Engineering topics

Ulbrich, N.

Publications and source records attributed to Ulbrich, N..

At least 19 records

NASA NTRS2020

Assessment of Temperature-Dependent Regression Model Terms of a RUAG Six-Component Block-Type Balance

A metric called the percent contribution was applied to regression models of temperature-dependent calibration data of a RUAG six-component block-type balance in order to assess the influence of temperature-dependent regression model terms on the balance load prediction. Regression models were examined that are needed if either the Iterative or the Non-Iterative Method is used for the load prediction. Computed values of the percent contribution confirmed that the cross-product term defined by a primary load and the temperature difference is the most influential temperature-dependent term of the regression model of a primary output that the Iterative Method needs. Similarly, the analysis showed that the cross-product term defined by a primary output and the temperature difference is the most influential temperature-dependent term of the regression model of a primary load that the Non-Iterative Method needs. Computed results support conclusions that were reported in an earlier theoretical study. This study asserted that the cross-product term defined by a primary load or output and the temperature difference models the temperature-dependent shift of the gage sensitivity. The influence of other temperature-dependent terms used in the regression models of the calibration data of RUAG's balance was negligible. This observation may be explained by the fact that RUAG's block-type balances have highly linear characteristics. Overall, the percent contribution has proven itself to be a reliable and easy-to-implement metric that may also be used for the assessment of the influence of temperature-dependent regression model terms on the load prediction of a six-component strain-gage balance.

Ulbrich, N.↗

NASA NTRS2019

Comparison of Electrical Output Format Options for the Analysis of Strain-Gage Balance Calibration Data

Fundamental characteristics of three gage output formats are discussed that may be used to both interpret and analyze wind tunnel strain-gage balance data. The first output format uses raw outputs, i.e., absolute voltage measurements, for the analysis. This choice requires an intercept term in the regression model of the outputs if the Iterative Method is chosen for the load prediction. Raw outputs can be used for the analysis of all known output characteristics as long as the Iterative Method is applied. However, raw outputs cannot be used to analyze data of a balance with bi-directional outputs if the Non-Iterative Method is chosen for the analysis. The second output format, i.e., difference type 1, uses the difference between raw outputs and the natural zeros of the balance gages for the analysis. In this case, the use of the intercept term becomes optional. Analysis results for difference type 1 will exactly match analysis results obtained by using raw outputs as long as identical math models are used for the regression analysis. In addition, difference type 1 may be used to analyze data of a balance with bi directional outputs if an analyst prefers to process data using the Non-Iterative Method. The third output format, i.e., difference type 2, uses the difference between raw outputs and the outputs of the zero load point of a load series for the data analysis. The application of this format is only recommended if the maximum magnitude of all tare loads of a given balance calibration data set is less than two percent of capacity. Data from the calibration of a force balance is used to illustrate the application of the three gage output formats.

Wind Tunnel Strain-Gage Balance↗

NASA NTRS2019

Fundamental Improvement of a Convergence Test for Iterative Strain-Gage Balance Load Predictions

A fundamental improvement of a convergence test for wind tunnel strain-gage balance load iterations was developed. The improvement became necessary because incorrect test results were obtained whenever the original test was applied to multi-component balances with large load capacity differences. The original test was first published in NASA TN D-6860. It uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions whenever the Iterative Method is applied. The Lipschitz constant is a function of the partial derivatives of each balance load component with respect to all other load components. Unfortunately, the original definition of the convergence test overlooked the fact that the Lipschitz constant is a dimensionless quantity and that the partial derivative of one load component with respect to another load component is not always dimensionless. Therefore, an improvement of the original test was successfully developed that uses load capacities to make all inputs for the calculation of the Lipschitz constant dimensionless before use. Results from the calibration data analysis of a six-component force balance and a five-component semi-span balance are used to illustrate the application of the improved load iteration convergence test.

Strain-Gage Balance↗

NASA NTRS2019

Calibration and Data Analysis Recommendations for Three-Component Moment Balances

Fundamental characteristics of design, calibration, and application of three-component moment balances are investigated in great detail. These balances are typically used to determine loads on control surfaces, canards, or other parts that are attached to a wind tunnel model. First, three different descriptions of the load state of a moment balance are reviewed. Then, load transformations between different load formats and the combined load diagram for two of the three load components are discussed. An error analysis showed that it is critical to maximize the product of the distance between the bending moment gages and their sensitivities in order to minimize the overall error in the normal force prediction. In addition, it is important to apply a sufficient number of calibration loadings near the first bending moment gage. Then, unwanted near-linear dependencies between the two bending moment gage outputs can be avoided. The error in the bending moment prediction is also investigated that results from the elastic deformation of the metric part of the balance under load. Finally, the application of the Non-Iterative Method to three-component moment balance calibration data is described in order to obtain regression models that can be used to predict loads from measured outputs during a wind tunnel test.

Strain-Gage Balance↗

NASA NTRS2019

Application of a Temperature-Dependent Load Prediction Method to a RUAG Six-Component Block-Type Balance

Temperature-dependent data of a RUAG six-component block-type balance was analyzed to assess the accuracy of two load prediction methods for temperature-dependent balance data. The supplied data was prepared for the analysis by splitting it into calibration and check load data subsets. The first calibration data subset was obtained at a temperature of 294 Kelvin. The second calibration data subset was obtained at a temperature of 315 Kelvin. A subset of 38 points was extracted from the second data set and used as check loads so that the accuracy of the two load prediction methods could be tested. First, the Iterative Method in combination with an extended independent and dependent variable set was used for the balance load prediction. This approach fits electrical outputs as a function of loads and the temperature and, afterwards, constructs a load iteration scheme from the regression coefficients so that loads can be predicted from outputs and the temperature during a wind tunnel test. The Non-Iterative Method was also used for the load prediction. This alternate method can more easily be implemented in a data system as loads are directly fitted as a function of electrical outputs and the temperature. Analysis results for the axial force are only discussed in the paper as similar results were obtained for the other five load components. Results for both methods clearly show that the cross-product term constructed from either a primary gage load or a primary gage output and the temperature explains the majority of the temperature-dependent part of the predicted balance load. This term models the temperature dependent nature of the gage sensitivity. Therefore, it is recommended to apply primary gage loadings at different temperatures during a balance calibration whenever temperature effects need to be described. These loadings will contain information about the temperature-dependent nature of the gage sensitivities that can be quantified by related cross-product terms in regression models of the data.

strain-gage balance↗

NASA NTRS2019

Influence of Strain-Gage Balance Characteristics on the Precision Error of the Drag Coefficient

Improvements and results of a new method are presented that computes a pre-test estimate of the precision error of the drag coefficient of a wind tunnel model. The error estimate is defined as the part of the drag coefficient's precision error that is primarily associated with the precision error of the angle of attack measurement and physical characteristics of the chosen strain-gage balance. The method indirectly describes the precision error of the angle of attack measurement by using an assumed balance gage output variation of one microV/V. The physical characteristics of the balance, on the other hand, are described by partial derivatives of the axial and normal forces with respect to the strain-gage outputs. These derivatives can directly be obtained from the data reduction matrix of the balance. The precision error estimate itself is calculated by applying a simple explicit equation that uses the model reference area, the dynamic pressure, the angle of attack, the coefficients of the linear terms of the data reduction matrix, and the electrical output variation of one microvolt per volt as input. Precision errors at constant angle of attack may be visualized as contour plots by plotting them, for example, versus the Mach number and the total pressure. Characteristics of NASA's MC60E balance are used in combination with the reference area of a generic wind tunnel model in order to demonstrate that error estimates are independent of both the balance load format and the units chosen for the description of balance loads, model reference area, and the dynamic pressure. Finally, experimental data from a wind tunnel test of the Ames Check Standard Model in the NASA Ames 11-foot Transonic Wind Tunnel illustrates the application of the method to real-world test data.

precision error↗

NASA NTRS2018

Implementation and Use of a Convergence Test for Iterative Wind Tunnel Balance Load Predictions

A modified and extended version of a convergence test for wind tunnel strain-gage balance load iterations was implemented. The test uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions if the Iterative Method is applied. Convergence is expected within the use envelope of the balance whenever this upper bound is less than the threshold of one. It is explained in great detail how the convergence test can be applied to the two load iteration equation types that are currently being used in the aerospace testing community. In addition, the application of the test to balances with bi-directional output characteristics is discussed. It is also shown how numerical differentiation can be used in order to obtain partial derivatives that are needed for the calculation of the Lipschitz constant. Finally, machine calibration data of NASA's MC60E six-component force balance is selected to demonstrate both implementation and use of the convergence test.

calibration analysis↗

NASA NTRS2018

Regression Analysis and Calibration Recommendations for the Characterization of Balance Temperature Effects

Analysis and use of temperature-dependent wind tunnel strain-gage balance calibration data are discussed in the paper. First, three different methods are presented and compared that may be used to process temperature-dependent strain-gage balance data. The first method uses an extended set of independent variables in order to process the data and predict balance loads. The second method applies an extended load iteration equation during the analysis of balance calibration data. The third method uses temperature-dependent sensitivities for the data analysis. Physical interpretations of the most important temperature-dependent regression model terms are provided that relate temperature compensation imperfections and the temperature-dependent nature of the gage factor to sets of regression model terms. Finally, balance calibration recommendations are listed so that temperature-dependent calibration data can be obtained and successfully processed using the reviewed analysis methods.

wind tunnel test↗

NASA NTRS2018

Use of the Ames Check Standard Model for the Validation of Wall Interference Corrections

The new check standard model of the NASA Ames 11-ft Transonic Wind Tunnel was chosen for a future validation of the facility's wall interference correction system. The chosen validation approach takes advantage of the fact that test conditions experienced by a large model in the slotted part of the tunnel's test section will change significantly if a subset of the slots is temporarily sealed. Therefore, the model's aerodynamic coefficients have to be recorded, corrected, and compared for two different test section configurations in order to perform the validation. Test section configurations with highly accurate Mach number and dynamic pressure calibrations were selected for the validation. First, the model is tested with all test section slots in open configuration while keeping the model's center of rotation on the tunnel centerline. In the next step, slots on the test section floor are sealed and the model is moved to a new center of rotation that is 33 inches below the tunnel centerline. Then, the original angle of attack sweeps are repeated. Afterwards, wall interference corrections are applied to both test data sets and response surface models of the resulting aerodynamic coefficients in interference-free flow are generated. Finally, the response surface models are used to predict the aerodynamic coefficients for a family of angles of attack while keeping dynamic pressure, Mach number, and Reynolds number constant. The validation is considered successful if the corrected aerodynamic coefficients obtained from the related response surface model pair show good agreement. Residual differences between the corrected coefficient sets will be analyzed as well because they are an indicator of the overall accuracy of the facility's wall interference correction process.

wind tunnel wall interferenc↗

NASA NTRS2017

Detection and Use of Load and Gage Output Repeats of Wind Tunnel Strain-Gage Balance Data

Criteria are discussed that may be used for the detection of load and gage output repeats of wind tunnel strain-gage balance data. First, empirical thresholds are introduced that help determine if the loads or electrical outputs of a pair of balance calibration or check load data points match. A threshold of 0.01 percent of the load capacity is suggested for the identification of matching loads. Similarly, a threshold of 0.1 microV/V is recommended for the identification of matching electrical outputs. Two examples for the use of load and output repeats are discussed to illustrate benefits of the implementation of a repeat point detection algorithm in a balance data analysis software package. The first example uses the suggested load threshold to identify repeat data points that may be used to compute pure errors of the balance loads. This type of analysis may reveal hidden data quality issues that could potentially be avoided by making calibration process improvements. The second example uses the electrical output threshold for the identification of balance fouling. Data from the calibration of a six-component force balance is used to illustrate the calculation of the pure error of the balance loads.

strain-gage balance↗

NASA NTRS2017

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

calibration analysis↗

NASA NTRS2017

A Universal Threshold for the Assessment of Load and Output Residuals of Strain-Gage Balance Data

A new universal residual threshold for the detection of load and gage output residual outliers of wind tunnel strain{gage balance data was developed. The threshold works with both the Iterative and Non{Iterative Methods that are used in the aerospace testing community to analyze and process balance data. It also supports all known load and gage output formats that are traditionally used to describe balance data. The threshold's definition is based on an empirical electrical constant. First, the constant is used to construct a threshold for the assessment of gage output residuals. Then, the related threshold for the assessment of load residuals is obtained by multiplying the empirical electrical constant with the sum of the absolute values of all first partial derivatives of a given load component. The empirical constant equals 2.5 microV/V for the assessment of balance calibration or check load data residuals. A value of 0.5 microV/V is recommended for the evaluation of repeat point residuals because, by design, the calculation of these residuals removes errors that are associated with the regression analysis of the data itself. Data from a calibration of a six-component force balance is used to illustrate the application of the new threshold definitions to real{world balance calibration data.

wind tunnel balance↗

NASA NTRS2017

Pre-Test Assessment of the Upper Bound of the Drag Coefficient Repeatability of a Wind Tunnel Model

A new method is presented that computes a pre{test estimate of the upper bound of the drag coefficient repeatability of a wind tunnel model. This upper bound is a conservative estimate of the precision error of the drag coefficient. For clarity, precision error contributions associated with the measurement of the dynamic pressure are analyzed separately from those that are associated with the measurement of the aerodynamic loads. The upper bound is computed by using information about the model, the tunnel conditions, and the balance in combination with an estimate of the expected output variations as input. The model information consists of the reference area and an assumed angle of attack. The tunnel conditions are described by the Mach number and the total pressure or unit Reynolds number. The balance inputs are the partial derivatives of the axial and normal force with respect to all balance outputs. Finally, an empirical output variation of 1.0 microV/V is used to relate both random instrumentation and angle measurement errors to the precision error of the drag coefficient. Results of the analysis are reported by plotting the upper bound of the precision error versus the tunnel conditions. The analysis shows that the influence of the dynamic pressure measurement error on the precision error of the drag coefficient is often small when compared with the influence of errors that are associated with the load measurements. Consequently, the sensitivities of the axial and normal force gages of the balance have a significant influence on the overall magnitude of the drag coefficient's precision error. Therefore, results of the error analysis can be used for balance selection purposes as the drag prediction characteristics of balances of similar size and capacities can objectively be compared. Data from two wind tunnel models and three balances are used to illustrate the assessment of the precision error of the drag coefficient.

drag coefficient measurement↗

NASA NTRS2016

Assessment of the Uniqueness of Wind Tunnel Strain-Gage Balance Load Predictions

A new test was developed to assess the uniqueness of wind tunnel strain-gage balance load predictions that are obtained from regression models of calibration data. The test helps balance users to gain confidence in load predictions of non-traditional balance designs. It also makes it possible to better evaluate load predictions of traditional balances that are not used as originally intended. The test works for both the Iterative and Non-Iterative Methods that are used in the aerospace testing community for the prediction of balance loads. It is based on the hypothesis that the total number of independently applied balance load components must always match the total number of independently measured bridge outputs or bridge output combinations. This hypothesis is supported by a control volume analysis of the inputs and outputs of a strain-gage balance. It is concluded from the control volume analysis that the loads and bridge outputs of a balance calibration data set must separately be tested for linear independence because it cannot always be guaranteed that a linearly independent load component set will result in linearly independent bridge output measurements. Simple linear math models for the loads and bridge outputs in combination with the variance inflation factor are used to test for linear independence. A highly unique and reversible mapping between the applied load component set and the measured bridge output set is guaranteed to exist if the maximum variance inflation factor of both sets is less than the literature recommended threshold of five. Data from the calibration of a six{component force balance is used to illustrate the application of the new test to real-world data.

strain-gage balance↗

NASA NTRS2016

A New Load Residual Threshold Definition for the Evaluation of Wind Tunnel Strain-Gage Balance Data

A new definition of a threshold for the detection of load residual outliers of wind tunnel strain-gage balance data was developed. The new threshold is defined as the product between the inverse of the absolute value of the primary gage sensitivity and an empirical limit of the electrical outputs of a strain{gage. The empirical limit of the outputs is either 2.5 microV/V for balance calibration or check load residuals. A reduced limit of 0.5 microV/V is recommended for the evaluation of differences between repeat load points because, by design, the calculation of these differences removes errors in the residuals that are associated with the regression analysis of the data itself. The definition of the new threshold and different methods for the determination of the primary gage sensitivity are discussed. In addition, calibration data of a six-component force balance and a five-component semi-span balance are used to illustrate the application of the proposed new threshold definition to different types of strain{gage balances. During the discussion of the force balance example it is also explained how the estimated maximum expected output of a balance gage can be used to better understand results of the application of the new threshold definition.

load residuals↗

NASA NTRS2016

Pre-Test Assessment of the Use Envelope of the Normal Force of a Wind Tunnel Strain-Gage Balance

The relationship between the aerodynamic lift force generated by a wind tunnel model, the model weight, and the measured normal force of a strain-gage balance is investigated to better understand the expected use envelope of the normal force during a wind tunnel test. First, the fundamental relationship between normal force, model weight, lift curve slope, model reference area, dynamic pressure, and angle of attack is derived. Then, based on this fundamental relationship, the use envelope of a balance is examined for four typical wind tunnel test cases. The first case looks at the use envelope of the normal force during the test of a light wind tunnel model at high subsonic Mach numbers. The second case examines the use envelope of the normal force during the test of a heavy wind tunnel model in an atmospheric low-speed facility. The third case reviews the use envelope of the normal force during the test of a floor-mounted semi-span model. The fourth case discusses the normal force characteristics during the test of a rotated full-span model. The wind tunnel model's lift-to-weight ratio is introduced as a new parameter that may be used for a quick pre-test assessment of the use envelope of the normal force of a balance. The parameter is derived as a function of the lift coefficient, the dimensionless dynamic pressure, and the dimensionless model weight. Lower and upper bounds of the use envelope of a balance are defined using the model's lift-to-weight ratio. Finally, data from a pressurized wind tunnel is used to illustrate both application and interpretation of the model's lift-to-weight ratio.

strain-gage balance↗

NASA NTRS2015

Improved Regression Analysis of Temperature-Dependent Strain-Gage Balance Calibration Data

An improved approach is discussed that may be used to directly include first and second order temperature effects in the load prediction algorithm of a wind tunnel strain-gage balance. The improved approach was designed for the Iterative Method that fits strain-gage outputs as a function of calibration loads and uses a load iteration scheme during the wind tunnel test to predict loads from measured gage outputs. The improved approach assumes that the strain-gage balance is at a constant uniform temperature when it is calibrated and used. First, the method introduces a new independent variable for the regression analysis of the balance calibration data. The new variable is designed as the difference between the uniform temperature of the balance and a global reference temperature. This reference temperature should be the primary calibration temperature of the balance so that, if needed, a tare load iteration can be performed. Then, two temperature{dependent terms are included in the regression models of the gage outputs. They are the temperature difference itself and the square of the temperature difference. Simulated temperature{dependent data obtained from Triumph Aerospace's 2013 calibration of NASA's ARC-30K five component semi{span balance is used to illustrate the application of the improved approach.

wind tunnel testing↗

NASA NTRS2015

Assessment of New Load Schedules for the Machine Calibration of a Force Balance

New load schedules for the machine calibration of a six-component force balance are currently being developed and evaluated at the NASA Ames Balance Calibration Laboratory. One of the proposed load schedules is discussed in the paper. It has a total of 2082 points that are distributed across 16 load series. Several criteria were applied to define the load schedule. It was decided, for example, to specify the calibration load set in force balance format as this approach greatly simplifies the definition of the lower and upper bounds of the load schedule. In addition, all loads are assumed to be applied in a calibration machine by using the one-factor-at-a-time approach. At first, all single-component loads are applied in six load series. Then, three two-component load series are applied. They consist of the load pairs (N1, N2), (S1, S2), and (RM, AF). Afterwards, four three-component load series are applied. They consist of the combinations (N1, N2, AF), (S1, S2, AF), (N1, N2, RM), and (S1, S2, RM). In the next step, one four-component load series is applied. It is the load combination (N1, N2, S1, S2). Finally, two five-component load series are applied. They are the load combination (N1, N2, S1, S2, AF) and (N1, N2, S1, S2, RM). The maximum difference between loads of two subsequent data points of the load schedule is limited to 33 % of capacity. This constraint helps avoid unwanted load "jumps" in the load schedule that can have a negative impact on the performance of a calibration machine. Only loadings of the single- and two-component load series are loaded to 100 % of capacity. This approach was selected because it keeps the total number of calibration points to a reasonable limit while still allowing for the application of some of the more complex load combinations. Data from two of NASA's force balances is used to illustrate important characteristics of the proposed 2082-point calibration load schedule.

wind tunnel testing↗