CHAPTER 1 INTRODUCTION
1.5 Thesis Outlines
In order to find the recoil force situation during firing, the force analysis and the mathematical model will be constructed based on Simulink® in this thesis. Simulink® is one of the packages in Matlab®. Furthermore, the model can help to realize the designs on the available products and literature, especially on the mechanism with some parameters. The brief description and outlines in this thesis contents are given as follows.
Chapter 2 is the literature review which includes brief introduction of some types of
recoil mechanism, and comparisons for different structures. Besides, there is a simple description about the procedure during firing.
Chapter 3 introduces the force analysis of the gun during firing, especially mathematical descriptions on the recoil force.
Chapter 4 proposes the dynamic analysis and the dynamic model creation of the recoil mechanism. It can be divided into five parts. With free body analyses and experimental data, the dynamic characters can be obtained from system equations. Using Matlab® Simulink, the dynamic model of system equations can be created into individual modulus.
Chapter 5 constructs a simulation model on Simulink®. The simulation results are analyzed with tendency forecasting to match the physical phenomenon. In addition, the simulation chooses some parameters to find the influence of these parameters on the performance of the recoil mechanism. Target and constraints of the optimization problem are defined according to the design requirements. Finally in this chapter, some improvement designs can be obtained by performing optimization.
Chapter 6 provides the concept of controlling the recoil length by controlling orifice area. When the relation between orifice area and recoil length is known, the recoil mechanism can be stopped at the desired recoil length.
Finally, Chapter 7 contains the conclusions and future works, which could assist some aspects for following works on this study.
CHAPTER 2 PRELIMINARY
2.1 Component of the Recoil Mechanism
The system of the recoil mechanism consists of eleven components: recoil piston rod, recoil piston, cushion, dish spring, recoil cylinder, recuperating cylinder, counterrecoil buffer, floating piston, recoil throttling valve, regulator, and regulator valve. All of these components have their respective different functions, which will be introduced in this section. The general functions are introduced as follows [3]:
1. Recoil piston rod: it is a tensile machine part; one end is connected with recoil piston, and the other with breech ring.
2. Recoil piston: the thickness of the piston is controlled by the space of cushion.
3. Cushion: it can prevent the moveable parts such as piston or piston rod from leakage. In Addition, the cushion presses the moveable surface strongly by fluid pressure and spring.
4. Dish spring: it can provide the pressure for the cushion. The dish spring can supply big load with small deformation in a small space.
5. Recoil cylinder: the inner diameter of the cylinder is determined by the diameter of the piston. Moreover, the tube thickness is determined by the pressure which cushion or fluid generates, and by the yielding stress of the material.
6. Recuperating cylinder: this part can store energy, and makes use of gas pressure to return the gun tube to the original position.
7. Counterrecoil buffer: it can be hydraulic or pneumatic. Besides, the buffer controls the velocity of the recuperating stroke.
8. Floating piston: this part is used to separate the liquid and gas in the recuperator cylinder.
9. Recoil throttling valve: this value can be used to control the hydraulic resistance flowing from recoil cylinder to recuperator cylinder.
10. Regulator: a tool, which is installed in the recuperator cylinder, can adjust pressure during recoil and recuperator. Besides, it has to control the flow of hydraulic fluid in any direction.
11. Regulator valve: a tool, which is installed in liquid end of recuperator cylinder, can adjust the flow of hydraulic fluid during recuperating period.
2.2 The Main Types
Because the recoil mechanism was developing for a long time, there are many available devices using in different kinds of guns. There is a general classification, hydrospring and hydropneumatic type, such as shown in Figure 2.2-1. The classification of the recoil mechanism is often seen in the national defense industry.
These two types of the recoil mechanism principally differ from their action components, one is the spring and the other is compressed gas. Generally speaking, recuperator was originally with the spring type [3] [4].
Figure 2.2-1 Classification of recoil mechanism [3]
2.2.1 Hydrospring
The hydrospring system is shown in Figure 2.2-2. There are a recoil brake, a recuperator, and a counterrecoil buffer. In fact, the device consists of two or three parts to ensure the structure more compact. Sometimes, there is a bigger spring which is wound around the barrel to get a more compact assembly.
The recuperator uses a mechanical spring, and the others use hydraulic systems.
Although this type is seldom used, there are still some advantages and disadvantage listed in Table 2.2-1. The design of the device is simple, low cost, rapid adjustment, easy manufacture, and there are fewer problems about the airtight leakage. But the life of the spring may not predictable. The volume is huge, and the component replacement is required frequently.
Figure 2.2-2 Hydrospring recoil mechanism [3]
Table 2.2-1 List the features of hydrospring system
Advantages Disadvantages
1. Simple design
2. Easy manufacture
3. Low cost
4. Rapid adjustment
5. Fewer airtight leakage
1. Maintenance
2. Big volume
3. Spring life
2.2.2 Hydropneumatic
For the hydropneumatic system, there are two different types: independent and dependent, as shown in Figure 2.2-3 and Figure 2.2-4 respectively. The recuperator fills with compressed gases, and the nitrogen gas is usually used because of its inactivity.
The recuperator of the independent type is separated from recoil brake completely.
Furthermore, the piston rods both directly connect with a back part. When the gun recoils, hydraulic fluid or oil will flow to the chamber of compressed gas. The fluid will then press on the gas to make the gas pressure rising, and the action will reverse during the recuperating time.
Figure 2.2-3 Hydropneumatic recoil mechanism (independent type) [3]
On the other hand, the recuperator of the dependent type is often connected to the recoil brake, but the gas is separated from fluid by the floating piston. Besides, the recoil piston rod links a back part simply. On the way of throttling, the fluid from recoil cylinder would be pressed on recuperating cylinder. Also, the advantages and disadvantages of the hydropneumatic system are listed in Table 2.2-2. The reliability of the hydropneumatic system is higher, the durability is better, the recoil distance is long, and the design is more flexible. However, the device needs specialized technology and the cost is expansive. In addition, the gas pressure will be easily changed by the atmosphere temperature, and affect the recoil velocity and recoil travel. So it needs some compensation. Moreover, the device is hard to keep the high firing frequency, because of the heat generation.
Figure 2.2-4 Hydropneumatic recoil mechanism (dependent type) [3]
Table 2.2-2 List the features of hydropneumatic system
Advantages Disadvantages
1. High reliability
2. Good durability
3. Flexible application
4. Long recoil distance
5. Easy maintenance
1. Hard manufacturing
2. Low firing frequency
3. High sensitivity on temperature
4. High cost
2.3 Forces and Procedures during Firing
During firing, a high gas pressure, which acts on the base of the projectile and accelerates it forward, arises in the combustion chamber of the tube. The same gas pressure also acts on the breechblock of the tube, which is forced to the rear with a gas recoil force, which is also called the breech force. The magnitude of this force is the same as the projectile accelerating force. This large gas recoil force on the gun tube does not act directly on the cradle of the tube but on the recoil mechanism.
The gun tube, which is accelerated back by the gas recoil force, is brought to stop by various braking components. These are the hydraulic braking force of the recoil mechanism, the force of the recuperator mechanism, and the friction forces among the components. The braking force acts as a forward direction on the recoil part of the gun to retard the recoil.
The braking of the recoil mechanism generates a mass inertial force, which in magnitude is equal to the total braking force, and acts towards the rear of the gun. Its line of
action goes through the center of gravity of the recoiling mechanism of the gun, regardless of where the individual braking force components act on. The recoil braking force knocks the gun backwards, while the baking force is a force which acts on the recoiling part of the gun in forward direction.
After the recoil motion is completed, the recuperating mechanism returns the gun tube to its original position. The required force is provided by mechanical springs or gas cushioning, which are compressed even more beyond their pretensioned state during the recoil of the tube. Therefore, at the end of counterrecoil, the gun gets no moving forward, and the recoil part is braked hydraulically at the end of counterrecoil by means of the recoil brake. The period which recoil force acts is from the projectile firing to the mechanism stopping. Therefore, this period is a complete cycle during firing [5] [6].
CHAPTER 3 FORCE ANALYSIS
3.1 Introduction
All kinds of recoil mechanisms operate according to same basic principles. The apparatus can control forces, through the specific recoil movement. In other words, it makes use of the force to retard the gun tube, and return the gun tube to original position.
When firing, owing to the action of the gas recoil force and the recoil braking force, the load on the gun body often varies from time to time. So, how to solve the force change of the recoil mechanism is a key discussion about this chapter.
Before the force analysis, some assumptions need to be established first. From a physical viewpoint, there is no external force acting on the artillery weapon during firing.
The process is the conservation of momentum, and it reflects properties and conditions of the artillery weapon. It also conforms to actual condition of firing. However, the energy conservation principle is difficult to apply because some energy is lost during firing [7].
The resistance force is composed of hydraulic braking force and spring force. Although these two forces act individually, it is treated as a resultant force in the system. Therefore, the overall system can be treated as a unit. Before the problem is defined, some assumptions have to be made as follows:
1. The boundary condition is free release and free recoil.
The analysis focuses on the motion of the recoil mechanism only. It uses systematic view to analyze the force behavior, and isn’t affected by external force of other components.
2. The supporting structure is immovable.
The supporting structure of the gun body is a rigid body. Its quantity of motion is very small. Thus, the motion of the supporting structure is neglected. It means that the analysis only focus on the first recoil effect.
3. The effect on the muzzle brake is ignored.
The recoil force is balanced by the muzzle brake and the recoil mechanism. The forces of these two parts are with a proportional relation, such as thirty percent for the muzzle brake and seventy percent for the recoil mechanism. Therefore, the effect on the muzzle brake could be ignored.
4. The analysis focuses on the bore period during firing.
The bore period means that a projectile moves along the bore of barrel until exiting the muzzle. After a projectile exits the muzzle, the bore pressure would drop to atmospheric pressure gradually. And the influence on recoil force is very small. For this reason, the analysis only focuses on the bore period.
According to the assumptions, the model can be simplified. Then, the equation of motion of the recoil mechanism can be defined. And the analysis of interior ballistics and the recoil motion can combine together so as to find the force conditions of all parts when the projectile exits.
3.2 Equation of Motion
Figure 3.2-1 1-D mode of gun
The equation of motion adopts a mode of single degree of freedom as shown in Figure 3.2-1. According to the Newton’s Second Law, the equation of motion of recoil mechanism is
( ) ( ) sin F=M Xr =B t −K t +Wr θ
∑
(3.2-1)where
∑
F is the total force on the recoil mechanism, M is the recoil mass, Xr is the recoil acceleration, B t( )is the breech force, K t( ) is the recoil braking force, is the recoil weight force, andWr
θ is the elevation.
∑
F consists of a breech force, a hydraulic braking force, a recuperator force, a frictional force, and the component of the weight, shown in Figure 3.2-2. There are somedescriptions about the forces on the recoiling parts during firing:
Figure 3.2-2 Forces on the parts moving in elevation
1. Forces acting parallel to the axis of the bore:
(1) Breech force B ( on the breechblock )
During firing, a high gas pressure arises in the combustion chamber of the tube; it acts on the base of the projectile and accelerates it forward. The same gas pressure also acts on the breechblock of the tube, so it is forced towards the rear as a gas recoil force, also called the breech force. The magnitude is the same as the projectile accelerating force.
(2) Hydraulic braking force H ( on the recoil piston rod )
acts towards the rear of the gun as a hydraulic braking force. This force can be basically produced by a fluid filled cylinder. Owing to the fact, the cylinder piston coupled to the recoiling masses presses the fluid through a narrow orifice. The magnitude of the force can be controlled by the valve cross-section. In addition, the cross-section and recoil travel have a constant relation.
(3) Recuperator force FR ( on the recuperator piston rod )
The counterrecoil mechanism returns the gun tube to its firing position. The force is often made used of mechanical springs or gas cushioning, which are compressed to store some recoil force during the recoil of the tube. Before firing, the device has to be an initial force in order to resist gravity, and keeps the gun at the original position. Figure 3.2-3 is the relation of the recuperator force and recoil travel. The force seems linear when the spring is used. If a nonlinear force is required, the gas cushion can be used.
(a) By spring (b) By gas cushion
Figure 3.2-3 Curves of recuperator force
(4) Frictional force R ( between pistons and the sliding track )
The frictional force is composed of frictions at the piston rod seals on the recoil brake and recuperator, and the piston seal in the recuperator. This force, called the packing friction R , is a constant. On the other hand, the sliding P track friction of the gun tube R is also a component of the frictional force. SL
(5) Weight component Wrsinθ ( on the center of gravity of the recoiling parts )
A component of recoil weight is a constant during recoil and recuperating time.
2. Forces acting perpendicular to the axis of the bore:
(1) Guide forces and ( on the tube claws ,and corresponding sliding surfaces of the gun tube )
N1 N2
The relation between the guide forces and sliding track friction force R is SL
1 2
A component of recoil weight force is a constant during recoil and recuperating time.
( )
B t is the breech force B. Besides, B t( ) can be indicated by the burning rate of powder as shown in Figure 3.2-4.
Figure 3.2-4 A Functional relation between B t( ) and time
( )
K t is the recoil braking force. This means that during the recoil braking, an inertial force has to be applied at the center of gravity of the recoiling parts in the direction of recoil, where is the braking retardation. This backwards directed inertial force is equal to the recoil braking force
R R
m a
aR
( )
K t . From the force equilibrium in the direction of the axis of the bore, the recoil braking force can be expressed as:
( ) R
K t =H+F + R (3.2-3)
where H is the hydraulic braking force, FR is the recuperator force, R is the friction force.
3.3 Analysis of Interior Ballistics
Figure 3.3-1 Three periods of recoil motion
The period of recoil motion, as shown in Figure 3.3-1, can divide into three parts [8]
[9]:
1. In bore period
The period means that a projectile moves along the bore of the barrel until exiting the muzzle. During this period, the motion of the recoil mass is an accelerative motion.
2. Aftereffect period
This period means that the bore pressure declines to approach the atmosphere pressure, after the projectile leaves the muzzle. During this period, the motion of recoil mass changes from positive to negative acceleration. Besides, the maximum velocity of recoil mass is generated in the period.
3. Inertia period
There is no bore pressure in this period, that is B= . The recoil mass moves by 0 the inertia force which is remained from the foregoing periods. In addition, the recoil device is retarded by a recoil resistance until the velocity is zero.
There are so many papers to describe the three periods. By the above-mentioned assumption, the analysis here focuses on the in-bore period to get a general theory.
3.3.1 Basic Equations
The basic equations refer to Figure 3.3-2, one listed as follows:
Figure 3.3-2 Moving projectile and barrel
x= + (3.3-1)s u
V du
= dt (3.3-2)
v ds
= dt (3.3-3)
b
P B
= A (3.3-4)
where x is the absolute displacement of the projectile, is the absolute displacement of the gun body, is the projectile travel, V is the projectile velocity, is the absolute
s
u v
velocity of the gun body, P is the recoil pressure, B is the gas force at the breech (or breech force) Ab is the bore area, and U0 is the barrel length.
Half mass of the combustion charge acts as the acceleration of a projectile, and the other half as the acceleration of a gun body. There are forces on a projectile and a gun body individually, and the force magnitude is equal but in opposite direction [10].
1 1
where Wc is the charge weight force, and Wp is the projectile weight force. Because 1 base of the projectile.
3.3.2 Determination of Le Duc Parameters: a and b
The projectile travel and projectile velocity in the bore can be expressed as a hyperbolic function which is also called Le Duc formula, as follows [10]:
V au
By rearrangement of Eq.(3.3-2), Eq.(3.3-7), and Eq.(3.3-10), B can be expressed as Eq.(3.3-11).
According to the muzzle position, is the barrel length, and is the muzzle velocity of the projectile. Then the values of a and b are attained as Eq.(3.3-14) and Eq.(3.3-15).
To simplify Eq.(3.3-14) and Eq.(3.3-15), a and b can be expressed as follows:
b=QU0 (3.3-16)
0( 1
3.3.3 Projectile Velocity and Breech Force
By rearranging of Eq.(3.3-9), Eq.(3.3-16), and Eq.(3.3-17), the projectile velocity as function of projectile travel is expressed as Eq.(3.3-18).
0
From Eq.(3.3-11), Eq.(3.3-16), and Eq.(3.3-17), the breech force is
2 2
By rearrangement of Eq.(3.3-19) and Eq.(3.3-20), the simplified breech force is represented as Eq.(3.3-21).
3.3.4 Relationship between Projectile Travel and Time
From
But Eq.(3.3-22) makes that the time is negative infinite when the beginning position of projectile ( ). For this reason, the time which the projectile exits muzzle can be found by the law of impulse and momentum.
0
where is the recoil velocity of the gun body when the projectile exits the muzzle, is projectile transit time, and
v0 tb
B is average breech force. The work of average breech force is
0
3.4 Determination of Total Resistance to Recoil
The basic principle of total resistance is assumed that the curve between K t( ) and time is a trapezoid as shown in Figure 3.4-1 [6]. Therefore, when the resistance reaches maximum, the value will be supposed as a constant. Therefore, the problem is to find the constant resistance. For this purpose, the section adopts the moment area method [8] [12].
The basic principle of total resistance is assumed that the curve between K t( ) and time is a trapezoid as shown in Figure 3.4-1 [6]. Therefore, when the resistance reaches maximum, the value will be supposed as a constant. Therefore, the problem is to find the constant resistance. For this purpose, the section adopts the moment area method [8] [12].