Method for simulating breech voltage of linear electromagnetic energy propelling device

Abstract

The invention belongs to the technical field of electromagnetic propulsion simulation, and particularly relates to a breech voltage simulation method of a linear electromagnetic energy propulsion device. The method comprises the following steps: firstly, constructing a mathematical model of a capacitive energy storage type pulse power supply formed by connecting a plurality of PFU units in parallel, and calculating a track current according to the model; then, constructing a mathematical model of the interaction of the armature and the rail, including calculation of equivalent inductance gradient, pivot rail friction force, pivot rail contact resistance, rail resistance gradient, armature acceleration, armature speed, armature displacement, air resistance, driving electromagnetic force, rail resistance, rail voltage, induced electromotive force, back electromotive force and breech voltage; and finally, according to the mathematical model of the interaction of the armature and the track, constructing a breech voltage simulation model. According to the method, various influence factors such as the current skin effect, the track conductivity dynamic change and the air resistance of the linear electromagnetic energy propulsion device under the large-current and ultra-high-speed operation working conditions are considered, the breech voltage simulation model is constructed, and the accuracy of simulation calculation is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic propulsion simulation, and specifically relates to a method for simulating the breech voltage of a linear electromagnetic energy propulsion device. Background Art

[0002] Linear electromagnetic energy propulsion refers to a driving method using electromagnetic energy. Electromagnetic energy propulsion can break through the energy and speed limits of traditional driving methods, and has significant advantages such as high launch kinetic energy, high system efficiency, high launch frequency, fast startup time, strong continuous launch ability, and strong load adjustability. The breech voltage is one of the important parameters of a linear electromagnetic energy propulsion device. Its magnitude directly affects the armature motion characteristics, and has a direct impact on the analytical calculation of the current density, inductance gradient, spatial magnetic field distribution, and launch efficiency of the linear electromagnetic energy propulsion device. Therefore, the simulation calculation of the breech voltage is of great significance.

[0003] Currently, there are few calculation methods for the breech voltage of electromagnetic energy linear propulsion devices. Most calculate the gun voltage through the finite element method, and it is difficult to achieve dynamic calculation; there is also direct measurement of the external leads of the power supply, but due to the power supply voltage impact, direct measurement has safety hazards. In addition, the linear electromagnetic energy propulsion process usually occurs under the combined action of multiple extreme conditions, such as high current and ultra-high speed operating conditions, which will increase the calculation difficulty of the breech voltage.

[0004] To solve the above problems, the present invention proposes a method for simulating the breech voltage of a linear electromagnetic energy propulsion device, which constructs a breech voltage simulation model based on the Simulink visual simulation software and using the causal modeling idea. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the technical problem to be solved by the present invention is to provide a method for simulating the breech voltage of a linear electromagnetic energy propulsion device.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A method for simulating the breech voltage of a linear electromagnetic energy propulsion device, characterized in that the method comprises the following steps:

[0008] Step 1: Construct a mathematical model of a capacitor energy storage type pulse power supply composed of multiple PFU units in parallel, and calculate the rail current according to this model;

[0009] Step 2: Construct a mathematical model of the interaction between the armature and the rail, including the calculation of equivalent inductance gradient, armature-rail friction force, armature-rail contact resistance, rail resistance gradient, armature acceleration, armature speed, armature displacement, air resistance, driving electromagnetic force, rail resistance, rail voltage, induced electromotive force, back electromotive force, and breech voltage;

[0010] The calculation formula for the track skin depth δ(t) is:

[0011]

[0012] Wherein, v(t) and v c (t) are the armature speed and the critical speed respectively, μ 0 is the magnetic permeability of the track material, σ r (t) is the dynamic conductivity of the track, f is the track current frequency, k is the proportionality factor, and λ is the effective length of the current generated by the contact between the armature and the track;

[0013] The calculation formula for the track resistance gradient R'(t) is:

[0014]

[0015] Wherein, h is the track height;

[0016] The track voltage U g (t) calculation formula is:

[0017] U g (t) = [R g (t) + R Q (t)]I(t) (15)

[0018] Wherein, R g (t) is the track resistance, R Q (t) is the armature-rail contact resistance, and I(t) is the track current;

[0019] The induced electromotive force U E (t) calculation formula is:

[0020]

[0021] Wherein, L(t) is the track inductance;

[0022] The back electromotive force E(t) calculation formula is:

[0023]

[0024] Wherein, L’ is the equivalent inductance gradient, v 0 is the initial armature speed, and M is the armature mass;

[0025] The breech voltage U w (t) calculation formula is:

[0026] U w (t) = U g (t) + U E (t) + E(t) (18)

[0027] Step 3: According to the mathematical model of the interaction between the armature and the track, use the Simulink simulation software to construct a breech voltage simulation model for the simulation calculation of the breech voltage.

[0028] Further, for the PFU unit, when the voltage across the capacitor is greater than 0, the circuit equation is:

[0029]

[0030] In the formula, L i is the harmonic modulation inductor, L c is the stray inductance of the capacitor branch, I E (t) is the discharge current of the PFU unit, R c is the stray resistance of the capacitor branch, R s is the on-state resistance of the thyristor, R i is the stray resistance of the harmonic modulation inductor branch, C is the capacitor;

[0031] When the voltage across the capacitor is 0, the circuit equation is:

[0032]

[0033] In the formula, L d is the stray inductance of the diode branch, R d is the stray resistance of the diode branch, R D is the on-state resistance of the diode.

[0034] Further, the breech voltage simulation model includes a capacitor energy storage type pulse power supply module, an equivalent inductance gradient simulation module, an armature-rail friction force simulation module, a contact resistance simulation module, a resistance gradient simulation module, a speed simulation module, a displacement simulation module, an air resistance simulation module, a driving electromagnetic force simulation module, a track resistance simulation module, an induced electromotive force simulation module, a back electromotive force simulation module, an acceleration simulation module, a track voltage simulation module and a breech voltage simulation module.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] The present invention considers various influencing factors such as the current skin effect, the dynamic change of the track conductivity, and the air resistance under the operating conditions of high current and ultra-high speed of the linear electromagnetic energy propulsion device, constructs a breech voltage simulation model, and improves the accuracy of the simulation calculation.

[0037] The high current and ultra-high speed operating conditions will cause the skin effect on the track. During different movement stages of the armature, the current distribution is affected by different skin effects. In the initial stage of the armature movement, it is mainly affected by the current skin effect, and when the armature speed is greater than the critical speed, it is mainly affected by the speed skin effect. Therefore, the present invention fully considers the armature speed and proposes a more detailed skin depth calculation method.

[0038] The capacitor energy storage type pulse power supply is composed of multiple PFU units in parallel, which can better simulate the power supply for the linear electromagnetic energy propulsion device under actual working conditions, so as to obtain the track current close to the actual working conditions and use it as the input of the breech voltage simulation model. Brief Description of the Drawings

[0039] Figure 1 It is a schematic structural diagram of the linear electromagnetic energy propulsion device;

[0040] Figure 2 It is a simulation model diagram of the breech voltage;

[0041] Figure 3 It is a circuit diagram of the capacitor energy storage type pulse power supply;

[0042] Figure 4 It is a schematic diagram of the PFU unit;

[0043] Figure 5 It is a schematic diagram of the induced electromotive force simulation module;

[0044] Figure 6 It is a schematic diagram of the back electromotive force simulation module;

[0045] Figure 7 It is a schematic diagram of the track voltage simulation module;

[0046] Figure 8 It is a simulation result diagram of the track conductivity;

[0047] Figure 9 It is a simulation result diagram of the track current;

[0048] Figure 10 It is a comparison diagram of the simulated value and the measured value of the armature speed;

[0049] Figure 11 It is a comparison diagram of the simulated value and the measured value of the armature displacement;

[0050] Figure 12 It is a simulation result diagram of the breech voltage. Detailed Implementation Manner

[0051] The following provides specific embodiments in conjunction with the drawings. The specific embodiments are only used to introduce the technical solutions of the present invention in detail and do not limit the protection scope of this application.

[0052] The present invention provides a method for simulating the breech voltage of a linear electromagnetic energy propulsion device (abbreviated as method, see Figures 1 to 12 ), which includes the following steps:

[0053] Step 1: Construct a mathematical model of a capacitive energy storage pulsed power supply composed of multiple PFU units, and calculate the rail current according to this model.

[0054] For the PFU unit, when the voltage across the capacitor is greater than 0, the capacitor discharges to the load, the thyristor switch conducts, and it is an RLC second-order discharge process. Then the circuit equation is:

[0055]

[0056] In the formula, L i is the wave modulation inductor, L c is the stray inductance of the capacitor branch, I E (t) is the discharge current of the PFU unit, R c is the stray resistance of the capacitor branch, R s is the on-state resistance of the thyristor, R i is the stray resistance of the wave modulation inductor branch, C is the capacitor, U w (t) is the breech voltage;

[0057] When the voltage across the capacitor is 0, the thyristor switch turns off, the wave modulation inductor supplies energy to the load, the diode conducts, and it is an RL first-order discharge process. The circuit equation is:

[0058]

[0059] In the formula, L d is the stray inductance of the diode branch, R d is the stray resistance of the diode branch, R D is the on-state resistance of the diode.

[0060] Step 2: Construct a mathematical model of the interaction between the armature and the rail, including the calculation of the equivalent inductance gradient, armature-rail friction force, armature-rail contact resistance, rail resistance gradient, armature acceleration, armature velocity, armature displacement, air resistance, driving electromagnetic force, rail resistance, induced electromotive force, back electromotive force, rail voltage, and breech voltage.

[0061] The rail inductance includes the self-inductance of the inner rail and the mutual inductance between the inner and outer rails. Then the calculation formula for the equivalent inductance gradient is:

[0062] L’ = L 1 ’ + 2M 12 ’ (3)

[0063] In the formula, L’ is the equivalent inductance gradient, L 1 ’ is the inner rail inductance gradient, M 12 ’ is the mutual inductance gradient between the inner and outer rails;

[0064] When the current flows from the track into the armature, an angle is generated. The driving electromagnetic force on the armature is the horizontal component force, and the calculation formula is:

[0065]

[0066] In the formula, F L (t) is the driving electromagnetic force on the armature; I(t) is the track current, which is equal to the sum of the discharge currents of all PFU units; θ is the current angle;

[0067] The armature-rail contact pressure is composed of the initial pre-tightening force between the armature and the rail and the vertical component force of the electromagnetic force. Then the calculation formula for the armature-rail contact pressure is:

[0068]

[0069] In the formula, F Q (t) is the armature-rail contact pressure, and F 0 is the initial pre-tightening force between the armature and the rail;

[0070] The calculation formula for the armature-rail frictional force is:

[0071] F f (t) = μF Q (t) (6)

[0072] In the formula, F f (t) is the armature-rail frictional force, and μ is the armature-rail friction coefficient;

[0073] The air resistance on the moving armature is calculated by the following formula:

[0074]

[0075] In the formula, F a (t) is the air resistance on the moving armature, γ is the specific heat ratio of air, ρ is the air density, A is the cross-sectional area of the armature, v(t) is the armature speed, a(t) is the armature acceleration, and c f is the viscosity coefficient of air and the inner wall of the track, l c is the perimeter of the cross-section of the armature, and x(t) is the armature displacement;

[0076] The calculation formula for the armature acceleration is:

[0077]

[0078] In the formula, M is the mass of the armature;

[0079] The calculation formula for the armature speed is:

[0080]

[0081] In the formula, v 0is the initial velocity of the armature;

[0082] The calculation formula for the armature displacement is:

[0083]

[0084] In the formula, x 0 is the initial position of the armature;

[0085] The armature-rail contact resistance changes the motion and temperature characteristics of the armature, thereby affecting the stability of the device and the system efficiency. The calculation formula for the armature-rail contact resistance is:

[0086]

[0087] In the formula, R Q (t) is the armature-rail contact resistance, ρ 1 is the resistivity of the armature, ρ 2 is the resistivity of the rail, H is the strength of the armature material, and ε, ω are material constants;

[0088] During the armature emission process, due to current diffusion, proximity effect, and velocity skin effect, the current is approximately distributed in a loop shape in the rectangular guide rail cross-section, and the current is more concentrated on the inner surface of the guide rail; in the initial stage of armature movement, the current change rate is large, and the current distribution is mainly affected by the current skin effect, and the skin depth continuously increases; when the armature velocity v(t) is greater than the critical velocity v c (t), the current distribution is mainly affected by the velocity skin effect, and the skin depth continuously decreases; therefore, the calculation formula for the rail skin depth is:

[0089]

[0090] In the formula, δ(t) is the rail skin depth, μ 0 is the magnetic permeability of the rail material, σ r (t) is the dynamic conductivity of the rail, f is the rail current frequency, k is the proportionality factor, and λ is the effective length of the current generated by the contact between the armature and the rail;

[0091] The calculation formula for the rail resistance gradient is:

[0092]

[0093] In the formula, R'(t) is the rail resistance gradient, and h is the rail height;

[0094] The calculation formula for the rail resistance is:

[0095] R g (t) = 2R'(t)[l + x(t)] (14)

[0096] In the formula, R g(t) is the track resistance and l is the length of the outer track;

[0097] Track voltage U g The calculation formula of (t) is:

[0098] U g (t) = [R g (t) + R Q (t)]I(t) (15)

[0099] The calculation formula of the induced electromotive force generated by the armature movement is:

[0100]

[0101] In the formula, U E (t) is the induced electromotive force generated by the armature movement and L(t) is the track inductance;

[0102] The calculation formula of the back electromotive force E(t) generated by the armature movement is:

[0103]

[0104] The calculation formula of the breech voltage is:

[0105] U w (t) = U g (t) + U E (t) + E(t) (18)

[0106] Step 3: According to the mathematical model of the interaction between the armature and the track, use the Simulink simulation software to construct a breech voltage simulation model, including a capacitor energy storage type pulse power supply module, an equivalent inductance gradient simulation module, an armature-rail friction force simulation module, a contact resistance simulation module, a resistance gradient simulation module, a speed simulation module, a displacement simulation module, an air resistance simulation module, a driving electromagnetic force simulation module, a track resistance simulation module, an induced electromotive force simulation module, a back electromotive force simulation module, an acceleration simulation module, a track voltage simulation module and a breech voltage simulation module;

[0107] The capacitor energy storage type pulse power supply is composed of multiple PFU units connected in parallel. The PFU unit is modeled according to equations (1) and (2), and the track current is output by the capacitor energy storage type pulse power supply;

[0108] The equivalent inductance gradient simulation module is modeled according to equation (3), inputs the inner track inductance gradient and the mutual inductance gradient between the inner and outer tracks, and outputs the equivalent inductance gradient;

[0109] The driving electromagnetic force simulation module is modeled according to equation (4), inputs the equivalent inductance gradient, the track current and the current angle, and outputs the driving electromagnetic force;

[0110] The pivot-rail friction force simulation module is modeled according to Equation (6). By inputting the pivot-rail contact pressure and the pivot-rail friction coefficient, it outputs the pivot-rail friction force. The pivot-rail contact pressure is modeled according to Equation (5).

[0111] The air resistance simulation module is modeled according to Equation (7). The inputs include the acceleration, velocity, and displacement of the armature, and it outputs the air resistance.

[0112] The acceleration simulation module is modeled according to Equation (8). The inputs include the driving electromagnetic force, pivot-rail friction force, air resistance, and the mass of the armature, and it outputs the armature acceleration.

[0113] The velocity simulation module is modeled according to Equation (9). The inputs include the initial velocity of the armature and the armature acceleration, and it outputs the armature velocity.

[0114] The displacement simulation module is modeled according to Equation (10). The inputs include the armature velocity and the initial position of the armature, and it outputs the armature displacement.

[0115] The contact resistance simulation module is modeled according to Equation (11). The inputs include the pivot-rail contact pressure, pivot-rail contact resistance, armature resistivity, track resistivity, and the strength of the armature material, and it outputs the pivot-rail contact resistance.

[0116] The resistance gradient simulation module is modeled according to Equation (13). The inputs include the track skin depth, track dynamic conductivity, and track permeability, and it outputs the track resistance gradient. The track skin depth is modeled according to Equation (12).

[0117] The track resistance simulation module is modeled according to Equation (14). The inputs are the track resistance gradient, the length of the outer track, and the armature displacement, and it outputs the track resistance.

[0118] The track voltage simulation module is modeled according to Equation (15). The inputs are the track current, contact resistance, and track resistance, and it outputs the track voltage.

[0119] The induced electromotive force simulation module is modeled according to Equation (16). The inputs include the equivalent inductance gradient, track current, track inductance, and armature velocity, and it outputs the induced electromotive force.

[0120] The back electromotive force simulation module is modeled according to Equation (17). The inputs include the equivalent inductance gradient, track current, initial velocity of the armature, and the mass of the track, and it outputs the back electromotive force.

[0121] The breech voltage simulation module is modeled according to Equation (18). The inputs are the track voltage, induced electromotive force, and back electromotive force, and it outputs the breech voltage.

[0122] Embodiment

[0123] The breech voltage simulation is carried out using the breech voltage simulation model, and the parameter settings are as follows: the rail current is a trapezoidal current with a peak value of 60 KA, the capacitance of the PFU unit is 2028.9 μF, the stray inductance of the capacitance branch is 0.03 μH, the stray resistance of the capacitance branch is 0.06 mΩ, the stray resistance of the wave - tuning inductor branch is 2.4 mΩ, the wave - tuning inductor is 20 μH, the on - state resistance of the thyristor is 1.1 mΩ, the stray inductance of the diode branch is 0.15 μH, the stray resistance of the diode branch is 2.6 mΩ, the on - state resistance of the diode is 0.9 mΩ; the inner - rail inductance gradient is 0.41 μh / m, the mutual inductance gradient between the inner and outer rails is 0.35 μh / m, the initial position of the armature is 0.08 m, the initial velocity of the armature is 0 m / s, the current angle is 22°, the duration of current inflow is 0.002 s, the material strength of the armature is 150 Mpa, the magnetic permeability of the rail material is 1.256 μh / m, the resistivity of the rail is 1.75 uΩ·m, the resistivity of the armature is 2.8 uΩ·m, the specific heat ratio of air is 1.4017, the density of air is 1.29, the viscosity coefficient between air and the inner wall of the electromagnetic rail is 0.003, the height of the rail is 0.03 m, the length of the outer rail is 2 m, the mass of the armature is 50 g, the perimeter of the armature cross - section is 69.76 mm, and the area of the armature cross - section is 2.69 cm 2 ; The capacitor - energy - storage type pulse power supply is composed of 6 PFU units in parallel. The discharge voltage of each PFU unit is 4500 v, and the initial resistance is 0.018 mΩ.

[0124] The comparison between the simulation values and the experimental measurement values can verify the accuracy of the model. The comparisons of the armature velocity and displacement are shown in Figure 10 and Figure 11 . The simulated value of the muzzle velocity of the armature is 1503 m / s, the measured value of the muzzle velocity of the armature is 1408 m / s, and the error between the simulation value and the measured value is 6.7%. At 2 ms, the measured value of the armature displacement is 2180 mm, the simulated value of the armature displacement is 2077 mm, and the error between the simulation value and the measured value is 4.72%. Through comparison, it can be seen that the error of the breech voltage simulation model is small. The breech voltage obtained by this model has high accuracy, and at the same time, the effectiveness of the simulation model is verified. The simulation results of the breech voltage are shown in Figure 12 .

[0125] Matters not covered by this invention are well - known technologies.

Claims

1. A method for simulating the tail voltage of a linear electromagnetic energy propulsion device, characterized in that: The method comprises the following steps: Step 1: Construct a mathematical model of a capacitive energy storage pulse power supply consisting of multiple PFU units connected in parallel, and calculate the track current based on this model; Step 2: Construct a mathematical model of the interaction between the armature and the track, including the calculation of equivalent inductance gradient, armature-track friction, armature-track contact resistance, track resistance gradient, armature acceleration, armature velocity, armature displacement, air resistance, driving electromagnetic force, track resistance, track voltage, induced electromotive force, back electromotive force and breech voltage; The orbital skin depth δ(t) is calculated as: In the formula, v(t), v c (t) are the armature speed and critical speed, μ0 is the magnetic permeability of the track material, σ r (t) is the dynamic conductivity of the track, f is the track current frequency, k is the proportionality factor, and λ is the effective length of the armature-track contact to generate current; The calculation formula of track resistance gradient R'(t) is: Where h is the orbital height; Track voltage U g (t) is calculated as: U g (t)=[R g (t)+R Q (t)]I(t) (15) In the formula, R g (t) is the track resistance, R Q (t) is the hinge-rail contact resistance, I(t) is the track current; Induced electromotive force U E (t) is calculated as: Where, L(t) is the track inductance; The back electromotive force E(t) calculation formula is: Where, L′ is the equivalent inductance gradient, v0 is the initial velocity of the armature, and M is the armature mass; Breech voltage U w (t) is calculated as: U w (t)=U g (t)+U E (t)+E(t) (18) Step 3: Based on the mathematical model of the interaction between the armature and the track, the breech voltage simulation model is constructed using Simulink simulation software for simulation calculation of the breech voltage.

2. The method for simulating tail voltage of a linear electromagnetic energy propulsion device according to claim 1, characterized in that: For the PFU unit, when the voltage across the capacitor is greater than 0, the circuit equation is: Where, L i is the modulation inductor, L c is the stray inductance of the capacitor branch, I E (t) is the discharge current of the PFU unit, R c is the stray resistance of the capacitor branch, R s is the on-state resistance of the thyristor, R i is the stray resistance of the modulating inductor branch, and C is the capacitance; When the voltage across the capacitor is 0, the circuit equation is: Where, L d is the stray inductance of the diode branch, R d is the diode branch stray resistance, R D is the diode on-state resistance.

3. The method for simulating tail voltage of a linear electromagnetic energy propulsion device according to claim 1 or 2, characterized in that: The tail voltage simulation model includes a capacitor energy storage pulse power supply module, an equivalent inductance gradient simulation module, a pivot rail friction simulation module, a contact resistance simulation module, a resistance gradient simulation module, a speed simulation module, a displacement simulation module, an air resistance simulation module, a driving electromagnetic force simulation module, a track resistance simulation module, an induced electromotive force simulation module, a back electromotive force simulation module, an acceleration simulation module, a track voltage simulation module and a tail voltage simulation module.

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