Method for calculating armature melting wear of an electromagnetic rail launcher

Abstract

The application discloses a method for calculating the melting abrasion of an armature of an electromagnetic orbit launcher, the electromagnetic orbit launcher comprising an orbit and an armature movable along the orbit, the armature comprising an armature body and an armature arm connected with the armature body, the armature arm being in contact with the orbit; the exciting current is calculated by fitting a formula with the exciting current; the friction heat between the armature and the orbit and the Joule heat between the armature and the orbit are calculated; the heat transferred to the orbit is calculated; and the melting abrasion rate of the armature is calculated based on the obtained friction heat between the armature and the orbit, the Joule heat between the armature and the orbit and the heat transferred to the orbit. The method is based on the heat distribution of the contact surface to calculate the melting abrasion of the armature of the electromagnetic orbit launcher, and is more accurate.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic catapult technology, and in particular relates to a method for calculating the armature melting and wear of an electromagnetic rail launcher. Background Technology

[0002] Electromagnetic orbital launch is a launch method that uses electromagnetic thrust to accelerate a load to ultra-high speeds. It offers advantages such as fast response, stable launch performance, and controllable thrust. An electromagnetic orbital launcher mainly consists of a track and an armature that moves along the track. During armature launch, due to Joule heating and frictional heat between the armature and track contact surfaces, the temperature at the armature contact surface can far exceed the melting point of the armature material. This results in a liquefied metal layer forming at the armature-track interface, leading to melting and wear of the armature. The state of melting and wear of the armature is as follows: Figure 1 As shown, Figure 1 This is a facial image of an armature arm injury.

[0003] Due to armature melting and wear, during launch, metal materials from the armature arm surface will splash a liquefied metal layer onto the track. Armature residue remaining on the track will cause wear and shorten its service life. When the track is reused, track wear may alter the armature-rail contact state, leading to localized temperature rises, arc discharges, and other issues that affect launcher performance.

[0004] Because electromagnetic rail launchers operate under extreme physical conditions of high-speed, current-carrying sliding friction and wear, the armature motion is accompanied by a variety of complex physical phenomena such as temperature rise, phase transition, arc discharge, and planing transition, making the study of armature melting wear particularly difficult. Most scholars, both domestically and internationally, measure armature melting wear experimentally. However, during launch, the armature experiences not only melting wear but also mechanical wear, planing, and erosion damage; therefore, experimental methods for measuring armature melting wear are not highly accurate. Summary of the Invention

[0005] The purpose of this invention is to provide a method for accurately calculating armature melting wear of an electromagnetic rail launcher.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for calculating armature melting wear in an electromagnetic rail launcher, the electromagnetic rail launcher comprising a rail and an armature movable along the rail, the armature comprising an armature body and an armature arm connected to the armature body, the armature arm being in contact with the rail; comprising the following steps:

[0008] S1. Calculate the excitation current I(t) using the excitation current fitting formula, which is: I(t) = p1t 7+p2t 6 +p3t 5 +p4t 4 +p5t 3 +p6t 2 +p7t+p8, where p1, p2, p3, p4, p5, p6, p7, and p8 are fitting coefficients;

[0009] S2, Calculate the frictional heat Q between the pivot rails. f Joule heating Q between the pivot and the rail j :

[0010]

[0011] Q j =I 2 (t)R0(t),

[0012] μ in the formula m Let be the coefficient of sliding friction between the armature and the track, v be the velocity of the armature, L' be the inductance gradient of the track, d1 be the dimension of the contact surface between the armature arm and the track along the extension direction of the track, θ be the inclination angle of the armature arm, X be the distance between the two opposing tracks, and R0(t) be the contact resistance between the armature and the track.

[0013] S3. Calculate the heat Q transferred to the orbit. r :

[0014] In the formula, 'a' represents the width of the track cross section, and 'T' represents the width of the track cross section. ma T0 is the melting point of the armature material, T0 is the initial temperature of the armature-rail contact surface, and k is the melting point of the armature material. r ρ is the thermal conductivity of the orbital material. r For the density of the orbital material, c r The specific heat capacity of the track material;

[0015] S4. Based on the obtained frictional heat Q between the pivot rails f Joule heating Q between pivots j and the heat Q transferred to the orbit r Calculate the armature melting wear rate w:

[0016] ρ in the formula a c is the density of the armature material. a h is the specific heat capacity of the armature material. a It is the latent heat of fusion of the armature material.

[0017] Furthermore, the melting wear volume V of the armature is calculated based on the armature's melting wear rate w:

[0018]

[0019] Furthermore, the contact resistance R0(t) between the pivot rails is calculated using the following formula:

[0020] In the formula Let H be the average resistivity of the pivot rail contact surface, H be the hardness of the pivot rail contact surface, C and z be material constants, and F be the average resistivity of the pivot rail contact surface. n (t) represents the component of the electromagnetic force acting on the armature arm in the direction perpendicular to the contact surface of the armature rail.

[0021] Furthermore, the component of the electromagnetic force acting on the armature arm in the direction perpendicular to the contact surface of the armature rail.

[0022] Furthermore, the armature velocity v is calculated using the following formula:

[0023] In the formula, m is the mass of the armature.

[0024] As can be seen from the above technical solutions, the method of the present invention uses the transient current generated by the pulse shaping network as the excitation source when calculating the armature melting wear rate. At the same time, it considers the changing contact resistance caused by the changing current. Based on the changing current and contact resistance, it calculates the frictional heat and Joule heat between the armature and the rail. Finally, it calculates the melting wear of the armature based on the frictional heat, Joule heat and heat transferred to the rail. This method is more consistent with the actual situation of the electromagnetic launch process and can accurately calculate the armature melting wear rate, providing theoretical support for the design of the armature structure. Attached Figure Description

[0025] To more clearly illustrate the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 Image showing the facial features of the armature arm injury;

[0027] Figure 2 This is a schematic diagram of heat transfer between the contact surfaces of the armature and the track.

[0028] Figure 3 This is a schematic diagram of the structural parameters of the armature;

[0029] Figure 4 This is a flowchart of the method of the present invention;

[0030] Figure 5 This is a force diagram of the armature;

[0031] Figure 6This is a schematic diagram of the circuit topology of a pulse shaping network;

[0032] Figure 7 The graph shows the change of excitation current over time obtained from the simulation.

[0033] Figure 8 This is a graph showing the change in melting wear rate over time.

[0034] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. Detailed Implementation

[0035] The present invention will now be described in detail with reference to the accompanying drawings. In the detailed description of the embodiments of the present invention, for ease of explanation, the drawings illustrating the device structure will be partially enlarged without adhering to the general scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of the present invention. It should be noted that the drawings are in a simplified form and use non-precise scales, solely for the purpose of conveniently and clearly illustrating the embodiments of the present invention. Additionally, in the description of this application, terms such as "first" and "second" are used only to distinguish descriptions and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Terms such as "positive," "negative," "bottom," "upper," and "lower" indicate orientation or positional relationships based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0036] Electromagnetic rail launchers mainly consist of a track and an armature. The armature moves at high speed along the track under electromagnetic thrust. The armature typically includes the armature body and a flexible armature arm connected to it. The load is mounted on the armature body, and the armature arm contacts the track with an interference fit. During launch, the high-current pulse causes excessively high temperatures at the armature-track contact surface, resulting in a liquefied metal layer and subsequent melting wear. Damage to the armature arm due to melting wear is particularly severe during launch. Excessive wear on the armature arm can disrupt the current flow between the armature and track, leading to contact failure and ultimately launch failure. Because the armature's movement involves various complex physical phenomena such as temperature rise, phase transition, arc discharge, and planing transition, calculating and predicting armature melting wear is extremely difficult. Currently, there are no suitable methods or tools to accurately calculate and predict the amount of armature melting wear.

[0037] Figure 2 This diagram illustrates heat transfer between the armature and rail contact surfaces. The rails of an electromagnetic rail launcher are typically arranged in a centrally symmetrical configuration, and the armature arms are also symmetrically positioned on the armature body. Figure 2The diagram only shows the contact state between one armature arm and the rail; the other armature arms are in the same condition. For example... Figure 2 As shown, during the launch process, the heat sources at the contact surface between armature 1 (armature arm) and track 2 are frictional heat and Joule heat. The heat at the contact surface between armature 1 and track 2 will first cause the temperature at the contact surface of armature to reach the melting point of the armature material, and armature 1 will begin to melt and wear. Then the remaining heat at the contact surface between armature 1 and track 2 will be divided into two parts. One part will be transferred to the interior of armature 1 to increase the latent heat of armature phase change, and the other part will be transferred to the interior of track 2.

[0038] To accurately assess armature melting wear, the inventors proposed a method for calculating armature melting wear. The method uses the armature melting wear rate w to evaluate armature melting wear. When calculating armature melting wear, the method comprehensively considers the frictional heat and Joule heat between the armature and rail, and uses a pulse shaping network to fit the excitation current, making the calculation of armature melting wear more consistent with the actual launch process and improving the accuracy of the calculation results.

[0039] The following is combined with Figure 3 The structural parameters of the armature are described. For example... Figure 3 As shown, the armature contacts the rail 2 via armature arm 1-1, and the armature arm 1-1 and rail 2 are in an interference fit. The dimension of armature arm 1-1 in the direction perpendicular to the armature-rail contact surface is defined as the thickness of the armature arm. The end of armature arm 1-1 closer to the armature body 1-2 is the head of armature arm 1-1, and the end of armature arm 1-1 farther from the armature body 1-2 is the tail of armature arm 1-1. The thickness of armature arm 1-1 gradually decreases from its head to its tail, and the thickness of the tail of armature arm 1-1 is denoted as d0. The dimension of the contact surface between armature arm 1-1 and rail 2 along the extension direction of rail 2 is denoted as d1. Armature arm 1-1 is in contact with track 2. The surface of armature arm 1-1 in contact with track 2 is defined as the outer surface of armature arm 1-1, and the opposite side of armature arm 1-1 is defined as the inner surface of armature arm 1-1. The angle between the inner surface of armature arm 1-1 and track 2 is defined as the inclination angle θ of the armature arm. Armature arm 1-1 is arranged in a centrally symmetrical manner, and track 2 is also arranged in a correspondingly centrally symmetrical manner. The distance between the two opposite tracks is defined as X. The dimension of armature body 1-2 in the direction perpendicular to the armature-track contact surface is defined as the height of the projectile loading area, denoted as h. The cross-sectional shape of track 2 is rectangular. The width of the track cross-section (rectangle) is denoted as a, and the length of the track cross-section (rectangle) is denoted as b (not shown in the figure).

[0040] The power supply of an electromagnetic rail launcher consists of capacitors. During launch, the current released is transient, generating transient contact pressure. This transient contact pressure determines the contact resistance, which in turn affects the contact pressure—a mutually coupled process. Armature melting wear is closely related to contact pressure, contact resistance, and excitation current, making the calculation of the melting wear rate extremely difficult. The inventors discovered that calculating armature melting wear based on fixed excitation current, contact resistance, and contact pressure does not accurately reflect the actual situation of armature launch and results in significant errors.

[0041] Therefore, when calculating the melting wear of the armature of an electromagnetic rail launcher based on the heat distribution of the contact surface, the method of the present invention uses a pulse shaping network to fit the excitation current, and calculates the frictional heat and Joule heat between the armature and the rail based on the excitation current obtained by the fitting formula. Since the frictional heat and Joule heat between the armature and the rail are calculated using a transient excitation current, the changing current produces a changing contact resistance and can reflect the changes in contact pressure and acceleration, which is more in line with the actual launch process, and the calculation of melting wear is more accurate.

[0042] The following is combined with Figure 4 The method of the present invention will be described below. For example... Figure 4 As shown, the steps of the calculation method for armature melting wear of the electromagnetic track launcher of the present invention are as follows:

[0043] S1. Calculate the excitation current I(t) using the excitation current fitting formula; the excitation current fitting formula is: I(t) = p1t 7 +p2t 6 +p3t 5 +p4t 4 +p5t 3 +p6t 2 +p7t+p8, where p1, p2, p3, p4, p5, p6, p7, and p8 are fitting coefficients;

[0044] S2, Calculate the frictional heat Q between the pivot rails. f Joule heating Q between the pivot and the rail j This invention uses a formula Calculate the frictional heat Q between the pivot rails f Through formula Q j =I 2 (t)R0(t) calculates the Joule heat Q between the pivots. j μ in the formula m Let t be the coefficient of sliding friction between the armature and the track, v be the velocity of the armature, L' be the inductance gradient of the track, and R0(t) be the contact resistance between the armature and the track.

[0045] S3. Calculate the heat transferred to the orbit. T in the formula ma T0 is the melting point of the armature material, T0 is the initial temperature of the armature-rail contact surface, and k is the melting point of the armature material. r ρ is the thermal conductivity of the orbital material. r For the density of the orbital material, c r The specific heat capacity of the track material;

[0046] S4. Excitation current I(t) and frictional heat Q between the pivot and rail obtained based on the aforementioned steps. f Joule heating Q between pivots j and the heat Q transferred to the orbit r Calculate the armature melting wear rate w:

[0047] ρ in the formula a c is the density of the armature material. a h is the specific heat capacity of the armature material. a It is the latent heat of fusion of the armature material.

[0048] After obtaining the armature melting wear rate w, the armature melting wear volume V can be further calculated based on the armature melting wear rate. The armature melting wear volume V is the volume of the armature that melts away during the firing process.

[0049] There is no requirement for the execution order of steps S2 and S3 in the method of the present invention. Calculating frictional heat, Joule heat or heat transferred to the track first will not affect the final calculation of the melting wear rate.

[0050] Optionally, the present invention uses the following formula to calculate the armature speed v: In the formula, m is the mass of the armature. The inductance gradient L' of the track can be calculated using the analytical algorithm for the high-frequency inductance gradient from Kerrisk's "Science and Technology of Electromagnetic Railguns".

[0051] In high-speed, high-current sliding electrical contacts, the contact pressure and contact type between the armature and rails change continuously with the changes in the armature's sliding and melting states, resulting in dynamic changes in contact resistance. To accurately reflect the melting wear of the armature, the contact resistance R0(t) between the armature and rails can be calculated using the following formula:

[0052] In the formula F is the average resistivity of the armature-rail contact surface, H is the hardness of the armature-rail contact surface, and C and z are material constants, which are determined based on the materials of the armature and rail. For example, when the armature material is aluminum and the rail material is copper, under pulsed high current, C = 1.0 and z = 0.59 are generally taken. n(t) represents the component of the electromagnetic force acting on the armature arm in the direction perpendicular to the contact surface of the armature rail.

[0053] like Figure 5 As shown, when the armature is mounted on rail 2, the armature arm 1-1 will be subjected to mechanical pressure provided by the interference fit between the armature arm 1-1 and rail 2, F g (t) represents the mechanical pressure provided by the interference fit between armature arm 1-1 and track 2 at initial contact; during launch, the armature arm is also subjected to electromagnetic force, and the electromagnetic force on the armature arm at time t is F. EM (t), F EM (t) can be decomposed into a component force in the armature firing direction and a component force perpendicular to the armature rail contact surface, F EM The component of force (t) in the armature firing direction is F. t (t), F EM (t) The component of the force perpendicular to the contact surface of the pivot rail is F. n (t). Furthermore,

[0054] If a constant current is used as the excitation source when calculating armature melting wear, it does not reflect the actual situation of the armature firing process, resulting in a large error in the calculated armature wear rate. The method of this invention calculates the excitation current using an excitation current fitting formula, where the excitation current is a transient value. The excitation current fitting formula is obtained by building a pulse shaping network using simulation software. In this embodiment, Maxwell Circuit Editor is used to build the pulse shaping network to generate the excitation current. Figure 6 The circuit topology diagram of the constructed pulse shaping network is shown below. Figure 6 In this diagram, C represents the energy storage unit, T represents the discharge switch, and R represents the discharge unit. C and L C These represent the internal resistance and stray inductance of the capacitor branch, respectively; R0 and L0 represent the load resistance and load inductance, respectively; R D and L D These are the stray resistance and stray inductance of the freewheeling branch, respectively. The parameters of each component in the equivalent circuit model of the electromagnetic rail launcher are set in the simulation software. In this embodiment, the simulation parameters are as follows: C = 40uF, 2kV, R... c =6uΩ, L c =2nH,R D =3mΩ, L D =2uH.

[0055] The simulation curve of the excitation current changing with time is as follows: Figure 7 As shown, from Figure 7It can be seen that the excitation current rises rapidly within 0–0.45 ms, increasing to approximately 650 kA before rapidly decreasing, reaching 67 kA at t = 2 ms. Using the polynomial function in the cftool module of MATLAB, the excitation current is fitted based on the time-varying data, resulting in the following formula: I(t) = p1t 7 +p2t 6 +p3t 5 +p4t 4 +p5t 3 +p6t 2 +p7t+p8, the fitting coefficients of this embodiment are p1=-622.8, p2=4643, p3=-13490, p4=18570, p5=-10560, p6=-973.1, p7=2774, p8=-1.898.

[0056] To verify the correctness of the method of the present invention, the armature melting wear volume calculated based on the armature melting wear rate calculated by the method of the present invention was compared with the armature arm loss measured by experimental means. The dimensional parameters of the electromagnetic rail launcher are shown in Table 1. The armature material of the electromagnetic rail launcher is aluminum, the rail material is copper, and the parameters related to the armature and rail materials of the electromagnetic rail launcher are shown in Table 2. The armature mass m is 0.134 kg.

[0057] Table 1 Dimensional parameters of the electromagnetic rail launcher

[0058]

[0059] Table 2 Material Parameters of Electromagnetic Orbiter Launchers

[0060]

[0061] The melting wear rate w of a single armature calculated by the method of this invention is as follows: Figure 8 As shown, the melting wear rate varies with time, and the wear volume of a single armature calculated based on the melting wear rate w is 633 mm. 3 The experimentally measured loss of a single armature arm was 657 mm. 3 The armature melting wear volume calculated by the method of this invention is smaller than the loss of a single armature arm measured experimentally. This is because during launch, the wear of the armature arm includes not only melting wear but also mechanical wear, planing wear, and wear caused by transition. Therefore, the wear measured experimentally actually includes wear caused by factors other than melting wear. However, the armature melting wear calculated by the method of this invention does not include wear caused by these factors, and can more intuitively reflect the wear caused by armature melting, with higher accuracy, providing better support for the design of armature structures.

[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for calculating armature melting wear of an electromagnetic rail launcher, the electromagnetic rail launcher comprising a rail and an armature movable along the rail, the armature comprising an armature body and an armature arm connected to the armature body, the armature arm being in contact with the rail; characterized in that, Includes the following steps: S1. Calculate the excitation current I(t) using the excitation current fitting formula. The excitation current fitting formula is: I(t) = p1t 7 +p2t 6 +p3t 5 +p4t 4 +p5t 3 +p6t 2 +p7t+p8, where p1, p2, p3, p4, p5, p6, p7 and p8 are the fitting coefficients; S2, Calculate the frictional heat Q between the pivot rails. f Joule heating Q between the pivot and the rail j : Q j =I 2 (t)R0(t), μ in the formula m Let be the coefficient of sliding friction between the armature and the track, v be the velocity of the armature, L' be the inductance gradient of the track, d1 be the dimension of the contact surface between the armature arm and the track along the extension direction of the track, θ be the inclination angle of the armature arm, X be the distance between the two opposing tracks, and R0(t) be the contact resistance between the armature and the track. S3. Calculate the heat Q transferred to the orbit. r : In the formula, 'a' represents the width of the track cross section, and 'T' represents the width of the track cross section. ma T0 is the melting point of the armature material, T0 is the initial temperature of the armature-rail contact surface, and k is the melting point of the armature material. r ρ is the thermal conductivity of the orbital material. r For the density of the orbital material, c r The specific heat capacity of the track material; S4, Based on the obtained frictional heat Q between the pivot rails f Joule heating Q between pivots j and the heat Q transferred to the orbit r Calculate the armature melting wear rate w: ρ in the formula a c is the density of the armature material. a h is the specific heat capacity of the armature material. a It is the latent heat of fusion of the armature material.

2. The method for calculating armature melting wear of an electromagnetic rail launcher as described in claim 1, characterized in that: Calculate the armature's melt wear volume V based on the armature's melt wear rate w:

3. The method for calculating armature melting wear of an electromagnetic rail launcher as described in claim 1, characterized in that: The contact resistance R0(t) between the pivot rails is calculated using the following formula: In the formula Let H be the average resistivity of the pivot rail contact surface, H be the hardness of the pivot rail contact surface, C and z be material constants, and F be the average resistivity of the pivot rail contact surface. n (t) represents the component of the electromagnetic force acting on the armature arm in the direction perpendicular to the contact surface of the armature rail.

4. The method for calculating armature melting wear of an electromagnetic track launcher as described in claim 3, characterized in that: The component of the electromagnetic force acting on the armature arm in the direction perpendicular to the contact surface of the armature rail.

5. The method for calculating armature melting wear of an electromagnetic rail launcher as described in claim 1, characterized in that: The armature velocity v is calculated using the following formula: In the formula, m is the mass of the armature.

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