Study on the influence of projectile on muzzle disturbance

Fei-fei Liu,Yn-ming Song,Hi-long Yu,Wen-ding Lin,Jie Zhng,Zhi-hui Si,Ming-kng Ding,Xio-ting Rui

aChina Weapon Industry Corporation NHIC Nanjing Research Institute,Nanjing,210000,China

bChina Weapon Industry Corporation NHIC,Baotou,014000,China

cInstitute of Launch Dynamics,Nanjing University of Science&Technology,Nanjing,210094,China

Keywords:Muzzle disturbance Orthogonal test Projectile-barrel coupling Firing dispersion

ABSTRACT In order to make an efficient analysis of muzzle disturbance influenced by projectile mass,mass eccentricity,dynamic unbalance,load deviation,and clearance between projectile and bore,the orthogonal test method is extended to analyze the launch dynamics.Taking a tank as the research object,the launch dynamics equations of a tank system are established.Based on the stochastic simulation principle,the tank launch dynamic simulation system is constructed and through the development of the orthogonal test method,the influence of projectile on muzzle disturbance is studied.The study results provided both theoretical foundation and simulation approaches for improving the firing dispersion of the tank.

1.Introduction

Firing dispersion is an important index to evaluate a gun's performance while muzzle disturbance plays a major role in those influence factors.During the launch process,the projectile will move in the bore and its mass,mass eccentricity,dynamic unbalance,load deviation,and the clearance between projectile and bore have a direct effect on the projectile-barrel coupling effect,which causes muzzle vibration.So far,a large number of research documents on the influence of muzzle disturbance have not taken account of the combined influence of the projectile mass,mass eccentricity,dynamic unbalance,load deviation,and the clearance between projectile and bore as well.This is because an efficient analysis of the influence of projectile on the muzzle disturbance requires the launch dynamics equations of a tank system,i.e.the launch dynamics equations of projectile and dynamics equations of tank system,and meanwhile a reasonable test design is necessary.

Rui et al.[1-7]made an in-depth investigation into the deduction method of launch dynamics equations of projectile and established uniform launch dynamics equations of projectile suitable for varieties of motion models.Compared to the Marting Model[8],these equations are characterized of more comprehensive and closer to reality in terms of involved factors,but also quite simple in form of differential equation of motion.Based on this progress,Liu et al.[9,10]deducted the launch dynamics equations of projectile during marching fire,set up a launch dynamics model of tank marching fire and obtained vibration characteristics of weapon system based on the new version transfer matrix method for multibody system[11-15].The orthogonal test method[16,17]is known as a design method which allows multi-factor test arranged and test result analyzed using the orthogonal array,featuring less test numbers,better results,more simple means,more convenient operation and higher efficiency as well.However,this research method fails to cover each test factor's influence on the statistical results of test index.Therefore,this paper made a development on the orthogonal test design method.

Based on previous studies,a tank launch dynamics simulation system is established,which is based on the stochastic simulation principle;and the tank dynamics,the projectile motion in-bore and the vertical target dispersion are simulated;meanwhile,the simulation results are verified by tests.Finally,the developed orthogonal test method is introduced to analyze details of the influence of projectile mass,mass eccentricity,dynamic unbalance,the load deviation,and the clearance between the projectile and the bore on the muzzle disturbance.

2.Tank launch dynamics simulation system

2.1.Launch dynamics equations of the tank

According to tank launch dynamics model[9]and based on the new version transfer matrix method for multibody system[11-15],the overall transfer equations of the tank multibody system can be obtained as

Taking projectile mass eccentricity,dynamic unbalance,clearance between projectile and bore and the flexible effect of the gun tube into consideration,the launch dynamics equations[9,10]of projectile during marching fire are

(4)When present time tiis not less than tfiring( firing time of projectile),assign values to projectile-gun system,and then make force analysis of projectile and gun to determine the interaction force between projectile and barrel,otherwise go to step(5).

(5)Solve the boundary acceleration of tank at tiaccording to system boundary and overall transfer equation.

(6)When present time tiis not less than tfiring( firing time of projectile),make the solution for the acceleration of projectile at ti,otherwise go to step(7).

(7)Use numerical integration method(i.e.classical Runge-Kutta method in this paper)to make the solution for displacement and speed of each components of tank at ti+1.In case of tinot less than tfiring( firing time of projectile),make joint solution for speed and displacement of projectile at ti+1.

(8)When ti+1is less than the time of end of simulation tend,repeat steps(3)to(8),otherwise complete one time of tank the physical meanings of symbols and the calculation methods of parameters coincide with those of Ref.[18].

2.2.Launch dynamics simulation system

According to the stochastic simulation principle and based on the tank launch dynamics model,the overall transfer equation of the tank multibody system and the launch dynamics equations of the projectile during marching fire,a simulation system for stochastic launch dynamics of tank is established using Monte Carlo random simulation technique.The simulation system consists of four modules,including general control module,stochastic module,launch dynamics module and post-processing module.Flow chart of simulation system is shown in Fig.1.

(1)General control module is used to preset simulation times,in-bore motion time,result output format,and to call the stochastic module.

(2)Stochastic module generates random numbers which are required for various function modules and complying with specified distribution,and then input those parameters into the simulation system such as spatial state and material properties of tank's road wheel,driving wheel,hull,turret,cradle,gun breech and barrel at initial time, finally call tank launch dynamics program.

(3)Tank system kinematics and force analysis;to determine kinematic relationships and force conditions of each elements.launch dynamics program simulation.

(9)When launch dynamics simulation times n is less than total simulation times N(200 taken in this paper),repeat steps(3)to(9),otherwise stop the simulation.

(10)Statistically process the simulation result from various stages and output the initial disturbance of projectile and muzzle disturbance.

3.Simulation of launch dynamics of the tank and its test verification

3.1.Main factors affecting muzzle disturbance

Muzzle disturbance is affected by multiple random factors including random change of system parameters of projectile,gun,ammunition during firing projectile and randomness of service environment and operation process.The influence of projectile mass distribution and projectile-gun geometry relationship on muzzle disturbance is studied in this paper,meanwhile,take the factors of projectile mass,mass eccentricity,dynamic unbalance,load deviation and clearance between projectile and bore into consideration.The projectile mass distribution and the projectilegun geometry relationship are shown in Fig.2.

3.2.Simulation of launch dynamics and its test verification

Table 1 Statistical characteristic of random quantities.

Table 2 Comparison of launch dynamics simulation results and test results.

Based on the tank launch dynamics simulation system and combined with projectile flight dynamics equation[1], firing and flight process of a tank are simulated in this paper.The recoil resistance is the force applied on the barrel in the process of recoiling,which originates from recoil system.One side of it applies on breech,and the other side applies on cradle.The simulate conditions are:the firing angle is 5mil,simulation time is 200,and statistical characteristics of partial random quantities are shown in Table 1.Partial simulation results and test results are given in Table 2.

The recoil resistance can be decomposed into two parts--the internal force and external force.And the internal force is proportional to the relative displacement.The calculation formula of internal force coincides with those of Ref.[18].

In Table 2,it shows that relative error of simulation result is less than 4%,which illustrates that launch dynamics model established in this paper is correct and believable and can reflect project practice.

4.Orthogonal test method

4.1.Development of orthogonal test method

Due to the disadvantage which fails to cover each test factor's influence on the statistical result of test index,this paper made a development on the orthogonal test design method.The development course of the orthogonal test method is as follows: firstly,the design factors of current orthogonal test should be developed to two parts,one is “factor”mean value,the other is “factor”mean square deviation,actually the two factors are independent;then the current orthogonal design level is developed to two parts,one is“factor”mean value level and the other is “factor”mean square deviation level; finally,the test index of current orthogonal test method should be developed to “test index”mean value.

4.2.Test index,test factors and factor level

Take the important factors,which affect firing dispersion,muzzle disturbance as test checking index,the muzzle disturbance refers to the mean value of muzzle end speed which consists of elevating speed mean value,and horizontal speed mean value;the mean value of angular velocity at muzzle end which consists of vertical angular velocity mean value&azimuth angular velocity mean value;Take the mean values and mean square deviations of clearance between projectile and bore e,projectile mass eccentricity Lm,projectile dynamic unbalance angleβDand projectile load deviation r as the test factors,they are mutual independence,and noted as A,B,C,D,E,F,G&H in sequence.Each factor includes 3 levels which are shown in Table 3.

4.3.Design scheme for orthogonal test

In order to analysis the influence of projectile on muzzle disturbance,8 factor tests of mean value and mean square deviation of clearance between projectile and bore e,projectile mass eccentricity Lm,projectile dynamic unbalance angleβDand projectile loading off r must be performed.Each test factor has 3 levels respectively,so use L27（38）orthogonal table,as shown in Table 4.

Table 3 Test factor level table.

Table 4 L27(38)orthogonal table.

5.Calculation of muzzle disturbance values with repetitive observed value

With the help of tank random launch dynamics simulation system,the calculation results as shown in Table 5 are obtained,which are corresponding to the muzzle disturbance with repetitive observed values given in Table 4.The simulation conditions are as follows:

1)Traversing angle/elevation are 0o/5mil respectively during tank brake firing;

2)Take the mean values and mean square deviation of clearance between projectile and bore projectile e,mass eccentricity Lm,projectile dynamic unbalance angleβDand projectile load deviation r from Table 4;

3)Suppose the following parameters which are not given are constant,as mass distributions and space locations of road wheels,hull body,turret,cradle and barrel,reamers rigidity,reamers damping;charge weight;powder burning rate coefficient;powder force;temperature and air pressure;

4)For the random parameters such as projectile weight,loading angle offset and projectile rotational inertia,simulate and calculate these data in case of the statistical law being unchanged.

Simulation times are as follows:in order to reduce the influence of random method on the effectiveness of simulation result,each test shall adopt the both methods of Latin super cubic sampling method and Monte-Carlo random sampling method to bring out the random numbers according to Table 4.Every test includes 200×2 times launch dynamics simulation,ie.the total simulation times is 27×200×2.Refer to Table 5,Timeans the sum of muzzle disturbance on level i for all factors,and Xiis the muzzle disturbance mean value on level i for all factors.

6.Analysis of muzzle disturbance variance

6.1.Analysis of variance for each factor-F inspection

The general variation of 27 observed values in this test is made up of variation between treatment,variation between group and error variation.So the analytic formula for sum of square and degree of freedom are as follow[19]:

Table 5 Calculation of muzzle disturbance orthogonal test result.

Table 6 Variance analysis for orthogonal test of muzzle velocity.

Table 7 Variance analysis for orthogonal test of muzzle angular velocity.

Where,SSTis the sum of squares for general variation;SStis the sum of squares for variation between treatment;SSris the sum of squares for variation between group;SSiis the sum of squares for factor variation;SSe1is the sum of squares for model error variation;SSe2is the sum of squares for test error variation;relevant degrees of freedom are dfT,dft,dfr,dfi,dfe1,dfe2.

The sum of squares,sum of mean squares,degrees of freedom and F inspection value of each index variation source are shown in Table 6 and Table 7.Inspect the significant difference between MSe1and MSe2.If it is not significant after F inspection,for increasing the precision of analysis,combine its sum of squares and degrees of freedom separately,calculate the combined error mean squares,and then take the F inspection and multiple comparison for other variation sources.If it is significant after F inspection,which illuminates there is interaction,the two items cannot be combined,now only take the F inspection and multiple comparison between MSe1and other variation sources.

Within the test range chosen by this paper,it is shown in Table 6:(1)the difference between model error mean square MSe1and test error mean square MSe2is not significant,which means interaction between test factors is not significant and so the difference between each factors can really reflect the main effect of factors.(2)The influence of factors A,C and G on muzzle velocity mean valueis significant and the sequence of factors is:mean value of projectile load deviation＞mean value of clearance between projectile and bore＞mean value of mass eccentricity.(3)The influence of factors A,C and D on muzzle velocity mean valueis significant and the sequence of factors is:meanvalue of clearance between projectile and bore＞mean value of mass eccentricity＞mean square deviation of mass eccentricity.

Within the test range chosen by this paper it is shown in Table 7:(1)the difference between model error mean square MSe1and test error mean square MSe2is not significant,which means interaction between test factors is not significant and so the difference between each factors can really reflect the main effect of factors;(2)The influence of A,C,D and G on muzzle angular velocity mean valueis significant or very significant and the sequence of factors is:mean value of projectile load deviation＞mean value of mass eccentricity＞mean value of clearance between projectile and bore＞mean-square deviation of mass eccentricity;(3)The influence of C and G on muzzle angular velocity mean value is significant or very significant and the sequence of factors is:mean value of projectile load deviation＞mean value of mass eccentricity.

6.2.Multiple comparisons between factors-SSR method

For discussion the difference between factors,SSR method is used for multiple comparison between factors and getting the optimum value of each random factor.Minimum significant margin Rpis used to compare the difference between two mean values in SSR method.The formula for Rpis[19]:

Where,Qp（p，f）is the data obtained from SSR table under the given level T with degree of freedom of test error f and number of mean value p,is mean square of error after combination,n is test number.

In this section SSR method is used for multiple comparison between factor levels,and find the way to get optimum values for each factor within the range chosen by this paper,but the conclusion is not completely congruous to the engineering practice.For example,to reduce the mean value of muzzle velocitythe clearance between projectile and bore should be as small as possible(0.1 mm),but to reduce the mean value of muzzle velocity vy,the clearance between projectile and bore should be as large as possible(0.5 mm),etc.It is illuminated that the orthogonal test scheme cannot satisfy the requirement on dealing with the optimum values with SSR methods.The main reason is that the relationship between muzzle disturbance and each random factor is highly non-linear,and at the same time the range and test time chosen by this paper is relative small for analyzing efficiently the influence of projectile on muzzle disturbance.Through the test of 200 round/time×27 time/group×2 group and F inspection,the main factor which influence muzzle disturbance has been found,and definite the primary and secondary sequence of influence of each factor to different index,and realize the main purpose of research.

In conclusion,(1)as far as this study is concerned;the influence of the projectile loading offset on muzzle disturbance is most significant.It reveals the essence of large difference of firing dispersion with various loading methods(automatic loading,manual loading and loading by different loaders).The different projectile loading conditions lead to different muzzle disturbance and different firing dispersion with two different loading methods--loading by different loaders and automatic loading;Besides,asymmetrical loading(including linear offset and angular offset)makes a restoring force and a restoring moment depending on the stiffness of bearing band and lateral shift apply on the bearing band during the fire process.The restoring force and restoring moment make the projectile have a high frequency wiggle.It can cause the consistency of muzzle disturbance is worse than that by symmetrical loading,and reduce the firing dispersion.Then,from the point of loading condition,take followings to improve firing dispersion:①strengthen loading skilling training of loaders to improve loading level;②develop high performance auto-loader to realize concentric loading and in-place loading;③on the premise of reasonable matching of rifle and bearing band,there is enough width of bearing band;④improve projectile processing and assembling process to make coaxiality of bearing band and projectile as small as possible;⑤on the premise of reasonable matching of inner diameter of forcing cone and outer diameter of bearing band,reduce the inclination of forcing cone;⑥on the premise of reasonable matching of projectile front center band and rifling lands,reduce clearance between projectile and bore.(2)as far as this study is concerned,clearance between projectile and bore has a significant effect on muzzle disturbance,this explains the essence of influence of gun wear on firing dispersion;gun wear increases the clearance between projectile and bore and changes muzzle disturbance,affect firing dispersion ultimately.So,take followings to control clearance between projectile and bore:①improve machining accuracy of barrel bore and projectile front center band; ②for chrome-plated barrel, improve and manufacturing quality of film plating;③for non-chrome-plated barrel,improve wear-resisting property and erosion resistant of barrel material;④on the premise of ensuring firing capability,reduce explosion temperature of propellant and decrease corrosion of barrel bore from propellant through improving slow-corrosion of charge.(3)as far as this study is concerned,mass eccentricity of projectile has significant effect on muzzle disturbance,besides,the influence of mass eccentricity of projectile on exterior ballistics cannot be negligible in flight process of projectile.Thus,in order to improve the firing dispersion of tank gun,it is necessary to strictly control every step of projectile design and manufacturing process to eliminate mass eccentricity of projectile.(4)as far as this study is concerned,dynamic unbalance of projectile has no prominent influence on muzzle disturbance,relative parameters of dynamic unbalance of projectile can be controlled as a minor factor.(5)due to a highly nonlinearity relationship between muzzle disturbance and random factors,in certain range(range for choosing parameters),in case of relatively small test,analysis results given by SSR has limitations.

7.Conclusion

Based on launch dynamics equation of tank,establish simulation system for launch dynamics of tank and analyze the influence of projectile mass,mass eccentricity,dynamic unbalance,load deviation and clearance between projectile and bore on muzzle disturbance combined with orthogonal test design method.The results show that the main factors which influence muzzle disturbance include the mean value of clearance between projectile and bore,mean value of projectile mass eccentricity,mean square deviation of projectile mass eccentricity and mean value of projectile load deviation.By application of variance analysis method-F inspection,discuss the primary and secondary sequence of each factor to different index sensitivity,analysis results explain the essence of the influence of different loading methods and barrel wear on firing dispersion,and give some suggestions to reduce muzzle disturbance of tank and improve firing dispersion of tank.This study provides the theory base and simulation method for controlling angle of muzzle disturbance to improve firing dispersion of tank.

Acknowledgement

The research programme was funded by the Natural Science Foundation of China Government(11472135).