mo stainless steel. Each cell was calibrated on its own to 0.05% FS. The assembled balance was then calibrated with dead weights and a linear 6x6 matrix fitted by least squares. Per-cell error is about 0.25% FS (3 sigma). Errors on the composite components reach 0.89% FS for pitching moment because no combined loads were applied in the calibration (p.4). The paper is short. It gives **no flexure dimensions** (the symbols Lt, b, h are defined but no values), no electronics/DAQ details beyond the excitation voltage, and no stiffness or deflection data. ## 2. Balance architecture (p.2, Fig.1, Fig.3; p.3, Fig.4) - Platform-type external balance. Parts (Fig.1 legend): 1 model, 2 main support strut, 3 tail support strut, 4 triangular platform, 5 pivot flexures, 6 rods, 7 load cells, 8 rotating frame, 9 fixed frame, 10 pitch mechanism, 11 yaw mechanism, 12 step motor. - The model hangs on 2 struts (main strut near the CG, tail strut aft for pitch) and the struts attach to the triangular platform. The platform connects to the rotating frame through **rods with pivot flexures at both ends**. Each rod carries only axial load, so each cell sees a single force. This is the stated way of keeping mechanical interaction low (p.2). - Pitch: a parallelogram mechanism with a lead screw drives the tail strut, range -20 to +30 deg. Yaw: worm gear on the fixed frame, range +/-180 deg. Both use step motors under PC control (p.2). - Cell layout (Fig.3): vertical cells ZPD and ZPL (left and right, at +/- l laterally, offset +f longitudinally) and ZZ (on the centreline, at -2f). Horizontal drag-direction cells XD and XL (at +/- n laterally). One side-force cell YY. O is the model reference point and O1 the balance reference point, separated vertically by c1 (for the drag cells) and c2 (for the side cell). - Load resolution (Eq.1, p.2): - X = XD + XL - Y = YY - Z = ZPD + ZPL + ZZ - L = c2*YY + l*ZPD - l*ZPL - M = -c1*XD - c1*XL + f*ZPD + f*ZPL - 2f*ZZ - N = -n*XD + n*XL Pitching moment is the difference between the vertical cells, combined with drag times the strut height c1. **The large transfer distance c1 multiplies drag into pitching moment**, so any drag error shows up in M. - Fig.4 (p.3) shows three CAD renderings. They highlight in red which rods and cells are loaded under rolling moment, pitching moment, and drag. ## 3. Load ranges (Table 1, p.2; Table 2, p.4) | Component | Design load | (US units) | |---|---|---| | Lift Z | 150 N | 33.7 lbf | | Drag X | 100 N | 22.5 lbf | | Side Y | 75 N | 16.9 lbf | | Pitch M | 7 N*m | 62 in-lbf | | Roll L | 7 N*m | 62 in-lbf | | Yaw N | 7 N*m | 62 in-lbf | Cell ranges: the vertical cells (ZPD, ZPL, ZZ) are 200 N each and the horizontal cells (XD, XL, YY) are 100 N each (p.3, p.4 Table 2). For comparison, our ranges are N = 15 lbf, A = 2 lbf, m = 10 in-lbf. Their drag range is **about 11x ours** and their pitch range about 6x ours. ## 4. Element geometry and material (p.3 Fig.5; p.4 Eq.2-4) - **Single-force cell (Fig.5):** a rectangular closed frame (a "binocular"/ring-frame cell). F is applied axially through a hole or stud at top and bottom. Inside the window there are two thin bending beams of length Lt, width b and thickness h. The beams act as guided (S-bending) beams. Gauges 1 and 2 sit at one end of the inner beam surface and gauges 3 and 4 at the other end, so two gauges are in tension and two in compression. The photo shows the cell in a loading fixture with a load stud on top. - Bending stress as printed (Eq.2): sigma_b = (1/2 * F * Lt) / (b h^2 / 6), and eps = sigma_b / E. (The guided-beam end moment per beam with 2 beams would be F*Lt/4. Check this constant before reusing it. Our `balance_sizing.py` uses (A/2)*L/2.) - **Full-scale design strain:** horizontal cells 966.7 ue (Eq.3), vertical cells 920.5 ue (Eq.4). These are about 2x the 500 ue target in our script. - All six cells use the same design. Only the measuring-section dimensions change with range (p.3). - Material: **ARMCO PH 13-8 Mo stainless steel**, chosen for its strength and corrosion resistance. The authors say VTI experience shows it is one of the best balance steels and that **material choice strongly affects hysteresis, creep and repeatability** (p.3-4). ## 5. Gauges, bridges and electronics (p.3-4) - Each cell has one full 4-active-arm Wheatstone bridge, with 2 gauges in tension and 2 in compression placed close together for thermal compensation (Fig.5 bridge diagram, p.3). - Gauges: **Vishay TK-06-S082R-350** for all cells. These are 350 ohm, K-alloy (Karma), self-temperature- compensated for steel (06), with a dual-grid "R" pattern. Selection followed Vishay TN-505-4 (p.4). - Excitation: **6 V**. The material and gauges allow up to 20 V (per TN-502), and the lower value was chosen to limit self-heating (p.4). - Output at FS: e1 = 11.6 mV for the horizontal cells (about 1.93 mV/V, consistent with GF = 2.0) and e2 = 11.97 mV for the vertical cells (Eq.5-6). Note that e2 implies k = 2.17, not 2.0, so either the strain or the output value is inconsistent in the paper. - No DAQ, amplifier, filtering or ADC details are given. The paper says only that the cells are connected to a data acquisition system and that the motors are PC-controlled. ## 6. Calibration method and rig (p.4, Fig.6) - Each load cell was calibrated individually **before** assembly, to **0.05% FS** (p.4). - Balance calibration used manual dead weights applied at precise points relative to the balance reference centre, both positive and negative, at several stations. The rig was the VTI T-38 calibration hall (p.1, p.4). - **Calibration body:** two crossed beams with precisely located load points, mounted on the support struts in place of the model. Each component was loaded in at least 5 increments from zero to maximum (p.4). - Data reduction is VTI's generalisation of Galway (NAE LR-600). It is related to the Single-Vector Force Calibration method (Parker et al., AIAA-2001-0170) and allows more than one composite load vector (p.4). - Model: {e} = [C]{F}, a **linear 6x6 matrix** (6 terms per cell) fitted by least squares. Here {F} is the set of cell forces, not the aero components; the aero components then come from Eq.1 (p.5, Eq.7-8). - **No combined loads** were used in this first calibration. The authors expect accuracy to improve when combined loads are added (p.5 Conclusion). ## 7. Accuracy and interactions (p.5, Eq.8, Fig.7, Tables 2-3) - **Calibration matrix (Eq.8):** the diagonal terms are about 7.9e-6 (vertical cells) and about 1.85e-5 (horizontal cells), in output units per N. - The largest off-diagonal terms are about 6.2e-7 (eZZ due to XL, about 8% of ZZ's own sensitivity) and about 5.9e-7 (eXL due to XD, about 3% of XL's own sensitivity). - Most other off-diagonal terms are 1e-8 to 2e-7, which is roughly 0.1-2%. - Conclusion: the rod/pivot decoupling is good but not perfect, and the matrix is needed. - **Fig.7 (p.5):** six strips of Err (% FS) against applied load (% FS, about -140 to +140), one per cell. Horizontal lines mark the nominal accuracy band, and all residuals stay well inside +/-0.5% FS. - **Table 2, per cell:** | Cell | Range | Max |Err| | Max |Err| | Std. dev. | |---|---|---|---|---| | ZPD | 200 N | 0.40 N | 0.198% FS | 0.056% FS | | ZPL | 200 N | 0.39 N | 0.195% FS | 0.064% FS | | ZZ | 200 N | 0.44 N | 0.222% FS | 0.080% FS | | XL | 100 N | 0.23 N | 0.226% FS | 0.082% FS | | XD | 100 N | 0.16 N | 0.162% FS | 0.039% FS | | YY | 100 N | 0.28 N | 0.281% FS | 0.084% FS | The checkout reused the same load set as the fit, so these errors are optimistic. - **Table 3, composite components:** | Component | Range | Max error | Std. dev. | |---|---|---|---| | X | 100 N | 0.338% FS | 0.103% FS | | Y | 75 N | 0.374% FS | 0.112% FS | | Z | 150 N | 0.218% FS | 0.085% FS | | L | 7 N*m | 0.886% FS | 0.213% FS | | M | 7 N*m | 0.871% FS | 0.246% FS | | N | 7 N*m | 0.414% FS | 0.154% FS | The moment components are the worst because they are differences of large cell forces multiplied by arm lengths. Roll and pitch were only calibrated to about 50-60% of range. - In our units, the drag error of 0.338 N equals 0.076 lbf, which is about **14 drag counts** on our qS = 5.48 lbf. That is **3.8% of our 2 lbf A full scale**. ## 8. Figure index | Fig. | Page | Content | |---|---|---| | 1 | p.2 | Photo/CAD of the full balance with 12-item legend: model on main and tail struts, triangular platform, rods with pivot flexures, cells, rotating and fixed frames, pitch/yaw mechanisms, step motor | | 2 | p.2 | Rendering of the model with lift, drag, side force and the three moments | | 3 | p.2 | Schematic of the cell arrangement with lengths c1, c2, f, l, n and reference points O and O1 | | 4 | p.3 | Three renderings showing loaded members (red) under roll, pitch and drag | | 5 | p.3 | Photo of a cell in a load fixture; CAD of the frame cell with beam dimensions Lt, b, h; gauge positions 1-4; full-bridge diagram | | 6 | p.4 | Two photos of the balance calibration setup in the T-38 calibration hall (calibration body on the struts, weight pans) | | 7 | p.5 | Six residual-plot strips showing Err % FS against load % FS for each cell, with +/-0.5% lines | | Tables 1-3 | p.2, p.5 | Design loads, per-cell accuracy, composite accuracy | | Eq.8 | p.5 | Full 6x6 calibration matrix | ## 9. Relevance to our design ### Ideas that transfer to the internal sting balance (`balance_sizing.py`) 1. **Element type confirmation.** Their frame cell uses two guided beams with gauges at the beam ends. That is the same mechanics as our 2-plate Z-parallelogram axial flexure, with the same 4-arm +e/-e/+e/-e bridge and the same GF*eps*U output relation (our `bridge_mVV`). A closed rectangular frame like Fig.5 is a robust form for a stand-alone axial element. It could be EDM-cut as the axial section, with the end-moment constant checked first (see section 4). 2. **Strain level.** They run about 920-970 ue at FS (about 1.9 mV/V) in PH 13-8 Mo. Our 500 ue target in 7075 is conservative. Raising the axial plates toward about 700-800 ue would help the weak A signal, provided fatigue, creep and the overload stops allow it. They explicitly attribute hysteresis and creep behaviour to the material. - Option: make the balance from **17-4 PH H1025 or PH 13-8 Mo** instead of 7075-T651. Use the -06 gauge STC, and consider K-alloy gauges for better creep and drift behaviour. Steel is about 3x stiffer, so a steel balance needs thinner sections for the same strain, which costs machining precision on our tiny A plates (0.025-in class). 3. **Rods with pivot flexures as load-path decouplers.** Each cell sees only axial force because the rods have flexure pivots at both ends. Internally, this argues for flexure-hinged guide or link elements that keep N and m out of the A gauges. That matters because our script flags N->A coupling from plate axial strain. 4. **Pre-calibrate the element before final assembly** (they reached 0.05% FS per cell). For a monolithic balance that is not possible, but an early bridge check is still worthwhile: a cantilever dead-weight check of each bridge before wiring the full harness. 5. **Calibration lessons.** - Use a crossed-beam calibration body with precisely located load points, and at least 5 increments in both signs. - **Include combined loads.** Leaving them out was their main accuracy shortfall: moment errors around 0.9% FS. - Do not quote accuracy from the same load set used for the fit. 6. Use **6 V excitation on 350 ohm gauges**. This matches our 5 V choice. ### External/platform balance as an alternative for our tunnel The paper's tunnel is a good analogue: 0.4-0.6 m square section (15.7-23.6 in) at up to 50 m/s (112 mph). Ours is 26.25 x 11.25 in at 70 mph. **Pros** - Size is not limited by the 2-in pod. The cells live under the floor, so they can be large, off-the-shelf or commercial (single-point or S-beam cells in the 5-25 lbf class), and no gauging inside the model is needed. - The model pod can be simpler, and models are easy to swap. - Cells sit out of the flow, so there are fewer thermal and flow effects on the gauges. - 6 components are easy, and alpha/beta drives integrate naturally (as in their pitch -20/+30 deg and yaw +/-180 deg). - Each cell can be calibrated individually. - With the short height (11.25 in), floor struts stay short, about 5 in to the centreline. **Cons** - **Strut tare and interference** land directly in the drag measurement. Two struts, each about 0.3-0.5 in across and 5 in long in the flow, can give drag comparable to our wing's minimum drag (only about 0.1-0.2 lbf). Shielding the struts with non-metric windshields is essentially mandatory, plus strut-tare runs (image or tare/interference procedure). - **Accuracy scaled to our loads is marginal.** Their drag error is 0.34% of 100 N. With commercial cells sized for lift (about 15-30 lbf), drag resolution of a few hundredths of a lbf is hard. A dedicated low-range drag cell or flexure stage is needed. - **Moment accuracy suffers from long arms.** Pitch is a difference of large forces and is coupled to drag through the strut height c1 (Eq.1). Their M error is 0.87% FS. - **Mechanical complexity is high.** Their 6-component version needs a platform, 6 rods with 12 flexure pivots, rotating and fixed frames, pitch and yaw mechanisms, a floor seal/labyrinth gap, and a pressure-balanced floor cut-out for the closed-return tunnel. That is roughly 3-5x the fabrication effort of one monolithic internal balance. - A **3-component platform** would be far simpler: 2 vertical cells plus 1 drag cell, a flexure-guided parallelogram platform, and a single strut with a tail pitch link. It is probably comparable in effort to the internal balance, with easier gauging (buy cells) but harder aerodynamic tares. - **A sidewall (one-piece) balance**, which the paper notes is used for half-models (p.1), would require a half-span model or a long cross-flow support to the pod. That is a poor fit for an 18-in full-span wing in a 26.25-in-wide section. **Verdict.** A platform external balance is credible at our scale and removes the hardest miniaturisation problem (the A flexure in a 2-in pod). It trades that for strut-tare and interference corrections and more machinery. For drag-polar quality data on a 2 lbf drag range, the internal sting balance remains the better-resolution option. A 3-component floor platform with commercial cells and a shielded strut is a reasonable fallback or prototype path.