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Analysis of SPR measurements from HART II
Aerospace Science and Technology 9 (2005) 409–420 www.elsevier.com/locate/aescte
Analysis of SPR measurements from HART II Oliver Schneider ∗ Institute of Flight Systems, German Aerospace Center (DLR), Germany Received 4 May 2004; received in revised form 21 December 2004; accepted 20 January 2005 Available online 23 May 2005
Abstract The wind tunnel test of HART II (Higher Harmonic Control Aeroacoustic Rotor Test), performed in October 2001 in the Large LowSpeed Facility (LLF) of the German-Dutch Wind-tunnel (DNW), is part of an international cooperative program by the German DLR, French ONERA, DNW, NASA Langley and the US Army Aeroflightdynamics Directorate (AFDD). The main objective of the program is the investigation of rotor wake and its influence on rotor blade–vortex interaction (BVI) noise with and without higher harmonic pitch control (HHC). For blade position and deflection measurements the Stereo Pattern Recognition (SPR) technique was used for the first time. This technique is based on a 3-dimensional reconstruction of visible marker locations by using stereo camera images. An evaluation of these images leads to the spatial position of markers which are attached to each of the four blades and to the bottom of the fuselage and thus to the blade motion parameters in flap, lead-lag and torsion. In this paper the different analysis methods and post-processing of SPR data and the final results for all four rotor blades are presented and the advantages, drawbacks and the potential of this technology are shown. 2005 Elsevier SAS. All rights reserved. Keywords: Stereo pattern recognition; Optical blade tracking; Wind tunnel test
1. Introduction
Table 1 Basic conditions in HART II
Within the framework of the US/German MoU and the US/French MoA the partners of the HART program performed a HHC rotor test called HART II in 2001 by using a 40% Mach scaled BO105 model rotor in order to now focus on the rotor wake and its development within the entire rotor disk [4,5]. This test was conducted within a three week test campaign in October 2001 in the LLF of the DNW. In 1994, the impact of HHC on rotor aerodynamics, dynamics, and noise radiation were deeply investigated within the HART test. At that time, the rotor was equipped with strain gages all along span in order to measure the bending moment distribution in flap, lead-lag and torsion by means of simple beam bending theory. Within the HART II test main emphasis was put on the baseline case of HART plus the shaft-angle-sweep of it, and
Variable
Nominal value
V rpm, µ Mt CT CMx = CMy αs BL MN MV αs -sweep
33 m/s 1041, 109 rad/s 0.15 0.641 4.4 e−3 0.0 5.3 deg θ3 = 0.0 deg θ3 = 0.8 deg, Ψ3 = 300.0 deg θ3 = 0.8 deg, Ψ3 = 180.0 deg −6.9 deg, −3.7 deg, 5.3 deg, 11.5 deg Ψ3 = 0 deg, . . . , 330 deg; Ψ3 = 30.0 deg
* Tel.: +49 531 295-2681; telefax: +49 531 295-2641.
E-mail address: [email protected] (O. Schneider). 1270-9638/$ – see front matter 2005 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2005.01.013
HHC phases
the two HHC cases with settings for minimum vibration and minimum noise radiation. Table 1 provides an overview of the fundamental conditions.
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Nomenclature List of symbols
Ψ
αsting αs ϑel Φ
Notations
Sting support angle measured by sting control Shaft angle Elastic blade torsion Roll angle
2. Setup and testing The SPR measurements required four cameras widely spaced on ground. One pair of cameras focused on the advancing side of the rotor disk, and the other one on the retreating side. With this method, the spatial position of markers attached to each of the four blades and to the bottom of the fuselage is determined optically. The SPR technique is based on a 3-dimensional reconstruction of visible marker locations by using stereo camera images. The accuracy of marker position recognition depends on the resolution and angular set-up of the cameras and on the marker shape and size. For the conditions used for the HART II SPR measurement the theoretical resolution reaches 0.4 mm in x-, yand z-direction. A more detailed description of the method is presented in [1]. In addition, the common support was used for one camera focusing on the 90 deg azimuth position of the blade, and a second tower was holding another camera for a view on the 135 deg position. These two cameras were focused only on the blade tip at the respective azimuth positions in order to independently measure the blade tip’s vertical, horizontal and pitch position. This setup was called BTD (blade tip deflection measurement). At these azimuths, the results of BTD can directly be used as validation of the SPR results. The test setup is schematically given in Fig. 1.
Fig. 1. Test setup for SPR and BTD measurements.
qc el
Azimuth of the rotor blade
Quarter chord line Elastic
The camera system was calibrated by using special calibration points. The markers of 25 mm diameter were suspended from the wind tunnel ceiling and covered a volume of 3.5 m × 3.5 m × 1 m corresponding to the location of the model rotor in all shaft angle positions. The calibration measurements were done by using Theodolites with an accuracy of 1 mm. By using a new improved least square calibration method 10 calibration markers plus 2 body marker locations (to extend the calibration volume over the complete body) were used (instead of 6 calibration markers as used for data in [2]) to calibrate each system of two SPR cameras (adv./ret. side). This formed the basis of the mathematical model to recompute the blade marker positions in space from the two camera images in the aftermath and led to a completely new set of raw data which are used for all calculations described in this paper. For the HART II test, a total of 36 markers (18 at the leading edge and 18 at the trailing edge, diameter 25 mm, called blade marker) were equipped on the lower side of each black painted rotor blade (see Fig. 2). Thus 18 radial stations were covered from r/R = 0.228 to 0.993. For purposes of hub center localization 4 markers were attached underneath the fuselage shell on a rectangular plate. These are called body markers herein. Data were taken at 15 deg azimuth increments totaling to 24 locations azimuthally such that the analysis allows synthesizing the lower harmonics from the time history of the blade motion over the entire length of the blade. SPR measurements were applied to the BL (base line configuration), MN (minimum noise configuration), MV (minimum vibration configuration) case, and to parts of the α-sweep, covering 6 deg and 3 deg climb and 12 deg descent (see Table 2). In total, 144 SPR measurements were made, wherein 24 contain 100 repeats (BL5.3) and the rest 50 repeats at the same location for statistical analysis. One raw data image was taken each third revolution. Since at each location all four blades are measured, this makes 33600 data sets of blade and body marker coordinates for post-processing. They stem from the same amount of camera raw data images. An exemplary image of one SPR camera is given in
Fig. 2. Distribution of SPR markers on the rotor blades.
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Table 2 Configurations of SPR measurements Configuration
Shaft angle αs /deg
cal90
5.05*
cal135
5.05*
cal270
5.05*
BL5.3 BL5.3 BL-3.7 BL11.5 MN5.3 MV5.3 BL-6.9
5.35 5.265 −3.663 11.488 5.315 5.335 −6.896
Comment Non-rotating calibration Ψ = 90 deg Non-rotating calibration Ψ = 135 deg Non-rotating calibration Ψ = 270 deg Base line adv. side, 6 deg descent Base line ret. side, 6 deg descent Base line, 3 deg climb Base line, 12 deg descent Minimum noise, 6 deg descent Minimum vibration, 6 deg descent Base line, 6 deg climb
Fig. 4. Deviation from mean value for body marker #2, measured in base line case at Ψ = 90 deg (100 images).
* α = 5.2 deg noted from DNW. s
Fig. 5. Maximum scatter (100 images) over all azimuths for body marker #2, r/R = 0.23 and for r/R = 0.99 measured in base line case, Ψ = 90 deg.
Fig. 3. SPR image of the rear right camera at Ψ = 90 deg.
Fig. 3. The blade is at a 90 deg azimuth position and the markers at leading and trailing edges as well as the body markers are clearly visible.
3. Preparation of raw data The analysis of SPR results requires some post-processing since the data contain only positions of the blade markers along leading and trailing edge in space, i.e. in the wind tunnel coordinate system. The goals are flap, lead-lag and torsion displacements of the quarter chord line in the shaft coordinate system with origin in the center of the rotor hub. To obtain these results, the position of the hub center must be known. 3.1. Averaging of raw data One data point is composed of mostly 50, some times 100 images. To get smooth data with reduced errors and elim-
inated vibrations it is necessary to determine averages of the coordinates. To average the marker coordinates a mean value for each marker of all repeats (if there were no errors) was computed. As described in [2] the scattering has a range of 2.6 mm in z-direction (positive up), of about 1.1 mm in x-direction (wt-system: positive downstream). In Fig. 4 the deviation from the mean value (wind tunnel coordinate system) for body marker #2 is shown exemplarily for the base line case at Ψ = 90 deg. The maximum deviations found were in y-direction (wt-system: positive right) of about 4.7 mm because of the minor stiffness of the wind tunnel sting in this direction and associated vibrations in a wide frequency range. In general the scattering of the blade markers depends on the distance to the rotor hub and the blade azimuth [3]. With increasing radius the scatter is growing because of the blade elasticity (blade flapping, lead-lag and torsion motion) in addition to the body vibrations and the sting motion (Fig. 5). 3.2. Drift compensation As described in [2] and [3] dynamic marker position displacements due to low frequency motions of the wind tunnel sting, vibrations of the rotor model and of the sting support were present during the measurements. Also a drift in sting
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Fig. 6. Marker drift in z-direction over measurement time for body marker #3 (wind tunnel system, case BL5.3).
yaw led to a lateral drift of the entire model. To correct this drift the drift of the body markers is used. The difference between the mean value of one azimuth to the mean value from all azimuths define the body drift. Based on this drift all blade marker coordinates were modified. On analyzing the raw data calibrated by using only 6 calibration markers it was necessary to separate into mean values of the advancing and retreating side, since the measured body marker coordinates have had a remarkable offset in each direction. That’s why the drift compensation was separated and independently applied to advancing and retreating side [2]. By using the improved calibration method (10 calibration markers plus 2 body marker locations) there is only a very small offset remaining and thus no separation in adv. and ret. side is necessary. In Fig. 6 the z-position of body marker #3 is shown and the drift in positive z-direction is clearly visible. After determination of the body marker drift the blade marker positions can be corrected by this drift. 3.3. Rotation by shaft and roll angle To obtain the parameters of blade motion, the data in DNW coordinate system have to be transformed into the rotor hub coordinate system (Fig. 12). This is done by rotating the coordinates by the rotor shaft angle into a coordinate system parallel to the rotor shaft and transformation (shifting) of all marker coordinates into the rotor hub location. The analysis of the data in the non-rotating system figured out that a model roll angle was present during the measurements, which also has to be considered in the rotation transformation. Previously the raw data were prepared without taking into account a model roll angle. But first investigations of the raw data in the non-rotating system (rotor not running) [2] led to an offset between advancing and retreating side in zdirection which is caused by a model roll angle. The correct model roll and shaft angles were identified by adapting the z-coordinates of the quarter chord lines of all blades available in the non-rotating system (45, 90, 135, 180, 225, 270 and 315 deg) to get a constant offset between them. Assuming similar blade material properties all quarter chord lines
Fig. 7. Quarter chord line z-positions in shaft parallel coordinate system (non-rotating data).
should have the same radial z-deflection zqc (r), which was verified in laboratory tests. In an optimization procedure different αs –Φ-transformations were computed. The calculation of an optimum by using all azimuths leads to the transformation angles αs = 5.1 deg and Φ = −0.145 deg. It can be seen in Fig. 7 that for this case there is a radius depending offset where the blade tips are getting off. In conclusion we have a good consistency of the measured values with a small difference in the optimal shaft and roll angles between the measurements at the 90 deg azimuth and the 135 deg azimuth, which were measured independently with the rotor rotated by hand in between. For calculation of the latest blade motion results the according transformations into the rotor hub coordinate system were done by using the roll angle of −0.145 deg. 3.4. Hub center determination in x–y-plane Three different calculation methods for determining the rotor hub x–y-position were evaluated [2] and the advantages and drawbacks of each method were described to find out the best qualified results. The hub center was intended to be computed by the 4 body markers which were taped on a plate underneath the fuselage shell (Fig. 3). With the known distance in z-direction between the plate and the rotor hub center and the distance between the body markers the rotor hub center position in the wind tunnel coordinate system can be computed. The recognition accuracy of the body marker theoretically is about 0.4 mm, thus the error magnification for the x- and y-position is about 7 mm. In addition there is the uncertainty of the body markers due to that they were outside of the measurement volume during calibration. Result would be a wide range of uncertainty. That’s why this method could not be used. A second method to get the position of the rotor hub center is the calculation of a point in space where extrapolated
O. Schneider / Aerospace Science and Technology 9 (2005) 409–420
Fig. 8. Exemplary best fit circles for r/R = 0.4, 0.77, 1.0.
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deviation is about 0.8 mm in x-direction and only 0.2 mm in y-direction. For further calculations only the results of the inner radii blade markers are used. They are not subject to significant flapping deflections and thus on more perfect circles than the outer markers. In conclusion the circular regression results are within the measurement accuracy and thus can be applied in the transformation procedure. In relation to it latest investigations of the blade markers have shown that there is a discontinuity between the data of the advancing and the retreating side. The data measured in the rotating system (rotor is running) led to differences of the marker distances in radial direction. The averaged distance between the innermost and the outermost marker at the advancing side is by about 4.5 mm smaller than at the retreating side, which means a different blade length independent of the azimuth position. The same investigation applied to the data in the nonrotating system led to a difference of about 3.6 mm. This blade length discontinuity influences the center point calculation. The errors increase with growing radius. This problem cannot be explained right now. One possible error source is the Theodolite measurement of the calibration markers. In the worst case the over-all error could have been up to 4 mm. Together with a possible error of the image distortion of about 1.2 mm this error size is imaginable. The inquiry of a possible influence of the different blade flap has figured out, that this influence is negligible since the blade length problem is visible in the non-rotating data as well and would also have different effects in the different flight configurations. 3.5. Hub center determination in z-direction
Fig. 9. Rotor hub center position by circular regression (MV5.3, blades #1 to #4).
blade quarter chord lines of each azimuth have an intersection. The accuracy of the results by using this method is very different. The largest differences found were of about 20 mm in x-direction and of about 22 mm in y-direction. Thus there is a wide range of intersection points and using this method is not accurate enough, too. The best method for center point determination was identified to be the circular regression [2] by computing best fit circles of the positions of one single blade marker over all azimuths. An example is shown in Fig. 8. It is assumed that each blade marker ideally travels along a circle around the hub center, which assumes no blade flapping motion. Fig. 9 shows a comparison of the hub center coordinates computed by circular regression for all four blades of the minimum vibration case. In all configurations a small drift in negative y-direction is identifiable with respect to increased blade marker radius. With regard to scattering there is a maximum of about 1.0 mm in x-direction and 1.1 mm in ydirection in all configurations. The maximum blade-to-blade
After the hub center coordinates in x- and y-direction are found, the position in z-direction of the rotor hub center is in demand. At first the coordinate system must be shifted into the x–y-hub center found so far. This means a transformation of all blade and body markers into a coordinate system with the origin in the rotor hub x–y-center point, while the origin in z is yet anywhere on the shaft axis. To identify the rotor hub z-coordinate, several different approaches were tried. Finally a polynomial of fourth order with an additionally constraint was found to be the most accurate approach. It is assumed that the gradient dz/dr at the blade attachment is equal to the pre-cone angle of 2.5 deg as a boundary condition (example for minimum noise case in Fig. 10). The least error squares method is used to obtain the remaining coefficients of the polynomial function. More information about this method can be found in [2]. Mainly caused by errors in the Theodolite calibration an offset in z0 between advancing and retreating side is present. Due to the improved raw data and the transformation with respect to the model roll angle the offset could be reduced to about 2.0 mm (Fig. 11). This offset range can be found in all other configurations as well. Since all blades exhibit this offset between advancing and retreating side this is a systematic
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4. Blade motion results 4.1. Blade lead-lag motion
Fig. 10. Best fit polynomials z(r/R) for different azimuths to get z0 (MN5.3).
Fig. 11. Rotor hub center z-coordinate (MN5.3, all blades).
The elastic blade lead-lag is given by the distance between the radial position of the quarter chord line and a straight line defined by the current azimuth position of the blade (lag positive). For the current azimuth position a possible model yaw angle has to be considered. In the investigations a yaw angle was found due to an unexplained behavior of the elastic blade lead-lag displacement in the time history of the cases BL5.3 and BL11.5 as found in [2]. The wind tunnel sting has two hinges with vertical axis. Thus it is possible to give the model a yaw angle (called beta). The angle of each hinge can be measured and the sum of both leads to the model yaw angle beta. For the HART II tests this yaw angle should have been zero, but caused by unknown reasons it has had a range between 0.24 deg and −0.02 deg (positive in rotation direction). This results in an apparent lag deflection of about 8 mm at the blade tip. To correct the model yaw angle in calculations the associated beta angle has to be added to the blade azimuth. There are measured data of the beta angle for each azimuth available. In Fig. 13 an example of the model yaw angle beta for the reference blade of the case BL5.3 is shown. It is clearly visible that there are higher yaw angles in between 15 deg and 75 deg, which is the range where the skip in the lag motion was found. When the yaw angle correction is applied to the lead-lag calculation the skips in the time history can be eliminated. The comparison of the lag deflection for the case BL5.3 at the blade tip with and without consideration of a model yaw angle is shown in Fig. 14. The skip between 75 deg and 90 deg is eliminated. The comparison of the concerned azimuth positions with the data for the model yaw angle leads to the result that even at these azimuth positions a higher yaw angle was present. Thus all calculations were made by using the yaw angle correction which leads to non-constant azimuth steps (15 deg ± 0.2 deg). The blade-to-blade comparison of the tip deflection time history leads to a maximum difference of
Fig. 12. Transformation procedures from wind tunnel into rotor hub coordinate system.
error with respect to the Theodolite calibration in combination with the two camera systems. Further it can be noticed that the blade-to-blade differences with an average of about 0.7 mm are very small (e.g. in Fig. 11). With the z-position of the rotor hub the coordinate system can be shifted into the final rotor hub coordinate system. Because of the offset the shifting is done separated with respect to advancing and retreating side. In Fig. 12 the complete transformation procedure from wind tunnel coordinate system into the rotor hub system is shown.
Fig. 13. Model yaw angle β (BL5.3, blade #1).
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Fig. 14. Blade tip lag motion with and w/o β correction (BL5.3, blade #1).
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Fig. 17. Radial distribution of blade lag motion, measured and polynomial (BL5.3, blade #1).
Fig. 15. Elastic blade tip lead-lag motion (MN5.3, all blades).
Fig. 18. Extrapolated quarter chord lines (BL5.3, blade #1).
Fig. 16. Radial distribution of blade lag motion at Ψ = 229 deg (MN5.3, all blades).
about 9 mm in the BL11.5 case and to a minimum difference of about 0.9 mm in the MN5.3 configuration (Fig. 15). The radial distributions of the elastic blade lag position are shown in Fig. 16 exemplarily for the case MN5.3. The results were chosen at an azimuth of Ψ = 229 deg. There is nearly a linear dependence of the lag value with respect to the radius in each configuration. Conspicuous is the curve at inner radii. The blades of a hingeless rotor as used in the HART II test should have a lead-lag value of zero and a gradient of zero at the position of the blade attachment at r/R = 0.1 (200 mm). However an extrapolation of the lead-
lag data in the rotating system to radius r/R = 0.1 with an additional constraint (gradient dyel /dr = 0) led to an offset of about 10 mm. Fig. 17 shows the radial distribution of different azimuths and the extrapolated quarter chord lines from the data in the rotating system exemplarily for blade #1 of the base line case at αs = 5.3 deg. In principle this offset indicates a distance of the quarter chord line to the rotor hub center. For a better understanding Fig. 18 shows the quarter chord lines extrapolated to the rotor hub center. Since this problem can be found in all configurations and all azimuths it is a systematic error. Perhaps due to the centrifugal forces in combination with a resulting play in the blade mounts a pre-lag angle is caused, which could explain a small part of the offset. But such an additional lead-lag angle would increase the offset. With regard to the non-rotating data a lead-lag deflection near zero is expected because there is no build-in pre-lag angle and no aerodynamic forces which influence the blade. Only a very small part of the gravity has an influence on
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the lag deflection in this way that due to the shaft angle of the model the blades of the advancing side can deflect in counter-rotating direction and the blades of the retreating side can deflect in rotating direction. Thus we could have a small blade lag at the advancing side and a small lead of the blade at the retreating side. Latest investigations have shown that regarding the non-rotating data no general offset is identifiable. In conclusion the lead-lag results from the non-rotating system show the expected values, but there is no comprehensive explanation for the offset of the extrapolated quarter chord lines to the rotor hub center in the lead-lag results from the rotating system.
4.3. Blade torsion motion As described in [2] the pure elastic pitch deformation (ϑel positive nose up) can be calculated by the distance of the z-coordinate of the front and rear blade marker, the associated pitch control angle, the pre-twist angle and the pitch offset in z-direction due to the different distance of the front and rear blade markers to the quarter chord line. Fig. 22 shows the time history of the elastic torsion of all four blades of the base line case at 5.3 deg. The blade-toblade differences have a range of about 0.3 deg to 1.1 deg.
4.2. Blade flap motion The elastic blade flap deflection zel (positive up) is given by the distance between the quarter chord line and a straight line defined by the pre-cone angle. Therefore approximately the distance of the quarter chord line z-position to the precone line at defined radial positions is used. Due to the correction of the raw data by the model roll angle and the improved calibration the skip between advancing and retreating side at Ψ = 180 deg is eliminated. Because of the direction of the roll angle the correction leads to lower elastic blade flap values at the advancing side and higher values at the retreating side. Fig. 19 shows the elastic blade tip deflection in z-direction in the rotor hub coordinate system for the reference blade of the case BL5.3 compared with the same results by using no roll angle correction. It clearly can be seen that the roll angle correction has a substantial influence to the elastic blade deflection. The maximum blade-to-blade difference is about 20 mm (see Fig. 20) mainly in the vicinity of Ψ = 180 deg. The maximum values can be found for the reference blade #1 followed by blade #4 and #2. In all configurations blade #3 has the smallest values. Reason could be an incorrect blade tracking at the beginning of the wind tunnel tests or different blade elasto-mechanical properties. The same tendency is visible in the radial distributions of all four blades which are shown in Fig. 21 for MN5.3 at an azimuth of Ψ = 90 deg.
Fig. 19. Elastic blade tip flap motion with and w/o Φ correction (BL5.3, blade #1).
Fig. 20. Elastic blade tip flap motion (MN5.3, all blades).
Fig. 21. Radial distribution of elastic blade flap (MN5.3, all blades, Ψ = 90 deg).
Fig. 22. Time history of the elastic blade torsion (BL5.3, all blades).
O. Schneider / Aerospace Science and Technology 9 (2005) 409–420
Fig. 23. Radial distribution of elastic torsion (BL5.3, all blades, Ψ = 139 deg).
The maximum blade-to-blade difference of up to 1.4 mm is found in the minimum vibration case at Ψ = 94 deg. Reason for these relatively large differences could be the used pitch control angles, which come not directly from the SPR measurements but from other acoustic measurements before. Only two blades were equipped with a pitch angle sensor, whose data were incorrect during the SPR measurements. A different setting of the root pitch angles of all four blades during blade tracking or a different loose in the blade pitch links can induce such blade-to-blade differences. In general blade #1 has the uppermost torsion values, the values of blade #3 are the smallest. Fig. 23 shows the radial distributions of the elastic blade pitch at an azimuth position of Ψ = 139 deg for the BL5.3 configuration. The maximum scatter found for a neighboring blade marker pair is about 0.8 deg. An assumed accuracy of marker position recognition of 0.4 mm and the distance between front and rear marker centers of 89 mm leads to a theoretical error of: 2 · 0.4 mm ≈ 0.52◦ . error = arctan 89 mm Thus the computed torsion values have a maximum scatter which is out of the range of the assumed measurement error. Furthermore at some azimuth positions the calculated blade pitch distribution has computed torsion values which are definitely outside of the expected curve (example in Fig. 24 grey range). Investigations have shown that reflections on the blade near the leading edge at azimuths near Ψ = 90 deg and Ψ = 270 deg have falsified the marker position recognition. This problem is found in all measurement configurations. The reflections are at the leading edge and they come from the stroboscopic flashes. Due to these reflections the usual black background is more brightly and the contrast to the white markers is small. The recognition of a correct marker bound is difficult and the recognized marker centers have incorrect coordinates, leading to errors in the blade torsion. A possibility to get smoother results is the computation of a regression function. To reduce measurement noise and smooth out irregularities, polynomial functions of fourth order were carefully fitted through the positions of the leading
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Fig. 24. Radial distribution of elastic torsion at Ψ = 90 deg (all configurations, grey: range of reflections).
Fig. 25. Elastic blade torsion, measurements and mode shape regression with standard deviation (MN5.3).
and trailing edge markers and differentiated to get the local pitch. The results by using this method were unacceptable at inner radii [2]. That is why a second approach was applied. The basis for the regression function is the first mode shape of blade torsion ϑ1 (r ∗ ) in the rotating system. The second torsion mode shape has not to be considered since the according natural frequency is at about 10/rev. By using the least error squares method the coefficients ϑ0 and ϑ1 were computed. ϑel (r) = ϑ0 + ϑ1 · Φ1 (r ∗ ), r − rE r∗ = , R − rE J Φ1 (r ∗ ) = cj · r ∗j . j =0
rE is the radius at the blade main bolt and Φ1 the first mode shape of torsion (coefficients by FEM). An example for different azimuths is shown in Fig. 25 for the reference blade of the minimum noise configuration. By using the mode shape representation the results are smooth curves with a value unequal zero at the blade attachment r/R = 0.1. In the example figure the radial distribution at an azimuth of Ψ = 244 deg has an elastic torsion value of 0.55 deg at this position. In general the elastic torsion values at inner radii lead to the
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Fig. 26. Elastic blade torsion mode shape regression (BL5.3).
conclusion that there is a systematic error, because most of the radial distributions have values in the vicinity of about ϑel = 0.5 deg at the blade attachment (compare Fig. 26). This root offset can have several reasons. The blade tracking was done by setting different root pitch offsets. A steady offset could also be caused by the used pitch data which come from the acoustic part of the test. During the SPR measurements there was a sensor defect. A possibility for a dynamic offset is the increasing loose of the pitch bearings in the course of the tests. The comparison of the time history of the blade torsion yields no major difference between the measured elastic torsion angle and the mode shape based regression function [3]. The results of the elastic torsion angle from data in the non-rotating system have shown that the scatter at each three azimuth positions is about ±0.5 deg. The maximum deviation of about 1.0 deg could be found at Ψ = 90 deg. In conclusion the results obtained for blade torsion depend on several conditions. There is the theoretical error by marker position recognition of about 0.5 deg, possible offsets due to the blade tracking and the accuracy of all 4 blades root pitch angle measurements. Further the calculation of the torsion angle by differentiation leads to increased errors. Thus to obtain better results for blade torsion a simultaneous measurement of the blade root pitch angle and SPR is necessary.
Fig. 27. Blade tip flap motion depending on azimuth for α-sweep (r/R = 99%, blade #1).
Fig. 28. Blade tip lead-lag motion depending on azimuth for α-sweep (r/R = 99%, blade #1).
4.4. Alpha sweep In Figs. 27, 28 and 29 the elastic flap, lead-lag and torsion motion of the reference rotor blade (blade #1) depending on azimuth are shown. There is a comparison of the α-sweep configurations at the blade position at r/R = 99%. In flapping and torsion a 2/rev motion is present in descent. In the lead-lag motion there are nearly constant amplitudes of about 10 mm in 1/rev at the blade tip. By using the new raw data and the model yaw angle correction the skips in the cases BL5.3 and BL11.5 are eliminated. The maximum lag value increases from descent to climb as expected by the increased power consumption. In the time history of the elastic torsion the 2/rev oscillation is stronger in descent than in climb condition.
Fig. 29. Elastic torsion motion depending on azimuth for α-sweep (r/R = 99%, blade #1).
4.5. HHC sweep Figs. 30, 31 and 32 show the comparison of the elastic flap, lead-lag and torsion motion of the rotor blade depending on azimuth for the configurations with higher harmonic control and the base line case at the blade position r/R = 99%. When 3/rev HHC is applied (cases MN and MV), a 3/rev flapping dominates the figure as expected (Fig. 30). The lo-
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minimum noise case and up to 2.5 deg in the minimum vibration case (Fig. 32).
5. Conclusions
Fig. 30. Blade tip flap motion depending on azimuth for HHC sweep (r/R = 99%).
Fig. 31. Blade tip lead-lag motion depending on azimuth for HHC sweep (r/R = 99%).
• The new calibration method leads to significantly improved accuracy of the raw data. The analysis of the calibration data has shown that the calibration accuracy should be improved in further wind tunnel tests by using more calibration markers than in the HART II test. • It was found that there still are problems in the camera calibration, because the blade length differs between advancing and retreating side which is unexplained up to now. • No solution could be found for the offset of the blade lead-lag at the blade root attachment. The extrapolation of the lead-lag bending to the rotor hub center with an additional boundary condition at the attachment leads to an offset of about 10 mm for all azimuths positions and in all configurations. Since this problem only is present in the results of the rotating system, a play in the blade mounts because of centrifugal forces could be one reason. • For blade torsion a simultaneous measurement of the blade root pitch angle and SPR is necessary because of the dependence of the results on the accuracy of blade root pitch measurement and the blade tracking. Recommendation: SPR measurements from the rotor hub center in the rotating system could eliminate lots of problems.
Acknowledgements
Fig. 32. Elastic torsion motion depending on azimuth for HHC sweep (r/R = 99%).
cal amplitudes are up to 12 mm off the BL position at the blade tip in the minimum noise case. The results of the blade lag motion show nearly identical values with 1/rev amplitudes of about 10 mm independent of the higher harmonic control (Fig. 31). With 3/rev HHC a strong 3/rev torsion is the response which was expected due to the natural frequency in torsion at 3.6/rev of this rotor. The local amplitudes in torsion are up to 1.5 deg off the BL position in the
An international test as complex as HART II requires a lot of engagement of all participants, both in the fore- and in the background. It would fill pages to name everybody. Instead, the teams are specifically addressed. These are: the prediction team, the test team and the management team, all of them consisting of US/French/German members working years ahead in real partnership preparing the rotor hardware, the measurement techniques, the test matrix and the funding. Specifically the funding of the test from US and French side, the development of 3C-PIV and preparation of the rotor and conduction of the test on DLR side shall be mentioned, and the strong support of DNW during the test. Without the enthusiasm of all of them this test would never have come true – thanks to all of them!
References [1] K. Pengel, R. Müller, B.G. van der Wall, Stereo pattern recognition – the technique for reliable rotor blade deformation and twist mea-
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surements, in: AHS International Meeting on Advanced Rotorcraft Technology and Life Saving Activities, Utsunomiya, Tochigi, Japan, 2002. [2] O. Schneider, B.G. van der Wall, K. Pengel, HART-II blade motion measured by stereo pattern recognition (SPR), in: 59th Annual Forum of the American Helicopter Society, Phoenix, USA, 2003. [3] O. Schneider, B.G. van der Wall, Final analysis of HART II blade deflection measurement, in: 29th European Rotorcraft Forum, Friedrichshafen, Germany, 2003.
[4] B.G. van der Wall, B. Junker, C.L. Burley, T.F. Brooks, Y.H. Yu, C. Tung, H. Richard, M. Raffel, W. Wagner, K. Pengel, E. Mercker, P. Beaumier, Y. Delrieux, The HART II test in the DNW – a major step towards rotor wake understanding, in: 28th European Rotorcraft Forum, Bristol, UK, 2002. [5] Y.H. Yu, The HART-II test: rotor wakes and aeroacoustics with higher-harmonic pitch control (HHC) inputs, in: The Joint German/French/Dutch/US Project, 58th Annual Forum of the American Helicopter Society, Montreal, Canada, 2002.
Analysis of SPR measurements from HART II Oliver Schneider ∗ Institute of Flight Systems, German Aerospace Center (DLR), Germany Received 4 May 2004; received in revised form 21 December 2004; accepted 20 January 2005 Available online 23 May 2005
Abstract The wind tunnel test of HART II (Higher Harmonic Control Aeroacoustic Rotor Test), performed in October 2001 in the Large LowSpeed Facility (LLF) of the German-Dutch Wind-tunnel (DNW), is part of an international cooperative program by the German DLR, French ONERA, DNW, NASA Langley and the US Army Aeroflightdynamics Directorate (AFDD). The main objective of the program is the investigation of rotor wake and its influence on rotor blade–vortex interaction (BVI) noise with and without higher harmonic pitch control (HHC). For blade position and deflection measurements the Stereo Pattern Recognition (SPR) technique was used for the first time. This technique is based on a 3-dimensional reconstruction of visible marker locations by using stereo camera images. An evaluation of these images leads to the spatial position of markers which are attached to each of the four blades and to the bottom of the fuselage and thus to the blade motion parameters in flap, lead-lag and torsion. In this paper the different analysis methods and post-processing of SPR data and the final results for all four rotor blades are presented and the advantages, drawbacks and the potential of this technology are shown. 2005 Elsevier SAS. All rights reserved. Keywords: Stereo pattern recognition; Optical blade tracking; Wind tunnel test
1. Introduction
Table 1 Basic conditions in HART II
Within the framework of the US/German MoU and the US/French MoA the partners of the HART program performed a HHC rotor test called HART II in 2001 by using a 40% Mach scaled BO105 model rotor in order to now focus on the rotor wake and its development within the entire rotor disk [4,5]. This test was conducted within a three week test campaign in October 2001 in the LLF of the DNW. In 1994, the impact of HHC on rotor aerodynamics, dynamics, and noise radiation were deeply investigated within the HART test. At that time, the rotor was equipped with strain gages all along span in order to measure the bending moment distribution in flap, lead-lag and torsion by means of simple beam bending theory. Within the HART II test main emphasis was put on the baseline case of HART plus the shaft-angle-sweep of it, and
Variable
Nominal value
V rpm, µ Mt CT CMx = CMy αs BL MN MV αs -sweep
33 m/s 1041, 109 rad/s 0.15 0.641 4.4 e−3 0.0 5.3 deg θ3 = 0.0 deg θ3 = 0.8 deg, Ψ3 = 300.0 deg θ3 = 0.8 deg, Ψ3 = 180.0 deg −6.9 deg, −3.7 deg, 5.3 deg, 11.5 deg Ψ3 = 0 deg, . . . , 330 deg; Ψ3 = 30.0 deg
* Tel.: +49 531 295-2681; telefax: +49 531 295-2641.
E-mail address: [email protected] (O. Schneider). 1270-9638/$ – see front matter 2005 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2005.01.013
HHC phases
the two HHC cases with settings for minimum vibration and minimum noise radiation. Table 1 provides an overview of the fundamental conditions.
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Nomenclature List of symbols
Ψ
αsting αs ϑel Φ
Notations
Sting support angle measured by sting control Shaft angle Elastic blade torsion Roll angle
2. Setup and testing The SPR measurements required four cameras widely spaced on ground. One pair of cameras focused on the advancing side of the rotor disk, and the other one on the retreating side. With this method, the spatial position of markers attached to each of the four blades and to the bottom of the fuselage is determined optically. The SPR technique is based on a 3-dimensional reconstruction of visible marker locations by using stereo camera images. The accuracy of marker position recognition depends on the resolution and angular set-up of the cameras and on the marker shape and size. For the conditions used for the HART II SPR measurement the theoretical resolution reaches 0.4 mm in x-, yand z-direction. A more detailed description of the method is presented in [1]. In addition, the common support was used for one camera focusing on the 90 deg azimuth position of the blade, and a second tower was holding another camera for a view on the 135 deg position. These two cameras were focused only on the blade tip at the respective azimuth positions in order to independently measure the blade tip’s vertical, horizontal and pitch position. This setup was called BTD (blade tip deflection measurement). At these azimuths, the results of BTD can directly be used as validation of the SPR results. The test setup is schematically given in Fig. 1.
Fig. 1. Test setup for SPR and BTD measurements.
qc el
Azimuth of the rotor blade
Quarter chord line Elastic
The camera system was calibrated by using special calibration points. The markers of 25 mm diameter were suspended from the wind tunnel ceiling and covered a volume of 3.5 m × 3.5 m × 1 m corresponding to the location of the model rotor in all shaft angle positions. The calibration measurements were done by using Theodolites with an accuracy of 1 mm. By using a new improved least square calibration method 10 calibration markers plus 2 body marker locations (to extend the calibration volume over the complete body) were used (instead of 6 calibration markers as used for data in [2]) to calibrate each system of two SPR cameras (adv./ret. side). This formed the basis of the mathematical model to recompute the blade marker positions in space from the two camera images in the aftermath and led to a completely new set of raw data which are used for all calculations described in this paper. For the HART II test, a total of 36 markers (18 at the leading edge and 18 at the trailing edge, diameter 25 mm, called blade marker) were equipped on the lower side of each black painted rotor blade (see Fig. 2). Thus 18 radial stations were covered from r/R = 0.228 to 0.993. For purposes of hub center localization 4 markers were attached underneath the fuselage shell on a rectangular plate. These are called body markers herein. Data were taken at 15 deg azimuth increments totaling to 24 locations azimuthally such that the analysis allows synthesizing the lower harmonics from the time history of the blade motion over the entire length of the blade. SPR measurements were applied to the BL (base line configuration), MN (minimum noise configuration), MV (minimum vibration configuration) case, and to parts of the α-sweep, covering 6 deg and 3 deg climb and 12 deg descent (see Table 2). In total, 144 SPR measurements were made, wherein 24 contain 100 repeats (BL5.3) and the rest 50 repeats at the same location for statistical analysis. One raw data image was taken each third revolution. Since at each location all four blades are measured, this makes 33600 data sets of blade and body marker coordinates for post-processing. They stem from the same amount of camera raw data images. An exemplary image of one SPR camera is given in
Fig. 2. Distribution of SPR markers on the rotor blades.
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Table 2 Configurations of SPR measurements Configuration
Shaft angle αs /deg
cal90
5.05*
cal135
5.05*
cal270
5.05*
BL5.3 BL5.3 BL-3.7 BL11.5 MN5.3 MV5.3 BL-6.9
5.35 5.265 −3.663 11.488 5.315 5.335 −6.896
Comment Non-rotating calibration Ψ = 90 deg Non-rotating calibration Ψ = 135 deg Non-rotating calibration Ψ = 270 deg Base line adv. side, 6 deg descent Base line ret. side, 6 deg descent Base line, 3 deg climb Base line, 12 deg descent Minimum noise, 6 deg descent Minimum vibration, 6 deg descent Base line, 6 deg climb
Fig. 4. Deviation from mean value for body marker #2, measured in base line case at Ψ = 90 deg (100 images).
* α = 5.2 deg noted from DNW. s
Fig. 5. Maximum scatter (100 images) over all azimuths for body marker #2, r/R = 0.23 and for r/R = 0.99 measured in base line case, Ψ = 90 deg.
Fig. 3. SPR image of the rear right camera at Ψ = 90 deg.
Fig. 3. The blade is at a 90 deg azimuth position and the markers at leading and trailing edges as well as the body markers are clearly visible.
3. Preparation of raw data The analysis of SPR results requires some post-processing since the data contain only positions of the blade markers along leading and trailing edge in space, i.e. in the wind tunnel coordinate system. The goals are flap, lead-lag and torsion displacements of the quarter chord line in the shaft coordinate system with origin in the center of the rotor hub. To obtain these results, the position of the hub center must be known. 3.1. Averaging of raw data One data point is composed of mostly 50, some times 100 images. To get smooth data with reduced errors and elim-
inated vibrations it is necessary to determine averages of the coordinates. To average the marker coordinates a mean value for each marker of all repeats (if there were no errors) was computed. As described in [2] the scattering has a range of 2.6 mm in z-direction (positive up), of about 1.1 mm in x-direction (wt-system: positive downstream). In Fig. 4 the deviation from the mean value (wind tunnel coordinate system) for body marker #2 is shown exemplarily for the base line case at Ψ = 90 deg. The maximum deviations found were in y-direction (wt-system: positive right) of about 4.7 mm because of the minor stiffness of the wind tunnel sting in this direction and associated vibrations in a wide frequency range. In general the scattering of the blade markers depends on the distance to the rotor hub and the blade azimuth [3]. With increasing radius the scatter is growing because of the blade elasticity (blade flapping, lead-lag and torsion motion) in addition to the body vibrations and the sting motion (Fig. 5). 3.2. Drift compensation As described in [2] and [3] dynamic marker position displacements due to low frequency motions of the wind tunnel sting, vibrations of the rotor model and of the sting support were present during the measurements. Also a drift in sting
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Fig. 6. Marker drift in z-direction over measurement time for body marker #3 (wind tunnel system, case BL5.3).
yaw led to a lateral drift of the entire model. To correct this drift the drift of the body markers is used. The difference between the mean value of one azimuth to the mean value from all azimuths define the body drift. Based on this drift all blade marker coordinates were modified. On analyzing the raw data calibrated by using only 6 calibration markers it was necessary to separate into mean values of the advancing and retreating side, since the measured body marker coordinates have had a remarkable offset in each direction. That’s why the drift compensation was separated and independently applied to advancing and retreating side [2]. By using the improved calibration method (10 calibration markers plus 2 body marker locations) there is only a very small offset remaining and thus no separation in adv. and ret. side is necessary. In Fig. 6 the z-position of body marker #3 is shown and the drift in positive z-direction is clearly visible. After determination of the body marker drift the blade marker positions can be corrected by this drift. 3.3. Rotation by shaft and roll angle To obtain the parameters of blade motion, the data in DNW coordinate system have to be transformed into the rotor hub coordinate system (Fig. 12). This is done by rotating the coordinates by the rotor shaft angle into a coordinate system parallel to the rotor shaft and transformation (shifting) of all marker coordinates into the rotor hub location. The analysis of the data in the non-rotating system figured out that a model roll angle was present during the measurements, which also has to be considered in the rotation transformation. Previously the raw data were prepared without taking into account a model roll angle. But first investigations of the raw data in the non-rotating system (rotor not running) [2] led to an offset between advancing and retreating side in zdirection which is caused by a model roll angle. The correct model roll and shaft angles were identified by adapting the z-coordinates of the quarter chord lines of all blades available in the non-rotating system (45, 90, 135, 180, 225, 270 and 315 deg) to get a constant offset between them. Assuming similar blade material properties all quarter chord lines
Fig. 7. Quarter chord line z-positions in shaft parallel coordinate system (non-rotating data).
should have the same radial z-deflection zqc (r), which was verified in laboratory tests. In an optimization procedure different αs –Φ-transformations were computed. The calculation of an optimum by using all azimuths leads to the transformation angles αs = 5.1 deg and Φ = −0.145 deg. It can be seen in Fig. 7 that for this case there is a radius depending offset where the blade tips are getting off. In conclusion we have a good consistency of the measured values with a small difference in the optimal shaft and roll angles between the measurements at the 90 deg azimuth and the 135 deg azimuth, which were measured independently with the rotor rotated by hand in between. For calculation of the latest blade motion results the according transformations into the rotor hub coordinate system were done by using the roll angle of −0.145 deg. 3.4. Hub center determination in x–y-plane Three different calculation methods for determining the rotor hub x–y-position were evaluated [2] and the advantages and drawbacks of each method were described to find out the best qualified results. The hub center was intended to be computed by the 4 body markers which were taped on a plate underneath the fuselage shell (Fig. 3). With the known distance in z-direction between the plate and the rotor hub center and the distance between the body markers the rotor hub center position in the wind tunnel coordinate system can be computed. The recognition accuracy of the body marker theoretically is about 0.4 mm, thus the error magnification for the x- and y-position is about 7 mm. In addition there is the uncertainty of the body markers due to that they were outside of the measurement volume during calibration. Result would be a wide range of uncertainty. That’s why this method could not be used. A second method to get the position of the rotor hub center is the calculation of a point in space where extrapolated
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Fig. 8. Exemplary best fit circles for r/R = 0.4, 0.77, 1.0.
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deviation is about 0.8 mm in x-direction and only 0.2 mm in y-direction. For further calculations only the results of the inner radii blade markers are used. They are not subject to significant flapping deflections and thus on more perfect circles than the outer markers. In conclusion the circular regression results are within the measurement accuracy and thus can be applied in the transformation procedure. In relation to it latest investigations of the blade markers have shown that there is a discontinuity between the data of the advancing and the retreating side. The data measured in the rotating system (rotor is running) led to differences of the marker distances in radial direction. The averaged distance between the innermost and the outermost marker at the advancing side is by about 4.5 mm smaller than at the retreating side, which means a different blade length independent of the azimuth position. The same investigation applied to the data in the nonrotating system led to a difference of about 3.6 mm. This blade length discontinuity influences the center point calculation. The errors increase with growing radius. This problem cannot be explained right now. One possible error source is the Theodolite measurement of the calibration markers. In the worst case the over-all error could have been up to 4 mm. Together with a possible error of the image distortion of about 1.2 mm this error size is imaginable. The inquiry of a possible influence of the different blade flap has figured out, that this influence is negligible since the blade length problem is visible in the non-rotating data as well and would also have different effects in the different flight configurations. 3.5. Hub center determination in z-direction
Fig. 9. Rotor hub center position by circular regression (MV5.3, blades #1 to #4).
blade quarter chord lines of each azimuth have an intersection. The accuracy of the results by using this method is very different. The largest differences found were of about 20 mm in x-direction and of about 22 mm in y-direction. Thus there is a wide range of intersection points and using this method is not accurate enough, too. The best method for center point determination was identified to be the circular regression [2] by computing best fit circles of the positions of one single blade marker over all azimuths. An example is shown in Fig. 8. It is assumed that each blade marker ideally travels along a circle around the hub center, which assumes no blade flapping motion. Fig. 9 shows a comparison of the hub center coordinates computed by circular regression for all four blades of the minimum vibration case. In all configurations a small drift in negative y-direction is identifiable with respect to increased blade marker radius. With regard to scattering there is a maximum of about 1.0 mm in x-direction and 1.1 mm in ydirection in all configurations. The maximum blade-to-blade
After the hub center coordinates in x- and y-direction are found, the position in z-direction of the rotor hub center is in demand. At first the coordinate system must be shifted into the x–y-hub center found so far. This means a transformation of all blade and body markers into a coordinate system with the origin in the rotor hub x–y-center point, while the origin in z is yet anywhere on the shaft axis. To identify the rotor hub z-coordinate, several different approaches were tried. Finally a polynomial of fourth order with an additionally constraint was found to be the most accurate approach. It is assumed that the gradient dz/dr at the blade attachment is equal to the pre-cone angle of 2.5 deg as a boundary condition (example for minimum noise case in Fig. 10). The least error squares method is used to obtain the remaining coefficients of the polynomial function. More information about this method can be found in [2]. Mainly caused by errors in the Theodolite calibration an offset in z0 between advancing and retreating side is present. Due to the improved raw data and the transformation with respect to the model roll angle the offset could be reduced to about 2.0 mm (Fig. 11). This offset range can be found in all other configurations as well. Since all blades exhibit this offset between advancing and retreating side this is a systematic
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4. Blade motion results 4.1. Blade lead-lag motion
Fig. 10. Best fit polynomials z(r/R) for different azimuths to get z0 (MN5.3).
Fig. 11. Rotor hub center z-coordinate (MN5.3, all blades).
The elastic blade lead-lag is given by the distance between the radial position of the quarter chord line and a straight line defined by the current azimuth position of the blade (lag positive). For the current azimuth position a possible model yaw angle has to be considered. In the investigations a yaw angle was found due to an unexplained behavior of the elastic blade lead-lag displacement in the time history of the cases BL5.3 and BL11.5 as found in [2]. The wind tunnel sting has two hinges with vertical axis. Thus it is possible to give the model a yaw angle (called beta). The angle of each hinge can be measured and the sum of both leads to the model yaw angle beta. For the HART II tests this yaw angle should have been zero, but caused by unknown reasons it has had a range between 0.24 deg and −0.02 deg (positive in rotation direction). This results in an apparent lag deflection of about 8 mm at the blade tip. To correct the model yaw angle in calculations the associated beta angle has to be added to the blade azimuth. There are measured data of the beta angle for each azimuth available. In Fig. 13 an example of the model yaw angle beta for the reference blade of the case BL5.3 is shown. It is clearly visible that there are higher yaw angles in between 15 deg and 75 deg, which is the range where the skip in the lag motion was found. When the yaw angle correction is applied to the lead-lag calculation the skips in the time history can be eliminated. The comparison of the lag deflection for the case BL5.3 at the blade tip with and without consideration of a model yaw angle is shown in Fig. 14. The skip between 75 deg and 90 deg is eliminated. The comparison of the concerned azimuth positions with the data for the model yaw angle leads to the result that even at these azimuth positions a higher yaw angle was present. Thus all calculations were made by using the yaw angle correction which leads to non-constant azimuth steps (15 deg ± 0.2 deg). The blade-to-blade comparison of the tip deflection time history leads to a maximum difference of
Fig. 12. Transformation procedures from wind tunnel into rotor hub coordinate system.
error with respect to the Theodolite calibration in combination with the two camera systems. Further it can be noticed that the blade-to-blade differences with an average of about 0.7 mm are very small (e.g. in Fig. 11). With the z-position of the rotor hub the coordinate system can be shifted into the final rotor hub coordinate system. Because of the offset the shifting is done separated with respect to advancing and retreating side. In Fig. 12 the complete transformation procedure from wind tunnel coordinate system into the rotor hub system is shown.
Fig. 13. Model yaw angle β (BL5.3, blade #1).
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Fig. 14. Blade tip lag motion with and w/o β correction (BL5.3, blade #1).
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Fig. 17. Radial distribution of blade lag motion, measured and polynomial (BL5.3, blade #1).
Fig. 15. Elastic blade tip lead-lag motion (MN5.3, all blades).
Fig. 18. Extrapolated quarter chord lines (BL5.3, blade #1).
Fig. 16. Radial distribution of blade lag motion at Ψ = 229 deg (MN5.3, all blades).
about 9 mm in the BL11.5 case and to a minimum difference of about 0.9 mm in the MN5.3 configuration (Fig. 15). The radial distributions of the elastic blade lag position are shown in Fig. 16 exemplarily for the case MN5.3. The results were chosen at an azimuth of Ψ = 229 deg. There is nearly a linear dependence of the lag value with respect to the radius in each configuration. Conspicuous is the curve at inner radii. The blades of a hingeless rotor as used in the HART II test should have a lead-lag value of zero and a gradient of zero at the position of the blade attachment at r/R = 0.1 (200 mm). However an extrapolation of the lead-
lag data in the rotating system to radius r/R = 0.1 with an additional constraint (gradient dyel /dr = 0) led to an offset of about 10 mm. Fig. 17 shows the radial distribution of different azimuths and the extrapolated quarter chord lines from the data in the rotating system exemplarily for blade #1 of the base line case at αs = 5.3 deg. In principle this offset indicates a distance of the quarter chord line to the rotor hub center. For a better understanding Fig. 18 shows the quarter chord lines extrapolated to the rotor hub center. Since this problem can be found in all configurations and all azimuths it is a systematic error. Perhaps due to the centrifugal forces in combination with a resulting play in the blade mounts a pre-lag angle is caused, which could explain a small part of the offset. But such an additional lead-lag angle would increase the offset. With regard to the non-rotating data a lead-lag deflection near zero is expected because there is no build-in pre-lag angle and no aerodynamic forces which influence the blade. Only a very small part of the gravity has an influence on
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the lag deflection in this way that due to the shaft angle of the model the blades of the advancing side can deflect in counter-rotating direction and the blades of the retreating side can deflect in rotating direction. Thus we could have a small blade lag at the advancing side and a small lead of the blade at the retreating side. Latest investigations have shown that regarding the non-rotating data no general offset is identifiable. In conclusion the lead-lag results from the non-rotating system show the expected values, but there is no comprehensive explanation for the offset of the extrapolated quarter chord lines to the rotor hub center in the lead-lag results from the rotating system.
4.3. Blade torsion motion As described in [2] the pure elastic pitch deformation (ϑel positive nose up) can be calculated by the distance of the z-coordinate of the front and rear blade marker, the associated pitch control angle, the pre-twist angle and the pitch offset in z-direction due to the different distance of the front and rear blade markers to the quarter chord line. Fig. 22 shows the time history of the elastic torsion of all four blades of the base line case at 5.3 deg. The blade-toblade differences have a range of about 0.3 deg to 1.1 deg.
4.2. Blade flap motion The elastic blade flap deflection zel (positive up) is given by the distance between the quarter chord line and a straight line defined by the pre-cone angle. Therefore approximately the distance of the quarter chord line z-position to the precone line at defined radial positions is used. Due to the correction of the raw data by the model roll angle and the improved calibration the skip between advancing and retreating side at Ψ = 180 deg is eliminated. Because of the direction of the roll angle the correction leads to lower elastic blade flap values at the advancing side and higher values at the retreating side. Fig. 19 shows the elastic blade tip deflection in z-direction in the rotor hub coordinate system for the reference blade of the case BL5.3 compared with the same results by using no roll angle correction. It clearly can be seen that the roll angle correction has a substantial influence to the elastic blade deflection. The maximum blade-to-blade difference is about 20 mm (see Fig. 20) mainly in the vicinity of Ψ = 180 deg. The maximum values can be found for the reference blade #1 followed by blade #4 and #2. In all configurations blade #3 has the smallest values. Reason could be an incorrect blade tracking at the beginning of the wind tunnel tests or different blade elasto-mechanical properties. The same tendency is visible in the radial distributions of all four blades which are shown in Fig. 21 for MN5.3 at an azimuth of Ψ = 90 deg.
Fig. 19. Elastic blade tip flap motion with and w/o Φ correction (BL5.3, blade #1).
Fig. 20. Elastic blade tip flap motion (MN5.3, all blades).
Fig. 21. Radial distribution of elastic blade flap (MN5.3, all blades, Ψ = 90 deg).
Fig. 22. Time history of the elastic blade torsion (BL5.3, all blades).
O. Schneider / Aerospace Science and Technology 9 (2005) 409–420
Fig. 23. Radial distribution of elastic torsion (BL5.3, all blades, Ψ = 139 deg).
The maximum blade-to-blade difference of up to 1.4 mm is found in the minimum vibration case at Ψ = 94 deg. Reason for these relatively large differences could be the used pitch control angles, which come not directly from the SPR measurements but from other acoustic measurements before. Only two blades were equipped with a pitch angle sensor, whose data were incorrect during the SPR measurements. A different setting of the root pitch angles of all four blades during blade tracking or a different loose in the blade pitch links can induce such blade-to-blade differences. In general blade #1 has the uppermost torsion values, the values of blade #3 are the smallest. Fig. 23 shows the radial distributions of the elastic blade pitch at an azimuth position of Ψ = 139 deg for the BL5.3 configuration. The maximum scatter found for a neighboring blade marker pair is about 0.8 deg. An assumed accuracy of marker position recognition of 0.4 mm and the distance between front and rear marker centers of 89 mm leads to a theoretical error of: 2 · 0.4 mm ≈ 0.52◦ . error = arctan 89 mm Thus the computed torsion values have a maximum scatter which is out of the range of the assumed measurement error. Furthermore at some azimuth positions the calculated blade pitch distribution has computed torsion values which are definitely outside of the expected curve (example in Fig. 24 grey range). Investigations have shown that reflections on the blade near the leading edge at azimuths near Ψ = 90 deg and Ψ = 270 deg have falsified the marker position recognition. This problem is found in all measurement configurations. The reflections are at the leading edge and they come from the stroboscopic flashes. Due to these reflections the usual black background is more brightly and the contrast to the white markers is small. The recognition of a correct marker bound is difficult and the recognized marker centers have incorrect coordinates, leading to errors in the blade torsion. A possibility to get smoother results is the computation of a regression function. To reduce measurement noise and smooth out irregularities, polynomial functions of fourth order were carefully fitted through the positions of the leading
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Fig. 24. Radial distribution of elastic torsion at Ψ = 90 deg (all configurations, grey: range of reflections).
Fig. 25. Elastic blade torsion, measurements and mode shape regression with standard deviation (MN5.3).
and trailing edge markers and differentiated to get the local pitch. The results by using this method were unacceptable at inner radii [2]. That is why a second approach was applied. The basis for the regression function is the first mode shape of blade torsion ϑ1 (r ∗ ) in the rotating system. The second torsion mode shape has not to be considered since the according natural frequency is at about 10/rev. By using the least error squares method the coefficients ϑ0 and ϑ1 were computed. ϑel (r) = ϑ0 + ϑ1 · Φ1 (r ∗ ), r − rE r∗ = , R − rE J Φ1 (r ∗ ) = cj · r ∗j . j =0
rE is the radius at the blade main bolt and Φ1 the first mode shape of torsion (coefficients by FEM). An example for different azimuths is shown in Fig. 25 for the reference blade of the minimum noise configuration. By using the mode shape representation the results are smooth curves with a value unequal zero at the blade attachment r/R = 0.1. In the example figure the radial distribution at an azimuth of Ψ = 244 deg has an elastic torsion value of 0.55 deg at this position. In general the elastic torsion values at inner radii lead to the
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Fig. 26. Elastic blade torsion mode shape regression (BL5.3).
conclusion that there is a systematic error, because most of the radial distributions have values in the vicinity of about ϑel = 0.5 deg at the blade attachment (compare Fig. 26). This root offset can have several reasons. The blade tracking was done by setting different root pitch offsets. A steady offset could also be caused by the used pitch data which come from the acoustic part of the test. During the SPR measurements there was a sensor defect. A possibility for a dynamic offset is the increasing loose of the pitch bearings in the course of the tests. The comparison of the time history of the blade torsion yields no major difference between the measured elastic torsion angle and the mode shape based regression function [3]. The results of the elastic torsion angle from data in the non-rotating system have shown that the scatter at each three azimuth positions is about ±0.5 deg. The maximum deviation of about 1.0 deg could be found at Ψ = 90 deg. In conclusion the results obtained for blade torsion depend on several conditions. There is the theoretical error by marker position recognition of about 0.5 deg, possible offsets due to the blade tracking and the accuracy of all 4 blades root pitch angle measurements. Further the calculation of the torsion angle by differentiation leads to increased errors. Thus to obtain better results for blade torsion a simultaneous measurement of the blade root pitch angle and SPR is necessary.
Fig. 27. Blade tip flap motion depending on azimuth for α-sweep (r/R = 99%, blade #1).
Fig. 28. Blade tip lead-lag motion depending on azimuth for α-sweep (r/R = 99%, blade #1).
4.4. Alpha sweep In Figs. 27, 28 and 29 the elastic flap, lead-lag and torsion motion of the reference rotor blade (blade #1) depending on azimuth are shown. There is a comparison of the α-sweep configurations at the blade position at r/R = 99%. In flapping and torsion a 2/rev motion is present in descent. In the lead-lag motion there are nearly constant amplitudes of about 10 mm in 1/rev at the blade tip. By using the new raw data and the model yaw angle correction the skips in the cases BL5.3 and BL11.5 are eliminated. The maximum lag value increases from descent to climb as expected by the increased power consumption. In the time history of the elastic torsion the 2/rev oscillation is stronger in descent than in climb condition.
Fig. 29. Elastic torsion motion depending on azimuth for α-sweep (r/R = 99%, blade #1).
4.5. HHC sweep Figs. 30, 31 and 32 show the comparison of the elastic flap, lead-lag and torsion motion of the rotor blade depending on azimuth for the configurations with higher harmonic control and the base line case at the blade position r/R = 99%. When 3/rev HHC is applied (cases MN and MV), a 3/rev flapping dominates the figure as expected (Fig. 30). The lo-
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minimum noise case and up to 2.5 deg in the minimum vibration case (Fig. 32).
5. Conclusions
Fig. 30. Blade tip flap motion depending on azimuth for HHC sweep (r/R = 99%).
Fig. 31. Blade tip lead-lag motion depending on azimuth for HHC sweep (r/R = 99%).
• The new calibration method leads to significantly improved accuracy of the raw data. The analysis of the calibration data has shown that the calibration accuracy should be improved in further wind tunnel tests by using more calibration markers than in the HART II test. • It was found that there still are problems in the camera calibration, because the blade length differs between advancing and retreating side which is unexplained up to now. • No solution could be found for the offset of the blade lead-lag at the blade root attachment. The extrapolation of the lead-lag bending to the rotor hub center with an additional boundary condition at the attachment leads to an offset of about 10 mm for all azimuths positions and in all configurations. Since this problem only is present in the results of the rotating system, a play in the blade mounts because of centrifugal forces could be one reason. • For blade torsion a simultaneous measurement of the blade root pitch angle and SPR is necessary because of the dependence of the results on the accuracy of blade root pitch measurement and the blade tracking. Recommendation: SPR measurements from the rotor hub center in the rotating system could eliminate lots of problems.
Acknowledgements
Fig. 32. Elastic torsion motion depending on azimuth for HHC sweep (r/R = 99%).
cal amplitudes are up to 12 mm off the BL position at the blade tip in the minimum noise case. The results of the blade lag motion show nearly identical values with 1/rev amplitudes of about 10 mm independent of the higher harmonic control (Fig. 31). With 3/rev HHC a strong 3/rev torsion is the response which was expected due to the natural frequency in torsion at 3.6/rev of this rotor. The local amplitudes in torsion are up to 1.5 deg off the BL position in the
An international test as complex as HART II requires a lot of engagement of all participants, both in the fore- and in the background. It would fill pages to name everybody. Instead, the teams are specifically addressed. These are: the prediction team, the test team and the management team, all of them consisting of US/French/German members working years ahead in real partnership preparing the rotor hardware, the measurement techniques, the test matrix and the funding. Specifically the funding of the test from US and French side, the development of 3C-PIV and preparation of the rotor and conduction of the test on DLR side shall be mentioned, and the strong support of DNW during the test. Without the enthusiasm of all of them this test would never have come true – thanks to all of them!
References [1] K. Pengel, R. Müller, B.G. van der Wall, Stereo pattern recognition – the technique for reliable rotor blade deformation and twist mea-
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surements, in: AHS International Meeting on Advanced Rotorcraft Technology and Life Saving Activities, Utsunomiya, Tochigi, Japan, 2002. [2] O. Schneider, B.G. van der Wall, K. Pengel, HART-II blade motion measured by stereo pattern recognition (SPR), in: 59th Annual Forum of the American Helicopter Society, Phoenix, USA, 2003. [3] O. Schneider, B.G. van der Wall, Final analysis of HART II blade deflection measurement, in: 29th European Rotorcraft Forum, Friedrichshafen, Germany, 2003.
[4] B.G. van der Wall, B. Junker, C.L. Burley, T.F. Brooks, Y.H. Yu, C. Tung, H. Richard, M. Raffel, W. Wagner, K. Pengel, E. Mercker, P. Beaumier, Y. Delrieux, The HART II test in the DNW – a major step towards rotor wake understanding, in: 28th European Rotorcraft Forum, Bristol, UK, 2002. [5] Y.H. Yu, The HART-II test: rotor wakes and aeroacoustics with higher-harmonic pitch control (HHC) inputs, in: The Joint German/French/Dutch/US Project, 58th Annual Forum of the American Helicopter Society, Montreal, Canada, 2002.