Airfoil profile

Information

  • Patent Grant
  • 11306594
  • Patent Number
    11,306,594
  • Date Filed
    Thursday, February 25, 2021
    3 years ago
  • Date Issued
    Tuesday, April 19, 2022
    2 years ago
Abstract
Compressor components, such as blades and vanes, having an airfoil portion with an uncoated, nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance in inches. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.
Description
TECHNICAL FIELD

The present invention generally relates to axial compressor components having an airfoil. More specifically, the present invention relates to an airfoil profile for compressor components, such as blades and/or vanes, that have a variable thickness and three-dimensional (“3D”) shape along the airfoil span in order to raise the natural frequency, improve airfoil mean stress and dynamic stress capabilities of the compressor component, and minimize risk of failure due to cracks caused by excitation of the component.


BACKGROUND

Gas turbine engines, such as those used for power generation or propulsion, include a compressor section. The compressor section includes a casing and a rotor that rotates about an axis within the casing. In axial-flow compressors, the rotor typically includes a plurality of rotor discs that rotate about the axis. A plurality of compressor blades extend away from, and are radially spaced around, an outer circumferential surface of each of the rotor discs. Typically, following each plurality of compressor blades is a plurality of compressor vanes. The plurality of compressor vanes usually extend from, and are radially spaced around, the casing. Each set of a rotor disc, a plurality of compressor blades extending from the rotor disc, and a plurality of compressor vanes immediately following the plurality of compressor blades is generally referred to as a compressor stage. The radial height of each successive compressor stage decreases because the blades and vanes increase the density, pressure and temperature of air passing through the stage. Specialized shapes of compressor blades and compressor vanes aid in compressing fluid as it passes through the compressor.


Compressor components, such as compressor blades and stator vanes, have an inherent natural frequency. When these components are excited by the passing air, as would occur during normal operating conditions of a gas turbine engine, the compressor components vibrate at different orders of engine rotational frequency. When the natural frequency of a compressor component coincides with or crosses an engine order, the compressor component can exhibit resonant vibration that in turn can cause cracking and ultimately failure of the compressor component.


SUMMARY

This summary is intended to introduce a selection of concepts in a simplified form that are further described below in the detailed description section of this disclosure. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in isolation to determine the scope of the claimed subject matter.


In brief, and at a high level, this disclosure describes gas turbine engine components, e.g., compressor components such as blades and vanes, having airfoil portions that optimize the interaction with other compressor stages, provide for aerodynamic efficiency, and meet aeromechanical life objectives. More specifically, the compressor components described herein have unique airfoil thicknesses, chord lengths, and 3D shaping that results in the desired natural frequency of the respective compressor component. Further, the airfoil thicknesses and 3D shaping at specified radial distances along the airfoil span may provide an acceptable level of mean stress in the airfoil sections, and also provide improved blade aerodynamics and efficiency while maintaining the desired blade natural frequency. The airfoil portion of the compressor components disclosed herein, such as blades or vanes, have a particular shape or profile as specified herein. For example, one such airfoil profile may be defined by at least some of the Cartesian coordinate values of X, Y, and Z set forth in Table 1. In this example, the Z coordinate values are distances measured perpendicular to the compressor centerline and the X and Y coordinate values for each Z distance define an airfoil section when the coordinate values are connected with smooth continuing arcs. In this example, the airfoil sections at each Z distance are further joined with smooth continuing arcs to define the 3D shape of the airfoil portion of the compressor component.





BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments disclosed herein relate to compressor component airfoil designs and are described in detail with reference to the attached drawing figures, which illustrate non-limiting examples of the disclosed subject matter, wherein:



FIG. 1 depicts a schematic view of a gas turbine engine, in accordance with aspects hereof;



FIG. 2 depicts a perspective view of a set of compressor blades coupled to a rotor disc, in accordance with aspects hereof;



FIG. 3 depicts a perspective view of a portion of the rotor disc of FIG. 2 and a compressor blade partially coupled thereto, in accordance with aspects hereof;



FIG. 4 depicts a top view of a compressor blade, in accordance with aspects hereof;



FIG. 5 depicts a perspective view of a pressure side of the compressor blade of FIG. 4, in accordance with aspects hereof;



FIG. 6 depicts a perspective view of a suction side of the compressor blade of FIG. 4, in accordance with aspects hereof;



FIG. 7 depicts a cross-section of the compressor blade of FIG. 4 taken along cut-line 7-7 in FIG. 5, in accordance with aspects hereof; and



FIG. 8 depicts a perspective view of the airfoil sections defined by the Cartesian coordinate values of X, Y, and Z set forth in Table 1, in accordance with aspects hereof.





DETAILED DESCRIPTION

The subject matter of this disclosure is described herein to meet statutory requirements. However, this description is not intended to limit the scope of the invention. Rather, the claimed subject matter may be embodied in other ways, to include different steps, combinations of steps, features, and/or combinations of features, similar to those described in this disclosure, and in conjunction with other present or future technologies.


In brief, and at a high level, this disclosure describes gas turbine engine components, e.g., compressor components such as blades and vanes, having airfoil portions that may optimize the interaction with other compressor stages, provide for aerodynamic efficiency, and improve aeromechanical life objectives. More specifically, the compressor components described herein may have, in different disclosed aspects, unique airfoil thicknesses, chord lengths, and 3D shaping that results in different performance characteristics being achieved, such as, e.g., an altered natural frequency of the associated compressor component. Further, the airfoil thicknesses and 3D shaping at specified radial distances along the airfoil span may provide an acceptable level of mean stress in the airfoil sections, and also provide improved blade aerodynamics and efficiency. The airfoil portion of the compressor components disclosed herein, such as blades or vanes, have a particular shape or profile as specified herein. For example, one such airfoil profile may be defined by the Cartesian coordinate values of X, Y, and Z set forth in Table 1. In this example, the Z coordinate values are distances measured perpendicular from the compressor centerline and the X and Y coordinate values at each Z distance define an airfoil section when the coordinate values are connected with smooth continuing arcs. In this example, the airfoil sections at each Z distance may be joined with smooth continuing arcs to define the 3D shape of the airfoil portion of the compressor component.


Referring now to FIG. 1, there is illustrated a portion of a compressor 10 having multiple compressor stages, including a stage zero 12 at the front of the compressor 10. Each compressor stage includes a rotor disc 14, a plurality of circumferentially spaced compressor blades 16 coupled to the rotor disc 14, and a plurality of compressor vanes 18 adjacent to, and following, the plurality of circumferentially spaced compressor blades 16. The plurality of compressor vanes 18 are circumferentially spaced around, and extend from, a casing 20 of the compressor 10.


One aspect of a compressor component is a compressor blade 16A, as depicted in FIGS. 2-6. As best seen in FIG. 3, the compressor blade 16A includes a root portion 22 configured to be coupled to the rotor disc 14, and an airfoil portion 26 extending from the root portion 22 to a tip 28. As best seen in FIGS. 5 and 6, the airfoil portion 26 generally includes a leading edge 30, a trailing edge 32, and a pressure side wall 34 and a suction side wall 36 each extending between the leading edge 30 and the trailing edge 32. The pressure side wall 34 generally presents a convex surface along the span of the airfoil portion 26. The suction side wall 36 generally presents a concave surface along the span of the airfoil portion 26. In some aspects, the tip 28 may include a squealer cut configured to thin the airfoil portion 26 at the tip 28.


A compressor component may be used in a land-based compressor in connection with a land-based gas turbine engine. Typically, compressor components in such a compressor only experience temperatures below approximately 850 degrees Fahrenheit. As such, these types of compressor components may be fabricated from a relatively low temperature alloy. For example, these compressor components may be made from a stainless-steel alloy.


A cross-section of one aspect of the airfoil portion 26 is depicted in FIG. 7. As seen in FIG. 7, a chord 40 is shown for this radial section of the airfoil portion 26. The thickness of the airfoil portion 26 (e.g., the distance between the pressure side wall 34 and the suction side wall 36) varies at each point along the chord 40. As is evident from FIGS. 4-6, the length and orientation of the chord 40 changes along the span of the airfoil portion 26.


By changing the airfoil thickness, chord, 3D shaping, and/or the distribution of material along the span of the airfoil portion 26 of the compressor component, the natural frequency of the compressor component may be altered. This may be advantageous for the operation of the compressor 10. For example, during operation of the compressor 10, the compressor component may move (e.g., vibrate) at various modes due to the geometry, temperature, and aerodynamic forces being applied to the compressor component. These modes may include bending, torsion, and various higher-order modes.


If excitation of the compressor component occurs for a prolonged period of time with a sufficiently high amplitude then the compressor component can fail due to high cycle fatigue. For example, a critical first and second bending mode for the compressor component may be 2-3 times or 6 times the 60 Hz frequency of the gas turbine engine, respectively. For this mode, the first bending mode must avoid the critical frequency ranges of 110-130 Hz and 160-200 Hz. Modifying the thickness, chord, and/or the 3D shape of the compressor component, and in particular that of the airfoil portion thereof, results in altering the natural frequency of the compressor component. Continuing with the above example, modifying the thickness, chord, and/or the 3D shape of the compressor component in accordance with the disclosure herein may result in the first bending natural frequency being increased to be between 130 and 160 Hz. This first bending natural frequency of the compressor component will therefore be between the second and third engine order excitation frequencies when the compressor is rotating at 60 Hz. More specifically, a compressor component having the thickness, chord, and/or the 3D shape as defined by the Cartesian coordinates set forth in Table 1 will have a natural frequency of first bending about halfway between 2nd and 3rd engine order excitations and second bending will be between the 5th and 6th engine order excitations, or between the 6th and 7th engine order. In other aspects, a compressor component having the thickness, chord, and/or the 3D shape as defined by the Cartesian coordinates set forth in Table 1 will have a natural frequency of first bending at least 5-10% greater than 2nd engine order excitations and at least 5-10% less than 3rd engine order excitations. In fact, a compressor component having the thickness, chord, and/or the 3D shape as defined by the Cartesian coordinates set forth in Table 1 will have a natural frequency for the lowest few vibration modes of at least 5-10% less than or greater than each engine order excitation.


In one embodiment disclosed herein, a nominal 3D shape of an airfoil portion, such as the airfoil portion 26 shown in FIGS. 5 and 6, of a gas turbine engine component, such as a compressor component of a gas turbine engine, may be defined by a set of X, Y, and Z coordinate values measured in a Cartesian coordinate system. For example, one such set of coordinate values are set forth, in inches, in Table 1 below. The Cartesian coordinate system includes orthogonally related X, Y, and Z axes. The positive X, Y, and Z directions are axial toward the exhaust end of the compressor, tangential in the direction of engine rotation, and radially outward toward the static case, respectively. Each Z distance is measured from an axially-extending centerline of the compressor 10 (which, in aspects, may also be a centerline of the gas turbine engine). The X and Y coordinates for each distance Z may be joined smoothly (e.g., such as by smooth continuing arcs, splines, or the like) to thereby define a section of the airfoil portion of the compressor component at the respective Z distance. Each of the sections of the airfoil portion from the coordinate values set forth in Table 1 below is shown in FIG. 8. Each of the defined sections of the airfoil profile is joined smoothly with an adjacent section of the airfoil profile in the Z direction to form a complete nominal 3D shape of the airfoil portion.


The coordinate values set forth in Table 1 below are for a cold condition of the compressor component (e.g., non-rotating state and at room temperature). Further, the coordinate values set forth in Table 1 below are for an uncoated nominal 3D shape of the compressor component. In some aspects, a coating (e.g., corrosion protective coating) may be applied to the compressor component. The coating thickness may be up to about 0.010 inches thick.


Further, the compressor component may be fabricated using a variety of manufacturing techniques, such as forging, casting, milling, electro-chemical machining, electric-discharge machining, and the like. As such, the compressor component may have a series of manufacturing tolerances for the position, profile, twist, and chord that can cause the compressor component to vary from the nominal 3D shape defined by the coordinate values set forth in Table 1. This manufacturing tolerance may be, for example, +/−0.120 inches in a direction away from any of the coordinate values of Table 1 without departing from the scope of the subject matter described herein. In other aspects, the manufacturing tolerances may be +/−0.080 inches. In still other aspects, the manufacturing tolerances may be +/−0.020 inches.


In addition to manufacturing tolerances affecting the overall size of the compressor component, it is also possible to scale the airfoil to a larger or smaller airfoil size. In order to maintain the benefits of this 3D shape, in terms of stiffness and stress, it is necessary to scale the compressor component uniformly in the X, Y, and Z directions. However, since the Z values in Table 1 are measured from a centerline of the compressor rather than a point on the compressor component, the scaling of the Z values must be relative to the minimum Z value in Table 1. For example, the first (i.e., radially innermost) profile section is positioned approximately 23.819 inches from the compressor centerline and the second profile section is positioned approximately 25.229 inches from the engine centerline. Thus, if the compressor component was to be scaled 20% larger, each of the X and Y values in Table 1 may simply be multiplied by 1.2. However, each of the Z values must first be adjusted to a relative scale by subtracting the distance from the compressor centerline to the first profile section (e.g., the Z coordinates for the first profile section become Z=0, the Z coordinates for the second profile section become Z=1.410 inches, etc.). This adjustment creates a nominal Z value. After this adjustment, then the nominal Z values may be multiplied by the same constant or number as were the X and Y coordinates (1.2 in this example).


The Z values set forth in Table 1 may assume a compressor sized to operate at 60 Hz. In other aspects, the compressor component described herein may also be used in different size compressors (e.g., a compressor sized to operate at 50 Hz, etc.). In these aspects, the compressor component defined by the X, Y, and Z values set forth in Table 1 may still be used, however, the Z values would be offset to account for the radial spacing of the differently sized compressors. The Z values may be offset radially inwardly or radially outwardly, depending upon whether the compressor is smaller or larger than the compressor envisioned by Table 1. For example, the rotor to which a blade is affixed may have a larger radius (e.g., 20%) than that envisioned by Table 1. In such a case, the minimum Z values (i.e., the radially innermost profile section) would be offset a distance equal to the difference in rotor radius size (e.g., the radially innermost profile section would be positioned approximately 28.583 inches from the engine centerline instead of 23.819 inches) and the remainder of the Z values would maintain their relative spacing to one another from Table 1 with the same scale factor as being applied to X and Y (e.g., if the scale factor is one then the second profile section would be positioned approximately 29.993 inches from the engine centerline—still 1.410 inches radially outward from the first profile section). Stated another way, the difference in radius of the rotor (e.g., 4.764 inches) would be added to all of the scaled Z values in Table 1.


Equation (1) provides another way to determine new Z values (e.g., scaled or translated) from the Z values listed in Table 1 when changing the relative size and/or position of the component defined by Table 1. In equation (1), Z1 is the Z value from Table 1, Z1min is the minimum Z value from Table 1, scale is the scaling factor, Z2min is the minimum Z value of the component as scaled and/or translated, and Z2 is the resultant Z value for the component as scaled and/or translated. Of note, when merely translating the component, the scaling factor in equation (1) is 1.000.

Z2=[(Z1−Z1min)*scale+Z2min]  (1)


In yet another aspect, the airfoil profile may be defined by a portion of the set of X, Y, and Z coordinate values set forth in Table 1 (e.g., at least 85% of said coordinate values).











TABLE 1





X
Y
Z

















0.415
1.227
23.819


0.372
1.276
23.819


0.330
1.326
23.819


0.292
1.380
23.819


0.260
1.437
23.819


0.238
1.498
23.819


0.236
1.563
23.819


0.273
1.615
23.819


0.336
1.631
23.819


0.401
1.624
23.819


0.464
1.606
23.819


0.525
1.583
23.819


0.583
1.552
23.819


0.642
1.522
23.819


0.699
1.494
23.819


0.834
1.428
23.819


0.969
1.365
23.819


1.106
1.304
23.819


1.244
1.245
23.819


1.383
1.188
23.819


1.522
1.133
23.819


1.662
1.080
23.819


1.803
1.029
23.819


1.944
0.979
23.819


2.085
0.930
23.819


2.227
0.882
23.819


2.369
0.834
23.819


2.512
0.787
23.819


2.654
0.741
23.819


2.797
0.696
23.819


2.940
0.650
23.819


3.083
0.606
23.819


3.226
0.562
23.819


3.369
0.518
23.819


3.512
0.475
23.819


3.656
0.432
23.819


3.799
0.389
23.819


3.943
0.346
23.819


4.086
0.303
23.819


4.230
0.259
23.819


4.373
0.216
23.819


4.516
0.171
23.819


4.659
0.127
23.819


4.802
0.082
23.819


4.945
0.036
23.819


5.087
−0.010
23.819


5.230
−0.056
23.819


5.372
−0.103
23.819


5.514
−0.150
23.819


5.656
−0.197
23.819


5.799
−0.244
23.819


5.941
−0.291
23.819


6.083
−0.338
23.819


6.225
−0.385
23.819


6.368
−0.431
23.819


6.510
−0.478
23.819


6.653
−0.523
23.819


6.714
−0.543
23.819


6.745
−0.552
23.819


6.776
−0.562
23.819


6.806
−0.575
23.819


6.827
−0.598
23.819


6.840
−0.628
23.819


6.848
−0.659
23.819


6.849
−0.692
23.819


6.839
−0.722
23.819


6.822
−0.749
23.819


6.797
−0.771
23.819


6.768
−0.784
23.819


6.736
−0.792
23.819


6.705
−0.798
23.819


6.637
−0.814
23.819


6.478
−0.848
23.819


6.319
−0.878
23.819


6.158
−0.904
23.819


5.998
−0.926
23.819


5.836
−0.945
23.819


5.675
−0.960
23.819


5.513
−0.971
23.819


5.350
−0.978
23.819


5.188
−0.982
23.819


5.026
−0.981
23.819


4.863
−0.977
23.819


4.701
−0.968
23.819


4.539
−0.955
23.819


4.378
−0.939
23.819


4.217
−0.917
23.819


4.057
−0.892
23.819


3.897
−0.862
23.819


3.739
−0.827
23.819


3.581
−0.787
23.819


3.425
−0.743
23.819


3.270
−0.694
23.819


3.117
−0.640
23.819


2.965
−0.583
23.819


2.815
−0.520
23.819


2.667
−0.454
23.819


2.521
−0.384
23.819


2.376
−0.310
23.819


2.233
−0.233
23.819


2.092
−0.152
23.819


1.954
−0.068
23.819


1.817
0.019
23.819


1.682
0.109
23.819


1.549
0.202
23.819


1.418
0.299
23.819


1.289
0.398
23.819


1.163
0.500
23.819


1.040
0.605
23.819


0.919
0.714
23.819


0.800
0.825
23.819


0.685
0.939
23.819


0.572
1.056
23.819


0.462
1.175
23.819


0.485
1.519
25.229


0.452
1.557
25.229


0.420
1.596
25.229


0.391
1.637
25.229


0.367
1.681
25.229


0.350
1.728
25.229


0.348
1.778
25.229


0.378
1.816
25.229


0.427
1.825
25.229


0.476
1.817
25.229


0.524
1.801
25.229


0.569
1.779
25.229


0.613
1.754
25.229


0.656
1.729
25.229


0.714
1.697
25.229


0.848
1.622
25.229


0.983
1.548
25.229


1.119
1.476
25.229


1.255
1.404
25.229


1.393
1.335
25.229


1.530
1.266
25.229


1.669
1.199
25.229


1.808
1.133
25.229


1.948
1.068
25.229


2.088
1.004
25.229


2.228
0.942
25.229


2.369
0.880
25.229


2.510
0.818
25.229


2.652
0.758
25.229


2.793
0.698
25.229


2.936
0.639
25.229


3.078
0.580
25.229


3.220
0.522
25.229


3.363
0.464
25.229


3.506
0.406
25.229


3.648
0.349
25.229


3.791
0.292
25.229


3.934
0.235
25.229


4.077
0.178
25.229


4.220
0.120
25.229


4.363
0.063
25.229


4.505
0.006
25.229


4.648
−0.052
25.229


4.791
−0.110
25.229


4.933
−0.168
25.229


5.076
−0.227
25.229


5.218
−0.285
25.229


5.360
−0.343
25.229


5.503
−0.402
25.229


5.645
−0.460
25.229


5.787
−0.519
25.229


5.930
−0.577
25.229


6.073
−0.635
25.229


6.215
−0.692
25.229


6.358
−0.749
25.229


6.501
−0.806
25.229


6.645
−0.862
25.229


6.706
−0.885
25.229


6.731
−0.894
25.229


6.755
−0.904
25.229


6.777
−0.918
25.229


6.795
−0.936
25.229


6.807
−0.960
25.229


6.812
−0.985
25.229


6.808
−1.011
25.229


6.798
−1.035
25.229


6.781
−1.055
25.229


6.759
−1.069
25.229


6.734
−1.076
25.229


6.708
−1.079
25.229


6.682
−1.082
25.229


6.613
−1.089
25.229


6.449
−1.105
25.229


6.286
−1.116
25.229


6.122
−1.124
25.229


5.959
−1.128
25.229


5.795
−1.128
25.229


5.631
−1.125
25.229


5.468
−1.117
25.229


5.304
−1.106
25.229


5.141
−1.091
25.229


4.978
−1.072
25.229


4.816
−1.049
25.229


4.655
−1.022
25.229


4.494
−0.992
25.229


4.334
−0.957
25.229


4.175
−0.918
25.229


4.016
−0.875
25.229


3.860
−0.828
25.229


3.704
−0.777
25.229


3.550
−0.722
25.229


3.397
−0.662
25.229


3.246
−0.598
25.229


3.097
−0.531
25.229


2.950
−0.459
25.229


2.804
−0.384
25.229


2.661
−0.305
25.229


2.519
−0.223
25.229


2.379
−0.138
25.229


2.241
−0.050
25.229


2.105
0.041
25.229


1.971
0.136
25.229


1.839
0.233
25.229


1.709
0.333
25.229


1.582
0.435
25.229


1.456
0.541
25.229


1.333
0.648
25.229


1.212
0.759
25.229


1.093
0.871
25.229


0.976
0.986
25.229


0.862
1.103
25.229


0.749
1.222
25.229


0.639
1.343
25.229


0.530
1.466
25.229


0.564
1.790
26.659


0.540
1.819
26.659


0.516
1.849
26.659


0.494
1.879
26.659


0.475
1.912
26.659


0.462
1.948
26.659


0.460
1.985
26.659


0.484
2.013
26.659


0.521
2.017
26.659


0.558
2.008
26.659


0.593
1.993
26.659


0.626
1.975
26.659


0.658
1.954
26.659


0.689
1.933
26.659


0.746
1.897
26.659


0.879
1.811
26.659


1.013
1.727
26.659


1.147
1.643
26.659


1.282
1.561
26.659


1.417
1.479
26.659


1.553
1.398
26.659


1.689
1.318
26.659


1.826
1.239
26.659


1.963
1.160
26.659


2.101
1.083
26.659


2.239
1.006
26.659


2.377
0.929
26.659


2.516
0.854
26.659


2.655
0.778
26.659


2.794
0.704
26.659


2.934
0.630
26.659


3.074
0.556
26.659


3.214
0.483
26.659


3.354
0.411
26.659


3.495
0.338
26.659


3.635
0.266
26.659


3.776
0.194
26.659


3.917
0.123
26.659


4.058
0.051
26.659


4.199
−0.021
26.659


4.339
−0.093
26.659


4.480
−0.165
26.659


4.621
−0.237
26.659


4.761
−0.309
26.659


4.902
−0.380
26.659


5.043
−0.452
26.659


5.184
−0.523
26.659


5.325
−0.595
26.659


5.466
−0.666
26.659


5.607
−0.737
26.659


5.749
−0.808
26.659


5.890
−0.878
26.659


6.032
−0.948
26.659


6.174
−1.018
26.659


6.316
−1.086
26.659


6.459
−1.154
26.659


6.602
−1.222
26.659


6.663
−1.250
26.659


6.683
−1.259
26.659


6.702
−1.269
26.659


6.720
−1.280
26.659


6.734
−1.295
26.659


6.743
−1.315
26.659


6.744
−1.336
26.659


6.740
−1.357
26.659


6.729
−1.375
26.659


6.713
−1.389
26.659


6.693
−1.397
26.659


6.672
−1.400
26.659


6.651
−1.399
26.659


6.630
−1.398
26.659


6.559
−1.396
26.659


6.394
−1.388
26.659


6.229
−1.376
26.659


6.065
−1.361
26.659


5.901
−1.343
26.659


5.737
−1.320
26.659


5.574
−1.294
26.659


5.412
−1.265
26.659


5.250
−1.233
26.659


5.089
−1.197
26.659


4.929
−1.157
26.659


4.769
−1.113
26.659


4.611
−1.067
26.659


4.454
−1.016
26.659


4.298
−0.962
26.659


4.143
−0.905
26.659


3.989
−0.844
26.659


3.837
−0.779
26.659


3.687
−0.711
26.659


3.538
−0.640
26.659


3.391
−0.565
26.659


3.245
−0.487
26.659


3.102
−0.406
26.659


2.960
−0.322
26.659


2.820
−0.235
26.659


2.681
−0.144
26.659


2.545
−0.052
26.659


2.410
0.044
26.659


2.277
0.142
26.659


2.146
0.242
26.659


2.017
0.345
26.659


1.890
0.450
26.659


1.764
0.558
26.659


1.641
0.667
26.659


1.519
0.779
26.659


1.400
0.893
26.659


1.282
1.008
26.659


1.166
1.126
26.659


1.051
1.245
26.659


0.938
1.365
26.659


0.827
1.487
26.659


0.718
1.611
26.659


0.610
1.736
26.659


0.653
2.043
28.099


0.633
2.067
28.099


0.613
2.091
28.099


0.595
2.116
28.099


0.579
2.143
28.099


0.568
2.172
28.099


0.566
2.203
28.099


0.586
2.225
28.099


0.617
2.226
28.099


0.647
2.216
28.099


0.675
2.202
28.099


0.701
2.184
28.099


0.726
2.166
28.099


0.751
2.147
28.099


0.806
2.105
28.099


0.937
2.008
28.099


1.067
1.912
28.099


1.199
1.816
28.099


1.330
1.721
28.099


1.462
1.626
28.099


1.595
1.532
28.099


1.728
1.439
28.099


1.861
1.347
28.099


1.995
1.254
28.099


2.129
1.163
28.099


2.264
1.072
28.099


2.398
0.981
28.099


2.533
0.890
28.099


2.668
0.800
28.099


2.804
0.711
28.099


2.940
0.622
28.099


3.076
0.533
28.099


3.212
0.445
28.099


3.349
0.357
28.099


3.485
0.269
28.099


3.622
0.182
28.099


3.760
0.095
28.099


3.897
0.008
28.099


4.034
−0.079
28.099


4.171
−0.166
28.099


4.308
−0.253
28.099


4.446
−0.340
28.099


4.583
−0.426
28.099


4.720
−0.513
28.099


4.858
−0.600
28.099


4.995
−0.686
28.099


5.133
−0.772
28.099


5.271
−0.857
28.099


5.410
−0.943
28.099


5.548
−1.028
28.099


5.686
−1.112
28.099


5.825
−1.197
28.099


5.964
−1.281
28.099


6.104
−1.364
28.099


6.244
−1.446
28.099


6.384
−1.528
28.099


6.525
−1.609
28.099


6.585
−1.644
28.099


6.602
−1.652
28.099


6.618
−1.661
28.099


6.633
−1.672
28.099


6.645
−1.687
28.099


6.651
−1.704
28.099


6.651
−1.723
28.099


6.645
−1.740
28.099


6.633
−1.755
28.099


6.617
−1.765
28.099


6.599
−1.768
28.099


6.581
−1.766
28.099


6.562
−1.763
28.099


6.544
−1.759
28.099


6.474
−1.745
28.099


6.311
−1.709
28.099


6.148
−1.671
28.099


5.987
−1.629
28.099


5.826
−1.584
28.099


5.666
−1.536
28.099


5.507
−1.485
28.099


5.349
−1.431
28.099


5.192
−1.374
28.099


5.036
−1.315
28.099


4.881
−1.252
28.099


4.728
−1.187
28.099


4.576
−1.119
28.099


4.425
−1.047
28.099


4.275
−0.973
28.099


4.127
−0.896
28.099


3.980
−0.816
28.099


3.835
−0.734
28.099


3.691
−0.649
28.099


3.549
−0.562
28.099


3.409
−0.472
28.099


3.269
−0.380
28.099


3.132
−0.285
28.099


2.996
−0.188
28.099


2.862
−0.089
28.099


2.729
0.012
28.099


2.597
0.115
28.099


2.468
0.220
28.099


2.340
0.327
28.099


2.213
0.436
28.099


2.088
0.547
28.099


1.965
0.659
28.099


1.843
0.773
28.099


1.722
0.888
28.099


1.603
1.005
28.099


1.485
1.124
28.099


1.369
1.243
28.099


1.254
1.364
28.099


1.141
1.487
28.099


1.028
1.611
28.099


0.918
1.735
28.099


0.808
1.861
28.099


0.699
1.988
28.099


0.719
2.288
29.509


0.703
2.308
29.509


0.686
2.328
29.509


0.671
2.349
29.509


0.658
2.372
29.509


0.648
2.396
29.509


0.647
2.422
29.509


0.664
2.440
29.509


0.690
2.439
29.509


0.714
2.429
29.509


0.736
2.415
29.509


0.757
2.400
29.509


0.777
2.383
29.509


0.797
2.366
29.509


0.852
2.320
29.509


0.980
2.212
29.509


1.109
2.104
29.509


1.238
1.997
29.509


1.367
1.891
29.509


1.497
1.785
29.509


1.627
1.679
29.509


1.758
1.574
29.509


1.888
1.469
29.509


2.019
1.365
29.509


2.151
1.261
29.509


2.282
1.157
29.509


2.413
1.053
29.509


2.545
0.949
29.509


2.677
0.846
29.509


2.809
0.743
29.509


2.942
0.640
29.509


3.074
0.538
29.509


3.207
0.436
29.509


3.340
0.334
29.509


3.474
0.232
29.509


3.607
0.131
29.509


3.740
0.029
29.509


3.874
−0.072
29.509


4.007
−0.173
29.509


4.140
−0.275
29.509


4.274
−0.376
29.509


4.407
−0.478
29.509


4.540
−0.580
29.509


4.673
−0.682
29.509


4.806
−0.784
29.509


4.939
−0.885
29.509


5.073
−0.986
29.509


5.207
−1.087
29.509


5.341
−1.188
29.509


5.475
−1.288
29.509


5.609
−1.388
29.509


5.744
−1.488
29.509


5.879
−1.587
29.509


6.015
−1.685
29.509


6.151
−1.783
29.509


6.288
−1.880
29.509


6.425
−1.977
29.509


6.483
−2.018
29.509


6.497
−2.027
29.509


6.510
−2.037
29.509


6.523
−2.047
29.509


6.533
−2.060
29.509


6.537
−2.076
29.509


6.536
−2.092
29.509


6.528
−2.107
29.509


6.517
−2.118
29.509


6.501
−2.124
29.509


6.485
−2.124
29.509


6.469
−2.120
29.509


6.454
−2.114
29.509


6.438
−2.109
29.509


6.369
−2.084
29.509


6.210
−2.025
29.509


6.051
−1.962
29.509


5.894
−1.897
29.509


5.738
−1.829
29.509


5.582
−1.758
29.509


5.429
−1.685
29.509


5.276
−1.609
29.509


5.125
−1.531
29.509


4.974
−1.450
29.509


4.826
−1.367
29.509


4.679
−1.281
29.509


4.533
−1.192
29.509


4.389
−1.102
29.509


4.246
−1.008
29.509


4.105
−0.913
29.509


3.965
−0.816
29.509


3.826
−0.717
29.509


3.688
−0.616
29.509


3.552
−0.513
29.509


3.418
−0.409
29.509


3.284
−0.303
29.509


3.152
−0.195
29.509


3.021
−0.086
29.509


2.892
0.025
29.509


2.764
0.137
29.509


2.637
0.251
29.509


2.511
0.366
29.509


2.387
0.483
29.509


2.264
0.601
29.509


2.142
0.720
29.509


2.021
0.840
29.509


1.901
0.961
29.509


1.783
1.084
29.509


1.666
1.207
29.509


1.549
1.332
29.509


1.434
1.458
29.509


1.320
1.585
29.509


1.207
1.712
29.509


1.095
1.841
29.509


0.985
1.970
29.509


0.875
2.100
29.509


0.765
2.231
29.509


0.766
2.522
30.909


0.753
2.538
30.909


0.740
2.555
30.909


0.727
2.573
30.909


0.717
2.591
30.909


0.709
2.611
30.909


0.708
2.632
30.909


0.723
2.646
30.909


0.744
2.644
30.909


0.763
2.635
30.909


0.781
2.623
30.909


0.797
2.609
30.909


0.813
2.594
30.909


0.828
2.580
30.909


0.883
2.530
30.909


1.009
2.412
30.909


1.136
2.295
30.909


1.263
2.178
30.909


1.391
2.062
30.909


1.519
1.946
30.909


1.647
1.830
30.909


1.775
1.714
30.909


1.904
1.599
30.909


2.032
1.484
30.909


2.161
1.368
30.909


2.290
1.254
30.909


2.419
1.139
30.909


2.548
1.024
30.909


2.677
0.909
30.909


2.806
0.795
30.909


2.936
0.680
30.909


3.065
0.566
30.909


3.194
0.451
30.909


3.324
0.337
30.909


3.453
0.223
30.909


3.583
0.109
30.909


3.713
−0.005
30.909


3.842
−0.120
30.909


3.971
−0.234
30.909


4.100
−0.349
30.909


4.229
−0.465
30.909


4.357
−0.581
30.909


4.485
−0.697
30.909


4.612
−0.813
30.909


4.740
−0.929
30.909


4.867
−1.046
30.909


4.995
−1.162
30.909


5.123
−1.278
30.909


5.251
−1.394
30.909


5.380
−1.509
30.909


5.509
−1.624
30.909


5.638
−1.739
30.909


5.767
−1.854
30.909


5.897
−1.968
30.909


6.027
−2.081
30.909


6.158
−2.194
30.909


6.289
−2.306
30.909


6.345
−2.355
30.909


6.356
−2.364
30.909


6.367
−2.373
30.909


6.378
−2.383
30.909


6.386
−2.395
30.909


6.389
−2.409
30.909


6.386
−2.423
30.909


6.379
−2.436
30.909


6.367
−2.444
30.909


6.353
−2.448
30.909


6.339
−2.445
30.909


6.325
−2.439
30.909


6.313
−2.433
30.909


6.299
−2.426
30.909


6.232
−2.393
30.909


6.077
−2.314
30.909


5.922
−2.232
30.909


5.770
−2.148
30.909


5.619
−2.060
30.909


5.469
−1.970
30.909


5.320
−1.878
30.909


5.174
−1.784
30.909


5.028
−1.687
30.909


4.884
−1.588
30.909


4.742
−1.486
30.909


4.602
−1.383
30.909


4.463
−1.277
30.909


4.326
−1.169
30.909


4.190
−1.059
30.909


4.055
−0.948
30.909


3.922
−0.835
30.909


3.790
−0.721
30.909


3.659
−0.606
30.909


3.529
−0.489
30.909


3.400
−0.371
30.909


3.272
−0.253
30.909


3.145
−0.133
30.909


3.019
−0.012
30.909


2.894
0.111
30.909


2.770
0.234
30.909


2.648
0.358
30.909


2.526
0.483
30.909


2.406
0.610
30.909


2.286
0.737
30.909


2.167
0.865
30.909


2.049
0.994
30.909


1.932
1.124
30.909


1.816
1.254
30.909


1.701
1.385
30.909


1.587
1.518
30.909


1.474
1.650
30.909


1.362
1.784
30.909


1.250
1.919
30.909


1.140
2.054
30.909


1.030
2.189
30.909


0.920
2.326
30.909


0.812
2.463
30.909


0.809
2.709
32.269


0.799
2.723
32.269


0.789
2.737
32.269


0.779
2.752
32.269


0.770
2.767
32.269


0.764
2.784
32.269


0.764
2.801
32.269


0.776
2.812
32.269


0.793
2.809
32.269


0.809
2.801
32.269


0.823
2.790
32.269


0.836
2.778
32.269


0.848
2.765
32.269


0.860
2.753
32.269


0.913
2.699
32.269


1.037
2.574
32.269


1.162
2.449
32.269


1.286
2.324
32.269


1.411
2.199
32.269


1.536
2.075
32.269


1.661
1.951
32.269


1.786
1.827
32.269


1.912
1.703
32.269


2.037
1.579
32.269


2.163
1.455
32.269


2.288
1.332
32.269


2.414
1.208
32.269


2.539
1.084
32.269


2.665
0.960
32.269


2.790
0.837
32.269


2.916
0.713
32.269


3.042
0.589
32.269


3.167
0.466
32.269


3.293
0.342
32.269


3.418
0.218
32.269


3.543
0.094
32.269


3.668
−0.031
32.269


3.792
−0.155
32.269


3.917
−0.280
32.269


4.040
−0.406
32.269


4.163
−0.532
32.269


4.286
−0.659
32.269


4.408
−0.786
32.269


4.529
−0.914
32.269


4.650
−1.042
32.269


4.771
−1.171
32.269


4.892
−1.299
32.269


5.013
−1.427
32.269


5.134
−1.555
32.269


5.255
−1.683
32.269


5.377
−1.811
32.269


5.498
−1.938
32.269


5.621
−2.065
32.269


5.743
−2.192
32.269


5.867
−2.318
32.269


5.990
−2.444
32.269


6.113
−2.570
32.269


6.166
−2.623
32.269


6.176
−2.633
32.269


6.185
−2.642
32.269


6.194
−2.651
32.269


6.201
−2.662
32.269


6.203
−2.675
32.269


6.200
−2.688
32.269


6.192
−2.698
32.269


6.181
−2.705
32.269


6.168
−2.706
32.269


6.156
−2.702
32.269


6.144
−2.696
32.269


6.133
−2.689
32.269


6.122
−2.682
32.269


6.057
−2.642
32.269


5.907
−2.548
32.269


5.758
−2.451
32.269


5.611
−2.351
32.269


5.465
−2.249
32.269


5.322
−2.144
32.269


5.180
−2.038
32.269


5.040
−1.929
32.269


4.901
−1.817
32.269


4.765
−1.704
32.269


4.630
−1.588
32.269


4.497
−1.471
32.269


4.365
−1.351
32.269


4.236
−1.230
32.269


4.107
−1.107
32.269


3.980
−0.984
32.269


3.853
−0.859
32.269


3.728
−0.732
32.269


3.604
−0.606
32.269


3.480
−0.478
32.269


3.357
−0.350
32.269


3.235
−0.221
32.269


3.114
−0.092
32.269


2.993
0.039
32.269


2.873
0.170
32.269


2.754
0.302
32.269


2.636
0.435
32.269


2.519
0.568
32.269


2.403
0.702
32.269


2.287
0.837
32.269


2.173
0.973
32.269


2.059
1.109
32.269


1.945
1.246
32.269


1.833
1.383
32.269


1.721
1.522
32.269


1.610
1.660
32.269


1.500
1.800
32.269


1.391
1.940
32.269


1.282
2.080
32.269


1.174
2.221
32.269


1.067
2.363
32.269


0.961
2.505
32.269


0.855
2.648
32.269


0.859
2.826
33.669


0.850
2.838
33.669


0.842
2.851
33.669


0.834
2.863
33.669


0.827
2.876
33.669


0.822
2.891
33.669


0.822
2.905
33.669


0.833
2.914
33.669


0.847
2.910
33.669


0.860
2.902
33.669


0.871
2.893
33.669


0.882
2.882
33.669


0.891
2.871
33.669


0.901
2.859
33.669


0.952
2.803
33.669


1.071
2.671
33.669


1.189
2.540
33.669


1.309
2.409
33.669


1.428
2.278
33.669


1.548
2.147
33.669


1.668
2.017
33.669


1.788
1.886
33.669


1.908
1.756
33.669


2.029
1.626
33.669


2.149
1.496
33.669


2.269
1.366
33.669


2.390
1.236
33.669


2.511
1.107
33.669


2.631
0.977
33.669


2.752
0.847
33.669


2.873
0.717
33.669


2.994
0.588
33.669


3.114
0.458
33.669


3.234
0.328
33.669


3.354
0.197
33.669


3.474
0.066
33.669


3.593
−0.065
33.669


3.712
−0.196
33.669


3.830
−0.329
33.669


3.947
−0.461
33.669


4.064
−0.595
33.669


4.180
−0.729
33.669


4.295
−0.863
33.669


4.409
−0.999
33.669


4.523
−1.135
33.669


4.636
−1.271
33.669


4.750
−1.407
33.669


4.863
−1.543
33.669


4.976
−1.679
33.669


5.090
−1.816
33.669


5.203
−1.952
33.669


5.317
−2.087
33.669


5.432
−2.223
33.669


5.546
−2.358
33.669


5.661
−2.493
33.669


5.777
−2.627
33.669


5.892
−2.761
33.669


5.942
−2.819
33.669


5.950
−2.828
33.669


5.958
−2.837
33.669


5.966
−2.847
33.669


5.972
−2.857
33.669


5.973
−2.869
33.669


5.970
−2.881
33.669


5.962
−2.890
33.669


5.951
−2.895
33.669


5.939
−2.895
33.669


5.928
−2.890
33.669


5.918
−2.883
33.669


5.908
−2.875
33.669


5.898
−2.868
33.669


5.837
−2.823
33.669


5.694
−2.717
33.669


5.552
−2.609
33.669


5.413
−2.498
33.669


5.276
−2.384
33.669


5.140
−2.269
33.669


5.006
−2.151
33.669


4.874
−2.031
33.669


4.744
−1.909
33.669


4.616
−1.786
33.669


4.490
−1.660
33.669


4.366
−1.532
33.669


4.243
−1.403
33.669


4.121
−1.273
33.669


4.001
−1.142
33.669


3.882
−1.009
33.669


3.763
−0.876
33.669


3.646
−0.742
33.669


3.529
−0.608
33.669


3.412
−0.473
33.669


3.296
−0.338
33.669


3.180
−0.203
33.669


3.064
−0.067
33.669


2.950
0.069
33.669


2.835
0.206
33.669


2.722
0.343
33.669


2.609
0.481
33.669


2.497
0.619
33.669


2.386
0.759
33.669


2.275
0.898
33.669


2.165
1.038
33.669


2.056
1.179
33.669


1.948
1.321
33.669


1.840
1.462
33.669


1.733
1.605
33.669


1.626
1.748
33.669


1.521
1.891
33.669


1.416
2.035
33.669


1.312
2.180
33.669


1.208
2.325
33.669


1.106
2.471
33.669


1.004
2.617
33.669


0.902
2.763
33.669


0.895
2.888
35.029


0.888
2.899
35.029


0.880
2.910
35.029


0.874
2.921
35.029


0.868
2.933
35.029


0.864
2.946
35.029


0.864
2.959
35.029


0.874
2.966
35.029


0.886
2.962
35.029


0.897
2.955
35.029


0.907
2.945
35.029


0.915
2.935
35.029


0.924
2.925
35.029


0.932
2.914
35.029


0.980
2.856
35.029


1.091
2.719
35.029


1.202
2.583
35.029


1.314
2.447
35.029


1.427
2.311
35.029


1.540
2.176
35.029


1.654
2.041
35.029


1.768
1.907
35.029


1.883
1.773
35.029


1.997
1.639
35.029


2.112
1.505
35.029


2.227
1.372
35.029


2.342
1.238
35.029


2.458
1.105
35.029


2.573
0.972
35.029


2.689
0.839
35.029


2.805
0.706
35.029


2.921
0.573
35.029


3.036
0.440
35.029


3.151
0.306
35.029


3.265
0.172
35.029


3.380
0.038
35.029


3.493
−0.097
35.029


3.606
−0.233
35.029


3.717
−0.369
35.029


3.829
−0.506
35.029


3.939
−0.643
35.029


4.049
−0.781
35.029


4.157
−0.920
35.029


4.265
−1.059
35.029


4.372
−1.199
35.029


4.479
−1.340
35.029


4.585
−1.480
35.029


4.691
−1.621
35.029


4.797
−1.762
35.029


4.903
−1.903
35.029


5.009
−2.043
35.029


5.116
−2.184
35.029


5.223
−2.324
35.029


5.330
−2.464
35.029


5.437
−2.604
35.029


5.545
−2.743
35.029


5.653
−2.882
35.029


5.699
−2.942
35.029


5.707
−2.951
35.029


5.714
−2.961
35.029


5.721
−2.970
35.029


5.727
−2.980
35.029


5.728
−2.992
35.029


5.724
−3.003
35.029


5.716
−3.011
35.029


5.705
−3.015
35.029


5.693
−3.014
35.029


5.683
−3.008
35.029


5.674
−3.001
35.029


5.665
−2.993
35.029


5.656
−2.986
35.029


5.598
−2.937
35.029


5.464
−2.822
35.029


5.332
−2.705
35.029


5.201
−2.585
35.029


5.072
−2.464
35.029


4.945
−2.341
35.029


4.820
−2.215
35.029


4.697
−2.088
35.029


4.576
−1.960
35.029


4.456
−1.829
35.029


4.339
−1.697
35.029


4.223
−1.563
35.029


4.108
−1.428
35.029


3.995
−1.293
35.029


3.882
−1.156
35.029


3.771
−1.018
35.029


3.660
−0.880
35.029


3.549
−0.742
35.029


3.439
−0.604
35.029


3.329
−0.465
35.029


3.219
−0.327
35.029


3.109
−0.188
35.029


2.999
−0.049
35.029


2.890
0.090
35.029


2.781
0.229
35.029


2.672
0.369
35.029


2.564
0.509
35.029


2.457
0.650
35.029


2.350
0.791
35.029


2.244
0.932
35.029


2.139
1.075
35.029


2.034
1.217
35.029


1.930
1.360
35.029


1.827
1.504
35.029


1.725
1.649
35.029


1.623
1.794
35.029


1.523
1.939
35.029


1.423
2.085
35.029


1.324
2.232
35.029


1.226
2.379
35.029


1.128
2.527
35.029


1.032
2.675
35.029


0.936
2.824
35.029


0.896
2.970
36.429


0.890
2.980
36.429


0.884
2.991
36.429


0.878
3.001
36.429


0.873
3.012
36.429


0.870
3.024
36.429


0.870
3.036
36.429


0.879
3.043
36.429


0.891
3.038
36.429


0.900
3.031
36.429


0.908
3.022
36.429


0.915
3.012
36.429


0.923
3.002
36.429


0.930
2.992
36.429


0.974
2.931
36.429


1.077
2.790
36.429


1.182
2.649
36.429


1.287
2.508
36.429


1.392
2.368
36.429


1.499
2.229
36.429


1.606
2.091
36.429


1.714
1.953
36.429


1.823
1.815
36.429


1.932
1.678
36.429


2.042
1.541
36.429


2.152
1.405
36.429


2.263
1.268
36.429


2.374
1.133
36.429


2.485
0.997
36.429


2.596
0.861
36.429


2.707
0.726
36.429


2.818
0.590
36.429


2.929
0.454
36.429


3.039
0.317
36.429


3.148
0.180
36.429


3.256
0.042
36.429


3.364
−0.096
36.429


3.471
−0.235
36.429


3.577
−0.375
36.429


3.682
−0.515
36.429


3.786
−0.656
36.429


3.890
−0.798
36.429


3.992
−0.940
36.429


4.094
−1.083
36.429


4.194
−1.226
36.429


4.294
−1.370
36.429


4.394
−1.515
36.429


4.493
−1.659
36.429


4.592
−1.804
36.429


4.691
−1.949
36.429


4.790
−2.093
36.429


4.890
−2.238
36.429


4.989
−2.382
36.429


5.089
−2.526
36.429


5.190
−2.670
36.429


5.290
−2.814
36.429


5.390
−2.958
36.429


5.433
−3.019
36.429


5.440
−3.029
36.429


5.446
−3.038
36.429


5.453
−3.048
36.429


5.458
−3.058
36.429


5.459
−3.069
36.429


5.454
−3.080
36.429


5.446
−3.088
36.429


5.435
−3.091
36.429


5.424
−3.089
36.429


5.415
−3.083
36.429


5.407
−3.075
36.429


5.398
−3.067
36.429


5.390
−3.059
36.429


5.336
−3.007
36.429


5.211
−2.883
36.429


5.087
−2.759
36.429


4.965
−2.632
36.429


4.845
−2.503
36.429


4.727
−2.373
36.429


4.610
−2.241
36.429


4.496
−2.108
36.429


4.383
−1.973
36.429


4.272
−1.837
36.429


4.163
−1.699
36.429


4.055
−1.560
36.429


3.948
−1.420
36.429


3.842
−1.280
36.429


3.738
−1.139
36.429


3.633
−0.997
36.429


3.530
−0.855
36.429


3.426
−0.713
36.429


3.322
−0.572
36.429


3.218
−0.430
36.429


3.114
−0.288
36.429


3.010
−0.147
36.429


2.906
−0.005
36.429


2.801
0.137
36.429


2.697
0.278
36.429


2.593
0.420
36.429


2.490
0.562
36.429


2.386
0.704
36.429


2.284
0.847
36.429


2.181
0.990
36.429


2.080
1.134
36.429


1.979
1.278
36.429


1.879
1.422
36.429


1.780
1.568
36.429


1.682
1.714
36.429


1.585
1.860
36.429


1.489
2.007
36.429


1.394
2.155
36.429


1.300
2.304
36.429


1.208
2.453
36.429


1.116
2.603
36.429


1.025
2.754
36.429


0.935
2.905
36.429


0.855
3.141
37.749


0.834
3.181
37.749


0.851
3.205
37.749


0.879
3.170
37.749


1.122
2.803
37.749


1.525
2.225
37.749


1.946
1.659
37.749


2.376
1.100
37.749


2.804
0.540
37.749


3.221
−0.028
37.749


3.622
−0.608
37.749


4.007
−1.198
37.749


4.381
−1.796
37.749


4.752
−2.396
37.749


5.126
−2.994
37.749


5.184
−3.087
37.749


5.176
−3.126
37.749


5.138
−3.110
37.749


4.953
−2.906
37.749


4.499
−2.366
37.749


4.074
−1.802
37.749


3.671
−1.222
37.749


3.279
−0.635
37.749


2.885
−0.049
37.749


2.486
0.534
37.749


2.088
1.117
37.749


1.698
1.706
37.749


1.326
2.306
37.749


0.976
2.919
37.749


0.850
3.151
37.749


0.832
3.192
37.749


0.860
3.198
37.749


0.886
3.160
37.749


1.221
2.657
37.749


1.629
2.082
37.749


2.053
1.519
37.749


2.483
0.961
37.749


2.910
0.399
37.749


3.323
−0.172
37.749


3.720
−0.755
37.749


4.102
−1.347
37.749


4.474
−1.946
37.749


4.846
−2.545
37.749


5.166
−3.058
37.749


5.188
−3.097
37.749


5.165
−3.129
37.749


5.130
−3.102
37.749


4.837
−2.774
37.749


4.390
−2.227
37.749


3.972
−1.658
37.749


3.573
−1.075
37.749


3.181
−0.488
37.749


2.785
0.097
37.749


2.386
0.679
37.749


1.989
1.263
37.749


1.603
1.855
37.749


1.237
2.458
37.749


0.891
3.074
37.749


0.844
3.161
37.749


0.832
3.204
37.749


0.867
3.189
37.749


0.927
3.097
37.749


1.321
2.512
37.749


1.734
1.941
37.749


2.160
1.379
37.749


2.591
0.821
37.749


3.014
0.257
37.749


3.423
−0.317
37.749


3.817
−0.902
37.749


4.195
−1.497
37.749


4.567
−2.096
37.749


4.939
−2.695
37.749


5.172
−3.067
37.749


5.189
−3.108
37.749


5.154
−3.126
37.749


5.122
−3.094
37.749


4.723
−2.639
37.749


4.283
−2.087
37.749


3.871
−1.513
37.749


3.475
−0.929
37.749


3.083
−0.341
37.749


2.686
0.243
37.749


2.286
0.825
37.749


1.891
1.410
37.749


1.509
2.004
37.749


1.149
2.611
37.749


0.839
3.171
37.749


0.841
3.210
37.749


0.873
3.179
37.749


1.024
2.950
37.749


1.423
2.368
37.749


1.839
1.799
37.749


2.268
1.240
37.749


2.698
0.681
37.749


3.118
0.115
37.749


3.523
−0.462
37.749


3.913
−1.050
37.749


4.288
−1.647
37.749


4.659
−2.246
37.749


5.033
−2.844
37.749


5.178
−3.077
37.749


5.184
−3.118
37.749


5.145
−3.119
37.749


5.071
−3.038
37.749


4.610
−2.503
37.749


4.178
−1.945
37.749


3.771
−1.368
37.749


3.377
−0.782
37.749


2.984
−0.195
37.749


2.586
0.388
37.749


2.187
0.971
37.749


1.794
1.558
37.749


1.417
2.155
37.749


1.062
2.765
37.749


0.767
3.476
39.239


0.763
3.485
39.239


0.758
3.495
39.239


0.754
3.505
39.239


0.750
3.515
39.239


0.748
3.525
39.239


0.748
3.536
39.239


0.756
3.541
39.239


0.766
3.536
39.239


0.773
3.529
39.239


0.779
3.520
39.239


0.785
3.511
39.239


0.790
3.501
39.239


0.795
3.492
39.239


0.834
3.425
39.239


0.925
3.270
39.239


1.017
3.116
39.239


1.111
2.962
39.239


1.207
2.809
39.239


1.304
2.658
39.239


1.403
2.507
39.239


1.503
2.358
39.239


1.605
2.210
39.239


1.708
2.062
39.239


1.812
1.915
39.239


1.917
1.769
39.239


2.022
1.622
39.239


2.127
1.476
39.239


2.231
1.329
39.239


2.335
1.182
39.239


2.439
1.035
39.239


2.541
0.887
39.239


2.643
0.738
39.239


2.743
0.589
39.239


2.843
0.439
39.239


2.941
0.288
39.239


3.038
0.136
39.239


3.134
−0.016
39.239


3.228
−0.169
39.239


3.322
−0.323
39.239


3.415
−0.477
39.239


3.506
−0.632
39.239


3.597
−0.788
39.239


3.686
−0.944
39.239


3.775
−1.101
39.239


3.862
−1.258
39.239


3.949
−1.416
39.239


4.035
−1.574
39.239


4.121
−1.733
39.239


4.206
−1.891
39.239


4.292
−2.049
39.239


4.378
−2.208
39.239


4.463
−2.366
39.239


4.549
−2.524
39.239


4.635
−2.683
39.239


4.721
−2.841
39.239


4.806
−2.999
39.239


4.843
−3.067
39.239


4.848
−3.077
39.239


4.854
−3.087
39.239


4.859
−3.097
39.239


4.863
−3.107
39.239


4.863
−3.118
39.239


4.858
−3.128
39.239


4.849
−3.135
39.239


4.838
−3.137
39.239


4.828
−3.134
39.239


4.820
−3.126
39.239


4.813
−3.117
39.239


4.806
−3.108
39.239


4.799
−3.099
39.239


4.751
−3.039
39.239


4.640
−2.897
39.239


4.531
−2.753
39.239


4.424
−2.609
39.239


4.319
−2.462
39.239


4.215
−2.315
39.239


4.114
−2.166
39.239


4.015
−2.016
39.239


3.917
−1.864
39.239


3.820
−1.712
39.239


3.725
−1.559
39.239


3.631
−1.405
39.239


3.538
−1.251
39.239


3.446
−1.096
39.239


3.355
−0.941
39.239


3.264
−0.786
39.239


3.172
−0.630
39.239


3.081
−0.475
39.239


2.989
−0.320
39.239


2.897
−0.165
39.239


2.804
−0.011
39.239


2.711
0.143
39.239


2.617
0.297
39.239


2.523
0.451
39.239


2.428
0.604
39.239


2.333
0.757
39.239


2.238
0.910
39.239


2.142
1.062
39.239


2.046
1.215
39.239


1.950
1.367
39.239


1.854
1.520
39.239


1.759
1.673
39.239


1.665
1.826
39.239


1.571
1.980
39.239


1.479
2.135
39.239


1.388
2.291
39.239


1.299
2.447
39.239


1.212
2.605
39.239


1.127
2.763
39.239


1.043
2.923
39.239


0.961
3.083
39.239


0.880
3.244
39.239


0.801
3.406
39.239


0.675
3.852
40.559


0.671
3.861
40.559


0.667
3.870
40.559


0.663
3.880
40.559


0.660
3.889
40.559


0.658
3.899
40.559


0.659
3.909
40.559


0.667
3.913
40.559


0.675
3.908
40.559


0.681
3.901
40.559


0.687
3.892
40.559


0.691
3.884
40.559


0.696
3.875
40.559


0.700
3.866
40.559


0.737
3.796
40.559


0.824
3.632
40.559


0.913
3.470
40.559


1.003
3.309
40.559


1.096
3.149
40.559


1.191
2.991
40.559


1.288
2.833
40.559


1.387
2.677
40.559


1.487
2.522
40.559


1.589
2.367
40.559


1.691
2.213
40.559


1.793
2.060
40.559


1.896
1.906
40.559


1.998
1.752
40.559


2.099
1.597
40.559


2.200
1.442
40.559


2.299
1.286
40.559


2.397
1.129
40.559


2.494
0.972
40.559


2.589
0.813
40.559


2.683
0.654
40.559


2.776
0.494
40.559


2.867
0.334
40.559


2.957
0.172
40.559


3.046
0.010
40.559


3.133
−0.153
40.559


3.219
−0.316
40.559


3.305
−0.480
40.559


3.389
−0.645
40.559


3.473
−0.810
40.559


3.555
−0.975
40.559


3.636
−1.141
40.559


3.716
−1.308
40.559


3.796
−1.475
40.559


3.875
−1.642
40.559


3.954
−1.809
40.559


4.033
−1.976
40.559


4.112
−2.143
40.559


4.190
−2.311
40.559


4.269
−2.478
40.559


4.348
−2.645
40.559


4.427
−2.812
40.559


4.505
−2.979
40.559


4.539
−3.051
40.559


4.544
−3.061
40.559


4.548
−3.072
40.559


4.553
−3.082
40.559


4.557
−3.092
40.559


4.557
−3.103
40.559


4.552
−3.113
40.559


4.543
−3.120
40.559


4.531
−3.121
40.559


4.521
−3.117
40.559


4.514
−3.108
40.559


4.508
−3.099
40.559


4.501
−3.090
40.559


4.495
−3.080
40.559


4.449
−3.015
40.559


4.345
−2.863
40.559


4.242
−2.709
40.559


4.142
−2.554
40.559


4.043
−2.398
40.559


3.946
−2.240
40.559


3.852
−2.081
40.559


3.759
−1.922
40.559


3.668
−1.761
40.559


3.578
−1.599
40.559


3.490
−1.437
40.559


3.402
−1.274
40.559


3.316
−1.111
40.559


3.230
−0.947
40.559


3.145
−0.783
40.559


3.060
−0.619
40.559


2.975
−0.455
40.559


2.890
−0.291
40.559


2.804
−0.127
40.559


2.718
0.037
40.559


2.631
0.200
40.559


2.544
0.363
40.559


2.456
0.525
40.559


2.367
0.687
40.559


2.277
0.849
40.559


2.187
1.010
40.559


2.096
1.171
40.559


2.004
1.332
40.559


1.912
1.492
40.559


1.820
1.652
40.559


1.727
1.812
40.559


1.635
1.972
40.559


1.543
2.132
40.559


1.451
2.293
40.559


1.361
2.454
40.559


1.272
2.616
40.559


1.185
2.779
40.559


1.100
2.944
40.559


1.018
3.109
40.559


0.937
3.275
40.559


0.858
3.442
40.559


0.781
3.610
40.559


0.707
3.780
40.559









Embodiment 1. A compressor component comprising a root portion; and an airfoil portion extending from the root portion, the airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, form an airfoil shape.


Embodiment 2. The compressor component of embodiment 1, wherein the root portion and the airfoil portion form at least part of a compressor blade.


Embodiment 3. The compressor component of any of embodiments 1-2, wherein the root portion is configured to couple with a first stage rotor disc of a compressor.


Embodiment 4. The compressor component of any of embodiments 1-3, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 5. The compressor component of any of embodiments 1-4, wherein the airfoil shape lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 6. The compressor component of any of embodiments 1-5, wherein the airfoil shape lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 7. The compressor component of any of embodiments 1-6, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinate values listed in Table 1.


Embodiment 8. The compressor component of any of embodiments 1-7, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.


Embodiment 9. A compressor blade, comprising an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.


Embodiment 10. The compressor blade of embodiment 9, wherein the X and Y coordinate values are scalable as a function of a same constant or number and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.


Embodiment 11. The compressor blade of any of embodiments 9-10, wherein the compressor blade is configured to couple with rotor discs having different sized radiuses, wherein the Z coordinate values set forth in Table 1 are offset by a distance equal to the difference in rotor disc radius to provide at least one of a radially outwardly offset or radially inwardly offset airfoil shape.


Embodiment 12. The compressor blade of any of embodiments 9-11, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 13. The compressor blade of any of embodiments 9-12, wherein the airfoil shape provides the compressor blade with a first bending natural frequency between 130 Hz and 160 Hz when scaled for use in a compressor with a 60 Hz rotation speed.


Embodiment 14. The compressor blade of any of embodiments 9-13, wherein the airfoil shape provides the compressor blade with a second bending natural frequency that differs by at least 5% from 5th, 6th, and 7th engine order excitations.


Embodiment 15. The compressor blade of any of embodiments 9-14, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinate values listed in Table 1.


Embodiment 16. The compressor blade of any of embodiments 9-16, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.


Embodiment 17. A compressor, comprising a casing; a rotor disc positioned within the casing; and a plurality of compressor blades coupled to the rotor disc, the plurality of compressor blades circumferentially spaced around the rotor disc about a center axis of the compressor, wherein each compressor blade of the plurality of compressor blades has an airfoil comprising an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.


Embodiment 18. The compressor of embodiment 17, wherein the rotor disc and the plurality of compressor blades form a compressor stage zero.


Embodiment 19. The compressor of any of embodiments 17-18, wherein the airfoil shape lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 20. The compressor of any of embodiments 17-19, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinate values listed in Table 1


Embodiment 21. An airfoil, comprising an airfoil profile substantially in accordance with the X, Y, and Z coordinates listed in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.


Embodiment 22. The airfoil of embodiment 21, wherein the airfoil is part of a blade of a gas turbine engine.


Embodiment 23. The airfoil of any of embodiments 21-22, wherein the blade is a compressor blade.


Embodiment 24. The airfoil of any of embodiments 21-23, wherein the airfoil shape lies within an envelope of +/−0.160 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 25. The airfoil of any of embodiments 21-24, wherein the airfoil shape lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 26. The airfoil of any of embodiments 21-25, wherein the airfoil shape lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 27. The airfoil of any of embodiments 21-26, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinates listed in Table 1.


Embodiment 28. The airfoil of any of embodiments 21-27, wherein the airfoil comprises a coating.


Embodiment 29. A gas turbine engine blade, comprising an airfoil portion, comprising an airfoil profile substantially in accordance with the X, Y, and Z coordinates listed in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.


Embodiment 30. The gas turbine engine blade of embodiment 29, wherein the airfoil shape defines an airfoil portion of a compressor blade.


Embodiment 31. The gas turbine engine blade of any of embodiments 29-30, wherein the gas turbine engine blade is one of a plurality of gas turbine engine blades that are assembled about an axis of a gas turbine to form an assembled gas turbine engine stage.


Embodiment 32. The gas turbine engine blade of any of embodiments 29-31, wherein the airfoil shape lies within an envelope of +/−0.160 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 33. The gas turbine engine blade of any of embodiments 29-32, wherein the airfoil shape lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 34. The gas turbine engine blade of any of embodiments 29-33, wherein the airfoil shape lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 35. The gas turbine engine blade of any of embodiments 29-34, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinates listed in Table 1.


Embodiment 36. The gas turbine engine blade of any of embodiments 29-35, wherein the airfoil comprises a coating.


Embodiment 37. A gas turbine engine, comprising a plurality of gas turbine engine blades circumferentially assembled about a center axis of the gas turbine engine, wherein at least one of the plurality of gas turbine engine blades has an airfoil comprising an airfoil profile substantially in accordance with the X, Y, and Z coordinates listed in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.


Embodiment 38. The gas turbine engine of embodiment 37, wherein the plurality of gas turbine engine blades form an assembled compressor stage.


Embodiment 39. The gas turbine engine of any of embodiments 37-38, wherein the airfoil shape lies within an envelope of +/−0.160 inches measured in a direction normal to any of the plurality of airfoil profile sections.


Embodiment 40. The gas turbine engine of any of embodiments 37-39, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinates listed in Table 1.


Embodiment 41. Any of the aforementioned embodiments 1-40, in any combination.


The subject matter of this disclosure has been described in relation to particular embodiments, which are intended in all respects to be illustrative rather than restrictive. Alternative embodiments will become apparent to those of ordinary skill in the art to which the present subject matter pertains without departing from the scope hereof. Different combinations of elements, as well as use of elements not shown, are also possible and contemplated.

Claims
  • 1. A compressor component comprising: a root portion; andan airfoil portion extending from the root portion, the airfoil portion having an uncoated nominal profile in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system,wherein at each Z distance, corresponding X and Y coordinates are connected by a smooth continuous arc to define one of a plurality of airfoil profile sections, andwherein the plurality of airfoil profile sections are joined together by smooth continuous arcs to form the airfoil profile.
  • 2. The compressor component of claim 1, wherein the root portion and the airfoil portion form at least part of a compressor blade.
  • 3. The compressor component of claim 1, wherein the root portion is configured to couple with a first stage rotor disc of a compressor.
  • 4. The compressor component of claim 1, wherein the airfoil profile lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
  • 5. The compressor component of claim 1, wherein the airfoil profile lies within an envelope of +/−0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.
  • 6. The compressor component of claim 1, wherein the airfoil profile lies within an envelope of +/−0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.
  • 7. The compressor component of claim 1, further comprising a coating applied to the airfoil profile, the coating having a thickness of less than or equal to 0.010 inches.
  • 8. A compressor blade, comprising: an airfoil portion having an uncoated nominal profile in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system,wherein at each Z distance, corresponding X and Y coordinates are connected by a smooth continuous arc to define one of a plurality of airfoil profile sections, andwherein the plurality of airfoil profile sections are joined together by smooth continuous arcs to define the airfoil profile.
  • 9. The compressor blade of claim 8, wherein the X and Y coordinate values are scalable as a function of a same constant or number and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.
  • 10. The compressor blade of claim 9, wherein the compressor blade is configured to couple with rotor discs having different sized radiuses, wherein the Z coordinate values set forth in Table 1 are offset by a distance equal to a difference in rotor disc radius to provide at least one of a radially outward offset or radially inward offset airfoil shape.
  • 11. The compressor blade of claim 8, wherein the airfoil profile lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
  • 12. The compressor blade of claim 8, wherein the airfoil profile provides the compressor blade with a first bending natural frequency between 130 Hz and 160 Hz when scaled for use in a compressor with a 60 Hz rotation speed.
  • 13. The compressor blade of claim 8, wherein the airfoil profile provides the compressor blade with a second bending natural frequency that differs by at least 5% from 5th, 6th, and 7th engine order excitations.
  • 14. The compressor blade of claim 8, further comprising a coating applied to the airfoil profile, the coating having a thickness of less than or equal to 0.010 inches.
  • 15. A compressor, comprising: a casing;a rotor disc positioned within the casing; anda plurality of compressor blades coupled to the rotor disc, the plurality of compressor blades circumferentially spaced around the rotor disc about a center axis of the compressor, wherein each compressor blade of the plurality of compressor blades has an airfoil comprising: an airfoil portion having an uncoated nominal profile in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system,wherein at each Z distance, corresponding X and Y coordinates are connected by a smooth continuous arc to define one of a plurality of airfoil profile sections, andwherein the plurality of airfoil profile sections are joined together by smooth continuous arcs to define the airfoil profile.
  • 16. The compressor of claim 15, wherein the rotor disc and the plurality of compressor blades form a compressor stage zero.
  • 17. The compressor of claim 15, wherein the airfoil profile lies within an envelope of +/−0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.
US Referenced Citations (10)
Number Name Date Kind
7517190 Latimer Apr 2009 B2
7540715 Latimer Jun 2009 B2
8057188 Parker et al. Nov 2011 B2
8113773 Hudson et al. Feb 2012 B2
8192168 Bonini et al. Jun 2012 B2
8556588 Shrum et al. Oct 2013 B2
8591193 Kathika et al. Nov 2013 B2
9523284 Miller et al. Dec 2016 B2
9890790 Miller et al. Feb 2018 B2
10801327 Song Oct 2020 B2