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INSTRUMENTATION OF AN F-16 PYLON FOR IN-FLIGHT MONITORING OF STORE LOADS

R.D. Richard and S. Putter

Rafael Ltd., Haifa, Israel

AbstractA custom-designed pylon was manufactured for attachment of an irregular store to an F-16 aircraft wing. To enable monitoring of the flight loads imposed on the wing by the store, strain gages were applied to the pylon inner surfaces at selected locations. The loads to be measured were pitching, yawing and rolling moments. Only very minor design modifications of the pylon were permitted to enable its utilization as a load measuring unit. Exploratory static tests were carried out in a structures laboratory to identify the most suitable gage locations and to produce calibration equations linking the gage response to the loads. Interactions between the load components were allowed for by means of a multiple regression analysis using the method of least squares. Selection of the most accurate combination of strain gage bridges to be used in the calibration equations was carried out by systematically calculating and comparing the probable error of each of the possible combinations of bridges. Out of a total of 20 bridges which were monitored in the calibration, 7 bridges (3 main and 4 back-up) were identified as optimal for the required load measurement. A final calibration was performed on-site with the pylon installed under the wing of the flight test aircraft. Typical accuracy levels of 2.5% full scale were obtained.

1. Introduction

As part of the introduction process of an irregularstore and pylon into service on an F-16 aircraft, information was required on the aerodynamic and inertial loads of the store under various flight conditions. In the absence of reliable load predictions a decision was made to measure these loads in a flight test program. This would provide the added benefit of monitored extension of the flight envelope in real time. No separation of aerodynamic and inertial loads was required. A feasibility assessment of the possibilities, noting the thin-walled and almost integral construction of the pylon, gave preference to utilization of the pylon itself as the load measuring instrument. The pylon was thus gaged for the measurement of pitching, rolling, and yawing moments. This proved possible even though the pylon was not designed to comply with the general rules of strain gage transducer design, and only very minor modifications were permitted to enable its utilization as a load measuring unit. The most suitable areas of the pylon on which to bond the gages had to be identified in terms of acceptable strain levels, linearity, repeatability, and absence of mounting

stresses. For this purpose an exploratory calibration was performed with strain gage bridges applied to numerous selected locations on the interior surfaces and the attachment plate of the pylon. The principles involved are analogous to those of wind tunnel straingage balances1. The calibration was carried out in astructures laboratory with the pylon installed on anF-16 wing, in preference to a calibration jig, for best simulation of boundary conditions. The resulting data enabled rejection of those gage locations which showed inadequate performance, and acceptance of the promising ones. Calibration coefficients were extracted from the accepted bridges by means of a least squares algorithm used for multiple regression analysis. Further processing highlighted the bridges which in combination would yield the maximumaccuracy. A number of check loads were subsequently applied to the calibrated pylon to verifythe accuracy levels. A second and final calibration was carried out on-site in the aircraft hangar, with the pylon installed under the wing of the flight test aircraft.

2. Instrumentation

2.1 Gaging and Wiring

The exploratory strain gage locations and circuits, comprising a total of 20 Wheatstone bridges, appear in Fig 2-1, which shows bridges (channels) 1–10. Bridges 11-20, not shown in the figure, are a near duplicate in terms of gage location and wiring. As the neighbouring arms of each Wheatstone bridge are in close proximity to one another, no significant temperature differences between them were expected. Thus the possible problems of temperature induced apparent strain were not considered to be of significant magnitude.

3. Calibration

3.1 Mechanical Setup

The mechanical setup for vertical loads is shown in Fig 3-1. It was designed to enable application of predetermined pitching (My), yawing (Mz) and rolling(Mx) moments about the pylon reference point (Fig 3-2). An F-16 aircraft wing was mounted to the load-carrying wall of the structures laboratory, and the pylon installed beneath the wing. A graduated

44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Confere7-10 April 2003, Norfolk, Virginia

AIAA 2003-1952

Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Fig 2-1: Gaging Diagram for Channels 1-10

- OUT Green (Pin ID 2)

- IN White (Pin ID 1)

26 27

25 28

21 23

2422

15168 710

14 9 11

12

13 1920

1 3 4 2

5 618

17

(39) 37

(40) 38

(29) 30

(31) 32 33

(36)

(35) 34

+ IN Black (Pin ID 4)

+ OUT Red (Pin ID 3)

1 2 3 4 5 6 7

8 9 10

Gage on inner surface

Gage on outer surface

Channel number8

Gage number on near surface38

Gage number on mirror-image (40)

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Wall MountingWing

Pylon

Calibration beam

Load cable

Load cell

Hydraulic Actuator

Fig 3-1: The Mechanical Setup for Vertical Loads

calibration beam simulated the store in terms of its mechanical interface with the pylon. The moments were created by point loads applied at successive stations of the beam in the vertical, axial, and lateral directions. A hydraulic actuator anchored to a ground structure produced the required tensile forces, which were monitored by means of a load cell in series with the actuator.

To allow for non-linear effects, the torsion angle α of the wing (Fig 3-2) was measured at each load step. The setup for lateral loading employed the same calibration beam, with horizontal forces acting through the load points.

4. Data Reduction Method

The calibration data reduction produces a set of equations relating the loads to the strain gage bridge signals. Multiple regression analysis using the method of least squares was applied. The least squares solution is of the form:

L = β1θ1 + β2θ2 + ----------- + βjθ j (4. 1 )

Where:L = Applied load componentβi = Calibration coefficientθ i = Signal of "i" th bridge

j = Total number of bridges

Expressing the solution in matrix form:

L = [ θ ] β ( 4.2 )

Defining n as the number of load components to be measured, L and β are vectors of n and j terms respectively; [ θ ] is an n x j matrix.

The least squares solution 2,3 is:

β = [ [[ θ ]T [ θ ]]-1 [ θ ]]T L (4. 3)

The probable error of the load is given by:

P.E. = .6745 √[(∑ε2)/(p-q)] (4.4)

Where: ε = residual (calculated load minus true load)p = number of load data points

q = number of terms in the load equation

Equation (4.1) may be derived for any combination of terms (strain gage bridges) from 1 to j, and the indices need not be consecutive. The optimum combination of terms is found by deriving (4.1) and its probable error (4.4) for each possible combination, and thereafter selecting the combination which yields the least probable error (an example of which is shown in section 5). Whilst the selected combination may include a large number of terms, practical considerations require that the number of terms in the equation (i.e. the number of active signals used) should be kept reasonably small.

5. Lab Calibration Results

5.1 Raw Data

A graphical example of data obtained is shown in Fig 5-1. This indicates reasonable linearity and good return to zero. Hence bridges 8 & 10 were selected as candidates for inclusion in the final calibration equations. Fig 5-2 shows a typical example of a channel which was rejected – the wide hysteresis loop disqualifying it for use as a load measuring device.

x

z

a

Loaded cable, tension F

b

Ref Pt

Fig 3-2: Geometric non-linearity of pitch

α

My = Fa {cosα – (b/a)sin α}

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-1000

-800

-600

-400

-200

0

200

-2500 -2000 -1500 -1000 -500 0Load (lb)

Out

put

(mic

rost

rain

)

Ch 8

Ch 10

-600

-500

-400

-300

-200

-100

0

-2500 -2000 -1500 -1000 -500 0

Load (lb)

Out

put

(mic

rost

rain

)

Fig 5-2: Example of rejected data

Fig 5-1: Example of accepted data

The calibration matrices were based on full-scale loads. Consequently, the flight test results will be most accurate in the full scale load region, which was of primary interest. Results in the mid-scale region are less accurate, but are potentially improvable by adapting the regression analysis to higher polynomials.

5.2 Selection of the Optimum BridgeCombinations

As previously indicated, the calculation of a single load component in a flight test may be based, with varying degrees of accuracy, on the signals of any combination of the "accepted" strain gage bridges, i.e. those with acceptable linearity, sensitivity and repeatability. In any given combination, certain accepted bridges are used whilst others are not. The data reduction process enables identification of the combinations which provide the most accurate load measurements. Reference to Fig 2-1 shows the location of the gages. Bridges 11-20, not shown in the figure, are a near duplicate of bridges 1-10 in terms of gage location. Out of bridges 1-10, five were accepted. These were bridges 5, 6, 8, 9, 10, which were labeled "Group 1". Similarly five bridges were accepted out of numbers 11-20 (specifically 11, 15, 18, 19, 20) and labeled “Group 2”. The remaining

task was to select out of each set of five bridges the combination which, acting alone, yields the most accurate load measurements. Given a set of 5 bridges, the number of ways of selecting one bridge or more is (25 –1), which makes 31 possible combinations in all. Limiting the selection to 3 bridges out of 5 (due to constraints of available flight test channels), reduces the possible number of combinations to 25. Out of these, one (optimum) combination must be selected for the calculation of Mx, one for My, and one for Mz. The βmatrix is based on the three selected combinations.

Table 5-1 shows the β coefficients for each of the 25 bridge combinations, shown in ascending order of P.E. Table 5-2 shows an example of the calculation of the P.E. It applies to Mx for the combination of bridges 8,9,10. – ref number 25 of Table 5-1. Tables such as 5-2 were similarly compiled for My and Mz. Fig 5-3 shows the P.E. of Mx for each bridge combination. Similar figures were drawn for My and Mz. Additional considerations governing the final choice of bridge combinations were:

a) The number of bridges selected per component were kept to a reasonable minimum. Selection of additional bridges which provided only a marginal increase of accuracy was avoided, owing to the reliability penalty in the telemetry transmissions. (However, data from all channels were recorded on-board, enabling the selection of any number of channels for later off-line processing).

b) Bridges 5 and 6, initially accepted, were eventually rejected owing to the appearance of strain readings caused by installation stresses. Typically these have poor repeatability and may vary during a load cycle.

c) P.E. values permitting, any bridge may serve more than one of the three components to be measured.

5.3 The Calibration Equations

Combination number 25 was selected from Fig 5-3 for Mx. Combinations 23 and 24, even though they indicate a lower P.E., were rejected because of inadequate performance of channels 5 and 6, as mentioned above. It can be readily seen from the figure that any combination which does not include both Beta9 and Beta10 (i.e. bridges 9 and 10) has a much higher P.E. (at least sevenfold) than those which include both Beta9 and Beta10. The combinations for My and Mz were selected by a similar process. Using these combinations, and denoting the output (microstrain) of channel "n" as θn, produces equations (5.1) to (5.3), which are the calibration equations for the Group 1 channels :

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Calibration Constants (lb-in per microstrain) †

Beta10Beta9Beta8Beta6Beta5

*

31.6545.04004.3723

32.1345.0009.41024

31.9044.863.760025

31.6244.9000022

039.100-272.73127.0711

24.25000015

24.5904.490019

24.60006.56017

24.260002.4516

25.95022.910-19.1620

23.99018.75-31.83021

25.670027.38-9.9018

037.34-72.65072.3413

032.38000 8

032.580-16.75010

032.55-4.190012

032.47003.55 9

031.8840.47-98.46014

000-204.2594.53 3

0017.32-227.3788.61 7

000-14.210 2

00002.22 1

00-2.2200 4

0050.01-115.250 6

00-39.09039.13 5

Table 5-1: Calibration constants for each Group1 bridge combination(Calibration of Mx)

* Combination reference number† Zero indicates unselected bridge

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Mx = 3.76 θ8 + 44.86 θ 9 + 31.90 θ10 lb-in (5.1)

My = 110.45 θ8 - 3.84 θ 9 + 4.43 θ10 lb-in (5.2)

Mz = 3.90 θ8 - 7.36 θ 9 + 36.82 θ10 lb-in (5.3)

* Where Mx=0 the load was My acting alone.

The use of bridges 8,9, and 10 for all three loads of Group 1, whilst economical in terms of channel usage, was selected because of the low probable errors. One or more additional bridges were permitted in practice, but would not have significantly improved the probable error. By a similar process 4 bridges were assigned to Group 2 (θ11, θ18, θ19, θ20). Thus for best accuracy the pylon utilized 7 bridges – a main and backup set consisting of 3 and 4 bridges respectively. The 7 bridges were selected out of the original 20 bridges which entered the exploratory calibration at the start of the process.

6. On-site Calibration

6.1 Purpose & Method

The lab calibration wing and the flight test wing have somewhat different local rigidities at the hardpoints where the pylon is installed. Thus it was necessary to check the applicability of the lab calibration to the flight test aircraft wing. For this purpose a calibration rig was set up in the aircraft hangar, as shown in Figures 6-1 and 6-2. The deflection angle α of the wing (Fig 3-2) was slightly greater than in the lab setup due mainly to the contribution of the landing gear. To reduce roll angle of the aircraft relative to the horizontal, the right wing was preloaded with a counterweight. To minimize the possibility of slippage in the lateral direction, the aircraft was set up in a heavy configuration, with full internal tanks and 2 full external tanks. The calibration load levels in the hangar were reduced to 75% of the lab-calibration levels , due to on-site safety rulings.

Signals (microstrain)

Ch8 Ch9 Ch10

AppliedMx

(lb-in)

*

CalculatedMx

(lb-in)

Residual

ε% f.s.

†

-980 -11 87 0 -1406 -1.45

-1102 16 118 0 335 0.34

-886 37 129 0 2441 2.51

-354 65 56 0 3370 3.47

165 90 -19 0 4053 4.17

526 46 -50 0 2448 2.52

548 -8 -36 0 555 0.57

-76 -515 1568 24070 26629 2.63

-75 -477 1821 34776 36408 1.68

-67 -171 1716 46770 46818 0.05

-77 722 1855 92640 91278 -1.4

29 1136 231 61789 58445 -3.44

55 1039 -495 32026 31031 -1.02

92 1445 -906 31348 36274 5.07

Table 5-2: Residuals for calculation of probable error of Mx using bridges 8,9,10

† Full scale Mx is 97000 lb-in Substituting in (4.4) p=11, q=3, and ε from the above table yields: Probable Error = 1.98% full scale.

0

5

10

15

20

25

30

P.E

. (%

full

scal

e)

5 6 4 1 2 7 3 14 19 12 10 8 13 18 21 20 16 17 19 15 11 22 25 24 23

56

8 910

Bri

dge

#

Fig 5-3: P.E. of Mx for each bridge combination

Combination reference #

Load string

Counterweight(MK 84)

Safety tether

Pylon

Fig 6-1: A/C configuration and mechanical set-up for vertical loading

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6.2 Results

The data was processed using the same method as for the lab-calibration. The equations produced in the on-site calibration check were very similar to the lab calibration equations, and were adopted for the flight test in preference to the laboratory equations. The accuracy levels achieved in the on-site check-load test are indicated in Table 6-1.

Table 6-1: Average accuracy of check-load results (% full scale)

Mx My Mz

Group1 1.33 2.04 1.28

Group2 1.42 2.28 1.38

7. Conclusions

The work described above demonstrates the feasibility of employing the pylon as a load measuring device even though it was not designed for the purpose. This was made possible by experimentally examining a large number of possible strain gage locations to determine which locations were basically suitable, and by employing a special purpose algorithm to determine which combinations of strain gage bridges should be employed for best results. The accuracy levels are inferior to those associated with strain gage transducers such as uniaxial load cells (typically 0.5% full scale or better), but given the overall complexity of the pylon as a 3-component measuring device the accuracy level of less than 2.5% full scale appears very reasonable, and has been accepted by the customerwithout reservation. Flight test data recorded from telemetry signals showed good return-to-zero of all channels, and processed results which fall within the predicted range. The measurements are at their most accurate in the vicinity of full scale values due to the linear approximations made to the raw data. Accuracy levels in the middle load range are potentially improvable by adapting the regression analysis to higher polynomials.

References

1. Richard R.D., Brosh A. and Seginer, A.A Parametric Investigation of an Elastic Parallelogram for the Measurement of Aerodynamic Drag. Technion Israel Institute of Technology, Dept of Aeronautical Engineering. T.A.E. Report No. 419, July 1980

2. Skopinski T.H., Aiken, W. S. Jr., and Huston W B. Calibration of Strain-Gage Installations in Aircraft Structures for the Measurement of Flight Loads. NACA Report 1178. 1954

3. Zacks S., The Theory of Statistical Inference. John Wiley & Sons, Inc.1971

Pylon

Loadstring

600 gal tanks (full)

Internal tanks (full)

Fig 6-2: A/C configuration and mechanical set-up for lateral loading