An improved method of calibrating a wind-tunnel force balance involves the use of a unique load application system integrated with formal experimental design methodology. The Single-Vector Force Balance Calibration System (SVS) overcomes the productivity and accuracy limitations of prior calibration methods.

A force balance is a complex structural spring element instrumented with strain gauges for measuring three orthogonal components of aerodynamic force (normal, axial, and side force) and three orthogonal components of aerodynamic torque (rolling, pitching, and yawing moments). Force balances remain as the state-of-the-art instrument that provide these measurements on a scale model of an aircraft during wind tunnel testing. Ideally, each electrical channel of the balance would respond only to its respective component of load, and it would have no response to other components of load. This is not entirely possible even though balance designs are optimized to minimize these undesirable interaction effects. Ultimately, a calibration experiment is performed to obtain the necessary data to generate a mathematical model and determine the force measurement accuracy.

In order to set the independent variables of applied load for the calibration experiment, a high-precision mechanical system is required. Manual dead-weight systems have been in use at Langley Research Center (LaRC) since the 1940s. These simple methodologies produce high confidence results, but the process is mechanically complex and labor-intensive, requiring three to four weeks to complete. Over the past decade, automated balance calibration systems have been developed. In general, these systems were designed to automate the tedious manual calibration process resulting in an even more complex system which deteriorates load application quality.

The current calibration approach relies on a one-factor-at-a-time (OFAT) methodology, where each independent variable is incremented individually throughout its full-scale range, while all other variables are held at a constant magnitude. This OFAT approach has been widely accepted because of its inherent simplicity and intuitive appeal to the balance engineer. LaRC has been conducting research in a "modern design of experiments" (MDOE) approach to force balance calibration. Formal experimental design techniques provide an integrated view to the entire calibration process covering all three major aspects of an experiment; the design of the experiment, the execution of the experiment, and the statistical analyses of the data.

In order to overcome the weaknesses in the available mechanical systems and to apply formal experimental techniques, a new mechanical system was required. The SVS enables the complete calibration of a six-component force balance with a series of single force vectors.

This new system improves on the "trusted" aspects of current manual calibration systems. The SVS enables the efficient execution of a formal experimental design, is relatively inexpensive to manufacture, requires minimal time to operate, and provides a high level of accuracy.The system allows for single vector calibration, meaning that single, calibrated dead-weight loads are applied in the gravitational direction generating six component combinations of load relative to the coordinate system of the balance. By utilizing this single force vector, load application inaccuracies caused by the conventional requirement to generate multiple force vectors are fundamentally reduced. The system features significantly fewer components than the LaRC manual system and therefore fewer sources of systematic error. The primary components include a non-metric positioning system, a multiple-degree-of-freedom load-positioning system, a three-axis orthogonal accelerometer system, and calibrated weights (see figure).

The three balance force components are a function of the applied load and the orientation of the balance in three-dimensional space. To generate a desired combination of the three forces, the balance is manipulated to a prescribed orientation using the non-metric positioning system and precisely measured on the metric end using the accelerometer system. This accelerometer system provides the components of the gravitational vector projected onto the three axes of the balance coordinate system. Combining the measured gravitational components on the balance axes and the known dead-weight enables the determination of the three force components.

The three balance moment components are a function of the three force vectors and the position of the point of load application in three-dimensional space relative to the balance moment center (BMC). The BMC is a defined location in the balance coordinate system that serves as a reference point in which the moment components are described. The point of load application is set using the multiple-degree-of-freedom load-positioning system. This system utilizes a novel system of bearings and knife-edge rocker guides to maintain the load orientation, regardless of the angular orientation of the balance, which makes the point of load application independent of the angular orientation of the balance. Stated another way, when the balance is manipulated in three-dimensional space, the point of load application remains constant.

The SVS performs rapid and accurate setting of the independent variables. Even though this load application system would greatly enhance the execution of the current OFAT design, it is particularly well suited to meet the requirements for the execution of a formal experimental design. The use of a single calibration load reduces the set-up time for the randomized multi-axis load combinations prescribed by a formal experimental design.

The purpose of using an MDOE approach is to efficiently achieve the primary objective of the calibration experiment; namely, the determination of an accurate mathematical model to estimate the aerodynamic loads from measured balance responses. Theoretical and experimental results have shown that MDOE makes it possible to perform a given calibration with an order of magnitude fewer data points than current methods.

The three fundamental MDOE quality-assurance principles are randomization, blocking, and replication. Randomization of data-point ordering ensures that a given balance load combination is just as likely to be applied early in the calibration as it is near the end. If some systematic variation (e.g., instrumentation drift, temperature effects, or operator fatigue) causes earlier measurements to be biased differently from later measurements, then randomization converts such unseen systematic errors to an additional component of simple random error.

Blocking entails organizing an experiment into relatively short blocks of time within which the randomization of point ordering ensures stable sample averages and statistical independence of measurements. While randomization defends against systematic within-block variations, substantial between-block systematic variations are also possible. Blocking makes it possible, during the subsequent analysis of the data, to remove this between-block component of the unexplained variance.

Averaging of genuine replicates causes random errors to cancel. These errors can include what would otherwise be undetectable systematic variations that are converted to random errors by randomizing the loading schedule. Replication also facilitates unbiased estimates of pure error, the component of error attributable to ordinary chance variations in the data. Estimates of pure error enable an objective assessment of the quality of fit of the mathematical model.

Integration of the single-vector hardware system with MDOE techniques has enabled an order of magnitude reduction in wind-tunnel balance calibration time and cost, while simultaneously increasing the quality of the information obtained from the calibration experiment. The SVS provides the basis for further advancement in force measurement technology in the areas of higher-order mathematical models, implementation of statistical process control, and an expansion of the calibration mathematical model to include temperature as an independent variable.

*This work was done by P. A. Parker and R. DeLoach of Langley Research Center.*

*This invention is in the process of being exclusively licensed. Inquiries concerning technical aspects of the invention may be directed to the inventor, Pete Parker, at (757) 864-4709. Inquiries concerning the licensing and commercialization of the invention may be directed to Barry Gibbens of the NASA LaRC Technology Commercialization Program Office at (757) 864-7141. LAR-16020.*

##### NASA Tech Briefs Magazine

This article first appeared in the October, 2003 issue of *NASA Tech Briefs* Magazine.

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