CN107918106B - Magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification - Google Patents
Magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification Download PDFInfo
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Abstract
The invention discloses a magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification, and belongs to the field of optical fiber sensing for structural health monitoring. The method comprises the following steps: the method comprises the following steps: designing a three-dimensional magnetic field sensing mechanism; step two: sensor layout; step three: deducing a stress function and a deformation response function; step four: constructing a relation model between the central wavelength offset of the fiber Bragg grating sensor and the curvature obtained based on the second derivative of the magnetic induction simply supported beam deformation function; step five: constructing a three-dimensional simply supported beam magnetic induction intensity and current double-parameter deduction model based on fiber bragg grating center wavelength offset; the deduction model of the magnetic induction intensity and current double-parameter optical fiber monitoring method is directly represented in an analytic mode, the relation between the measured parameter and the response characteristic of the optical fiber sensor is clear, the direction of a magnetic field can be identified, and the method has the characteristics of simple structure, quick response, high engineering practicability and the like.
Description
Technical Field
the invention relates to a magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification, and belongs to the field of optical fiber sensing for structural health monitoring.
background
magnetic field sensing technology is a hot spot direction of current international research and application, and has rapidly developed in recent decades. Although the Hall device with wide application is convenient to use and low in price, the precision is still insufficient, and the temperature stability is not good. At present, many researches on optical fiber magnetic field sensors are reported, but most of the researches are based on interferometers, and the researches and the applications are difficult to deepen due to the severe restriction of factors such as the long-term performance stability and the reliability of the optical fiber and the external interference.
in addition, there are many reports on an optical fiber magnetic field sensor using the magnetostrictive effect, and the main problem is that the magnetostrictive material itself has a certain influence on the measured magnetic field, and is greatly influenced by the temperature in practical use, and the effect is not ideal.
The optical fiber magnetic field sensor made of the ferrofluid material has the advantages that the sensor needs to wrap liquid around the sensing optical fiber, so that the requirement on the packaging condition of the sensor is high, the maximum value of the refractive index of the magnetic fluid is limited, the measurement magnetic field range is restricted, the refractive index of the magnetic fluid can change along with the temperature when the temperature changes in the use process, and the measurement precision is influenced.
the invention provides a magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification, which is characterized by anti-electromagnetic interference, high sensitivity, wide dynamic range, compact structure, high reliability, low cost and the like of an optical fiber sensor by means of the Lorentz force principle and by adopting a three-dimensional simple beam as a sensing medium of deformation caused by a magnetic field and the central wavelength offset of an optical fiber grating, thereby avoiding the influence of a magnetostrictive material on the magnetic field and having wider application prospect.
Disclosure of Invention
The invention aims to provide a magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification.
the method comprises the following steps: three-dimensional magnetic field sensing mechanism design based on simply supported beam model and Lorentz force excitation
Defining a three-dimensional magnetic field coordinate system XYZ according to a right-hand rule; the three-dimensional magnetic field simply supported packaging model is composed of three simply supported beams and an insulating shell outside each simply supported beam, and the simply supported beams are made of conductive metal; the insulating shell on each simple-supported beam is of a cuboid structure, the three simple-supported beams are pairwise perpendicular to each other and are respectively superposed with an X axis, a Y axis and a Z axis under an XYZ coordinate system, the extension lines of the central lines of the three simple-supported beams are intersected at a point O, the three simple-supported beams are respectively stranded with the three insulating shells at the point close to the point O), and the three simple-supported beams are respectively fixedly supported with the three insulating shells at the point far from the point O); three leads led out from the O point are respectively connected with three simply-supported beams near the O point, and the three simply-supported beams are respectively connected to the outside of the three-dimensional magnetic field simply-supported encapsulation model through the other three leads at one ends far away from the O point);
Step two: distributed fiber Bragg grating form sensor layout
2-1 establishing xoy coordinate system of three simply supported beams
The simple supporting beam is positioned on an X axis of an XYZ coordinate system and used for sensing a magnetic field in a Z direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the positive direction of the X axis is the positive direction of the X axis of the xoy coordinate system, and the positive direction of the Y axis is the positive direction of the Y axis of the xoy coordinate system;
the simple supporting beam is positioned on a Y axis of an XYZ coordinate system and used for sensing a magnetic field in an X direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the positive direction of the Y axis is the positive direction of the X axis of the xoy coordinate system, and the positive direction of the Z axis is the positive direction of the Y axis of the xoy coordinate system;
The simple supporting beam is positioned on a Z axis of an XYZ coordinate system and used for sensing a magnetic field in a Y direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the negative direction of the Z axis is the positive direction of an X axis of the xoy coordinate system, and the positive direction of the X axis is the positive direction of a Y axis of the xoy coordinate system;
2-2 fiber grating arrangement
two ends of the simply supported beam are fixed through an insulating shell, wherein one end of the simply supported beam is a twisted support, and the other end of the simply supported beam is a fixed support; the effective sensing length of the simply supported beam in the insulating shell is l; and taking the middle point of the simply supported beam as an original point o, symmetrically pasting fiber gratings at two sides of four positions of x ═ l/2, -l/4, l/4 and l/2 of the simply supported beam under the xoy coordinate system according to a right hand rule, wherein the selected central wavelengths of the fiber gratings at the same position are consistent, and the selected central wavelengths of the fiber gratings at different positions are inconsistent.
Step three: simple supported beam model stress function and deformation response function derivation for magnetic field induction
when current with certain magnitude and direction passes through the aluminum simply-supported beams which are positioned in the insulating shell and fixed at the two ends of the insulating shell, the simply-supported beams fixed at the two ends of the insulating shell can generate deformation related to the magnitude and the direction of the external magnetic field according to the Lorentz force generation principle and the ampere force principle under the condition that the external magnetic field exists.
if the current with the magnitude of I flows through the simply supported beam and the external magnetic field B acts on the simply supported beam, the stress function and the deformation function generated by the simply supported beam are as follows:
In the formula, σ x and σ y are positive stresses in x and y directions respectively, τ xy represents the tangential strain of the xy plane of the beam, q is the uniform load borne by the simply supported beam, E is the elastic modulus of the simply supported beam, J is the inertia moment of the simply supported beam, l is the length of the simply supported beam, h is the cross section height of the simply supported beam, and μ is the Poisson's ratio of the material of the simply supported beam.
step four: construction of relation model between central wavelength offset of optical fiber Bragg grating sensor and curvature obtained based on magnetic induction simple beam deformation function second derivative
The fiber bragg gratings at the two ends of any simple supporting beam have the same deformation as the simple supporting beam because of
In the formula, Pe represents an elastic-optical coefficient, λ B represents an initial wavelength of the fiber grating, α represents a thermal expansion coefficient of the fiber, ζ represents a thermal-optical coefficient of the fiber, Δ T represents a temperature variation, Δ λ d, and ∈ d represent wavelength offset and strain of the fiber grating attached to the lower surface of the simply supported beam, and Δ λ u, and ∈ u represent wavelength offset and strain of the fiber grating attached to the upper surface of the simply supported beam, and then a relationship between a central wavelength offset of the fiber grating in the neutral layer and strain received by the simply supported beam is as follows:
and (4) subtracting the (3) and the (4) to realize temperature compensation.
The relation model between the central wavelength offset of the optical fiber Bragg grating sensor and the curvature obtained based on the second derivative of the deformation function of the magnetic induction simply supported beam is as follows:
in the formula, Δ λ m, ∈ m, and ρ m are offset, strain, and curvature of the wavelength of the fiber grating in the neutral layer of the simply supported beam, and D is the fiber diameter.
step five: three-dimensional simply supported beam magnetic induction intensity and current double-parameter deduction model construction based on fiber bragg grating center wavelength offset
(1) Magnetic field size identification
When x is-l/2, according to formula (6), the solution is obtained
when x is-l/4, the following is solved according to formula (6):
The equations for symmetry x l/4 and x l/2 are converted into:
In the formula, q is the uniform load borne by the simple beam, E is the elastic modulus of the simple beam, J is the inertia moment of the simple beam, l is the length of the simple beam, h is the cross section height of the simple beam, mu is the Poisson's ratio of the material of the simple beam, λ B represents the initial wavelength of the fiber grating, and Pe is the elastic-optical coefficient.
when the current magnitude I is a constant value, i.e., I1, I2, I3, I4, and x is-l/2, -l/4, and l/2, the shift amounts of the central wavelength of the fiber grating are Δ λ -l/2, Δ λ -l/4, Δ λ l/4, and Δ λ l/2, respectively, and the magnetic induction intensities obtained by the equations (7) to (10) are B1, B2, B3, and B4, respectively, the magnitudes of the external measured magnetic induction intensities are:
The size of the magnetic field can be identified.
(2) Magnetic field direction identification
the simple beams on the X axis are used for sensing a magnetic field in the Z direction, the simple beams on the Y axis are used for sensing the magnetic field in the X direction, the simple beams on the Z axis are used for sensing the magnetic field in the Y direction, and the three simple beams have the same method for identifying the direction of the magnetic field;
and under a corresponding two-dimensional xoy coordinate system, the central wavelength offset of two fiber gratings at the symmetrical positions of the front and back surfaces of any simple support beam is respectively set as delta lambda u and delta lambda d. If the delta lambda u is a negative value and the delta lambda d is a positive value, the simply-supported beam bends towards the negative y axis; when current passes through the simply-supported beam along the positive direction of the x axis, the direction of the magnetic field is perpendicular to the paper surface outwards under the corresponding two-dimensional coordinate system, and when current passes through the simply-supported beam along the negative direction of the x axis, the direction of the magnetic field is perpendicular to the paper surface inwards under the corresponding two-dimensional coordinate system.
if the delta lambda u is a positive value and the delta lambda d is a negative value, the simply-supported beam bends towards the positive y axis; when current passes through the simply-supported beam along the positive direction of the x axis, the direction of the magnetic field is inward of the vertical paper surface under the corresponding two-dimensional coordinate system, and when current passes through the simply-supported beam along the negative direction of the x axis, the direction of the magnetic field is outward of the vertical paper surface under the corresponding two-dimensional coordinate system.
(3) current intensity monitoring
when the magnetic induction B is a constant value, that is, when B1, B2, B3, B4, and x is-l/2, -l/4, and l/2, the amounts of shift of the center wavelength of the fiber grating are Δ λ -l/2, Δ λ -l/4, Δ λ l/4, and Δ λ l/2, respectively, and the magnitudes of currents obtained by equations (7) to (10) are I1, I2, I3, and I4, respectively, the magnitudes of the currents are:
the current intensity monitoring can be realized.
(4) Current direction identification
The method for identifying the magnetic field direction of the three simply-supported beams for sensing the magnetic field in the Y direction is the same;
And under a corresponding two-dimensional xoy coordinate system, the central wavelength offset of two fiber gratings at the symmetrical positions of the front and back surfaces of any simple support beam is respectively set as delta lambda u and delta lambda d. If the delta lambda u is a negative value and the delta lambda d is a positive value, the simply-supported beam bends towards the negative y axis; when the direction of the magnetic field is vertical to the paper surface and faces outwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the positive direction of the x axis; when the direction of the magnetic field is perpendicular to the paper surface and faces inwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the negative direction of the x axis.
if the delta lambda u is a positive value and the delta lambda d is a negative value, the simply-supported beam bends towards the negative y axis; when the direction of the magnetic field is vertical to the paper surface and faces outwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the negative direction of the x axis; when the direction of the magnetic field is perpendicular to the paper surface and faces inwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the positive direction of the x axis. .
according to the analysis, the magnetic induction intensity and current double-parameter optical fiber monitoring method based on the bending form identification has the advantages that: firstly, a deduction model of the magnetic induction intensity and current double-parameter optical fiber monitoring method is directly represented in an analytic mode, and the relation between a measured parameter and the response of the central wavelength offset of the optical fiber grating sensor is clear; secondly, the size of the magnetic field and the current can be measured, and the direction of the magnetic field and the current can be identified; and thirdly, by means of the symmetry of the fiber grating about the simply supported beam, the central wavelength offset of the grating caused by temperature can be directly offset, and the influence of external temperature on a magnetic field and current is ingeniously eliminated. In addition, the traditional magnetostrictive material and magnetic fluid material are not adopted any more, so that the influence of the sensing structure on the magnetic field and the current is small.
Drawings
FIG. 1 is a schematic diagram of a sensor design structure for a magnetic induction and current dual-parameter optical fiber monitoring method based on bending form identification according to the present invention;
FIG. 2 is a schematic diagram of a three-dimensional structure sensor design for a magnetic induction and current double-parameter optical fiber monitoring method based on bending form identification according to the present invention;
Fig. 3 is a schematic diagram of a simply supported beam before and after deformation based on a bending form identification magnetic induction intensity and current double-parameter optical fiber monitoring method.
Number designation in the figures:
1-an insulating housing; 2-an aluminum simply supported beam; 3-a fiber grating sensor; 4-connecting points of the conducting wires and the simply supported beams; 5-a wire; 6-three-dimensional magnetic field simply supported encapsulation model; 7-the deformed simply supported beam; 8-axial displacement of the simply supported beam;
Detailed Description
the method comprises the following steps: three-dimensional magnetic field sensing mechanism design based on simply supported beam model and Lorentz force excitation
Referring to fig. 1, 2 and 3, the present invention relates to a magnetic induction and current dual-parameter optical fiber monitoring method based on bending shape identification.
Defining a three-dimensional magnetic field coordinate system XYZ according to a right-hand rule; the three-dimensional magnetic field simply supported packaging model (6) is composed of three simply supported beams (2) and an insulating shell (1) outside each simply supported beam, the insulating shell (1) on each simply supported beam is of a cuboid structure, the three simply supported beams are pairwise perpendicular to each other and are respectively superposed with an X axis, a Y axis and a Z axis under an XYZ coordinate system, extension lines of central lines of the three simply supported beams intersect at a point O, the three simply supported beams are respectively stranded with the three insulating shells (1) at the point O, and the three simply supported beams are respectively fixedly supported with the three insulating shells (1) at the point O; three leads (5) led out from the O point are respectively connected with three simply-supported beams near the O point, and one ends of the three simply-supported beams far away from the O point are respectively connected to the outside of the three-dimensional magnetic field simply-supported encapsulation model (6) through the other three leads (5);
Step two: distributed fiber Bragg grating form sensor layout
2-1 establishing xoy coordinate system of three simply supported beams
The simple supporting beam is positioned on an X axis of an XYZ coordinate system and used for sensing a magnetic field in a Z direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the positive direction of the X axis is the positive direction of the X axis of the xoy coordinate system, and the positive direction of the Y axis is the positive direction of the Y axis of the xoy coordinate system;
the simple supporting beam is positioned on a Y axis of an XYZ coordinate system and used for sensing a magnetic field in an X direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the positive direction of the Y axis is the positive direction of the X axis of the xoy coordinate system, and the positive direction of the Z axis is the positive direction of the Y axis of the xoy coordinate system;
the simple supporting beam is positioned on a Z axis of an XYZ coordinate system and used for sensing a magnetic field in a Y direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the negative direction of the Z axis is the positive direction of an X axis of the xoy coordinate system, and the positive direction of the X axis is the positive direction of a Y axis of the xoy coordinate system;
2-2 fiber grating arrangement
Two ends of the simply supported beam are fixed through an insulating shell (1), wherein one end of the simply supported beam is a twisted support, and the other end of the simply supported beam is a fixed support; the effective sensing length of the simply supported beam in the insulating shell is l; and taking the middle point of the simply supported beam as an original point o, symmetrically pasting fiber gratings (3) on two sides of four positions of x ═ -l/2, -l/4, l/4 and l/2 of the simply supported beam under the xoy coordinate system according to the right-hand rule, wherein the selected central wavelengths of the fiber gratings at the same position are consistent, and the selected central wavelengths of the fiber gratings at different positions are inconsistent. The magnetic field and the current value to be measured are converted into the axial displacement (8) of the simply supported beam by means of a deformation curve (7) of the simply supported beam under the action of a magnetic field or current, and further the central wavelength of the sensing fiber bragg grating at the symmetrical positions of the front side and the back side of the simply supported beam is changed. The simply supported beam connected to the insulating shell (1) and the sensing fiber grating stuck to the simply supported beam are coincided with the rectangular symmetrical axis of the insulating shell (1). And the sensing fiber bragg grating is stuck on the simply supported beam and used for sensing the bending deformation of the simply supported beam. In order to increase the sensitivity of the sensing fiber grating, the same pre-tightening force is applied when the sensing fiber grating is fixedly adhered to the simply supported beam.
step three: simple supported beam model stress function and deformation response function derivation for magnetic field induction
for an external magnetic field to be measured, when directional current flows through the simply supported beam at a fixed position, the simply supported beam will deform correspondingly, and the central wavelength of the sensing fiber bragg grating attached to the symmetrical positions of the front and back sides of the simply supported beam changes.
the measured wavelength offset values of the sensing fiber bragg gratings stuck on the simply supported beam are respectively delta lambda u and delta lambda d, if the current passing through the simply supported beam is I, the current flows through the simply supported beam from left to right, and the whole simply supported beam can generate bending deformation under the action of ampere force due to the existence of a magnetic field with the magnetic field induction intensity B in the external environment. If the magnetic field passing through the simply-supported beam is B and the direction is vertical to the paper surface and inwards, the whole simply-supported beam can generate bending deformation under the action of ampere force due to the fact that current passes through the simply-supported beam. As shown in fig. 3, the shape of the simply supported beam changes before and after being stressed, and a certain amount of deflection is generated, so that the sensing fiber grating connected with the simply supported beam and stuck on the simply supported beam is subjected to axial stress, and further, the central wavelength of the fiber grating deviates. If the deformation is shown in fig. 3, the direction of the measured magnetic field is perpendicular to the paper surface and inward, and the direction of the measured current flows through the simply supported beam from left to right.
in order to quantitatively analyze the relationship between the magnetic field and the current and the central reflection wavelength offset of the fiber bragg grating attached to the symmetrical positions of the front and the back of the three simply supported beams, a stress-strain function and deformation response function model among the magnetic field and the current and the central wavelength offset of the fiber bragg grating needs to be established:
assuming that the coordinate system of the three-dimensional magnetic field simple support encapsulation model in fig. 2 is XYZ, the equilibrium differential equation of the simple support beam of the present invention is:
wherein σ X, σ Y, and σ Z are positive stresses in X, Y, Z directions, τ XY, τ XZ, and τ YZ are shear stresses in XY, XZ, and YZ planes, and O, P, Q represents the physical force applied to the simply-supported beam in X, Y, Z directions. The simple beam geometry equation can be expressed as:
Wherein ε X, ε Y and ε Z are positive strains in the direction of X, Y, Z respectively; shear strain in directions of X, Y, Z of gamma YZ, gamma ZX and gamma XY respectively; as can be seen from the geometric equation, the six strain components are determined entirely by the partial derivatives of the three displacement components with respect to the coordinates. Therefore, the six strain components are not independent, and a three-dimensional magnetic induction simply supported beam model deformation coordination equation is derived as follows:
For a simply supported beam structure, under unidirectional stress, the stress and strain in the elastic stage are in a linear relationship, i.e.
σ＝Eε (4)
And E in the formula is the elastic modulus of the simply supported beam. When the simply supported beam is acted by three-way stress, the formula (4) is rewritten as follows:
Wherein Cij is a strain coefficient, and since the simple beam structure material is isotropic and has only two independent variables, formula (5) is simplified as follows:
Where e ═ ε X + ε Y + ε Z, and μ is the Poisson's ratio of the simple beam material.
Assuming that θ, δ, and ζ are direction cosines of an included angle between an outer normal N of a regular hexahedral infinitesimal bisector plane of the simply supported beam and each coordinate axis, that is, θ is cos (N, X), δ is cos (N, Y), and ζ is cos (N, Z), the balance conditions Σ FX is 0, Σ FY is 0, and Σ FZ is 0, we obtain:
In the formula, the external forces in the X, Y, Z-axis direction are represented, respectively. For the two-dimensional coordinate xoy of each branch of the three-dimensional magnetic field simple support packaging model, when the elastic mechanical plane problem is caused under the condition of normal physical strength, the formula can be further simplified into
σ x and σ y are positive stresses in the x and y directions, respectively, τ xy represents the shear strain of the xy plane of the beam, defined as laplacian, and the resulting solution satisfies the stress boundary condition:
the above equation is solved in full:
wherein for the stress function, it must be satisfied:
The simple support beam can be equivalent to a plurality of strip-shaped simple support beam units, the length is l, the height is h, and the thickness is 1 (the ratio of the length to the height to the thickness is far more than 10); the physical strength is omitted, namely X is equal to Y is equal to 0, and the uniform load is equal to q is equal to BI.
When uniformly distributed load caused by ampere force acts on the simply supported beam, bending stress sigma x borne by the simply supported beam is mainly caused by bending moment, shearing stress tau xy is mainly caused by shearing force, and extrusion stress sigma y is mainly caused by uniformly distributed load q. Where q is constant and does not vary with the x-axis coordinate. It can thus be determined that σ y is also invariant with the x-axis coordinate, and is a function only with respect to the y-axis coordinate, namely:
integrating x yields:
bringing (14) into (12) to obtain
In order to make the equation equal on both sides, both the coefficient term and the constant term of the quadratic equation need to be equal to zero, i.e.
Integrating the above three equations can obtain:
Where A, B, C, D, E, F, G, H, K are all undetermined constants, the constant term of f1(y), the primary term of f2(y), and the constant term may all be omitted because they do not affect the stress component. Bringing (17) into (14) to obtain:
Substituting equation (18) into equation (11) to obtain:
Since the simple beam unit is left-right symmetric, σ x and σ y are even functions with respect to x, and τ xy is an odd function with respect to x, then E ═ F ═ G ═ 0. Applying stress boundary conditions
substituting formula (20) into formula (19) to obtain
substituting formula (21) into formula (19) yields:
bringing (22) into formula (6) and finishing to obtain:
The simple beam section inertia moment J is h3/12, and then:
the first equation integrates x and the second equation integrates y to yield:
In the formula: f (y) and g (x) are pending functions. For computational convenience, the coefficients q/2EJ are added before these two functions. To determine the two pending functions, (25) is substituted into the third formula of (24) under the boundary conditions x ═ 0, u ═ 0, x ═ l/2, y ═ 0, and v ═ 0, resulting in:
In the formula, u represents displacement in the x-axis direction, and v is a deflection curve of the simply supported beam unit.
step four: constructing a relation model between the central wavelength offset of the fiber Bragg grating sensor and the curvature obtained based on the second derivative of the magnetic induction simply supported beam deformation function;
the distributed optical fiber sensor is pasted on the symmetrical surface of the front and the back of the simply supported beam, so that the deformation and deflection curve of the front and the back surfaces of the simply supported beam can be approximately equivalent to the deformation and deflection curve of the optical fiber pasted on the simply supported beam. By
(27) in the formulae (D) and (28), D represents the diameter of the optical fiber, Pe represents the elasto-optic coefficient, ε represents the strain generated by the optical fiber grating, λ B represents the initial wavelength of the optical fiber grating, α represents the thermal expansion coefficient of the optical fiber, ζ represents the thermo-optic coefficient of the optical fiber, and Δ T represents the temperature change amount.
when the central wavelengths of the fiber gratings at the symmetrical positions of the front surface and the back surface are subtracted, the temperature influence can be eliminated:
In the formula, Δ λ d and ∈ d are the wavelength offset and strain of the fiber grating adhered to the lower surface of the simply supported beam, and Δ λ u and ∈ u are the wavelength offset and strain of the fiber grating adhered to the upper surface of the simply supported beam. Because the curvature change of the simply supported beam unit is consistent, then:
In the formula, the delta lambda m, the epsilon m and the rho m are offset, strain and curvature of the fiber grating wavelength of the neutral layer of the simply supported beam, and the formula (31) is a relation model between the offset of the central wavelength of the fiber Bragg grating sensor and the curvature obtained based on the second derivative of the magnetic induction simply supported beam deformation function.
step five: constructing a three-dimensional simply supported beam magnetic induction intensity and current double-parameter deduction model based on fiber bragg grating center wavelength offset;
the compound is obtained by the formula (31):
when x is-l/2, according to formula (32), the solution is:
when x is-l/4, according to formula (32), the solution is:
the equations for symmetry x l/4 and x l/2 are converted into:
In the formula, q is the uniform load borne by the simple beam, E is the elastic modulus of the simple beam, J is the inertia moment of the simple beam, l is the length of the simple beam, h is the cross section height of the simple beam, mu is the Poisson's ratio of the material of the simple beam, λ B represents the initial wavelength of the fiber grating, and Pe is the elastic-optical coefficient.
When the current magnitude I is a constant value, i.e., I1, I2, I3, I4, and x is-l/2, -l/4, and l/2, the shift amounts of the central wavelength of the fiber grating are Δ λ -l/2, Δ λ -l/4, Δ λ l/4, and Δ λ l/2, respectively, and the magnetic induction intensities obtained by the equations (33) - (36) are B1, B2, B3, and B4, respectively, the magnitudes of the external measured magnetic induction intensities are:
When the magnetic induction B is a constant value, that is, when B1, B2, B3, B4, and x is-l/2, -l/4, and l/2, the amounts of shift of the center wavelength of the fiber grating are Δ λ -l/2, Δ λ -l/4, Δ λ l/4, and Δ λ l/2, respectively, and the magnitudes of currents obtained by equations (33) to (36) are I1, I2, I3, and I4, respectively, the magnitudes of currents are:
Magnetic field direction identification:
the simple beams on the X axis are used for sensing a magnetic field in the Z direction, the simple beams on the Y axis are used for sensing the magnetic field in the X direction, the simple beams on the Z axis are used for sensing the magnetic field in the Y direction, and the three simple beams have the same method for identifying the direction of the magnetic field;
and under a corresponding two-dimensional xoy coordinate system, the central wavelength offset of two fiber gratings at the symmetrical positions of the front and back surfaces of any simple support beam is respectively set as delta lambda u and delta lambda d. If the delta lambda u is a negative value and the delta lambda d is a positive value, the simply-supported beam bends towards the negative y axis; when current passes through the simply-supported beam along the positive direction of the x axis, the direction of the magnetic field is perpendicular to the paper surface outwards under the corresponding two-dimensional coordinate system, and when current passes through the simply-supported beam along the negative direction of the x axis, the direction of the magnetic field is perpendicular to the paper surface inwards under the corresponding two-dimensional coordinate system.
If the delta lambda u is a positive value and the delta lambda d is a negative value, the simply-supported beam bends towards the positive y axis; when current passes through the simply-supported beam along the positive direction of the x axis, the direction of the magnetic field is inward of the vertical paper surface under the corresponding two-dimensional coordinate system, and when current passes through the simply-supported beam along the negative direction of the x axis, the direction of the magnetic field is outward of the vertical paper surface under the corresponding two-dimensional coordinate system.
current direction identification:
the method for identifying the magnetic field direction of the three simply-supported beams for sensing the magnetic field in the Y direction is the same;
and under a corresponding two-dimensional xoy coordinate system, the central wavelength offset of two fiber gratings at the symmetrical positions of the front and back surfaces of any simple support beam is respectively set as delta lambda u and delta lambda d. If the delta lambda u is a negative value and the delta lambda d is a positive value, the simply-supported beam bends towards the negative y axis; when the direction of the magnetic field is vertical to the paper surface and faces outwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the positive direction of the x axis; when the direction of the magnetic field is perpendicular to the paper surface and faces inwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the negative direction of the x axis.
If the delta lambda u is a positive value and the delta lambda d is a negative value, the simply-supported beam bends towards the negative y axis; when the direction of the magnetic field is vertical to the paper surface and faces outwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the negative direction of the x axis; when the direction of the magnetic field is perpendicular to the paper surface and faces inwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the positive direction of the x axis.
the foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.
Claims (1)
1. A magnetic induction intensity and current double-parameter optical fiber monitoring method based on bending form identification comprises the following steps:
The method comprises the following steps: three-dimensional magnetic field sensing mechanism design based on simply supported beam model and Lorentz force excitation
defining a three-dimensional magnetic field coordinate system XYZ according to a right-hand rule; the three-dimensional magnetic field simply supported packaging model (6) is composed of three simply supported beams (2) and an insulating shell (1) outside each simply supported beam, and the simply supported beams are made of conductive metal materials; the insulating shell (1) on each simple-supported beam is of a cuboid structure, the three simple-supported beams are pairwise perpendicular to each other and are respectively superposed with an X axis, a Y axis and a Z axis under an XYZ coordinate system, extension lines of central lines of the three simple-supported beams are intersected at a point O, the three simple-supported beams are respectively hinged with the three insulating shells (1) at the point O, and the three simple-supported beams are respectively fixedly supported with the three insulating shells (1) at the point O; three leads (5) led out from the O point are respectively connected with three simply-supported beams near the O point, and one ends of the three simply-supported beams far away from the O point are respectively connected to the outside of the three-dimensional magnetic field simply-supported encapsulation model (6) through the other three leads (5);
Step two: distributed fiber Bragg grating form sensor layout
2-1 establishing xoy coordinate system of three simply supported beams
the simple supporting beam is positioned on an X axis of an XYZ coordinate system and used for sensing a magnetic field in a Z direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the positive direction of the X axis is the positive direction of the X axis of the xoy coordinate system, and the positive direction of the Y axis is the positive direction of the Y axis of the xoy coordinate system;
The simple supporting beam is positioned on a Y axis of an XYZ coordinate system and used for sensing a magnetic field in an X direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the positive direction of the Y axis is the positive direction of the X axis of the xoy coordinate system, and the positive direction of the Z axis is the positive direction of the Y axis of the xoy coordinate system;
the simple supporting beam is positioned on a Z axis of an XYZ coordinate system and used for sensing a magnetic field in a Y direction, the middle point of an effective long sensing length section of the simple supporting beam is used as an origin o of the xoy coordinate system, the negative direction of the Z axis is the positive direction of an X axis of the xoy coordinate system, and the positive direction of the X axis is the positive direction of a Y axis of the xoy coordinate system;
2-2 fiber grating arrangement
two ends of the simply supported beam are fixed through an insulating shell (1), wherein one end of the simply supported beam is a twisted support, and the other end of the simply supported beam is a fixed support; the effective sensing length of the simply supported beam in the insulating shell is l; taking the middle point of the simply supported beam as an original point o, symmetrically pasting fiber gratings (3) on two sides of four positions of x ═ l/2, -l/4, l/4 and l/2 of the simply supported beam under the xoy coordinate system according to the right hand rule, wherein the selected central wavelengths of the fiber gratings at the same position are consistent, and the selected central wavelengths of the fiber gratings at different positions are inconsistent;
step three: simple supported beam model stress function and deformation response function derivation for magnetic field induction
when current with certain magnitude and direction passes through the simply supported beams which are positioned in the insulating shell (1) and fixed at two ends of the insulating shell (1), under the condition that a magnetic field exists outside, the simply supported beams fixed at two ends of the insulating shell (1) can generate deformation related to the magnitude and direction of the external magnetic field according to the Lorentz force generation principle and the ampere force principle;
If the current with the magnitude of I flows through the simply supported beam and the external magnetic field B acts on the simply supported beam, the stress function and the deformation function generated by the simply supported beam are as follows:
in the formula, sigma x and sigma y are respectively positive stress in x and y directions, τ xy represents the tangential strain of the xy plane of the beam, q is the uniformly distributed load borne by the simply supported beam, E is the elastic modulus of the simply supported beam, J is the inertia moment of the simply supported beam, l is the length of the simply supported beam, h is the cross section height of the simply supported beam, and mu is the Poisson ratio of the material of the simply supported beam;
Step four: construction of relation model between central wavelength offset of optical fiber Bragg grating sensor and curvature obtained based on magnetic induction simple beam deformation function second derivative
The deformation of the fiber grating at the two ends of any simple supporting beam is the same as that of the simple supporting beam because of the
In the formula, Pe represents an elastic-optical coefficient, λ B represents an initial wavelength of the fiber grating, α represents a thermal expansion coefficient of the fiber, ζ represents a thermal-optical coefficient of the fiber, Δ T represents a temperature variation, Δ λ d, and ∈ d represent wavelength offset and strain of the fiber grating attached to the lower surface of the simply supported beam, and Δ λ u, and ∈ u represent wavelength offset and strain of the fiber grating attached to the upper surface of the simply supported beam, and then a relationship between a central wavelength offset of the fiber grating in the neutral layer and strain received by the simply supported beam is as follows:
Subtracting the (3) and the (4) to realize temperature compensation;
The relation model between the central wavelength offset of the optical fiber Bragg grating sensor and the curvature obtained based on the second derivative of the deformation function of the magnetic induction simply supported beam is as follows:
in the formula, delta lambda m, epsilon m and rho m are offset, strain and curvature of the wavelength of the fiber grating of the neutral layer of the simply supported beam, and D is the diameter of the optical fiber;
Step five: three-dimensional simply supported beam magnetic induction intensity and current double-parameter deduction model construction based on fiber bragg grating center wavelength offset
(1) Magnetic field size identification
when x is-l/2, according to formula (6), the solution is:
when x is-l/4, the following is solved according to formula (6):
the equations for symmetry x l/4 and x l/2 are converted into:
In the formula, q is uniformly distributed load borne by the simple beam, E is the elastic modulus of the simple beam, J is the inertia moment of the simple beam, l is the length of the simple beam, h is the cross section height of the simple beam, mu is the Poisson's ratio of the material of the simple beam, lambda B represents the initial wavelength of the fiber grating, and Pe is the elastic-optical coefficient;
When the current magnitude I is a constant value, i.e., I1, I2, I3, I4, and x is-l/2, -l/4, and l/2, the shift amounts of the central wavelength of the fiber grating are Δ λ -l/2, Δ λ -l/4, Δ λ l/4, and Δ λ l/2, respectively, and the magnetic induction intensities obtained by the equations (7) to (10) are B1, B2, B3, and B4, respectively, the magnitudes of the external measured magnetic induction intensities are:
(2) magnetic field direction identification
the simple beams on the X axis are used for sensing a magnetic field in the Z direction, the simple beams on the Y axis are used for sensing the magnetic field in the X direction, the simple beams on the Z axis are used for sensing the magnetic field in the Y direction, and the three simple beams have the same method for identifying the direction of the magnetic field;
Setting central wavelength offsets of two fiber gratings at symmetrical positions of the front and back surfaces of any simple support beam as delta lambda u and delta lambda d respectively under a corresponding two-dimensional xoy coordinate system; if the delta lambda u is a negative value and the delta lambda d is a positive value, the simply-supported beam bends towards the negative y axis; when current passes through the simply supported beam along the positive direction of the x axis, the direction of the magnetic field is outward of the vertical paper surface under the corresponding two-dimensional coordinate system, and when current passes through the simply supported beam along the negative direction of the x axis, the direction of the magnetic field is inward of the vertical paper surface under the corresponding two-dimensional coordinate system;
If the delta lambda u is a positive value and the delta lambda d is a negative value, the simply-supported beam bends towards the positive y axis; when the current passes through the simply supported beam along the positive direction of the x axis, the direction of the magnetic field is inward of the vertical paper surface under the corresponding two-dimensional coordinate system, and when the current passes through the simply supported beam along the negative direction of the x axis, the direction of the magnetic field is outward of the vertical paper surface under the corresponding two-dimensional coordinate system;
(3) current intensity monitoring
when the magnetic induction B is a constant value, that is, when B1, B2, B3, B4, and x is-l/2, -l/4, and l/2, the amounts of shift of the center wavelength of the fiber grating are Δ λ -l/2, Δ λ -l/4, Δ λ l/4, and Δ λ l/2, respectively, and the magnitudes of currents obtained by equations (7) to (10) are I1, I2, I3, and I4, respectively, the magnitudes of the currents are:
(4) current direction identification
the method for identifying the magnetic field direction of the three simply-supported beams for sensing the magnetic field in the Y direction is the same;
Setting central wavelength offsets of two fiber gratings at symmetrical positions of the front and back surfaces of any simple support beam as delta lambda u and delta lambda d respectively under a corresponding two-dimensional xoy coordinate system; if the delta lambda u is a negative value and the delta lambda d is a positive value, the simply-supported beam bends towards the negative y axis; when the direction of the magnetic field is vertical to the paper surface and faces outwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the positive direction of the x axis; when the direction of the magnetic field is perpendicular to the paper surface and faces inwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the negative direction of the x axis;
if the delta lambda u is a positive value and the delta lambda d is a negative value, the simply-supported beam bends towards the negative y axis; when the direction of the magnetic field is vertical to the paper surface and faces outwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the negative direction of the x axis; when the direction of the magnetic field is perpendicular to the paper surface and faces inwards under the corresponding two-dimensional coordinate system, the current passes through the simply supported beam along the positive direction of the x axis.
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