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MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENCE ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY DO DINH LAO RESEARCH ON THE EFFECT OF SEVERAL STRUCTURAL PARAMETERS ON THE DYNAMICAL PARAMETERS, SOUND REDUCTION LEVEL, MOTION STABILITY AND PRECISION OF SOUND REDUCTION MORTAR SHELLS BASED ON THE INVERTED MOTION PISTON PRINCIPLE Specialization: Mechanical engineering Code: 52 01 01 SUMMARY OF PhD THESIS IN ENGINEERING HA NOI - 2019 The work has been completed at: Academy of Military Science and Technology Scientific supervisors: Prof Dr Bui Ngoc Hoi Dr Dang Hong Trien Reviewer 1: Prof Dr Nguyen Hong Lanh Military Technical Academy Reviewer 2: Dr Phan Van Chuong Academy of Military Science and Technology Reviewer 3: Dr Nguyen Phuc Linh General Department of Defense Industry The thesis was defended in front of the Doctoral Evaluating Examining Committee level held at Academy of Military Science and Technology at… ,…., 2019 The thesis can be found at: - Vietnam National Library - Library of Academy of Military Science and Technology INTRODUCTION The urgency of research Based on the request of the army, in recent years, the PhD student along with the research team of the Weapon Institute have carried out some research projects on sound reduction mortar system based on inverted motion piston principle These studies have achieved certain results in structural principles, built a certain basis of theory, as well as gaining some features of the product However, it is necessary to continue researching and completing models of the movement of mortar shell in the barrel and on its ballistic trajectory, investigating the influence of several structural parameters on dynamical parameters, sound reduction level, motion stability and precision of the sound reduction mortar shells In order to solve the above remaining issues and directly assist for the calculation, design and manufacture of sound reduction mortar shells based on inverted motion piston principle, the PhD student chose the thesis topic: "Research on the effect of several structural parameters on the dynamical parameters, sound reduction level, motion stability and precision of the sound reduction mortar shells on the inverted motion piston principle” The goal of the research - Building a model of the internal ballistics problem and a model of motion problem of the sound reduction mortar shells on the inverted motion piston principle on its trajectory in accordance with the structure of the sound reduction mortar shells, reflecting the nature of the dynamical process - Building a scientific basis for the reasonable selection of structural parameters of the sound reduction mortar shells to meet the requirements of sound reduction level, motion stability and precision of the shells Objects and scope of research of the thesis Object of research: a sound reduction mortar shell working based on the inverted motion piston principle and the focus is on the 50 mm calibre shell Scope of the research: focusing on researching and building a problem of movement of the sound reduction mortar shells in the bore For the problem of movement of mortar shells outside the bore, the thesis only builds a model of the movement of mortar shells taking into account the vibration of the projectile axis to calculate the trajectory, determine the maximum range and evaluate the ability to stabilize the movement of the mortar shells on its ballistic trajectory; Do not study factors affecting the movement and dispersion of the mortar shells Focusing on investigating the effect of the group of structural elements and structural parameters on dynamical parameters, sound reduction level and motion stability of 50 mm caliber sound reduction mortar shell; Do not investigate the effect of the group of factors on the stuffing conditions on the dynamical parameters of the mortar shells, but based on the results of the studies of the works [15], [16] to choose an existing propellant that met to the technical-tactical feature requirements of 50 mm caliber sound reduction mortar shell (spherical propellant C-LP100) Research Methodology Combining theoretical and empirical research: - Applying the basic theory of internal and external ballistics of conventional artillery and mortar guns to build and perfect the model of the internal ballistics and a model of the movement of mortar shells on the its ballistic trajectory appropriate with structural characteristics and the dynamical process of the sound reduction mortar shells on the inverted motion piston principle Using Matlab software to programmatically solve the problem of internal ballistics, the problem of the motion of mortar shells on the ballistic trajectory built by the thesis, investigating the separate and synthetic effects of a number of structural parameters to dynamical parameters as the basis for the reasonable selection of structural parameters of the sound reduction mortar shells Use Ansys software to examine the stress and deformation status of the piston-cylinder pair when firing to check and evaluate the stability of the movement of mortar shells in the bore and sound reduction level of shells - Building an experimental method to measure the sound level, velocity, pressure, range and precision of the mortar shells in accordance with the structural characteristics and working principle of 50 mm caliber sound reduction mortar shell The experimental results are the basis for verifying and assessing the suitability of the theoretical problem models that have been built by the thesis, and contemporary evaluating the effect of the gap of fitting between the piston and cylinder to sound reduction level of the sound reduction mortar shells that the current theoretical method has not solved Scientific and practical significance of the thesis Scientific significance: - Building and perfecting the structural model and mathematical models to reflect correctly the dynamic nature of the sound reduction mortar shells; - Building the scientific basis to select reasonable structural design parameters to meet the technical-tactical feature requirements of the sound reduction mortar shells Practical significance: Solving the problems of the basis of calculation theory, design of the sound reduction mortar shells that our army is needing to equip for the special forces The scientific basis is fully studied to help designers have an orientation in the design of the sound reduction mortar shells to meet the technical-tactical feature requirements of the order agencies as well as solve arising problems in the exploitation and use of the sound reduction mortar shells when they are put into equipment for our army Layout and content of the thesis The thesis consists of the preface, conclusion and chapters: Chapter Overview of the sound reduction weapons and the sound reduction mortar shells; Chapter Building structural model and models of dynamical problems of the sound reduction mortar shells; Chapter Investigating to the effect of several structural parameters on dynamical parameters, sound reduction level, motion stability and precision of the sound reduction mortar shells; Chapter Experimental research The entire content of the thesis is presented in 130 pages of A4 paper including 86 figures, 32 tables, published works of the author, references and annexes Chapter OVERVIEW OF THE SOUND REDUCTION WEAPONS AND THE SOUND REDUCTION MORTAR SHELLS Currently, the sound reduction weapons in the world mainly use silencers and sound reduction shells The sound reduction shells have two basic principles, namely sound reduction shells based on forward direction motion piston principle and sound reduction shells based on inverted motion piston principle 1.1 The sound reduction shells based on forward direction motion piston principle Figure 1.1 shows the structural principle model of the sound reduction shell based on forward direction motion piston principle [33] 1.The firing mechanism, Cylinder (cartridge), Piston, Projectile Figure 1.1 Model of structure of the sound reduction shells based on forward direction motion piston principle 1.2 The sound reduction shells based on inverted motion piston principle Figure 1.2 is the general structure model of the sound reduction shells based on inverted motion piston principle The piston mechanism is mounted with a firing pin, Cylinder, Piston, Propellant, Projectile Figure 1.2 Model of structure of the sound reduction shells based on inverted motion piston principle Due to the different working principles, it leads to the scope of use, the structure of the shells and the characteristics of the ballistics between the two types of shells are much differences, this has been carefully analyzed in section 1.1.2, chapter of the thesis 1.3 Overview of the research situation of the sound reduction shells based on forward direction motion piston principle and inverted motion piston principle 1.3.1 Research situation abroad a) The sound reduction shells based on forward direction motion piston principle: The sound reduction shells based on forward direction motion piston principle have been studied and manufactured by the Soviet Union since the 1960s and put into equipment such as 7.62 mm PZA, PZAM, 7.62 mm SP2, SP-3, SP-4 [33] b) The sound reduction shells based on inverted motion piston principle: Currently, many countries around the world have designed, manufactured and put it into equipment for the army such as: The 51 mm caliber FLY-K 8111 TN sound reduction mortar system of France, the 50 mm caliber Norinco sound reduction mortar system of China, the 60 mm caliber Delta sound reduction mortar system of Georgia Recently, the Federal Republic of Russia has studied and manufactured the 82 mm caliber sound reduction mortar system of which operation based on the principle of the inverted motion piston Due to the demand of military secrets, the research projects on the sound reduction mortar shells were hardly published 1.3.2 Research situation in our country a) The sound reduction shells based on forward direction motion piston principle: Over the past few years, author Bui Ngoc Hoi has had a number of researching works about the system of sound reduction weapon based on forward direction motion piston principle [18], [19] This is a system of weapon that incorporates between ammunition and bore in order to create sound reduction effects when firing The bore can also be a cylinder that makes the gun having a compact size and eases to camouflage In the work [33], the author Vo Thien Son has studied quite complete about the 5.6mm caliber sound reduction bullet which operates based on the principle of forward direction motion piston for YRS-007 revolver, built a structural model of the sound reduction bullet, built and perfected the theoretical basis of internal ballistics calculation, provided scientific basis and built algorithms to study the dynamics of piston-cylinder system; studied the effect of several structural parameters, dynamical parameters to the sound reduction level and the working ability of the bullet The research results [18], [19], [33] have partly suggested the research direction of the thesis However, due to the differences between the sound reduction mortar shells based on inverted motion piston principle and the sound reduction shells based on forward direction motion piston principle about the structure, size and operation principle, it is necessary to have a separate study in terms of structure, ballistics as well as factors affecting the features of the sound reduction mortar shells based on inverted motion piston principle b) The sound reduction shells based on inverted motion piston principle: In the works [15], [16], [17], the author Nguyen Dinh Hao has studied, calculated and built a structural model of 50 mm caliber sound reduction mortar shell and gun operating based on the inverted motion piston principle In general, the above studies on the sound reduction mortar shells have achieved certain results in structural principles, built a certain basis of theory as well as achieved some features of the product However, the scientific basis for research, calculation and design of the sound reduction mortar shells still has some shortcomings such as have not yet studied completely the model of the movement problem of mortar shell in the bore and on its ballistic trajectory, have not studied and fully investigated the state of stress, deformation of the pair of piston-cylinder on the moving journey and when it collides at the end of the moving journey, have not surveyed and fully evaluated the influence of structural parameters on the dynamic parameters of the sound reduction mortar shells Therefore, there has not been a basis for reasonable selection of structural parameters of shells to meet the technical-tactical feature requirements of the sound reduction mortar shells 1.4 Research direction of the thesis To solve the above-mentioned problems, the thesis focuses on researching the follofin main issues: - Building and perfecting the structural model, internal ballistics problem model, model of motion problem and stabilizing movement of mortar shells on the trajectory Problem models were built to investigate the effects of structural parameters on the dynamical parameters, stabilizing the movement of shells in the bore and on the trajectory, as well as calculating the trajectory and range of the sound reduction mortar shells Investigating the stress state, deformation of the piston-cylinder pair when moving on the journey and when colliding at the end of the moving journey; investigating the effect of the gap between the piston and cylinder to the dynamic parameters, to stabilizing the movement in the bore and sound reduction level of the sound reduction mortar shells These investigating results are the scientific basis for the reasonable selection of the gap between the piston and cylinder, the taper angle of the piston and cylinder to meet the requirements of sound reduction level, stabilizing the movement of the sound reduction mortar shells in the bore - Investigating the influence of several structural parameters on dynamical parameters, investigating the influence of stable pipe length, number of stable fins and stable fin length to stabilize movement on the trajectory and precision of the shells The results of this investigation along with investigating the gap between the piston and cylinder mentioned above are the basis for evaluating and selecting the reasonable structural parameters of the sound reduction mortar shells - Selection of structure and structural parameters of the 50 mm caliber sound reduction mortar shells in the investigating value area to manufacture and experiment in order to verify the correctness of the theoretical calculation models built by the thesis Conclusion of chapter - Among the sound reduction solutions for the weapon system, the solution which reduces sound for the shells based on the principle of piston- cylinder has the outstanding advantages: the sound is small when firing, without smoke and flash at the muzzle, compact structure, suitable to equip for individuals to perform special tasks such as special task force and task force - Based on the evaluation of research results of sound reduction shells at domestic and abroad, the thesis has pointed out the remaining problems and research directions of the thesis (Section 1.4) In addition, the thesis has built the quality requirements of the 50 mm caliber sound reduction mortar shell in which as the basis for the following research contents in the following chapters Chapter BUILDING STRUCTURAL MODEL AND MODELS OF DYNAMIC PROBLEMS OF THE SOUND REDUCTION MORTAR SHELLS 2.1 Structural model and dynamic process of the sound reduction mortar shells 2.1.1 Structural model of the sound reduction mortar shells based on the inverted motion piston principle The structural model of the sound reduction mortar shells based on the inverted motion piston principle is shown in Figure 2.1 Detonator; Projectile; Propellant; Piston; Cylinder; Stable fins Figure 2.1 Structural model of the sound reduction mortar shells based on the inverted motion piston principle 2.1.2 The dynamic process of the sound reduction mortar shells Dynamic process of the sound reduction mortar shells is divided into four periods of shoot phenomenon (Figure 2.4) Preliminary period: The preliminary period is started from the time when the propellant is fired by the primer until the flange of the piston is completely pulled-off, the piston is released from the connection with the cylinder and rests close to the force transmission handle of the gun The gas 11 2.2.1 System of the differential equations of internal ballistics of the sound reduction mortar shells On the basis of the structural model, analysis of dynamic process and internal ballistics characteristics, together with the assumptions given by the thesis, the thesis has built the system of differential equations of internal ballistics of the sound reduction mortar shells based on the inverted motion piston principle as follows:  0 dz p  k1 ; k1   z  dt Ik 1   d     (  2 z   z )z; dt   f (   ) ;  p  pmoi    W0  (  )  (   )  SL    ( k  )1mvv  d   ;   dt     (   )  ( k  )  f     d 2 K0 St p ;   dt   f    0 dv Sp v   k2 ; k2   dt m  1   L  v  dL  dt z 1 z 1 (2.22) p  pdt p  pdt The system of differential equations (2.22) has been newly built on the basis of applying the basic knowledge of internal ballistics of conventional weapons to the specific structure of the sound reduction mortar shells based on the inverted motion piston principle In which, consider the pistoncylinder system of the shell is an open thermodynamic system, including the gas that passes through the gap between the piston and the cylinder Therefore, the system of differential equations (2.22) correctly demonstrates the nature of the dynamic process that takes place when performing a shot, and represents the analytical relationship between the structural parameters and dynamical parameters 12 Solve (2.22) to receive results of the velocity parameters of the shell v(t), v(L) and the gas pressure in the cylinder bore p(t), p(L) Together with the expression (2.21), we calculate the muzzle velocity of the shell v0 2.2.2 Calculation of internal ballistics of 50 mm caliber sound reduction mortar shell by theory Figure 2.11 and figure 2.12 are the velocity graph of the shell and the gas pressure in the cylinder according to the movement journey and movement time of the sound reduction mortar shells (theoretical calculation graph) Figure 2.11 Graph of velocity of shell according to the movement journey and time Figure 2.12 Graph the gas pressure according to the movement journey and time Graph of variation of gas pressure according to the time p(t) of theoretical calculation results (Figure 2.12) is consistent with graph p(t) of experimental results (Figure 4.13) Error between theoretical calculation and experiment in chapter (relative error of muzzle velocity is 1.84%, relative error of gas pressure is 4.05%) The results showed that the problem of internal ballistics of the sound reduction mortar shell was built properly, consistent with the experiment 13 2.3 Build the system of differential equations of shell motion taking into account the oscillation of the shell axis and assess the motion stability of the sound reduction mortar shells on the trajectory The system of differential equations of motion of mortar shells taking into account the oscillation of the shell axis in the vertical plane on the entire trajectory is constructed by the thesis as follows:   b v  b v 2    b v ; R d c  d c d  g cos     v  aN v d ;     aR v  g sin  ;   x  v cos  ;  y  v sin  (2.35) The differential equations system (2.35) allows the calculation of the external ballistics to determine the trajectory and the range of the projectile and investigate the oscillation of the shell axis on the vertical plane The system of differential equations of oscillation of the sound reduction mortar shell axis in the inclined plane on the entire trajectory that the thesis constructed as follows:   b v  b v 2    b v ; C  n C n R n    aN v n ;     aR v (2.36) The thesis has calculated and verified the model of the sound reduction mortar shell motion problem with 82 mm mortar shell The relative error of the maximum range of the theoretical calculation results compared to the firing table is approximately equal to 0.35%, the relative error in the oscillation wavelength of the theoretical calculation results compared to the document [45] approximately equal to 2.2% 14 The sound reduction mortar shell is said to be stable on the trajectory if it satisfies the follofin two requirements: - On the straight line of the trajectory: if the dimensionless wavelength of the designed sound reduction mortar shells is smaller than the dimensionless wavelength of the existing finned ammunition has been verified to be stable bstk  bshc ; - On the curve of the trajectory: if the maximum dynamic equilibrium angle appears near the trajectory peak cbmax  100 Conclusion of chapter - Structure, working principle, characteristics of internal ballistics and dynamics process of the sound reduction mortar shells are completely different from conventional mortar shells and other types of ammunition The sound reduction mortar shells don’t have the last effect period of the gas The propellant gas is sealed almost completely when the piston is closed tightly to the cylinder, thus creating a superior sound reduction effect compared to conventional ammunition - The thesis has built a model of the internal ballistics problem of the sound reduction mortar shells in the form of differential equations system (2.22) and model of motion problem of the sound reduction mortar shells on its trajectory taking into account oscillation of the shell axis in the form of differential equations (2.35) and (2.36) These problem models are consistent with the structure and they have been verified by experimental results with small errors within the allowed range The research results in Chapter are important basis to investigate the quantitative effects of structural parameters on dynamic parameters, sound reduction level, motion stability of the sound reduction mortar shells in Chapter It is also a basis for reference with experimental research results in chapter of the thesis 15 Chapter INVESTIGATING TO THE EFFECT OF SEVERAL STRUCTURAL PARAMETERS ON DYNAMICAL PARAMETERS, SOUND REDUCTION LEVEL, MOTION STABILITY AND PRECISION OF THE SOUND REDUCTION MORTAR SHELLS 3.1 Investigate to the effect of several structural parameters on the dynamic parameters of the shell Applying the problem model and the internal ballistics calculation program built in Chapter 2, the thesis investigates the individual effects of seven structural parameters to the dynamic parameters of the 50 mm caliber sound reduction mortar shell From the investigation results, the thesis draws the law of the qualitative and quantitative effects of each structural parameter to the dynamic parameters of the shell (muzzle velocity of shell v0, maximum pressure of gas pmax ) As follows: - When increasing mass of shell m, pmax increases rapidly according to linear rule, v0 decreases according to linear rule but it is slower than the increase of gas pressure (when m increases from 0.9 kg to kg, v0 decreased approximately 2.3%, pmax increased approximately 7.7%) - The mass of the piston mpt does not affect pmax and the velocity of the shells on the movement distance of the cylinder but only slightly affects v0 due to the piston mass is relatively small, it value ranges between 20 grams and 40 grams (mpt increases 10 grams, v0 decrease approximately 1%) - When increasing pressure pulling out piston’s flange pdt, both pmax and v0 increase according to the linear rule, pmax increases faster than v0 (pmax increases approximately 22.5%, v0 increases approximately 5%) Therefore, increasing pdt will be beneficial in increasing v0 but not in terms of shell strength because pmax increases much faster than v0 From the technical tactical requirements of the sound reduction mortar shell (especially the requirement of pmax) and the experimental results of assessing the stability of pulling the piston’s flange, pdt should be limited between 14 MPa and 17 MPa - When increasing the movement journey of cylinder Lđ, both v0 and pmax increase, pmax increases according to linear rule, v0 increases with 16 nonlinear rule; v0 increased rapidly when increasing Lđ from 0.1 m to 0.2 m (increased 11.9%), when Lđ > 0.2 m, v0 increased very slowly (increased less than or equal to 4.7%) Therefore, increasing Lđ is only effective for v0 in the range of 0.1 m to 0.2 m - When increasing the inner diameter of cylinder D, both pmax and v0 decrease according to the nonlinear rule Specifically: when increasing D from 0,015 m to 0,02 m, pmax decreases 57%, v0 decreases 13.3%; when increasing D from 0.02 m to 0.025 m, pmax decreases 48.8%, v0 decreases 18.2%; when D> 0,025 m, both v0 and pmax decrease very fast, v0 is not satisfactory The survey results show that the D value in the area of 0.02 m is reasonable - When increasing the combustion chamber volume W0, both pmax and v0 decrease according to nonlinear rules When W0 increased from 2.10-6 m3 to 5.10-6 m3, pmax decreased much faster than v0 (pmax decreased 81.6%, v0 decreased 26.2%) From the survey results, the value zone of W0 ranges from 3.1.10-6 m3 to 3.6.10-6 m3 meeting the requirements of v0 and pmax - When increasing the cross-sectional area, the gap between the piston and the cylinder St from 1.10-6 m2 to 4.57.10-6 m2, both v0 and pmax are reduced according to the law of almost linear (v0 decreases 12.4 %, pmax decreased 22.6%) From the investigating results and experiments, the value of St from 1.5.10-6 to 2.5.10-6 m2 meets the requirements of v0, pmax, sound reduction level, motion stability and ability to meet tolerance for manufacturing piston-cylinder pair From the survey results of these seven parameters, the thesis has preliminarily selected the structural parameters of the 50 mm caliber sound reduction mortar shell (table 3.8 of the thesis) The thesis has builded an algorithm diagram (Figure 3.8) and the program investigates the general effect of structural parameters on dynamical parameters Survey results affect the combination with the technical-tactical requirements of the product and the ability to meet the technology tolerances for manufacturing piston-cylinder pairs, the thesis has selected the set of structural parameters reasonable of the 50 mm caliber sound reduction mortar shell (table 3.10) 17 Table 3.10 Selecting several structural parameters of the 50 mm caliber sound reduction mortar shell Order Structural parameters number Mass of shell (including piston) Mass of piston Inner diameter of cylinder The cylinder movement journey Combustion chamber volume Cross-sectional area of the gap between the piston and the cylinder (gap between the piston and cylinder) Pressure pulls off the piston’s flange Mass of spherical propellant C-LP100 symbol unit m mpt D Lđ W0 St (0) pdt  kg Value 0.981.0 kg 0.0200.024 m 0.0200.0201 m 0.150.16 m3 3.1.10-6÷ 3.2.10-6 m2 1.5.10-6 ÷ 2.5.10-6 (m) (0.048.10-30.08.10-3) MPa kg 1417 (2.050.001).10-3 \ 3.2 Investigating to the effect of several structural parameters to motion stability in the bore and the ability of sound reduction of the shell - Investigating to the state of stress, deformation of the piston, cylinder on the moving journey and when colliding at the end of the moving journey - Investigating to the effect of several structural parameters to motion stability in the bore and the ability of sound reduction of the shells The result is that it has been to select the appropriate conical angle of piston and cylinder vc=150200; The gap between the piston and cylinder selected in table 3.10 has been checked to meet the requirements of motion stability of the shell in the bore and sound reduction ability of the 50 mm caliber sound reduction mortar shell 3.3 Investigating to the effect of several structural parameters on the motion stability on the trajectory and precision of the shells The thesis has investigated the effect of several main structural parameters (stable pipe length, number of stable fins, stable fin length) to the parameters of oscillation and motion stability of the shell on the trajectory; investigated the effect of structural parameters on the precision of the 50 mm caliber sound reduction mortar shell The investigating results have selected the reasonable parameters of stable pipe and stable fins (table 3.19) 18 Table 3.19 Selecting a reasonable value domain of stable and stable fins Order Parameters of stable pipe and stable fins number The length of stable pipe Value 100110 mm (2.0d2.2d) The length of stable fins 6590 mm (1.3d1.8d) The number of stable fins 810 fins Conclusion of chapter - Each structural parameter has a different effect on the dynamical parameters of the sound reduction mortar shells Therefore, the investigation of the aggregate effect of structural parameters on the dynamic parameters is very important in the reasonable selection of structural parameters to meet the technical-tactical feature requirements of the shell (reasonable structural parameters of the 50 mm caliber sound reduction mortar shell are selected in table 3.10) - The effect of sound reduction and motion stability in the bore of the sound reduction mortar shell depend mainly on the structure and structural parameters of the piston-cylinder pair In particular, the gap between the piston and cylinder has a great influence on the sound reduction level, the velocity of the shell, the gas pressure and motion stability in the bore (reasonable clearance of the 50 mm caliber sound reduction mortar shell selected in table 3.10); The conical bottom structure of piston and cylinder (with cone angle vc=150200) meets the requirement of completely sealing the gas in the cylinder at the end of the moving journey, thus creating a sound reduction effect for the 50 mm caliber sound reduction mortar shell - Motion stability of the sound reduction mortar shell on the trajectory depends on many structural parameters In particular, stable pipe length, fin length and number of stable fins are important structural parameters, which have a decisive influence on motion stability of the sound reduction mortar shell on the trajectory Research results have selected the reasonable structural parameters of stable pipe and stable fins as shown in Table 3.19 19 Chapter EXPERIMENTAL RESEARCH 4.1 The purpose of empirical research Demonstrating the correctness of the structural model of the 50 mm caliber sound reduction mortar shell based on inverted motion piston principle and models of motion problem of the sound reduction mortar shells were built in chapter and theoretical research results in chapter of the thesis by the experimental firing and measurement results of the sound reduction mortar shell which was manufactured by the thesis 4.2 Experimental measurement of muzzle velocity and pressure of the 50 mm caliber sound reduction mortar shell 4.2.1 Experimental results of measuring muzzle velocity of shell Testing firing groups (7 rounds per group) with dimension zones of gap between piston and cylinder: group (StTB =1.71.10-6 m2), group (StTB = 3.01.10-6 m2), group (StTB = 4.57.10-6 m2) Experimental results: group (v0TB = 77.12 m/s, rv0 = 0.25 m/s), group (v0TB = 72.83 m/s, rv0 = 0.74 m/s), group (v0TB = 69.1 m/s, rv0 = 0.35 m/s) Specific results are presented in table 4.3 of the thesis 4.2.2 Experimental results of measuring gas pressure in cylinder Testing firing groups (group 1: fire rounds, group and group fire rounds per group) corresponding to dimension zones of the gap between the piston and cylinder: group (StTB=1.71.10-6 m2), group (StTB=3.01.10-6 m2), group (StTB=4.57.10-6 m2) Experimental results: group (pmaxTB=185.4 MPa), group (pmaxTB= 62.7 MPa), group (pmaxTB=142.8 MPa) Specific results are presented in Table 4.4 of the thesis Figure 4.13 is a graph showing the variation in the gas pressure in the cylinder over time of the 50 mm caliber sound reduction mortar shell 20 Figure 4.13 Graph of variation gas pressure in cylinder according to time 4.2.3 Evaluate experimental results - Graph of variation of gas pressure p(t) according to theoretical calculations in Chapter (Figure 2.12) in accordance with graph p(t) of experimental results (Figure 4.13) - The results of calculating the theory of internal ballistics problem in Chapter by the method of numerical integration: the muzzle velocity of v0LT = 78.54 m/s, the maximum pressure of the gas inside the cylinder pmaxLT = 192.9 MPa Experimental results measuring the muzzle velocity of the shell and the maximum pressure of the gas in the cylinder: v0TN = 77.12 m/s, pmaxTN = 185.4 MPa Relative error of muzzle velocity of 1.84%, relative error of maximum gas pressure of 4.05% - When the cross-sectional area of the gap between the piston and cylinder St increases in a very small range (1.71.10-6  4.57.10-6 m2), the muzzle velocity of the shell and the gas pressure decrease very fast (experimentally, muzzle velocity reduced from 77.12 m/s to 69.1 m/s, approximately equal to 10.4%; gas pressure decreased from 185.4 MPa to 142.8 MPa, approximately equal to 23%) - The error value of the probability of muzzle velocity of three firring groups is very small (rv0 = 0.25÷0.74 m/s), proving that the muzzle velocity 21 of the rounds in the group is very stable This is the factor that helps increase the precision of the sound reduction mortar shell 4.3 Experimental measurement of sound level of the 50 mm caliber sound reduction mortar shell Test results of sound level measurement of firing groups (7 rounds per group) of the 50mm caliber sound reduction mortar shell (corresponding to dimension zones of gap between the piston and cylinder StTB=1.71.10-6 m2  4.57.10-6 m2) and rounds of 60 mm mortar shell in Table 4.6 and Table 4.7 of the thesis show that: - The measured sound level of each round of the 50 mm caliber sound reduction mortar shell (according to the frequency  63.3 dB) The sound level according to the frequency meets the technical tactical feature requirements of the 50 mm caliber sound reduction mortar shell ( 65 dB) When increasing the gap between the piston and the cylinder, the sound level received when firing increases significantly - The average sound level according to time of groups of the 50 mm caliber sound reduction mortar shell (89.1 dB) is less than 33.4 dB of sound non-reduction mortar sound level (sound level of 60 mm mortar shells is 122.5 dB) This proves that the sound reduction mortar shells based on the principle of piston-cylinder are effective to reduce sound significantly compared to conventional mortar shells of the same size 4.4 Experimental measurement of the firing range and precision of the 50mm caliber sound reduction mortar shell Testing firing groups (group fire 10 rounds, group 2, 3, fire rounds per group) Experimental results are presented in table 4.8 of the thesis From the experimental results, the thesis comments as follows: - The 50 mm caliber sound reduction mortar shell works reliably (100% fire), motion stability in the barrel and on the trajectory (the shell moves in accordance with the trajectory, not yawing, without making whistle and unusual expression, ); - The precision of firring groups is high and meets the technical tactical feature requirements of the 50 mm caliber sound reduction mortar shell (LD/ X ≤1/50, LH/ X ≤ 1/150) 22 Conclusion of chapter - Experimental method of measuring the muzzle velocity of the shells, the gas pressure, sound level, range and precision of shells are reliable, in accordance with the structural model of the sound reduction mortar system and the existing equipment in the country - Experimental results of measuring the muzzle velocity of the shells, gas pressure in the cylinder and the calculation results of the internal ballistics problem of the 50 mm caliber sound reduction mortar shell built in Chapter by the thesis are consistent and reflective correct the law of qualitative and quantitative with the error in the allowed range (relative error between theoretical calculations and experimentation: muzzle velocity of 1.84%, gas pressure of 4.05%) - Experimental results of measuring the sound level of the shells when the piston-cylinder pair is fabricated in a reasonable gap zone (St =1.5.10-6  2.5.10-6 m2) meet the technical-tactical feature requirements of the 50 mm caliber sound reduction mortar shell (sound level of each round: according to the frequency  63.3 dB, according to the time 98.3 dB) - Experimental results of measuring the maximum range and precision of the 50 mm caliber sound reduction mortar shell proved that the model of the movement problem of the sound reduction mortar shell built by the thesis in chapter is correct and appropriate to practice (the maximum range error between experimentation and theoretical calculation is less than 5%; the precision of the four firing groups meets the technical tactical feature requirements of the 50 mm caliber sound reduction mortar shell) - The gap between the piston and cylinder has a great influence on the sound reduction level, the muzzle velocity of the shells, the gas pressure and the maximum range of the 50 mm caliber sound reduction mortar shell (when St increased from 1.71.10-6 m2 to 3.01.10-6 m2, the sound level when firing increases approximately 8.6%, the muzzle velocity of the shells decreases approximately 5.6%, the maximum pressure of the gas decreases approximately 12.2%, the maximum range of shells decreases approximately 10%) 23 CONCLUSION The dynamic process of the sound reduction mortar shells mainly takes place in the piston and cylinder, including periods of firing phenomenon and there is no period of the last effect of the propellant gas like conventional guns and mortars The model of internal ballistics problem of the sound reduction mortar shells built in chapter by the thesis is consistent with the structural characteristics and dynamic process of the shells, reflecting correct the law of qualitative and quantitative with small errors in permissible range (relative error between theoretical calculation and experimentation: muzzle velocity error of 1.84%, gas pressure error of 4.05%) The model of motion problem of the sound reduction mortar shells on the trajectory taking into account the oscillation of the bullet axis built in chapter by the thesis is suitable to reality with small errors in the allowable scope (relative error when calculating verification for 82 mm mortar shell: maximum range error of 0.35%, wavelength error of 2.2%; relative error of maximum range of the 50 mm caliber sound reduction mortar shell between theoretical calculation and experimentation less than 5%) The effect of sound reduction and motion stability in the bore of the sound reduction mortar shells mainly depend on the structure and structure parameters of the piston-cylinder pair In particular, the gap between the piston and the cylinder has a great influence on the sound reduction level, the muzzle velocity of the shells, the gas pressure and the maximum range of the shells Calculated and experimental results draw a reasonable gap between piston and cylinder 0=0.048.10-30.08.10-3 m (St=1.5.10-62.5.10-6 m2) and reasonable conical angle of piston bottom and cylinder bottom vc= 150200 Each of the structural parameters of the sound reduction mortar shells has a different law of influence on the dynamical parameters So the investigation of the aggregate effect of the structural parameters on the dynamical parameter has a significant meaning in the reasonable selection of structural parameters to meets the technical- tactical feature requirements of the 50 mm caliber sound reduction mortar shell (reasonable structure 24 parameters of the 50 mm caliber sound reduction mortar shell were investigated and selected in table 3.10 and table 3.19) Motion stability of the sound reduction mortar shells on the trajectory depends on many parameters, in which stable pipe length, fin length and number of stable fins are important structural parameters and they have a decisive influence (reasonable parameters of the stable pipe and the stable fins are given in table 3.19) The research results of the thesis are new, meaningful science and practice, providing a scientific basis for the design and manufacturing of the sound reduction mortar shells currently in need of equipment for our army New contribution of the thesis: - Built the model of the internal ballistics problem and motion problem of the sound reduction mortar shells based on inverted motion piston principle on the its ballistic trajectory In particular, some parameters of the research model have been verified by experimental results - Investigated and evaluated effect of several the structural parameters to the dynamical parameters, the sound reduction level, motion stability and precision of the sound reduction mortar shells Hence, built a scientific basis for the reasonable selection of the structural parameters of the shells to meet the requirements of the sound reduction level, motion stability and precision of the 50 mm caliber sound reduction mortar shell Further research: - Investigating to the effects of the stuffing conditions (type of propellant, mass of propellant, stuffing density, total impulse of gas pressure during combustion of propellant, ) to dynamical parameters of the sound reduction mortar shells; - Researching and evaluating more fully the effect of the gap between the piston and cylinder to the sound reduction level of the sound reduction mortar shells; - Researching on the effect of structural parameters, dynamic parameters and meteorological conditions on the precision of the sound reduction mortar shells 25 LIST OF PUBLISHED SCIENTIFIC WORKS Do Dinh Lao, Vo Thien Son, Bui Ngoc Hoi, "Research on durability calculation of cylinder of bullet silencer on piston-cylinder principle" Journal of Military science and technology research, Academy of Military Science and Technology, No 43, June 2016, pp 171-176 Do Dinh Lao, Dang Hong Trien, Bui Ngoc Hoi, "Research on the characters of ballistics, bulding the mathemetics model for internal ballistics of silent mortar shell based on the inverted motion piston principle” Journal of Military science and technology research, Academy of Military Science and Technology, special issue, No 09, September 2019, pp 181-190 Do Dinh Lao, Ngo Phi Hung, Bui Ngoc Hoi, " Research, build the expression for calculating the muzzle velocity of silent mortar shell" Journal of Military science and technology research, Academy of Military Science and Technology, No 51, October 2017, pp 157-164 Do Dinh Lao, Dang Hong Trien, Bui Ngoc Hoi, "Research on the effect of several structural parameters on the dynamical parameters of silent mortar based on the inverted motion piston principle" Journal of Military science and technology research, Academy of Military Science and Technology, No 52, December 2017, pp 205-214 Do Dinh Lao, "The experiment to evaluate the gas pressure characteristics of the 50 mm silent mortar shell based on the principle of contrary motion piston" Journal of Military science and technology research, Academy of Military Science and Technology, No 57, October 2018, pp 185-192 Ngo Phi Hung, Do Dinh Lao, Bui Ngoc Hoi, "Establishing mathematical models to study collisions and deformations of solid conical cones moving in absolute hard face" Journal of Military science and technology research, Academy of Military Science and Technology, No 61, June 2019, pp 197-203 ... group) with dimension zones of gap between piston and cylinder: group (StTB =1.71.10-6 m2), group (StTB = 3.01.10-6 m2), group (StTB = 4.57.10-6 m2) Experimental results: group (v0TB = 77.12 m/s,... dimension zones of the gap between the piston and cylinder: group (StTB=1.71.10-6 m2), group (StTB=3.01.10-6 m2), group (StTB=4.57.10-6 m2) Experimental results: group (pmaxTB=185.4 MPa), group... 0=0.048.10-30.08.10-3 m (St=1.5.10-62.5.10-6 m2) and reasonable conical angle of piston bottom and cylinder bottom vc= 150200 Each of the structural parameters of the sound reduction mortar shells