Blade tip gap capacitive measurement method for carbon fiber composite material

Abstract

The invention discloses a capacitive measurement method for a blade tip gap of a blade for a carbon fiber composite material. A probe of the capacitive sensor is arranged in a groove formed in an engine casing, and the probe is prepared by cladding three materials with increasing thermal expansion coefficients layer by layer through a laser sintering layer-by-layer cladding process; a pressure correction coefficient and a temperature correction coefficient are introduced to carry out dynamic compensation on a dielectric constant, and a projection factor and a conductive efficiency factor are introduced to carry out dynamic correction on an effective induction area. And according to the dielectric constant after dynamic compensation, the effective induction area after dynamic correction and a dynamic capacitance value measured by the capacitance sensor, the dynamic blade tip gap is calculated. According to the invention, dynamic measurement of the tip gap of the carbon fiber composite blade can be realized, and the measurement precision is high.

Description

Technical Field

[0001] This invention belongs to the field of aviation technology testing, specifically relating to a capacitive measurement method for the tip clearance of carbon fiber composite blades. Background Technology

[0002] As the core power source of aircraft, the performance of aero-engines is closely linked to their tip clearance, with appropriate tip clearance leading to better energy utilization efficiency. However, existing tip clearance measurement technologies have many limitations: optical measurements are prone to performance degradation, optical path deviation, or signal distortion under the high temperature, high pressure, high vibration, and strong electromagnetic interference environments within the engine; capacitive measurements are susceptible to interference from complex electromagnetic fields, resulting in unstable measurements, and sensor deviations can occur at high temperatures, especially for composite blades with anisotropic conductivity. Therefore, there is an urgent need to design a novel method for real-time, dynamic, and accurate measurement of tip clearance in high-speed deformed carbon fiber composite blades under extreme operating conditions. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and propose a capacitive measurement method for the tip gap of carbon fiber composite blades.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] This invention provides a capacitive measurement method for the tip clearance of carbon fiber composite blades, as detailed below:

[0006] Step 1: Place the probe of the capacitive sensor in the groove opened on the engine casing, with the detection surface of the probe tangent to the inner wall of the casing.

[0007] Step 2: The engine rotates at a preset speed, and the dynamic tip clearance when the blades sweep past the probe is calculated as follows:

[0008]

[0009] In the formula, For the effective sensing area, This is the capacitance value. is the dielectric constant.

[0010] Step 3: Let Δt be the total time from when the blade tip projection enters the probe's detection range to when it completely leaves the probe's detection range as the blade sweeps across it. Dynamically compensate for the dielectric constant as follows:

[0011]

[0012] In the formula, Reference air gap temperature and reference airflow pressure The dielectric constant of the following, and The actual airflow pressure and actual air gap temperature at time t within a total time period Δt are measured by pressure and temperature sensors installed on the inner wall of the casing, respectively. and These are the pressure correction factor and the temperature correction factor, respectively.

[0013] Step 4: Introduce projection factor and conductivity efficiency factor to correct the effective sensing area, thus obtaining the corrected effective sensing area. .

[0014] Step 5: Using the dynamically compensated dielectric constant, the corrected effective sensing area, and the capacitance value detected by the capacitance sensor... The dynamic tip clearance was calculated as follows:

[0015] .

[0016] Preferably, the pressure correction factor and temperature correction factor The process of obtaining the capacitance value is as follows: Measure the static blade tip clearance d0 when the engine is not rotating. Position the probe of the capacitance sensor directly opposite a carbon fiber composite plate with an area larger than the probe's detection surface, setting the clearance to d0. At this point, the effective sensing area S0 is the probe's detection surface area. Place the probe of the capacitance sensor and the carbon fiber composite plate at the initial airflow pressure and initial air gap temperature, respectively, using the initial airflow pressure and initial air gap temperature as reference airflow pressure and reference air gap temperature. Measure the capacitance value. Based on the formula The dielectric constant was obtained by calculation based on the initial airflow pressure and initial air gap temperature. Then, the air gap temperature is the reference air gap temperature. With the pressure constant, the airflow pressure was increased in increments of 50 kPa up to 0.8 MPa, and the airflow pressures at different levels were measured. The corresponding capacitance value Based on the formula Different airflow pressures were obtained through calculation. The corresponding dielectric constant By fitting curves The pressure correction factor is obtained. The value; then, with the airflow pressure as the reference airflow pressure remaining constant, the air gap temperature is set at 50... o C increases incrementally to 525 o C, the temperature of different air gaps was measured. The corresponding capacitance value Based on the formula Different air gap temperatures were obtained through calculation. The corresponding dielectric constant By fitting curves The temperature correction coefficient is obtained. The value of ; where the static tip clearance d0 is measured by laser interferometry when the engine is not rotating.

[0017] More preferably, the corrected effective sensing area is

[0018]

[0019] In the formula, and These are the corrected conductivity factor and projection factor of the k-th layer at time t, respectively; , and These represent the instantaneous projected area of ​​the cross section of the k-th layer when the blade is not fully inside, fully inside, and outside the probe detection surface at time t, respectively.

[0020] More preferably, the process of obtaining the ply projection factor of the k-th layer at time t is as follows: taking the midpoint of the blade root profile as the origin, the direction parallel to the probe detection surface and tangent to the cylindrical surface of the casing inner wall is the x-axis direction, the direction of the blade rotation axis is the y-axis direction, and the direction perpendicular to the x-axis and y-axis is the z-axis direction. The positive direction of the x-axis is set towards the blade rotation direction, and the positive direction of the y-axis is set towards the blade leading edge. A Cartesian coordinate system is established to obtain the blade rotation coordinate system, and the z-axis is defined as 0. o Reference axis, z-axis direction vector The initial k-th layer layup angle correction on the blade, transformed to the blade rotation coordinate system, is the angle of rotation.

[0021]

[0022] In the formula, To correct the direction vector of the k-th carbon fiber layer;

[0023] Over the entire time interval [0, Δt], the spatial angle is updated. Then, in the blade rotation coordinate system, the spatial angle of the k-th layer at time t is...

[0024]

[0025] In the formula, Let be the blade angular velocity, and , This refers to the blade rotation speed;

[0026] The projection factor of the k-th layer at time t is

[0027] .

[0028] More preferably, the process of obtaining the conductivity factor of the k-th ply at time t after correction is as follows: At the reference air gap temperature, the conductivity of each ply in the blade tip region is measured using the four-probe method. Four equally spaced probes are placed in contact with the corresponding ply surfaces in the blade tip region. A constant current I is applied to the two outer probes, and the voltage drop V is measured by the two inner probes. The conductivity of the k-th ply is then calculated.

[0029]

[0030] In the formula, The probe spacing, The area of ​​the cross section through which the current passes is the k-th ply, which is obtained by multiplying the thickness of the k-th ply by the blade length;

[0031] The conductivity factor of the k-th layer is

[0032]

[0033] In the formula, As the reference conductivity, and , The volume ratio of carbon fibers in the k-th layer layup;

[0034] The conductivity of each layup is corrected, and the conductivity of the k-th layup at time t is then corrected.

[0035]

[0036] In the formula, This is the temperature compensation coefficient;

[0037] After correcting the resin volume, the resin volume in the k-th layer at time t is:

[0038]

[0039] In the formula, is the linear thermal expansion coefficient of the resin. To correct the resin volume in the k-th layer before the correction;

[0040] After correction, the volume ratio of carbon fibers in the k-th layer at time t is:

[0041]

[0042] The corrected conductivity factor of the k-th layer at time t is

[0043] .

[0044] More preferably, the orientation of carbon fibers in each layer of the ply before correction, the volume ratio of carbon fibers in each layer of the ply, and the volume of resin in each layer of the ply are all measured by CT scanning. The process is as follows: at the reference air gap temperature, the blade is scanned using a CT scanner. The scanning results show the distribution of carbon fibers in each layer of the ply. The scanning data is tomographically processed to obtain images of each layer of the ply. In each layer of the ply image, the carbon fibers will show a dark linear structure. The carbon fiber orientation vector is extracted by combining image analysis: the edge contour of the carbon fibers is extracted using the Canny operator, the main direction of the carbon fibers is identified using directional filtering technology, and the components of the carbon fiber orientation vector in the x, y, and z directions are calculated. Based on the density difference between carbon fibers and resin, which causes them to show different gray values ​​in the scanning results, a gray value threshold is set to distinguish between the carbon fiber region and the resin region. By statistically analyzing the pixel points in the carbon fiber region and the pixel points in the overall region, the volume ratio of carbon fibers in each layer of the ply and the volume of resin in each layer of the ply are obtained.

[0045] More preferably, the equation of the projection line of the blade tip profile onto the plane of the probe's detection surface is:

[0046]

[0047] In the formula, L is the length of the projection line in the x-axis direction. The x-axis coordinate value on the projection line is The y-coordinate of the point. Let x be the x-axis coordinate of the point on the x-axis that is the largest distance from the probe detection surface to the blade tip projection that is about to enter the probe detection surface. , , , This represents the change in the y-axis direction between the highest and lowest points of the blade tip profile.

[0048] The x-axis coordinate value on the projection line is Point thickness expression function:

[0049]

[0050] Among them, W f W represents the maximum thickness at the leading edge of the leaf tip. r The thickness at the trailing edge of the leaf tip;

[0051] Then, at time t, when the blade has not fully entered the probe detection surface, the instantaneous projected area of ​​the cross-section of the k-th ply is:

[0052]

[0053] In the formula, This refers to the number of abrupt signal changes detected by the THz device near the blade entry side of the probe detection surface. for right The derivative of the axis, the proportionality coefficient of the thickness of the k-th layer. , The number of layers, , The interval of the probe's detection surface along the x-axis is denoted as M[x]. L x R ],and The x-axis coordinate value on the projection line is The displacement of the point relative to the probe's x-axis at time t , The x-axis coordinate value on the projection line is The radius of rotation of the point corresponding to the point on the blade tip profile;

[0054] The instantaneous projected area of ​​the cross section of the k-th ply when the blade is fully inside the probe detection surface at time t is:

[0055]

[0056] The instantaneous projected area of ​​the cross section of the k-th ply when the blade leaves the probe detection surface at time t is:

[0057]

[0058] In the formula, This refers to the number of abrupt signal changes detected by the THz device near the blade departure side of the probe detection surface.

[0059] Preferably, the equivalent tip clearance is calculated within the total time Δt from when the blade tip projection enters the probe detection range to when it completely leaves the probe detection range as the blade sweeps across the probe. This serves as the measured value of the blade tip gap when the blade sweeps across the probe. The calculation is as follows:

[0060] .

[0061] Preferably, the probe is prepared using a laser sintering layer-by-layer cladding process, comprising an inner layer, a middle layer, and an outer layer. The materials of the inner layer, middle layer, and outer layer are Invar 36 alloy, SiC-Si3N4 composite ceramic, and YSZ ceramic, respectively. The inner layer is bonded and fixed to the casing. The middle layer has a spiral microchannel with a YSZ coating deposited on the inner wall of the spiral microchannel. The outer layer has an interface communicating with the spiral microchannel. The interface is connected to an air vent on the casing via an alloy bellows, allowing oxygen to enter the spiral microchannel sequentially through the air vent, the alloy bellows, and the interface, where it undergoes an endothermic reaction with the YSZ coating for cooling.

[0062] The present invention has the following beneficial effects:

[0063] This invention enables dynamic measurement of the tip clearance of carbon fiber composite blades with high accuracy. Specifically, the invention uses a capacitive sensor to measure the tip clearance. The sensor probe is fabricated by laser sintering layer-by-layer cladding of three materials with increasing coefficients of thermal expansion, reducing probe deformation and preventing cracking due to high temperature and pressure inside the engine. Furthermore, a YSZ coating is deposited on the inner wall of the spiral microchannel in the middle layer of the probe. The introduced oxygen reacts with the YSZ coating endothermally to cool it, reducing the impact of temperature on the measurement accuracy of the capacitive sensor, lowering errors, and effectively extending the probe's lifespan, thus reducing engine maintenance costs. Further, based on the formula used for measuring tip clearance with a capacitive sensor, this invention introduces pressure correction to the dielectric constant. Dynamic compensation using positive coefficients and temperature correction coefficients improves the measurement accuracy of subsequent dynamic blade tip clearance. A projection factor and conductivity efficiency factor are introduced to dynamically correct the effective sensing area. The projection factor is obtained by dynamically correcting the ply angles after considering the changes in ply angles as the blade rotates. The conductivity efficiency factor is obtained by dynamically correcting the conductivity and carbon fiber volume ratio after considering the influence of temperature on the conductivity of the carbon fiber composite material. This further improves the measurement accuracy of the effective sensing area. Finally, the dynamic blade tip clearance is calculated based on the dynamically compensated dielectric constant, the dynamically corrected effective sensing area, and the dynamic capacitance value measured by the capacitance sensor, thus achieving accurate measurement of the dynamic blade tip clearance. Attached Figure Description

[0064] Figure 1 This is a cross-sectional schematic diagram of the inner, middle and outer three-layer structure of the probe of the capacitive sensor in this invention;

[0065] Figure 2 This is a schematic diagram of the middle layer structure of the capacitive sensor probe in this invention. Detailed Implementation

[0066] The present invention will now be further described with reference to the accompanying drawings.

[0067] This invention provides a capacitive measurement method for the tip clearance of carbon fiber composite blades, as detailed below:

[0068] Step 1: Place the capacitive sensor probe into the groove cut into the engine casing, with the probe's detection surface tangent to the inner wall of the casing. Install two THz devices 4 (which can be terahertz lasers) on both sides of the capacitive sensor probe, ensuring the laser optical axis of the THz devices is in contact with the side of the probe. Figure 1 and Figure 2As shown, the probe is fabricated using a laser sintering layer-by-layer cladding process, comprising an inner layer 1, a middle layer 2, and an outer layer 3. The materials for the inner, middle, and outer layers are Invar 36 alloy, SiC-Si3N4 composite ceramic, and YSZ ceramic, respectively. The inner layer is bonded and fixed to the casing. The middle layer has a spiral microchannel 2-1, with a YSZ coating deposited on the inner wall of the spiral microchannel. The outer layer has an interface 2-2 communicating with the spiral microchannel. The interface is connected to an air vent on the casing via an alloy bellows, allowing oxygen to sequentially enter the spiral microchannel through the air vent, the alloy bellows, and the interface, where it undergoes an endothermic reaction with the YSZ coating, resulting in cooling. The YSZ ceramic contains 8 wt%... It possesses high temperature resistance and wear resistance properties. As an outer layer, it can directly contact the high-temperature airflow at the blade tip, while also serving as an insulating layer to avoid electromagnetic interference. Its coefficient of thermal expansion, CTE, is... ; Composite ceramics (SiC and With a mass ratio of 7:3, it combines high-temperature strength and thermal shock resistance, and its coefficient of thermal expansion CTE = With a thermal expansion coefficient between that of YSZ ceramic and Invar 36, it can serve as an intermediate layer to balance the thermal expansion differences between the inner and outer layers; the thermal expansion coefficient CTE of Invar 36 alloy (containing 36wt% Ni) is... The thermal expansion coefficient is matched to that of the engine casing material (usually a nickel-based alloy), serving as the inner layer connected to the engine casing. In this embodiment, an air bleed port is opened at the trailing edge of the fifth-stage stator ring of the aero-engine (i.e., 1.2m axially from the compressor inlet, with a circumferential angle at the 3 o'clock position on the casing clock). The airflow pressure here can reach 350 kPa, and the temperature can reach 480°C. o C, the oxygen concentration is greater than 18%, which meets the reaction requirements.

[0069] Step 2: The engine rotates at a preset speed, and each blade sweeps past the probe in sequence. As each blade sweeps past the probe, the capacitance between it and the probe's detection surface changes with the blade tip clearance. The dynamic blade tip clearance under engine rotation conditions is then measured. for

[0070]

[0071] In the formula, For the effective sensing area, This is the capacitance value. is the dielectric constant.

[0072] Step 3: Let Δt be the total time from when the blade tip projection enters the probe detection range to when it completely leaves the probe detection range as the blade sweeps past the probe. In this embodiment, only one blade is periodically measured. Time 0 is the moment when the blade enters the probe detection range, and time 0 is recorded again after the blade completes one rotation cycle. Since the engine operates in a high-temperature and high-pressure environment, it has a significant impact on the dielectric constant. Therefore, considering the influence of air gap temperature and airflow pressure, the dielectric constant is dynamically compensated. The compensated dielectric constant is:

[0073]

[0074] In the formula, The dielectric constant is given by the reference air gap temperature and the reference gas flow pressure, and the reference air gap temperature is... 25 o C, Reference airflow pressure It is 0.1 MPa. and The values ​​represent the actual airflow pressure and actual air gap temperature at time t within the entire time interval [0, Δt], respectively, measured by pressure and temperature sensors installed on the inner wall of the casing. and The pressure correction coefficient and temperature correction coefficient are respectively obtained through calibration tests. The process is as follows: The static blade tip clearance d0 is measured when the engine is not rotating. The probe of the capacitive sensor is aligned with a carbon fiber composite plate whose area is larger than the probe's detection surface, and the gap is set to d0. At this time, the effective sensing area S0 is the probe's detection surface area. The probe of the capacitive sensor and the carbon fiber composite plate are then subjected to the initial airflow pressure and initial air gap temperature, which are respectively the reference airflow pressure and reference air gap temperature. That is, the initial airflow pressure is... The initial air gap temperature is The capacitance values ​​at the initial airflow pressure and initial air gap temperature were measured. Based on the formula The dielectric constant was obtained by calculation based on the initial airflow pressure and initial air gap temperature. Then, the air gap temperature is the reference air gap temperature. With the pressure constant, the airflow pressure was increased in increments of 50 kPa up to 0.8 MPa, and the airflow pressures at different levels were measured. The corresponding capacitance value Based on the formula Different airflow pressures were obtained through calculation. The corresponding dielectric constant By fitting curves The pressure correction factor is obtained. The value; then, with the airflow pressure as the reference airflow pressure remaining constant, the air gap temperature is set at 50...o C increases incrementally to 525 o C, the temperature of different air gaps was measured. The corresponding capacitance value Based on the formula Different air gap temperatures were obtained through calculation. The corresponding dielectric constant By fitting curves The temperature correction coefficient is obtained. The value of ; where the static tip clearance d0 is measured by laser interferometry when the engine is not rotating.

[0075] Step 4: When the blade rotates, the layup angles of each layer (of carbon fiber composite material) change in real time with the rotation axis of the installed blade, resulting in different projected areas at different times. This causes the projection direction of the effective sensing area parameter of the capacitive sensor to deviate from the theoretical value. In addition, the conductivity of carbon fiber composite material changes with increasing temperature and exhibits different characteristics in different directions. This anisotropy of conductivity causes the signal response of the capacitive sensor to fluctuate at different temperatures, indirectly affecting the accurate measurement of the effective sensing area. Therefore, projection factors and conductivity efficiency factors are introduced to correct the effective sensing area at different times in terms of layup angle and conductivity, respectively.

[0076] (1) Introduce projection factors and conductivity efficiency factors for different times regarding the layup angle and conductivity respectively:

[0077] ① Correct the ply angles of each layer at different times: Using the midpoint of the blade root profile as the origin, the x-axis is defined as the direction parallel to the probe detection surface and tangent to the cylindrical surface of the casing inner wall. The y-axis is defined as the direction of the blade rotation axis (i.e., the central axis of the blade's rotation). The z-axis is defined as the direction perpendicular to both the x and y axes (i.e., one of the radial directions of the cylindrical surface of the casing inner wall). The positive direction of the x-axis points towards the blade rotation direction, and the positive direction of the y-axis points towards the blade leading edge. Establish a Cartesian coordinate system to obtain the blade rotation coordinate system, defining the z-axis as 0. o Reference axis, z-axis direction vector The initial k-th layer layup angle correction on the blade, transformed to the blade rotation coordinate system, is the angle of rotation.

[0078]

[0079] In the formula, This is to correct the direction vector of the k-th carbon fiber layer.

[0080] Over the entire time interval [0, Δt], the spatial angle is updated. Then, in the blade rotation coordinate system, the spatial angle of the k-th layer at time t is...

[0081]

[0082] In the formula, Let be the blade angular velocity, and , The blade rotation speed, i.e. the shaft rotation speed, is obtained through an encoder mounted on the shaft.

[0083] The projection factor of the k-th layer at time t is

[0084]

[0085] ② Regarding conductivity: At the reference air gap temperature, the conductivity of each ply layer was measured in the blade tip region using the four-probe method. Four equally spaced probes were placed in contact with the corresponding ply surfaces in the blade tip region. A constant current I was applied to the two outer probes, and the voltage drop V was measured by the two inner probes. The conductivity of the k-th ply layer was then calculated.

[0086]

[0087] In the formula, The probe spacing, The area of ​​the cross section through which the current passes is the k-th ply, which is obtained by multiplying the thickness of the k-th ply by the blade length;

[0088] Since the resin is essentially non-conductive, carbon fiber dominates in each layer, and the conductivity factor of the k-th layer is:

[0089]

[0090] In the formula, This is the baseline conductivity (the maximum theoretical conductivity of carbon fiber), and S / m, The volume ratio of carbon fibers in the k-th layer is given by [reference to a specific layer]. Characterizing the maximum theoretical electrical conductivity of carbon fiber composites;

[0091] Furthermore, considering the effect of temperature on the conductivity of each ply, the conductivity of each ply is corrected. After correction, the conductivity of the k-th ply at time t is...

[0092]

[0093] In the formula, The temperature compensation coefficient is obtained through calibration tests. In this embodiment... .

[0094] During engine operation, the internal temperature and pressure are high, causing thermal expansion of the ply layers and changes in ply thickness and carbon fiber volume ratio. Therefore, corrections to the ply thickness and carbon fiber volume ratio are necessary. Since the coefficient of thermal expansion of carbon fibers in the ply is much smaller than that of resin, the overall thermal expansion of the ply is mainly contributed by the resin. Therefore, the correction of the ply thickness and carbon fiber volume ratio for each layer focuses on the resin. After correction, the thickness of the k-th ply at time t is...

[0095]

[0096] In the formula, This represents the thickness of the k-th layer before correction. Let be the linear coefficient of thermal expansion of the resin, and .

[0097] Furthermore, since resin is an isotropic material, its coefficient of volumetric expansion (approximately) is three times its coefficient of linear expansion. Therefore, the volume of resin in the k-th layer at time t after correction is:

[0098]

[0099] In the formula, This represents the resin volume in the k-th layer before correction.

[0100] Then, the volume ratio of carbon fibers in the k-th layer at time t after correction is:

[0101]

[0102] The corrected conductivity factor of the k-th layer at time t is

[0103] .

[0104] Before correction, the orientation (layout angle) of carbon fibers in each layup, the thickness of each layup, the volume ratio of carbon fibers in each layup, the volume of resin in each layup, and the volume of carbon fibers in each layup were all measured by CT scan. The process was as follows: at the reference air gap temperature, the blade was scanned using a CT scanner. The scan results showed the distribution of carbon fibers in each layup. The scan data was tomographically processed to obtain images of each layup. In the images of each layup, carbon fibers would appear as dark linear structures. Combined with image analysis, the carbon fiber orientation vector was extracted: the edge contour of carbon fibers was extracted using the Canny operator, the main direction of carbon fibers was identified using directional filtering technology, and the components of the carbon fiber orientation vector in the x, y, and z directions were calculated. The thickness of each layup was obtained by direct measurement. Based on the density difference between carbon fibers and resin, which causes them to appear with different gray values ​​in the scan results, a gray value threshold was set to distinguish between carbon fiber areas and resin areas. By statistically analyzing the pixel points in the carbon fiber area and the pixel points in the overall area, the volume ratio of carbon fibers in each layup and the volume of resin and carbon fibers in each layup were obtained.

[0105] (2) The calculation process of the effective sensing area before correction is as follows: The equation of the projection line of the blade tip profile onto the detection surface of the probe is as follows:

[0106]

[0107] In the formula, L is the length of the projection line in the x-axis direction. The x-axis coordinate value on the projection line is The y-coordinate of the point. Let x be the x-axis coordinate of the point on the x-axis that is the largest distance from the probe detection surface to the blade tip projection that is about to enter the probe detection surface. , , , This represents the change in the y-axis direction between the highest and lowest points of the blade tip profile.

[0108] Simultaneously, based on the trend of the blade tip profile change, the x-axis coordinate value on the projection line is defined as... Point thickness expression function:

[0109]

[0110] Among them, W f W represents the maximum thickness at the leading edge of the leaf tip (i.e., the diameter of the arc at the leading edge). r The thickness is measured at the trailing edge of the leaf tip.

[0111] The area of ​​the blade entering the probe detection surface is solved by integrating the area of ​​the blade's infinitesimal element. Since the profiles of each layer of the blade are consistent, the values ​​only have a multiple relationship in the y-axis direction. Therefore, the area infinitesimal element is determined by the x-axis coordinate value on the projection line. The thickness value at a point is obtained by multiplying the y-component of the thickness value by the infinitesimal change dx of the x-axis coordinate; for Taking the derivative yields , That is, the projection line is at coordinate value The slope of the tangent at point t; since the thickness direction is perpendicular to the tangent direction, the instantaneous projected area of ​​the k-th ply cross-section when the blade has not fully entered the probe detection surface at time t is calculated as follows:

[0112]

[0113] In the formula, The number of abrupt changes detected by the THz device near the blade entry side of the probe detection surface (when the interface between adjacent plies passes through the THz device, the THz device will detect an abrupt change signal, thus distinguishing which ply begins to enter the probe detection surface), and the proportionality coefficient of the thickness of the k-th ply. , The number of layers, , The interval of the probe's detection surface along the x-axis is denoted as M[x]. L x R ],and The x-axis coordinate value on the projection line is The displacement of the point relative to the probe's x-axis at time t , For blade rotation speed, The x-axis coordinate value on the projection line is The radius of rotation of the point on the blade tip profile is the distance from the corresponding point on the profile to the center axis of the rotation shaft.

[0114] Calculate the instantaneous projected area of ​​the k-th ply cross section when the blade is fully inside the probe detection surface at time t.

[0115]

[0116] Calculate the instantaneous projected area of ​​the cross-section of the k-th ply when the blade leaves the probe detection surface at time t.

[0117]

[0118] In the formula, This refers to the number of abrupt signal changes detected by the THz device near the blade departure side of the probe detection surface.

[0119] (3) The effective sensing area is corrected by introducing the effective conductivity factor and projection factor. The corrected effective sensing area is:

[0120]

[0121] Step 5: Using the dynamically compensated dielectric constant, the corrected effective sensing area, and the capacitance value detected by the capacitance sensor... The dynamic tip clearance was calculated as follows:

[0122] .

[0123] To simplify the data, an equivalent tip clearance can also be calculated over the total time Δt from when the blade tip projection enters the probe's detection range until it completely leaves the probe's detection range as the blade sweeps across it. This serves as the measured value of the blade tip gap when the blade sweeps across the probe. The calculation is as follows:

[0124] .

Claims

1. A capacitive measurement method for the tip clearance of carbon fiber composite blades, characterized in that: Specifically as follows: Step 1: Place the probe of the capacitive sensor in the groove opened on the engine casing, with the probe's detection surface tangent to the inner wall of the casing. Step 2: The engine rotates at a preset speed, and the dynamic tip clearance when the blades sweep past the probe is calculated as follows: In the formula, For the effective sensing area, This is the capacitance value. It is the dielectric constant; Step 3: Let Δt be the total time from when the blade tip projection enters the probe's detection range to when it completely leaves the probe's detection range as the blade sweeps across it. Dynamically compensate for the dielectric constant as follows: In the formula, Reference air gap temperature and reference airflow pressure The dielectric constant of the following, and The actual airflow pressure and actual air gap temperature at time t within a total time period Δt are measured by pressure and temperature sensors installed on the inner wall of the casing, respectively. and These are the pressure correction factor and the temperature correction factor, respectively. Step 4: Introduce projection factor and conductivity efficiency factor to correct the effective sensing area, thus obtaining the corrected effective sensing area. ; Step 5: Using the dynamically compensated dielectric constant, the corrected effective sensing area, and the capacitance value detected by the capacitance sensor... The dynamic tip clearance was calculated as follows: 。 2. The capacitive measurement method for blade tip clearance of carbon fiber composite materials according to claim 1, characterized in that: Pressure correction factor and temperature correction factor The process of obtaining the capacitance value is as follows: Measure the static blade tip clearance d0 when the engine is not rotating. Position the probe of the capacitance sensor directly opposite a carbon fiber composite plate with an area larger than the probe's detection surface, setting the clearance to d0. At this point, the effective sensing area S0 is the probe's detection surface area. Place the probe of the capacitance sensor and the carbon fiber composite plate at the initial airflow pressure and initial air gap temperature, respectively, using the initial airflow pressure and initial air gap temperature as reference airflow pressure and reference air gap temperature. Measure the capacitance value. Based on the formula The dielectric constant was obtained by calculation based on the initial airflow pressure and initial air gap temperature. ; Then, the air gap temperature is the reference air gap temperature. With the pressure constant, the airflow pressure was increased in increments of 50 kPa up to 0.8 MPa, and the airflow pressures at different levels were measured. The corresponding capacitance value Based on the formula Different airflow pressures were obtained through calculation. The corresponding dielectric constant By fitting curves The pressure correction factor is obtained. The value; then, with the airflow pressure as the reference airflow pressure remaining constant, the air gap temperature is set at 50... o C increases incrementally to 525 o C, the temperature of different air gaps was measured. The corresponding capacitance value Based on the formula Different air gap temperatures were obtained through calculation. The corresponding dielectric constant By fitting curves The temperature correction coefficient is obtained. The value of ; where the static tip clearance d0 is measured by laser interferometry when the engine is not rotating.

3. The capacitive measurement method for blade tip clearance of carbon fiber composite materials according to claim 2, characterized in that: The corrected effective sensing area is In the formula, and These are the corrected conductivity factor and projection factor of the k-th layer at time t, respectively; , and These represent the instantaneous projected area of ​​the cross section of the k-th layer when the blade is not fully inside, fully inside, and outside the probe detection surface at time t, respectively.

4. The method for capacitive measurement of blade tip clearance of carbon fiber composite materials according to claim 3, characterized in that: The process of obtaining the projection factor of the k-th layer at time t is as follows: Taking the midpoint of the blade root profile as the origin, the x-axis is defined as the direction parallel to the probe detection surface and tangent to the cylindrical surface of the casing inner wall; the y-axis is defined as the direction of the blade rotation axis; and the z-axis is defined as the direction perpendicular to both the x-axis and y-axis. The positive direction of the x-axis points towards the blade rotation direction, and the positive direction of the y-axis points towards the blade leading edge. A Cartesian coordinate system is established to obtain the blade rotation coordinate system, and the z-axis is defined as 0. o Reference axis, z-axis direction vector The initial k-th layer layup angle correction on the blade, transformed to the blade rotation coordinate system, is the angle of rotation. In the formula, To correct the direction vector of the k-th carbon fiber layer; Over the entire time interval [0, Δt], the spatial angle is updated. Then, in the blade rotation coordinate system, the spatial angle of the k-th layer at time t is... In the formula, Let be the blade angular velocity, and , This refers to the blade rotation speed; The projection factor of the k-th layer at time t is 。 5. The capacitive measurement method for blade tip clearance of carbon fiber composite materials according to claim 4, characterized in that: The process of obtaining the conductivity factor of the k-th ply at time t after correction is as follows: At the reference air gap temperature, the conductivity of each ply in the blade tip region is measured using the four-probe method. Four equally spaced probes are placed in contact with the corresponding ply surfaces in the blade tip region. A constant current I is applied to the two probes on the outer side, and the voltage drop V is measured by the two probes on the inner side. The conductivity of the k-th ply is then calculated. In the formula, The probe spacing, The area of ​​the cross section through which the current passes is the k-th ply, which is obtained by multiplying the thickness of the k-th ply by the blade length; The conductivity factor of the k-th layer is In the formula, As a reference conductivity, The volume ratio of carbon fibers in the k-th layer layup; The conductivity of each layup is corrected, and the conductivity of the k-th layup at time t is then corrected. In the formula, This is the temperature compensation coefficient; After correcting the resin volume, the resin volume in the k-th layer at time t is: In the formula, is the linear thermal expansion coefficient of the resin. To correct the resin volume in the k-th layer before the correction; After correction, the volume ratio of carbon fibers in the k-th layer at time t is: The corrected conductivity factor of the k-th layer at time t is 。 6. The method for capacitive measurement of blade tip clearance of carbon fiber composite materials according to claim 5, characterized in that: The orientation of carbon fibers in each layer of the ply before correction, the volume ratio of carbon fibers in each layer of the ply, and the volume of resin in each layer of the ply were all measured by CT scan. The process was as follows: at the reference air gap temperature, the blade was scanned with a CT scanner. The scan results showed the distribution of carbon fibers in each layer of the ply. The scan data was processed by tomography to obtain images of each layer of the ply. In each layer of the ply image, the carbon fibers would show a dark linear structure. The carbon fiber orientation vector was extracted by combining the image analysis: the edge contour of the carbon fibers was extracted using the Canny operator, the main direction of the carbon fibers was identified using directional filtering technology, and the components of the carbon fiber orientation vector in the x, y, and z directions were calculated. The density difference between carbon fiber and resin causes them to exhibit different grayscale values ​​in the scanning results. A grayscale threshold is set to distinguish between carbon fiber areas and resin areas. By statistically analyzing the number of pixels in the carbon fiber area and the total number of pixels in the whole area, the volume ratio of carbon fiber in each layer and the volume of resin in each layer are obtained.

7. The method for capacitive measurement of blade tip clearance of carbon fiber composite materials according to claim 4, characterized in that: The equation of the projection line of the blade tip profile onto the plane of the probe's detection surface is: In the formula, L is the length of the projection line in the x-axis direction. The x-axis coordinate value on the projection line is The y-coordinate of the point. Let x be the x-axis coordinate of the point on the x-axis that is the largest distance from the probe detection surface to the blade tip projection that is about to enter the probe detection surface. , , , This represents the change in the y-axis direction between the highest and lowest points of the blade tip profile. The x-axis coordinate value on the projection line is Point thickness expression function: Among them, W f W represents the maximum thickness at the leading edge of the leaf tip. r The thickness at the trailing edge of the leaf tip; Then, at time t, when the blade has not fully entered the probe detection surface, the instantaneous projected area of ​​the cross-section of the k-th ply is: In the formula, This refers to the number of abrupt signal changes detected by the THz device near the blade entry side of the probe detection surface. for right The derivative of the axis, the proportionality coefficient of the thickness of the k-th layer. , The number of layers, , The interval of the probe's detection surface along the x-axis is denoted as M[x]. L x R ],and The x-axis coordinate value on the projection line is The displacement of the point relative to the probe's x-axis at time t , The x-axis coordinate value on the projection line is The radius of rotation of the point corresponding to the point on the blade tip profile; The instantaneous projected area of ​​the cross section of the k-th ply when the blade is fully inside the probe detection surface at time t is: The instantaneous projected area of ​​the cross section of the k-th ply when the blade leaves the probe detection surface at time t is: In the formula, This refers to the number of abrupt signal changes detected by the THz device near the blade departure side of the probe detection surface.

8. The capacitive measurement method for blade tip clearance of carbon fiber composite materials according to claim 1, characterized in that: The equivalent tip clearance is calculated within the total time Δt of the blade tip projection from entering the probe's detection range to completely leaving the probe's detection range as the blade sweeps past the probe. This serves as the measured value of the blade tip gap when the blade sweeps across the probe. The calculation is as follows: 。 9. The method for capacitive measurement of blade tip clearance of carbon fiber composite materials according to claim 1, characterized in that: The probe is fabricated using a laser sintering layer-by-layer cladding process, comprising an inner layer, a middle layer, and an outer layer. The materials for the inner, middle, and outer layers are Invar 36 alloy, SiC-Si3N4 composite ceramic, and YSZ ceramic, respectively. The inner layer is bonded and fixed to the casing. The middle layer has a spiral microchannel with a YSZ coating deposited on its inner wall. The outer layer has an interface communicating with the spiral microchannel. The interface is connected to an air vent on the casing via an alloy bellows, allowing oxygen to sequentially enter the spiral microchannel through the air vent, the alloy bellows, and the interface, where it undergoes an endothermic reaction with the YSZ coating, resulting in cooling.

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