Method and system for calculating inductance value of excitation coil of electromagnetic repulsion mechanism
By employing the asymptotic expansion of the complete elliptic integral and the Landen transform, the problem of calculating the mutual inductance of circular toroidal conductors with unequal radii is solved, providing an accurate calculation method and supporting the rapid design of excitation coils.
Patent Information
- Application Number
- CN202511646859.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-11
- Publication Date
- 2026-01-13
AI Technical Summary
Existing technologies struggle to quickly and accurately calculate the mutual inductance between circular conductors with unequal radii, especially in the engineering calculation of the self-inductance of circular conductors with rectangular cross-sections, where a simple and easy-to-implement method is lacking.
By employing the asymptotic expansion of the complete elliptic integral combined with the Landen transform, the mutual inductance equation is derived to calculate the mutual inductance between concentric conducting rings with rectangular cross sections. The Landen transform is used to accelerate series convergence and simplify the calculation process.
It achieves high-precision and high-efficiency calculation of mutual inductance and self-inductance between concentric circular conductors with rectangular cross sections, and supports rapid parametric design of excitation coils for repulsion mechanisms.
Smart Images
Figure CN121328148A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of inductance calculation, in particular to a method and system for calculating inductance of a magnetic repulsion mechanism excitation coil. BACKGROUND
[0002] The DC power grid has higher requirements for the ultra-fast breaking capacity of fault current. Due to low conduction loss and high efficiency, mechanical circuit breakers and combined circuit breakers are widely used in engineering, and the core executive components thereof rely on the dynamic performance of ultra-fast mechanical switches. The power response speed, accuracy and consistency of the switch directly determine the arc in the breaking process, the timing of establishing a safe opening distance and the success rate of breaking. The electromagnetic repulsion mechanism is the most widely used driving scheme for ultra-fast mechanical switches. The mechanism is composed of an excitation coil and a conductive repulsion disc. The coil releases a large current in a very short time by a pre-charging capacitor, excites eddy current in the disc and generates strong Lorentz repulsive force, so as to drive the contacts to establish a safe opening distance within a few milliseconds. As a magnetic field generating element, the turns, cross-sectional size and magnetic circuit of the excitation coil jointly affect the output curve and equivalent time constant; at the same time, the resistance change caused by temperature rise will affect the consistency of the action of the repulsion mechanism. Therefore, quickly and accurately determining the inductance parameters of the coil is the basis for meeting the timing control and reliability requirements.
[0003] The primary difficulty faced by the fine design of the coil turns, cross-sectional area and the like is the lack of a simple and easy-to-implement inductance calculation method. Although there are many approximate formulas for calculating the mutual inductance between rectangular cross-section circular ring conductors, most of the formulas are only applicable to circular rings with equal radii. For circular ring conductors with unequal radii, the existing formulas are mainly based on the equivalent filament method, and directly use the Maxwell formula for calculation, which involves special functions such as complete elliptic integral, and it is difficult to directly use for engineering calculation of the self-inductance of rectangular cross-section circular ring conductors. SUMMARY
[0004] The purpose of the embodiments of the present application is to provide a method and system for calculating the inductance of the excitation coil of the electromagnetic repulsion mechanism, which solves the problem of quickly and accurately calculating the mutual inductance between circular rings with unequal radii.
[0005] In order to achieve the above-mentioned purpose, one aspect of the embodiments of the present application provides a method for calculating the inductance of the excitation coil of the electromagnetic repulsion mechanism, which comprises: constructing a single-layer filament model of the conductor circular ring; establishing a mutual inductance equation between the conductor circular rings according to the single-layer filament model of the conductor circular ring; performing Landen transformation on the mutual inductance equation; calculating the mutual inductance value of the mutual inductance equation according to the asymptotic series of complete elliptic integral.
[0006] Optionally, constructing a single-layer filament model of the conductor torus comprises: constructing a pair of concentric tori of the equal cross-section conductor, the tori comprising a first torus and a second torus; the first torus and the second torus are both composed of a plurality of filaments, the filaments of the first torus and the filaments of the second torus are arranged in a single layer along a cross-section height of the torus at an average radius, and the plurality of filaments are coaxial; a differential current is passed through each of the filaments.
[0007] Optionally, establishing a mutual inductance equation between the conductor tori according to the single-layer filament model of the conductor torus comprises: determining a complete elliptic integral modulus corresponding to a pair of filaments in the first torus and the second torus according to formula (1), , (1) integrating and summing mutual inductances between all pairs of filaments to obtain the mutual inductance equation between the first torus and the second torus according to formula (2), , (2) wherein, is a first modulus, is the mutual inductance between the first torus and the second torus, is a vacuum permeability, is a radius of the first torus, is a radius of the second torus, is a first complete elliptic integral function, is a second complete elliptic integral function, is an axial coordinate of a filament in the first torus, is an axial coordinate of a filament in the second torus, is a torus height.
[0008] Optionally, performing Landen transformation on the mutual inductance equation comprises: performing Landen transformation on the mutual inductance equation according to formula (3) to (4), , (3) , (4) wherein, is a second modulus.
[0009] Optionally, calculating a mutual inductance value of the mutual inductance equation according to an asymptotic series of the complete elliptic integral comprises: approximating the complete elliptic integral by an asymptotic series according to formula (5) to (6), , (5) , (6) The mutual inductance value is calculated according to formulas (7) to (15). (7) (8) (9) (10) (11) (12) (13) (14) (15) in, It is the sum of the radii of the first and second rings. For the module corresponding to the concentric conducting rings, As the first intermediate parameter, As the second intermediate parameter, As the third intermediate parameter, The fourth intermediate parameter, The fifth intermediate parameter, The sixth intermediate parameter, The seventh intermediate parameter, .
[0010] Optionally, the calculation method further includes: Construct a magnetic coupling circuit model for the repulsion mechanism; Construct an equivalent inductor circuit model based on the magnetic coupling circuit model of the repulsion mechanism; The target self-inductance of the excitation coil is determined based on the equivalent inductance circuit model and the expected action time of the repulsion mechanism. The number of coil turns is determined based on the mutual inductance value and the target self-inductance of the excitation coil.
[0011] Optionally, determining the target self-inductance of the excitation coil based on the equivalent inductance circuit model and the expected operating time of the repulsion mechanism includes: The equivalent inductance of the circuit model is calculated according to formula (16). (16) The target self-inductance of the excitation coil is calculated from the equivalent inductance of the circuit according to formula (17). (17) in, For equivalent inductance, The capacitor that powers the excitation coil. The discharge time of the capacitor that powers the excitation coil. The target self-inductance of the excitation coil, This represents the coupling coefficient of the magnetically coupled circuit.
[0012] Optionally, determining the coil turns based on the mutual inductance and the target self-inductance includes: The number of coil turns for a given wire diameter is obtained using formula (18). (18) in, For the first turn and the first Mutual inductance between the rings Total number of turns The inner diameter of the coil. The width of the circular line.
[0013] On the other hand, the present invention also provides a system for calculating the inductance value of the excitation coil of an electromagnetic repulsion mechanism, the system including a processor for executing the calculation method as described above.
[0014] In another aspect, the present invention also provides a computer-readable storage medium storing instructions for being read by a computer to cause the computer to perform any of the calculation methods described above.
[0015] Through the above technical solution, this invention provides a method and system for calculating the inductance value of the excitation coil of an electromagnetic repulsion mechanism. Starting with the asymptotic expansion of a complete elliptic integral and combining it with the Landen transform to accelerate series convergence, a mutual inductance equation is derived. This equation can be used to calculate the mutual inductance between concentric conducting rings with rectangular cross-sections, and also to determine the self-inductance of the conducting rings. Based on this equation, the self-inductance of a multi-turn coil wound from a rectangular cross-section conductor can be further calculated, thus providing an accurate and feasible method for designing repulsion mechanism coils. The calculation method of this invention has high accuracy, fast calculation efficiency, and is easy to implement, supporting the rapid parametric design of excitation coils for repulsion mechanisms.
[0016] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description
[0017] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of a calculation method according to one embodiment of the present invention; Figure 2This is a flowchart illustrating the construction of a mutual inductance model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a single-layer filament model according to an embodiment of the present invention; Figure 4 This is a flowchart of constructing mutual inductance equations according to one embodiment of the present invention; Figure 5 This is a flowchart of the Landen transformation according to one embodiment of the present invention; Figure 6 This is a flowchart for calculating mutual inductance values according to one embodiment of the present invention; Figure 7 This is a schematic diagram of the excitation coil of a repulsive mechanism according to an embodiment of the present invention; Figure 8 This is a circuit diagram of a magnetic coupling circuit model and an equivalent inductor circuit model of a repulsion mechanism according to an embodiment of the present invention. Figure 9 This is a flowchart illustrating the determination of the target self-inductance of an excitation coil according to an embodiment of the present invention; Figure 10 This is a typical parameter configuration diagram according to an embodiment of the present invention; Figure 11 This is a graph showing the self-inductance-turns relationship according to one embodiment of the present invention.
[0018] Explanation of reference numerals in the attached figures Detailed Implementation
[0019] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.
[0020] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with relevant laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.
[0021] Figure 1 This is a flowchart of a calculation method according to an embodiment of the present invention, in which the calculation method includes: In step S1, a single-layer filament model of a conductor ring is constructed.
[0022] In step S2, the mutual inductance equation between the conductor rings is established based on the single-layer filament model of the conductor rings.
[0023] In step S3, the Landen transformation is performed on the mutual inductance equation.
[0024] In step S4, the mutual inductance value of the mutual inductance equation is calculated based on the asymptotic series of the complete elliptic integral.
[0025] In steps S1 to S4, by simplifying the conducting rings into a single-layer filament model, the geometry of the conductor is simplified, transforming the complex electromagnetic calculation problem into a manageable mathematical model. Based on the electromagnetic properties of the conducting rings, equations describing the mutual inductance between them are established. By processing the mutual inductance equations using the Langdon transform, the asymptotic series of the elliptic integral under the new modulus achieves faster convergence, thereby improving computational accuracy. Using the asymptotic series of the complete elliptic integral, the mutual inductance between the conducting rings is accurately calculated.
[0026] In existing technologies, the calculation of mutual inductance between circular conductors of unequal radii is mostly based on equivalent filaments and Maxwell's formulas. However, the special functions involved, such as the complete elliptic integral, are difficult to directly apply to the engineering calculation of the self-inductance of a circular conductor with a rectangular cross-section. This invention starts from the asymptotic expansion of the complete elliptic integral, introduces the Landen transform to accelerate series convergence, and derives an analytical approximate expression consisting only of rational expressions and elementary functions. This expression can be uniformly used for calculating the mutual inductance between concentric circular conductors with rectangular cross-sections and the self-inductance of circular conductors, improving both the accuracy and efficiency of the calculation.
[0027] In this embodiment, the constructed model for calculating mutual inductance can be of various types known to those skilled in the art. In one example of the present invention, the method for constructing the mutual inductance model can be as follows: Figure 2 The method shown. In Figure 2 In this calculation method, the following are included: In step S11, a pair of concentric rings of conductors with equal cross-sections are constructed, the rings including a first ring and a second ring.
[0028] In step S12, both the first and second rings are composed of multiple filaments. The filaments of the first and second rings are arranged in a single layer along the cross-sectional height of the rings at their average radius, and the multiple filaments are coaxial. The axial distance between any two filament rings is... and the sum of their radii They are all quite small in comparison.
[0029] In step S13, a differential current is passed through each filament.
[0030] In steps S11 to S13, the single-layer filament model of the constructed conductor ring can be as follows: Figure 3As shown. It is assumed that each conductor consists of a single-layered circular loop of fine filaments, each carrying a differential current. The currents in the multiple filaments within a single conductor loop are connected in parallel, and their sum is the current in that conductor loop. The concentric conductor loops involved in the calculation of the self-inductance of the repulsion disk coil all have rectangular cross-sections and a large height-to-width ratio. Therefore, the above approximate assumptions can be made to calculate the mutual inductance between the coils, i.e., the self-inductance of the repulsion disk coil.
[0031] In this embodiment, the steps for constructing the mutual inductance equation can be of various kinds known to those skilled in the art. In one example of the present invention, the method for constructing the mutual inductance equation can be as follows: Figure 4 The method shown. In Figure 4 The calculation method also includes: In step S21, the modulus of the perfect elliptic integral corresponding to a pair of filaments in the first and second annulus is determined according to formula (1). (1) In step S22, the mutual inductance between all filament pairs is integrated and summed according to formula (2) to obtain the mutual inductance equation between the first and second rings. (2) in, For the first modulus, The mutual inductance between the first and second rings. The permeability of free space, Let be the radius of the first ring. Let be the radius of the second ring. This is the first type of complete elliptic integral function. This is the second type of fully elliptic integral function. Let be the axial coordinate of the filament in the first ring. Let be the axial coordinate of the filament in the second ring. This represents the height of the ring.
[0032] In step S23, the complementary modulus of the filament carrying the differential current is determined. (19) in, For the first modulus, The complementary modulus of the first modulus, The mutual inductance between the first and second rings. The permeability of free space, Let be the radius of the first ring. Let be the radius of the second ring. This is the first type of complete elliptic integral function. This is the second type of fully elliptic integral function. Let be the axial coordinate of the filament in the first ring. Let be the axial coordinate of the filament in the second ring. This represents the height of the ring.
[0033] In steps S21 to S23, the mutual inductance formula is expressed using a complete elliptic integral. Combined with the assumption of small axial distances between the annexes, the quantitative relationship of small complementary moduli is derived, allowing the originally difficult-to-analyze integral to be calculated using asymptotic series expansion. Using asymptotic expansion greatly simplifies the complex calculations in the mutual inductance equation, significantly reducing the computational load while maintaining high accuracy.
[0034] To further improve the convergence speed of the asymptotic series, in this implementation, the integrand of the mutual inductance equation is subjected to a Landen transformation. Specifically, as follows: Figure 5 As shown, the following steps may be included: In step S31, the mutual inductance equation is transformed according to formulas (3) to (4). (3) (4) In step S32, the complementary modulus of the second modulus is determined according to formula (12). (20) in, This is the second modulus, i.e., the modulus after the Landen transform. It is the complementary modulus of the second modulus.
[0035] In steps S31 to S32, the integrand of the mutual inductance equation is subjected to a Landen transformation, resulting in... It can be seen that the asymptotic series of the complete elliptic integral in formula (4) converges faster than before the transformation. Therefore, the computational efficiency is greatly optimized by the Landen transformation.
[0036] In this embodiment, after performing a Langdon transform on the mutual inductance equation, the mutual inductance value is calculated based on the asymptotic series of the complete elliptic integral. The specific steps may be as follows: Figure 6 The method is shown in [the document]. Figure 6 The calculation method also includes: In step S41, the complete elliptic integral is approximated using asymptotic series according to formulas (5) to (6). (5) (6) In step S42, the mutual inductance value is calculated according to formulas (7) to (15). (7) (8) (9) (10) (11) (12) (13) (14) (15) in, It is the sum of the radii of the first and second rings. For the module corresponding to the concentric conducting rings, As the first intermediate parameter, As the second intermediate parameter, As the third intermediate parameter, The fourth intermediate parameter, The fifth intermediate parameter, The sixth intermediate parameter, The seventh intermediate parameter, In addition, it should be noted that It is the module corresponding to the coaxial fine filament round wire, and It is the module corresponding to the concentric circular conductor, so its parameters only include the average radius of the two conductor rings, and not the axial coordinates.
[0037] In this embodiment, starting with the asymptotic expansion of the complete elliptic integral and combining it with the Landen transform to accelerate series convergence, a mutual inductance equation is derived. This equation can be used to calculate the mutual inductance between concentric circular conductors with rectangular cross-sections, and also to determine the self-inductance of the circular conductor. Based on this equation, the self-inductance of a multi-turn coil wound from a rectangular cross-section conductor can be further calculated, thus providing a precise and feasible method for designing repulsion mechanism coils. Specifically, this can include, for example... Figure 1 The steps shown are in Figure 1 The calculation method also includes: In step S5, a magnetic coupling circuit model of the repulsion mechanism is constructed. The schematic diagram of the excitation coil of the repulsion mechanism can be as follows: Figure 7 As shown.
[0038] In step S6, an equivalent inductor circuit model is constructed based on the magnetic coupling circuit model of the repulsion mechanism. The circuit diagrams of the magnetic coupling circuit model of the repulsion mechanism and the equivalent inductor circuit model can be as follows: Figure 8 As shown.
[0039] In step S7, the target self-inductance of the excitation coil is determined based on the equivalent inductance circuit model and the expected operating time of the repulsion mechanism.
[0040] In step S8, the number of coil turns is determined based on the mutual inductance value and the target self-inductance of the excitation coil.
[0041] In steps S5 to S8, formula (4) is extended to the rapid and accurate evaluation of the self-inductance of a multi-turn coil wound with a rectangular cross-section conductor, thus providing an implementable methodology for the parameter design of the excitation coil of the repulsion mechanism. Under constraints such as wire diameter, cross-sectional dimensions, and inner diameter, a self-inductance-turns design curve is generated, and a combination of turns and wire diameter that satisfies the target self-inductance of the excitation coil is selected. This invention has high accuracy and high computational efficiency under the condition of a rectangular cross-section conductor with a large aspect ratio, avoiding the complexity of directly solving the complete elliptic integral, and is suitable for the parameterized design of the excitation coil of an ultra-fast mechanical switching repulsion mechanism.
[0042] In this embodiment, the methods for determining the target self-inductance of the excitation coil can be various and known to those skilled in the art. In one example of the present invention, the method for determining the target self-inductance of the excitation coil can be... Figure 9 The method shown. Figure 9 The calculation method also includes: In step S71, the equivalent inductance of the equivalent inductor circuit model is calculated according to formula (16). (16) In step S72, the target self-inductance of the excitation coil is calculated from the equivalent inductance of the circuit according to formula (17). (17) in, For equivalent inductance, The capacitor that powers the excitation coil. The discharge time of the capacitor that powers the excitation coil. The target self-inductance of the excitation coil, This represents the coupling coefficient of the magnetically coupled circuit.
[0043] In steps S71 to S72, based on the opening sequence of the ultra-fast mechanical switch, the discharge time of the energy storage capacitor, i.e., the excitation coil power supply capacitor, is set to approximately one-quarter of the opening time. The energy storage capacitor can be determined by the maximum kinetic energy, energy conversion rate, and charging voltage when the mechanical switch operates. The target self-inductance of the excitation coil is determined based on the equivalent inductance of the equivalent inductance circuit model and the magnetic coupling equivalence.
[0044] In this embodiment, each turn of the rectangular cross-section conductor is modeled as a single-layer continuous filament circulation distribution. The derived analytical formula for mutual inductance is used to calculate the mutual inductance between any two turns. Then, the self-inductance of the multi-turn coil is obtained through double summation, including: The number of coil turns for a given wire diameter is obtained using formula (18). (18) in, For the first turn and the first Mutual inductance between the rings Total number of turns The inner diameter of the coil. The line width is for the circular ring. Under given design constraints, first determine a reasonable line diameter. Then, according to formula (18), the relationship curve between the target self-inductance of the excitation coil and the number of turns is plotted. Finally, according to the target self-inductance of the excitation coil determined by formula (17), a suitable number of coil turns is selected. In one example of the present invention, according to Figure 10 The parameters shown are used to calculate the design value of the target self-inductance of the excitation coil as 112.6 μH according to equation (17). Further calculations are performed based on equation (18) as follows: Figure 11 The curve showing the self-inductance-turns relationship ultimately determined the coil turns to be 32. Figure 10 In That is, in formula (16) Furthermore, the first and second rings in formula (4), i.e., mutual inductance... In this context, 1 and 2 are general terms: 1 and 2 represent any two conductor loops in the coil, one marked as 1 and the other as 2, according to formula (18). Specifically refers to the first excitation coil turn and the first A circular ring of conductors. It is according to The expression replaces 1 with 2 replaced with get.
[0045] On the other hand, the present invention provides a system for calculating the inductance value of the excitation coil of an electromagnetic repulsion mechanism, the system including a processor for executing the calculation method as described above.
[0046] In another aspect, the present invention also provides a computer-readable storage medium storing instructions for being read by a computer to cause the computer to perform any of the calculation methods described above.
[0047] Through the above technical solution, this invention provides a method and system for calculating the inductance value of the excitation coil of an electromagnetic repulsion mechanism. Starting with the asymptotic expansion of a complete elliptic integral and combining it with the Landen transform to accelerate series convergence, a mutual inductance equation is derived. This equation can be used to calculate the mutual inductance between concentric conducting rings with rectangular cross-sections, and also to determine the self-inductance of the conducting rings. Based on this equation, the self-inductance of a multi-turn coil wound from a rectangular cross-section conductor can be further calculated, thus providing an accurate and feasible method for designing repulsion mechanism coils. The calculation method of this invention has high accuracy, fast calculation efficiency, and is easy to implement, supporting the rapid parametric design of excitation coils for repulsion mechanisms.
[0048] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0049] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0050] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0051] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0052] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.
[0053] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.
[0054] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.
[0055] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.
[0056] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.
Claims
1. A method for calculating the inductance value of the excitation coil of an electromagnetic repulsion mechanism, characterized in that, The calculation method includes: Construct a single-layer filament model of a conductor ring; The mutual inductance equation between the conductor rings is established based on the single-layer filament model of the conductor rings. Perform the Landen transform on the mutual inductance equation; The mutual inductance value of the mutual inductance equation is calculated based on the asymptotic series of the complete elliptic integral.
2. The calculation method according to claim 1, characterized in that, Constructing a single-layer filament model of a conductor ring includes: Construct a pair of concentric rings of a conductor with equal cross-section, the rings comprising a first ring and a second ring; Both the first and second rings are composed of multiple filaments. The filaments of the first ring and the second ring are arranged in a single layer along the cross-sectional height of the ring at the average radius, and the multiple filaments are coaxial. A differential current is passed through each of the aforementioned filaments.
3. The calculation method according to claim 2, characterized in that, The mutual inductance equations between the conductor rings are established based on the single-layer filament model of the conductor rings, including: The modulus of the perfect elliptic integral corresponding to a pair of filaments in the first and second annulus is determined according to formula (1). ，（1） According to formula (2), the mutual inductance between all pairs of filaments is integrated and summed to obtain the mutual inductance equation between the first and second rings. ，（2） in, For the first modulus, The mutual inductance between the first and second rings. The permeability of free space, Let be the radius of the first ring. Let be the radius of the second ring. This is the first type of complete elliptic integral function. This is the second type of fully elliptic integral function. Let be the axial coordinate of the filament in the first ring. Let be the axial coordinate of the filament in the second ring. This represents the height of the ring.
4. The calculation method according to claim 3, characterized in that, Performing the Landen transformation on the mutual inductance equation includes: The mutual inductance equations are subjected to Landen transformation according to formulas (3) to (4). ，（3） ，（4） in, This is the second modulus.
5. The calculation method according to claim 4, characterized in that, Calculating the mutual inductance value of the mutual inductance equation based on the asymptotic series of the complete elliptic integral includes: Based on formulas (5) to (6), the complete elliptic integral is approximated using an asymptotic series. ，（5） ，（6） The mutual inductance value is calculated according to formulas (7) to (15). ，（7） ，（8） ，（9） ，（10） ，（11） ，（12） ，（13） ，（14） ，（15） in, It is the sum of the radii of the first and second rings. For the module corresponding to the concentric conducting rings, As the first intermediate parameter, As the second intermediate parameter, As the third intermediate parameter, The fourth intermediate parameter, The fifth intermediate parameter, The sixth intermediate parameter, The seventh intermediate parameter, .
6. The calculation method according to claim 5, characterized in that, The calculation method further includes: Construct a magnetic coupling circuit model for the repulsion mechanism; Construct an equivalent inductor circuit model based on the magnetic coupling circuit model of the repulsion mechanism; The target self-inductance of the excitation coil is determined based on the equivalent inductance circuit model and the expected action time of the repulsion mechanism. The number of coil turns is determined based on the mutual inductance value and the target self-inductance of the excitation coil.
7. The calculation method according to claim 6, characterized in that, Determining the target self-inductance of the excitation coil based on the equivalent inductance circuit model and the expected operating time of the repulsion mechanism includes: The equivalent inductance of the circuit model is calculated according to formula (16). ，（16） The target self-inductance of the excitation coil is calculated from the equivalent inductance of the circuit according to formula (17). ，（17） in, For equivalent inductance, The capacitor that powers the excitation coil. The discharge time of the capacitor that powers the excitation coil. The target self-inductance of the excitation coil, This represents the coupling coefficient of the magnetically coupled circuit.
8. The calculation method according to claim 7, characterized in that, Determining the coil turns based on the mutual inductance and the target self-inductance includes: The number of coil turns for a given wire diameter is obtained using formula (18). ，（18） in, For the first turn and the first Mutual inductance between the rings Total number of turns The inner diameter of the coil. The width of the circular line.
9. A system for calculating the inductance value of the excitation coil of an electromagnetic repulsion mechanism, characterized in that, The system includes a processor for performing the computation method as described in any one of claims 1 to 8.
10. A computer-readable storage medium, characterized in that, The storage medium stores instructions that are read by a computer to cause the computer to perform the calculation method as described in any one of claims 1 to 8.