Metal embedded multipoint fiber grating strain sensor and preparation method thereof

Abstract

The invention provides a metal embedded multipoint fiber bragg grating strain sensor and a preparation method thereof, the sensor comprises a multipoint fiber bragg grating string, a metal protective sleeve and a transition tube, two measuring points on the multipoint fiber bragg grating string are in a group, one measuring point is used for temperature compensation of the other strain measuring point, and the metal protective sleeve is used for packaging. According to the invention, the multi-point fiber bragg grating string is embedded into the metal structure through an ultrasonic additive process to realize embedded strain measurement of the metal structure, and the temperature compensation structure can compensate thermal strain of the to-be-measured structure in the strain measurement process and measurement result distortion caused by cross sensitivity of measurement points to temperature. Accurate sensing of mechanical state information of the metal structure is achieved, strain information of multiple sets of measuring points on multiple sensors can be collected at the same time in cooperation with a multi-channel demodulator, and embedded quasi-distribution measurement is achieved. The method is suitable for strain monitoring scenes with severe temperature change, such as rocket engines, gas pipelines and satellite sailboards.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of measurement testing technology, in particular to a metal-embedded multi-point fiber grating strain sensor and a preparation method thereof. BACKGROUND

[0002] With the development of reusable launch vehicles, deep space probes, lunar scientific research stations and other aerospace equipment and engineering, the long-life requirements of spacecraft and the intelligentization needs of equipment such as digital twinning have become prominent. Currently, the sensors for monitoring the health of metal structures are basically surface-mounted or installed nearby, which cannot achieve true in-situ measurement of the metal, resulting in large measurement deviation, exposure to damage, and messy surface wiring, which seriously restricts their use.

[0003] Embedding the sensing element into the metal structure can effectively solve the above-mentioned pain points. With the development of ultrasonic metal additive technology, it is possible to embed the sensing element into the metal structure. As a low-temperature additive manufacturing technology, ultrasonic metal additive technology does not generate high temperature during the preparation process, and the metal deformation is small, so it does not damage the embedded sensor structure. At the same time, fiber grating sensors have the advantages of anti-electromagnetic interference, high precision, and multiplexing capability, and as embedded sensors, they have great development potential. In 2018, Adam Hehr et al. embedded fiber gratings into aluminum alloy structures using a high-power ultrasonic additive device and conducted a tensile test. The results showed that before the material yielded, the FBG center wavelength changed linearly with the load. MENG Bao et al. proposed a method and device for embedding FBG optical fiber sensors into metal substrates (CN115846847A), which embedded fiber gratings into metal substrates using an ultrasonic additive device, obtaining a structure / function integrated intelligent structure.

[0004] However, current research on metal fiber-embedded strain sensors does not consider temperature compensation. In the field of aerospace, the strain of metal structures often changes with a dramatic change in temperature, and the embedded grating sensor will inevitably be affected by the thermal strain of the material. At the same time, the grating itself is cross-sensitive to strain and temperature. Therefore, it cannot accurately monitor the strain caused by the actual mechanical load of the metal, making the monitoring results unable to reflect the mechanical state of the structure.

[0005] Therefore, there is a need for a sensor that can resist the interference of temperature changes on strain. SUMMARY

[0006] The present application is to solve the problem of temperature interference in the strain measurement process, and provides a metal embedded multi-point fiber grating strain sensor and a preparation method thereof, which comprises a multi-point fiber grating string, a metal protective sleeve and a transition pipe, wherein two measuring points of the multi-point fiber grating string are a group, one measuring point is used for temperature compensation of another strain measuring point, and the metal protective sleeve is used for packaging.

[0007] The present application provides a metal embedded multi-point fiber grating strain sensor, which comprises a multi-point grating fiber string embedded on the surface of a to-be-measured metal structure, a metal protective sleeve packaged on the outer periphery of the multi-point grating fiber string, and a transition pipe connected to the leading part of the multi-point grating fiber string. Two grating measuring points in the multi-point grating fiber string are a group, each grating measuring point group is composed of a strain grating measuring point and a temperature compensation grating measuring point, and the metal protective sleeve is packaged outside the temperature compensation grating measuring point. The strain grating measuring point is fixed in the to-be-measured metal structure and changes the center wavelength with the strain and / or temperature change of the to-be-measured metal structure; the temperature compensation grating measuring point is loosely coupled with the to-be-measured metal structure and is isolated from the strain of the to-be-measured metal structure through the metal protective sleeve, so that the temperature compensation grating measuring point is only affected by the temperature of the to-be-measured metal structure; and the temperature compensation grating measuring point is a temperature compensation point of the strain grating measuring point.

[0008] The temperature change of the to-be-measured metal structure can be obtained according to the measurement result of the temperature compensation grating measuring point, and the center wavelength drift amount of the strain grating measuring point Δλ ε The accurate strain value of the to-be-measured metal structure caused by mechanical load is obtained after correction ε, The specific calculation method is as follows: ; ; Wherein ε is the accurate strain value of the to-be-measured metal structure caused by mechanical load measured by the sensor after eliminating thermal strain; ΔT is the temperature change value; Δλ ε is the center wavelength drift amount of the strain grating measuring point; ΔλT is the center wavelength drift amount of the temperature compensation grating measuring point; k ε is the sensitivity coefficient (the drift amount of the measuring point reflection spectrum under unit strain change) of the strain grating measuring point; kT The temperature compensation grating measuring point sensitivity coefficient (the center wavelength of the measuring point reflection spectrum drifts under unit temperature change); γ εT The temperature compensation grating measuring point temperature compensation sensitivity coefficient can be obtained through strain and temperature calibration tests.

[0009] The length of the grating area of the strain grating measuring point and the temperature compensation grating measuring point is less than 1 mm, and the interval between the strain grating measuring point and the temperature compensation grating measuring point is less than 10 mm.

[0010] The length of the grating area of the strain grating measuring point and the temperature compensation grating measuring point is less than 1 mm, and the interval between the strain grating measuring point and the temperature compensation grating measuring point is less than 10 mm.

[0011] The length of the grating area of the strain grating measuring point and the temperature compensation grating measuring point is less than 1 mm, and the interval between the strain grating measuring point and the temperature compensation grating measuring point is less than 10 mm. The U-shaped groove includes a multi-point grating fiber string U-shaped groove, a metal protective sleeve U-shaped groove and a transition pipe U-shaped groove. The width and depth of the multi-point grating fiber string U-shaped groove are the same as the outer diameter of the multi-point grating fiber string. The width and depth of the metal protective sleeve U-shaped groove are greater than or equal to 1.3 times the outer diameter of the metal protective sleeve. The metal foil has the same material as the measured metal structure and a thickness of less than 0.15 mm.

[0012] The length of the grating area of the strain grating measuring point and the temperature compensation grating measuring point is less than 1 mm, and the interval between the strain grating measuring point and the temperature compensation grating measuring point is less than 10 mm.

[0013] The length of the grating area of the strain grating measuring point and the temperature compensation grating measuring point is less than 1 mm, and the interval between the strain grating measuring point and the temperature compensation grating measuring point is less than 10 mm.

[0014] The application provides a preparation method of a metal-embedded multipoint fiber grating strain sensor. S1, a U-shaped groove is pre-processed on the surface of a to-be-measured metal structure according to the arrangement requirement of measuring points, and the U-shaped groove is used for placing a multipoint grating fiber string, a metal protective sleeve and a transition pipe; S2, the multipoint fiber grating strain sensor is placed into the U-shaped groove, and both ends of the multipoint grating fiber string are fixed to prevent the fiber from escaping from the groove during embedding; S3, the metal foil is placed on the surface of the to-be-measured metal structure and covers the multipoint fiber grating strain sensor and the U-shaped groove, the metal foil and the to-be-measured metal structure are solidified through an ultrasonic additive process, so that the strain grating measuring points are solidified in the to-be-measured metal structure, and the deformation of the to-be-measured metal structure can be effectively transmitted to the strain grating measuring points. Since the width and depth of the U-shaped groove of the metal protective sleeve are greater than those of the metal protective sleeve, the solidified layer of the metal foil and the surface of the to-be-measured metal structure cannot wrap the metal protective sleeve, thereby forming loose coupling, and the deformation of the to-be-measured metal structure cannot be transmitted to the temperature compensation grating measuring points.

[0015] As a preferred mode, in step S3 of the preparation method of the metal-embedded multipoint fiber grating strain sensor, the ultrasonic frequency is 20 KHz, the amplitude is 20-25 mu m, the rolling speed of the pressure head is 70 mm / min, and the pressure is 0.35 MPa.

[0016] As a preferred mode, in step S3 of the preparation method of the metal-embedded multipoint fiber grating strain sensor, the metal foil is solidified through an ultrasonic additive pressure head.

[0017] The application has the following advantages: The multipoint fiber grating string is embedded into the metal structure through the ultrasonic additive process to realize embedded strain measurement of the metal structure. The designed temperature compensation structure can compensate the thermal strain of the to-be-measured structure and the distortion of the measurement result caused by the cross-sensitivity of the measuring points to temperature during measurement, so as to realize accurate measurement of the mechanical state of the metal structure, and is suitable for strain monitoring scenes such as rocket engines, gas pipelines and satellite sails with large temperature changes. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 It is a multipoint fiber grating string embedded metal structure effect diagram of a metal-embedded multipoint fiber grating strain sensor and a preparation method thereof. Figure 2 It is a multipoint fiber grating and metal protective sleeve schematic diagram of a metal-embedded multipoint fiber grating strain sensor and a preparation method thereof. Figure 3A schematic diagram of a U-shaped groove pre-processed on the metal structure to be tested, which is a metal-embedded multi-point fiber optic strain sensor and its fabrication method. Figure 4 A schematic diagram of a metal-embedded multi-point fiber Bragg grating strain sensor and its fabrication method, showing the embedding of the fiber Bragg grating sensor using metal ultrasonic additive manufacturing technology; Figure 5 This is a schematic diagram showing the output strain values ​​at the measuring points during the application of a pressure load on a metal-embedded multi-point fiber optic strain sensor and its fabrication method. Figure 6 A comparison of strain measurement point output values ​​before and after temperature compensation during the heating process of a metal-embedded multi-point fiber optic strain sensor and its fabrication method; Figure 7 This is an enlarged view of the output values ​​of strain measurement points during the temperature-compensated heating process of a metal-embedded multi-point fiber optic strain sensor and its fabrication method.

[0019] Figure label: 1. Multi-point fiber optic grating string; 2. Metal protective sleeve; 3. Transition tube; 4. Strain grating measuring point; 5. Temperature compensation grating measuring point; 6. U-groove; 61. U-groove of multi-point grating fiber optic string; 62. U-groove of metal protective sleeve; 63. U-groove of transition tube; 7. Metal foil; 8. Fiber optic pigtail protection tube; 9. Ultrasonic pressure head. Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Example 1

[0021] like Figures 1-4 As shown, an embedded strain sensor based on metal ultrasonic additive manufacturing process includes a multi-point fiber Bragg grating string 1, a metal protective sleeve 2, and a transition tube 3. The multi-point fiber Bragg grating string 1 is coated with polyimide and has a diameter of 150 μm. Each grating string has eight measuring points, arranged in pairs: strain grating measuring point 4 and temperature compensation grating measuring point 5. The distance between two measuring points is 10 mm, and the distance between measuring points in each group is 200 mm. The temperature compensation grating measuring point 5 is encapsulated in the metal protective sleeve 2. The metal sleeve 2 has an inner diameter of 0.4 mm, an outer diameter of 1 mm, and a length of 3 mm. The optical fibers at both ends of the temperature compensation grating measuring point 5 are encapsulated within the metal protective sleeve 2 and fixed with high-hardness structural adhesive.

[0022] The to-be-tested metal structure is an aluminum alloy plate with a length of 300 mm, a width of 50 mm, a thickness of 10 mm, and a brand of 6061. A U-shaped groove 6 is etched on the surface of the aluminum alloy plate by using a laser, for placing a multi-point fiber grating string 1, a metal protective sleeve 2, and a transition pipe 3. The depth and width of the U-shaped groove 62 of the metal protective sleeve are 1.3 mm, the depth and width of the U-shaped groove 61 of the multi-point grating fiber string are 150 μm, and the depth and width of the U-shaped groove 63 of the transition pipe are 1.5 mm.

[0023] A layer of metal foil 7 is covered on the U-shaped groove 6, the thickness of the metal foil 7 is 0.2 mm, the width is 10 mm, and the material is an aluminum alloy with a brand of 6061. The metal foil 7 is solidified by an ultrasonic additive pressure head 9. The vibration frequency of the ultrasonic pressure head 9 is 20 KHZ, the amplitude is 20-25 μm, the rolling rate is 700 mm / min, and the pressure is 0.35 Mpa. The multi-point fiber grating string 1 is wrapped into the solidified layer through high-rate plastic deformation and atomic diffusion between the metal foil 7 and the surface of the to-be-tested metal structure, and the strain grating measuring point 4 is solidified in the metal. When the to-be-tested metal structure deforms, the strain thereof is transmitted to the strain grating measuring point 4, so that the center wavelength thereof drifts. The inversion of the strain information of the to-be-tested metal structure at the measuring point position can be realized by measuring the center wavelength of the strain grating measuring point 4. The fiber tail cable protection pipe 8 is used for protecting the optical fiber drawn out of the metal structure and penetrating into the transition pipe 3 through crimping fixation.

[0024] Since the groove depth of the metal protective sleeve U-shaped groove 62 is 1.3 times the diameter of the metal protective sleeve 2, the part of the metal foil 7 and the surface of the to-be-tested metal structure cannot be wrapped by the solidified layer, so the metal protective sleeve 2 is loosely coupled with the to-be-tested metal structure, and the strain of the to-be-tested metal structure cannot be transmitted to the metal protective sleeve 2. At the same time, since the temperature compensation measuring point is encapsulated in the metal protective sleeve 2, the strain is isolated by the metal protective sleeve and cannot be transmitted to the temperature compensation grating measuring point 5, and the center wavelength thereof only drifts with the change of temperature. According to the measured temperature, and combining the temperature compensation sensitivity coefficient calibrated in advance, the center wavelength drift amount of the strain measuring point caused by the temperature and thermal strain can be calculated, so as to eliminate the influence of this part on the measurement result. The specific calculation method is shown in the following formulas (1) and (2).

[0025] The preparation method of the metal-embedded multi-point fiber grating strain sensor is as follows: S1, according to the demand of measuring point arrangement, pre-process U-shaped groove 6 on the surface of the metal structure to be measured for placing the multi-point fiber grating strain sensor and the transition pipe 3 of the fiber outgoing part. The U-shaped groove 62 for placing the metal protective sleeve pipe 2 has a groove depth, width and length of 1.3 times the diameter of the metal protective sleeve pipe 2, and the U-shaped groove 62 for placing the multi-point grating fiber string 1 has the same groove depth and width as the diameter of the multi-point grating fiber string 1. The fiber is led out from the metal structure to be measured through the transition pipe 3.

[0026] A layer of metal foil 7 with a thickness of 0.2mm is covered on the multi-point fiber grating strain sensor, the vibration frequency of the ultrasonic pressure head 9 is adjusted to 20KHz, the amplitude is 20-25μm, the rolling speed is 5mm / s, and the pressure is 0.35Mpa. Z The fiber is wrapped into the consolidation layer through the high-speed plastic deformation and atomic diffusion between the metal foil 7 and the metal structure to be measured, which ensures the tight coupling between the strain grating measuring point 4 and the metal structure to be measured, and the deformation of the metal structure to be measured can be effectively transmitted to the strain grating measuring point 4 for strain measurement. Since the groove depth of the metal protective sleeve pipe U-shaped groove 62 is 1.3 times the diameter of the metal protective sleeve pipe 2, the part of the metal foil 7 cannot be wrapped with the surface consolidation layer of the metal structure to be measured, and the strain of the metal structure to be measured cannot be transmitted to the metal protective sleeve pipe 2. At the same time, since the temperature compensation grating measuring point 5 is packaged in the metal protective sleeve pipe 2, the strain is isolated by the metal protective sleeve pipe 2 and cannot be transmitted to the temperature compensation grating measuring point 5, and the center wavelength change is only related to the temperature. According to the measured temperature, and combining the temperature compensation sensitivity coefficient (the center wavelength drift amount of the strain measuring point caused by temperature and material thermal expansion under unit temperature change) calibrated in advance, the center wavelength drift amount of the strain measuring point caused by temperature and thermal strain can be calculated, so as to eliminate the influence of this part on the measurement result. The specific calculation method is as follows: (1) (2) Wherein, ε is the accurate strain value of the metal structure to be measured caused by mechanical load measured by the sensor after eliminating the thermal strain; ΔT is the temperature change value; Δλ ε is the center wavelength drift amount of the reflection spectrum of the strain grating measuring point; Δλ T is the center wavelength drift amount of the reflection spectrum of the temperature compensation grating measuring point; k ε is the sensitivity coefficient of the strain grating measuring point (the reflection spectrum drift amount of the measuring point under unit strain change); k T is the sensitivity coefficient of the temperature compensation grating measuring point (the center wavelength drift amount of the reflection spectrum of the measuring point under unit temperature change);γ εT In order to compensate the sensitivity coefficient of the strain grating measuring point for temperature, the temperature sensitivity coefficient of the measuring point can be obtained through strain and temperature calibration tests.

[0027] A certain pressure load is applied to the sample prepared above, and one group of strain measuring points and the center wavelength of the temperature measuring point with the change of the applied load is shown in Table 1. As shown in Table 1, according to the strain measuring point sensitivity coefficient of 1.2 pm / με, the strain change value of the sample can be inversely calculated, and the center wavelength of the temperature measuring point almost does not change, which proves that the structure effectively isolates the influence of strain on the temperature measuring point and is only sensitive to temperature. Figure 5 k ε As shown in Table 1, the sample is placed in a temperature chamber and heated from room temperature to 100℃. Although no load is applied to the sample, due to the thermal expansion of the material and the cross-influence of temperature on the strain measuring point, the measurement result of the strain measuring point seriously drifts, and the drift amount can reach 2400με. The result measured by the temperature measuring point is used to compensate the strain measuring point, which effectively reduces the influence of temperature change on the strain measuring point. In this embodiment, the temperature compensation measuring point sensitivity coefficient is 25.7 pm / ℃, and the strain measuring point temperature compensation sensitivity coefficient is 38.5 pm / ℃. Figure 6 T k γ εT As shown in Table 1, the sample is placed in a temperature chamber and heated from room temperature to 100℃. Although no load is applied to the sample, due to the thermal expansion of the material and the cross-influence of temperature on the strain measuring point, the measurement result of the strain measuring point seriously drifts, and the drift amount can reach 2400με. The result measured by the temperature measuring point is used to compensate the strain measuring point, which effectively reduces the influence of temperature change on the strain measuring point. In this embodiment, the temperature compensation measuring point sensitivity coefficient is 25.7 pm / ℃, and the strain measuring point temperature compensation sensitivity coefficient is 38.5 pm / ℃. Figure 7

[0028] Table 1 Center wavelength change of measuring points with different loads

[0029] The above merely describes the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can make equivalent replacements or changes to the technical solutions and the inventive concept of the present application within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.​​​​

Claims

1. A metal embedded multipoint fiber optic grating strain sensor, characterized by: The multi-point fiber grating string (1) is embedded in the surface of the metal structure to be measured, the metal protective sleeve (2) is encapsulated in the local outer periphery of the multi-point fiber grating string (1), and the transition pipe (3) is connected to the leading part of the multi-point fiber grating string (1); Two grating measuring points in the multi-point fiber grating string (1) form a group, each grating measuring point group is composed of a strain grating measuring point (4) and a temperature compensation grating measuring point (5), and the metal protective sleeve (2) is encapsulated outside the temperature compensation grating measuring point (5); The strain grating measuring point (4) is fixed in the metal structure to be measured and changes the center wavelength with the strain and / or temperature change of the metal structure to be measured; the temperature compensation grating measuring point (5) is loosely coupled with the metal structure to be measured and is isolated from the strain of the metal structure to be measured by the metal protective sleeve (2), and the temperature compensation grating measuring point (5) is a temperature compensation measuring point of the strain grating measuring point (4); According to the measurement result of the temperature compensation grating measuring point (5), the temperature change of the metal structure to be measured can be obtained, and the temperature compensation coefficient of the strain grating measuring point (4) is combined to obtain the center wavelength drift of the strain grating measuring point (4) Δλ ε After correction, the accurate strain value of the metal structure to be measured caused by mechanical load after eliminating thermal strain is measured.

2. The metal embedded multipoint fiber grating strain sensor according to claim 1, wherein: The grating region length of the strain grating measuring point (4) and the temperature compensation grating measuring point (5) is less than 1mm, and the spacing between the strain grating measuring point (4) and the temperature compensation grating measuring point (5) is less than 10mm.

3. The metal embedded multipoint fiber grating strain sensor according to claim 1, wherein: The inner diameter of the metal protective sleeve (2) matches the outer diameter of the multi-point fiber grating string (1), and the length is longer than the grating region length of the temperature compensation grating measuring point (5), the whole grating and the fiber at both ends of the temperature compensation grating measuring point (5) are encapsulated in the metal protective sleeve (2), and the multi-point fiber grating string (1) and the metal protective sleeve (2) are fixed by using high-hardness structural glue.

4. The metal embedded multipoint fiber grating strain sensor according to claim 1, wherein: The multi-point fiber grating string (1) is embedded in the U-shaped groove (6) in the surface of the metal structure to be measured, the metal foil (7) covers the U-shaped groove (6) and is fixed with the metal structure to be measured by the ultrasonic additive process and wraps the multi-point fiber grating string (1) inside the metal structure to be measured; The U-shaped groove (6) includes a multi-point fiber grating string U-shaped groove (61), a metal protective sleeve U-shaped groove (62), and a transition pipe U-shaped groove (63); The width and depth of the multi-point fiber grating string U-shaped groove (61) are the same as the outer diameter of the multi-point fiber grating string (1); The width and depth of the metal protective sleeve U-shaped groove (62) are greater than or equal to 1.3 times the outer diameter of the metal protective sleeve (2); The material of the metal foil (7) is the same as that of the metal structure to be measured, and the thickness is less than 0.15mm.

5. The metal embedded multipoint fiber grating strain sensor according to claim 4, wherein: The transition pipe (3) is connected outside the fiber cable protection pipe (8), the fiber of the multi-point fiber grating string (1) is led out of the metal structure to be measured through the fiber cable protection pipe (8), the fiber cable protection pipe (8) protects the fiber led out of the metal structure to be measured, and the transition pipe (3) is embedded in the transition pipe U-shaped groove (63).

6. The metal embedded multipoint fiber grating strain sensor according to claim 5, wherein: The inner diameter of the transition pipe (3) is the same as the outer diameter of the fiber cable protection pipe (8), and the wall thickness is 0.1mm-0.2mm, and the fiber cable protection pipe (8) and the transition pipe (3) are fixed by crimping.

7. The method of claim 1-6, wherein the method further comprises: The method comprises the following steps: ​ S1, according to the demand of the measuring point arrangement, pre-process U-shaped groove (6) on the surface of the metal structure to be measured, the U-shaped groove (6) is used to place the multi-point fiber grating string (1), the metal protective sleeve (2) and the transition pipe (3); S2, put the multi-point fiber grating strain sensor into the U-shaped (6) groove, and fix the two ends of the multi-point fiber grating string (1) to prevent the fiber from escaping out of the groove during embedding process; S3, place the metal foil (7) on the surface of the metal structure to be measured, cover the multi-point fiber grating strain sensor and the U-shaped groove (6), and solidify the metal foil (7) with the metal structure to be measured by ultrasonic additive process, so that the strain grating measuring point (4) is solidified in the metal structure to be measured, and the deformation of the metal structure to be measured can be effectively transmitted to the strain grating measuring point (4); Because the width and depth of the metal protective sleeve U-shaped groove (62) are greater than those of the metal protective sleeve (2), the solidified layer of the metal foil (7) and the surface of the metal structure to be measured cannot wrap the metal protective sleeve (2), thereby forming loose coupling, so that the deformation of the metal structure to be measured cannot be transmitted to the temperature compensation grating measuring point (5).

8. The method of claim 7, wherein the method further comprises: In step S3, the ultrasonic frequency is 20 KHz, the amplitude is 20-25 μm, the rolling speed of the pressure head is 70 mm / min, and the pressure is 0.35 MPa. ​

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