WO2018200088A2

WO2018200088A2 - Systems and methods for determining alignment

Info

Publication number: WO2018200088A2
Application number: PCT/US2018/022076
Authority: WO
Inventors: Phillip Cormier; Clark DEVER; John FUTSCHER; Michael GAZZO; Evan GERTIS; Chris HOEN; Chris LANGFORD; Stephen PETONIAK
Original assignee: Research And Engineering Development, Llc
Priority date: 2017-03-12
Filing date: 2018-03-12
Publication date: 2018-11-01
Also published as: WO2018200088A3

Abstract

The present disclosure describes systems, apparatuses, and methods for aligning surfaces, including aligning a drive shaft. According to certain embodiments, computer vision can be used to determine a differential angle between two surfaces. According to other embodiments, a plurality of inclinometers can determine a differential angle between two surfaces. The disclosure has applications in shipboard maintenance, oil platform maintenance, space, etc.

Description

SYSTEMS AND METHODS FOR DETERMINING ALIGNMENT

Statement Regarding Federally Sponsored Research

[0001] This invention was made with government support under contract no. N68335-16-

2-0083 (HQ0034-15-BAA-RIF-0001) awarded by the Naval Air Warfare Center, Aircraft Division (NAWC/AD) AIR 4.5. The government has certain rights in the invention.

Cross-Reference to Related Applications

[0002] This application claims priority to U.S. Provisional Application No. 62/470,326, filed on March 12, 2017, and U.S. Provisional Application No. 62/470,330, filed on March 12, 2017, now pending, the disclosures of which are incorporated herein by reference in their entirety.

Field of the Disclosure

[0003] The present disclosure relates to aligning surfaces, and in particular, aligning drive shafts.

Background of the Disclosure [0004] Tail rotor drive shaft components must be in alignment for safe operation of a helicopter. Misaligned drive shafts may result in driveline failure, which can cause a crash. For this reason, tail rotor drive shaft components must be checked for alignment to ensure the components are within specifications. Previous alignment check techniques involve measuring a relative angle between different segments of the tail rotor drive shaft using hand-held inclinometers (see Figure 1). The angle across each of four hangar bearings must be measured. The manual nature of the previous techniques require approximately four hours to perform, and must be performed on a static ground plane. For this reason, aircraft that are aboard ships will need to be moved to a static ground plane in order to be checked. The movement of the aircraft to a ground location may take days or weeks. [0005] Accordingly, there is a long-felt need for the ability to perform an alignment check with reduced downtime for the actual check process, as well as the ability to perform the check while in a dynamic environment (e.g., at sea). Brief Summary of the Disclosure

[0006] Some embodiments of the present disclosure leverage computer vision to determine a differential angle between two drive shaft segments. The present measurement system can determine the total misalignment of the shafts, which eliminates the need for estimating the vertical plane. As such, measurements can be made in the absence of a static ground plane. As a result, the presently-disclosed systems and methods have applications in shipboard maintenance, oil platform maintenance, space, etc., and no downtime is incurred to move the aircraft to a ground location.

[0007] According an embodiment of the present disclosure, a shaft alignment apparatus is provided. The shaft alignment apparatus can comprise a first bracket having a display mounted thereon. The first bracket can be configured to be removably attached to a first shaft such that a primary plane of the display panel is substantially perpendicular to the first shaft. The apparatus can include a second bracket having a camera mounted thereon. The second bracket may be configured to be removably attached to a second shaft such that the camera is oriented substantially parallel to the second shaft. The apparatus can also include a processor in electronic communication with the camera and the display panel. The processor may be programmed to display on the display panel a target pattern; capture, using the camera, a plurality of images of the target pattern; calculate a 6DOF position of the camera with respect to the display panel based on the plurality of images; and determine, using the 6DOF position of the camera, an alignment of the first shaft with respect to the second shaft.

[0008] According another embodiment of the present disclosure, a method for shaft alignment is provided. The method can include attaching a display panel to a first shaft using a first bracket. A camera can be attached to a second shaft using a second bracket. At least a portion of the display panel is within a field of view of the camera. A target partem is displayed on the display panel. A plurality of images of the target pattern can be captured using the camera. A 6DOF position of the camera is calculated with respect to the display panel based on the plurality of images. Using the 6DOF position of the camera, an alignment of the first shaft with respect to the second shaft is determined.

[0009] In yet another embodiment, a shaft alignment apparatus is provided. The apparatus can include a reference inclinometer configured to be mounted to a reference platform and to provide a pitch and a roll of a reference plane. A first inclinometer may be configured to be mounted on a first shaft and to provide a pitch and a roll of a first sensor plane. The pitch of the first sensor plane may be equal to a pitch of the first shaft. A second inclinometer can be configured to be mounted on a second shaft and to provide a pitch and a roll of a second sensor plane. The pitch of the first sensor plane may be equal to a pitch of the first shaft. A processor can be in electronic communication with the reference inclinometer, the first inclinometer, and the second inclinometer. The processor can be programmed to: calculate a shaft alignment as a pitch angle between the first shaft and the second shaft based on the pitch and the roll of the reference plane, the first sensor plane, and the second sensor plane; and repeat the alignment calculation over time to determine an average alignment and standard deviation of the alignment until the standard deviation is less than a pre-determined threshold.

[0010] According to another embodiment, a method for shaft alignment is provided. The method can include attaching a reference inclinometer to a reference platform to provide a pitch and a roll of a reference plane. A first inclinometer can be attached to a first shaft to provide a pitch and a roll of a first sensor plane. A second inclinometer can be attached to a second shaft to provide a pitch and roll of a second sensor plane. A shaft alignment pitch angle is calculated between the first shaft and the second shaft based on the pitch and the roll of the reference plane, the first sensor plane, and the second sensor plane. The alignment calculation is repeated over time to determine an average alignment and standard deviation of the alignment until the standard deviation is less than a pre-determined threshold. [0011] Another embodiment of the present disclosure is a drive shaft sensor mount. The mount can include a base member having a first pivot, a second pivot, a sensor, and one or more upper drive shaft engagement surfaces configured to engage a drive shaft in an engaged position. A first arm pivotably can be connected to the first pivot, the first arm including one or more lower drive shaft engagement surfaces configured to engage the drive shaft in the engaged position. A second arm pivotably can be connected to the second pivot, the second arm including one or more lower drive shaft engagement surfaces configured to engage the drive shaft in the engaged position. The first arm and the second arm may be biased into the engaged position by one or more biasing mechanisms. The sensor can be located between the first arm and the second arm. Description of the Drawings

[0012] For a fuller understanding of the nature and objects of the disclosure, reference should be made to the following detailed description taken in conjunction with the

accompanying drawings, in which: Figure 1 depicts a tailboom of a helicopter and portions of a tail rotor drive train;

Figure 2 is a perspective view of an alignment apparatus according to an embodiment of the present disclosure, wherein the alignment apparatus is shown in place on drive shafts; Figure 3A is an exemplary target pattern display on a display panel of an alignment apparatus during calibration;

Figure 3B is a composite pattern generated using the target pattern of Figure 3 A;

Figure 3 C is an exemplary target pattern for display on a display panel used during image capture;

Figure 4 depicts a method according to another embodiment of the present disclosure;

Figure 5 is a perspective view of an alignment apparatus according to another embodiment of the present disclosure;

Figure 6 depicts a method according to another embodiment of the present disclosure;

Figure 7A is a perspective view of a sensor mount system according to another aspect of the present disclosure, wherein the sensor mount system includes a camera;

Figure 7B is a partial view of the sensor mount system of Figure 7A, wherein components have been hidden to better show the internal configuration;

Figure 8 is a perspective view of another sensor mount system wherein a display panel is mounted thereon;

Figure 9 is a schematic showing sensor image points mapped to geometrical image points; Figure 10 shows graphs of the recorded alignment angle (top) and angular rate of change (bottom) over time during a shipboard trial;

Figure 11 shows graphs with detailed portions of the graphs of Figure 10 (zoomed in to the time between 2,380 seconds and 2,600 seconds);

Figure 12 shows graphs with detailed portions of the graphs of Figs. 1 and 11 (zoomed in to the time between 2,459 seconds and 2,478 seconds);

Figure 13 shows graphs with detailed portions of the graphs of Figs. 10-12 (zoomed in to the time between 2,468 seconds and 2,470 seconds); and Figure 14 shows graphs of a laboratory test to evaluate the impact of jitter, wherein the top graph shows alignment angle and the bottom graph shows the angular rate of change.

Detailed Description of the Disclosure

[0013] In a first aspect, the present disclosure may be embodied as a shaft alignment apparatus 100. With reference to Figs. 2 and 8, the shaft alignment apparatus 100 also includes a first bracket 110 having a display panel 112 mounted thereon. The first bracket 110 is configured to be removably attached to a first shaft 90. The first bracket 110 is further configured such that, when mounted to a shaft, the display panel 112 is oriented substantially perpendicular to the shaft— i.e., a primary plane of the display panel 112 is substantially perpendicular to a longitudinal axis of the shaft. By substantially perpendicular, it is intended that the first bracket 110 is configured such that a primary plane of the display panel is within five degrees of the perpendicular to the longitudinal axis of the shaft.

[0014] In an exemplary embodiment, a display panel was selected to have the following characteristics:

Display size < 6.5 in (diagonal)

Brightness > 1000 cd/m2

Pixel pitch > .18

Native resolution 640x480

Contrast ratio > 500: 1

Operating temperature between -20 °C and 55 °C

Readable in sunlight

[0015] The use of a display panel, and in particular, an LCD display panel, provides a number of benefits over previously-used targets (e.g., etched glass, paper, etc.), for example:

[0016] Number of Points, Increased Accuracy: Use of the LCD target display allows the generation and acquisition of grids various sizes. For example, an exemplary target size of

448x544 object points has been successfully used. It has been shown via analysis and simulation the increasing the number of object points increases the accuracy. For example, if the number of points is doubled from 10x 10 to 20x20 then the accuracy of the system doubles. [0017] Illumination: An LCD display is an active light source. In particular, an LCD display panel includes an internal light source and as such does not require external illumination. If shrouded properly, then the light that is introduced to the camera sensor is controlled and predictable. No backlighting or reflective light source is necessary. [0018] Signal Fidelity: The camera sensor processes a light profile for each target pixel that is turned on. These light profiles are uniform, they are essentially the same from target pixel to target pixel. They are also small. This results in a very high repeatability in camera signal pulse measurements (subpixel repeatability of 0.01 sensor pixels has been obtained). This results in a fidelity that could not be obtained with traditional glass spot arrays. [0019] Cost: An LCD display is much cheaper than use of glass engraved spot arrays, which utilize semiconductor engraving techniques.

[0020] Flexibility: The use of a display panel allows for flexibility in the target pattern used. For example, a target pattern used to calibrate the apparatus may be different from a target partem used for measurement purposes. In another example, a target used for measuring a static system (e.g., a system on ground rather than at sea) may be different from a target pattern used for measuring a dynamic system.

[0021] Multi-Purpose: In addition to the primary purpose of displaying target patterns for camera pose determination, the display panel may be used to display information, such as instructions, to an operator. In this way, the time required to perform the alignment process may be further reduced.

[0022] The shaft alignment apparatus 100 includes a second bracket 120 having a camera 122 mounted thereon (see, e.g., Figs. 7A and 7B). The second bracket 120 is configured to be removably attached to a second shaft 95. The second bracket 120 is further configured such that, when mounted to a shaft, the camera 122 is oriented substantially parallel to the shaft— i.e., an optical axis of the camera is substantially parallel to a longitudinal axis of the shaft. By substantially parallel, it is intended that the second bracket 120 is configured to orient the optical axis of the camera 122 to within five degrees of the longitudinal axis of the shaft (inclusive). The camera 122 and the display panel 112 are positioned such that at least a portion of the display panel 112 is within a field of view of the camera 122. [0023] In an exemplary embodiment, a camera was selected to have the following characteristics:

4:3 aspect ratio

Dimensions approximately 29 mm high, 44 mm wide, 57 mm long

Monochromatic

GigE Interface

Shutter range of 20 to 30 s

Gain range of 0 dB to 48 dB

Operating temperature between -20°C and 55°C

Global shutter

C type lens mount

12- or 16-bit image depth

[0024] A processor can be in electronic communication with the camera 122 and the display panel 112. The processor can be programmed to display a target partem on the display partem. For example, the target pattern shown in Fig. 3C may be displayed. Other target patterns may be used. In some embodiments, more than one target pattern is used. Using a display panel 112 allows for different target patterns to be displayed without requiring any movement of the display panel itself. In some embodiments, the display panel 112 may also be used to display instructions to the operator.

[0025] The processor captures a plurality of images of the target pattern with the camera 122. In other words, the processor can be programmed to send a signal to the camera 122 to capture a plurality of images and of the target partem. For example, in an exemplary embodiment used for testing, 40 images were captured over a 20 second period. The processor calculates position of the camera 122 with respect to the display panel 112 based on the plurality of images. The camera position is calculated in six degrees-of-freedom ("6DOF")— x, y, z, pitch, roll, and yaw. For convenience, the following convention will be used through the remainder of this disclosure: the -axis is positive to the front of the shaft, the x-axis is positive to the right (when facing toward the front), the z-axis is positive upwards, pitch is rotation about the x-axis, roll is rotation about the -axis, and yaw is rotation about the z-axis (see Fig. 1).

[0026] Using the 6DOF position of the camera 122, an alignment of the first shaft 90 can be determined with respect to the second shaft 95. [0027] In some embodiments a Perspective N-Point ("PnP") technique is used to determine the 6DOF camera position. In a test system, the camera position was determined using the following process:

[0028] First, the apparatus is calibrated and a camera matrix is determined. The camera matrix includes an estimation of the focal length. This step is further defined below under the head "Exemplary Calibration Procedure."

[0029] Second, a list of known object point coordinates is generated. The list includes the coordinates of the target display pixels that are activated. The coordinates can be readily derived from the known target partem displayed on the display panel and the known pixel pitch (the distance between pixels).

[0030] Third, the images of the target pattern (target pixels) are captured and the list of image point coordinates is obtained relative to the camera sensor plane. There is a one-to-one correspondence between the list of known object point coordinates (step 2 above) and the list of image point coordinates— each object point corresponds to an image point. The object points are the three-dimensional coordinates of the target pixels in a world reference frame, and the image points are the two-dimensional coordinates of the projection of the object points into the sensor plane.

[0031] Fourth, the camera matrix, the object point list, and the image point list are run through a PnP procedure to determine a relative 6DOF position of the camera relative to the display panel. The PnP procedure projects the list of known object points into a list of expected image points. The projection is mediated using the camera matrix and an estimate of the 6DOF camera position. Then, the difference between the expected and actual image points is used to perform a least squares sum on the errors. This process is iterated to generate improved 6DOF estimations (nonlinear optimization routine). The process results in a final estimate of the 6DOF camera position.

Exemplary Calibration Procedure

[0032] The following is an exemplary procedure that may be used to generate calibration tables {see also Fig. 9): • Set the camera and the target display into a calibration test fixture that sets them into substantially an identity orientation and translation (which may include an offset if applicable to the application at hand).

• Obtain an image of a 300x200 target object points at the identity transformation. Repeat the image capture a number of times and averages to increase accuracy. In some embodiments, the target object points comprised four points that may be arranged as shown in Fig. 3A. A number of images may be taken with the four-point target moving around the display of the display panel (i.e., where the four-point partem is displayed at different positions on the display). In this way, a composite reading of the entire display can be made (for example, see Fig. 3B).

• Store the obtained image points in a calibration sensor image point rectangular array.

• Using the identity 6DOF position, project the target object points into a

geometrical image point rectangular array.

• For each point in the image point array, calculate coefficient records in a calibration table array. Calculate the coefficients for both a first degree (linear) and a second degree calibration interpolation.

Example - Calibrating the sensor image points to obtain the geometrical image points

[0033] The following procedure may be used to calibrate each acquired sensor image point to obtain a corresponding geometrical image point:

• Search for the sensor image point and to determine the cell of the calibration sensor image point array in which it is located.

• Use the calibration table coefficients to obtain an estimate of where the point is located in the geometrical image point table. This is a mapping from the sensor image point plane to the geometrical image point plane. This estimate may be obtained via either a first degree (bilinear) interpolation or a second degree interpolation.

[0034] In some embodiments, the processor calculates a 6DOF position of the camera 122 by processing the plurality of images to remove changes caused by a dynamic oscillation of the first shaft and second shaft with respect to each other ("motion nullification"). For example, the processor may be programmed to discard any images of the plurality of images that are blurred due to motion. The processor then calculates the 6DOF camera position based on a first undiscarded image of the plurality of images. The processor repeats the calculation of camera position for additional undiscarded images. The processor averages the calculated 6DOF camera positions and calculates a standard deviation of the averaged 6DOF camera positions. If the calculated standard deviation is above a pre-determined threshold (for example, 0.0025, although other values may be used), the steps of calculating the 6DOF camera position based on a next undiscarded image, averaging the calculated 6DOF positions, and calculating a standard deviation are repeated for at least an additional undiscarded image. If the standard deviation is determined to be below a pre-determined threshold, then the processing of images to determine camera position is stopped. Other motion nullification processes may be used and a test embodiment is further described below.

Motion Nullification Angular Rates [0035] An exemplary alignment apparatus should be able to estimate the relative alignment angle between drive shaft segments while a helicopter is subjected to shipboard motion. As such, the instantaneous alignment angle will change over time and that the estimation algorithms must do some type of smart averaging. The accuracy of such smart averaging will depend on the angular rates that will be encountered. Smart Averaging

Smart averaging may include:

• detecting if captured image points have been blurred due to high angular rates and if so, then discarding them;

• averaging the six components of calculated camera positions; and

· terminating the averaging when its standard deviation falls below a threshold.

Analysis of Shipboard Trial Data

[0036] An analysis of relevant recorded data from a shipboard trial was performed with the purpose of determining typical angular rates that will be encountered. It was determined that the most likely worst case rate that was 0.3 degrees/second. The smart averaging algorithms are designed to ignore outliers that are caused by higher rates.

[0037] Figs. 10-13 provide representative plots from the shipboard trial hour 59, which was the worst encountered. These plots provide an idea of the magnitude of the variation and frequency that may be encountered when at sea.

Mathematical Jitter Analysis

[0038] A mathematical analysis of the jitter that will be caused in a camera sensor pulse measurement was performed. The jitter is a measure of how much a pulse will be blurred by angular motion. It is analogous to pulse jitter that is seen on an oscilloscope in the time domain, but here the pulses are in the spatial domain. This analysis was based on the angular rate of 0.3 degrees/second, a camera focal length of 13 mm, a camera exposure time of 50 ms, and a camera sensor size of 2048x2448 pixels.

[0039] The jitter analysis estimates a deviation of only one sensor pixel blurring. A typical pulse measurement point estimation involves a centroid calculation of 190 samples, so this deviation due to motion blurring should be negligible.

Laboratory Measurements

[0040] A motor and cam were attached to a test jig and measurements were performed with an angular rate amplitude of 0.3 degrees/second. Images of a UGrid target were captured and pulse statistics were compared with images captures under static conditions. It was found that the static and dynamic cases were indistinguishable {see Fig. 14).

[0041] Color information may be used (e.g., color pixels of the display panel and/or sensor). In some embodiments, only one color is used. For example, in some embodiments, only the blue pixels of the camera and the display panel are used.

[0042] With reference to Fig. 4, another embodiment of the present disclosure is a method 200 for shaft alignment, including attaching 203 a display panel to a first shaft using a first bracket. A camera is attached 206 to a second shaft using a second bracket. The display panel and camera are attached such that at least a portion of the display panel is within a field of view of the camera. A target pattern is displayed 209 on the display panel. The camera is used to capture 212 a plurality of images of the target pattern. A 6DOF position of the camera (with respect to the display panel) is calculated 215 based on the plurality of images. An alignment of the first shaft with respect to the second shaft is determined 218 using the calculated 215 6DOF position of the camera. [0043] In some embodiments, images that are blurred due to motion are discarded 224.

The 6DOF position is determined 227 based on a first undiscarded image. The step of determining a 6DOF camera position is repeated 230 for additional undiscarded images until a standard deviation of the determined positions is below a pre-determined threshold.

[0044] In another embodiment of the present disclosure (see Fig. 5), a shaft alignment apparatus 300 utilizes inclinometers to determine a pitch angle between a first shaft 90 and a second shaft 95. It is known that an inclinometer will measure tilt angles between the inclinometer (i.e., the object to which is attached) and a gravitational horizontal plane. Two-axis inclinometers provide values corresponding to pitch ("TiltX"— rotation about the x-axis) and roll ("TiltY"— rotation about the -axis). TiltX is the angle between the gravitational horizontal plane and the sensor -axis. TiltX is positive when the positive y-axis moves upward. TiltY is the angle between the gravitational horizontal plane and the sensor x-axis. TiltY is positive when the positive x-axis moves downward.

[0045] In inclinometer-based embodiments, the shaft alignment apparatus 300 includes a reference inclinometer 310 configured to be mounted to a reference platform 99. The reference platform 99 can be a platform that is in mechanical communication with both the first shaft 90 and the second shaft 95 (e.g. a deck of a vessel). The reference inclinometer 310 is configured to provide a pitch and a roll of a reference plane, h.

[0046] The shaft alignment apparatus 300 further includes a first inclinometer 320 configured to be mounted to a first shaft 90. The first inclinometer 320 is configured to provide a pitch and a roll of a first sensor plane, a. The pitch of the first sensor plane, a, is equal to a pitch of the first shaft 90. On the other hand, due to the nature of mounting an inclinometer to a shaft, a roll value measured by the first inclinometer 320 may not be the same as a roll of the first shaft 90.

[0047] The shaft alignment apparatus 300 further includes a second inclinometer 330 configured to be mounted to a second shaft 95. The second inclinometer 330 is configured to provide a pitch and a roll of a second sensor plane, b. The pitch of the second sensor plane, b, is equal to a pitch of the second shaft 95. As above, a roll value measured by the second inclinometer 330 may not be the same as a roll of the second shaft 95.

[0048] The shaft alignment apparatus 300 has a processor in electronic communication with the reference inclinometer, the first inclinometer, and the second inclinometer. The processor is programmed to calculate a shaft alignment as a pitch angle between the first shaft 90 and the second shaft 95 based on the pitch and the roll of the reference plane, h, the first sensor plane, a, and the second sensor plane, b. The calculation of alignment may be repeated by the processor over time to determine an average alignment and standard deviation of the alignment. The calculation is repeated until the calculated standard deviation is below a pre-determined threshold as described above.

Discussion of Inclinometer Calculations for Helicopter Shaft Application

Notation for Coordinate Systems, Vectors, and Bases

[0049] The underlying structure used here is that of a vector space on R³ and is used to characterize coordinate systems and rotations in a Euclidean space. Different coordinate systems correspond to different sets of basis vectors defined for the vector space. Coordinate systems are symbolized with the indexed symbols S₀, S_t, S₂, etc.

[0050] Coordinate systems are defined by their basis vectors, which use the symbols:

[0051] Vectors are related to basis vectors via their components:

[0052] The components of a vector, in a given basis, are symbolized by column matrices:

The components, in the S₁ basis, of the vector

The components of a basis vector, in a given basis, are also symbolized by

The components, in the S₀ basis, of the basis vector

The components, in the S₁ basis, of the basis vector

Notation for Rotations and Rotation Matrices

[0054] Rotations are defined as linear operators that act on basis vectors in a certain way: is a linear operator in component free notation.

[0055] Rotations as linear operators have matrix representations:

Transformation of vector components

[0056] Rotation matrices are used to transform the components of a vector from one coordinate system to another. This is known as a passive or alias transformation (as opposed to an active or alibi transformation). For example, given a rotation matrix R₀₁ in standard form, and given the components of a vector in the S₀ and S-^ coordinate systems (the components of a single vector in two different coordinate systems) then the vector components are related as follows:

Also:

Where:

And:

where V_a and V_b are the components of

in S_a and S_b. The matrix R_ab is used to transform components between the two coordinate systems. The components of R_ab are relative to the S, basis.

[0057] For the following, R₀₁ is the matrix with components such that the columns of the matrix contain the components of the S_t basis vectors relative to the S₀ basis:

Such that:

Or, for example:

[0058] Also note that R₀i has components that are the direction cosines between the two sets of basis vectors:

Successive Transformations

[0059] Sequences of rotations are realized via rotation matrix multiplications. For example, consider a sequence of three rotations involving four different coordinate systems: S₀, S- , S₂, S₃. Here, S₀ is rotated to obtain 5_1; Sy is rotated to obtain S₂, and S₂ is rotated to obtain S₃. The components of a vector V, relative to the different bases, are transformed as follows:

[0060] These can be combined:

[0061] With inverse:

Rotations About Body Axes

[0062] Rotations about body axes are represented by the following rotation matrices.

These are rotations where the axis of rotation is a basis vector and the angle of rotation is a given angle.

[0063] Also note:

the inverse of a rotation about

Similarity Transformations of matrix components for Linear Operators

[0064] Rotation matrices are used to transform the components of a matrix from one coordinate system to another. Here, the matrix is a representation of some linear operator. For example, given a rotation matrix R₀₁ in standard form, and given the components of a matrix in the S₀ and S-^ coordinate systems (the components of the matrix representation of some linear operator in two different coordinate systems) then the matrix components are related as follows:

Also:

[0065] If a linear operator is represented in S₀ and S-^ by the matrices A₀ and A₁ then,

for some vectors

And, if

So

Where

Sensor Gravity Normal Vector

[0066] The sensor measures tilt angles with respect to an artificial gravitational horizontal plane. The tilt angles are used to calculate the components of a vector that is normal to the gravitational plane. Normal vectors are used to define planes. This normal vector is directly used in the calculations that involve sensor measurements. The components are relative to the sensor coordinate system basis. The normal vector is

It points up. Its components given as a function of the tilt angles are as follows. The signs are chosen to be consistent with a right handed coordinate system. The components, in the S-^ basis, of the vector

Also:

Generalized Angle Between a Straight Line and a Plane

[0067] The angle between the straight line:

[0068] And (its projection on) the plane:

[0069] iven by:

Mathematical Model

[0070] This section establishes a mathematical model of the system that facilitates the inclinometer calculations. Coordinate Systems

[0071] The following coordinate systems are used in the inclinometer alignment calculations. These coordinate systems are associated with one reference sensor that is fixed to a platform and two sensors that are fixed to two shafts that are fixed to the same platform. The alignment calculation determines the angle between the projections of the two shafts onto the vertical YZ plane of the reference. The sensors are designated H, A, B for reference sensor H, shaft A sensor, and shaft B sensor.

World coordinates

Platform coordinates

Coordinate Transformations

[0072] The following coordinate system transformations are relevant:

[0073] Combining:

Successive Rotations

[0074] The coordinate systems are related by transformations that are obtained by sequences of rotations about body axes:

[0075] The rotation sequence for sensor H is:

RotationHl : Initially align 5_1; the Platform basis, with S₀, the World basis, and then rotate the Sy basis arbitrarily. In other words, the platform basis can be rotated arbitrarily. The reference basis S_hl is the same as Sy. [0076] The rotation sequence for sensor A is:

RotationAl : Initially align 5_1; the Platform basis, with S₀, the World basis, and then rotate the S₁ basis arbitrarily. In other words, the platform basis can be rotated arbitrarily.

RotationA2: Initially align S_a2, the Shaft A basis, with 5_1; the Platform basis, and then rotate the S_a2 basis about by a pitch angle θ_α. In other words, rotate Shaft A up or down the Platform

by a pitch angle θ_α.

RotationA3: Initially align S_a3, the Sensor A basis, with S_a2, the Shaft A basis, and then rotate the S_a3 basis about by a roll angle φ_α. In other words, rotate Sensor A around Shaft A by a

roll angle φ_α.

[0077] Likewise, the rotation sequence for sensor B is:

RotationBl : Initially align S_{1 ;} the Platform basis, with S₀, the World basis, and then rotate the S-^ basis arbitrarily. In other words, the platform basis can be rotated arbitrarily.

RotationB2: Initially align S_b2, the Shaft B basis, with 5_1; the Platform basis, and then rotate the S_b2 basis about by a pitch angle θ_b. In other words, rotate Shaft B up or down the Platform

by a pitch angle θ_b.

RotationB3: Initially align S_b3, the Sensor B basis, with S_b2, the Shaft B basis, and then rotate the S_b3 basis about by a roll angle φ b . In other words, rotate Sensor B around Shaft B by a

roll angle cp_b.

[0078] Note that RotationHl, RotationAl and RotationBl are the same, an arbitrary platform rotation. Also, the shafts of this analysis are constrained mechanically such that their only degree of freedom is a pitched rotation, resulting in Rotations A₂ and B₂. Furthermore, because of the way that the sensors are mounted on the V-blocks, the sensors are mechanically constrained such that their only degree of freedom is a roll about the shaft, resulting in Rotations A₃ and B₃. Resulting Successive Transformations

[0079] The preceding successive rotations result in the following transformations:

[0080] R₀₁ is arbitrary. For simulation purposes, the following two can be used:

arbitrary roll followed by arbitrary pitch, yaw doesn't matter

arbitrary pitch followed by arbitrary roll, yaw doesn't matter

[0081] For the H reference sensor:

[0082] For the A shaft and sensor:

[0083] Likewise, for the B shaft and sensor:

Measured, Known Quantities

[0084] The following measured quantities are available to the alignment calculation:

The components, in the S_hl basis, of the gravity normal vector N.

The components, in the S_3a basis, of the gravity normal vector N.

The components, in the S_3b basis, of the gravity normal vector N

So that the set of known variables is

Relationships between the Known Quantities [0085] The following relationships hold:

And

So that:

Therefore:

where are the known measured quantities and are the unknown

quantities and the body axis rotation matrices are as follows:

[0086] The alignment angle is:

[0087] In another embodiment, the present disclosure may be a method 400 for shaft alignment (Fig. 6). The method 400 includes attaching 403 a reference inclinometer to a reference platform to provide a pitch and a roll of a reference plane. A first inclinometer is attached 406 to a first shaft to provide a pitch and roll of a first sensor plane. A second inclinometer is attached 409 to a second shaft to provide a pitch and roll of a second sensor plane. A shaft alignment pitch angle is calculated 412 between the first shaft and the second shaft based on the pitch and the roll of the reference plane, the first sensor plane, and the second sensor plane. The step of calculating a shaft alignment pitch angle is repeated 415 over time to determine an average alignment and standard deviation of the alignment until the standard deviation is less than a pre-determined threshold. Through the use of electronic inclinometers and a processor for calculation, the pitch values and roll values may be sampled at a high frequency (e.g., greater than 1 Hz, 2 Hz, 4 Hz, or higher) in order to nullify motion due to, for example, tailboom deflection. As such, use of the present method 400 allows for alignment measurement while the environment is moving (e.g., at sea, etc.)

[0088] The present disclosure also provides for a sensor mount system 500. With reference to Figs. 7A, 7B, and 8, a sensor mount system 500 can include a base member 510, a sensor 520, and arms 530. The sensor mount system may be used to mount a sensor to a surface D (illustrated generally in Fig. 8). For example, the sensor mount system 500 can be configured to mount to a drive shaft, such as a tail boom of a helicopter, for determining alignment of the drive shaft, which can be used to perform maintenance thereon. Although the surface D is illustrated in Fig. 8 as a cylindrical object, it should generally be understood that the sensor mount system can be configured to mount to variously-shaped surfaces (e.g., cubic, conical, irregular, etc.)

[0089] The base member 510 can include pivots 511, a biasing mechanism (e.g., springs 512), and one or more upper engagement surfaces 513 that are configured to engage a driveshaft. The one or more upper engagement surfaces 513 can include a pair of walls 514. The walls 514 can be planar for engaging a surface D (illustrated generally in Fig. 8) in a tangential manner. The walls 514 can lie along respective planes that intersect one another. It should be understood that the walls 514 can be arranged at various angles depending upon the application for the sensor mount system 500. In one particular example, the walls 514 can be orthogonally arranged relative to one another, which can help maximize the clamping force of the sensor mount system 500 to a cylindrical object, such as a drive shaft. A central trough 515 can be provided between each wall 514. The central trough 515 can allow the sensor mount system 500 be positioned on a rectilinear prism, and help reduce manufacturing costs.

[0090] Each arm 530 can include an upper grip portion 531, a central portion 532, and a lower engagement portion 533. Each upper grip portion 531 may be indented relative to the central portion 532 to allow a user to grasp both grip portions 531 with a single hand. For example, the distance between each grip portion 531 when the device is in the engaged state (i.e., shown in Fig. 7A) can be between 3-5 inches.

[0091] The central portion 532 of each arm can be generally parallel to one another, for example arranged at an angle that is ±20° relative to one another. The central portion 532 of each arm can be offset relative to one another to define a cavity 534. One or more sensors 520 can be mounted on the base member 510 within the cavity 534. In this way, the arms 531 and/or base member 510 can protect the one or more sensors 520 from physical damage (e.g., in the event that the user accidentally drops the system 500).

[0092] The arms 530 may be pivotably connected to a respective pivot 511 at the central portion 532 of each arm 511. One or more springs 512 can provide a bias to urge each arm 530 into the engaged state (i.e., shown in Fig. 7 A). The clamping force of the arms 530 can be such that the sensor mount system 500 can remain securely mounted on a surface that is in motion. In one example, a plurality of springs 512 are provided, which collectively exert 15-25 foot pounds of torque. In turn, the leverage provided by each arm acting about a pivot can in turn require approximately 40 pounds or less of compression force at the grip portion 531 in order to urge the arms 530 between a disengaged and engaged state. In one particular example, 16 pounds of compression force may be required by a user at the grip portions 531 to urge the arms 530 between a disengaged and engaged state.

[0093] The lower engagement portion 533 can be defined to be angled relative to the central portion 532 and include one or more interior lower shaft engagement surfaces 535 that are configured to engage a drive shaft D. In the engaged position, the engagement surfaces 535 may contact the surface D in a tangential manner. In one example, the clamping force at the engagement surfaces 535 can be between 80-120 pounds. In one particular example, the engagement surfaces 514, 535 may contact the shaft D at four contact points. This can be useful, for example, to distribute the clamping force on a surface to help minimize damage to the surface (e.g., a drive shaft of a helicopter). The engagement surfaces 514, 535 can be made of different materials depending on the particular application. A compressible material (e.g., a rubber) can be used to preserve a sensitive surface (e.g., prone to scratching). A more aggressive material and/or surface can be used for the engagement surfaces 514, 535 (e.g. , textured, hardened steel) could be used in situations where the surface D is less sensitive. According to other embodiments, the engagement surfaces 514, 535 can include more than one type of material/surface to provide different friction coefficients to maintain proper position of the system 500 while in motion. [0094] The system 500 can have a relatively compact design, and be made of plastic and/or metal. For example, the system 500 can be made of a suitable engineering plastic to withstand a corrosive/solvent environment. Fig. 7B is a perspective view where components have been hidden to better show the internal configuration of the system 500. Specifically, Fig. 7B shows the arms 530 can be made of a plurality of subcomponents 536 that are affixed to one another, for example, with fasteners 537. The use of a plurality of subcomponents 536 with fasteners 537 can help improve strength and/or manufacturability of the arms. Alternatively, the arms 530 can be monolithic. The base member 510 can similarly be made of a combination of a plastic housing 516 (shown in Fig. 7A) having an internal metal frame 517. The metal frame 517 can help improve strength and durability of the base member 510, including for applications where the system 500 is subject to high temperatures. In order to reduce weight of the system 500, the metal frame 517 can be made of aluminum or magnesium. In applications where the system 500 may be exposed to corrosives, the metal frame 517 can be stainless steel. The sensor 520 can be removably detachable to the plastic exterior 516 and/or metal frame 517.

[0095] Fig. 8 illustrates another embodiment of the sensor mount system 500. The system 500 is shown in an engaged position on a surface D. The system 500 is carrying a display screen 550, which can cooperate with a sensor (e.g., sensor 520 shown in Figs. 7A and 7B).

According to certain embodiments, the display screen 550 may be carried in front of arms 530

(i.e., the display screen is not located between arms 530). It may be necessary to position the display screen 550 in front of arms 530 for various reasons, including to accommodate a larger display screen 550, to allow for adjustment of the screen location relative to the remainder of the system 500, and or due to size constraints of the remainder of the system (e.g., arms 530).

However, the display screen can alternatively be positioned between arms 530 such that the arms 530 protect the display screen 550 from physical damage (e.g., in the event that the user accidentally drops the system 500).

[0096] The drive shaft sensor mount system 500 of the present disclosure can have several advantages. For example, the system 500 can have a relatively compact design.

According to one embodiment, the overall dimensions of a system 500 can be 3.5 x6x8.5 inches or less. According to certain embodiments, the system can be lightweight. By manufacturing the system 500 with plastic components (in some examples, the majority of the components can be made of plastic), the overall weight can be kept to a minimum for improved handling, placement, transport, and grip. Another advantage of the system 500 is that the center of gravity can be placed above the axis of rotation, which can help reduce the possibility of unwanted rotation of the system (which can contribute to sensor inaccuracies). It should be realized that the system 500 can have a center of gravity that is coincident with the surface, or coincident with the center axis of the surface (i.e., to minimize torque on the system 500 from motion). According to embodiments of the present disclosure, one or more counterweights can be used to lower the center of gravity. For example, one or more counterweights can be placed at or adjacent to the lower engagement portion 533 of each arm 530. Additionally, the system can have a fixed clamp force (e.g., via biasing members 512), which can avoid a user from applying too much force (which can damage the drive shaft) or too little force (which can lead to sensor inaccuracies) to the drive shaft. [0097] The system can be intuitive to use, reliable, and durable. For example, the clamping force can be preset, and not require adjustments by a user. The system can have few moving parts and require little to no maintenance. The system can additionally be operated with a single hand and provide a high mechanical advantage to the user. The system can have engagements surfaces that self-align to the drive shaft. Moreover, when placing systems on respective portions of a drive shaft, the roll angle of each system (i.e., rotational angle of the system relative to the drive shaft) can be easily adjusted for applications involving a cylindrical surface. The arms of the system serve as a protective barrier for sensors and the engagement surfaces, thereby improving durability of sensors and increasing the reliability of measurements taken by the sensors. [0098] Although the present disclosure has been described with respect to one or more particular embodiments, it will be understood that other embodiments of the present disclosure may be made without departing from the spirit and scope of the present disclosure. Hence, the present disclosure is deemed limited only by the appended claims and the reasonable interpretation thereof.

Claims

What is claimed is:

1. A shaft alignment apparatus, comprising:

a first bracket having a display mounted thereon, wherein the first bracket is configured to be removably attached to a first shaft such that a primary plane of the display panel is substantially perpendicular to the first shaft;

a second bracket having a camera mounted thereon, wherein the second bracket is configured to be removably attached to a second shaft such that the camera is oriented substantially parallel to the second shaft; and

a processor in electronic communication with the camera and the display panel, wherein the processor is programmed to:

display on the display panel a target pattern;

capture, using the camera, a plurality of images of the target partem;

calculate a 6DOF position of the camera with respect to the display panel based on the plurality of images; and

determine, using the 6DOF position of the camera, an alignment of the first shaft with respect to the second shaft.

2. The shaft alignment apparatus of claim 1, wherein the processor calculating a 6DOF position of the camera includes processing the plurality of images to remove changes caused by a dynamic oscillation of the first shaft and second shaft with respect to each other.

3. The shaft alignment apparatus of claim 2, wherein the processor is further programmed to: discard any images of the plurality of images that are blurred due to motion;

calculate the 6DOF camera position based on a first undiscarded image of the plurality of images;

averaging the calculated 6DOF camera positions and calculating a standard deviation of the averaged 6DOF camera positions; and

if the calculated standard deviation is above a pre-determined threshold, repeating the steps of calculating the 6DOF camera position based on a next undiscarded image, averaging the calculated 6DOF positions, and calculating a standard deviation.

4. The shaft alignment apparatus of claim 2, wherein the processor calculates a 6DOF position of the camera using a Perspective-n-Point procedure.

5. The shaft alignment apparatus of claim 1, wherein the display panel comprises an LCD display.

6. The shaft alignment apparatus of claim 1, wherein the LCD display has a diagonal size of 6.5 inches or less and a native resolution of 640x480 pixels.

7. The shaft alignment apparatus of claim 1, wherein the display panel is arranged in a portrait configuration and the alignment of the first shaft and the second shaft is determined as a pitch angle.

8. A method for shaft alignment, comprising:

attaching a display panel to a first shaft using a first bracket;

attaching a camera to a second shaft using a second bracket, wherein at least a portion of the display panel is within a field of view of the camera;

displaying a target pattern on the display panel;

capturing, using the camera, a plurality of images of the target pattern;

calculating a 6DOF position of the camera with respect to the display panel based on the plurality of images; and

determining, using the 6DOF position of the camera, an alignment of the first shaft with respect to the second shaft.

9. A shaft alignment apparatus, comprising:

a reference inclinometer configured to be mounted to a reference platform and to provide a pitch and a roll of a reference plane;

a first inclinometer configured to be mounted on a first shaft and to provide a pitch and a roll of a first sensor plane, wherein the pitch of the first sensor plane is equal to a pitch of the first shaft;

a second inclinometer configured to be mounted on a second shaft and to provide a pitch and a roll of a second sensor plane, wherein the pitch of the first sensor plane is equal to a pitch of the first shaft; and

a processor in electronic communication with the reference inclinometer, the first

inclinometer, and the second inclinometer, wherein the processor is programmed to: calculate a shaft alignment as a pitch angle between the first shaft and the second shaft based on the pitch and the roll of the reference plane, the first sensor plane, and the second sensor plane; and repeat the alignment calculation over time to determine an average alignment and standard deviation of the alignment until the standard deviation is less than a predetermined threshold.

10. A method for shaft alignment, comprising:

attaching a reference inclinometer to a reference platform to provide a pitch and a roll of a reference plane;

attaching a first inclinometer to a first shaft to provide a pitch and a roll of a first sensor plane;

attaching a second inclinometer to a second shaft to provide a pitch and roll of a second sensor plane;

calculating a shaft alignment pitch angle between the first shaft and the second shaft based on the pitch and the roll of the reference plane, the first sensor plane, and the second sensor plane; and

repeating the alignment calculation over time to determine an average alignment and

standard deviation of the alignment until the standard deviation is less than a predetermined threshold.

11. A drive shaft sensor mount comprising:

a base member including a first pivot, a second pivot, a sensor, and one or more upper drive shaft engagement surfaces configured to engage a drive shaft in an engaged position; a first arm pivotably connected to the first pivot, the first arm including one or more lower drive shaft engagement surfaces configured to engage the drive shaft in the engaged position;

a second arm pivotably connected to the second pivot, the second arm including one or more lower drive shaft engagement surfaces configured to engage the drive shaft in the engaged position;

wherein the first arm and the second arm are biased into the engaged position by one or more biasing mechanisms;

wherein the sensor is located between the first arm and the second arm.

12. The drive shaft sensor mount of claim 11, wherein the one or more upper drive shaft engagement surfaces include a pair of walls.

13. The drive shaft sensor mount of claim 12, wherein the pair of walls are planar.

14. The drive shaft sensor mount of claim 13, wherein each of the pair of walls lie along a respective plane that intersect one another.

15. The drive shaft sensor mount of claim 12, wherein the pair of walls are separated by a central trough.

16. The drive shaft sensor mount of claim 11, wherein the first arm and the second arm include a respective upper grip portion, a lower engagement portion, and a central portion located between the upper grip portion and the lower engagement portion.

17. The drive shaft sensor mount of claim 16, wherein the first arm and the second arm are pivotably connected to the base member at the central portion.

18. The drive shaft sensor mount of claim 11, wherein rotating the upper grip of the first arm toward the upper grip of the second arm moves the drive shaft sensor mount from the engaged position to a disengaged position.

19. The drive shaft sensor mount of claim 18, wherein in the disengaged position, the one or more lower drive shaft engagement surfaces of the first arm and the one or more lower drive shaft engagement surfaces of the second arm are located further away from one another than in the engaged position.

20. The drive shaft sensor mount of claim 11, wherein the one or more biasing mechanisms apply a fixed force to the drive shaft.

21. The drive shaft sensor mount of claim 11, wherein the one or more upper drive shaft engagement surfaces and the one or more lower drive shaft engagement surfaces are made of plastic.