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Analysis of the muzzle dynamic response interval based on the bond space method

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Abstract

Accurate analysis of the dynamic response of the muzzle shows a vital role in improving the accuracy of small-caliber artillery burst fire. However, the complex small-caliber artillery system and the uncertainty of parameters make the muzzle dynamic response analysis more difficult. To solve the problem that it is difficult to analyze the dynamic response of small-caliber artillery containing uncertain parameters by traditional methods, the critical uncertain parameters are regarded as interval variables, and the bonded space theory is used to establish the muzzle dynamic response model of small-caliber artillery with continuous firing, and combined with Chebyshev polynomial expansion method to solve it, and finally the muzzle dynamic response interval is obtained. Through computational analysis and experimental testing, 84.6 % and 95 % of the tested muzzle dynamic response curves in the horizontal and vertical directions fall into the simulation interval, respectively. Meanwhile, the error of the mean, the variance, the most value, and the amplitude of the test and simulation are less than 10 %, which verifies the method’s accuracy. In addition, by adjusting the optimized parameters, the amplitude of the dynamic response of the muzzle was reduced by 78.67 %. We conclude that the muzzle dynamic response interval method works well for analyzing and controlling the muzzle dynamic response problem with the desired accuracy.

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Abbreviations

m i :

The mass of the i-th equivalent concentrated mass

Jx i :

The rotational inertia in the x-direction of the i-th equivalent concentrated mass

Jy i :

The rotational inertia in the y-direction of the i-th equivalent concentrated mass

Jz i :

The rotational inertia in the z-direction of the i-th equivalent concentrated mass

1 :

The common flow element

0 :

The common effort element

E :

The effort source element

Sf :

The flow source element

I :

The inertial element

C :

The capacitive element

R :

The resistive element

TF :

The speed-transmission ratio element

p :

The generalized momentum of the independent single-port element

q :

The generalized displacement of the independent single-port element

e :

The interaction force

E ndd :

The combined force of artillery chamber

E 3-2 :

Force between the projectile belt and the barrel

Sf 3-2 :

Relative velocity between the projectile belt and the barrel

E 3-3 :

Force between the projectile head section and the barre

Sf 3-3 :

Relative velocity between the projectile head section and the barrel

T i :

Velocity ratio matrix characterizing the barrel structure

T 1-1~T 1-5 :

Velocity ratio matrix characterizing the artillery box structure

C i :

Capacitive matrix characterizing material properties

R i :

Resistive matrix characterizing material properties

C 1-1~C 1-4 :

Capacitive matrix characterizing contact

R 1-1~R 1-4 :

Resistive matrix characterizing contact

P :

The combined matrix of generalized momentum

Q :

The combined matrix of generalized displacement

q k :

The matrix of the muzzle dynamic response

\({\boldsymbol{q}}_k^I\) :

The interval matrix of the muzzle dynamic response

\({\boldsymbol{q}}_k^L\) :

Lower limit of the muzzle dynamic response interval matrix

\({\boldsymbol{q}}_k^U\) :

Upper limit of the muzzle dynamic response interval matrix

α :

The set of deterministic parameters

U I :

The set of interval parameters

p :

The number of uncertain parameters

m :

The number of interpolation points

\(u_i^c\) :

The median value of the interval parameters

β i :

The uncertainty coefficient

\({u_{i,{j_i}}}\) :

The i-th interpolation point of the ji-th uncertain parameter

\(u_i^U\) :

Upper limit of the i-th interpolation point

\(u_i^L\) :

Lower limit of the i-th interpolation point

\({\theta _{{j_i}}}\) :

Interpolation factor

I 1,…,I p :

The serial number of the terms in the numerical integration

\({f_{{l_1}, \ldots,{l_p}}}(t)\) :

The coefficients in the gaussian chebyshev numerical integration

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Acknowledgments

This work was supported by the Fund of study on the mechanism of aerogun burst XXX (in Chinese, Fund No.2019 JCXXX135), China.

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Authors and Affiliations

  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China

    Fu He, Jinsong Dai, Shengye Lin & Maosen Wang

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  1. Fu He
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  2. Jinsong Dai
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Correspondence to Jinsong Dai.

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The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Additional information

He Fu is a Ph.D. student in the School of Mechanical Engineering at Nanjing University of Technology. He received his M.S. degree in mechanical engineering from Nanjing University of Technology. His research interests include dynamics of artillery automata, mechanical vibration and interval uncertainty theory.

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He, F., Dai, J., Lin, S. et al. Analysis of the muzzle dynamic response interval based on the bond space method. J Mech Sci Technol 37, 5003–5014 (2023). https://doi.org/10.1007/s12206-023-0907-6

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  • DOI: https://doi.org/10.1007/s12206-023-0907-6

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