Bitter coil self-torque calculation method and system, and storage medium

Abstract

The application discloses a Bitter coil self-torque calculation method and system and a storage medium, relates to the technical field of water-cooled magnets, and comprises the following steps: acquiring basic parameters of each coil of a water-cooled magnet, dividing conductors in the upper half coil or the lower half coil of the coil into a plurality of annular grids, and determining grid center point coordinates based on the basic parameters; calculating total radial magnetic field components of each grid center point; utilizing integral results of current density distribution of each grid on a single-turn cross-sectional area of the coil being equal to a target current passing through the coil to solve current density distribution at positions of each grid; calculating a helical angle sine value of a helical path of a current in the grid according to a helical path plane of the grid; calculating axial current density components of each grid according to the current density distribution at the positions of each grid and the corresponding helical angle sine value; and calculating electromagnetic torque when the target current passes through the coil according to the total radial magnetic field components and the axial current density components of each grid.

Description

Technical Field

[0001] This invention relates to the field of water-cooled magnet technology, specifically to a method, system, and storage medium for calculating the torque of a Bitter coil. Background Technology

[0002] Water-cooled magnets are fundamental devices for generating steady-state strong magnetic fields, typically consisting of several nested bit coils from the inside out. Assuming all coils are ideally positioned, the water-cooled magnet coils themselves exhibit a torque during operation. This torque is caused by the helical flow of current within the coils. During operation, this torque is symmetrical about the mid-plane of the magnet coils, with equal magnitudes but opposite directions. The macroscopic effect of this electromagnetic torque is a gradually increasing electromagnetic shear torque on the coil fixing rod, minimum at the ends of the coil, gradually increasing towards the mid-plane, reaching its maximum at the mid-plane. The greatest danger of this torque is that it can cause fatigue fracture of the coil fixing rod due to repeated shear torque, leading to magnet accidents. For example, patent application CN121583721A improves the water-cooled magnet's fixing structure's resistance to large electromagnetic torques by optimizing its structural strength.

[0003] In addition, in related technologies, patent application CN117332183A proposes a method for quickly and accurately calculating the magnetic field of a spiral coil magnet to solve the problem of calculating the spatial magnetic field of water-cooled magnets and superconducting magnets; patent application CN121212053A uses the calculation of the magnetic field of a magnet to achieve the design and assembly of a high-uniformity Bitter coil; and there are also related documents on the calculation of mutual inductance and interaction force between coils during the installation of magnet coils. For example, patent application CN120104918A describes a calculation scheme for the mutual inductance of two Bitter coils placed at arbitrary positions in space.

[0004] Therefore, existing research mostly focuses on improving the structural strength of water-cooled magnets or on the macroscopic assessment of the electromagnetic forces acting on the coils as a whole, but there is little research on methods for calculating the electromagnetic torque of the water-cooled magnet coils themselves. In the engineering design and application of water-cooled magnets, the mechanical stability of the coils in a strong magnetic field environment is one of the key factors determining the safe operation of the magnet. Therefore, it is necessary to explore a method for calculating the electromagnetic torque of the water-cooled magnet coils themselves, which can accurately calculate the electromagnetic torque of each coil when the water-cooled magnet is under stable operating conditions, serving as a theoretical reference for the design of the shear resistance of the water-cooled magnet coil fixing rod. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to accurately calculate the electromagnetic torque of the Bitter coil itself.

[0006] The present invention solves the above-mentioned technical problems through the following technical means:

[0007] A method for calculating the self-torque of a bitter coil is proposed, the method comprising: Obtain the basic parameters of each coil of the water-cooled magnet, and take the upper or lower half of the coil whose torque is to be calculated as the target coil; The conductor in the target coil is divided into several ring grids, and the coordinates of the center point of each ring grid are determined based on the basic parameters; Calculate the total radial magnetic field component of the center point of each annular grid in cylindrical coordinates; The current density distribution of each annular grid is used to solve for the current density distribution at each annular grid location within a single-turn conductor by integrating the cross-sectional area of ​​the single-turn torque coil to be calculated, which is equal to the target current flowing through the torque coil. Calculate the sine value of the helix angle of the current helix path within each annular grid based on the helix path plane of each annular grid. Based on the current density distribution and the corresponding helix angle sine value of each annular grid in a single-turn conductor, calculate the axial current density component of each annular grid in cylindrical coordinates. The electromagnetic torque of the coil to be calculated when the target current is applied is calculated based on the total radial magnetic field component and the axial current density component of each annular grid.

[0008] Furthermore, the basic parameters include the inner radius, outer radius, number of turns, bit thickness, insulation thickness, and current applied to the coil.

[0009] Furthermore, the step of dividing the conductor in the target coil into several annular grids and determining the coordinates of the center point of each annular grid based on the basic parameters includes: The target coil is divided into grids to form... A circular grid, The number of segments along the radial direction. The number of turns of the target coil; Based on the aforementioned fundamental parameters, determine the coordinates of the center point of each annular grid in cylindrical coordinates. , For the target coil The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

[0010] Furthermore, in the coordinates of the center point of each of the said annular grids:

[0011]

[0012]

[0013]

[0014] In the formula, Let the inner radius of the torque coil to be calculated be . Let be the outer radius of the torque coil to be calculated. The thickness of a single-turn conductor in the torque coil to be calculated is... For the thickness of the insulating sheet, Let be the axial distance of a spiral loop rising in a ring-shaped grid current. Indicates the first Turn conductor, Indicates the first A circular grid, The radial width of each ring grid.

[0015] Further, the calculation of the total radial magnetic field component of each annular grid center point in cylindrical coordinates includes: Calculate the radial magnetic field value of each coil of the water-cooled magnet at the center of the annular grid; The total radial magnetic field component of the annular grid is calculated based on the radial magnetic field value of each coil at the center of the grid, expressed by the following formula:

[0016]

[0017] In the formula, The first part representing the water-cooled magnet The coil is at the center point of the circular grid. The radial magnetic field value, The total number of coils, The permeability of free space, For the first coil and The relevant current density distribution, Let be the radial distance from the infinitesimal element of the integrator within the coil to the coil axis. For the first The inner radius of the coil, For the first outer radius of the coil, Let be the circumferential angle of the infinitesimal element within the coil. For the first The lower coordinate of the coil, For the first The upper coordinate of the coil, For the integrator element inside the coil to Distance between planes, From the infinitesimal element of the integrator inside the coil to the center point of the ring grid The distance, the integral volume infinitesimal element is ; For the target coil The first turn of the conductor The radial distance from the center point of each annular grid to the coil axis. For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

[0018] Furthermore, the integral result of the current density distribution of each annular grid on the single-turn cross-sectional area of ​​the torque coil to be calculated is equal to the target current flowing through the torque coil to be calculated, and the solution for the current density distribution at each annular grid within the single-turn conductor includes: The integral of the single-turn cross-sectional area of ​​the torque coil to be calculated, based on the current density distribution of each annular grid, equals the target current flowing through the torque coil. The current density value at the inner radius of the torque coil can then be calculated using the formula:

[0019] In the formula, The value of the current density at the inner radius of the torque coil to be calculated is... Let the inner radius of the torque coil to be calculated be . Let be the outer radius of the torque coil to be calculated. The thickness of a single-turn conductor in the torque coil to be calculated is... The target current flowing through the torque coil to be calculated is... Represents the natural logarithm; Based on the current density value at the inner diameter of the coil to be calculated and the inner radius of the coil to be calculated, the current density distribution at each annular grid location within a single turn of the coil to be calculated is calculated, expressed by the formula:

[0020] In the formula, For the first torque coil to be calculated The first turn on the conductor Current density distribution at each annular grid For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis.

[0021] Furthermore, based on the spiral path plane of each annular grid, the sine value of the spiral angle of the current spiral path within each annular grid is calculated, expressed by the formula:

[0022] In the formula, It is a sine function. For the first torque coil to be calculated The first turn on the conductor The helix angle of the current spiral path within a ring grid. For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. The axial distance of a spiral loop rising in a ring grid current.

[0023] Furthermore, based on the current density distribution and corresponding helix angle sine value at each annular grid location within a single-turn conductor, the axial current density component of each annular grid in cylindrical coordinates is calculated, as expressed by the formula:

[0024] In the formula, For the first torque coil to be calculated The first turn on the conductor Axial current density components of a ring grid in cylindrical coordinates For the first torque coil to be calculated The first turn on the conductor Current density distribution at each annular grid Helix angle The sine value, For the first torque coil to be calculated The first turn on the conductor The helix angle of the current spiral path within a ring grid. For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. The value of the current density at the inner radius of the torque coil to be calculated is... Let the inner radius of the torque coil to be calculated be . The axial distance of a spiral loop rising in a ring grid current.

[0025] Further, the step of calculating the electromagnetic torque of the torque coil under calculation when the target current is applied, based on the total radial magnetic field component and axial current density component of each annular grid, includes: Based on the total radial magnetic field component and axial current density component of each annular grid, calculate the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system by each annular grid. The electromagnetic torque when the target current is applied to the coil is obtained by summing the torques corresponding to all the annular grids on the target coil.

[0026] Further, the calculation of the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system of each annular grid based on the total radial magnetic field component and axial current density component of each annular grid includes: Based on the total radial magnetic field component and axial current density component of the annular grid on the target coil, the angle... Circular from 0 to 2 After integration, the torque generated by the electromagnetic force on the origin of each annular grid volume element is obtained, expressed by the formula:

[0027] In the formula, For the first torque coil to be calculated The first turn on the conductor The torque generated about the origin by the electromagnetic force on a small element of a ring-shaped grid volume. For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the first The first turn on the conductor The volume of the annular grid is affected by the axial current density component and the circumferential angle. Irrelevant For the coil number The first turn of the conductor The axial current density components of a ring-shaped grid, For the first torque coil to be calculated The first turn on the conductor The total radial magnetic field component of the annular grid.

[0028] Furthermore, the summation of the torques corresponding to all annular grids on the target coil yields the electromagnetic torque when the target current flows through the coil to be calculated, expressed by the following formula:

[0029] In the formula, Each ring grid represents all the ring grids obtained by dividing the target coil. The number of segments along the radial direction. The number of turns of the torque coil to be calculated. For the first torque coil to be calculated The first turn on the conductor The torque generated about the origin by the electromagnetic force on a small element of a ring-shaped grid volume. The electromagnetic torque is the torque when the target current is applied to the torque coil to be calculated.

[0030] Furthermore, this invention also proposes a system for calculating the self-torque of a Bitter coil, the system comprising: The parameter acquisition module is used to acquire the basic parameters of each coil of the water-cooled magnet and to take the upper or lower half coil of the coil whose torque is to be calculated as the target coil. The mesh generation module is used to divide the conductor in the target coil into several ring-shaped meshes and determine the coordinates of the center point of each ring-shaped mesh based on the basic parameters; The magnetic field component calculation module is used to calculate the total radial magnetic field component of each annular grid center point in cylindrical coordinates. The current density calculation module is used to solve for the current density distribution at each annular grid location within a single-turn conductor by using the integral result of the current density distribution of each annular grid within each annular grid to the current density distribution of the single-turn cross-sectional area of ​​the torque coil to be calculated, which is equal to the target current flowing through the torque coil to be calculated. The helix angle calculation module is used to calculate the sine value of the helix angle of the current helix path in each annular grid based on the helix path plane of each annular grid. The axial current density component calculation module is used to calculate the axial current density components of each annular grid in cylindrical coordinates based on the current density distribution and the corresponding helix angle sine value at each annular grid location within a single-turn conductor. The electromagnetic torque calculation module is used to calculate the electromagnetic torque of the coil to be calculated when a target current is applied, based on the total radial magnetic field component and axial current density component of each annular grid.

[0031] Furthermore, the present invention also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for calculating the self-torque of the Bitter coil as described above.

[0032] The advantages of this invention are: This invention, through specific theoretical analysis and derivation of a water-cooled magnet coil model, divides the conductors in the upper or lower half of the coil, where the torque needs to be calculated, into several annular grids. By solving for the current density distribution within a single turn of the annular grid and the helix angle of the current spiral path within the annular grid, the axial current density distribution of the annular grid is further calculated. Thus, based on the axial current density and the total radial magnetic field component of the annular grid, the torque generated by the electromagnetic force on the annular grid can be calculated. The sum of the torques generated by each annular grid is then used as the maximum electromagnetic torque of the coil when the target current is applied. This invention can accurately calculate the maximum electromagnetic torque of each coil when the water-cooled magnet is in a stable operating condition, providing magnet designers with a basis for designing the shear resistance of the coil fixing rod.

[0033] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0034] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0035] Figure 1 This is a schematic cross-sectional view of the spatial arrangement of the water-cooled magnet in cylindrical coordinates in one embodiment of the present invention; Figure 2 This is one embodiment of the present invention. Schematic diagram of coil current flow; Figure 3 This is a structural diagram of a water-cooled magnet in one embodiment of the present invention. A schematic diagram of the radial grid division of each turn of the conductor in the upper half of the coil; Figure 4 This is a point in one embodiment of the present invention. Current path unfolded diagram; Figure 5 In one embodiment of the present invention, from A schematic diagram of the electromagnetic force acting on the annulus when viewed from above the axis; Figure 6 This is a flowchart illustrating a method for calculating the self-torque of a Bitter coil according to an embodiment of the present invention. Figure 7 This is a schematic diagram of a Bitter coil self-torque calculation system proposed in an embodiment of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] In this embodiment, to explore a method for calculating the electromagnetic torque of the water-cooled magnet coil itself, a specific theoretical analysis and derivation are performed on the water-cooled magnet coil model. The analysis process is as follows: Figure 1 The water-cooled magnet shown is made of A , B , C These three coils are used to calculate the concentration of the water-cooled magnet. ATaking the coil's own electromagnetic torque as an example, the basic parameters of each coil in the water-cooled magnet are shown in Table 1.

[0038] Table 1. Parameters of each coil in the water-cooled magnet

[0039] Because the electromagnetic torque of the water-cooled magnet coil increases from the top and bottom ends towards the mid-plane, with the maximum torque accumulated at the mid-plane, and the torque values ​​at both ends of the mid-plane being equal but opposite, resembling a twisted rope. Therefore, in order to calculate the working torque of the magnet... A The maximum torque of the coil on the mid-plane can be taken as A The torque is accumulated and calculated for either the upper or lower half of the coil.

[0040] assumed A The current flow in the coil follows the right-hand screw method, as shown below. Figure 2 As shown, for A The axial pitch of the coil current is numerically the sum of the thickness of one turn of conductor and the thickness of one turn of insulation (see...). Figure 3 ), pitch and A single-turn conductor thickness of the coil Insulating sheet thickness The relationship is shown in formula (1).

[0041] exist Figure 2 In the cylindrical coordinate system shown, the spiral flow of current causes the corresponding current density to be decomposed into two directions, one being the circumferential direction. direction One is Axial direction Current density per turn of the coil The distribution can be represented by formula (2). The magnetic field of the water-cooled magnet is axially symmetric, and the magnetic field distribution can be decomposed into radial components in cylindrical coordinates. magnetic field components and axial Magnetic field components in direction The magnetic field distribution can be represented by formula (3).

[0042] (1) (2) (3) In the formula, Indicates current density, Indicates the distribution of the magnetic field. coordinates of points in cylindrical coordinate system The circumferential current density at that location, coordinate point The axial current density at that location, coordinate point The circumferential unit vector at that location, coordinate point The axial unit vector at that location, coordinate point The radial magnetic field value at that location, coordinate point The axial magnetic field value at that location.

[0043] Assuming A The upper half of the coil is used as the target coil for calculation. A The sum of the torques in the upper half of the coil, A The upper half of the coil has a total of Turn conductor, for A The number of conductor turns in the coil; A Each turn of the conductor in the upper half of the coil is divided into equal parts along the radial direction. Parts, forming A circular grid, such as Figure 3 As shown. Assume point For the first The first turn on the conductor The center point of a ring grid, from point Starting grid current After passing through a spiral loop, it ascends by an axial distance. , reached the +1 turn of conductor The center points of the ring-shaped grid, when connected sequentially, form a spiral loop for current flow, as shown in the image. Figure 2 As shown.

[0044] In cylindrical coordinates, the ring-shaped mesh The corresponding magnetic field distribution is decomposed into radial magnetic field components. and axial magnetic field components Water-cooled magnet coil in grid radial magnetic field value at the center The following formula can be used to calculate: (4) (5) In the formula, The permeability of free space, For the first coil and The relevant current density distribution, Let be the radial distance from the infinitesimal element of the integrator within the coil to the coil axis. For the first The inner radius of each coil, For the first The outer radius of each coil, Let be the circumferential angle of the infinitesimal element within the coil. For the first The lower coordinate of the magnet coil, For the first The upper coordinate of the magnet coil, For the infinitesimal element of the integrator inside the coil to Distance between planes, The coordinates of the infinitesimal element within the coil to the center point of the grid. The distance, the integral volume infinitesimal element is .

[0045] Assuming the water-cooled magnet has Composed of coils, a circular grid is formed. Total radial magnetic field Total transverse magnetic field It can be expressed by the following equations (6) and (7): (6) (7) In the formula, For the first The coil of the first The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the first The coil of the first The axial distance from the turn conductor to the origin, in hour, for A On the coil and The relevant current density distribution, for A The radial distance from any point inside the coil to the coil axis. for A inner radius of the coil , The outer radius of the coil .

[0046] exist Figure 3 In the middle, set up points The coordinates on the cross-section are Then we have formulas (8) to (10): (8) (9) (10) In the formula, since it is based on A If the coil is analyzed as the coil with the torque to be calculated, then... For the calculated self-torque coil A inner radius , For the calculated self-torque coil A outer radius , for A The thickness of a single-turn conductor in the coil, For the thickness of the insulating sheet, Let be the axial distance of a spiral loop rising in a ring-shaped grid current. The radial width of each annular grid, Indicates the first Turn conductor, Indicates the first A circular grid.

[0047] Due to the current density in a single turn of the bit coil Present distributed( (Radial distance from any point inside the coil to the coil axis) Current density distribution inside the coil This can be expressed by formula (11): (11) In the formula, The inner diameter of the torque coil to be calculated The current density value at that location, Let the inner diameter of the torque coil to be calculated be... The radial distance from any point inside the torque coil to be calculated to the coil axis is denoted as .

[0048] The target current can be obtained by integrating the cross-sectional area of ​​a single turn using the current density distribution formula (11). For example, in formula (12): (12) From formula (12), we can obtain The expression is as shown in formula (13): (13) Then point Current in the ring grid This can be expressed by formula (14): (14) Assumption A The target current flowing through the coil is Solve A Coil inner radius Current density at With single-turn conductor Current density at The distribution formulas are expressed as follows: (15) (16) In the formula, for A The current density at the inner radius of the coil, for A The thickness of a single-turn conductor in the coil, for A The target current flowing through the coil.

[0049] Let's calculate the points. Current in the ring grid The helix angle of the spiral path .point The spiral path plane of the ring-shaped grid unfolds as follows Figure 4 As shown, the helix angle can be obtained. The formula for calculating the sine value is (17): (17) In the formula, It is a sine function. For the coil number The first turn of the conductor The helix angle of the current spiral path within a ring grid. For the coil number The first turn of the conductor The radial distance from the center point of each annular grid to the coil axis. The axial distance of a spiral loop rising in a ring grid current.

[0050] From formula (17), it can be seen that the current in the grid cell of the water-cooled magnet coil is... helix angle and related, The larger the helix angle The smaller, Smaller helix angle The larger. Point Current in the ring grid Axial current density component This can be expressed by formula (18): (18) In the formula, For the first torque coil to be calculated The first turn of the conductor Current density distribution at each annular grid

[0051] Next, place the point P The ring-shaped grid is surrounded by The axial current density within the volume of the annulus through which the shaft rotates one revolution. It exhibits an axisymmetric distribution, and the axial current density distribution is similar to... It is unrelated; the magnetic field is also axially symmetric and related to... Irrelevant.

[0052] point P The volume element of the ring The electromagnetic force experienced can be expressed by formula (19). Figure 5 From The formula for the top view angle of the axis (19) represents the quantities of each quantity, where The axis is perpendicular to the paper and faces upwards.

[0053] (19) In the formula, A ring-shaped grid of electrically conductive volume elements The electromagnetic force it experiences A ring-shaped grid of electrically conductive micro-elements The current density vector in For electrically conductive infinitesimal volume elements Medium magnetic field vector, It is a volume infinitesimal element. The current density vector at the circumferential angle The amount on, The current density vector at the circumferential angle The amount on, The magnetic field vector in the radial direction The amount on, For the magnetic field vector in Components on the axis.

[0054] Volumetric micro-element The electromagnetic force acting on the origin The lever arm vector of the generated torque This can be expressed by formula (20): (20) Volumetric micro-element The electromagnetic force acting on the origin The generated torque This can be expressed by formula (21): (twenty one) In the formula, A ring-shaped grid of electrically conductive volume elements dV The electromagnetic force experienced.

[0055] Formula (21) can be decomposed into three component expressions, as shown in formulas (22)-(24): (twenty two) (twenty three) (twenty four) In the formula, Torque radial component, Torque Circular component, Torque The axial component.

[0056] By analyzing formulas (22), (23) and (24), the torque can be determined. of and Components with angle Changes in direction and volume of infinitesimal elements The magnitude of the torque remains constant, therefore the angle... The result after circumferential integration is 0; torque axial Quantity The direction remains unchanged, but the angle remains the same. Circular from 0 to After integration, we get formula (25): (25) In the formula, For the coil number The first turn of the conductor The electromagnetic force on the origin of each ring grid The generated torque For the first The first turn of the conductor The volume of the annular grid is affected by the axial current density component. With radial magnetic field component It is axially symmetric, that is, along the circumferential angle. Numerical magnitude and circumferential angle Irrelevant, therefore , .

[0057] Using formula (26) A All of the upper half coil Summing will give us the result. A Current is passed through the coil in the water-cooled magnet electromagnetic torque at time : (26) Based on the above analysis, as Figure 6 As shown, the first embodiment of the present invention proposes a method for calculating the torque of a Bitter coil, the method comprising the following steps: S10. Obtain the basic parameters of each coil of the water-cooled magnet, and take the upper or lower half of the coil of the torque to be calculated as the target coil. It should be noted that in this embodiment, the basic parameters of the water-cooled magnet coil and the coil current rise pitch in Table 1 are entered by opening the input file database.inp of the water-cooled magnet magnetic field calculation program.

[0058] S20. Divide the conductor in the target coil into several ring grids, and determine the coordinates of the center point of each ring grid based on the basic parameters; Specifically, the bit coil for which the electromagnetic torque is to be calculated is identified as the torque coil to be calculated, and the number of turns of the upper part of the coil is determined. Number of radial segments The settings are used to perform mesh generation, obtaining unique coordinate points representing each ring mesh. Save the settings and close database.inp.

[0059] S30. Calculate the total radial magnetic field component of the center point of each annular grid in cylindrical coordinates; It should be noted that the calculation process of the radial magnetic field component of the center point of the annular grid in cylindrical coordinates in this embodiment is similar to the content described in the patent application document with publication number CN117332183A.

[0060] S40. Using the current density distribution of each annular grid, the integral result of the single-turn cross-sectional area of ​​the torque coil to be calculated is equal to the target current flowing through the torque coil to be calculated, and the current density distribution at each annular grid in the single-turn conductor is solved. S50. Based on the spiral path of each annular grid, calculate the sine value of the spiral angle of the current spiral path in each annular grid.

[0061] Specifically, the formula for calculating the sine value of the helix angle of the current helix path in each annular grid is shown in formula (17).

[0062] S60. Based on the current density distribution within a single turn of each annular grid and the corresponding helix angle sine value, calculate the axial current density components of each annular grid in cylindrical coordinates. Specifically, the axial current density component of the ring grid in cylindrical coordinates is calculated using formula (18).

[0063] S70. Calculate the electromagnetic torque of the torque coil to be calculated when the target current is applied, based on the total radial magnetic field component and axial current density component of each annular grid.

[0064] As a further preferred technical solution, step S20: dividing the conductor in the target coil into several annular grids, and determining the coordinates of the center point of each annular grid based on the basic parameters, specifically includes the following steps: S21. Divide the target coil into a grid, forming... A circular grid, The number of segments along the radial direction. The number of turns of the target coil; S22. Determine the coordinates of the center point of each annular grid in cylindrical coordinates based on the aforementioned basic parameters. , For the target coil The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

[0065] Specifically, the coordinates of the center point of each annular grid in cylindrical coordinates are determined based on the aforementioned basic parameters. See formula (1) and formula (8)-(10) above.

[0066] As a further preferred technical solution, step S30: calculating the total radial magnetic field component of each annular grid center point in cylindrical coordinates, specifically: Calculate the radial magnetic field value of each coil of the water-cooled magnet at the center of the annular grid; The total radial magnetic field component of the annular grid is calculated based on the radial magnetic field value of each coil at the center of the annular grid.

[0067] Specifically, the calculation process of the radial magnetic field component and axial magnetic field component of the center point of the ring grid in cylindrical coordinate system is shown in formulas (6)-(7).

[0068] As a further preferred technical solution, step S40: using the current density distribution of each annular grid and the integral result of the single-turn cross-sectional area of ​​the torque coil to be calculated equal to the target current flowing through the torque coil to be calculated, the current density distribution at each annular grid location within the single-turn conductor is solved, specifically including the following steps: S41. Using the current density distribution of each annular grid, the integral result of the single-turn cross-sectional area of ​​the torque coil to be calculated is equal to the target current flowing through the torque coil to be calculated. Solve for the current density value at the inner radius of the torque coil to be calculated, as shown in formula (13).

[0069] S42. Based on the current density value at the inner diameter of the torque coil to be calculated and the inner radius of the torque coil to be calculated, calculate the current density distribution at each annular grid in the single-turn conductor of the torque coil to be calculated, as shown in formula (11).

[0070] Specifically, assuming the calculation of the water-cooled magnet's first... The electromagnetic torque of the upper half coil of each coil is given by the following formula:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] It can be understood as the first Current density at the inner radius of each coil With the body Current density at The distribution formulas are expressed as follows:

[0079]

[0080] In the formula, For the first Current density values ​​at the inner radius of each coil For the first The thickness of a single-turn conductor in a coil For the first The target current passed through each coil For the first The number of conductors in a coil.

[0081] As a further preferred technical solution, step S70: calculating the electromagnetic torque of the torque coil to be calculated when the target current is applied based on the total radial magnetic field component and axial current density component of each annular grid, specifically including the following steps: S71. Based on the total radial magnetic field component and axial current density component of each annular grid, calculate the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system by each annular grid. Specifically, the formula for calculating the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system by the ring grid is shown in equation (25).

[0082] S72. Sum the torques corresponding to all annular grids on the target coil to obtain the electromagnetic torque when the target current is applied to the coil to be calculated.

[0083] Specifically, the maximum electromagnetic torque when the target current is applied to each coil is calculated using the formula shown in equation (26).

[0084] Furthermore, to illustrate the specific calculation process of the program, this embodiment sets... and The program's calculation results were pasted into an Excel spreadsheet, and formula (26) was used to... A Electromagnetic torque of each ring in the upper half of the coil (all turns) A summation calculation was performed.

[0085] get A The total electromagnetic torque of the upper half of the coil (A total of 1050 lines of electromagnetic torque) The summation result is 1.2761095E+02. Table 2 only shows the first 22 rows of data.

[0086] Table 2 Calculation results of electromagnetic torque in the upper half of the coil

[0087] In addition, such as Figure 7 As shown, the second embodiment of the present invention also proposes a system for calculating the self-torque of a Bitter coil, the system comprising: The parameter acquisition module 10 is used to acquire the basic parameters of each coil of the water-cooled magnet and to take the upper or lower half coil of the coil whose torque is to be calculated as the target coil. The meshing module 20 is used to divide the conductor in the target coil into several ring-shaped meshes and determine the coordinates of the center point of each ring-shaped mesh based on the basic parameters; The magnetic field component calculation module 30 is used to calculate the total radial magnetic field component of each annular grid center point in cylindrical coordinates. The current density calculation module 40 is used to solve the current density distribution at each annular grid location within a single-turn conductor by using the integral result of the current density distribution of each annular grid to the cross-sectional area of ​​the torque coil to be calculated, which is equal to the target current flowing through the torque coil to be calculated. The helix angle calculation module 50 is used to calculate the sine value of the helix angle of the current helix path in each annular grid based on the helix path plane of each annular grid. The axial current density component calculation module 60 is used to calculate the axial current density component of each annular grid in cylindrical coordinates based on the current density distribution at each annular grid location in a single-turn conductor and the corresponding helix angle sine value. The electromagnetic torque calculation module 70 is used to calculate the electromagnetic torque of the coil to be calculated when the target current is applied, based on the total radial magnetic field component and axial current density component of each annular grid.

[0088] As a further preferred technical solution, the mesh division module 20 specifically includes: Mesh generation cells are used to divide the target coil into meshes, forming... A circular grid, The number of segments along the radial direction. The number of turns of the target coil; The center point determination unit is used to determine the coordinates of the center point of each annular grid in cylindrical coordinates based on the aforementioned basic parameters. , For the target coil The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

[0089] As a further preferred technical solution, the current density calculation module 40 specifically includes: The current density calculation unit is used to calculate the current density value at the inner radius of the torque coil to be calculated by using the integral result of the single-turn cross-sectional area of ​​the torque coil to be calculated, which is equal to the target current flowing through the torque coil to be calculated. The current density distribution calculation unit is used to calculate the current density distribution at each annular grid location within a single turn of the torque coil to be calculated, based on the current density value at the inner diameter of the torque coil to be calculated and the inner radius of the torque coil to be calculated.

[0090] As a further preferred technical solution, the electromagnetic torque calculation module 70 specifically includes: The torque calculation unit is used to calculate the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system based on the total radial magnetic field component and axial current density component of each annular grid. The torque summation unit is used to sum the torques corresponding to all annular grids on the target coil to obtain the electromagnetic torque when the target current is applied to the coil to be calculated.

[0091] Furthermore, the third embodiment of the present invention also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the Bitter coil self-torque calculation method as described in the first embodiment above.

[0092] It should be noted that other embodiments or specific implementation methods of the Bitter coil self-torque calculation system and storage medium described in this invention can be referred to the above-mentioned method embodiments, and will not be repeated here.

[0093] It should be noted that the computer-readable medium disclosed in this embodiment may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, and portable compact disk read-only memory (CD-ROM). ROM, optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this disclosure, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0094] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device. The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the Bitter coil self-torque calculation method described in the above embodiments.

[0095] Computer program code for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server.

[0096] In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0097] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0098] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0099] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" or "several" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0100] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the self-torque of a bitter coil, characterized in that, include: Obtain the basic parameters of each coil of the water-cooled magnet, and take the upper or lower half of the coil whose torque is to be calculated as the target coil; The conductor in the target coil is divided into several ring grids, and the coordinates of the center point of each ring grid are determined based on the basic parameters; Calculate the total radial magnetic field component of the center point of each annular grid in cylindrical coordinates; The result of integrating the current density distribution of each annular grid onto the single-turn cross-sectional area of ​​the torque coil to be calculated is equal to the target current flowing through the torque coil. Solving for the current density distribution at each annular grid within a single-turn conductor involves: integrating the current density distribution of each annular grid onto the single-turn cross-sectional area of ​​the torque coil to be calculated, which equals the target current flowing through the torque coil, and then solving for the current density value at the inner radius of the torque coil. The formula is expressed as: In the formula, The value of the current density at the inner radius of the torque coil to be calculated is... Let the inner radius of the torque coil to be calculated be . Let be the outer radius of the torque coil to be calculated. The thickness of a single-turn conductor in the torque coil to be calculated is... The target current flowing through the torque coil to be calculated is... Represents the natural logarithm; Based on the current density value at the inner diameter of the coil to be calculated and the inner radius of the coil to be calculated, the current density distribution at each annular grid location within a single turn of the coil to be calculated is calculated, expressed by the formula: In the formula, For the first torque coil to be calculated The first turn on the conductor Current density distribution at each annular grid For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis; Calculate the sine value of the helix angle of the current helix path within each annular grid based on the helix path plane of each annular grid. Based on the current density distribution and the corresponding helix angle sine value of each annular grid in a single-turn conductor, calculate the axial current density component of each annular grid in cylindrical coordinates. The electromagnetic torque of the coil to be calculated when the target current is applied is calculated based on the total radial magnetic field component and the axial current density component of each annular grid.

2. The method for calculating the self-torque of the Bitter coil as described in claim 1, characterized in that, The basic parameters include the inner radius, outer radius, number of turns, bit thickness, insulation thickness, and current applied to the coil.

3. The method for calculating the self-torque of the Bitter coil as described in claim 1, characterized in that, The step of dividing the conductor in the target coil into several annular grids and determining the coordinates of the center point of each annular grid based on basic parameters includes: The target coil is divided into grids to form... A circular grid, The number of segments along the radial direction. The number of turns of the target coil; Based on the aforementioned fundamental parameters, determine the coordinates of the center point of each annular grid in cylindrical coordinates. , For the target coil The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

4. The method for calculating the self-torque of the Bitter coil as described in claim 2, characterized in that, In the coordinates of the center point of each of the aforementioned annular grids: In the formula, Let the inner radius of the torque coil to be calculated be . Let be the outer radius of the torque coil to be calculated. The thickness of a single-turn conductor in the torque coil to be calculated is... For the thickness of the insulating sheet, Let be the axial distance of a spiral loop rising in a ring-shaped grid current. Indicates the first Turn conductor, Indicates the first A circular grid, The radial width of each annular grid, This refers to the number of segments into which each turn of the target coil is divided radially.

5. The method for calculating the self-torque of the Bitter coil as described in claim 1, characterized in that, The calculation of the total radial magnetic field component of the center point of each annular grid in cylindrical coordinates includes: Calculate the radial magnetic field value of each coil of the water-cooled magnet at the center of the annular grid; The total radial magnetic field component of the annular grid is calculated based on the radial magnetic field value of each coil at the center of the grid, expressed by the following formula: In the formula, The first one represents the water-cooled magnet. The coil is at the center point of the circular grid. The radial magnetic field value, The total number of coils, The permeability of free space, For the first coil and The relevant current density distribution, Let be the radial distance from the infinitesimal element of the integrator within the coil to the coil axis. For the first The inner radius of the coil, For the first outer radius of the coil, Let be the circumferential angle of the infinitesimal element within the coil. For the first The lower coordinate of the coil, For the first The upper coordinate of the coil, For the integrator element inside the coil to Distance between planes, From the infinitesimal element of the integrator inside the coil to the center point of the ring grid The distance, the integral volume infinitesimal element is ; For the target coil The first turn of the conductor The radial distance from the center point of each annular grid to the coil axis. For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

6. The method for calculating the self-torque of the Bitter coil as described in claim 1, characterized in that, The helix angle sine of the current helix path within each annular grid is calculated based on the helix path plane of each annular grid, expressed by the formula: In the formula, It is a sine function. For the first torque coil to be calculated The first turn on the conductor The helix angle of the current spiral path within a ring grid. For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. The axial distance of a spiral loop rising in a ring grid current.

7. The method for calculating the self-torque of the Bitter coil as described in claim 1, characterized in that, The axial current density components of each annular grid in cylindrical coordinates are calculated based on the current density distribution and corresponding helix angle sine value at each location within a single-turn conductor. The formula is as follows: In the formula, For the first torque coil to be calculated The first turn on the conductor Axial current density components of a ring grid in cylindrical coordinates For the first torque coil to be calculated The first turn on the conductor Current density distribution at each annular grid Helix angle The sine value, For the first torque coil to be calculated The first turn on the conductor The helix angle of the current spiral path within a ring grid. For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. The value of the current density at the inner radius of the torque coil to be calculated is... Let the inner radius of the torque coil to be calculated be . The axial distance of a spiral loop rising in a ring grid current.

8. The method for calculating the self-torque of the Bitter coil as described in claim 1, characterized in that, The calculation of the electromagnetic torque of the torque coil under test when a target current is applied, based on the total radial magnetic field component and axial current density component of each annular grid, includes: Based on the total radial magnetic field component and axial current density component of each annular grid, calculate the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system by each annular grid. The electromagnetic torque when the target current is applied to the coil is obtained by summing the torques corresponding to all the annular grids on the target coil.

9. The method for calculating the self-torque of the Bitter coil as described in claim 8, characterized in that, The calculation of the torque generated by the electromagnetic force on the origin of the cylindrical coordinate system about each annular grid based on the total radial magnetic field component and axial current density component of each annular grid includes: Based on the total radial magnetic field component and axial current density component of the annular grid on the target coil, the angle... Circular from 0 to 2 After integration, the torque generated by the electromagnetic force on the origin of each annular grid volume element is obtained, expressed by the formula: In the formula, For the first torque coil to be calculated The first turn on the conductor The torque generated about the origin by the electromagnetic force on a small element of a ring-shaped grid volume. For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis. For the first The first turn on the conductor The volume of a ring-shaped grid; due to the axial current density component and the circumferential angle Irrelevant For the first torque coil to be calculated The first turn of the conductor The axial current density components of a ring-shaped grid, For the first torque coil to be calculated The first turn on the conductor The total radial magnetic field component of the annular grid For the target coil The center point of all the ring grids of the turn conductor to Distance between planes.

10. The method for calculating the self-torque of a Bitter coil as described in claim 8, characterized in that, The summation of the torques corresponding to all annular grids on the target coil yields the electromagnetic torque when the target current is applied to the coil to be calculated. The formula is as follows: In the formula, The number of segments along the radial direction. The number of turns of the target coil. For the target coil The first turn on the conductor The torque generated about the origin by the electromagnetic force on a small element of a ring-shaped grid volume. The electromagnetic torque is the torque when the target current is applied to the torque coil to be calculated.

11. A system for calculating the self-torque of a bitter coil, characterized in that, include: The parameter acquisition module is used to acquire the basic parameters of each coil of the water-cooled magnet and to take the upper or lower half of the coil of the torque to be calculated as the target coil. The mesh generation module is used to divide the conductor in the target coil into several ring-shaped meshes and determine the coordinates of the center point of each ring-shaped mesh based on the basic parameters; The magnetic field component calculation module is used to calculate the total radial magnetic field component of each annular grid center point in cylindrical coordinates. The current density calculation module is used to calculate the current density distribution at each annular grid location within a single-turn conductor by integrating the current density distribution of each annular grid with the cross-sectional area of ​​the single-turn conductor. This integration equals the target current flowing through the conductor. Specifically, it calculates the current density at the inner radius of the annular grid by integrating the current density distribution of each annular grid with the cross-sectional area of ​​the single-turn conductor. The formula is as follows: In the formula, The value of the current density at the inner radius of the torque coil to be calculated is... Let the inner radius of the torque coil to be calculated be . Let be the outer radius of the torque coil to be calculated. The thickness of a single-turn conductor in the torque coil to be calculated is... The target current flowing through the torque coil to be calculated is... Represents the natural logarithm; Based on the current density value at the inner diameter of the coil to be calculated and the inner radius of the coil to be calculated, the current density distribution at each annular grid location within a single turn of the coil to be calculated is calculated, expressed by the formula: In the formula, For the first torque coil to be calculated The first turn on the conductor Current density distribution at each annular grid For the first torque coil to be calculated The first turn on the conductor The radial distance from the center point of each annular grid to the coil axis; The helix angle calculation module is used to calculate the sine value of the helix angle of the current helix path in each annular grid based on the helix path plane of each annular grid. The axial current density component calculation module is used to calculate the axial current density components of each annular grid in cylindrical coordinates based on the current density distribution and the corresponding helix angle sine value at each annular grid location within a single-turn conductor. The electromagnetic torque calculation module is used to calculate the electromagnetic torque of the coil to be calculated when a target current is applied, based on the total radial magnetic field component and axial current density component of each annular grid.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating the self-torque of the Bitter coil as described in any one of claims 1-10.

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