CN107832509B - Method for designing parameters of micro-planar electric ignition assembly under design of safe current - Google Patents

Method for designing parameters of micro-planar electric ignition assembly under design of safe current Download PDF

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CN107832509B
CN107832509B CN201711030104.7A CN201711030104A CN107832509B CN 107832509 B CN107832509 B CN 107832509B CN 201711030104 A CN201711030104 A CN 201711030104A CN 107832509 B CN107832509 B CN 107832509B
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ignition
micro
current
temperature
formula
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CN107832509A (en
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焦清介
杨贵丽
纪冲
钟明寿
李兴华
刘健峰
余洋
周游
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Beijing Institute of Technology BIT
Army Engineering University of PLA
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Army Engineering University of PLA
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Abstract

The invention discloses a method for designing parameters of a micro-planar electric ignition component under the condition of designing safe current, which comprises the following steps: constructing a physical model; constructing a mathematical model; solving a theoretical calculation formula of the critical ignition current of the micro-plane type electric ignition assembly; carrying out an ignition current sensitivity experiment on a plurality of micro-planar electric ignition components with the same structures as those of the micro-planar electric ignition components to be designed, comparing experimental data with a calculation result, and verifying whether the model is feasible or not; and correcting the theoretical calculation formula to obtain the theoretical calculation formula of the safety current of the micro-plane type electric ignition assembly, inputting the design parameters of the micro-plane type electric ignition assembly, calculating to obtain the safety current of the micro-plane type electric ignition assembly and reversely solving the design parameters. The invention has the advantages of less required experimental samples and times, low experimental cost and time consumption and accurate parameter design.

Description

Method for designing parameters of micro-planar electric ignition assembly under design of safe current
Technical Field
The invention relates to the technical field of design of electric initiating explosive devices, in particular to a method for designing parameters of a micro-planar electric ignition component under the condition of designing safe current.
Background
The micro-plane type electric ignition component is an electric ignition device in an electric initiating explosive device. The micro-plane type electric ignition component consists of a micro-plane energy conversion element and an ignition agent. The structure of the micro-plane transducer element is shown in figures 1-3, the micro-plane transducer element is composed of a metal bridge membrane (2), a bonding pad (1) and a substrate (3), common bridge membrane materials are chromium, platinum tungsten or nickel-chromium alloy, the bridge membrane area is square, the side length is expressed by l, the side length is generally 0.05mm-0.3mm, and the thickness is 0.3μm-1.5μm. The matrix is a cube, the height is represented by H, the bottom side length is represented by L, the bottom side length is 2.5mm-3mm, and the height is 0.3mm-0.5 mm. Calculated, the side length of the matrix is 8-60 times of that of the bridge membrane area, and the area of the bridge membrane area is 0.0025mm2-0.09mm2The area of the substrate is 6.25mm2-9mm2The area of the matrix is 69-3600 times of that of the bridge membrane area, and the side length of the matrix is 5-10 times of the height.
The micro-plane type electric ignition component consists of a micro-plane energy conversion element and an ignition agent, and the structure is shown in figure 4. The ignition agent (5) is arranged in the ceramic ring (4), the charge can be porous copper nitride or porous silver nitride and other initiating explosive, the diameter of the charge is expressed by R, and is generally 1.5mm-2mm, and the height is 0.5mm-1 mm. The charge diameter was estimated to be comparable to the height.
The energy loading modes of the micro-plane type electric ignition assembly are two, namely constant current excitation and capacitance discharge excitation. When the constant current excitation is carried out, the micro-plane energy conversion element converts electric energy into joule heat, the temperature of the bridge diaphragm is increased, meanwhile, the energy is transferred to the square base body, the bonding pad and the primer in a heat conduction mode, the temperature of the base body, the bonding pad and the primer is increased, when the joule heat generated by the energy conversion element is equal to the dissipated heat, the temperature of the primer is kept unchanged, and a steady-state heat transfer stage is carried out. The temperature rise process of the bridge film is shown in FIG. 5 when the steady-state temperature T is reachedlWhen the current is just equal to the ignition point of the medicament, the corresponding current is the critical ignition current of the micro-planar electric ignition component, which is also called as the theoretical maximum safetyThe current is applied.
Safe current is an important performance parameter of a micro-planar electrical ignition assembly. At present, the design of the safety current of the micro-plane type electric ignition component mostly adopts an experimental method. The general steps are that parameters of the existing product are changed on the basis of existing experimental data, samples with various specifications are prepared, and the micro-planar electric ignition assembly meeting the technical requirements is obtained through an ignition experiment. The method is characterized by needing a large number of experimental samples and multiple experiments, and consuming the experimental cost and time.
Disclosure of Invention
The invention aims to provide a method for designing parameters of a micro-planar electric ignition component under a designed safe current, aiming at the defects of the prior art.
The technical scheme adopted by the invention is as follows.
The method for designing parameters of the micro-planar electric ignition component under the design of safe current comprises the following steps:
step 1: constructing a physical model of the micro-plane type electric ignition assembly during constant-current excitation;
step 2: constructing a mathematical model during constant current excitation according to the physical model;
and step 3: solving the mathematical model to obtain a theoretical calculation formula of the critical ignition current of the micro-planar electric ignition assembly;
and 4, step 4: carrying out an ignition current sensitivity experiment on a plurality of micro-planar electric ignition assemblies with the same structures as the micro-planar electric ignition assemblies to be designed, comparing experimental data with the critical ignition current of the micro-planar electric ignition assemblies with the structures calculated by adopting the formula in the step 3, and verifying whether the model is feasible or not; if the difference value between the theoretical calculation result of the critical ignition current and the experimental data is smaller than a given threshold value, outputting the model, otherwise, returning to the step 2, modifying the model parameters and reconstructing the mathematical model during constant current excitation;
and 5: according to the theoretical calculation formula of the critical ignition current of the micro-plane type electric ignition assembly output in the step 4, correcting the parameter which can reduce the critical ignition current in the formula into the parameter and the engineering deviation of the parameter, correcting other parameters in the formula into the parameter and subtracting the engineering deviation of the parameter to obtain the theoretical calculation formula of the safe current of the micro-plane type electric ignition assembly, and inputting the design parameter of the micro-plane type electric ignition assembly to obtain the safe current of the micro-plane type electric ignition assembly;
step 6: calculating the difference value between the safety current and the designed safety current, and if the difference between the safety current and the designed safety current is smaller than a given threshold value, outputting the design parameters of the micro-planar electric ignition assembly, and ending the process; otherwise, returning to the step 5.
As a preferred technical scheme, in the step 1, the micro-plane type electric ignition assembly consists of a micro-plane energy conversion element, an ignition chemical and a ceramic ring, wherein the micro-plane energy conversion element consists of a base body, a bridge membrane and a bonding pad from bottom to top, the ceramic ring is arranged on the base body, and the ignition chemical is filled in the ceramic ring; under the condition of constant direct current excitation, the micro-plane energy conversion element converts electric energy into joule heat, the temperature of a bridge membrane is raised, the energy is transferred to the ignition medicament and the matrix in a heat conduction mode, the ignition medicament and the matrix dissipate heat to the environment, when the joule heat generated by the ignition assembly is equal to the dissipated heat, the temperature of the ignition assembly is kept unchanged, a steady-state heat transfer stage is entered, and when the steady-state temperature of the ignition medicament is just equal to an ignition point, the corresponding current is critical ignition current.
As a preferred technical solution, in step 1, when establishing the physical model, in order to simplify the model, the following assumptions need to be made:
(1) the substrate is regarded as a cylinder with the same height as the substrate, and the square bridge membrane is regarded as a certain diameter r positioned at the center of the top surface of the substrate0The ignition agent is regarded as an equivalent hemisphere;
(2) because the height of the matrix is smaller than the transverse and longitudinal dimensions, the thermal resistance of the matrix in the thickness direction is smaller, the temperature gradient of the matrix in the thickness direction is neglected, only the transverse and longitudinal heat conduction is considered, and the matrix heat conduction can be regarded as a cylinder wall model;
(3) the bridge membrane is in good contact with both the base body and the ignition agent, and the contact thermal resistance between the bridge membrane and the base body is neglected, namely the contact position of the bridge membrane and the ignition agent is isothermal;
(4) the radiation heat dissipation of the ignition assembly to the environment and the convection heat exchange of the upper surface and the lower surface to the environment are ignored;
(5) the physical and chemical parameters of the ignition component do not change along with the temperature;
(6) neglecting the chemical reaction heat release of the ignition agent in the action process;
(7) only the radial heat transfer of the ignition agent is considered, and the heat transfer in other directions and the heat radiation are ignored;
(8) the heat conductivity coefficient of the energy conversion element is the comprehensive parameters of the matrix and the bridge membrane, wherein the matrix and the bridge membrane respectively account for a certain weight, the sum of the matrix and the bridge membrane is equal to 1, and the weight of the bridge membrane is not more than 10%.
As a preferred technical solution, in step 2, the constructed mathematical model mainly includes two parts, specifically as follows:
1) when the ignition assembly enters a steady state for heat conduction, the temperature does not change along with the time and keeps constant, a cylindrical coordinate system is established by taking the center of the bridge membrane as the origin of coordinates and the direction vertical to the bridge membrane as the z axis, as shown in FIG. 7, the temperature control differential equation and the solution condition of the energy conversion element are
Figure BDA0001447525190000031
In the combined formula, the first formula is a temperature control equation of the micro-plane type transducer element, the second formula is a boundary of the transducer element contacted with the primer, and the third formula is a boundary of the transducer element contacted with the environment, and belongs to a third class of boundary conditions.
2) Taking the center of the bridge membrane as the origin of coordinates, a spherical coordinate system is established, as shown in FIG. 8, and the charging temperature control equation and the definite conditions are
Figure BDA0001447525190000032
In this combined formula, the first formula is a temperature control equation of the ignition charge, and the second formula is an inner boundary condition of the ignition charge, Te=TmIndicating that the contact with the bridge film, the charging temperature and the matrix temperature are equal. The third formula is the boundary where the initiating agent is in contact with the environment, and belongs to the third class of boundary conditions.
In the above formula: t ism-transducer temperature (K); t ise-primer temperature (K); lambda [ alpha ]m-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]m=kλb+(1-k)λj,λbThermal conductivity of the bridge film (W/m/K), lambdaj-thermal conductivity of the substrate (W/m/K), K-the weight taken up by the bridge film heat transfer; lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); r-spatial variation of the transducer element and the propellant; i-excitation current (A); r is0-the equivalent radius of the bridge membrane (m),
Figure BDA0001447525190000041
l-square bridge membrane side length (m); a-equivalent Cylinder inner wall area (m)2),A=2πr0H; h-substrate height (m); l-length of the substrate (m); r ism∞-the equivalent radius (m) of the matrix,
Figure BDA0001447525190000042
R0initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element hmHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2);T0-ambient temperature (K); s-area of inner wall of equivalent hemisphere of primer agent (m)2),S=l2R-radius of charge (m) of the ignition agent ξ1,ξ2Respectively, representing the heat distribution coefficient, ξ12=1。
As a preferred technical solution, in step 3, the theoretical calculation formula of the critical ignition current is as follows:
Figure BDA0001447525190000043
in the above formula: i isec-a critical firing current (a); t ise0-the firing temperature (K) of the pyrotechnic agent;T0-ambient temperature (K); r0Initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element lambdam-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); l-square bridge membrane side length (m); h-substrate height (m); l-length of the substrate (m); h ismHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2) (ii) a R is the charging radius (m) of the ignition agent.
As a preferred technical scheme, when the model parameters are modified in the step 4 to reconstruct the mathematical model of the constant current excitation, the method comprises the steps of increasing or reducing the diameter r of the equivalent circular membrane0And/or increasing or decreasing the weight of the bridge membrane in the composite parameter.
Preferably, the parameter capable of reducing the critical firing current includes a resistance R of the transducer element0The parameters capable of improving the critical ignition current include the bridge membrane side length L, the height H and the length L of the matrix.
Preferably, the engineering deviation of the parameter is the standard deviation of the parameter of the sample used in the firing current sensitivity test in step 4.
As a preferred technical scheme, when an ignition current sensitivity experiment is carried out, the number of samples is not less than 20.
As a preferred technical scheme, the material of the bridge membrane is a metal thin film.
Preferably, the substrate is made of an insulating material, such as glass or ceramic.
Preferably, the initiating explosive is an initiating explosive and comprises lead Staphylofenate (LTNR) and lead azide (PbN)6) And copper azide.
The invention has the beneficial effects that: whether the safe current of the sample meets the requirements can be judged through theoretical calculation before the sample is prepared, then the parameters of the sample are continuously corrected, and parameters of the micro-planar electric ignition component under the designed safe current are obtained.
Drawings
Fig. 1 is a diagram of a micro-planar transducer cell.
Fig. 2 is a top view of a micro-planar transducer element.
Fig. 3 is a front view of a micro-planar transducer element.
Fig. 4 is a view showing the structure of the micro-plane ignition module.
FIG. 5 is a schematic diagram of the temperature rise of the bridge membrane during constant current excitation.
FIG. 6 is a flow chart of a method for designing parameters of a micro-planar electrical ignition module at a safe current.
FIG. 7 is a diagram of an equivalent geometric model of a substrate.
Figure 8 is a diagram of an equivalent geometric model of the charge.
FIG. 9 is a plot of critical firing current I versus bridge film length l for an LTNR firing element.
FIG. 10 is a graph of the critical firing current I of chromium bridge films with different charges as a function of the bridge film length l.
FIG. 11 is a graph of critical firing current I versus bridge film length l for firing assemblies constructed with different bridge films and LTNR.
FIG. 12 shows the critical firing current I and the transducer resistance R of firing elements formed by different bridge films and LTNR0The relationship between them.
Wherein: a bonding pad-1; a bridge membrane-2; a substrate-3; a ceramic ring-4; and (4) charging 5.
Detailed Description
The invention is further illustrated by the following figures and examples.
Example 1. The method for designing parameters of the micro-planar electric ignition component under the design of safe current is characterized by comprising the following steps of:
step 1: constructing a physical model of the micro-plane type electric ignition assembly during constant-current excitation;
step 2: constructing a mathematical model during constant current excitation according to the physical model;
and step 3: solving the mathematical model to obtain a theoretical calculation formula of the critical ignition current of the micro-planar electric ignition assembly;
and 4, step 4: carrying out an ignition current sensitivity experiment on a plurality of micro-planar electric ignition assemblies with the same structures as the micro-planar electric ignition assemblies to be designed, comparing experimental data with the critical ignition current of the micro-planar electric ignition assemblies with the structures calculated by adopting the formula in the step 3, and verifying whether the model is feasible or not; if the difference value between the theoretical calculation result of the critical ignition current and the experimental data is smaller than a given threshold value, outputting the model, otherwise, returning to the step 2, modifying the model parameters and reconstructing the mathematical model of constant current excitation;
and 5: according to the theoretical calculation formula of the critical ignition current of the micro-plane type electric ignition component output in the step 4, correcting the parameter capable of reducing the critical ignition current in the formula into the parameter plus the engineering deviation of the parameter, and correcting the parameter capable of improving the critical ignition current in the formula into the parameter minus the engineering deviation of the parameter, so as to obtain the theoretical calculation formula of the safe current of the micro-plane type electric ignition component, and input the design parameter of the micro-plane type electric ignition component, so as to obtain the safe current of the micro-plane type electric ignition component;
step 6: calculating the difference value between the safe current and the designed safe current, and if the difference value between the safe current and the designed safe current is smaller than a given threshold value, outputting the design parameters of the micro-plane type electric ignition assembly, and ending the process; otherwise, returning to the step 5.
In the step 1, the micro-plane type electric ignition assembly consists of a micro-plane energy conversion element, an ignition chemical and a ceramic ring, wherein the physical structure of the micro-plane energy conversion element consists of a base body, a bridge membrane and a bonding pad from bottom to top, the ceramic ring is arranged on the base body, and the ignition chemical is filled in the ceramic ring; under the condition of constant direct current excitation, the micro-plane energy conversion element converts electric energy into joule heat, the temperature of a bridge membrane is raised, meanwhile, the energy is transferred to the ignition medicament and the matrix in a heat conduction mode, the ignition medicament and the matrix dissipate heat to the environment, when the joule heat generated by the ignition assembly is equal to the dissipated heat, the temperature of the ignition assembly keeps unchanged, a steady-state heat transfer stage is started, and when the steady-state temperature of the ignition medicament is just equal to an ignition point, the corresponding current is critical ignition current.
In step 1, when a physical model is established, in order to simplify the model, the following assumptions are made:
(1) the substrate is regarded as a cylinder with the same height as the substrate, and the square bridge membrane is regarded as a certain diameter r positioned at the center of the top surface of the substrate0The ignition agent is regarded as an equivalent hemisphere;
(2) because the height of the matrix is smaller than the transverse and longitudinal dimensions, the thermal resistance of the matrix in the thickness direction is smaller, and the heat conduction of the matrix can be regarded as a cylinder wall model by neglecting the temperature gradient of the matrix in the thickness direction;
(3) the bridge membrane is in good contact with both the base body and the ignition agent, and the contact thermal resistance between the bridge membrane and the base body is neglected, namely the contact position of the bridge membrane and the ignition agent is isothermal;
(4) the radiation heat dissipation of the system to the environment and the convection heat exchange of the upper surface and the lower surface to the environment are neglected;
(5) the physical and chemical parameters of the ignition component do not change along with the temperature;
(6) neglecting the chemical reaction heat release of the ignition agent in the action process;
(7) only the radial heat transfer of the charge is considered, and the heat transfer in other directions and the heat radiation are ignored;
(8) the heat conductivity coefficient of the energy conversion element is the comprehensive parameters of the matrix and the bridge membrane, wherein the matrix and the bridge membrane respectively account for a certain weight, the sum of the matrix and the bridge membrane is equal to 1, and the weight of the bridge membrane is not more than 10%.
In step 2, the constructed mathematical model mainly comprises two parts, specifically as follows:
1) when the ignition assembly enters a steady state for heat conduction, the temperature does not change along with the time and keeps constant, a cylindrical coordinate system is established by taking the center of the bridge membrane as the origin of coordinates and the direction vertical to the bridge membrane as the z axis, as shown in FIG. 7, the temperature control differential equation and the solution condition of the energy conversion element are
Figure BDA0001447525190000071
In the combined formula, the first formula is a temperature control equation of the micro-plane type transducer element, the second formula is a boundary of the transducer element contacted with the primer, and the third formula is a boundary of the transducer element contacted with the environment, and belongs to a third class of boundary conditions.
2) Taking the center of the bridge membrane as the origin of coordinates, a spherical coordinate system is established, as shown in FIG. 8, and the charging temperature control equation and the definite conditions are
Figure BDA0001447525190000072
In this combined formula, the first formula is a temperature control equation of the ignition charge, and the second formula is an inner boundary condition of the ignition charge, Te=TmIndicating that the charge temperature and the matrix temperature were equal at the contact with the bridge membrane. The third formula is the boundary where the initiating agent is in contact with the environment, and belongs to the third class of boundary conditions.
In the above formula: t ism-transducer temperature (K); t ise-primer temperature (K); lambda [ alpha ]m-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]m=kλb+(1-k)λj,λbThermal conductivity of the bridge film (W/m/K), lambdaj-thermal conductivity of the substrate (W/m/K), K-the weight taken up by the bridge film heat transfer; lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); r-spatial variation of the transducer element and the propellant; i-excitation current (A); r is0-the equivalent radius of the bridge membrane (m),
Figure BDA0001447525190000073
l-square bridge membrane side length (m); a-equivalent Cylinder inner wall area (m)2),A=2πr0H; h-substrate height (m); l-length of the substrate (m); r ism∞-the equivalent radius (m) of the matrix,
Figure BDA0001447525190000074
R0initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element hmHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2);T0-RingAmbient temperature (K); s-area of inner wall of equivalent hemisphere of primer agent (m)2),S=l2R-radius of charge (m) of the ignition agent ξ1,ξ2Respectively, representing the heat distribution coefficient, ξ12=1。
In step 3, the theoretical calculation formula of the critical ignition current is as follows:
Figure BDA0001447525190000081
in the above formula: i isec-a critical firing current (a); t ise0-the firing temperature (K) of the pyrotechnic agent; t is0-ambient temperature (K); r0Initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element lambdam-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); l-square bridge membrane side length (m); h-substrate height (m); l-length of the substrate (m); h ismHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2) (ii) a R is the charging radius (m) of the ignition agent.
In step 4, when the model parameters are modified to reconstruct the mathematical model of the constant current excitation, the diameter r of the equivalent circular membrane is increased or reduced0And/or increasing or decreasing the weight k of the bridge membrane in the composite parameter.
The parameter capable of reducing critical ignition current comprises a transducer resistor R0The parameters capable of improving the critical ignition current include the bridge membrane side length L, the height H and the length L of the matrix.
The engineering deviation of the parameter is the standard deviation of the parameter of the sample used in the firing current sensitivity test in step 4.
When an ignition current sensitivity experiment is carried out, the number of samples is not less than 20.
The bridge membrane is made of a metal film, including chromium, platinum-tungsten, nickel-chromium alloy and the like.
The substrate is made of insulating materials, including glass, ceramic and the like.
The initiating explosive is a primary explosive and comprises lead stigmatisate, lead azide, copper azide and the like.
Example 2. The method for designing parameters of the micro-planar electric ignition component under the design of safe current comprises the following steps:
step 1: and constructing a physical model of the micro-plane type electric ignition assembly during constant-current excitation.
Step 2: and constructing a mathematical model during constant current excitation according to the physical model.
And step 3: and solving the mathematical model to obtain a theoretical calculation formula of the critical ignition current of the micro-planar electric ignition assembly.
And 4, step 4: carrying out an ignition current sensitivity experiment on a plurality of micro-planar electric ignition assemblies with the same structures as the micro-planar electric ignition assemblies to be designed, comparing experimental data with the critical ignition current of the micro-planar electric ignition assemblies with the structures calculated by adopting the formula in the step 3, and verifying whether the model is feasible or not; and if the difference value between the theoretical calculation result of the critical ignition current and the experimental data is smaller than a given threshold value, outputting the model, otherwise, returning to the step 2, modifying the model parameters and reconstructing the mathematical model of constant current excitation.
And 5: according to the theoretical calculation formula of the critical ignition current of the micro-plane type electric ignition component output in the step 4, correcting the parameter capable of reducing the critical ignition current in the formula into the parameter plus the engineering deviation of the parameter, correcting the parameter capable of improving the critical ignition current in the formula into the parameter minus the engineering deviation of the parameter, obtaining the theoretical calculation formula of the safe current of the micro-plane type electric ignition component, inputting the design parameter of the micro-plane type electric ignition component, and obtaining the safe current of the micro-plane type electric ignition component.
Step 6: calculating the difference value between the safety current and the designed safety current, and if the difference between the safety current and the designed safety current is smaller than a given threshold value, outputting the design parameters of the micro-planar electric ignition assembly, and ending the process; otherwise, returning to the step 5.
As a preferred technical scheme, in the step 1, the micro-plane type electric ignition assembly consists of a micro-plane energy conversion element, an ignition chemical and a ceramic ring, wherein the micro-plane energy conversion element consists of a base body, a bridge membrane and a bonding pad from bottom to top, the ceramic ring is arranged on the base body, and the ignition chemical is filled in the ceramic ring; under the condition of constant direct current excitation, the micro-plane energy conversion element converts electric energy into joule heat, the temperature of a bridge membrane is raised, the energy is transferred to the ignition medicament and the matrix in a heat conduction mode, the ignition medicament and the matrix dissipate heat to the environment, when the joule heat generated by the ignition assembly is equal to the dissipated heat, the temperature of the ignition assembly is kept unchanged, a steady-state heat transfer stage is entered, and when the steady-state temperature of the ignition medicament is just equal to an ignition point, the corresponding current is critical ignition current.
A physical model.
During constant-current excitation, an ignition model is established for the ignition assembly so as to obtain the relation between the temperature and the excitation current when the ignition member enters the steady-state heat transfer, and further obtain the critical ignition current of the ignition assembly.
When constant current is introduced, part of joule heat generated by the micro-plane energy conversion element is transferred to the charge, and the other part of joule heat is transferred to the matrix. Because the height of the matrix is smaller than the transverse and longitudinal dimensions, the thermal resistance of the matrix in the thickness direction is smaller, and the thermal conductivity of the matrix can be regarded as a cylinder wall model by neglecting the temperature gradient of the matrix in the thickness direction, as shown in fig. 7.
For cylindrical charges, due to the fact that the height and the diameter of the charges are equivalent, heat is transmitted along the axial direction and the radial direction, the temperature distribution is point-symmetric, and therefore a hemispherical charge is selected as a research object, as shown in fig. 8.
For model simplification, the following assumptions are also made:
(1) the square bridge membrane is regarded as a certain diameter r positioned in the center of the top surface of the substrate0The equivalent circular membrane of (a);
(2) the bridge membrane is in good contact with both the base body and the ignition agent, and the contact thermal resistance between the bridge membrane and the base body is neglected, namely the contact position of the bridge membrane and the ignition agent is isothermal;
(3) the radiation heat dissipation of the system to the environment and the convection heat exchange of the upper surface and the lower surface to the environment are neglected;
(4) the physical and chemical parameters of the ignition component do not change along with the temperature;
(5) neglecting the chemical reaction heat release of the ignition agent in the action process;
(6) only the radial heat transfer of the ignition agent is considered, and the heat transfer in other directions and the heat radiation are ignored;
(7) the heat conductivity coefficient of the energy conversion element is the comprehensive parameters of the matrix and the bridge membrane, wherein the matrix and the bridge membrane respectively account for a certain weight, the sum of the matrix and the bridge membrane is equal to 1, and the weight of the bridge membrane is not more than 10%.
A mathematical model.
When the ignition assembly enters a steady state for heat conduction, the temperature does not change along with time and keeps constant, a cylindrical coordinate system is established by taking the center of the bridge membrane as the origin of coordinates and the direction perpendicular to the bridge membrane as the z axis, and as shown in fig. 7, the temperature control differential equation and the solution conditions of the energy conversion element are as follows:
Figure BDA0001447525190000101
and (3) establishing a spherical coordinate system by taking the center of the bridge membrane as the origin of coordinates, wherein as shown in figure 8, the charging temperature control equation and the fixed solution conditions are as follows:
Figure BDA0001447525190000102
in the above formula: t ism-transducer temperature (K); t ise-primer temperature (K); lambda [ alpha ]m-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]m=kλb+(1-k)λj,λbThermal conductivity of the bridge film (W/m/K), lambdaj-thermal conductivity of the substrate (W/m/K), K-the weight taken up by the bridge film heat transfer; lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); r-spatial variation of the transducer element and the propellant; i-excitation current (A); r is0-the equivalent radius of the bridge membrane (m),
Figure BDA0001447525190000103
l-square bridge membrane side length (m); a-equivalent Cylinder inner wall area (m)2),A=2πr0H; h-substrate height (m); l-length of the substrate (m); r ism∞-the equivalent radius (m) of the matrix,
Figure BDA0001447525190000104
R0initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element hmHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2);T0-ambient temperature (K); s-area of inner wall of equivalent hemisphere of primer agent (m)2),S=l2R-radius of charge (m) of the ignition agent ξ1,ξ2Respectively, representing the heat distribution coefficient, ξ12=1。Te=TmIndicating that the charge temperature and the matrix temperature were equal at the contact with the bridge membrane.
The above equation set is a second-order homogeneous linear differential equation, and the analytic solution can be directly solved.
And (6) theoretical solution.
To solve for convenience, let θm=Tm(r)-T0,θe=Te(r)-T0Respectively solving the combination formula (1) and the combination formula (2) to obtain
Figure BDA0001447525190000111
Figure BDA0001447525190000112
When r is r0When theta is greater than thetam(r0)=θe(r0)=θ0Respectively converting the formula (3) and the formula (4) to obtain
Figure BDA0001447525190000113
Figure BDA0001447525190000114
According to ξ12When the value is 1, it can be obtained
Figure BDA0001447525190000115
Further transformed into
Figure BDA0001447525190000116
Suppose the ignition point of the ignition member is Te0Then thetae0=Te0-T0Then, the corresponding critical firing current is:
Figure BDA0001447525190000117
make A2 pi r0H,
Figure BDA0001447525190000118
S=l2Substituting into the formula (9) to obtain the critical ignition current of the ignition component as follows:
Figure BDA0001447525190000121
as can be seen from the analysis formula (10), the critical firing current of the micro-planar firing member is related to the thermal conductivity of the charge and the matrix, the thickness of the charge and the size of the matrix, in addition to the bridge resistance and the size. The critical firing current is inversely proportional to the square root of the transducer's initial resistance. When the exciting current is smaller than the critical ignition current, the micro-plane ignition piece does not ignite and is in a safe state.
(1) Law of influence of matrix material on critical ignition current
Taking the case of a firing element composed of a chromium bridge film and LTNR as an example, the bridge film initial resistance was 1 Ω. The side length of the matrix is 2.5mm, the charging diameter is 2mm, and the physicochemical parameters of the material are shown in tables 1-3. The parameters are substituted into the formula (10) for calculation, and the relationship between the critical ignition current and the size of the bridge film of the ignition piece consisting of the chromium bridge film and the LTNR of different base materials is shown in FIG. 9.
TABLE 1 basic parameters of the bridge film materials
Figure BDA0001447525190000122
TABLE 2 basic parameters of the base materials
Figure BDA0001447525190000123
TABLE 3 basic parameters of the pyrotechnic compositions
Figure BDA0001447525190000124
(2) Law of influence of charging on critical ignition current
Taking an ignition piece consisting of a chromium bridge film and different charges as an example, the initial resistance of the transduction element is 1 omega, the side length of the ceramic matrix is 2.5mm, and the diameter of the charges is 2 mm. The relationship between the critical firing current and the size of the bridge film of the firing member composed of the chromium bridge film and different charges of the ceramic matrix is calculated as shown in fig. 10.
(3) Law of influence of bridge film material on critical ignition current
Taking the ignition element composed of LTNR as an example, the initial resistance of the bridge film is 1 Ω. The ceramic matrix side length is 2.5mm, the charging diameter is 2mm, and the relationship between the critical ignition current and the bridge diaphragm size of the ignition piece consisting of different bridge diaphragms and LTNR is calculated as shown in FIG. 11.
(4) Law of influence of bridge film resistance on critical ignition current
Taking the ignition part composed of LTNR as an example, the ceramic substrate side length is 2.5mm, the charging diameter is 2mm, and the relationship between the critical ignition current and the resistance of the ignition part composed of different bridge membranes and LTNR is calculated and shown in FIG. 12.
The engineering deviation of the parameter is the standard deviation of the parameter of the sample used in the firing current sensitivity test in step 4.
When an ignition current sensitivity experiment is carried out, the number of samples is not less than 20.
The bridge membrane is made of a metal film and comprises nickel-chromium alloy, chromium or platinum-tungsten.
The substrate is made of insulating materials, including glass, ceramic and the like.
The initiating explosive is a primary explosive and comprises lead stigmatisate, lead azide, copper azide and the like.
Example 3. This embodiment is different from embodiment 1 in that: and 6, designing parameters of the ignition assembly, and outputting safe current meeting the requirements, wherein the parameters comprise the size parameters of the bridge membrane, the size parameters of the base body and the type of the ignition agent.
It is required to design an ignition module with a safe current not lower than 240 mA. Firstly, selecting a transduction element bridge film material as chromium, a substrate material as Pyrex7740 glass, and a fire-generating agent as lead stalactite; secondly, designing bridge membranes with different sizes and resistances, designing the side length of a base body to be 1mm, the height to be 0.5mm, the designed charging diameter to be 1mm, assuming that the engineering tolerance of the energy conversion element is 5%, substituting pre-designed parameters and physicochemical parameters of selected materials into a critical ignition current calculation formula, and calculating the critical ignition current and the safety current of the ignition assembly to be shown in table 4 when the bridge membranes are different in size and resistance. The 1#, 2#, 3#, and 4# products theoretically meet the requirements, in order to guarantee a certain degree of advance and guarantee other performance indexes (full ignition voltage) of the ignition assembly, a 3# product preparation sample is selected, samples are prepared according to the parameters, the critical ignition current of the ignition assembly of the specification is 0.398A and the safe current is 0.335A through tests, the deviation between the theoretical calculation result of the critical ignition current and the safe current and the test result is 1.5% and 2.1% respectively, and the deviation is less than 10%, so that the critical ignition current calculation formula has theoretical guiding significance for the design of the micro-plane ignition assembly, and the design method is feasible.
TABLE 4 theoretical calculation values of critical ignition current and safe current of chromium bridge membranes with different sizes
Figure BDA0001447525190000141
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. The method for designing parameters of the micro-planar electric ignition component under the design of safe current is characterized by comprising the following steps of:
step 1: constructing a physical model of the micro-plane type electric ignition component during constant direct current excitation;
step 2: constructing a mathematical model during constant direct current excitation according to the physical model;
and step 3: solving the mathematical model to obtain a theoretical calculation formula of the critical ignition current of the micro-planar electric ignition assembly;
and 4, step 4: carrying out an ignition current sensitivity experiment on a plurality of micro-planar electric ignition assemblies with the same structures as the micro-planar electric ignition assemblies to be designed, comparing experimental data with the critical ignition current of the micro-planar electric ignition assemblies with the structures calculated by adopting the formula in the step 3, and verifying whether the model is feasible or not; if the difference value between the theoretical calculation result of the critical ignition current and the experimental data is smaller than a given threshold value, outputting the model, otherwise, returning to the step 2, modifying the model parameters and reconstructing the constant direct current excitation physical model;
and 5: according to the theoretical calculation formula of the critical ignition current of the micro-plane type electric ignition component output in the step 4, correcting the parameter which can reduce the critical ignition current in the formula into the parameter and the engineering deviation of the parameter, correcting other parameters in the formula into the parameter and subtracting the engineering deviation of the parameter to obtain the theoretical calculation formula of the safe current of the micro-plane type electric ignition component, inputting the design parameter of the micro-plane type electric ignition component, and calculating to obtain the safe current of the micro-plane type electric ignition component;
step 6: calculating the difference value between the safety current and the designed safety current, and if the difference between the safety current and the designed safety current is smaller than a given threshold value, outputting the design parameters of the micro-planar electric ignition assembly, and ending the process; otherwise, returning to the step 5;
in the step 1, the micro-plane type electric ignition assembly consists of a micro-plane energy conversion element, an ignition chemical and a ceramic ring, wherein the micro-plane energy conversion element consists of a base body, a bridge membrane and a bonding pad from bottom to top, the ceramic ring is arranged on the base body, and the ignition chemical is filled in the ceramic ring; under the condition of constant direct current excitation, the micro-plane energy conversion element converts electric energy into joule heat, the temperature of a bridge membrane is raised, meanwhile, the energy is transferred to the ignition medicament and the matrix in a heat conduction mode, the ignition medicament and the matrix dissipate heat to the environment, when the joule heat generated by the ignition assembly is equal to the dissipated heat, the temperature of the ignition assembly is kept unchanged, a steady-state heat transfer stage is entered, and when the steady-state temperature of the ignition medicament is just equal to an ignition point, the corresponding current is critical ignition current;
in step 1, when a physical model is established, in order to simplify the model, the following assumptions are made:
(1) the substrate is regarded as a cylinder with the same height as the substrate, and the square bridge membrane is regarded as a certain diameter r positioned at the center of the top surface of the substrate0The ignition agent is regarded as an equivalent hemisphere;
(2) because the height of the matrix is smaller than the transverse and longitudinal dimensions, the thermal resistance of the matrix in the thickness direction is smaller, and the heat conduction of the matrix can be regarded as a cylinder wall model by neglecting the temperature gradient of the matrix in the thickness direction;
(3) the bridge membrane is in good contact with both the base body and the ignition agent, and the contact thermal resistance between the bridge membrane and the base body is neglected, namely the contact position of the bridge membrane and the ignition agent is isothermal;
(4) the radiation heat dissipation of the system to the environment and the convection heat exchange of the upper surface and the lower surface to the environment are neglected;
(5) the physical and chemical parameters of the ignition component do not change along with the temperature;
(6) neglecting the chemical reaction heat release of the ignition agent in the action process;
(7) only the radial heat transfer of the charge is considered, and the heat transfer in other directions and the heat radiation are ignored;
(8) the heat conductivity coefficient of the energy conversion element is the comprehensive parameters of the matrix and the bridge membrane, wherein the matrix and the bridge membrane respectively account for a certain weight, the sum of the matrix and the bridge membrane is equal to 1, and the weight of the bridge membrane is not more than 10%;
in step 2, the constructed mathematical model mainly comprises two parts, specifically as follows:
1) when the ignition assembly enters into steady state heat conduction, the temperature does not change along with the time and keeps constant, and the temperature control equation and the definite solution condition of the energy conversion element are
Figure FDA0002627601150000021
In the combined formula, the first formula is a temperature control equation of the micro-plane type transducer element, the second formula is a boundary of the transducer element contacted with the primer, and the third formula is a boundary of the transducer element contacted with the environment, and belongs to a third class of boundary conditions;
2) the charging temperature control equation and the definite solution condition are
Figure FDA0002627601150000022
In this combined formula, the first formula is a temperature control equation of the ignition charge, and the second formula is an inner boundary condition of the ignition charge, Te=TmIndicating that the contact part with the bridge membrane has the same charging temperature and the same matrix temperature; the third formula is the boundary of the contact of the initiating explosive and the environment, and belongs to the third class of boundary conditions;
in the above formula: t ism-transducer temperature (K); t ise-primer temperature (K); lambda [ alpha ]m-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]m=kλb+(1-k)λj,λbThermal conductivity of the bridge film (W/m/K), lambdaj-thermal conductivity of the substrate (W/m/K), K-the weight taken up by the bridge film heat transfer; lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); r-spatial variation of the transducer element and the propellant; i-excitation current (A); r is0-the equivalent radius of the bridge membrane (m),
Figure FDA0002627601150000031
l-square bridge membrane side length (m); a-equivalent Cylinder inner wall area (m)2),A=2πr0H; h-substrate height (m); l-length of the substrate (m); r ism∞-the equivalent radius (m) of the matrix,
Figure FDA0002627601150000032
R0initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element hmHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2);T0-ambient temperature (K); s-area of inner wall of equivalent hemisphere of primer agent (m)2),S=l2R-radius of charge (m) of the ignition agent ξ1,ξ2Respectively, representing the heat distribution coefficient, ξ12=1;
In step 3, the theoretical calculation formula of the critical ignition current is as follows:
Figure FDA0002627601150000033
in the above formula: i isec-a critical firing current (a); t ise0-the firing temperature (K) of the pyrotechnic agent; t is0-ambient temperature (K); r0Initial resistance (omega) of transducer element α temperature coefficient of resistance (1/K) of transducer element lambdam-thermal conductivity of the transducer element (W/m/K); lambda [ alpha ]e-thermal conductivity of the pyrotechnic agent (W/m/K); l-square bridge membrane side length (m); h-substrate height (m); l-length of the substrate (m); h ismHeat transfer coefficient of the substrate to the environment (W/m)2);heHeat transfer coefficient (W/m) of the propellant to the environment2) (ii) a R is the charging radius (m) of the ignition agent.
2. The method for designing parameters of a micro-planar electric ignition module under a designed safety current as claimed in claim 1, wherein in step 4, the model parameters are modified to reconstruct the constant currentMathematical models of flow excitation, involving increasing or decreasing the diameter r of the equivalent circular membrane0And/or increasing or decreasing the weight of the bridge film heat transfer in the composite parameter.
3. The method for designing parameters of a micro-planar electric ignition module under a designed safe current as claimed in claim 1, wherein: the parameter capable of reducing critical ignition current comprises a transducer resistor R0The parameters capable of improving the critical ignition current include the bridge membrane side length L, the height H and the length L of the matrix.
4. The method for designing parameters of a micro-planar electric ignition module under a designed safe current as claimed in claim 1, wherein: the engineering deviation of the parameter is the standard deviation of the parameter of the sample used in the firing current sensitivity test in step 4.
5. The method for designing parameters of a micro-planar electric ignition module under a designed safe current as claimed in claim 1, wherein: when an ignition current sensitivity experiment is carried out, the number of samples is not less than 20.
6. The method for designing parameters of a micro-planar electric ignition module under a designed safe current as claimed in claim 1, wherein: the bridge membrane comprises one or more of nickel-chromium alloy, chromium and platinum-tungsten; the substrate is made of an insulating material.
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