1.Introduction

Cased telescoped ammunition(CTA)is a kind of charge structure with a projectile embedded in the cartridge case.Compared with concepts using conventional ammunition,the length of CTA is small and the appearance of CTA is simple[1,2].Because of its unique structure,the feeding mechanism is simple and the feeding distance is much shorter.Thus,ammunition storage space can be effectively used.Compared with the conventional ammunition of the same caliber,the overall performance of CTA is more superior.

Due tothe superior performance of CTA,manycountries,such as USA[3-5],England and France[6,7],have launched a study of CTA technology and obtained many achievements in this field.For example,the 45M911 45 mm CTA gun is developed by France.The 40 mm cased telescoped weapon system(CTWS)is developed by a joint Anglo-French project.These results fully illustrate the feasibility of the CTA weapon system used for equipment.

(3)Cu,Fe,ZnXXⅣ矿体。位于研究区西区南部，矿体赋存于印支期侵入岩花岗闪长岩与大理岩接触带形成的矽卡岩中，含矿岩石为透辉石、石榴子石矽卡岩，矿体呈近东西向展布，以铁为主的铁、锌、铜复合矿体。矿体呈长条状产出，矿体总长130 m，平均厚4.66 m。铁品位25.75×10-2～48×10-2，平均品位27.05×10-2；锌品位0.6×10-2～1.70×10-2；铜品位0.31×10-2～0.34×10-2，平均品位0.39×10-2。

The sketch of a typical CTA structure is shown in Fig.1.It can be seen that there is a big difference in the structure between CTA and conventional ammunition.Thus the interior ballistic process is different from the conventional ammunition.In the process of CTA interior ballistic,the fast burning propellant in the auxiliary chamber at the bottom of the projectile is ignited by the primer after the primer is struck.The propellant gases,generated by the fast burning propellant,drive the projectile to move forward along the control tube.Then the projectile is propelled into the barrel with a certain velocity.At this time,due to the special structure of CTA,the main charge around the center igniting primer and controlling tube is ignited and a large volume of gas is generated to propel the projectile along the barrel until the projectile exists the muzzle.

In order to achieve successful shooting,there is a need for a reasonable design of CTA interior ballistics because of the particularity of CTA interior ballistics.The interior ballistic design,usually based on the interior performance requirements and design indices,is to determine the structure elements and loading parameters of the gun system.If a conventional Engineering design method is used,the CTA interior ballistic scheme maybe feasible,but it can't be ensured that the scheme is optimal.In recent years,the intelligent optimization algorithm has been applied to variable fields.Among it,the genetic algorithm is most widely used.In this paper,we will apply a genetic algorithm to produce an optimal design by taking a 35 mm CTA interior ballistic model as an example.

Fig.1.The sketch of CTA structure.

2.Interior ballistic model of CTA

The main components of the genetic algorithm include the group,the coding method,the selection strategy and the genetic operation.

对于不对称的环氧化合物(环氧丙烷衍生物),在发生开环反应时,有着不同的进攻位置,两个位置发生比例不仅与所使用的引发剂种类有关,还与该位置上所连接的R基团大小和性质有密切关系(见图1).

自发性气胸为临床常见的急症之一,多见于老年男性群体,随着我国人口老龄化现象的进一步加重,该病发病率将会呈现出逐年上升的态势,已经引起了世界各国的广泛关注[1]。为探讨老年人自发性气胸的临床特点,指导临床工作,提高治愈率。我们收集了本院自2008~2018年收治的60岁以上自发性气胸患者94例,与同期的60岁以下中青年自发性气胸52例进行了比较,结果如下:

Among that,ψbis the burned percentage of fast burning propellant,χband λbare shape characteristic quantity of fast burning propellant,Zbis the burned relative thickness

Among that u1b,nb,and e1bis the burning rate coefficient,burning rate-pressure exponent and arc thickness of the fast burning propellant respectively

Among that,m is the mass of projectile,v is the velocity of the projectile,S is the maximum cross-section area of the projectile,p is the pressure in the chamber.

Among that,lbis the travel of the projectile in the controlling tube.

Among that,φbis the secondary power coefficient of the first ignition stage,m is the mass of the projectile,lψbis equivalent length of the free volume of the first stage,fb,αb,ρpb,ωband Δbis the gunpowder force,covolume,density,charge quantity and charge density of fast burning propellant respectively,θb= γ-1 and γis specific heat ratio,V0band l0bis the chamber volume and equivalent length of the fast burning propellant respectively.

两大流派的研究各有其优势、贡献和不足。工作意义流派的研究见长于分析个人行为动机和过程。通过深入观察多种职业员工的工作重塑现象，此类研究发现了各种不同的行为策略，归纳出了覆盖范围较广的工作重塑行为方式，洞察了认知重塑对个人工作意义和工作身份的重要影响。这些研究深化了人们对工作重塑理论的认识，也发展了理论模型。同时，由于此类视角的研究往往采取更加耗时的质性方法，对研究者的时间、精力和分析理解能力都要求较高，所以相应的研究数量也很有限。

The interior ballistic equations of the second ignition stage are as follows

where,ψand Z is the burned percentage and burned relative thickness of main charge propellant respectively,χandλis the shape characteristic quantity of the main charge propellant,u1,n,e1 is the burning rate coefficient,burning rate-pressure exponent and arc thickness of the main charge propellant respectively,l is the travel of the projectile in the barrel,p is the average pressure behind the projectile,Fr is the engraving resistance,φ is the secondary power coefficient of the second stage,lψis equivalent length of the free volume of the second stage,V0and l0is the chamber volume and equivalent length of main charge propellant,respectively,f,ω,Δ,α and ρpis the gunpowder force,main charge quantity,charge density,covolume and density of the main charge.

Fig.2.The flow chart of the simulation process.

Fig.2 shows the flow chart of the simulation process.As the figure shows,at the beginning of the simulation,the initial value of the interior ballistic parameters is calculated according to the loading parameters.After that,loop calculation of the interior ballistic parameters is conducted with the first stage equations until the projectile exists the control tube.After the projectile enter into the gun tube,loop calculation is conducted with the second stage equations until the projectile exists the gun tube.Finally,the calculation results are outputted,including the velocity and pressure.

值得注意的是，教师课后要及时批阅学生习作并反馈，除关注单词拼写或语法错误外，应更多关注语篇的逻辑结构、语言表达方式等；可采用分期面批的形式，用激励性评价，鼓励学生大胆表达；同时，要提出修改建议，让学生清楚自己写作的优劣，不断取得进步；最后，布置学生制作班级写作板报，把优秀作品张贴到学习园地里，进行展示或交流，或发送到QQ群、微信群里，与家人、好友共赏，提高学生写作的兴趣和积极性。

3.Optimization

3.1.Genetic algorithm

The main idea of the genetic algorithm is the law in the natural field,which is the survival of the fittest[12-14].This algorithm is to establish objective function and constraint conditions for solving the problem.The genetic algorithm will encode the scheme parameters and then continue the selection,crossover and mutation of the population of candidate solutions.Byconstantly updating the population,the solution to the problem is gradually evolved to an optimum.Table 1 shows the relationship between biological genetic concepts and genetic algorithm concepts.

The object of CTA interior ballistic design is the interior ballistic process.Thus interior ballistic equations are used for the design[8].In this paper,we take a 35 mm CTA as the research object and establish a CTA zero-dimensional interior ballistic model with combining the characteristics of interior ballistic process[9-11].

(1)In the genetic algorithm,the group is composed of a certain number of individuals,and each individual corresponds to a solution.The individuals in original group are randomly generated,and the size of the group is a linear multiple of the length of the code.

(2)Coding is the basic work of the genetic algorithm,which determines relationship between the solutions and the genetic codes.

插秧机横向仿形插深自适应调节系统是以2ZG630A水稻高速插秧机为主机架构设计完成的。该水稻高速插秧机是由中机南方机械股份有限公司设计、生产，采用液压仿形，可实现高速度、高质量插秧生产，性能指标达到国际同类产品水平[5]。

自然属性包含了典型性、独特性、自然性、完整性和优美性五项指标。其中典型性是指拥有浙江省典型生态系统（如河口、海湾、海岛、湿地等），或是珍稀濒危生物或重要经济鱼类的“三场一通道”[9]（产卵场、索饵场、越冬场和洄游通道等）。

(3)The selection strategy in the genetic algorithm is choosing the most adaptable individuals in the group,which are evaluated by the adaptive function.

The interior ballistic process can be divided into two stages based its characteristics,which are first ignition stage and second ignition stage.The first ignition stage mainly involves the combustion of fast burning propellant and the interior ballistic equations are as follows

(4)The most important part of the genetic algorithm is the genetic operation,including mating and variation operation.

Fig.3 shows the flow chart of the optimization process.The genetic algorithm firstly needs to encode the optimal problem and construct the fitness function.Then the evolution usually starts from a population of randomly generated individuals,and is an iterative process,with the population in each iteration called a generation.In each generation,the fitness of every individual in the population is evaluated.The individuals are stochastically selected from the current population based on the fitness.Those more fit individuals are recombined and mutated to form a new generation.The fitness of the new generation is closer to the optimal solution than that of the initial population by comparative selection and code update.The solutions of the population will approach to the optimal solution by iterations of the algorithm.The solution of the last generation can be regarded as the optimal solution to the problem.

3.2.Determination of optimal variables

In the process of interior ballistic design,there is some in fluence of the gun structure and charge conditions on the interior ballistic characteristics.Thus,more variables are involved in the CTAoptimal design,such as the length of barrel,propellant chamber volume,charge quantity and charge shape of the propellant.The variables selected should be mutual independent and have most direct and biggest in fluence on the scheme.The propellant chamber volume and charge quantity have considerable in fluence on the peak pressure of the gun and muzzle velocity of the projectile.So we will select those two parameters as design variables and conduct an optimal design.

There are many constraints used to satisfy the schemes,but not of all are optimal.Thus we need an objective function to evaluate the quality of the scheme.The main goal of the interior ballistic optimal design is to obtain a larger muzzle velocity of projectile with pressure as small as possible.Thus we select the muzzle velocity of projectile as the optimized objective function.

Table 1 The relationship between biological genetic concepts and genetic algorithm concepts.

Biological genetic Genetic algorithm Individual A solution The survival An optimization solution Chromosome Coding of the solution Gene The eigenvalues of the code Adaptability Value of the adaptive function Group Selected set of solutions Mating Producing a new set of solutions based on the crossover principle Variation The process of changing a certain component of the code

Fig.3.The flow chart of the optimization process.

3.3.Constraint conditions

As mentioned above,the boundary conditions of the design variables were chamber volume V0∈[0.33,0.41]dm3and main charge densityΔ∈[0.75,0.95]kg/dm3.The upper limit of the peak pressure is set to be 322 MPa as a constraint.

In the process of interior ballistic design,the constraint conditions are determined based on the material of the gun,ammunition charge condition and related prior art.The usually used constraint conditions in the interior ballistic design are peak pressure,chamber volume and charge density.The peak pressure is an important index in the interior ballistic design.To determine the peak pressure should not only consider the interior ballistic performance but also consider the factors of gun barrel material strength.The size of the chamber volume will affect the performance of artillery.If the size of chamber volume is too large,it will occupy larger space and apply adverse effects on other features of the weapon system.The charge density is in fluenced by the charge shape and density of the propellant,and should be chosen according to the current state of art.

3.4.Objective function

心脑血管疾病对人类生命健康造成很大威胁，该病的发生与患者的饮食习惯、遗传、自身疾病等多种因素有关。其临床表现主要包括：胸闷、心悸、呼吸困难等，若病情严重还会伴有呕吐、上腹疼痛、窒息等问题。缬沙坦药物属于拮抗剂，具有高安全、毒副作用少等特点，对降低血压、增加血管张力、舒张血管、提高血灌注量有重要作用，因此在心血管疾病临床治疗中具备应用优势[4]。

Table 2 Charge parameters of CTA.

Parameters Value Parameters Value ωb/g 1 ω/g 320 u1b 2×10-8 u1 1.75×10-8 nb 0.83 n 0.83 ρp/(kg·m-3) 1600 f/(J·kg-1) 980000 mq/kg 0.55 p0b/MPa 2.5 V0/m3 3.45×10-4 S/m2 9.621×10-4 l1/m 0.09 lg/m 3.29

Table 3 Comparison between simulation results and experiment data.

vg/(m·s-1) pm/MPa Experiment 1160 320 Calculated 1168.5 321.8

4.Result and analysis

4.1.Numerical simulation of 35 mm CTA interior ballistic

Numerical simulation is conducted based on an initial scheme of 35 mm CTA firing experiment and then an optimal design is carried out.The charge parameters of the CTA experiment is shown in Table 2.

The comparison between numerical results and experiment data is shown in Table 3.The maximum relative error of projectilemuzzle velocity and peak pressure is 0.68%and 0.56%,respectively.The calculated results are in good agreement with the experimental results,which validates the model.

除上述各因素外，还需要综合考虑电动机运行的可靠性，备品备件的通用性、安装维修的难易程度、以及产品价格、运行费用和维修费用等各项经济指标，达到安全运行和节约能源的目的.

Table 4 Genetic algorithm parameters.

Parameters Value population size 50 number of iterations 20 probability of performing crossover 0.8 probability of mutation 0.1

Fig.4.The evolution of individuals during iterations.

4.2.Results of optimal design

The parameters of the genetic algorithm adopted in the calculation were shown in Table 4.

The convergence process of genetic algorithm of generations is shown in Fig.4.It can be seen that the design variables of chamber volume V0and charge densityΔ,constraint condition of peak pressure pmand objective function of vgoscillate largely in the early stage of the iterations.However,the oscillation decreases gradually as the genetic algorithm continues.Due to the mutation of some individuals during the generation in the convergence process,the design variables of chamber volume V0and charge densityΔ,constraint condition of peak pressure pmand objective function of vgmutate occasionally in the convergence process.However,it doesn't affect the convergence of optimization results.Thus,the optimal design of obtaining largest muzzle velocity of CTA projectile is V0=0.3869 dm3,Δ=0.8728 g/cm3and the optimized initial velocity of CTA is vg=1182 m/s.

Table 5 Optimization results.

V0/dm3 Δ/(kg·dm-3) vg/(m·s-1) pm/MPa 0.3888 0.8705 1182.5 321.9 0.3870 0.8727 1182.1 322.0 0.3868 0.8729 1182.0 321.9 0.3898 0.8694 1182.6 322.0

Four independent optimal calculations were carried out and the optimal results of each optimization were shown in Table 5.As can be seen in Table 5,the optimal results of chamber volume V0,charge densityΔand peak pressure were in the constraint range.The optimal results meet the actual situation and the design requirements and were better than that of the initial scheme.Comparingof the fouroptimal results,it can be seen that the results of each calculation are not the same.The deference between the optimal results is due to the existence of some certain randomness of the genetic algorithm in iterations.At first,the individuals of the initial population were randomly generated.Then,the individuals,which were chose to recombined,were selected randomly.The location of the coding recombination is also stochastic.In addition,whether the individual is to mutate and the location of coding mutation is also random.Though a difference of each optimization exists,the difference is small and the results are basically the same.At the same time,the difference in the peak pressure and projectile muzzle velocity of each optimization is very small.The optimization results are constantly approaching to the optimal results,which imply that using a genetic algorithm to optimize the interior ballistic design is feasible.

4.3.Comparison of optimized scheme with the experimental scheme

The numerical results of the interior ballistic characteristics of the last optimized scheme in Table 4 were compared with that of the initial scheme,which were shown in Fig.5 and Fig.6.

Fig.5.Comparison of pressure.

Fig.6.Comparison of velocity.

From Fig.5,it can be seen that pressure change of the pressure curve of the optimized scheme is small at the early stage of the interior ballistic process.This is because of a smaller charge density than that of the initial scheme.However,the charge quantity of the optimized scheme is much larger.At the late stage of the interior ballistic process,as the space behind the bottom of projectile increases,the in fluence due to the bigger chamber volume gradually decreases.The pressure of the optimized scheme would exceed that of the original scheme.Thus the pressure change of the optimized scheme is relatively gentler.

From Fig.6,in the process of projectile motion,the projectile velocity increases slower,because the pressure behind the bottom of projectile is relatively small.At the late stage,the pressure behind the bottom of projectile is relatively large,the acceleration rate is larger.Comparing the two schemes,the total impulse obtained in the whole interior ballistic process of the optimized scheme is larger at almost the same peak pressure.The muzzle velocity of the projectile increases by 14 m/s.The new scheme obtained by the genetic algorithm is more optimal than the original one.It's feasible to optimize the CTA interior ballistic design using a genetic algorithm.

5.Conclusions

A two stage ignition model of CTA interior ballistics was established using the classical interior ballistic theory.A numerical simulation was carried out based on the experimental condition and the calculated results are in good agreement with the experimental data.

(3)Al2O3:1～3质量及分子14.71、144,15.82、150,13.82、135；4～6质量及分子18.99、186,14.07、183,15.66、156；7～8质量及分子17.07、168,11.31、111；

An optimal design of CTA interior ballistics was established using a genetic algorithm.The best optimal scheme is obtained by setting the peak pressure,setting the present range of chamber volume V0and charge densityΔ.

Four different optimized results were obtained by four independent optimal calculations.The difference between each scheme is small and the calculated performance parameters are similar.The optimal results constantly approach the best optimal solution.

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