WO2021114604A1 - 一种超导重力梯度仪及其灵敏度的提高方法 - Google Patents

一种超导重力梯度仪及其灵敏度的提高方法 Download PDF

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WO2021114604A1
WO2021114604A1 PCT/CN2020/097619 CN2020097619W WO2021114604A1 WO 2021114604 A1 WO2021114604 A1 WO 2021114604A1 CN 2020097619 W CN2020097619 W CN 2020097619W WO 2021114604 A1 WO2021114604 A1 WO 2021114604A1
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superconducting
stiffness
coil
inspection
superconducting coil
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PCT/CN2020/097619
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English (en)
French (fr)
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刘向东
刘习凯
马东
王璐璐
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华中科技大学
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Priority to US17/629,414 priority Critical patent/US20220299674A1/en
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
    • G01V7/02—Details
    • G01V7/04—Electric, photoelectric, or magnetic indicating or recording means
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F6/00—Superconducting magnets; Superconducting coils
    • H01F6/06—Coils, e.g. winding, insulating, terminating or casing arrangements therefor
    • H—ELECTRICITY
    • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H10N60/00—Superconducting devices
    • H10N60/80—Constructional details
    • H10N60/83—Element shape

Definitions

  • the invention relates to the technical field of gravity measurement, and more specifically, to a superconducting gravity gradiometer and a method for improving its sensitivity.
  • the superconducting gravity gradiometer is a time-varying gravity gradient measuring instrument constructed using superconductivity. It works at 4.2K liquid helium temperature and has the advantages of low inherent noise, high resolution, and stable grid value.
  • the aerial superconducting gravity gradiometer which aims at mineral resource exploration, has the potential to break through the resolution limit of normal temperature gravity gradiometer instruments, and is expected to become an important tool for deep resource exploration.
  • a typical construction method of superconducting gravity gradiometer is to use the magnetic interaction between the superconductor current-carrying coil and the superconducting inspection mass, and use the superconducting circuit to couple the superconducting inspection masses placed separately into a two-degree-of-freedom Magnetic spring vibrator, the vibrator movement can be decomposed into two natural modes, common mode and differential mode. By measuring the differential mode displacement of the vibrator, the change of gravity gradient with time is given.
  • the differential mode stiffness is small and the common mode stiffness is large.
  • Gravity gradient is measured in the form of differential gravitational acceleration.
  • Small differential mode stiffness means that the transfer function from gravity gradient to differential displacement is large, which is beneficial to improve the sensitivity and resolution of the instrument.
  • the motion acceleration of the platform is sensed by the instrument in the form of common mode acceleration, which needs to be subtracted by differential.
  • the large common mode stiffness means that it is insensitive to platform motion, which is beneficial to improve the common mode rejection ratio of the instrument and weaken it. The interference of instrument installation platform vibration on gradient measurement.
  • the common mode differential mode stiffness ratio In the superconducting gravity gradiometer, there are many factors that limit the improvement of the common mode differential mode stiffness ratio. For example, in a full magnetic levitation superconducting gravity gradiometer that measures the vertical diagonal component of the gravity gradient, the magnetic repulsion between the superconducting coil and the test mass needs to be large enough to offset the gravity of the test mass, thereby suspending Check the quality. Limited by this factor, the inherent frequency of the differential mode in the prior art is generally greater than 10 Hz, and the ratio of the common mode stiffness to the differential mode stiffness is also small.
  • the purpose of the present invention is to solve the technical problem that the improvement of the common mode differential mode stiffness ratio of the existing superconducting gravity gradiometer is limited, which is not conducive to improving the sensitivity and resolution of the gravity gradiometer.
  • the present invention provides a superconducting gravity gradiometer, including: two sets of superconducting magnetic spring vibrators and a superconducting circuit;
  • Each group of superconducting magnetic spring vibrator includes: close-wound disc-type superconducting coil, inspection quality, solenoid superconducting coil and coil bobbin;
  • the inspection quality is a semi-closed superconducting cylinder with an opening below;
  • the coil bobbin is located in the inspection quality
  • the single-layer densely wound disk-type superconducting coil is wound on the top of the coil bobbin, and the solenoid superconducting coil is wound on the bottom of the coil bobbin; the single-layer densely wound disk-type superconducting coil and the solenoid superconducting coil are wound on the bottom of the coil bobbin.
  • the magnetic repulsion between the conducting coil and the inspection mass balances the gravity of the inspection mass, and the inspection mass is magnetically suspended; the magnetic repulsion is a function of the displacement of the inspection mass, and the combined force of the magnetic force and gravity on the inspection mass has the property of restoring force and constitutes a super Magnetic force spring vibrator;
  • the vertical magnetic repulsion force exerted by the single-layer densely wound disk-type superconducting coil on the test mass changes in proportion to the displacement of the test mass from the equilibrium position, and the direction of the change is opposite to the displacement direction, which contributes a positive stiffness to the superconducting magnetic spring vibrator ;
  • a part of the magnetic field lines of the solenoid superconducting coil is in a compressed state in the enclosed space of the inspection quality, and the other part is in an expanded state outside the enclosed space of the inspection quality.
  • the vertical magnetic repulsion force exerted by the solenoid superconducting coil on the inspection quality follows
  • the displacement of the inspection mass from the equilibrium position changes proportionally, and the direction of the change is the same as the displacement direction, which contributes negative stiffness to the superconducting magnetic spring vibrator;
  • the stiffness of the superconducting magnetic spring vibrator is controlled by the single-layer densely wound disc-type superconducting coil The current value and the current value of the solenoid superconducting coil are adjusted;
  • the superconducting circuit connects the closely wound disk-type superconducting coils of the two sets of superconducting magnetic spring vibrators and the solenoid superconducting coils to form a superconducting loop through superconducting wires to couple the two sets of superconducting magnetic spring vibrators into two free
  • the spring vibrator of high degree constitutes a superconducting gravity gradiometer; the ratio of the common mode stiffness of the superconducting gravity gradiometer to the differential mode stiffness is compared with the common mode stiffness of the superconducting gravity gradiometer that does not include the solenoid superconducting coil The ratio of differential mode stiffness is high.
  • the common mode stiffness k c and the differential mode stiffness k d of the superconducting gravity gradiometer are respectively:
  • L 0 and I 0 respectively represent the effective inductance and superconducting current intensity of the positive-stiffness single-layer densely wound disk-type superconducting coil at the equilibrium position
  • l 0 and i 0 respectively represent the negative-stiffness solenoid superconducting coil at the equilibrium position
  • the effective inductance and superconducting current intensity of, l(z) represents the effective inductance of the negative stiffness solenoid superconducting coil with the displacement of the inspection mass
  • L(z) represents the change of the single-layer densely wound disc-type superconducting coil with the displacement of the inspection mass
  • the effective inductance of, L p represents the inductance connected to the middle branch of the superconducting circuit
  • z represents the displacement of the test mass relative to the equilibrium position.
  • d 2 L(z)/dz 2 ⁇ 0; d 2 l(z)/dz 2 >0.
  • the superconducting gravity gradiometer further includes: a structural member; the structural member is used to connect the coil bobbins of the two sets of superconducting magnetic spring vibrators up and down.
  • both the densely wound disk-type superconducting coil and the solenoid superconducting coil may include multiple sets of superconducting coils.
  • the present invention provides a method for improving the sensitivity of a superconducting gravity gradiometer.
  • the superconducting gravity gradiometer includes a superconducting magnetic spring vibrator with two degrees of freedom. The method includes the following steps:
  • the negative stiffness superconducting coil is connected in series to form a superconducting loop through a superconducting wire to reduce the differential mode stiffness of the superconducting gravity gradiometer and improve the sensitivity of the superconducting gravity gradiometer.
  • the superconducting magnetic spring vibrator of each degree of freedom includes: a closely wound disk-type superconducting coil, an inspection quality, and a coil bobbin; the inspection quality is a semi-closed superconducting cylinder with a lower opening; the coil bobbin is located in the inspection quality
  • the single-layer densely wound disk-type superconducting coil is wound on the top of the coil bobbin; the magnetic repulsion between the single-layer densely wound disk-type superconducting coil and the inspection mass balances the gravity of the inspection quality, and the inspection quality is magnetically suspended
  • the magnetic repulsion is a function of the displacement of the inspection mass, and the resultant force of the magnetic force and gravity on the inspection mass has the property of restoring force, constituting a superconducting magnetic spring vibrator; the single-layer densely wound disc-type superconducting coil is applied to the inspection mass
  • the vertical magnetic repulsive force changes proportionally with the displacement of the test mass from the equilibrium position, and the direction of the change is opposite
  • Solenoid superconducting coils are wound at the bottom of the two coil bobbins. A part of the magnetic field lines of the solenoid superconducting coil is compressed in the enclosed space for inspection quality, and the other part is expanded outside the enclosed space for inspection quality.
  • the vertical magnetic repulsion force exerted by the solenoid superconducting coil on the inspection mass changes proportionally with the displacement of the inspection mass from the equilibrium position, and the direction of the change is the same as the displacement direction, which contributes negative stiffness to the superconducting magnetic spring oscillator;
  • the stiffness of the superconducting magnetic spring oscillator is adjusted by the current value of the single-layer densely wound disk-type superconducting coil and the current value of the solenoid superconducting coil.
  • the invention provides a superconducting gravity gradiometer and a method for improving its sensitivity.
  • a pair of superconducting coils of negative stiffness are introduced into the double inspection mass and two degrees of freedom superconducting magnetic spring vibrator of the superconducting gravity gradiometer, which is respectively connected with
  • the superconducting inspection mass interacts, and the negative stiffness superconducting coil is included in the superconducting loop in series, effectively reducing the differential mode stiffness of the spring oscillator, increasing the ratio of common mode stiffness to differential mode stiffness, and increasing the superconducting gravity gradient
  • the sensitivity of the instrument is a pair of superconducting coils of negative stiffness.
  • the invention reduces the differential mode stiffness, increases the differential mode acceleration, that is, the transfer function from the gravity gradient to the differential mode displacement, improves the sensitivity of the gradient measurement, and reduces the noise level; by increasing the ratio of the common mode stiffness to the differential mode stiffness, the common mode suppression is improved Ratio, suppress the interference of the installation platform motion acceleration to the gradient measurement.
  • Figure 1 is a schematic diagram of the structure of a superconducting gravity gradiometer provided by the present invention
  • FIG. 2 is an equivalent schematic diagram of the superconducting circuit of the positive stiffness superconducting coil of the superconducting gravity gradiometer provided by the present invention
  • Fig. 3 is an equivalent schematic diagram of the superconducting circuit of the negative stiffness superconducting coil of the superconducting gravity gradiometer provided by the present invention
  • FIG. 4 is a schematic diagram of the relationship curve between the effective inductance of the positive stiffness superconducting coil and the displacement provided by the present invention
  • FIG. 5 is a schematic diagram of the relationship curve between the effective inductance of the negative stiffness superconducting coil and the displacement provided by the present invention
  • 1 is the upper single-layer close-wound disc-type superconducting coil
  • 2 is the upper inspection quality
  • 3 is the upper solenoid superconducting coil
  • 4 is the upper coil bobbin
  • 5 is the lower single-layer densely wound disk-type superconducting coil
  • 6 is the lower inspection quality
  • 7 is the lower solenoid superconducting coil
  • 8 is the lower coil bobbin
  • 9 is the structural member.
  • the present invention proposes a construction of a two-degree-of-freedom coupled magnetic spring with low differential mode stiffness and large ratio of common mode stiffness to differential mode stiffness
  • the core of the vibrator method is to include a pair of negative stiffness superconducting coils and a pair of positive stiffness superconducting coils at the same time.
  • the two superconducting coils in a pair interact with two superconducting inspection masses and are connected to the same
  • the introduction of a pair of negative stiffness superconducting coils significantly reduces the differential mode stiffness of the coupled spring oscillator and increases the ratio of common mode stiffness to differential mode stiffness.
  • Using the invention to construct a superconducting gravity gradiometer sensitive probe can significantly improve the gradient measurement sensitivity and improve the ability of the gradiometer to resist external vibration interference.
  • the present invention provides a coupled superconducting magnetic spring vibrator that can be applied to construct a superconducting gravity gradiometer, including: a pair of superconducting inspection quality, a pair of negative stiffness superconducting coils, a pair of positive stiffness superconducting coils, and A superconducting circuit that couples the paired inspection masses into a two-degree-of-freedom superconducting magnetic spring vibrator.
  • the main point is to introduce negative stiffness superconducting coils, and use superconducting wires to connect the negative stiffness superconducting coils in series into a superconducting loop, reduce the differential mode stiffness of the two-degree-of-freedom superconducting magnetic spring oscillator, and improve the sensitivity of gradient measurement; improve the common mode stiffness
  • the ratio of the stiffness to the differential mode restrains the interference of the movement acceleration of the installation platform on the gradient measurement.
  • Fig. 1 is a schematic diagram of the structure of a superconducting gravity gradiometer provided by the present invention. As shown in Fig. 1, it includes: an upper single-layer densely wound disc-type superconducting coil 1, an upper inspection mass 2, an upper solenoid superconducting coil 3.
  • the above-mentioned upper element has the same parameters as the corresponding lower element, and the installation method of the upper single-layer densely wound disc-type superconducting coil and solenoid coil is the same as that of the lower part.
  • the axis of the upper coil bobbin and the axis of the lower coil bobbin are aligned with each other along the plumb line, but are staggered up and down by a certain distance, which is the baseline of the gradiometer.
  • the materials for the inspection quality, the negative stiffness superconducting coil, the positive stiffness superconducting coil and the superconducting circuit are all superconductors, and the negative stiffness superconducting coil and the positive stiffness superconducting coil exist between the inspection quality after storing the superconducting current Magnetic repulsion.
  • the magnetic repulsion is
  • L eff (z) is the effective inductance of the superconducting coil that depends on the displacement of the test mass
  • I is the current in the coil.
  • the positive stiffness superconducting coil is a superconducting coil whose effective inductance L eff (z) is negative to the second derivative of the inspection quality at the sensitive degree of freedom displacement z, that is, d 2 L eff (z)/dz 2 ⁇ 0
  • the negative stiffness superconducting coil is a superconducting coil whose effective inductance L eff (z) is positive for the second derivative of the inspection quality at the sensitive degree of freedom displacement z, that is, d 2 L eff (z)/dz 2 > 0.
  • the effective inductance is defined as the ratio of the magnetic flux of the coil to its current.
  • the magnetic flux of the coil refers to the sum of the magnetic flux generated by the coil's own current and the magnetic flux generated by the superconducting shielding current of the inspection surface interacting with it.
  • the effective inductance of the superconducting coil that interacts with the inspection mass varies with the displacement of the inspection mass. The functional relationship between the two represents the entire Meissner effect-based magnetic interaction between the current-carrying superconducting coil and the superconducting inspection mass. characteristic.
  • the superconducting circuit is a superconducting network formed by superconducting coils connected by superconducting wires, and is composed of a single or multiple loops.
  • the circuit has the property of conservation of magnetic flux, namely Where Is the effective inductance of the i-th superconducting coil that interacts with the inspection mass in the loop, and is a function of the displacement of the inspection mass, I i (z 1 , z 2 ) is the current flowing through the i-th superconducting coil, by The displacements of the two inspection masses are jointly determined; L j and I j (z 1 , z 2 ) are the superconducting coil in the loop that does not interact with the inspection mass and the superconducting current in the superconducting coil, z 1 is the first The displacement of one inspection mass, z 2 is the displacement of the second inspection mass.
  • the two superconducting inspection masses are placed separately, and the pairs of superconducting coils interacting with the two inspection masses are connected to the superconducting circuit, and the motions of the two inspection masses are coupled through the superconducting circuit to form Superconducting magnetic spring vibrator with two degrees of freedom.
  • a vertical vibrator Take a vertical vibrator as an example.
  • the current-carrying superconducting coils L 1 and L 2 are used to maglevate two superconducting inspection masses of the same mass separately placed in the vertical direction.
  • the effective inductance is a function of the displacement of the test mass relative to the equilibrium position. Connect L 1 and L 2 to the same superconducting loop.
  • m is the mass
  • ⁇ is the angular frequency
  • g 1 and g 2 are the time-varying gravitational accelerations at the center of mass of the upper and lower test masses respectively
  • a is the motion acceleration of the installation platform
  • k ii represents the rigidity provided by the single-layer densely wound superconducting coil and solenoid superconducting coil that directly interact with the inspection quality i; when i ⁇ j, k ij represents the same as the i-th inspection quality
  • the interacting single-layer densely wound superconducting coil and solenoid superconducting coil are coupled through the superconducting circuit to provide the j-th inspection quality stiffness.
  • the two inspection quality parameters are generally required to be the same.
  • the inspection quality is the same as the magnetic interaction parameter of the superconducting coil.
  • the spring vibrator of the gradiometer has a small differential mode stiffness in order to obtain a high sensitivity of gravity gradient measurement.
  • the gradiometer has a larger common-mode stiffness to improve the common-mode rejection ratio. This is because there are inevitably errors in the processing and production, and a small amount of common-mode displacement is mixed into the differential-mode displacement detected by the gradiometer, and the common-mode stiffness The larger the value, the less common-mode displacement signal mixed in, and the stronger the ability of the gradiometer to resist the interference of the acceleration of the installation platform.
  • L 0 is the effective inductance of the superconducting coils L 1 and L 2 when the inspection mass is in a balanced position.
  • L 1 (z 1 ) and L 2 (z 2 ) are the function of the effective inductance of the two superconducting coils with the displacement of the inspection mass that interacts with them.
  • L 0 and I 0 can be used to represent the effective inductance and superconducting current intensity of the superconducting coil interacting with the test mass at the equilibrium position
  • dL 1 (z 1 )/dz 1 dL 2 (z 2 )/dz 2 , Uniformly expressed by dL(z)/dz.
  • I 1 (z 1 ,z 2 ), I 2 (z 1 ,z 2 ) and I p (z 1 ,z 2 ) are the superconducting coils L 1 , L 2 and L p when the two inspection masses are displaced.
  • the expression of the magnetic force between the superconducting coil and the inspection quality is Specifically, when the superconducting coils interacting with the two inspection masses are connected to form a superconducting loop, the magnetic forces on the two inspection masses are:
  • the stiffness coefficient of the spring oscillator with two degrees of freedom is:
  • the differential mode stiffness k d and the common mode stiffness k c are respectively:
  • Equation (7) shows that the common-mode stiffness is always greater than the differential-mode stiffness, and the difference is determined by the last term of the k d and k c expressions.
  • the relative position of the superconducting coil and the inspection quality in Fig. 3 is not of practical significance. The figure only shows that the superconducting coils interact with the superconducting inspection quality. Since the positive stiffness coil and the negative stiffness coil work together on the superconducting inspection quality, the total stiffness coefficient of the vibrator is the sum of the stiffness coefficients provided by the interaction of the two types of coils with the inspection quality. The contribution of the negative stiffness coil to the stiffness coefficient is:
  • k′ ii represents the stiffness provided by the solenoid superconducting coil directly interacting with the inspection mass i; when i ⁇ j, k′ ij represents the solenoid interacting with the i-th inspection mass
  • the superconducting coil is coupled through the superconducting circuit to provide the stiffness of the j-th inspection mass
  • l(z) is the effective inductance of the negative stiffness superconducting coil with the displacement of the inspection mass
  • l 0 and i 0 are respectively the inspection quality in equilibrium
  • the effective inductance and superconducting current strength of the negative stiffness superconducting coil at the location is:
  • the differential mode stiffness and common mode stiffness of the vibrator are:
  • the differential mode stiffness is more than the first term of the K d expression.
  • the negative stiffness superconducting coil has the property of d 2 l(z)/dz 2 >0. After the stiffness of the superconducting coil, the differential mode stiffness will decrease. Adjusting the current i 0 of the negative stiffness superconducting coil can make the differential mode stiffness of the vibrator to a small positive value, and a positive stiffness is the basic condition for forming a spring vibrator. After adding the negative stiffness superconducting coil, the common mode stiffness of the vibrator is more than the first and third terms of the K c expression.
  • the first term is negative, which is the same as the decrease of the differential mode stiffness
  • the third term is always positive. Value, indicating that even if the common mode stiffness becomes smaller, the decrease value is always smaller than the decrease value of the differential mode stiffness. Without the introduction of the negative stiffness superconducting coil, the common mode is always greater than the differential mode stiffness. Therefore, after the introduction of the negative stiffness superconducting coil, the ratio of the spring vibrator's common mode stiffness to the differential mode stiffness always increases.
  • the superconducting current in the negative stiffness superconducting coil and the positive stiffness superconducting coil can be adjusted under the guidance of formula (10) to meet different design requirements.
  • both the negative stiffness superconducting coil and the positive stiffness superconducting coil may include multiple sets of superconducting coils.
  • the superconducting circuit connected to the positive stiffness superconducting coil may have a different form from that shown in Fig. 2, and the superconducting circuit connected to the negative stiffness superconducting coil as shown in Fig. 3 can be connected in series without interacting with the inspection quality.
  • superconducting coils Of superconducting coils.
  • the positive stiffness coil group and the negative stiffness coil group can be used to provide vertical magnetic force, offset the gravity on the inspection mass, and jointly suspend the inspection mass, as shown in Figure 1, constructing a vertical pair
  • the vertical magnetic spring vibrator of the angular component T zz superconducting gravity gradiometer provides a time-varying gravity gradient value by detecting the differential mode displacement of the vibrator.
  • the introduction of the negative stiffness superconducting coil can overcome the technical defect that the differential mode stiffness has a lower limit under the condition of using the positive stiffness coil alone to inspect the quality, significantly reduce the differential mode stiffness, and increase the ratio of the common mode stiffness to the differential mode stiffness, thereby Improve the gradient measurement sensitivity and improve the common mode rejection ratio.
  • the gravity gradient tensor has 5 independent components, of which the vertical diagonal component T zz represents the rate of change of gravitational acceleration in the vertical direction.
  • the signal of this component is large, and the T zz aviation superconducting gravity gradiometer has important application prospects in the field of resource exploration.
  • a negative stiffness superconducting coil can be introduced to construct a coupled superconducting magnetic spring vibrator with other degrees of freedom to measure different components in the gravity gradient tensor.
  • the inspection quality is a superconductor cylinder with a sealing cover at the upper end, a single-layer densely wound disk-type superconducting coil is placed adjacently under the inner cover of the cylinder, and the outer diameter of the solenoid coil is slightly smaller than the inner diameter of the inspection quality cylinder.
  • the ground is placed at the opening of the inspection quality cylinder.
  • 110 turns of densely wound single-layer disc coils are made with 36 # niobium wire, and the inspection mass is a circular cylinder with an inner diameter of 47.5 mm.
  • the finite element calculation results of the dependence curve of the effective inductance of the coil on the displacement z of the inspection mass As shown in Figure 4.
  • the curve is a concave function, and its second derivative d 2 L eff (z)/dz 2 ⁇ 0 is a superconducting coil with positive stiffness.
  • a cylindrical superconductor made of niobium of the same size is used for quality inspection, and a solenoid coil is coaxially arranged at the open end of the inspection quality.
  • the solenoid uses 36 # niobium wire with 4 layers ⁇ 50 turns on the ⁇ 45 frame.
  • the solenoid coil is coaxially arranged with the inspection quality, the upper part of the coil winding is placed in the inspection quality cylinder, and the lower part extends 2mm from the lower end of the inspection quality.
  • the dependence curve of the effective inductance of the coil on the displacement z of the inspection mass is obtained as shown in Figure 5.
  • the curve is a convex function, and its second derivative d 2 l eff (z)/dz 2 >0 is a superconducting coil with negative stiffness.
  • the finite element numerical calculation method with an axisymmetric structure can refer to the prior art, and the key is to calculate the shielding current distribution on the surface of the superconductor.
  • the currents of n current loops are obtained, and then the total magnetic flux generated by all current loops in the superconducting coil is obtained according to the Ampere's theorem, plus the magnetic flux generated by the current of the superconducting coil itself, divided by the superconducting
  • the current of the coil is the effective inductance of the superconducting coil under a given inspection mass displacement.
  • the finite element numerical calculation method can be used to find the structural parameters that meet the design requirements, including the geometric shape of the inspection quality and the geometric and electromagnetic parameters of the superconducting coil.
  • the spring vibrator that constructs the gravity measurement inertial sensor must have a positive stiffness. Therefore, a superconducting coil with a negative stiffness property must be used in combination with a superconducting coil with a positive stiffness property.
  • the differential mode stiffness and common mode stiffness of the superconducting magnetic spring vibrator are adjusted by adjusting the current values of the two types of superconducting coils, so that the vibrator can meet the application requirements.
  • the content of the present invention is applied to construct a diagonal vertical component T zz superconducting gravity gradiometer.
  • a typical method is to use superconducting coils to magnetically levitate the two inspection masses placed vertically separately, and use superconducting circuits to connect the superconducting coils that interact with the inspection masses into a superconducting loop, with the aid of the coupling of the superconducting loop
  • a magnetic spring vibrator with two degrees of freedom is formed, and the gravity gradient is given by measuring the differential mode displacement of the vibrator.
  • the second derivative Is d 2 L eff (z)/dz 2 -17.4 ⁇ H/mm 2
  • the effective inductance of the negative stiffness solenoid superconducting coil is 999 ⁇ H
  • the differential mode stiffness of the two-degree-of-freedom spring vibrator is 42.9N/m
  • the common mode stiffness is 1248.8N/m
  • the ratio of the common mode stiffness to the differential mode stiffness can be given. Is 29. If the negative stiffness superconducting coil is not introduced, the current of the positive stiffness disc-type superconducting coil must be increased to 6.38A to suspend the inspection mass to the same height.
  • the differential mode stiffness of the two-degree-of-freedom spring vibrator is 411.4N/m
  • the common mode stiffness is 2484.8N/m
  • the ratio of common mode stiffness to differential mode stiffness is 6.

Abstract

一种超导重力梯度仪及其灵敏度提高方法，包括：成对的超导检验质量（2，6）、成对的负刚度超导线圈（3，7）、成对的正刚度超导线圈（1，5）以及将成对检验质量（2，6）耦合成两自由度超导磁力弹簧振子的超导电路。其要点是引入负刚度超导线圈（3，7），并使用超导线将负刚度超导线圈（3，7）串联成超导回路，降低两自由度超导磁力弹簧振子的差模刚度，增大共模刚度与差模刚度的比值。使用该方法构建超导重力梯度仪的磁力弹簧振子，特别是构建检验质量（2，6）全磁悬浮的垂向对角分量超导重力梯度仪时，能显著提高梯度测量的灵敏度；增大共模抑制比，抑制安装平台运动加速度对梯度测量的干扰。

Description

一种超导重力梯度仪及其灵敏度的提高方法 【技术领域】
本发明涉及重力测量技术领域，更具体地，涉及一种超导重力梯度仪及其灵敏度的提高方法。
【背景技术】
超导重力梯度仪是利用超导电性构建的时变重力梯度测量仪器，工作在4.2K液氦温度，具有仪器固有噪声低、分辨率高、格值稳定等优点。以矿产资源勘查为应用目标的航空超导重力梯度仪，具有突破常温重力梯度测量仪器的分辨率极限的潜力，可望成为深部资源勘查的重要工具。
一种典型的超导重力梯度仪构建方法是利用超导体载流线圈与超导检验质量之间的磁相互作用，使用超导电路将成对的分开放置的超导检验质量耦合成一个两自由度的磁力弹簧振子，振子运动可分解为共模与差模两种自然模态，通过测量振子的差模位移，给出重力梯度随时间的变化量。
对于构建梯度仪的耦合磁力弹簧振子，希望其差模刚度小，共模刚度大。重力梯度是以差分重力加速度的形式被测量，小的差模刚度意味着从重力梯度到差分位移的传递函数大，有利于提高仪器的灵敏度与分辨率。在运动平台上，平台的运动加速度以共模加速度的形式被仪器感知，是需要通过差分扣除的，大的共模刚度意味着对平台运动不敏感，有利于提高仪器的共模抑制比，弱化仪器安装平台振动对梯度测量的干扰。
在超导重力梯度仪中，有多种因素限制了共模差模刚度比值的提高。例如，在测量重力梯度的垂向对角分量的检验质量全磁悬浮超导重力梯度仪中，超导线圈与检验质量之间的磁斥力需要足够大，能够抵消检验质量所受的重力，从而悬浮检验质量。受这一因素的限制，现有技术中的差模固有频率一般大于10Hz，共模刚度与差模刚度比值也较小。
【发明内容】
针对现有技术的缺陷，本发明的目的在于解决现有超导重力梯度仪的共模差模刚度比值提高受限制，不利于提高重力梯度仪的灵敏度和分辨率的技术问题。
为实现上述目的，第一方面，本发明提供一种超导重力梯度仪，包括：两组超导磁力弹簧振子和超导电路；
每组超导磁力弹簧振子包括：密绕盘型超导线圈、检验质量、螺线管超导线圈以及线圈骨架；检验质量为下方开口的半封闭超导筒体；所述线圈骨架位于检验质量的下方；所述单层密绕盘型超导线圈绕制在线圈骨架的顶部，螺线管超导线圈绕制在线圈骨架的底部；单层密绕盘型超导线圈和螺线管超导线圈与检验质量之间的磁斥力平衡检验质量的重力，将检验质量进行磁悬浮；所述磁斥力是检验质量位移的函数，检验质量所受磁力和重力的合力具有恢复力的性质，构成超导磁力弹簧振子；
所述单层密绕盘型超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相反，为超导磁力弹簧振子贡献正的刚度；螺线管超导线圈磁力线的一部分处于检验质量的封闭空间内呈压缩状态，另一部分处于检验质量的封闭空间外呈扩展状态，螺线管超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相同，为超导磁力弹簧振子贡献负的刚度；所述超导磁力弹簧振子的刚度通过单层密绕盘型超导线圈的电流值和螺线管超导线圈的电流值调节；
所述超导电路通过超导线将两组超导磁力弹簧振子的密绕盘型超导线圈和螺线管超导线圈连接构成超导回路，以将两组超导磁力弹簧振子耦合成两自由度的弹簧振子，构成超导重力梯度仪；所述超导重力梯度仪的共模刚度与差模刚度的比值相比不包括螺线管超导线圈的超导重力梯度仪的共模刚度与差模刚度的比值高。
可选地，所述超导重力梯度仪的共模刚度k c和差模刚度k d分别为：
Figure PCTCN2020097619-appb-000001
其中，L 0、I 0分别表示平衡位置处正刚度单层密绕盘型超导线圈的有效电感和超导电流强度，l 0、i 0分别表示平衡位置处负刚度螺线管超导线圈的有效电感和超导电流强度，l(z)表示负刚度螺线管超导线圈随检验质量位移变化的有效电感，L(z)表示单层密绕盘型超导线圈随检验质量位移变化的有效电感，L p表示超导电路中间支路所接电感，z表示检验质量相对于平衡位置的位移。
可选地，d 2L(z)/dz 2<0；d 2l(z)/dz 2>0。
可选地，该超导重力梯度仪还包括：结构件；所述结构件用于上下连接两组超导磁力弹簧振子的线圈骨架。
可选地，所述密绕盘型超导线圈和螺线管超导线圈均可以包括多组超导线圈。
第二方面，本发明提供一种超导重力梯度仪灵敏度的提高方法，所述超导重力梯度仪包括两个自由度的超导磁力弹簧振子，该方法包括如下步骤：
在所述两个自由度的超导磁力弹簧振子中均引入负刚度超导线圈；
通过超导线将负刚度超导线圈串联成超导回路，以降低所述超导重力梯度仪的差模刚度，提高所述超导重力梯度仪的灵敏度。
可选地，每个自由度的超导磁力弹簧振子包括：密绕盘型超导线圈、检验质量以及线圈骨架；检验质量为下方开口的半封闭超导筒体；所述线圈骨架位于检验质量的下方；所述单层密绕盘型超导线圈绕制在线圈骨架的顶部；单层密绕盘型超导线圈与检验质量之间的磁斥力平衡检验质量的重力，将检验质量进行磁悬浮；所述磁斥力是检验质量位移的函数，检验质量所受磁力和重力的合力具有恢复力的性质，构成超导磁力弹簧振子； 所述单层密绕盘型超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相反，为超导磁力弹簧振子贡献正的刚度；
在所述两个自由度的超导磁力弹簧振子中均引入负刚度超导线圈，包括如下步骤：
在两个线圈骨架的底部均绕制螺线管超导线圈，所述螺线管超导线圈磁力线的一部分处于检验质量的封闭空间内呈压缩状态，另一部分处于检验质量的封闭空间外呈扩展状态，螺线管超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相同，为超导磁力弹簧振子贡献负的刚度；所述超导磁力弹簧振子的刚度通过单层密绕盘型超导线圈的电流值和螺线管超导线圈的电流值调节。
总体而言，通过本发明所构思的以上技术方案与现有技术相比，具有以下有益效果：
本发明提供一种超导重力梯度仪及其灵敏度的提高方法，在构建超导重力梯度仪的双检验质量两自由度超导磁力弹簧振子中，引入成对的负刚度超导线圈，分别与超导检验质量相互作用，负刚度超导线圈以串联的形式包含在超导回路中，有效地降低弹簧振子的差模刚度，提高共模刚度与差模刚度的比值，提高了超导重力梯度仪的灵敏度。本发明通过降低差模刚度，增大差模加速度，即重力梯度到差模位移的传递函数，提高梯度测量的灵敏度，降低噪声水平；通过提高共模刚度与差模刚度的比值，提高共模抑制比，抑制安装平台运动加速度对梯度测量的干扰。
【附图说明】
图1为本发明提供的超导重力梯度仪的结构示意图；
图2为本发明提供的超导重力梯度仪的正刚度超导线圈的超导电路等效示意图；
图3为本发明提供的超导重力梯度仪的负刚度超导线圈的超导电路等效示意图；
图4为本发明提供的正刚度超导线圈有效电感对位移的关系曲线示意图；
图5为本发明提供的负刚度超导线圈有效电感对位移的关系曲线示意图；
在所有附图中，相同的附图标记用来表示相同的元件或结构，其中，1为上部单层密绕盘型超导线圈、2为上部检验质量、3为上部螺线管超导线圈、4为上部线圈骨架、5为下部单层密绕盘型超导线圈、6为下部检验质量、7为下部螺线管超导线圈、8为下部线圈骨架以及9为结构件。
【具体实施方式】
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。
本发明针对现有技术中两自由度超导磁力弹簧振子只包含正刚度超导线圈的情况，提出一种构建差模刚度小、共模刚度与差模刚度比值大的两自由度耦合磁力弹簧振子的方法，其核心是在振子同时包含成对负刚度超导线圈和成对正刚度超导线圈，成对的两个超导线圈分别与两个超导检验质量相互作用，并连接在同一个超导电路中，负刚度超导线圈对的引入显著降低耦合弹簧振子的差模刚度，增大共模刚度与差模刚度比值。利用本发明构建超导重力梯度仪敏感探头，可显著提高梯度测量灵敏度，改善梯度仪抵抗外部振动干扰的能力。
本发明提供一种可应用于构建超导重力梯度仪的耦合超导磁力弹簧振 子，包括：成对的超导检验质量、成对的负刚度超导线圈、成对的正刚度超导线圈以及将成对检验质量耦合成两自由度超导磁力弹簧振子的超导电路。其要点是引入负刚度超导线圈，并使用超导线将负刚度超导线圈串联成超导回路，降低两自由度超导磁力弹簧振子的差模刚度，提高梯度测量的灵敏度；提高共模刚度与差模刚度的比值，抑制安装平台运动加速度对梯度测量的干扰。
图1为本发明提供的一种超导重力梯度仪的结构示意图，如图1所示，包括：上部单层密绕盘型超导线圈1、上部检验质量2、上部螺线管超导线圈3、上部线圈骨架4、下部单层密绕盘型超导线圈5、下部检验质量6、下部螺线管超导线圈7、下部线圈骨架8以及刚性连接上部线圈骨架4和下部线圈骨架8的结构件9。上述上部元件与对应的下部元件具有相同的参数，上部单层密绕盘型超导线圈和螺线管线圈的安装方式与下部相同。上部线圈骨架轴线与下部线圈骨架轴线沿铅锤线相互对准，但上下错开一定距离，该距离为梯度仪的基线。
所述检验质量、负刚度超导线圈、正刚度超导线圈和超导电路的材料均为超导体，所述负刚度超导线圈和正刚度超导线圈在存储超导电流后与检验质量之间存在磁斥力。
根据电磁学原理，磁斥力为
Figure PCTCN2020097619-appb-000002
式中L eff(z)是依赖检验质量位移的超导线圈的有效电感，I为线圈中的电流。所述正刚度超导线圈是其有效电感L eff(z)对检验质量在敏感自由度位移z的二阶导数为负值的超导线圈，即d 2L eff(z)/dz 2<0；所述负刚度超导线圈是其有效电感L eff(z)对检验质量在敏感自由度位移z的二阶导数为正值的超导线圈，即d 2L eff(z)/dz 2>0。所述有效电感定义为线圈的磁通量与其电流的比值，线圈磁通量指线圈本身电流产生的磁通和与其相互作用的检验质量表面的超导屏蔽电流产生的磁通之和。与检验质量相互作用的超导线圈的有效电感随检验质量位移变化，两者之间的函数关系表征了载流超导线圈与超导检验质量之间基于迈 斯纳效应的磁相互作用的全部特性。
所述超导电路，是由超导线将超导线圈连接而成的超导网络，由单个或多个回路构成。回路具有磁通守恒的性质，即
Figure PCTCN2020097619-appb-000003
式中
Figure PCTCN2020097619-appb-000004
是回路中与第i个与检验质量相互作用的超导线圈的有效电感，是该检验质量位移的函数，I i(z 1,z 2)是流经第i个超导线圈的电流，由两个检验质量的位移共同决定；L j和I j(z 1,z 2)分别是回路中不与检验质量相互作用的超导线圈和该超导线圈中的超导电流，z 1是第一个检验质量的位移，z 2是第二个检验质量的位移。
可以理解的是，将两个超导检验质量分开放置，将分别与两个检验质量相互作用的成对超导线圈连接到超导电路中，两个检验质量的运动通过超导电路耦合，构成两自由度的超导磁力弹簧振子。以一种垂向振子为例，如图2所示，使用载流超导线圈L 1和L 2分别对在垂向分开放置的两个质量相同的超导检验质量进行磁悬浮，超导线圈的有效电感是检验质量相对平衡位置位移的函数。将L 1和L 2连接到同一个超导回路中，根据超导回路磁通守恒原理，其中一个检验质量发生位移，与另一个检验质量作用的超导线圈中电流会随之变化，因此两个检验质量的运动通过超导电路相互耦合，形成两自由度的弹簧振子。不计阻尼，检验质量的动力学方程做傅里叶变换后可写为：
Figure PCTCN2020097619-appb-000005
式中，m为质量，ω为角频率，g 1和g 2分别为上下两个检验质量质心处的时变重力加速度，a为安装平台的运动加速度，k ij为系统弹簧振子的刚度参数，其中i＝1，2和j＝1，2。当i＝j时，k ii表示直接与检验质量i相互作用的单层密绕超导线圈和螺线管超导线圈提供的刚度；当i≠j时，k ij表示与第i个检验质量相互作用的单层密绕超导线圈和螺线管超导线圈，通过超导电路耦合，提供给第j个检验质量的刚度。梯度仪设计中，一般要求两个 检验质量参数相同，检验质量与超导线圈的磁作用参数相同，超导电路关于两个检验质量对称，我们将这种情况称为理想匹配，此时有k 11＝k 22，k 12＝k 21。做坐标变换，令差模位移z d＝z 1-z 2，共模位移z c＝(z 1+z 2)/2，动力学方程组的解为：
Figure PCTCN2020097619-appb-000006
式中，a d(ω)＝g 1(ω)-g 2(ω)，称为差模加速度，包含时变重力梯度的信息，在梯度仪中通常通过检测差模位移z d得到重力梯度；式中a c(ω)＝a(ω)+[g 1(ω)+g 2(ω)]/2，称为共模加速度，包含平台运动加速度。从式(2)可以看出，(k 11-k 12)为差模刚度，(k 11+k 12)/2为共模刚度。通常希望梯度仪弹簧振子具有较小的差模刚度，以获得较高的重力梯度测量灵敏度。通常希望梯度仪有较大的共模刚度，以提高共模抑制比，这是因为加工制作不可避免地存在误差，有小量共模位移混入被梯度仪检测的差模位移中，共模刚度越大，混入的共模位移信号越少，梯度仪抵抗安装平台运动加速度干扰的能力越强。
以图2所示超导电路为例，向超导电路中注入超导持久电流，使线圈L 1和L 2中的电流为I 0，检验质量处于平衡位置，中间支路L p中没有电流，超导回路磁通守恒原理要求在此后任意时刻，各超导线圈中的电流均满足以下方程组：
Figure PCTCN2020097619-appb-000007
式中：L 0为检验质量处于平衡位置时，超导线圈L 1和L 2的有效电感。L 1(z 1)和L 2(z 2)分别是两个超导线圈有效电感随与之相互作用的检验质量位移变化的函数关系，在理想匹配情况下，成对超导线圈的参数相同，可以用L 0、I 0表示平衡位置处与检验质量相互作用超导线圈的有效电感和超导 电流强度，且有dL 1(z 1)/dz 1＝dL 2(z 2)/dz 2，统一用dL(z)/dz表示。I 1(z 1,z 2)、I 2(z 1,z 2)和I p(z 1,z 2)分别是两个检验质量发生位移时，超导线圈L 1、L 2和L p中的电流。由式(3)可求到I 1(z 1,z 2)、I 2(z 1,z 2)。
如前面已论述的，超导线圈与检验质量之间的磁力表达式为
Figure PCTCN2020097619-appb-000008
Figure PCTCN2020097619-appb-000009
具体地，当与两个检验质量相互作用的超导线圈连接成超导回路后，两个检验质量受到的磁力分别为：
Figure PCTCN2020097619-appb-000010
对应地，两自由度弹簧振子的刚度系数为：
Figure PCTCN2020097619-appb-000011
由式(5)可给出在平衡位置附近，图2所示两自由度弹簧振子的刚度系数为：
Figure PCTCN2020097619-appb-000012
差模刚度k d和共模刚度k c分别为：
Figure PCTCN2020097619-appb-000013
对于正刚度超导线圈，有效电感对检验质量位移的二阶导数小于零，即d 2L(z)/dz 2<0。式(7)表明，共模刚度恒大于差模刚度，其差值由k d和k c表达式的最后一项决定。
可以理解的是，引入与两个检验质量分别作用的负刚度超导线圈对，并用超导线将两个线圈串联构成超导回路，与正刚度线圈共同构建两自由度超导磁力弹簧振子，可以有效地降低差模刚度，增大共模刚度与差模刚度的比值。仍然以一种垂向两自由度振子为例，在图2的基础上增加一对负刚度超导线圈，分别与两个超导检验质量相互作用，且负刚度线圈串联成超导回路，如图3所示。需要说明的是，图3中超导线圈与检验质量的相对位置不具有实际意义，图中只是表示超导线圈均与超导检验质量发生相互作用。由于正刚度线圈和负刚度线圈共同作用于超导检验质量，振子的总刚度系数是两类线圈分别与检验质量相互作用提供的刚度系数之和，负刚度线圈对刚度系数的贡献为：
Figure PCTCN2020097619-appb-000014
式中，k′ ij为两螺线管线圈提供的刚度，其中i＝1，2和j＝1，2。当i＝j时，k′ ii表示直接与检验质量i相互作用的螺线管超导线圈提供的刚度；当i≠j时，k′ ij表示与第i个检验质量相互作用的螺线管超导线圈，通过超导电路耦合，提供给第j个检验质量的刚度，l(z)为负刚度超导线圈随检验质量位移变化的有效电感，l 0和i 0分别是检验质量处于平衡位置处负刚度超导线圈的有效电感和超导电流强度。弹簧振子的总刚度系数为：
Figure PCTCN2020097619-appb-000015
引入负刚度超导线圈之后，振子的差模刚度和共模刚度为：
Figure PCTCN2020097619-appb-000016
与没有负刚度超导线圈的式(7)比较，差模刚度多了K d表达式的第一项，负刚度超导线圈具有d 2l(z)/dz 2>0的性质，加入负刚度超导线圈之后差模刚度会减小。调节负刚度超导线圈的电流i 0，可以使振子的差模刚度为一个较小的正值，刚度为正值是形成弹簧振子的基本条件。加入负刚度超导线圈之后振子的共模刚度多了K c表达式的第一项和第三项，第一项为负值，与差模刚度的减小值相同，第三项恒为正值，表明共模刚度即便是变小，其减小值也恒小于差模刚度的减小值。在没有引入负刚度超导线圈情况下，共模恒大于差模刚度，因此，引入负刚度超导线圈后，弹簧振子共模刚度与差模刚度的比值总是增大的。
可选地，可以在公式(10)的指导下，调节负刚度超导线圈和正刚度超导线圈中的超导电流，满足不同的设计需求。
可选地，所述负刚度超导线圈和正刚度超导线圈均可以包括多组超导线圈。
可选地，连接正刚度超导线圈的超导电路可以具有与图2不同的形式，如图3所示的连接负刚度超导线圈的超导回路中可以再串入不与检验质量相互作用的超导线圈。
可选地，可依照本发明的方法，可以使用正刚度线圈组和负刚度线圈组提供垂向的磁作用力，抵消检验质量所受重力，共同悬浮检验质量，如图1，构建垂向对角分量T zz超导重力梯度仪的垂向磁力弹簧振子，通过检测振子的差模位移给出时变重力梯度值。负刚度超导线圈的引入，能克服单独使用正刚度线圈悬浮检验质量情况下，差模刚度存在下限值的技术缺陷，显著降低差模刚度，提高共模刚度与差模刚度的比值，从而提高梯度测量灵敏度，改善共模抑制比。
具体地，重力梯度张量有5个独立分量，其中的垂向对角分量T zz表征重力加速度在垂向的变化率。该分量信号大，T zz航空超导重力梯度仪在资源勘查领域有重要的应用前景。
可选地，可引入负刚度超导线圈构建其它自由度的耦合超导磁力弹簧振子，用来测量重力梯度张量中的不同分量。
具体地，检验质量为上端有封口盖板的超导体圆筒，单层密绕盘型超导线圈比邻安置在筒内盖板下方，螺线管线圈外径略小于检验质量圆筒内径，同轴地安置在检验质量圆筒开口位置。选择合适的几何参数，单层密绕盘型超导线圈为正刚度超导线圈，螺线管线圈为负刚度超导线圈。
具体地，以36 #铌线绕制110匝密绕单层盘形线圈，检验质量为内经为47.5mm的圆形筒体，线圈有效电感对检验质量位移z的依赖关系曲线的有限元计算结果如图4所示。曲线为凹函数，其二阶导数d 2L eff(z)/dz 2<0，是正刚度超导线圈。
具体地，使用同样尺寸的铌制圆筒形超导检验质量，在检验质量开口端同轴安置一个螺线管线圈，螺线管用36 #铌线以4层×50匝方式在φ45骨架上密绕而成，螺线管线圈与检验质量同轴安置，线圈绕组上部置于检验质量筒内，下部伸出检验质量下端面2mm。使用有限元数值计算方法，得到线圈有效电感对检验质量位移z的依赖关系曲线如图5所示。曲线为凸函数，其二阶导数d 2l eff(z)/dz 2>0，是负刚度超导线圈。
更具体地，具有轴对称结构的有限元数值计算方法可参考现有技术，其关键是计算超导体表面的屏蔽电流分布。在有限元数值计算中，将超导体表面连续分布的屏蔽电流离散成众多电流环I i(i＝1,2…n)，分别计算任意两个屏蔽电流环之间的互感M ij(i,j＝1,2…n,i≠j)，每一个屏蔽电流环与超导线圈间的互感M i0(i＝1,2…n)，以及每一个屏蔽电流环的自感L i(i＝1,2…n)，超导体的迈斯纳效应要求在超导线圈中注入电流I 0后，第i个屏蔽电流环的磁通Φ i(i＝1,2…n)为零，据此可列出n个方程：
Figure PCTCN2020097619-appb-000017
……
Figure PCTCN2020097619-appb-000018
……
Φ n＝L nI n+M n0I 0+∑ j≠nM njI j＝0    (11)
通过数值求解方程组，得到n个电流环的电流，进而根据安培定理求得所有电流环在超导线圈中产生的总磁通，加上超导线圈本身电流产生的磁通，除以超导线圈的电流，即为超导线圈在给定检验质量位移下的有效电感。在上述负刚度超导线圈的构建方法指导下，可使用有限元数值计算方法寻找符合设计需求的结构参数，包括检验质量的几何形状和超导线圈的几何参数与电磁参数。
构建重力测量惯性传感器的弹簧振子必须具有正的刚度，因此，具有负刚度性质的超导线圈必须与具有正刚度性质的超导线圈组合使用。通过调节两类超导线圈的电流值来调节超导磁力弹簧振子的差模刚度和共模刚度，使振子满足应用需求。
具体地，将本发明内容应用于构建对角垂向分量T zz超导重力梯度仪。一种典型的方法是使用超导线圈将垂向分开放置的两个检验质量进行磁悬浮，使用超导电路将分别与检验质量相互作用的超导线圈连接成超导回路，借助超导回路的耦合构成两自由度的磁力弹簧振子，通过测量振子的差模位移给出重力梯度。
使用图1所示的结构和图3所示的超导电路构建两自由度超导磁力弹簧振子，在前面所述的正刚度线圈中注入超导电流4.58A，在前面所述的负刚度线圈中注入超导电流2.56A，两个超导线圈共同悬浮检验质量，将两个100克的检验质量悬浮在正刚度密绕单层盘形线圈上方0.8mm处，构成两自由度的垂向超导磁力弹簧振子。根据有限元数值计算结果，此时正刚度盘型超导线圈有效电感为L 0＝44.2μH，对检验质量位移的一阶导数为dL eff(z)/dz＝48.1μH/mm，二阶导数为d 2L eff(z)/dz 2＝-17.4μH/mm 2；负刚度螺线管超导线圈有效电感为999μH，对检验质量位移的一阶导数为 dl eff(z)/dz＝144.7μH/mm，二阶导数为d 2l eff(z)/dz 2＝51.6μH/mm 2。设定Lp为800μH，依照前文给出的计算方法，可给出二自由度弹簧振子的差模刚度为42.9N/m，共模刚度为1248.8N/m，共模刚度与差模刚度的比值为29。如果不引入负刚度超导线圈，则正刚度盘型超导线圈的电流需增加到6.38A才能将检验质量悬浮到相同的高度，此时二自由度弹簧振子的差模刚度为411.4N/m，共模刚度为2484.8N/m，共模刚度与差模刚度的比值为6。这些计算结果清楚地表明，引入负刚度超导线圈，能显著地降低弹簧振子的差模刚度，显著地提高共模刚度与差模刚度的比值。更系统的计算与分析表明，在不同的悬浮高度下，或正刚度超导线圈的超导电路采用不同的形式与参数情况下，引入负刚度超导悬浮线圈均能不同程度地降低差模刚度，提高共模刚度与差模刚度的比值。
需要说明的是，本领域技术人员可以理解的是本发明给出的螺线管线圈或单层密绕盘型线圈仅作为超导线圈的一种举例，凡是采用其他类型的超导线圈实现弹簧振子的正、负刚度控制的技术方案，均应属于本发明的保护范围。
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (7)

  1. 一种超导重力梯度仪，其特征在于，包括：两组超导磁力弹簧振子和超导电路；
    每组超导磁力弹簧振子包括：单层密绕盘型超导线圈、检验质量、螺线管超导线圈以及线圈骨架；检验质量为下方开口的半封闭超导筒体；所述线圈骨架位于检验质量的下方；所述单层密绕盘型超导线圈绕制在线圈骨架的顶部，螺线管超导线圈绕制在线圈骨架的底部；单层密绕盘型超导线圈和螺线管超导线圈与检验质量之间的磁斥力平衡检验质量的重力，将检验质量进行磁悬浮；所述磁斥力是检验质量位移的函数，检验质量所受磁力和重力的合力具有恢复力的性质，构成超导磁力弹簧振子；
    所述单层密绕盘型超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相反，为超导磁力弹簧振子贡献正的刚度；螺线管超导线圈磁力线的一部分处于检验质量的封闭空间内呈压缩状态，另一部分处于检验质量的封闭空间外呈扩展状态，螺线管超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相同，为超导磁力弹簧振子贡献负的刚度；所述超导磁力弹簧振子的刚度通过单层密绕盘型超导线圈的电流值和螺线管超导线圈的电流值调节；
    所述超导电路通过超导线将两组超导磁力弹簧振子的密绕盘型超导线圈和螺线管超导线圈连接构成超导回路，以将两组超导磁力弹簧振子耦合成两自由度的弹簧振子，构成超导重力梯度仪；所述超导重力梯度仪的共模刚度与差模刚度的比值相比不包括螺线管超导线圈的超导重力梯度仪的共模刚度与差模刚度的比值高。
  2. 根据权利要求1所述的超导重力梯度仪，其特征在于，所述超导重力梯度仪的共模刚度k c和差模刚度k d分别为：
    Figure PCTCN2020097619-appb-100001
    其中，L 0、I 0分别表示平衡位置处正刚度单层密绕盘型超导线圈的有效电感和超导电流强度，l 0、i 0分别表示平衡位置处负刚度螺线管超导线圈的有效电感和超导电流强度，l(z)表示负刚度螺线管超导线圈随检验质量位移变化的有效电感，L(z)表示单层密绕盘型超导线圈随检验质量位移变化的有效电感，L p表示超导电路中间支路所接电感，z表示检验质量相对于平衡位置的位移。
  3. 根据权利要求2所述的超导重力梯度仪，其特征在于，d 2L(z)/dz 2<0；d 2l(z)/dz 2>0。
  4. 根据权利要求1至3任一项所述的超导重力梯度仪，其特征在于，还包括：结构件；
    所述结构件用于上下连接两组超导磁力弹簧振子的线圈骨架。
  5. 根据权利要求1至3任一项所述的超导重力梯度仪，其特征在于，所述单层密绕盘型超导线圈和螺线管超导线圈均可以包括多组超导线圈。
  6. 一种超导重力梯度仪灵敏度的提高方法，所述超导重力梯度仪包括两个自由度的超导磁力弹簧振子，其特征在于，包括如下步骤：
    在所述两个自由度的超导磁力弹簧振子中均引入负刚度超导线圈；
    通过超导线将负刚度超导线圈串联成超导回路，以降低所述超导重力梯度仪的差模刚度，提高所述超导重力梯度仪的灵敏度。
  7. 根据权利要求6所述的超导重力梯度仪灵敏度的提高方法，其特征在于，每个自由度的超导磁力弹簧振子包括：密绕盘型超导线圈、检验质量以及线圈骨架；检验质量为下方开口的半封闭超导筒体；所述线圈骨架位于检验质量的下方；所述单层密绕盘型超导线圈绕制在线圈骨架的顶部； 单层密绕盘型超导线圈与检验质量之间的磁斥力平衡检验质量的重力，将检验质量进行磁悬浮；所述磁斥力是检验质量位移的函数，检验质量所受磁力和重力的合力具有恢复力的性质，构成超导磁力弹簧振子；所述单层密绕盘型超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相反，为超导磁力弹簧振子贡献正的刚度；
    所述在所述两个自由度的超导磁力弹簧振子中均引入负刚度超导线圈，包括如下步骤：
    在两个线圈骨架的底部均绕制螺线管超导线圈，所述螺线管超导线圈磁力线的一部分处于检验质量的封闭空间内呈压缩状态，另一部分处于检验质量的封闭空间外呈扩展状态，螺线管超导线圈施加于检验质量的垂向磁斥力随检验质量偏离平衡位置的位移成比例变化，变化量方向与位移方向相同，为超导磁力弹簧振子贡献负的刚度；所述超导磁力弹簧振子的刚度通过单层密绕盘型超导线圈的电流值和螺线管超导线圈的电流值调节。
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102608668A (zh) * 2011-12-19 2012-07-25 华中科技大学 重力梯度测量系统及其测量方法
WO2014007848A1 (en) * 2012-07-02 2014-01-09 SRC, Inc Gravity gradiometer
CN105911487A (zh) * 2016-04-14 2016-08-31 中国科学院上海微系统与信息技术研究所 一种超导磁传感器探测线圈及探测器
CN107795631A (zh) * 2016-09-07 2018-03-13 香港理工大学 用于产生负刚度的电磁设备和振动控制的方法
CN108918913A (zh) * 2018-05-16 2018-11-30 华中科技大学 一种固有频率可调的垂向超导磁力弹簧振子
CN111007573A (zh) * 2019-12-13 2020-04-14 华中科技大学 一种超导重力梯度仪及其灵敏度的提高方法

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2729570C (en) * 2008-09-25 2017-11-21 Technological Resources Pty Ltd A detector for detecting a gravity gradient
CN107092038B (zh) * 2017-06-19 2019-02-01 华中科技大学 一种mems重力仪

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102608668A (zh) * 2011-12-19 2012-07-25 华中科技大学 重力梯度测量系统及其测量方法
WO2014007848A1 (en) * 2012-07-02 2014-01-09 SRC, Inc Gravity gradiometer
CN105911487A (zh) * 2016-04-14 2016-08-31 中国科学院上海微系统与信息技术研究所 一种超导磁传感器探测线圈及探测器
CN107795631A (zh) * 2016-09-07 2018-03-13 香港理工大学 用于产生负刚度的电磁设备和振动控制的方法
CN108918913A (zh) * 2018-05-16 2018-11-30 华中科技大学 一种固有频率可调的垂向超导磁力弹簧振子
CN111007573A (zh) * 2019-12-13 2020-04-14 华中科技大学 一种超导重力梯度仪及其灵敏度的提高方法

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
LIU XIANG-DONG, LIU XI-KAI; MA DONG; CHEN LIANG; ZHANG NING: "Superconducting Gravity Instrument:Opportunities and Challenges", NAVIGATION AND CONTROL, vol. 18, no. 3, 1 June 2019 (2019-06-01), pages 48 - 48, XP055822754, ISSN: 1674-9030 *

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