Method for analyzing reliability of gunpowder igniter in low-temperature ignition failure mode

Abstract

The invention discloses a method for analyzing the reliability of a gunpowder igniter in a low-temperature ignition failure mode, which comprises the following steps of: firstly, carrying out characterization analysis on the ignition failure mode of the gunpowder igniter in a low-temperature environment, identifying main uncertain factors influencing the low-temperature ignition reliability by adopting a fault tree method (FTA), and determining the probability distribution characteristic of the main uncertain factors; then, an implicit performance function of the failure mode is established. In order to clarify a deterministic relationship between a performance parameter and a design variable, an inner ballistic simulation model for low-temperature ignition of a gunpowder igniter is constructed based on an inner ballistic theory, and a Kriging agent model is further established by using the simulation model. And finally, sampling and solving the Kriging model through an MCS method (Monte Carlo simulation) to obtain the failure probability and reliability of the low-temperature ignition failure mode of the gunpowder igniter. The reliability of the gunpowder igniter under the low-temperature condition can be accurately evaluated, and a theoretical basis is provided for product improvement design.

Description

Technical Field

[0001] This invention belongs to the field of aerospace and liquid rocket engine technology, and more specifically relates to a reliability analysis method for propellant igniters under cryogenic ignition failure modes. Background Technology

[0002] Liquid propellant igniters are a type of pyrotechnic ignition device. These liquid rocket engine ignition devices possess advantages such as extremely rapid response, high energy density, and high synchronization, and are therefore widely used in the separation systems of aerospace launch vehicles, ballistic missiles, air-to-air missiles, and underwater vehicles. However, this device also has insurmountable drawbacks: single-use, poor safety, and low reliability at low temperatures. Therefore, ensuring the reliability of propellant igniters is crucial.

[0003] Because liquid rocket engine propellant igniters typically employ multi-stage propellant transfer combustion to generate a high-temperature flame that enters the gas generator and ignites the mixture of liquid hydrogen and liquid oxygen propellants in the engine, their internal ignition sequence must possess high precision and timing consistency. Especially in extreme environments, where the device faces complex operating conditions and variable external loads, the risk of failure is increasingly prominent. If the propellant inside the igniter fails to burn as designed, it could lead to engine ignition failure, resulting in mission failure and significant economic and social losses.

[0004] In practical operation, the ignition sequence of a liquid rocket engine propellant igniter typically includes multiple stages, such as electric ignition, propellant combustion, propellant combustion, gas pressure build-up, and finally, the output of a high-temperature flame. Any stage affected by uncertainties—such as ignition delay, combustion instability, or inappropriate shell size design—can lead to the failure of the entire ignition sequence. Therefore, achieving high reliability has become a fundamental prerequisite for the application of such devices in major aerospace missions.

[0005] Currently, there is a lack of reliability analysis research on gunpowder igniters, especially on reliability analysis under cryogenic ignition failure modes. Therefore, there is an urgent need to establish an analytical method that can accurately predict the reliability of cryogenic ignition, providing theoretical support for product optimization design. Summary of the Invention

[0006] In view of this, the present invention provides a reliability analysis method for gunpowder igniters under low-temperature ignition failure mode, so as to overcome the above problems or at least partially solve the above problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A reliability analysis method for gunpowder igniters under low-temperature ignition failure modes includes the following steps: Step 1: Analyze the low-temperature ignition failure of the gunpowder igniter and select key performance parameters to characterize the failure mode; The test igniter ignited normally at both room temperature and high temperature. However, at -40°C, the igniter exhibited unstable combustion and failure to ignite the main charge. Dissection of the malfunctioning product revealed that the BPN propellant in the ignition cartridge had burned; the MLR propellant was incompletely burned, and the aluminum foil was not broken.

[0008] Based on the analysis of the failure phenomena and working principle of the gunpowder igniter, it is proposed to adopt ignition impulse... Characterizing this failure mode, the ignition impulse is the integral of the pressure generated by the combustion of the propellant in the ignition cartridge over time, and its expression is: (1.1) In the formula, P pry The pressure generated by the combustion of the propellant inside the ignition box. t s The duration of pressure generated by the combustion of the propellant inside the ignition cartridge. t s Defined as the critical moment when the gas pressure inside the ignition cartridge drops to a level that allows the main charge to be ignited.

[0009] Step 2: Based on the FTA method, determine the uncertain factors affecting the low-temperature ignition failure of the gunpowder igniter, and establish the implicit function of the failure mode in combination with the failure threshold. To identify the key design variables affecting the cryogenic ignition failure of the propellant igniter, the Free-Foreign Atmosphere Analysis (FTA) method will be used. First, the abnormal cryogenic ignition failure of the propellant igniter is identified as the apex event, and a fault tree for cryogenic ignition is established using the FTA analysis method. Based on the FTA analysis results and considering the complexity of subsequent reliability modeling analysis, the main design variables affecting the cryogenic ignition failure of this propellant igniter are determined to be the nozzle diameter, the BPN charge in the ignition cartridge, and the MLR charge in the ignition cartridge.

[0010] To enable the gunpowder igniter to ignite at low temperatures, an implicit limit state function for the gunpowder igniter is established based on the stress-intensity interference model, with the ignition impulse as the output response. : (1.2) In the formula, These are design variables that affect the ignition function of a gunpowder igniter. Let be the ignition impulse function of the gunpowder igniter; I min The failure threshold for the ignition impulse of a gunpowder igniter is determined according to design requirements. I minIt is 0.87 MPa·s.

[0011] Step 3: Establish the Kriging model based on the ballistic simulation model of the gunpowder igniter; In order to establish a deterministic relationship between the ignition impulse of the gunpowder igniter and the design variables, a low-temperature ignition internal ballistic simulation model of the gunpowder igniter will be established below.

[0012] Based on classical internal ballistics theory and the working principle of gunpowder igniters, the cryogenic ignition process of a gunpowder igniter was simulated using the Simulink module of Matlab. The internal ballistic equations are as follows.

[0013] The shape function of a simple gunpowder that satisfies the geometrical law of combustion is: (1.3) (1.4) In the formula, ψ The ratio of the mass of the burned gunpowder to the initial mass of the gunpowder; Z The relative thickness of the gunpowder burned away. e 0 represents the thickness of the gunpowder particle at any given time. e 1 represents the initial thickness; χ , λ , μ All of these are shape coefficients of gunpowder.

[0014] The burning rate of gunpowder follows Saint-Robert's Law: (1.5) In the formula, This is the burning rate coefficient of the gunpowder. For gunpowder pressure P The exponent. Substituting (1.5) into equation (1.4) yields: (1.6) So, what are the mass formation rates of combustion products from the BPN propellant, the MLR propellant in the ignition cartridge, and the MLR in the main charge chamber? for: (1.7) In the formula, m (·) denoted as the initial mass of the gunpowder; (·) represents different gunpowder pellets.

[0015] Since the device chamber is well-sealed and there is no mass exchange between the system and the outside world, according to the law of conservation of mass: (1.8) (1.9) In the formula, The rate of mass change inside the ignition powder box; The rate of change of the internal mass of the main charge; and These are the mass generation rates of gunpowder combustion products in the ignition box and the main charge chamber, respectively. , These are the product flow rates from the ignition box chamber into the main charge chamber and the combustion product flow rates through the nozzle, respectively. Based on gas flow theory, Calculated using the following formula: (1.10) In the formula, A e This refers to the cross-sectional area of ​​the hole at the bottom of the ignition box (or the cross-sectional area of ​​the nozzle). k The adiabatic coefficient of the combustion gas products; R It is the gas constant; P IC The pressure inside the ignition box; P MC The pressure inside the main charge chamber (or atmospheric pressure); T IC It refers to the indoor temperature of the ignition box.

[0016] According to the law of conservation of energy, the ignition cartridge and the main charge chamber have the following characteristics: (1.11) (1.12) In the formula, c p and c v The constant volume specific heat and constant pressure specific heat of the gunpowder products; T IC and T MC These are the temperatures of the ignition powder box and the main powder chamber, respectively. The isobaric explosion temperature of gunpowder represents the flame temperature during isobaric adiabatic combustion of gunpowder. , These refer to the heat exchange rates between the ignition box and the main charge chamber and the outside environment, respectively.

[0017] The intermolecular attraction of the high-temperature, high-pressure gaseous products produced by gunpowder combustion is very small compared to the pressure within the chamber. The gaseous products in both the ignition box and the main charge chamber obey the Nobel-Abel equation of state. (1.13) (1.14) In the formula, m ICand m MC These refer to the mass of the mixed gas in the ignition box and the main charge chamber, respectively. α (·) The remaining volume of the mixed gas in the chamber (subscript IC indicates the ignition cartridge, subscript MC indicates the main charge chamber); V IC Indicates the internal volume of the ignition powder box; V MC Indicates the volume of the main loading chamber; , These are the gas constants in the ignition box and the main charge chamber, respectively.

[0018] Differentiating both sides of equation (1.13) yields: (1.15) For gaseous products: (1.16) In the formula, k (·) The adiabatic coefficient of the gaseous products; α IC This indicates the remaining capacity of the ignition powder box.

[0019] Substituting equations (1.15) and (1.16) into equation (1.13), we can obtain the rate of change of pressure inside the ignition box as follows: (1.17) Similarly, the rate of change of pressure in the main charge chamber can be obtained: (1.18) Due to the combustion of gunpowder, the volume of the combustion chamber changes, and the rate of change of the volume of the ignition powder box and the main charge chamber... and It can be calculated using equation (1.19): (1.19) In the formula, The mass formation rate of gunpowder combustion products; This represents the density of the solid gunpowder.

[0020] A zero-dimensional model of heat exchange between the cavity wall and the outside environment is established, along with the heat exchange law between the ignition cartridge and the main charge chamber and the outside environment. , They are respectively: (1.20) (1.21) In the formula, h The convective heat transfer coefficient; Tw This refers to the temperature of the inner wall of the cavity, i.e., the external temperature. σ s It is the Stepan-Boltzmann constant; A r The absorption rate of the container wall; E m The net emissivity of the gunpowder product; A W(IC) and A W(MC) These are the inner wall surface areas of the ignition powder box and the main powder chamber, respectively.

[0021] To establish a Kriging model for gunpowder ignition, experimental design was conducted to investigate the key design parameters affecting gunpowder ignition. Since there are three key design parameters for gunpowder ignition, Latin Hypercube Sampling (LHS) was used for sampling. Simulations were performed using an internal ballistic simulation model of the gunpowder ignition, and the resulting ignition impulse response values ​​were obtained.

[0022] Through simulation, a Kriging model of a gunpowder igniter is established with ignition impulse as the performance response quantity. The leave-one-out cross-validation method is used to verify the estimation error of the model. The smaller the value, the better the predictive performance of the model, because a smaller estimation error means that the deviation between the model's predicted value and the actual value is smaller. This proves that the model has good fitting accuracy and can be used for reliability modeling of low-temperature ignition of gunpowder igniters.

[0023] Step 4: Solve the Kriging model of the gunpowder igniter using the MCS method (Monte Carlo Simulation) to obtain the failure probability and reliability of the low-temperature ignition failure mode of the gunpowder igniter.

[0024] The Kriging model, established using ignition impulse as the performance response quantity, and its inferences are then applied. g ( x pyr The expression is then used to perform reliability analysis on the gunpowder igniter using the MCS method.

[0025] The reliability analysis of the release nut was performed using a combination of the Kriging model and MCS. The specific steps are as follows: (1) Generate test sample point set: Select test sample point set using MCS random sampling method. x test The set of test sample points generated in this step is mainly used for reliability analysis after the proxy model is established; (2) Calculate the predicted value I K (x pyr ): The test sample points generated in (1) x test Substitute these values ​​into step 3 to obtain the predicted values ​​from the surrogate model. I K ( x pyr ) set, and I K ( x pyr Substituting into equation (1.2) establishes the limit state function. g K ( x pyr ); (3) Reliability calculation: The failure probability is calculated and solved using the MCS method.

[0026] As described above, this invention discloses a reliability analysis method for propellant igniters under cryogenic ignition failure modes. The method includes: firstly, characterizing and analyzing the ignition failure modes of the propellant igniter in a cryogenic environment, and using the fault tree method (FTA) to identify the main uncertainties affecting the reliability of cryogenic ignition and determine their probability distribution characteristics. Subsequently, an implicit function of the failure mode is established. To clarify the deterministic relationship between performance parameters and design variables, an internal ballistic simulation model of cryogenic ignition of the propellant igniter is constructed based on internal ballistic theory, and a Kriging surrogate model is further established using this simulation model. Finally, the Kriging model is sampled and solved using the MCS method to obtain the failure probability and reliability of the cryogenic ignition failure modes of the propellant igniter. This invention can accurately evaluate the reliability of propellant igniters under cryogenic conditions and provides a theoretical basis for product improvement design. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0028] Figure 1 A flowchart of a method for analyzing the reliability of a gunpowder igniter under low-temperature ignition failure mode provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of a gunpowder igniter provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the unstable combustion Pt curve of a gunpowder igniter provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the PT curve and characteristic parameters of a gunpowder igniter provided in an embodiment of the present invention; Figure 5a and Figure 5b This is a schematic diagram of a low-temperature ignition fault tree for a gunpowder igniter provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of a gunpowder igniter test provided in an embodiment of the present invention; Figure 7 This is a test diagram of a gunpowder igniter provided in an embodiment of the present invention; Figure 8 This is a comparison chart of the simulated pt curve and experimental results of the gunpowder igniter at -40℃ provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of the simulation process for the ignition reliability of a gunpowder igniter provided in an embodiment of the present invention; Figure 10 This is a schematic diagram of the response surface of the Kriging model for cryogenic ignition of a gunpowder igniter provided in an embodiment of the present invention; wherein, part (a) shows I p and( m B , d A (a) shows the three-dimensional relationship, and (b) shows the relationship between the three dimensions. I p and( m M , d A The three-dimensional relationship of (c) is shown in part (c). I p and( m B , m M The three-dimensional relationship; Figure 11 A schematic diagram showing the results of the low-temperature ignition failure probability analysis of the gunpowder igniter using the Kriging-MCS reliability method provided in this embodiment of the invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] like Figure 1As shown in the figure, this invention discloses a reliability analysis method for gunpowder igniters under low-temperature ignition failure modes, which mainly includes the following steps: S1. Analyze the low-temperature ignition failure of the gunpowder igniter and select the main performance parameters to characterize the failure mode. S2. Based on the FTA method, determine the uncertain factors affecting the low-temperature ignition failure of the gunpowder igniter, and establish the implicit function of the failure mode in combination with the failure threshold. S3. Establish the Kriging model based on the internal ballistic simulation model of the gunpowder igniter; S4. Solve the Kriging model of the gunpowder igniter based on the MCS method to obtain the failure probability and reliability of the low-temperature ignition failure mode of the gunpowder igniter.

[0031] The following is a reference. Figure 2 The structure of the gunpowder igniter in the embodiments of the present invention is described.

[0032] like Figure 2 The diagram shows the structure of a propellant igniter provided in an embodiment of the present invention. The propellant igniter mainly includes a shell, an electric igniter, an ignition cartridge, propellant, and a nozzle. The ignition cartridge contains a boron-potassium nitrate (BPN) ignition charge and small MLR (multi-base) propellant charges with a low burning rate across the entire combustion surface; the main charge is entirely MLR propellant. The igniter's operation can be divided into three stages: Ignition stage: Power is simultaneously supplied to two electric igniters, which detonate and ignite the BPN charge in the ignition cartridge; Ignition stage: This occurs within the ignition cartridge, where the burning of the BPN charge releases high-energy particles that ignite the MLR propellant charges. The energy released from the simultaneous combustion of both ignites breaks through the aluminum foil at the bottom of the ignition cartridge, subsequently igniting the main MLR propellant charge; Combustion stage: This occurs in the main charge chamber, where the propellant combustion produces a large amount of gas, which breaks through the diaphragm, and the flame enters the gas generator, igniting the mixture of liquid hydrogen and liquid oxygen propellants in the engine.

[0033] This type of gunpowder igniter can ignite normally at both room temperature and high temperature. However, the gunpowder igniter exhibited unstable combustion and unignited main charge at -40℃, such as... Figure 3 As shown. Dissection of the defective product revealed that the BPN propellant in the ignition cartridge had burned; the MLR propellant was not completely burned, and the aluminum foil was not broken.

[0034] Based on the analysis of the failure phenomena and working principles of the gunpowder igniter, it is proposed to use ignition impulse to characterize this failure mode. Ignition impulse is the integral of the pressure generated by the combustion of the propellant in the ignition box over time, and its expression is: (1.1) In the formula, The pressure generated by the combustion of the propellant inside the ignition box. The duration of pressure generated by the combustion of the propellant inside the ignition box, such as... Figure 4 As shown. Figure 4 middle p m Peak ignition pressure p i The transient pressure at the end of the ignition phase. t v The total combustion time of the igniter.

[0035] Furthermore, to establish a fault tree for the cryogenic ignition of the propellant igniter, the abnormal failure of cryogenic ignition is first identified as the top event. The fault tree for cryogenic ignition of the propellant igniter is then established using the FTA analysis method, as follows: Figure 5a and Figure 5b As shown. Figure 5a and Figure 5b Table 1 shows the symbols, meanings, and probability values ​​of the top event, intermediate events, and bottom events in the fault tree. The probability values ​​were determined after checking each bottom event one by one.

[0036] Table 1. Symbols, meanings, and probability values ​​of the top event, intermediate events, and bottom event in the fault tree of the gunpowder igniter.

[0037] (1) Qualitative analysis: Assuming that the bottom events are independent of each other, the expression for the top event in the fault tree of the gunpowder igniter is:

[0038] Using the descending method, a qualitative analysis of the above equation yields the minimum cut sets of the fault tree for the gunpowder igniter: {X1-1}, {X1-2}, {X2-1}, {X3-1}, {X3-2}, {X3-3}, {X3-4}, {X4-1}, {X4-2}, {X4-3}, {X4-4}, {X4-5}, {X4-6}, {X5-1}, {X5-2}, {X5- 3}, {X5-4}, {X5-5}, {X5-6}, {X6-1}, {X6-2}, {X6-3}, {X6-4}, {X6-5}, {X6-6}, {X6-7}, {X6-8}, {X6-9}, {X6-10}, {X6-11}, {X6-12}, {X6-13}, {X6-14}, {X6-15}, {X6-16}.

[0039] Qualitative analysis of the fault tree of the gunpowder igniter shows that any bottom event will lead to the occurrence of the top event, that is, cause the gunpowder igniter to fail.

[0040] (2) Quantitative calculation: 1) Calculate the failure probability of the top event occurring: The fault tree of the gunpowder igniter has 35 unique minimum cut sets, and the probability of each bottom event is less than 0.01. The probability of the top event, the low-temperature ignition anomaly of the gunpowder igniter, is calculated as follows:

[0041] 2) Calculate the importance of the critical probability of the bottom event: In this invention, the critical probability importance of each bottom event of the fault tree of the gunpowder igniter was calculated, and the calculation results are shown in Table 2.

[0042] Table 2. Critical Probability Importance of Each Base Event in the Fault Tree of the Explosive Igniter

[0043] Based on the FTA analysis results of the above-mentioned gunpowder igniter, and considering the complexity of subsequent reliability modeling analysis, the main design variables affecting the low-temperature ignition failure of the gunpowder igniter are determined to be the nozzle diameter, the amount of BPN propellant in the ignition box, and the amount of MLR propellant in the ignition box.

[0044] To enable the gunpowder igniter to ignite at low temperatures, an implicit limit state function for the gunpowder igniter is established based on the stress-intensity interference model, with the ignition impulse as the output response. : (1.2) In the formula, The design variables that affect the ignition function of the gunpowder igniter are shown in Table 3. Let be the ignition impulse function of the gunpowder igniter; I min The failure threshold for the ignition impulse of a gunpowder igniter is determined according to design requirements. I min It is 0.87 MPa·s.

[0045] Table 3 Main Design Parameters Affecting the Ignition of Gunpowder Ignition Devices

[0046] Furthermore, in order to establish a deterministic relationship between the ignition impulse of the gunpowder igniter and the design variables, a low-temperature ignition internal ballistic simulation model of the gunpowder igniter will be established below.

[0047] Based on classical internal ballistics theory and the working principle of gunpowder igniters, the cryogenic ignition process of a gunpowder igniter was simulated using the Simulink module of Matlab. The internal ballistic equations are as follows.

[0048] The shape function of a simple gunpowder that satisfies the geometrical law of combustion is: (1.3) (1.4) In the formula, ψ The ratio of the mass of the burned gunpowder to the initial mass of the gunpowder; Z The relative thickness of the gunpowder burned away. e 0 represents the thickness of the gunpowder particle at any given time. e 1 represents the initial thickness; χ , λ , μ All of these are shape coefficients of gunpowder.

[0049] The burning rate of gunpowder follows Saint-Robert's Law: (1.5) In the formula, This is the burning rate coefficient of the gunpowder. Let be the gunpowder pressure index. Substituting (1.5) into equation (1.4) yields: (1.6) So, what are the mass formation rates of combustion products from the BPN propellant, the MLR propellant in the ignition cartridge, and the MLR in the main charge chamber? for: (1.7) In the formula, m (·) denoted as the initial mass of the gunpowder; (·) represents different gunpowder pellets.

[0050] Since the device chamber is well-sealed and there is no mass exchange between the system and the outside world, according to the law of conservation of mass: (1.8) (1.9) In the formula, The rate of mass change inside the ignition powder box; The rate of change of the internal mass of the main charge; and These are the mass generation rates of gunpowder combustion products in the ignition box and the main charge chamber, respectively. , These are the product flow rates from the ignition box chamber into the main charge chamber and the combustion product flow rates through the nozzle, respectively. Based on gas flow theory, Calculated using the following formula: (1.10) In the formula, A e This refers to the cross-sectional area of ​​the hole at the bottom of the ignition box (or the cross-sectional area of ​​the nozzle). k The adiabatic coefficient of the combustion gas products; R It is the gas constant; P IC The pressure inside the ignition box chamber (or the main charge chamber); P MC The pressure inside the main charge chamber (or atmospheric pressure); T IC It refers to the indoor temperature of the ignition box.

[0051] According to the law of conservation of energy, the ignition cartridge and the main charge chamber have the following characteristics: (1.11) (1.12) In the formula, c p and c v The constant volume specific heat and constant pressure specific heat of the gunpowder products; T IC and T MC These are the temperatures of the ignition powder box and the main powder chamber, respectively. The isobaric explosion temperature of gunpowder represents the flame temperature during isobaric adiabatic combustion of gunpowder. , These refer to the heat exchange rates between the ignition box and the main charge chamber and the outside environment, respectively.

[0052] The intermolecular attraction of the high-temperature, high-pressure gaseous products produced by gunpowder combustion is very small compared to the pressure within the chamber. The gaseous products in both the ignition box and the main charge chamber obey the Nobel-Abel equation of state. (1.13) (1.14) In the formula, m IC and m MC These refer to the mass of the mixed gas in the ignition box and the main charge chamber, respectively. α Indicates the remaining volume of the mixed gas within the chamber; V IC Indicates the internal volume of the ignition powder box; VMC This indicates the volume of the main loading chamber.

[0053] Differentiating both sides of equation (1.13) yields: (1.15) For gaseous products: (1.16) In the formula, k (·) The adiabatic coefficient of the gaseous products; α IC This indicates the remaining capacity of the ignition powder box.

[0054] Substituting equations (1.15) and (1.16) into equation (1.13), we can obtain the rate of change of pressure inside the ignition box as follows: (1.17) Similarly, the rate of change of pressure in the main charge chamber can be obtained: (1.18) Due to the combustion of gunpowder, the volume of the combustion chamber changes, and the rate of change of the volume of the ignition powder box and the main charge chamber... and It can be calculated using equation (1.19). (1.19) In the formula, The mass formation rate of gunpowder combustion products; This represents the density of the solid gunpowder.

[0055] A zero-dimensional model of heat exchange between the cavity wall and the outside environment is established, along with the heat exchange law between the ignition cartridge and the main charge chamber and the outside environment. , They are respectively: (1.20) (1.21) In the formula, h The convective heat transfer coefficient; T w This refers to the temperature of the inner wall of the cavity, i.e., the external temperature. σ s It is the Stepan-Boltzmann constant; A r The absorption rate of the container wall; E m The net emissivity of the gunpowder product; A W(IC) and A W(MC)These represent the surface areas of the inner walls of the ignition cartridge and the main propellant chamber, respectively. In this invention, the initial main parameters of the ballistic simulation model within the gunpowder igniter are shown in Table 4.

[0056] Table 4 Initial Main Parameters of the Ballistic Simulation Model of the Gunpowder Igniter

[0057] To verify the established simulation model, an ignition test was conducted using the developed gunpowder igniter. A schematic diagram of the gunpowder igniter test is shown below. Figure 6 As shown in the photograph. Figure 7 As shown. A strain sensor was used to test the pressure of the gunpowder igniter. Three ignition tests were conducted at -40℃, and the results are as follows. Figure 8 As shown. From Figure 8 As can be seen, the simulation results are consistent with the experimental results. Table 5 below summarizes the characteristic parameters of the simulation model and the experiment: Table 5 Comparison of simulation model and experimental characteristic parameters

[0058] As can be seen from Table 5 above, the relative difference between the experimental results and the simulation analysis results is very small, and the error is within an acceptable range.

[0059] To establish a Kriging model for gunpowder ignition, experimental designs were conducted to investigate the key design parameters affecting gunpowder ignition. Since there are three key design parameters for gunpowder ignition, 15 experimental designs using LHS sampling of gunpowder ignition were implemented. The 15 experimental designs were simulated using an internal ballistic simulation model of the gunpowder ignition, and the ignition impulse response values ​​for the 15 experimental designs are shown in Table 6.

[0060] Table 6. 15 sets of experimental designs and ignition impulse response values ​​of the main design parameters affecting the ignition of gunpowder igniters

[0061] Based on the reliability analysis steps, a simulation workflow for the ignition reliability of a gunpowder igniter is constructed using gunpowder igniter simulation, such as... Figure 9 As shown. Figure 9 The descriptions of each node are shown in Table 7.

[0062] Table 7. Workflow Node Description for Gunpowder Igniter Reliability Simulation

[0063] pass Figure 9The simulation process establishes a Kriging model for a gunpowder igniter using ignition impulse as the performance response variable. Leave-one-out cross-validation is used to verify that the model's estimation error is 0.013. A smaller value indicates better predictive performance, as a smaller estimation error means a smaller deviation between the model's predicted and actual values, demonstrating that the model has good fitting accuracy and can be used for reliability modeling of low-temperature ignition in gunpowder igniters. The Kriging model response surface for design variables and ignition impulse is shown below. Figure 10 As shown.

[0064] Furthermore, the Kriging model, which establishes the ignition impulse as the performance response quantity, and its inferences are then applied. g ( x pyr The expression is then used to perform a reliability analysis using the gunpowder igniter reliability analysis process, and the results are as follows: Figure 11 As shown in Table 8.

[0065] Table 8 Reliability Analysis Results of Low-Temperature Ignition of Gunpowder Igniters

[0066] Depend on Figure 11 As shown in Table 8, the reliability analysis of the ignition of the gunpowder igniter using the Kriging-MCS method reveals that, under the current design conditions, the reliability of the low-temperature ignition of the gunpowder igniter is relatively low, necessitating an improvement design for the gunpowder igniter.

[0067] As described in the above embodiments, those skilled in the art will understand that the present invention provides a reliability analysis method for gunpowder igniters under cryogenic ignition failure modes. This method first characterizes and analyzes the ignition failure modes of gunpowder igniters in cryogenic environments, and uses the fault tree method (FTA) to identify the main uncertainties affecting the reliability of cryogenic ignition and determine their probability distribution characteristics. Subsequently, an implicit function of the failure mode is established. To clarify the deterministic relationship between performance parameters and design variables, an internal ballistic simulation model of cryogenic ignition of gunpowder igniters is constructed based on internal ballistic theory, and a Kriging surrogate model is further established using this simulation model. Finally, the Kriging model is sampled and solved using the MCS method to obtain the failure probability and reliability of the cryogenic ignition failure modes of gunpowder igniters. The present invention can accurately evaluate the reliability of gunpowder igniters under cryogenic conditions and provides a theoretical basis for product improvement design.

[0068] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0069] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A reliability analysis method for gunpowder igniters under low-temperature ignition failure modes, characterized in that, Includes the following steps: Step 1: Analyze the failure of low-temperature ignition of gunpowder igniters and select performance parameters to characterize the failure mode; Step 2: Use the fault tree method to analyze and determine the factors affecting the low-temperature ignition failure of the gunpowder igniter, and establish the limit state function of the failure mode in combination with the failure threshold. Step 3: Establish a Kriging proxy model based on the ballistic simulation model of the gunpowder igniter; Step 4: Based on the Kriging surrogate model and the limit state function, the Monte Carlo simulation method is used to perform sampling and solution to obtain the failure probability and reliability of the gunpowder igniter in the low-temperature ignition failure mode.

2. The method according to claim 1, characterized in that, In step 1, ignition impulse is used. The failure mode is characterized by the ignition impulse, which is the integral of the pressure generated by the combustion of the propellant in the ignition cartridge over time, and its expression is: In the formula, P pry The pressure generated by the combustion of the propellant inside the ignition box. The duration of pressure generated by the combustion of the propellant inside the ignition box.

3. The method according to claim 2, characterized in that, In step 2, firstly, the abnormal failure of the low-temperature ignition of the propellant igniter is identified as the apex event, and a fault tree for the low-temperature ignition of the propellant igniter is established. Then, based on the fault tree analysis results, the key design variables affecting the low-temperature ignition failure of the propellant igniter are determined. Finally, based on the stress-strength interference model, with the ignition impulse as the output response, the implicit limit state function of the propellant igniter is established. : In the formula, These are design variables that affect the ignition function of a gunpowder igniter. Let be the ignition impulse function of the gunpowder igniter; I min The failure threshold for the ignition impulse of a gunpowder igniter.

4. The method according to claim 3, characterized in that, The key design variables include: nozzle diameter, BPN charge in the ignition cartridge, and MLR charge in the ignition cartridge.

5. The method according to claim 4, characterized in that, In step 3, based on internal ballistics theory and the working principle of gunpowder igniters, the low-temperature ignition process of the gunpowder igniter is simulated using Matlab to establish an internal ballistics simulation model of the gunpowder igniter, including: The shape function of gunpowder is: In the formula, ψ The ratio of the mass of the burned gunpowder to the initial mass of the gunpowder; Z The relative thickness of the gunpowder burned away. Let be the thickness of the gunpowder particle at any given time. This is the initial thickness; χ , λ , μ All are shape coefficients of gunpowder; The burning rate of gunpowder satisfy: In the formula, This is the burning rate coefficient of the gunpowder. For gunpowder pressure P The index; Mass formation rate of combustion products of BPN propellant, MLR propellant in the ignition cartridge, and MLR in the main charge chamber for: In the formula, This represents the initial mass of the gunpowder; Representing different gunpowder columns; The gaseous products in both the ignition cartridge and the main charge chamber obey the Nobel-Abel equation of state: In the formula, , These are the pressures in the ignition box and the main charge chamber, respectively. V IC , V MC These represent the volumes of the ignition powder box and the main powder chamber, respectively. , The remaining space in the ignition powder box and the main powder chamber are respectively. and These refer to the mass of the mixed gas in the ignition box and the main charge chamber, respectively. , These are the gas constants in the ignition box and the main charge chamber, respectively. T IC and T MC These are the temperatures of the ignition powder box and the main powder chamber, respectively. A zero-dimensional model of heat exchange between the cavity wall and the outside environment is established, along with the heat exchange law between the ignition cartridge and the main charge chamber and the outside environment. , They are respectively: In the formula, h The convective heat transfer coefficient; T w This refers to the temperature of the inner wall of the cavity, i.e., the external temperature. σ s It is the Stepan-Boltzmann constant; A r The absorption rate of the container wall; The net emissivity of the gunpowder product; A W(IC) and A W(MC) These are the inner wall surface areas of the ignition powder box and the main charge chamber, respectively. The internal ballistic simulation model of the gunpowder igniter was used for simulation. Through the simulation process, the Kriging proxy model of the gunpowder igniter was established with the ignition impulse as the performance response quantity.

6. The method according to claim 5, characterized in that, The prediction accuracy of the Kriging surrogate model was evaluated using leave-one-out cross-validation.

7. The method according to claim 1, characterized in that, In step 4, the number of samples in the Monte Carlo simulation is no less than 10. 4 Second-rate.

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