The internal ballistic problem for the 23 mm cannon using case telescoped ammunition

oretical research process to manufacture and use 23 mm case telescoped ammunition. Keywords: 23 mm cannon; Internal ballistic; Case telescoped ammunition. 1. INTRODUCTION A traditional medium calibre weapon system uses rounds of ammunition having the propulsion system fitted on the rear half of the projectile. The case containing the propellant has a larger diameter than the projectile, and hence the ammunition looks like a bottle. The Case Telescoped Ammunition (CTA) has a special structure whereby the projectile is completely embedded inside the case. Compared with the traditional ammunition with the same caliber, CTA yields better terminal performances and a 30% reduction in bulk volume. In addition, with CTA the loading of the round into the gun chamber is done without connectors. Therefore, the weapon systems using CTA can effectively prevent weapon jamming and thus are more reliable. Currently, CTA is still a new weapon that has not been studied in Vietnam. When fired, the CTA has a stage where the projectile moves in the control tube before cutting the band. This is a very different period from conventional artillery. Researching the CTA's internal ballistic problem is the basis for understanding the phenomenon of firing and the characteristics and the advantages/disadvantages of the weapon system using CTA to use them effectively. Figure 1. Structure of 23 mm Case Telescoped Ammunitions 1. Primer; 2. Case; 3. Propellant Grain; 4. Control Tube; 5. Projectile. 2. THE PHENOMENON OF FIRING AND THE INTERNAL BALLISTIC PROBLEM OF CTA 2.1. The phenomenon of firing and periods of the firing phenomenon When fired, the firing-pin acts on the bottom of the primer to ignite the booster charge and then ignite the propellant grain. The control tube and the forward case seal will work to seal the Cơ kỹ thuật & Cơ khí động lực 156 N. T. Dung, D. H. Son, “The internal ballistic problem using case telescoped ammunition.” gas. When the gas pressure was high enough to open the forward case seal, the projectile began moving in the control tube, during which the projectile moved freely. The projectile moving until the rotating band contacts with the barrel will perform band cutting. After cutting the projectile guided by the barrel, the gas continued to expand to make the projectile achieve the required speed at the muzzle. Preliminary period: The primer ignites the propellant grain and releases the gas. The projectile moves in the control tube until the rotating band contacts with the barrel, in this period, the pressure increased continuously until the pressure at the bottom of the projectile was equal to the linkage force between the rotating band and the control tube. The period of projectile movement in the control tube: In this period, the pressure increased continuously until the pressure at the bottom of the projectile was greater than the linkage force between the rotating band and the control tube. The projectile starts moving in the control tube until the roating band cutting into the barrel, the speed when the roating band contacts barrel 20 40 /gv m s  . First period: Starts from the moment the roating band is completely cut into the barrel until the propellant burns out. The pressure of the gas will increase, pushing the projectile to move in the barrel, increasing the volume of the gas behind the bottom of the projectlie, this will be the factor that reduces the pressure. In this period, the pressure reached the maximum value Pmax. The second period: Start from the moment the propellant burns out until the projectile comes out of the muzzle. During this period, the gas still had high reserves of energy, so it continued to expand, increasing the speed of the projectile and the reverse speed of the barrel. Due to the movement distance of this period was very short, the speed of the projectile was fast, so the time of this period was very short that allowed us to ignore the heat transfer from the gas to the barrel. Thus, this period can be considered as the adiabatic expansion period of gas. The last period of the gas effects: After the projectile comes out of the muzzle, the gas continues to flow, increasing the speed of the projectile and the reverse speed of the weapon system. That effect is called the final effect of the gas. At the end of this period, the speed of the projectile reaches its maximum value vmax. 2.2. The internal ballistic problem of CTA 2.2.1. Assumptions To make it easy to set up equations describing the firing phenomena and solving the internal ballistic problem, we accept the following assumptions [2]: - Burning of the propellant grains follow the law of geometric fire; - Burning of the propellant grains follow the law of linear fire speed: u = u1p; - All propellant burn under the same pressure conditions and equal to pressure P; - The composition of the combustion product is constant, the characteristics of the propellant grains f and are constants; - The adiabatic exponent k=1+ is considered as a constant and is equal to its average value in the temperature range from the combustion temperature of the gas to the temperature of the gas at the time the projectile flew out of the barrel; - By the time the gas pressure reaches the pressure P0, the rotating band was cut immediately, and the projectile started moving; - The movement of a projectile is considered until the moment the projectile flies out of the muzzle. 2.2.2. The differential equations system of the internal ballistic problem - The gas-generating equation of propellant: 32 ..... zzz   Nghiên cứu khoa học công nghệ Tạp chí Nghiên cứu KH&CN quân sự, Số 71, 02 - 2021 157 - The combustion rate equation of propellant: K dz P dt I  - The motion equation of projectile: m PS dt dv . .   - The basic equation of internal ballistic: 2. ( ) . . . . 2 S P l l f m v        Transform the above equations gives us a differential equations system of the internal ballistic problem with: Z - Relative thickness of fire; P - Average pressure in the barrel [kG/cm 2 ]; S - Cross section of the barrel [dm 2 ]; f - Propellant power [kG.dm/kG]; Ik - Total momentum of the gas [kG.s/dm 2 ]; Φ - Coefficients for calculating secondary work; Ψ - The amount of propellant was relatively burnt; W - The volume behind the projectile bottom [dm 3 ]; l - Distance of projectile movement over time t [dm]; t - The motion time of projectile [s]. Solving the system (2) we identify the relationships: (z, Ψ, P, V, l, W) = f(t) (z, Ψ, P, V, t, W) = f(l) Initial conditions of the differential equations system: Propellant power of the primer fmoi=250000 [kG.dm/kG]; Ignition pressure Pmoi=5000 [KG/dm 2 ]; Shot start pressure P0=30000 [KG/dm 2 ]. when t=0 then v=0; l=0; z=0; P=Pmoi;    1 11 0      moi moi P f 2.2.3. Solving the internal ballistic problem for Case Telescoped Ammunition 23 mm The input data of the 23 mm CTA is designed and manufactured by the Weapon Faculty - Military Technical Academy as follows: - Cross section of barrel S: S = ηs.d 2 ηs is the depth characteristic of the groove, and ηs= 0,80÷0,83. take ηs= 0,80 and we get: S = 0,80.(0,23) 2 = 0,042 dm 2 . - Coefficients for calculating secondary work: q K   . 3 1  With 23 mm cannon, we get K = 1,05 so: 092,1 157,0 02,0 . 3 1 05,1  We will choose any 5 values to calculate. The values are given in table 1: Table 1. Values of ω ,φ. ω 0,02 0,025 0,03 0,037 0,04 φ 1,092 1,103 1,113 1,128 1,134 - The shape characteristics of the propellant [3]: Calculate the shape characteristics of propellant according to the formulas in the document [2]. Intermediate parameters: 1 2,2 7.0,2 5,5 . 0,653; 2 D n d c       Cơ kỹ thuật & Cơ khí động lực 158 N. T. Dung, D. H. Son, “The internal ballistic problem using case telescoped ammunition.” 2 2 2 2 1 2 2 2,2 7.0,2 0,151; 4.2,75 . 4 Q D n d c      .073,0 75,2 2,01  c e  The shape characteristics of the propellant: 1 1 1 2 2.0,655 0,151 .0,073 0,73 0,151 Q Q         1 1 1 1 2 7 1 2.0,655 0,073 0,233 2 0,151 2.655 n Q              2 2 1 1 1 1 7 0,127 0,018 2 0,455 2.1,137 n Q            The input data to calculate the internal ballistic problem for 23 mm CTA is given in table 2. Table 2. Input data to calculate the internal ballistic problem for 23 mm CTA. Quantity Sign Sign on computer Unit Value Gun caliber d d dm 0,23 Cross-sectional area S S dm 2 0,042 Combustion chamber volume W0 W0 dm 3 0,0447 Distance traveled of projectile lđ lđ dm 9,2 Projectile weight q q kG 0,157 Propellant weight  omega kG 0,020 Propellant power f f kG.dm/kG 988000 Cumulative of gas  anfa dm 3 / kG 1,053 Density of the propellant  deta kG/dm 3 1,6 Total momentum Ik Ik kG.s/dm 2 300 The shape characteristics of the propellant χ λ  capa lamda muy - - 0,73 0,233 -0,018 Adiabatic exponent θ teta - 0,240 Shot start pressure P0 po kG/dm 2 30000 Gravitational acceleration g g dm/s 2 98,1 Figure 2. Algorithm solving the internal ballistic problem of CTA. Nghiên cứu khoa học công nghệ Tạp chí Nghiên cứu KH&CN quân sự, Số 71, 02 - 2021 159 The results of solving the internal ballistic problem for 23 mm CTA with 0,04 kg propellant using MatLab software are shown in the following figures: Figure 3. The result of calculating the internal ballistic with ω=0,04 kG. From the calculation results and data [3] we can see: - At the time the pressure reaches its maximum value: Pm = 2751,68 (kG/cm 2 ); Vd = 768,8 (m/s); Comparing the calculation results of internal ballistic with data [3] we can see: Maximum pressure: Pmlt= 2800 (kG/cm 2 ) difference is 48,3 (kG/cm 2 ); Tolerance is 48,3/2800 = 1,73%; Muzzle velocity: Vdlt = 720 (m/s) difference is 48,8 (m/s); Tolerance is 48,8/720 = 6,77%. Thus, the maximum pressure difference and the muzzle velocity calculated with [3] are 1.73% and 6.77%, respectively, within the allowable limits. 3. CONCLUSION The article investigated the firing phenomenon of weapons using CTA. The paper also reviewed the process of firing phenomena, established the internal ballistic model of the CTA, set up the differential equations system of the internal ballistic problem, and calculated the internal ballistic problem for 23 mm CTA is designed and manufactured by the Weapon Faculty - Military Technical Academy. The results show that there is still a mismatch between theoretical and internal ballistic problem calculations. However, the error about the maximum pressure difference and the muzzle velocity is within the permissible limits. REFERENCES [1]. Nghiêm Xuân Trình, Nguyễn Quang Lượng, Nguyễn Trung Hiếu, Ngô Văn Quảng, “Thuật phóng trong”, Học viện Kỹ thuật Quân sự, 2015. [2]. Nguyễn Quang Lượng, Nguyễn Thanh Điền, “Thuật phóng trong thời kì tống đạn”, NXB Quân đội nhân dân, Hà Nội, 2015. [3]. Nguyễn Quang Lượng, Trần Quốc Trình, “Số liệu vũ khí - đạn”, Học viện Kỹ thuật Quân sự, Hà Nội 2009. Cơ kỹ thuật & Cơ khí động lực 160 N. T. Dung, D. H. Son, “The internal ballistic problem using case telescoped ammunition.” [4]. “A Simplified Model and Numerical Simulation of the Combustion and Propulsion Process for Cased Telescoped Ammunition”, 2014 International conference on mechanics and materials Engineering (ICMME 2014). [5]. “Technical Evaluation of the DoD Cased Telescoped Ammunition and Gun Technology Programe” (Project No. 5PT-8016), 1996. [6]. “Experimental Study and Numerical Simulation of Propellant Ignition and Combustion for Cased Telescoped Ammunition in Chamber”, Xin Lu, Yanhuang Zhou, Yonggang Yu, School of Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China. [7]. В.Ф. Захаренков, “Внутренняя баллистика и автоматизация проекти-рования артиллерийских орудий: [учебник]”, Балт. гос. техн. ун-т. –СПб., 2010. –276 с.ISBN 978-5- 85546-580-8. TÓM TẮT BÀI TOÁN THUẬT PHÓNG TRONG CHO PHÁO 23 MM SỬ DỤNG ĐẠN ỐNG LỒNG Bài báo xây dựng mô hình tính toán và kết quả giải bài toán thuật phóng trong cho đạn ống lồng 23 mm. Các kết quả thu được cho thấy rõ ưu điểm của đạn ống lồng và là cơ sở khoa học cho quá trình nghiên cứu lý thuyết để chế tạo và sử dụng đạn ống lồng 23 mm. Từ khóa: Pháo 23 mm; Thuật phóng trong; Đạn ống lồng. Received 22 nd June 2020 Revised 30 th July 2020 Published 5 th February 2021 Author affiliations: Le Quy Don Technical University. *Corresponding author: thaidung1966@gmail.com.