Systems and methods for capacitive proximity sensing

A system includes first, second, third and fourth capacitive sensors, each disposed about a longitudinal axis. The first capacitive sensor is disposed along a first axis radial to the longitudinal axis, and the third capacitive sensor is disposed along the first axis opposite the first capacitive sensor. The second capacitive sensor is disposed along a second axis radial to the longitudinal axis, the fourth capacitive sensor is disposed along the second axis opposite the second capacitive sensor, and the second axis is different from the first axis. Each capacitive sensor is configured to transmit a respective signal based at least in part on a position of a rotational component along the respective axis relative to the longitudinal axis.

BACKGROUND

The subject matter disclosed herein relates to systems and methods for capacitive proximity sensing, and in particular, to systems and methods for capacitive proximity sensing of rotational components.

Rotary equipment, such as turbomachinery, has one or more rotating components, such as a shaft, a rotor, an impeller, compressor blades, turbine blades, or wheels. Each of the one or more rotating components may rotate about a centerline, and the centerlines of rotating components may not be mutually coaxial or parallel. Furthermore, rotating components may be arranged within compact enclosures having limited available space for equipment to monitor the rotating components. Unfortunately, magnetic fields near rotating components may complicate the use of monitoring equipment and/or limit the effectiveness of the monitoring equipment.

BRIEF DESCRIPTION

In a first embodiment, a system includes a first capacitive sensor, a second capacitive sensor, a third capacitive sensor, and a fourth capacitive sensor. The first capacitive sensor is disposed about a longitudinal axis and along a first axis radial to the longitudinal axis. The first capacitive sensor is configured to transmit a first signal based at least in part on a first position of a rotational component along the first axis relative to the longitudinal axis. The second capacitive sensor is disposed about the longitudinal axis and along a second axis radial to the longitudinal axis, where the second axis is different from the first axis. The second capacitive sensor is configured to transmit a second signal based at least in part on a second position of the rotational component along the second axis relative to the longitudinal axis. The third capacitive sensor is disposed about the longitudinal axis and along the first axis opposite to the first capacitive sensor, wherein the third capacitive sensor is configured to transmit a third signal based at least in part on a third position of the rotational component along the first axis. The fourth capacitive sensor is disposed about the longitudinal axis and along the second axis opposite to the second capacitive sensor, wherein the fourth capacitive sensor is configured to transmit a fourth signal based at least in part on a fourth position of the rotational component along the second axis.

In a second embodiment, a system includes a shaft configured to rotate about a longitudinal axis and a first sensor assembly disposed about the longitudinal axis at a first axial position. The shaft includes a shaft axis. The first sensor assembly includes a first capacitive sensor having a first face disposed a first distance from the shaft along a first axis. The first capacitive sensor is configured to transmit a first signal based at least in part on the first distance. The first sensor assembly includes a second capacitive sensor having a second face disposed a second distance from the shaft along a second axis that is perpendicular to the first axis. The second capacitive sensor is configured to transmit a second signal based at least in part on the second distance. The first sensor assembly includes a third capacitive sensor having a third face disposed a third distance from the shaft along the first axis opposite the first capacitive sensor. The third capacitive sensor is configured to transmit a third signal based at least in part on the third distance. The first sensor assembly includes a fourth capacitive sensor having a fourth face disposed a fourth distance from the shaft along the second axis opposite the second capacitive sensor. The fourth capacitive sensor is configured to transmit a fourth signal based at least in part on the fourth distance. The first sensor assembly includes a controller configured to determine a first parameter of the system at the first axial position based at least in part on the first signal, the second signal, the third signal, and the fourth signal, where the first parameter includes a first location of the shaft relative to the longitudinal axis at the first axial position, a first vibration of the shaft about the longitudinal axis, or any combination thereof.

In a third embodiment, a method includes transmitting a first signal from a first capacitive sensor to a controller based at least in part on a first distance between the first capacitive sensor and a rotational component, transmitting a second signal from a second capacitive sensor to the controller based at least in part on a second distance between the second capacitive sensor and the rotational component, transmitting a third signal from a third capacitive sensor to the controller based at least in part on a third distance between the third capacitive sensor and the rotational component, transmitting a fourth signal from a fourth capacitive sensor to the controller based at least in part on a fourth distance between the fourth capacitive sensor and the rotational component, and determining a parameter of a rotational system comprising the rotational component based at least in part on the first signal and the second signal. The first capacitive sensor is disposed along a first axis radial to the longitudinal axis, the second capacitive sensor is disposed along a second axis radial to the longitudinal axis and perpendicular to the first axis, the third capacitive sensor is disposed along the first axis opposite the first capacitive sensor, and the fourth capacitive sensor is disposed along the second axis opposite the second capacitive sensor. The parameter includes a first location of the rotational component relative to the longitudinal axis, a first vibration of the rotational component about the longitudinal axis, a characteristic of a fluid disposed about the rotational component, or any combination thereof.

DETAILED DESCRIPTION

Capacitive sensors of a monitoring system provide feedback to a controller (e.g., a processor-based industrial controller) to determine operational parameters (e.g., position, movement, vibration) of rotational components and/or characteristics of fluids disposed about rotational components. For example, the rotational components may include shafts of a motor, pump, wheel, generator, turbine, compressor, or various turbomachinery, and fluids disposed about rotational components may include lubricants, coolants, or any combination thereof. The controller may monitor a distance between each of the capacitive sensors of the monitoring system and the rotational component. Each capacitive sensor may transmit a signal to the controller based at least in part on a voltage between the respective capacitive sensor and the rotational component. For each capacitive sensor, the controller may determine the distance between the respective capacitive sensor and the rotational component based at least in part on a functional relationship between the transmitted signal and the distance. Each capacitive sensor is aligned along an axis, thereby enabling the controller to determine the position of the rotational component along the axis relative to the respective capacitive sensor. Utilizing multiple capacitive sensors aligned along different radial axes, the controller may determine one or more operational parameters (e.g., position, movement, vibration) of a rotational component relative to a longitudinal axis. The capacitive sensors may be arranged in a predefined orientation and spacing relative to the longitudinal axis.

The controller may determine the position, movement, and/or vibration of the rotational component relative to the longitudinal axis utilizing various arrangements of the capacitive sensors about the rotational component. For example, a first set of two or more capacitive sensors may be arranged within the same plane, such that the respective radial axes through the capacitive sensors are perpendicular to each other through the longitudinal axis. The perpendicular arrangement of the first set of capacitive sensors enables the controller to determine the position of the rotational component relative to the longitudinal axis along independent radial axes (e.g., X-axis, Y-axis). An additional second set of capacitive sensors arranged opposite to the first set of capacitive sensors enables the controller to readily factor out common mode noise, the permittivity of materials in the spaces between each capacitive sensor and the rotational component, or any combination thereof. As discussed in detail below, two or more capacitive sensors may be arranged about the rotational component in various configurations. In some embodiments, two or more capacitive sensors may be arranged circumferentially about a longitudinal axis at approximately equal angular positions, such as every 10, 20, 30, 45, 60, 90, or 180 degrees.

The capacitive sensors may be arranged separately about the rotational component, or within a common capacitive sensor housing. The capacitive sensors may be arranged about the rotational component near and/or adjacent to a bearing assembly or a drive assembly. In some embodiments, capacitive sensors may be arranged within a bearing or drive assembly. Furthermore, a rotational system may include multiple capacitive sensor housings, each capacitive sensor housing having capacitive sensors arranged in a configuration discussed below. The capacitive sensor housing may be disposed with a rotational system within an enclosure. For example, the capacitive sensor housing may be disposed within a motor, pump, or generator enclosure. In some embodiments, the capacitive sensor housing is mounted about a rotational component along a longitudinal axis of the rotational component (e.g., shaft). In some embodiments, the capacitive sensor housing and/or the enclosure may be subject to various pressure environments including, but not limited to, high altitude environments (e.g., 11 kPa), sea level environments (e.g., 101 kPa), and subsea environments (e.g., 103 MPa), or any combination thereof. As discussed in detail below, the shape, area, and arrangement of each of the capacitive sensors about the rotational component may affect the determination of operational parameters (e.g., position, movement, vibration) of the rotational component.

Turning to the drawings,FIG. 1is a schematic diagram that illustrates an embodiment of a rotational system10(e.g., rotary machinery such as turbomachinery) and a rotational monitoring system12. In the rotational system10, a driver14rotates a shaft16coupled to one or more loads18. The driver14may include, but is not limited to, a gas turbine, a steam turbine, a wind turbine, a hydro turbine, a reciprocating engine (e.g., diesel, gasoline, pneumatic), an electric motor, a hydraulic motor, a pneumatic motor, or any combination thereof. The driver14provides a rotational output via the shaft16to the one or more loads18, each of which may include, but is not limited to, a vehicle or a stationary load. In some embodiments, the one or more loads18may include a propeller on an aircraft, an electrical generator in a power plant, a compressor, a pump, a fan, a machine, any suitable device capable of being powered by the rotational output of the driver14, or any combination thereof. The shaft16rotates along an axis20. In some embodiments, the rotational system10includes multiple shafts coupled to one another. Each shaft16rotates along a respective axis20as shown by arrow22.

The monitoring system12monitors the rotational system10and determines one or more operational parameters of rotational components (e.g., driver14, shaft16, load18) of the rotational system10. Operational parameters may include position, movement, or vibration, or any combination thereof. One or more capacitive sensors24arranged along the rotational system10are spaced apart from a rotational component (e.g., shaft16) at one or more axial locations of the rotational system10. For example, the capacitive sensors24may be arranged at an end26of the shaft16, about the shaft16adjacent to a bearing assembly28or gearbox30, or about the shaft16separate from a bearing assembly28or gearbox30, or any combination thereof. As discussed in detail below, multiple (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, or more) capacitive sensors24at each axial location may be disposed in a capacitive sensor housing32. Multiple capacitive sensors24at an axial location may be arranged on opposite sides and/or orthogonal sides of a rotational component (e.g., shaft16), thereby improving the accuracy of the monitoring system12to determine a position, movement, and/or vibration of the rotational component. Furthermore, the capacitive sensors24may be disposed in an external environment34or within an internal environment36, such as within enclosures38about the driver14and/or the load18. In some embodiments, the external environment34may include a subsea environment at a pressures including, but not limited to, 34.5 MPa, 69 MPa, 103 MPa, or more (e.g., 5,000 psi, 10,000 psi, or 15,000 psi, or more).

Each capacitive sensor24transmits feedback (e.g., signals) via signal lines40to a controller42based at least in part on a voltage between the capacitive sensor24and the rotational component, such as the shaft16. As discussed in detail below, the voltage between the capacitive sensor24and the rotational component (e.g., shaft16) may be proportional to the distance between the capacitive sensor24and the rotational component. A processor44of the controller42determines one or more operational parameters from the received signals of the capacitive sensors24. The controller42may store received signals and/or instructions or code for processing the received signals in a non-transitory machine-readable medium46, such as memory. The non-transitory machine-readable medium46(e.g., memory) does not include transitory signals, and may be volatile memory or non-volatile memory. In some embodiments, the non-transitory machine-readable medium46may include, but is not limited to, random access memory (RAM), read-only memory (ROM), flash memory, a hard drive, or any other optical, magnetic, and/or solid-state storage media, or some combination thereof. In some embodiments, the controller42may include an industrial controller, a workstation, a laptop, a mobile device, or a tablet.

In some embodiments, the shaft16may be arranged within a passage48(e.g., bore) of the driver14, gearbox30, or load18, or any combination thereof. The passage48may enable a fluid50(e.g., gas, liquid) to at least partially fill a space between the shaft16and the passage48. The fluid50may be a lubricant (e.g., oil), a coolant (e.g., water, air), or any combination thereof. In some embodiments, the fluid50within the passage48may be a fluid bearing for the shaft16. A pump52may circulate the fluid50to the passage48from a reservoir54. The passage48may be aligned along a longitudinal axis56, substantially parallel (e.g., within less than 1, 2, 3, 4, or 5°) with the shaft axis20. For example, the shaft axis20may be coaxial with the longitudinal axis56of the passage48during operation of the rotational system10.

FIG. 2illustrates a perspective view of an embodiment of the capacitive sensor housing32about the shaft16. In some embodiments, an inner wall70(e.g., inner annular wall) of the sensor housing32may be a wall of the passage48about the shaft16. The capacitive sensor housing32may be of any shape, such that capacitive sensors24disposed within the capacitive sensor housing32are arranged about the shaft16. For example, the capacitive sensor housing32may be an annular ring as illustrated inFIG. 2. In some embodiments, the capacitive sensor housing32may be an open ring (e.g., C-shaped) that only partially surrounds the shaft16. For example, the capacitive sensor housing32may circumferentially surround at least approximately 25, 50, 75, or 90 percent or more of the shaft16. In other words, the capacitive sensor housing32may extend circumferentially around 45, 60, 90, 180, 270, or 360 degrees of the shaft16. The capacitive sensor housing32may be a non-electrically conductive material, including but not limited to, ceramic, plastic, rubber, or any combination thereof.

The passage48about the shaft16forms a space74(e.g., annular space) that may be at least partially filled with the fluid50, as discussed above. In certain situations, forces on the shaft16may move the shaft16within the passage48, such that the shaft axis16is askew with the longitudinal axis56of the passage48and/or the shaft axis16is not centered in the passage. For example, gravity may pull the shaft16toward a bottom portion of the passage48during operation of the rotational system10and during down periods of the rotational system10. Additionally, operation of rotational system10may cause the axis20of the shaft16to change position (e.g., translate) relative to the longitudinal axis56. For example, vibrations may be induced to the shaft16via a component coupled to the shaft16, and/or the shaft16may thermally expand or thermally contract as the operating temperature within rotational system10changes. Each capacitive sensor24of the monitoring system12enables the controller42to measure and/or monitor the position (e.g., proximity, clearance), the movement (e.g., radial movement), and/or the amount of vibration (e.g., frequency, amplitude, phase) of the shaft16relative to each capacitive sensor24. For example, the controller42may monitor the position, movement, and/or vibration sensed by the capacitive sensors24to identify trends in the behavior of the shaft16. In some embodiments, the controller42may identify resonant behavior of the shaft16via capacitive sensors24. As discussed above, each capacitive sensor24, such as capacitive sensors24disposed within the capacitive sensor housing32, transmit a signal representative of the measured position, movement, and/or the amount of vibration of the shaft to controller32for processing, analysis, and/or storage.

FIG. 3illustrates a cross-sectional view of the capacitive sensor housing32and shaft16ofFIG. 2, taken along line3-3. The shaft16positioned within the space74has a shaft radius90from the shaft axis20, and the passage48has a passage radius92from the longitudinal axis56to the inner wall70. The capacitive sensors24within the capacitive sensor housing32are arranged along radial axes relative to the longitudinal axis56. For example, a first capacitive sensor94is arranged along a first radial axis96(e.g., Y-axis), and a second capacitive sensor98is arranged along a second radial axis100(e.g., X-axis). As may be appreciated,FIG. 3illustrates a planar cross-section of the capacitive sensor housing32that is perpendicular to the longitudinal axis56, such that the first radial axis96and the second radial axis100are perpendicular to the longitudinal axis56through the passage48.

Each capacitive sensor24(e.g., first capacitive sensor94, second capacitive sensor98) may be spaced an offset distance102from the inner wall70(e.g., inner annular wall) of the passage48. For example, the capacitive sensors24may be spaced an offset distance102greater then 1, 5, 10, 25, 50, or 100 mm or more from the inner wall70. In some embodiments, one or more capacitive sensors24at an axial location about the shaft16may be disposed on the inner wall70, such that the offset distance102is approximately 0 mm. Additionally, or in the alternative, one or more capacitive sensors24at an axial location about the shaft16may be differently spaced from the inner wall70, such that the respective offset distance102for the first capacitive sensor94varies from the respective offset distance102for the second capacitive sensor98. As may be appreciated, an approximately uniform offset distance102for each capacitive sensor24may simplify the calculations performed by the controller42, as discussed below.

During operation of the monitoring system12, each capacitive sensor24transmits a signal to the controller42based at least in part on a respective voltage between the capacitive sensor24and the shaft16. As may be appreciated, the capacitance of a capacitor may be defined by Equation 1:
C=q/VEquation 1
where C is capacitance (farad), q is the charge (coulomb) on plates of the capacitor, and V is the voltage between the plates. Additionally, the capacitance between two parallel plates may be determined by Equation 2:
C=(A*ε)/DEquation 2
where C is the capacitance of the two plates, A is the area of overlap of the two plates, ε is the electrical permittivity (e.g., dielectric constant) of the materials between the two plates, and D is the distance between the two plates. The controller42may execute instructions to determine the capacitance between each capacitive sensor24and the shaft16utilizing an equation that relates C, A, ε, and D. In some embodiments, the controller42may approximate C utilizing Equation 2 by considering the capacitive sensor24and the shaft16as parallel plates. In some embodiments with curved capacitive sensors24and the shaft16, the controller42may determine C as defined by Equation 3:
C=(2*π*ε*L)/(ln(b/a)*s)  Equation 3
where C is the capacitance between the capacitive sensor24and the shaft16, ε is the electrical permittivity of the materials between the capacitive sensor24and the shaft16, L is the axial length of the capacitive sensor24, b is the sum of the passage radius92and the sensor offset distance102, a is the shaft radius90, and s is the fraction of the circumference at distance b along which the capacitive sensor24extends. Electromagnetic fields near the capacitive sensor24may have a reduced effect on the operation of the capacitive sensor24relative to other types of sensors, such as eddy current sensors. Accordingly, the capacitance between each capacitive sensor24and the shaft16may be determined based on geometric properties and material properties of the capacitive sensor24, the shaft16, and the materials (e.g., capacitive sensor housing32, fluid50) between the capacitive sensor24and the shaft16.

The first capacitive sensor94is spaced a first distance104and the offset distance102along the first radial axis96from a face106of the shaft16, and the second capacitive sensor98is spaced a second distance108and the offset distance102along the second radial axis100from the face106of the shaft16. According to Equations 1 and 2, the voltage (e.g., V1) sensed by the first capacitive sensor94is functionally related to the first distance104(e.g., D1) and the offset distance102. Likewise, the voltage (e.g., V2) sensed by the second capacitive sensor98is functionally related to the second distance108(e.g., D2) and the offset distance102. The first capacitive sensor94transmits a first signal to the controller42based at least in part on the voltage V1, and the second capacitive sensor98transmits a second signal to the controller42based at least in part on the voltage V2. The controller42may execute instructions to determine the first distance104(e.g., D1) based at least in part on the first voltage V1, and the controller42may execute instructions to determine the second distance108(e.g., D2) based at least in part on the second voltage V2. The controller42may execute instructions to determine the position of the shaft axis20relative to the longitudinal axis56based at least in part on the first distance104and the second distance108. In some embodiments, the controller42may execute instructions to determine the clearance between the face106and the inner wall70from the first distance104and the second distance108.

In some embodiments, the controller42may execute instructions to determine movement of the shaft16relative to the longitudinal axis56with Y-axis96coordinates based on the first distance104, and with X-axis100coordinates based on the second distance108. In the illustrated embodiment, an angle109between the Y-axis96and the X-axis100is 90 degrees (e.g., perpendicular), thereby enabling the respective first and second distances104,108to independently describe the position of the shaft axis20relative to the longitudinal axis56.

In some embodiments, a third capacitive sensor110is spaced a third distance112and the offset distance102along a third radial axis114from the face106of the shaft16, and a fourth capacitive sensor116is spaced a fourth distance118and the offset distance102along a fourth radial axis120from the face106of the shaft16. The third radial axis114may be the first radial axis96(e.g., Y-axis), and the fourth radial axis120may be the second radial axis100(e.g., X-axis), such that the third capacitive sensor110is opposite (e.g., diametrically opposed to) the first capacitive sensor94and the fourth capacitive sensor116is opposite (e.g., diametrically opposed to) the second capacitive sensor98. The voltage (e.g., V3) sensed by the third capacitive sensor110is functionally related to the third distance112(e.g., D3) and the offset distance102. Likewise, the voltage (e.g., V4) sensed by the fourth capacitive sensor116is functionally related to the fourth distance118(e.g., D4) and the offset distance102. The third capacitive sensor110transmits a third signal to the controller42based at least in part on the voltage V3, and the fourth capacitive sensor116transmits a fourth signal to the controller42based at least in part on the voltage V4. The controller42may execute instructions to determine the third distance112(e.g., D3) based at least in part on the third voltage V3, and the controller42may execute instructions to determine the fourth distance118(e.g., D4) based at least in part on the fourth voltage V4. The arrangement of the third capacitive sensor110opposite to the first capacitive sensor94along the Y-axis96and the arrangement of the fourth capacitive sensor116opposite to the second capacitive sensor98along the X-axis100may improve the accuracy of the determination by the controller42of the position of the shaft axis20relative to the longitudinal axis56. Additionally or in the alternative, the configuration of capacitive sensors24on opposite sides of the shaft16may simplify the determination of the position of the shaft axis20within the passage48relative to the determination by proximity sensors in other configurations. For example, when the capacitive sensors24are arranged in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more opposing pairs about the shaft16, the controller42may reject common mode noise from the respective distances determined along each radial axis. In some embodiments, the opposing pairs may be circumferentially spaced about the longitudinal axis56from one another at increments of 10, 20, 30, 45, 60, 90, or 180 degrees, or any combination thereof. The controller42may execute instructions to determine the position of the shaft axis20relative to the longitudinal axis56based at least in part on the first distance104, the second distance108, the third distance112, and the fourth distance118.

Additionally, or in the alternative, capacitive sensors24may be arranged about the shaft16along radial axes other than the Y-axis96and the X-axis100. For example, a fifth capacitive sensor122is spaced a fifth distance124and the offset distance102along a fifth radial axis126from the face106of the shaft16, and a sixth capacitive sensor128is spaced a sixth distance130and the offset distance102along a sixth radial axis132from the face106of the shaft16. An angle134between the fifth radial axis126and the sixth radial axis132may be greater than or less than 90 degrees. The angle134may include, but is not limited to, an angle between 0 to 90 degrees or between 90 to 180 degrees. The controller42may execute instructions to determine the fifth distance124(e.g., D5) based at least in part on a fifth voltage V5sensed by the fifth capacitive sensor122, and the controller42may execute instructions to determine the sixth distance130(e.g., D6) based at least in part on a sixth voltage V6sensed by the sixth capacitive sensor128. The controller42may execute instructions to determine coordinates of the shaft axis20along the Y-axis96and the X-axis100utilizing two or more distances along different radial axes. That is, the controller42may factor out the Y-axis component of the shaft axis20position two distances along different radial axes, and the controller42may factor out the X-axis component of the shaft axis20position from two or more distances along different radial axes. For example, the controller42may execute instructions to determine coordinates of the shaft axis20utilizing various combinations of two or more distances along different radial axes, including but not limited to, (A) the first distance104and the second distance108, (B) the first distance104and the fifth distance124, (C) the fifth distance and the sixth distance130, (D) the first distance104, the second distance108, the third distance112, and the fourth distance118, or (E) the first distance104, the second distance108, the third distance112, the fourth distance118, the fifth distance124, and the sixth distance130, or any combination thereof.

As discussed above with Equation 2, the capacitance between parallel plates is based at least in part on the electrical permittivity e (e.g., dielectric constant) of the materials between the two plates. The electrical permittivity e of the fluid50within the passage48between the capacitive sensors24and the shaft16may affect the sensed voltage by each capacitive sensor24. During operation of the rotational system10, the electrical permittivity ε of the fluid50may change based at least in part on characteristics of the fluid50, such as temperature, entrained particles, or any combination thereof. Accordingly, the fluid50may have a first electrical permittivity ε1at startup of the rotational system10when the fluid50is at a first temperature (e.g., 10° C.), and a second electrical permittivity ε2during steady-state operation of the rotational system when the fluid50is at a second temperature (e.g., 50° C.). In some embodiments, the controller42may execute instructions to determine the electrical permittivity of the fluid50, such as via temperature measurement, direct measurement, computer models, equations, look-up tables, or any combination thereof. Additionally or in the alternative, the controller42may execute instructions to factor out the electrical permittivity of the fluid50from the determination of the respective distances. For example, the controller42may determine the electrical permittivity ε of the fluid50from measurements obtained by the first capacitive sensor94, measurements obtained from the opposing third capacitive sensor110, and the relationship between D1and D3along the Y-axis96. That is, the controller42may solve for the electrical permittivity ε of the fluid50utilizing a set of equations and determined relationships. Additionally, or in the alternative, the electrical permittivity of the fluid50may be assumed to be approximately homogenous (e.g., within 5 percent or less) within the passage48for each of the capacitive sensors24at an axial location about the shaft16. In some embodiments, the controller42may determine characteristics of the fluid50through comparison of determined values of the electrical permittivity to previously determined electrical permittivity values, computer models, equations, look-up tables, or any combination thereof.

The overlapping area A of each of the capacitive sensors24relative to the face106of the shaft16affects the capacitance, and thereby the sensed voltage, of each capacitive sensor24. In some embodiments, each of the capacitive sensors24has approximately the same area A facing the shaft16, thereby enabling the controller42to determine distance through Equations 1 and 2 with one value for the overlapping area A. Additionally, utilizing capacitive sensors24with approximately equal areas A may enable a technician to quickly replace a capacitive sensor24with another capacitive sensor24without changing the overlapping area A value utilized by the controller42. In some embodiments, one or more capacitive sensors24(e.g., first, second, third, and fourth capacitive sensors94,98,110,116) may be flexible and/or molded into a curved or arcuate shape, thereby enabling the capacitive sensor24to be positioned about the rotational component (e.g., shaft16), such that various points on an inner face136of the capacitive sensor24are approximately equidistant from the face106of the shaft16when centered along the longitudinal axis56. For example, in some embodiments a capacitive sensor may be shaped into a semi-cylindrical plate, a C-shape, or a curved shape with radius of curvature approximately equal to the radius of curvature of the inner wall70of the capacitive sensor housing32. In some embodiments, the one or more flexible capacitive sensors24may be flexible printed circuit boards. Additionally, or in the alternative, the capacitive sensor24may be disposed on a curved or arcuate shape. In some embodiments, the capacitive sensor24may be a metal (e.g., copper, aluminum, silver) plate that is sufficiently isolated from the shaft16and other components to enable the development and measurement of a capacitance. The curved inner face136(e.g., first capacitive sensor94) may enable the controller42to determine the respective distance with increased accuracy relative to a non-curved (e.g., flat, planar) capacitive sensor24(e.g., fifth and sixth capacitive sensors122,128).

The controller42may execute instructions to determine each distance (e.g., D1, D2, D3, D4, D5, D6) based at least in part on a functional relationship between the voltage sensed by the respective capacitive sensor24. In some embodiments, the functional relationship may be approximated by Equation 4:
Dx=k*VxEquation 4
where Dxis the distance between the capacitive sensor24and the face106of the shaft16, Vxis the voltage sensed by the capacitive sensor24, and k is a scaling factor. The scaling factor k may be based at least in part on the overlapping area A, the electrical permittivity ε of the materials between the capacitive sensor24and the shaft16, and the charge stored on the inner face136of the capacitive sensor24. In some embodiments, the controller42may execute instructions to utilize the same scaling factor k for each distance determination because of the assumed homogeneity of the fluid50and the common overlapping areas A of each capacitive sensor24. The memory46may store various values for the scaling factor k corresponding to different operating conditions of the rotational system10(e.g., temperature, dielectric material, gap linearization factor)

As discussed above, the controller42may execute instructions to determine the position of the shaft axis20relative to the longitudinal axis56based at least in part on the voltages received from the capacitive sensors24. Additionally, or in the alternative, the controller42may execute instructions to determine the position of the shaft face106relative to the inner wall70of the passage48. The controller42may be coupled to a display138, which may provide an indication140(e.g., graphical, numerical) of the position of the shaft axis20and/or the shaft face106to an operator. The controller42may execute instructions to provide an indication to the operator when the shaft face106is within a predetermined distance (e.g. 10, 5, or 1 mm or less) of the inner wall70, thereby enabling the operator to adjust the position of the shaft16or to schedule a maintenance session to adjust the clearance of the shaft16. The controller42may execute instructions to sample the position of the shaft axis20periodically or substantially continuously during operation of the rotational system10. The sample rate for the capacitive sensors24of the monitoring system12during operation of the rotational system10may be approximately 1 Hz, 1 kHz, 10 kHz, 100 kHz, or more. In some embodiments, the controller42may execute instructions to sample the position of the shaft axis20prior to start up of the rotational system10to inform the operator of the position of the shaft16. That is, the controller42may execute instructions to sample the position of the shaft axis20when the rotational system10is at rest (e.g., not rotating).

The controller42may execute instructions to store some or all of the sampled positions of the shaft axis20in memory46, thereby generating a history of the position of the shaft axis20during operation of the rotational system10. The controller42may execute instructions to review the history to identify patterns, trends, and/or anomalies. For example, the controller42may execute instructions to identify loading events (e.g., engagement or disengagement of load, changes in the load) on the shaft16via identifying changes to position of the shaft axis20. Additionally, or in the alternative, the controller42may execute instructions to identify vibrations of the shaft through analysis of the history of the position of the shaft axis20over a period of time. The history of the position of the shaft axis20may be displayed on the display138. In some embodiments, capacitive sensors24may be arranged near a component (e.g., bearing assembly28, gearbox30, rotor, turbine stage, compressor stage) along the shaft16, thereby enabling the controller42to determine vibrations of the component.

As discussed above, the capacitive sensor housing32at least partially circumferentially surrounds the shaft16. For example, the capacitive sensor housing32may extend circumferentially around 45, 60, 90, 180, 270, or 360 degrees of the shaft16. In some embodiments, the capacitive sensor housing32may be a split ring (i.e., split axially or having a plurality of sections), thereby enabling the capacitive sensor housing32to be installed about the shaft16and/or passage48from a radial direction (e.g., along the Y-axis96or X-axis100). While an outer wall142of the capacitive sensor housing32illustrated by the solid line ofFIG. 3has a circular or annular form, one may appreciate that the outer wall142may have various geometries including, but not limited to, triangular, rectangular144, pentagonal, hexagonal, octagonal, and so forth. In some embodiments, the capacitive sensors24are disposed within the capacitive sensor housing32at fixed positions (e.g., along the Y-axis96and the X-axis100), thereby enabling a technician to install the capacitive sensors24about the shaft16in a known relationship relative to one another. That is, the capacitive sensor housing32enables the technician to simultaneously dispose multiple capacitive sensors24at defined positions/orientations rather than sequentially disposing multiple capacitive sensors24about the shaft16.

FIG. 4illustrates a flow chart of an embodiment of a computer-implemented method158for utilizing the monitoring system12described above to determine a parameter of a rotational component of a rotational system10. In some embodiments, the rotational system10may supply (block160) a fluid about one or more rotational components. For example, the rotational system10may supply a fluid (e.g., air, water, oil, coolant, nitrogen, etc.) at least partially about a rotational component for lubrication and/or cooling of the rotational component (e.g., shaft16). The first capacitive sensor positioned along a first radial axis (e.g. Y-axis96) at a first axial position senses (block162) a first voltage V1, and a second capacitive sensor positioned along a second radial axis (e.g., X-axis100) at the first axial position senses (block164) a second voltage V2. In some embodiments, the first axial position may be a position about the shaft16near a bearing assembly28, a gearbox30, or a loading point (e.g., rotor, gear, turbine stage, compressor stage) of the driver14or the load18. The first and second radial axes96,100may form a reference frame that may be utilized to define a position of the rotational component. In some embodiments, the third capacitive sensor positioned along a third radial axis at the first axial position senses (block166) a third voltage V3. In some embodiments, the fourth capacitive sensor positioned along a fourth radial axis at the first axial position senses (block168) a fourth voltage V4. As discussed above, the third radial axis may be the first radial axis (e.g., Y-axis) and the fourth radial axis may be the second radial axis (e.g., X-axis), such that the third capacitive sensor is opposite (e.g., diametrically opposed to) the first capacitive sensor and the fourth capacitive sensor is opposite (e.g., diametrically opposed to) the second capacitive sensor. Each of the capacitive sensors of the monitoring system12transmits (block170) a signal to the controller42of the monitoring system12based at least in part on the sensed voltages. In some embodiments, the signals transmitted to the controller42are the sensed voltages. Accordingly, the controller42may receive sensed voltages from two, three, four, or more capacitive sensors positioned at an axial location about the rotational component.

The controller42executes instructions to determine (block172) the distances of the rotational component from each of the respective capacitive sensors. In some embodiments, the controller42executes instructions to determine the distances based at least in part on a functional relationship between the distance and the sensed voltage. The controller42may execute instructions to utilize the arrangement of the capacitive sensors relative to the rotational component, the areas of the capacitive sensors24, and/or a determined or predefined value for the electrical permittivity of the fluid to simplify the distance determinations. For example, a common area of the capacitive sensor plates may enable the controller42to utilize the same value for A in Equation 2. Additionally, or in the alternative, the controller42may execute instructions to determine or receive a value for the electrical permittivity of the fluid and utilize a scaling factor to determine the respective distances between the capacitive sensors24and the rotational component from the sensed voltages. Whereas measurements of eddy current sensors and other types of proximity sensors may be adversely affected by electromagnetic fields, the voltage sensed by the capacitive sensors24may be primarily based on the geometric properties and/or material properties of the capacitive sensors, the rotational component, and the materials between the capacitive sensors and the rotational component. That is, the sensed voltages by the capacitive sensors24may be substantially unaffected by electromagnetic fields. Accordingly, the capacitive sensors24may be utilized in monitoring systems in environments that may be susceptible to electromagnetic fields during operation, such as near windings of a generator or motor. The controller42may execute instructions to determine the position of the rotational component within the reference frame based at least in part on the determined distances. For example, the controller42may execute instructions to determine the position of a shaft axis20relative to a longitudinal56axis, where the first radial axis96and the second radial axis100are mutually perpendicular through the longitudinal axis56as shown inFIG. 3.

In some embodiments, the controller42executes instructions to store (block174) some or all of the determined distances in a memory, generating a history of the distances corresponding to the sample times. Additionally, or in the alternative, the controller42may execute instructions to store the position of the rotational component relative to the reference frame (e.g., longitudinal axis56). The controller42and/or the operator may analyze (block176) the stored data. For example, analysis of the stored distance or position data may identify patterns, trends, loading events, or vibration profiles, or any combination thereof, of the rotational component. The controller42may execute instructions to display (block178) the results of block172and/or block176. That is, the controller42may display the determined distances of the rotational component relative to the capacitive sensors, the current position of the rotational component within the reference frame, the movement of the rotational component over a period of time, timings of loading events, a vibration profile, or any combination thereof. While method158describes a method of operating a set of two or more capacitive sensors about a rotational component at a first axial position, the controller42may be utilized to monitor the same rotational component at a second axial position and/or to monitor another rotational component of the rotational system.

As described above, the monitoring system utilizes two or more capacitive sensors to determine operational parameters of a rotational component. The capacitive sensors may be utilized in environments subject to electromagnetic fields that may disrupt eddy current sensors and other types of proximity sensors. The arrangement and/or quantity of the capacitive sensors disposed about a rotational component may simplify the determination of the distance between the rotational component (e.g., shaft) and the capacitive sensors. The monitoring system may determine and display to an operator the determined operational parameters. The operational parameters may include, but are not limited to, the current position of the rotational component relative to a reference frame, the historical movement of the rotational component, loading events of the rotational component, or a vibration profile of the rotational component, or any combination thereof.