Dynamic analysis of firing mechanism of underwater pistol

The important problem of designing underwater pistol was analysed and calculated the dynamics of firing mechanism. On the basis of analyzing the performance of the underwater pistol, the paper presents a theoretical model for analysing the dynamics of firing mechanism of underwater pistol with the with the resistance of water acting on firing pin and slide. The result of this research can be applied to design the underwater pistol and underwater firearm.


INTRODUCTION
HE underwater pistol is designed to destroy enemy personnel at ranges of up to 20m under water (depending on diving depth) [1].Firing under water is possible from all swimmer positions as well as against surface targets from under water.The pistol is intended for combat swimmers.Two kinds of typical underwater pistol current are HKP11 of Germany (Fig. 1a) and SPP-1M of Russian (Fig. 1b) [2].
In Vietnam, the research on underwater pistol is limited and water commando forces have not been equipped with this weapon.The researches are mainly focused on projectile's motion under water.So design underwater pistol has become a hot topic.
Manuscript Received on July 13 th , 2016.Manuscript Revised December 06 th , 2016.This research is funded by the state-level project "Design and manufacture underwater pistol and projectile to serve the water commando forces" code: KC.03.TN08/11-15.We are also grateful to our colleagues from Department of Weapons for valuable discussions which help to conduct the study.
Dung Nguyen Thai is Dean of the Faculty of Weapons and Director of the Technical Center for Weapons, Military Technical Academy (e-mail: thaidung1966@gmail.com).
Hung Nguyen Van is with the Department of Weapons, Faculty of Weapons, Military Technical Academy (e-mail: hungnv_mta@mta.edu.vn).
In the design process, the dynamic analysis of firing mechanism is a fundamental problem and very important [3].So the article focuses on solving this problem with the research object is firing mechanism of SPP-1M underwater pistol.The principle of operation of firing mechanism of underwater pistol based on the operation of typical pistol but it is improved to reduce the resistance of water [4].The firing mechanism of underwater pistol consists of: trigger, slide, slide latch, firing pin, and return spring [5,6,7,8].Fire process comprising two stages (fig.The dynamic model of firing mechanism of underwater pistol is built on the basis of the following assumptions: 1.The objects in the firing mechanism are absolute hard. 2. Ignore the resistance of water acting on the objects rotation in mechanism (Trigger and Slide latch).
3. Ignore the resistance of water acting on the return spring and Slide.
4. Ignore friction force acting on the objects when moving.
5. In stage II, Silde and firing pin are blocked into an object with mass is 3,4 m and it move forward.Hence the model of firing mechanism is simple model as shown in firgure 3.

Angular velocity of Trigger around origin O is constant.
In order to analyse dynamics of firing mechanism, at first we consider kinematic in stage I.In Fig. 2 it is seen that: Derivative equation system 1 we obtain: Derivative equation system 2 we obtain: In equation systems ( 1), ( 2), (3): 2 In stage I, external forces acting on the systerm as follows (Fig. 1): 1. Elastic force of the return spring F . 2. The Moment of trigger pull of the gunner p M .
3. The resistance moment of trigger spring RS M .
Assumption u M is useful moment acting on trigger to fire, we have: The total kinetic energy of the system given by [9]:   The dynamic equations of firing mechanism are in the Lagrangian form given by [10]: From Eq. ( 4), ( 5), (6) we have: Because the angular velocity of Trigger is constant (assumption 6), so 0 = .From Eq.7 we obtain: In stage II, the article only studying the dynamic of firing pin.So from the Fig. 3 we have: where 3,4 m is the total mass of slide and firing pin.
H is the original length of the spring.k is a constant factor characteristic of the spring., R R are resistance forces of water acting on firing pin and its are determined by the formula [11]: where 1 2 , A A are the area of firing pin at nose and body; is density of water; x is velocity of firing pin; From Eq.9, 10 we have: where 1 2 A A A = is the section area of firing pin.Initial conditions to solve equations (11)

Figure 1 .
Figure 1.Two kinds of typical underwater pistol a. HKP11 underwater pistol; b.SPP-1M underwater pistol 2 DYNAMIC MODEL OF FIRING MECHANISM OF UNDERWATER PISTOL 2): Stage I: Slide and firing pin moves backward.After pulling the trigger, trigger (1) motions and impacts on B point on the slide (3) to make slide and firing pin moving backwards.Stage I ended when the catch (2) is not contact with B point on on the slide.Stage II: Slide and firing pin moves forward.After the catch (2) is not contact with B point, Slide (3) and firing pin (4) move forward under the Dynamic analysis of firing mechanism of underwater pistol Dung Nguyen Thai, Hung Nguyen Van T action of recoil force of the spring.Firing pin moving forward and strike the primer on bullet to fire.

1 J
are the kinetic energy of Trigger, Slide latch and Slide is the moment of inertial of Trigger.

2 m
is the mass of Slide latch.

3 , 4 m
is the total mass of slide anf firing pin.

Figure 3 .
Figure 3. Model of firing mechanism of underwater pistol in stage II the dynamic equations of firing pin in stage II are:

Figure 4 .
Figure 4. Displacement, velocity and acceleration of slide in stage I