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MATHEMATICAL MODEL OF AUTOMATIC FIRING SYSTEM OF GAS-OPERATED MACHINE GUN
Authors:
Vo Van Bien1
,
Nguyen Duy Phon1
,
Nguyen Minh Phu1
1The Faculty of Special Equipments, Le Quy Don Technical University, Hanoi City, 100000, Vietnam
Received: 27 March 2023
Revised: 21 July 2023
Accepted: 7 August 2023
Published: 30 September 2023
Abstract:
This paper mentions a new approach to accurately and fully describe the mathematical model of the automatic firing system of gas-operated machine guns. The mathematical model is established based on Lagrange’s equations of the second kind. A numerical method was used to solve the research problem. The automatic firing system of the PKMS machine gun (of Russian origin) was selected for calculation and testing. After the research model is calculated, a comparison is made between the theoretical calculation results and the experimental results to verify the mathematical model. The comparison results between the calculation from the theoretical model and the results obtained from the experiment show that the mathematical model is suitable and reliable, the maximum velocity error of the bolt carrier is only 6.53%. The results obtained from this study are the basis for evaluating the working ability of the automatic firing system. This is also a reliable theoretical basis for designers to optimize the structure for automatic firing systems of gas-operated automatic weapons.
Keywords:
The automatic firing system, the PKMS machine gun, gas-operated weapons, Lagrange‘s equation
References:
[1] M. Macko, B.V. Vo, Q.A. Mai, Dynamics of Short Recoil-operated Weapon. Problems of Mechatronics. Armament, Aviation, Safety Engineering, 12(3), 2021: 9-26. https://doi.org/10.5604/01.3001.0015.2432
[2] P.H. Chuong, Textbook of structure and calculation on automatic firing system. Military Technical Academy, Hanoi, 1998. (in Vietnamese)
[3] L.A. Florio, Finite-Volume Modelling of System with Compressible Flow Propelled and Actuated Body Motion. Applied Mathematical Modelling, 33(8), 2009: 3360-3381.
https://doi.org/10.1016/j.apm.2008.11.005
[4] D.V. Doan, V.V. Bien, M.A. Quang, N.M. Phu, A Study on Multi-Body Modeling and Vibration Analysis for Twin-Barrel Gun While Firing on Elastic Ground. Applied Engineering Letters, 8(1), 2023: 36-43.
https://doi.org/10.18485/aeletters.2023.8.1.5
[5] D. Allsop, L. Popelinsky, J. Balla, V. Cech, S. Prochazka, J. Rosicky, Brasseys Essential Guide to Military Small Arms. Brasseys, London, United Kingdom, 1997.
[6] M. Fiser, L. Popelinsky, Small Arms. University of Defence, Brno, Czech Republic, 2007.
[7] M. Fiser, J. Balla, S. Prochazka, Automatic weapons – design and testing, Textbook. Alexander University of Trencin, Slovak Republic, 2007.
[8] M. Fiser, Design of small arms – impacts in mechanisms. Military Academy, Brno, Czech Republic, 1999.
[9] L. Popelinsky, Design of automatic weapons – calculation of functional diagram of automatic weapon. Military Academy, Brno, Czech Republic, 2000.
[10] L. Popelinsky, J. Balla, High rate of fire automatic weapons – design and projecting, Textbook. University of Defence, Brno, Czech Republic, 2004.
[11] B.V. Vo, L. Dobsakova, N.V. Dung, D.P. Nguyen, T. D. Nguyen, M.P. Nguyen, A Study on Firing Stability of Howitzer Mounted on Wheeled Vehicles. 2023 International Conference on Military Technologies (ICMT), Brno, Czech Republic, 2023, pp.1-7. https://doi.org/10.1109/ICMT58149.2023.10171322
[12] N.M. Mutafchiev, Methodology for Determining the Parameters of Gas Engine of Automatic Small Weapons. International Scientific Conference “Defense Technology Forum 2015”, Shumen, Bulgaria, 2015.
[13] L. Popelinsky, Gas Drive of Gas-Operated Automatic Weapons. University of Defence, Brno, Czech Republic, 1993.
[14] J. Balla, J. Horvath, Gas driver of machine gun. International Conference on Military Technologies 2011, Brno, Czech Republic, 2011.
[15] V.D. Tien, The Calculating Model of Impulse Force Diagram of Gas-Operated Automatic Weapons, Master Thesis. University of Defence, Brno, Czech Republic, 2013.
[16] D. Jevtic, D. Mickovic, S. Jaramaz, P. Elek, M. Markovic, S. Zivkovic, Modelling of Gas Parameters in the Cylinder of the Automatic Gun During Firing. Thermal Science, 24(6), 2020: 4135-4215.
https://doi.org/10.2298/TSCI200118152J
[17] V.D. Tien, M. Macko, S. Procházka, V. V. Bien, Mathematical Model of a Gas-Operated Machine Gun. Advances in Military Technology, 17(1), 2022: 63–77. https://doi.org/10.3849/aimt.01449
[18] G.S. Karthik, K.J.Y. Kumar, V. Seshadri, Prediction of Performance Characteristics of Orifice Plate Assembly for Non-Standard Conditions Using CFD. International Journal of Engineering and Technical Research (IJETR), 3(5), 2015: 162-167.
[19] A. Bagaskara, M.A. Moelyadi, CFD Based Prediction of Discharge Coefficient of Sonic Nozzle with Surface Roughness. Journal of Physics: Conference Series, 1005, 2018: 012010. https://doi.org/10.1088/1742-6596/1005/1/012010
[20] V. Horak, D.D. Linh, R. Vitek, S. Beer, Q.H. Mai, Prediction of the Air Gun Performance. Advances in Military Technology, 9(1), 2014: 31-44.
[21] V.D. Tien, S. Procházka, V. Horák, R. Vítek, P.B. Thanh, CFD Simulation of the Gas-Operated Weapon Drive Applied to the UK-59 Machine Gun. Advances in Military Technology, 17(2), 2022: 397-410.
https://doi.org/10.3849/aimt.01743
[22] T.T. Hieu, U.S. Quyen, Using the experimental method to determine the dynamic parameters of the automatic weapon when firing. Journal of Science and Technique, No.123, 2008: 118-123.
[23] N.H. Lanh, N.V. Dung, V.X. Long, N.Q. Vinh, An experimental method for measuring the dynamics of automatic firearms when firing. Journal of Science and Technique, No.148, 2012: 175-182.
[24] D.D. Tran, M.P. Nguyen, V.B. Vo, D.P. Nguyen, M. Macko, M. Vitek, Analysis of gas flow losses in a gas-operated gun. 2023 International Conference on Military Technologies (ICMT), 23-26 May 2023, Brno, Czech Republic, pp.1-7. https://doi.org/10.1109/ICMT58149.2023.10171337
[25] A.A. Shabana, Dynamics of multibody systems. Cambridge University Press, Cambridge, United Kingdom, 2020.
[26] J. Balla, Contribution to Determining of Load Generated by Shooting from Automatic Weapons. 2019 International Conference on Military Technologies (ICMT), 30-31 May 2019, Brno, Czech Republic, pp.1-6.
[27] J. Balla, V.D. Nguyen, Z. Krist, M.P. Nguyen, V.B. Vo, Study Effects of Shock Absorbers Parameters to Recoil of Automatic Weapons. 2021 International Conference on Military Technologies (ICMT), 8-11 June 2021, Brno, Czech Republic, pp.1-6. https://doi.org/10.1109/ICMT52455.2021.9502825
[28] P.N. Thieu, K.Đ. Tuy, Typical armament of synthetic weapons, part 5. Military Technical Academy, Hanoi, 2004. (in Vietnamese)
[29] J. Balla, L. Popelisky, Z. Krist, Theory of High Rate of Fire Automatic Weapon with Together Bound Barrels and Breeches. WSEAS Transactions on Applied and Theoretical Mechanics, 5(1), 2010: 71-80.
[30] S. Beer, L. Jedlicka, B. Plihal, Barrel Weapons Interior Ballistics. University of Defence, Brno, Czech Republic, 2004. (in Czech).
© 2023 by the authors. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0)
Volume 10
Number 1
March 2025
Last Edition
Volume 10
Number 1
March 2025
How to Cite
V.V. Bien, N.D. Phon, N.M. Phu, Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun. Applied Engineering Letters, 8(3), 2023: 91–100.
https://doi.org/10.18485/aeletters.2023.8.3.1
More Citation Formats
Bien, V.V., Phon, N.D. & Phú M.N. (2023). Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun. Applied Engineering Letters, 8(3), 91–100. https://doi.org/10.18485/aeletters.2023.8.3.1
Vo Van Bien, et al. “Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun.” Applied Engineering Letters, vol. 8, no. 3, 2023, pp. 91–100, https://doi.org/10.18485/aeletters.2023.8.3.1.
Vo Van Bien, Nguyen Duy Phon, and Nguyễn Minh Phú. 2023. “Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun.” Applied Engineering Letters 8 (3): 91–100. https://doi.org/10.18485/aeletters.2023.8.3.1.
Bien, V.V., Phon, N.D. and Phú M.N. (2023). Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun. Applied Engineering Letters, 8(3), pp.91–100. doi: 10.18485/aeletters.2023.8.3.1.
MATHEMATICAL MODEL OF AUTOMATIC FIRING SYSTEM OF GAS-OPERATED MACHINE GUN
Authors:
Vo Van Bien1
,
Nguyen Duy Phon1
,
Nguyen Minh Phu1
1The Faculty of Special Equipments, Le Quy Don Technical University, Hanoi City, 100000, Vietnam
Received: 27 March 2023
Revised: 21 July 2023
Accepted: 7 August 2023
Published: 30 September 2023
Abstract:
This paper mentions a new approach to accurately and fully describe the mathematical model of the automatic firing system of gas-operated machine guns. The mathematical model is established based on Lagrange’s equations of the second kind. A numerical method was used to solve the research problem. The automatic firing system of the PKMS machine gun (of Russian origin) was selected for calculation and testing. After the research model is calculated, a comparison is made between the theoretical calculation results and the experimental results to verify the mathematical model. The comparison results between the calculation from the theoretical model and the results obtained from the experiment show that the mathematical model is suitable and reliable, the maximum velocity error of the bolt carrier is only 6.53%. The results obtained from this study are the basis for evaluating the working ability of the automatic firing system. This is also a reliable theoretical basis for designers to optimize the structure for automatic firing systems of gas-operated automatic weapons.
Keywords:
The automatic firing system, the PKMS machine gun, gas-operated weapons, Lagrange‘s equation
References:
[1] M. Macko, B.V. Vo, Q.A. Mai, Dynamics of Short Recoil-operated Weapon. Problems of Mechatronics. Armament, Aviation, Safety Engineering, 12(3), 2021: 9-26. https://doi.org/10.5604/01.3001.0015.2432
[2] P.H. Chuong, Textbook of structure and calculation on automatic firing system. Military Technical Academy, Hanoi, 1998. (in Vietnamese)
[3] L.A. Florio, Finite-Volume Modelling of System with Compressible Flow Propelled and Actuated Body Motion. Applied Mathematical Modelling, 33(8), 2009: 3360-3381.
https://doi.org/10.1016/j.apm.2008.11.005
[4] D.V. Doan, V.V. Bien, M.A. Quang, N.M. Phu, A Study on Multi-Body Modeling and Vibration Analysis for Twin-Barrel Gun While Firing on Elastic Ground. Applied Engineering Letters, 8(1), 2023: 36-43.
https://doi.org/10.18485/aeletters.2023.8.1.5
[5] D. Allsop, L. Popelinsky, J. Balla, V. Cech, S. Prochazka, J. Rosicky, Brasseys Essential Guide to Military Small Arms. Brasseys, London, United Kingdom, 1997.
[6] M. Fiser, L. Popelinsky, Small Arms. University of Defence, Brno, Czech Republic, 2007.
[7] M. Fiser, J. Balla, S. Prochazka, Automatic weapons – design and testing, Textbook. Alexander University of Trencin, Slovak Republic, 2007.
[8] M. Fiser, Design of small arms – impacts in mechanisms. Military Academy, Brno, Czech Republic, 1999.
[9] L. Popelinsky, Design of automatic weapons – calculation of functional diagram of automatic weapon. Military Academy, Brno, Czech Republic, 2000.
[10] L. Popelinsky, J. Balla, High rate of fire automatic weapons – design and projecting, Textbook. University of Defence, Brno, Czech Republic, 2004.
[11] B.V. Vo, L. Dobsakova, N.V. Dung, D.P. Nguyen, T. D. Nguyen, M.P. Nguyen, A Study on Firing Stability of Howitzer Mounted on Wheeled Vehicles. 2023 International Conference on Military Technologies (ICMT), Brno, Czech Republic, 2023, pp.1-7. https://doi.org/10.1109/ICMT58149.2023.10171322
[12] N.M. Mutafchiev, Methodology for Determining the Parameters of Gas Engine of Automatic Small Weapons. International Scientific Conference “Defense Technology Forum 2015”, Shumen, Bulgaria, 2015.
[13] L. Popelinsky, Gas Drive of Gas-Operated Automatic Weapons. University of Defence, Brno, Czech Republic, 1993.
[14] J. Balla, J. Horvath, Gas driver of machine gun. International Conference on Military Technologies 2011, Brno, Czech Republic, 2011.
[15] V.D. Tien, The Calculating Model of Impulse Force Diagram of Gas-Operated Automatic Weapons, Master Thesis. University of Defence, Brno, Czech Republic, 2013.
[16] D. Jevtic, D. Mickovic, S. Jaramaz, P. Elek, M. Markovic, S. Zivkovic, Modelling of Gas Parameters in the Cylinder of the Automatic Gun During Firing. Thermal Science, 24(6), 2020: 4135-4215.
https://doi.org/10.2298/TSCI200118152J
[17] V.D. Tien, M. Macko, S. Procházka, V. V. Bien, Mathematical Model of a Gas-Operated Machine Gun. Advances in Military Technology, 17(1), 2022: 63–77. https://doi.org/10.3849/aimt.01449
[18] G.S. Karthik, K.J.Y. Kumar, V. Seshadri, Prediction of Performance Characteristics of Orifice Plate Assembly for Non-Standard Conditions Using CFD. International Journal of Engineering and Technical Research (IJETR), 3(5), 2015: 162-167.
[19] A. Bagaskara, M.A. Moelyadi, CFD Based Prediction of Discharge Coefficient of Sonic Nozzle with Surface Roughness. Journal of Physics: Conference Series, 1005, 2018: 012010. https://doi.org/10.1088/1742-6596/1005/1/012010
[20] V. Horak, D.D. Linh, R. Vitek, S. Beer, Q.H. Mai, Prediction of the Air Gun Performance. Advances in Military Technology, 9(1), 2014: 31-44.
[21] V.D. Tien, S. Procházka, V. Horák, R. Vítek, P.B. Thanh, CFD Simulation of the Gas-Operated Weapon Drive Applied to the UK-59 Machine Gun. Advances in Military Technology, 17(2), 2022: 397-410.
https://doi.org/10.3849/aimt.01743
[22] T.T. Hieu, U.S. Quyen, Using the experimental method to determine the dynamic parameters of the automatic weapon when firing. Journal of Science and Technique, No.123, 2008: 118-123.
[23] N.H. Lanh, N.V. Dung, V.X. Long, N.Q. Vinh, An experimental method for measuring the dynamics of automatic firearms when firing. Journal of Science and Technique, No.148, 2012: 175-182.
[24] D.D. Tran, M.P. Nguyen, V.B. Vo, D.P. Nguyen, M. Macko, M. Vitek, Analysis of gas flow losses in a gas-operated gun. 2023 International Conference on Military Technologies (ICMT), 23-26 May 2023, Brno, Czech Republic, pp.1-7. https://doi.org/10.1109/ICMT58149.2023.10171337
[25] A.A. Shabana, Dynamics of multibody systems. Cambridge University Press, Cambridge, United Kingdom, 2020.
[26] J. Balla, Contribution to Determining of Load Generated by Shooting from Automatic Weapons. 2019 International Conference on Military Technologies (ICMT), 30-31 May 2019, Brno, Czech Republic, pp.1-6.
[27] J. Balla, V.D. Nguyen, Z. Krist, M.P. Nguyen, V.B. Vo, Study Effects of Shock Absorbers Parameters to Recoil of Automatic Weapons. 2021 International Conference on Military Technologies (ICMT), 8-11 June 2021, Brno, Czech Republic, pp.1-6. https://doi.org/10.1109/ICMT52455.2021.9502825
[28] P.N. Thieu, K.Đ. Tuy, Typical armament of synthetic weapons, part 5. Military Technical Academy, Hanoi, 2004. (in Vietnamese)
[29] J. Balla, L. Popelisky, Z. Krist, Theory of High Rate of Fire Automatic Weapon with Together Bound Barrels and Breeches. WSEAS Transactions on Applied and Theoretical Mechanics, 5(1), 2010: 71-80.
[30] S. Beer, L. Jedlicka, B. Plihal, Barrel Weapons Interior Ballistics. University of Defence, Brno, Czech Republic, 2004. (in Czech).
© 2023 by the authors. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0)
Volume 10
Number 1
March 2025
Last Edition
Volume 10
Number 1
March 2025
How to Cite
V.V. Bien, N.D. Phon, N.M. Phu, Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun. Applied Engineering Letters, 8(3), 2023: 91–100.
https://doi.org/10.18485/aeletters.2023.8.3.1
More Citation Formats
Bien, V.V., Phon, N.D. & Phú M.N. (2023). Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun. Applied Engineering Letters, 8(3), 91–100. https://doi.org/10.18485/aeletters.2023.8.3.1
Vo Van Bien, et al. “Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun.” Applied Engineering Letters, vol. 8, no. 3, 2023, pp. 91–100, https://doi.org/10.18485/aeletters.2023.8.3.1.
Vo Van Bien, Nguyen Duy Phon, and Nguyễn Minh Phú. 2023. “Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun.” Applied Engineering Letters 8 (3): 91–100. https://doi.org/10.18485/aeletters.2023.8.3.1.
Bien, V.V., Phon, N.D. and Phú M.N. (2023). Mathematical Model of Automatic Firing System of Gas-Operated Machine Gun. Applied Engineering Letters, 8(3), pp.91–100. doi: 10.18485/aeletters.2023.8.3.1.