Series armature equivalence-based electromagnetic repulsion mechanism output characteristic rapid calculation method

Abstract

The invention discloses an electromagnetic repulsion mechanism output characteristic rapid calculation method based on series armature equivalence, and the method comprises the following steps: carrying out the abstract modeling of a solved actual physical problem, converting the solved actual physical problem into a solvable mathematical model, and determining a to-be-solved variable in an electromagnetic repulsion mechanism; according to the Kirchhoff's law, listing a voltage-current equation of the electromagnetic repulsion mechanism to obtain a differential equation set; calculating driving coil resistance and armature equivalent coil resistance; using a self-inductance and mutual inductance calculation method to obtain the self-inductance of the driving coil, the self-inductance of the armature equivalent coil and the mutual inductance of the driving coil and the armature equivalent coil, and then writing a matrix form and a discrete form of a differential equation set; the speed and displacement of an armature are calculated according to the calculated electromagnetic repulsion, and a dynamic characteristic calculation result of the electromagnetic repulsion mechanism is obtained through iterative calculation. According to the method, the problems that the solving efficiency is reduced and the parameter updating time of the inductance matrix is long due to a large-scale inductance matrix in an equivalent circuit method can be solved.

Description

Technical Field

[0001] The invention relates to a method for quickly calculating the output characteristics of an electromagnetic repulsion mechanism, and in particular to a method for quickly calculating the output characteristics of an electromagnetic repulsion mechanism based on series armature equivalence. Background Art

[0002] The electromagnetic repulsion mechanism has the advantages of high output efficiency and short mechanical delay, and is a common driving mechanism for fast mechanical switches. The design process of the electromagnetic repulsion mechanism usually adopts the method of mutual iteration and combination of digital prototype and experiment. Therefore, the computational efficiency of the digital prototype will directly affect the development speed and efficiency of the mechanical switch. The digital prototype of the electromagnetic repulsion mechanism is usually constructed using the finite element method and the equivalent circuit method. The finite element method is widely used in numerical calculations, and many commercial simulation software use this method. However, the finite element method uses the traditional Newton iteration method to solve nonlinear equations, which brings serious time-consuming problems, and different structural parameters need to be remodeled many times. The equivalent circuit method is an analytical method for solving the dynamic characteristics of the electromagnetic repulsion mechanism. It is necessary to divide the repulsion disk into many conductive areas and calculate the circuit parameters such as self-inductance and mutual inductance of each area separately, which leads to problems such as increased inductance matrix size and decreased computational efficiency. In addition, parameters such as inductance and inductance gradient are not easy to obtain, and the finite element method is usually used for calculation, which further increases the calculation time.

[0003] Therefore, under the premise of ensuring calculation accuracy, it is necessary to explore a method that can quickly update the inductance-related circuit parameters and reduce the size of the inductance matrix to solve the problem of long solution time and low efficiency of the dynamic characteristics of the electromagnetic repulsion mechanism. Summary of the invention

[0004] The purpose of the present invention is to provide a method for quickly calculating the output characteristics of an electromagnetic repulsion mechanism based on the equivalent of a series armature, which can effectively reduce the dimensions of the inductance and inductance gradient matrix, and is used to solve the problems of decreased solution efficiency and long update time of inductance matrix parameters caused by large-scale inductance matrix in the equivalent circuit method. The present invention mainly solves the dynamic characteristics of the electromagnetic repulsion mechanism quickly and is applied to the two-dimensional axisymmetric case.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for quickly calculating the output characteristics of an electromagnetic repulsion mechanism based on series armature equivalence comprises the following steps:

[0007] Step 1: Abstractly model the actual physical problem to be solved and transform it into a solvable mathematical model, and determine the variables to be solved in the electromagnetic repulsion mechanism. The variables to be solved are capacitor voltage, coil current, armature speed, and armature displacement;

[0008] Step 2: According to Kirchhoff's law, the voltage-current equation of the electromagnetic repulsion mechanism is listed to obtain a set of differential equations:

[0009]

[0010] Among them, i d is the current driving the coil, R d is the resistance of the drive coil loop, Ψ d is the flux through the driving coil, L d is the self-inductance of the driving coil, M1 is the mutual inductance between the driving coil and the armature equivalent coil, i x is the current of the armature equivalent coil, R x is the resistance of the armature equivalent coil, Ψ x is the magnetic flux of the armature equivalent coil, L x is the self-inductance of the armature equivalent coil, c is the capacitance of the energy storage capacitor, u c is the capacitor voltage;

[0011] The initial conditions of the equation system are:

[0012]

[0013] Among them, i d with i x The initial moment is 0, u0 is the initial charging voltage of the capacitor;

[0014] During the armature motion, the total energy of the magnetic field is:

[0015]

[0016] Taking the derivative of displacement, we get the expression of electromagnetic force. Due to the self-inductance L d With L x are independent of position, so the electromagnetic force is:

[0017]

[0018] Calculate the dynamic characteristic parameters of the armature's acceleration a, velocity v and displacement x based on the electromagnetic force:

[0019]

[0020] Among them, v0 is the initial velocity of the armature, and x0 is the initial displacement of the armature. In the calculation, both parameters are 0;

[0021] Step 3: Perform Laplace transform on the differential equations in step 2, replace s with jω, and get:

[0022]

[0023] Considering the high frequency of the electromagnetic repulsion mechanism driving circuit, the ω 2 All terms can be ignored, and the real part and the imaginary part are separated to obtain the equivalent resistance and equivalent inductance of the electromagnetic repulsion mechanism:

[0024]

[0025] Step 4: If the number of turns of the coil is N0, the conductivity of the coil material is ρ d , the conductor cross section is rectangular, the conductor width is w0, the height is h0, and the radius of the nth turn is r n , then the driving coil resistance R d for:

[0026]

[0027] Step 5: Based on step 3, the armature is connected in series, the number of turns of the armature is set, and the armature equivalent coil resistance is calculated based on the number of turns. The specific calculation method is as follows:

[0028] Step 5.1: First, calculate the resistance of the armature region when it is not equivalent. The conductivity of the armature region is ρ x , the inner radius is r in , the outer radius is r out , height h r According to the definition formula of resistance, take a circular ring sheet with a radius of r in the metal ring area, and its resistance is:

[0029]

[0030] Where dr is the length of the metal ring axial element; the circular ring sheets are connected in parallel, so the armature area resistance R a The reciprocal of is 1 / R a =∑(1 / dR a );This formula is calculated by integration to obtain the armature area resistance R a for:

[0031]

[0032] Step 5.2: If the armature area is equivalent and the number of turns is set to N, multiply the right side by N 2 , get the armature equivalent coil resistance R x ;

[0033] Step 6: When the current density is uniformly distributed, use the following formula to calculate the mutual inductance of any two coaxial rectangular cross-section circular coils (hereinafter referred to as coil p and coil s):

[0034]

[0035] Among them, A p and A s is the cross-sectional area of ​​coil p and coil s, M ij is the mutual inductance between the corresponding current micro-circles i and j in the two coils, r i is the radius of the current micro-circle i, r j is the radius of the current microcircle j, z p is the axial height of coil p, z z is the axial height of coil s, C i With C j is the path of the current micro-circles i and j, dl i For dl j is the length element on the current microcircle, r is dl i and dl j The distance between them; expand the differential term to obtain the calculation formula of the mutual inductance of coil p and coil s, and differentiate the displacement to obtain the formula of the mutual inductance gradient:

[0036]

[0037] Among them, N p and N s is the number of turns of coil p and coil s, z s is the axial center distance between coil p and coil s, R1 and R2 are the inner and outer radii of coil p, z1 and z2 are the axial height coordinates of coil p, R3 and R4 are the inner and outer radii of coil s, z3 and z4 are the axial height coordinates of coil s, and θ is dl i and dl j The phase angle on the axial projection, μ0 is the magnetic permeability in vacuum;

[0038] Step 7: When calculating the self-inductance of the coil, the formula for calculating the mutual inductance M in step 6 can still be used. It is only necessary to modify the upper and lower limits of the third and fourth integrals to the relevant geometric parameters of the calculated coil. The specific calculation formula is as follows;

[0039]

[0040] Step 8: Use the self-inductance and mutual inductance calculation methods in steps 6 and 7 to obtain the self-inductance L of the drive coil d , armature equivalent coil self-inductance L x After calculating the mutual inductance M1 between the drive coil and the armature equivalent coil, write out the matrix form and discrete form of the equation group in step 2, where:

[0041] The matrix form of the system of equations is as follows:

[0042]

[0043] Among them, v is the armature speed, F is the amplitude of electromagnetic repulsion, L is the inductance matrix, is the inductance gradient matrix, R is the resistance column vector, I is the current column vector, and U is the voltage column vector. The corresponding matrix is ​​shown as follows:

[0044]

[0045] Where, u is the capacitor voltage value;

[0046] The discrete form of the system of equations is as follows:

[0047]

[0048] The current vector and electromagnetic repulsion are calculated based on the initial value of the capacitor charging voltage, where n and n+1 represent the nth and n+1th time steps of the calculation, and h is the time step length;

[0049] Step 9: Calculate the velocity and displacement of the armature based on the electromagnetic repulsion calculated in step 8. The discrete format is as follows:

[0050]

[0051] After the displacement x is obtained, the inductance matrix and the inductance gradient matrix are updated using the calculation formulas of the coil self-inductance, the mutual inductance between the two coils, and the mutual inductance gradient. After iterative calculation, the dynamic characteristic calculation results of the electromagnetic repulsion mechanism are obtained.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1. The present invention uses an analytical method to calculate the self-inductance, mutual inductance and inductance gradient of the rectangular area divided by the drive coil and the armature. Compared with the finite element method to calculate the inductance related parameters, this method only needs to modify the geometric parameters without re-establishing the geometric model. Moreover, under the premise of similar calculation accuracy, the calculation speed is faster than the finite element method, and the inductance parameters can be updated in real time in each iteration step.

[0054] 2. The present invention uses a series armature equivalent method, which effectively reduces the dimensions of the inductance and inductance gradient matrix and improves the calculation speed of the dynamic characteristics of the electromagnetic repulsion mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is the equivalent schematic diagram of series armature;

[0056] Figure 2 It is a schematic diagram of the arrangement of two coaxial rectangular coils;

[0057] Figure 3 It is a schematic diagram of calculating the mutual inductance of two current loop micro-elements;

[0058] Figure 4The armature current density distribution diagrams at different times: (a) 1ms armature current density distribution, (b) 2ms armature current density distribution, (c) 3ms armature current density distribution;

[0059] Figure 5 Solve the flow chart for the series armature equivalent method;

[0060] Figure 6 It is a dynamic characteristic test platform of electromagnetic repulsion mechanism, 1-electromagnetic repulsion mechanism prototype, 2-high-speed camera, 3-PC;

[0061] Figure 7 Comparison of experimental test, finite element method and series armature equivalent method calculation results, a armature displacement curve, b driving coil current, c capacitor discharge voltage, d electromagnetic repulsion amplitude. DETAILED DESCRIPTION

[0062] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0063] The present invention provides a method for quickly calculating the output characteristics of an electromagnetic repulsion mechanism based on the equivalent of a series armature. Figure 5 As shown, the method comprises the following steps:

[0064] Step 1: Abstractly model the actual physical problem to be solved and transform it into a solvable mathematical model, and determine the variables to be solved in the electromagnetic repulsion mechanism. The variables to be solved are capacitor voltage, coil current, armature speed, and armature displacement.

[0065] Step 2: According to Kirchhoff's law, the voltage-current equation of the electromagnetic repulsion mechanism is listed to obtain a set of differential equations:

[0066]

[0067] Among them, i d is the current of the closing coil, R d is the resistance of the closing coil circuit, Ψ d is the flux through the closing coil, L d is the inductance of the closing coil, M1 is the mutual inductance between the closing coil and the armature equivalent coil, i x is the current of the equivalent coil, R x is the resistance of the equivalent coil, Ψ x is the magnetic flux of the equivalent coil, L x is the inductance of the equivalent coil, c is the capacitance of the energy storage capacitor, u c is the capacitor voltage.

[0068] The initial conditions of the equation system are:

[0069]

[0070] Among them, i d with i x The initial moment is 0, and u0 is the initial charging voltage of the capacitor.

[0071] During the armature motion, the total energy of the magnetic field is:

[0072]

[0073] Taking the derivative of displacement, we can get the expression of electromagnetic force. Due to the self-inductance L d With L x are independent of position, so the electromagnetic force is:

[0074]

[0075] According to the electromagnetic force, the dynamic characteristic parameters of the armature, such as acceleration a, velocity v and displacement x, can be calculated:

[0076]

[0077] Among them, v0 is the initial velocity of the armature, x0 is the initial displacement of the armature, and both parameters are 0 in the calculation.

[0078] Step 3: Perform series connection of the armature, set the number of turns of the armature in series, and calculate the equivalent resistance, equivalent self-inductance, and mutual inductance of the armature with the coil based on the number of turns.

[0079] The equivalent schematic diagram is as follows Figure 1 As shown, the armature divided into p rows and q columns can be equivalent to a multi-turn coil with a total number of turns of p×q. When dividing and equating the armature, only the part that overlaps with the drive coil in the axial direction is considered, and the non-overlapping part does not contribute much to the electromagnetic repulsion and is therefore not considered.

[0080] Armature resistance and coil resistance are important parameters for calculating current. If the number of turns of the coil is N0, the conductivity of the coil material is ρ c , the conductor cross section is rectangular, the conductor width is w0, the height is h0, and the radius of the nth turn is r n , the total resistance R of the coil can be calculated d for:

[0081]

[0082] The conductivity of the armature region is ρ x , the inner radius is r in , the outer radius is r out , height h rAccording to the definition formula of resistance, take a circular ring sheet with a radius of r in the metal ring area, and its resistance is:

[0083]

[0084] Where dr is the length of the metal ring axial element; the circular ring sheets are connected in parallel, so the armature area resistance R a The reciprocal of is 1 / R a =∑(1 / dR a );This formula is calculated by integration to obtain the armature area resistance R a for:

[0085]

[0086] If the equivalent number of turns of the armature is N, multiply the right side by N 2 That's it.

[0087] The geometric arrangement of two coaxial rectangular cross-section coils is as follows: Figure 2 As shown, the schematic diagram of the calculation of the mutual inductance of the two current loop microelements is as follows Figure 3 When the current density is uniformly distributed, the mutual inductance of any two coaxial rectangular cross-section circular coils (hereinafter referred to as coil p and coil s) is calculated using the following formula:

[0088]

[0089] Among them, A p and A s is the cross-sectional area of ​​coil p and coil s, for example, coil p is the primary coil and coil s is the secondary coil, M ij is the mutual inductance between the corresponding current micro-circles i and j in the two coils, r i is the radius of the current micro-circle i, r j is the radius of the current microcircle j, z p is the axial height of coil p, z z is the axial height of coil s, C i With C j is the path of the current micro-circles i and j, dl i For dl j is the length element on the current microcircle, r is dl i and dl j The distance between them; expand the differential term to obtain the calculation formula of the mutual inductance of coil p and coil s, and differentiate the displacement to obtain the formula of the mutual inductance gradient:

[0090]

[0091] Among them, N p and N s is the number of turns of coil p and coil s, zs is the axial center distance between coil p and coil s, R1 and R2 are the inner and outer radii of coil p, z1 and z2 are the axial height coordinates of coil p, R3 and R4 are the inner and outer radii of coil s, z3 and z4 are the axial height coordinates of coil s, and θ is dl i and dl j The phase angle on the axial projection, μ0 is the magnetic permeability in vacuum.

[0092] When calculating the self-inductance of the coil, the formula for calculating the mutual inductance M can still be used. It is only necessary to modify the upper and lower limits of the third and fourth integrals to the relevant geometric parameters of the calculated coil. The calculation formula is as follows:

[0093]

[0094] Step 4: Use the self-inductance and mutual inductance calculation method in step 3 to obtain the self-inductance L of the drive coil d , equivalent coil self-inductance L x After calculating the mutual inductance M1 of the two coils, write out the matrix form and discrete form of the equations in step 2, where:

[0095] The matrix form of the system of equations is as follows:

[0096]

[0097] Among them, v is the armature speed, F is the amplitude of electromagnetic repulsion, L is the inductance matrix, is the inductance gradient matrix, R is the resistance column vector, I is the current column vector, and U is the voltage column vector. The corresponding matrix is ​​shown as follows:

[0098]

[0099] Where, u is the capacitor voltage value;

[0100] The discrete form of the system of equations is as follows:

[0101]

[0102] The current vector and electromagnetic repulsion are calculated according to the initial value of the capacitor charging voltage, where n and n+1 represent the nth and n+1th time steps of the calculation, and h is the time step length.

[0103] Step 5: Calculate the velocity and displacement of the armature based on the electromagnetic repulsion calculated in step 4. The discrete format is as follows:

[0104]

[0105] After the displacement x is obtained, the coil self-inductance, the mutual inductance between the two coils and the mutual inductance gradient calculation formula in step 3 are used to update the inductance matrix and the inductance gradient matrix in step 4. After iterative calculation, the dynamic characteristic calculation results of the electromagnetic repulsion mechanism can be obtained.

[0106] Figure 4 The armature current density distribution results calculated at different times using the analytical method and the finite element method are shown in the figure. It can be found that the calculation results of the two methods are very close.

[0107] The present invention proposes a series armature equivalent method, performs Laplace transformation on the equation in step 2, replaces s with jω, and obtains the following by rearrangement:

[0108]

[0109] Considering the high frequency of the electromagnetic repulsion mechanism driving circuit, the ω 2 All terms can be ignored. By separating the real part and the imaginary part in the formula, the equivalent resistance and equivalent inductance of the mechanism can be obtained as follows:

[0110]

[0111] From step 3, we know that the coil self-inductance L∝N 2 , N is the number of coil turns, the mutual inductance of the two coils M∝N1 N2, N1 and N2 are the number of turns of the two coils respectively, and the coil resistance R∝N 2 It can be seen that the second term on the right side of the equivalent inductance and equivalent resistance is only related to the number of turns of the drive coil, but not to the number of turns of the equivalent coil. Therefore, it is a reasonable assumption to regard the armature as a multi-turn series coil. When using this assumption, the dimensions of the inductance matrix and the inductance gradient matrix can be reduced from p*q+1 to 2, which greatly reduces the scale of matrix operations and can effectively improve the calculation efficiency.

[0112] against Figure 6 The dynamic characteristics of the electromagnetic repulsion mechanism shown in the figure are calculated, and the calculation results are compared with Figure 7 It can be found that the armature displacement, drive coil current, capacitor voltage, and electromagnetic force curves calculated using the finite element software are very close to the calculation results of the proposed series armature equivalent method, and the armature displacement curve is also very close to the experimental measurement results.

[0113] Taking the capacitor charging voltage of 180V as an example, the calculation speed of the three calculation methods, namely, experimental test, finite element method, and series armature equivalent method, is compared. The total calculation time is 5ms, and the calculation step is 0.01ms. The average absolute relative error is defined by the following formula:

[0114]

[0115] Where n is the total number of simulation time points, which is 501 in this example, i represents the i-th time point, and X Pi is the calculation result of the series armature equivalent method, X Ci The calculation results of the finite element model are shown in Tables 1 and 2.

[0116] Table 1 Statistics of mean absolute relative error

[0117]

[0118] Table 2 Comparison of total calculation time

[0119]

[0120] By comparing the calculation error with the total calculation time, it is found that the calculation accuracy of the method of the present invention is slightly different from the test results and the finite element calculation results, and the calculation time used is greatly advantageous.

Claims

1. A method for quickly calculating the output characteristics of an electromagnetic repulsion mechanism based on the equivalent of a series armature, characterized in that The method comprises the following steps: Step 1: Abstractly model the actual physical problem to be solved and transform it into a solvable mathematical model, and determine the variables to be solved in the electromagnetic repulsion mechanism. The variables to be solved are capacitor voltage, coil current, armature speed, and armature displacement; Step 2: According to Kirchhoff's law, the voltage-current equation of the electromagnetic repulsion mechanism is listed to obtain a set of differential equations: Among them, i d is the current driving the coil, R d is the resistance of the drive coil loop, Ψ d is the flux through the driving coil, L d is the self-inductance of the driving coil, M1 is the mutual inductance between the driving coil and the armature equivalent coil, i x is the current of the armature equivalent coil, R x is the resistance of the armature equivalent coil, Ψ x is the magnetic flux of the armature equivalent coil, L x is the self-inductance of the armature equivalent coil, c is the capacitance of the energy storage capacitor, u c is the capacitor voltage; During the armature motion, the total energy of the magnetic field is: Taking the derivative of displacement, we get the expression of electromagnetic force. Due to the self-inductance L d With L x are independent of position, so the electromagnetic force is: Calculate the dynamic characteristic parameters of the armature's acceleration a, velocity v and displacement x based on the electromagnetic force: Where, v0 is the initial velocity of the armature, and x0 is the initial displacement of the armature; Step 3: Perform Laplace transform on the differential equations in step 2, replace s with jω, and get: Considering the high frequency of the electromagnetic repulsion mechanism driving circuit, the ω 2 The terms are all ignored, and the real part and the imaginary part are separated to obtain the equivalent resistance and equivalent inductance of the electromagnetic repulsion mechanism: Step 4: If the number of turns of the coil is N0, the conductivity of the coil material is ρ d , the conductor cross section is rectangular, the conductor width is w0, the height is h0, and the radius of the nth turn is r n , then the driving coil resistance R d for: Step 5: Based on step 3, the armature is connected in series, the number of turns of the armature is set, and the armature equivalent coil resistance R is calculated based on this number of turns. x ; Step 6: When the current density is uniformly distributed, use the following formula to calculate the mutual inductance of any two coaxial rectangular cross-section circular coils: Among them, A p and A s is the cross-sectional area of ​​coil p and coil s, M ij is the mutual inductance between the corresponding current micro-circles i and j in the two coils, r i is the radius of the current micro-circle i, r j is the radius of the current microcircle j, z p is the axial height of coil p, z z is the axial height of coil s, C i With C j is the path of the current micro-circles i and j, dl i For dl j is the length element on the current microcircle, r is dl i and dl j The distance between them; expand the differential term to obtain the calculation formula of the mutual inductance of coil p and coil s, and differentiate the displacement to obtain the formula of the mutual inductance gradient: Among them, N p and N s is the number of turns of coil p and coil s, z s is the axial center distance between coil p and coil s, R1 and R2 are the inner and outer radii of coil p, z1 and z2 are the axial height coordinates of coil p, R3 and R4 are the inner and outer radii of coil s, z3 and z4 are the axial height coordinates of coil s, and θ is dl i and dl j The phase angle on the axial projection, μ0 is the magnetic permeability in vacuum; Step 7: Calculate the coil self-inductance using the formula as follows; Step 8: Use the self-inductance and mutual inductance calculation methods in steps 6 and 7 to obtain the self-inductance L of the drive coil d , armature equivalent coil self-inductance L x After calculating the mutual inductance M1 between the drive coil and the armature equivalent coil, write out the matrix form and discrete form of the equation group in step 2, where: The matrix form of the system of equations is as follows: Among them, v is the armature speed, F is the amplitude of electromagnetic repulsion, L is the inductance matrix, is the inductance gradient matrix, R is the resistance column vector, I is the current column vector, and U is the voltage column vector; The discrete form of the system of equations is as follows: The current vector and electromagnetic repulsion are calculated based on the initial value of the capacitor charging voltage, where n and n+1 represent the nth and n+1th time steps of the calculation, and h is the time step length; Step 9: Calculate the velocity and displacement of the armature based on the electromagnetic repulsion calculated in step 8. The discrete format is as follows: After the displacement x is obtained, the inductance matrix and the inductance gradient matrix are updated using the calculation formulas of the coil self-inductance, the mutual inductance between the two coils, and the mutual inductance gradient. After iterative calculation, the dynamic characteristic calculation results of the electromagnetic repulsion mechanism are obtained.

2. The method for quickly calculating the output characteristics of the electromagnetic repulsion mechanism based on the series armature equivalence according to claim 1 is characterized in that In step 2, the initial conditions of the equation system are: Among them, i d with i x The initial moment is 0, and u0 is the initial charging voltage of the capacitor.

3. The method for quickly calculating the output characteristics of the electromagnetic repulsion mechanism based on the series armature equivalence according to claim 1 is characterized in that In step 5, the armature equivalent coil resistance R x The specific calculation method is as follows: Step 5.1: First, calculate the resistance of the armature region when it is not equivalent. The conductivity of the armature region is ρ x , the inner radius is r in , the outer radius is r out , height h r According to the definition formula of resistance, take a circular ring sheet with a radius of r in the metal ring area, and its resistance is: Where dr is the length of the metal ring axial element; the circular ring sheets are connected in parallel, so the armature area resistance R a The reciprocal of is 1 / R a =∑(1 / dR a );This formula is calculated by integration to obtain the armature area resistance R a for: Step 5.2: If the armature area is equivalent and the number of turns is set to N, multiply the right side by N 2 , get the armature equivalent coil resistance R x .

4. The method for quickly calculating the output characteristics of the electromagnetic repulsion mechanism based on the series armature equivalence according to claim 1 is characterized in that In step 8, the inductance matrix L and the inductance gradient matrix The resistance column vector R, current column vector I, and voltage column vector U are: Where u is the capacitor voltage value.

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