LIST OF SYMBOL USED

Design of the Recoil Mechanism for 175mm Gun

Introduction

A recoil system is the part of a Gun which takes care of the firing loads on the supporting

structures by prolonging the time of reaction force caused to the projectile fired and

propellant gasses.

Construction of the recoil system.

The recoil system consists of three basic components: A recoil buffer, a counter recoil

mechanism which includes the recuperator. Apart from these the system has different

valves, seals etc.

The floating piston separates the liquid from the gas within the recuperator. It has no piston rod in it and moves freely as the gas undergoes change in its volume.

As referred to the figure the piston has two heads joined integrally by a shank.

Functioning

A force is generated opposing the recoil force by the restricting the fluid flow through the

hydraulic cylinder. The magnitude of this restricting force is a function of the fluid flow

through one or more orifices, whose size is again varied with the velocity of the recoil.

The recoil energy absorbed by this resisting force is ultimately dissipated as heat.

Now as the gun has moved rearward on the cradle so it has to be brought back in its

battery position which is done with the help of a recuperator .If the recoiling mass is

moved very fast then there is a chance of the whole gun to topple down, this is prevented

by a component known as the buffer.

In this report an attempt has been made to design the recoil system of 175mm field gun

which is capable of launching a 74kg projectile with a muzzle velocity of 700m/sec.

The recoil system designed is of Single recoil type for simplicity, and the recuperator is

of gas spring type.

Description of the Recoil Cycle.

As the gun is fired, initially only the recuperator and frictional forces acts against

the recoil force. Now as the barrel starts moving, along with above forces the

hydraulic force also starts acting against the recoil force as the gun traverse. With

the recoil piston moving rearwards, the oil from the recoil cylinder is transferred

to the recuperator cylinder through a valve which pushes a floating piston and

compresses the gas which is present on the other side of the piston. The recoiling

parts reach the maximum velocity when the retarding force reaches the propellant

gas force.

At the completion of the recoil stroke, the recuperator starts acting and the energy

in the compressed gas is utilized in pushing the whole recoil mass to the battery

position of the gun .This force of counter recoil should never be less than the

weight of all the recoiling components .From this it is quite clear that the part of

the areas of the force-distance curve which represents the stored counter recoil

energy is predetermined

At the end of the counter recoil phase, there is control valve, which prevents the

jerk, which occurs at the end of the recoil. This control valve is designed such that

at the end of the counter recoil, the remaining counter recoil energy in the system

is absorbed. The buffer should be designed such that the recoiling parts just stop

at the end of the counter recoil.

Thus at the end of the counter recoil the weapon is again ready for the second

firing.

Definition of the problem

On the basis of the given inputs such as the Caliber of the weapon, weight of the

ammunition and the muzzle velocity, recoil system of the gun has to be determined, while

determining the total recoil force, different components of the recoil system such as the

buffer, recuperator and the control valve has to be designed. It should also be ensured that

the total recoil force, recoil velocity and recoil length should be realistic enough for the

gun structure stability and laying of it at different angles.

Mathematical model of the Recoil system

Considering the basic equation of the recoil system we have

The above equation is based on the d’Alembert’s principle, which defines that summation of all the external forces is equal to the inertial force.

Now to convert the above dynamic problem to problem of static equilibrium, we consider the inertial force of the recoil assembly is equal to the total recoil braking force acting in the opposite direction of the inertial force.So we have the total braking force as.

Solution of the problem using Matlab and Simulink

Based on the inputs given in the problem and referring to the standard references,

the recoiling mass, sealing and sliding frictions are determined and all these inputs

are fed into a summation box.

The output of this summation box is multiplied with a gain, which equals to the

mass of the recoil system.

The output from this gain is then double integrated to first get the velocity and

then the displacement.

The velocity and the displacement so obtained is then utilized by two different

wings or branch .One of which is the recuperator and the other is buffer.

Recuperator Force (Frecup)

For a hydro pneumatic type of recoil system the pressure in the recuperator cylinder is given by

Where x is the only variable on which the recuperator pressure depends, this value of x is derived from the integration of the acceleration as we have discussed earlier. All other values such as the recuperator piston area and the initial volume of the recuperator are assumed. This recuperator pressure when multiplied with recuperator cylinder area gives the recuperator force which is again fed into the control feedback loop in the equation of motion.

Hydraulic braking force (Buffer force) (H)

When the recoil fluid passes through the narrow orifice of the control valve, a braking force is generated, which is given by

Where

(Considering that the orifice area is being varied in terms of a parabolic function.)Where A, B and C are constants.Considering the maximum area of the orifice as m2

We have Therefore by modifying the equation

We get

In equation no …. We observe that the orifice area is a function of , this square of the displacement variable is obtained in a similar way by doubly integrating the acceleration and then squaring it. So equation no… is obtained by multiplying gain value which equals to constant A and then doing the necessary algebraic calculation.

The other constant value which does not depend on the displacement variable x and is used as an input to the main equation of motion are.

Weight of the recoiling mass at a particular angle It is given by , considering the gun is elevated at 20 degrees we have the weight component as 11970.1N, where g =10m/sec 2 (Approximately).

Frictional forces in the guide system

Frictional force at 20 degrees is given by

= =9867N.

Sealing friction.The sealing friction is considered to be 200N.

Pressure forceThe pressure force curve versus time is taken as an input to calculate the variation of the force which is acting through the centerline of the barrel to the breech by multiplying. This pressure versus time graph is converted into a 795 by 2 cell matrix and thus transformed to a .mat file.

DESIGN CALCULATIONS.

Design of Recuperator

Design of the Recuperator cylinder

For the design of the recuperator cylinder, following data which has been calculated and optimized through SIMULINK can be taken as an input. In the present context, initially some of the physical dimensions of the recuperator cylinder are assumed based on the space constraint. Once the values are obtained, these are checked for the failure criteria as follows………….

Maximum force of the recuperator N (from the

figure)Area of the recuperator piston * Or from equation we have maximum pressure in the recuperator cylinder Precup max = 12.73 Mpa.

Materials selection: ASTM A542/A542M Quenched and tempered.Ultimate tensile strength σut = 745 Mpa Yield tensile strength σy = 350 Mpa

From Lame's equation of thick cylinder we have

The maximum radial stress

and minimum radial stress is (At the outer radius of the cylinder).

Similarly the maximum tensile strength

Now, inner radius of the cylinder can be calculated from the area of the recuperator and the outer radius can be calculated simply by adding the thickness of the cylinder to it.

Thus ri = 66mm t = 7mm ro = ri+t = 73mm

or

= 126.61 Mpa

Now for the calculation of factor of safety we will use St Venant’s principle

Or - =

Or 126.61+12.73 =

Or FOS =

= 2.5 Approximately

Design of the pneumatic seal

Material selection:

The radial pressure acting on the packing materials is given by

Where, k =1.3 for 175mm gun floating piston.Or

Now

=9.93 Mpa

Or This multiplied with the crossection of the seal on which the pneumatic pressure is given by

= =61300.2 N

Where K is the Wahl’s stress factor

and C = = = 4.1

Or,

=1.39

Or by putting this value in equation we have

=53.25Mpa

Now maximum shear stress is given by

=0.577 =202 Mpa

Therefore the factor of safety is FOS = = 3.79.

And the total deflection is given by the equation

Now based on this axial force the seal fixing spring can be designed.

As there is a lot less space and huge force is required to seal so, rectangular type of spring is used.Or induced shear stress is given by

Design of the flange:

Design of the Floating pistonThe strength of the flange is determined, conservatively, by treating a sector cut out by a small angle. This flange from the side view can be considered as a cantilever with the axial force acting due to the gas pressure in the recuperator.

Total maximum axial force is given as

= 139823.65 NOr the moment due to this is given by

= 10207126.45 NmmNow the section modulus of the flange is given by Z = 0.5×35×732

= 93257.5 mm3

Or the bending stress is given by =

= 109.45 Mpa

Factor of safety is given by

Initially based on the requirement that the gun should be moved back to the battery position after the recoil, within a given time and depending on the rate of fire requirement of the gun. A suitable value of the recuperator force can be calculated from the equation below

Where =1.15 (constant)

After calculating this approximate recuperator force, inner diameter of the recuperator cylinder is estimated based on the space as well as the weight constraint.. From this area the volume of the recuperator cylinder is calculated.

Once is calculated, the value of maximum pressure in the recuperator cylinder is can also be calculated using

The pressure obtained from the above equation is again multiplied with area of the cylinder and fed into the feedback loop. Thus as the loop goes on, the recuperator force is calculated with the incremental values of the recoil displacement or the stroke length.

Based on the above procedure, following values are obtained

N

= 0.09or

=8 Mpa

Design of the buffer

Initially a suitable value Maximum pressure in the .

GIVEN DATAL = 1800mmVm=700m/secWr=3500kgWg=12kg

=16m/sec

= 260632.2N

This is the total recoil force used. Assuming a recoil piston diameter as 106mm The area on which the pressure is acting is

=29650000N/mm^2

Recuperator force:

=

Initial recuperator pressure = = 4.27Mpa

Volume displaced = 0.016m^3 (Recuperator pressure at the end of recoil)

Velocity of counter recoil

The counter recoil velocity is very important when the stability of the gun is a concern.It should be such that the gun should move very steady and at the same time it should stop at the end of the recoil and not affecting the stability of the gun. Higher counter recoil is desired where a high rate of fire is required as in the case of a air-defense gun,where as in the case of heavy guns a high counter recoil velocity is undesirable.

In the present design the recuperator is a mechanical spring so the available energy is given by:

Some of the recuperator energy is used to overcome the static resistance of the system.

Where is the static resistance to the counter recoil which is expressed as

Initially just before the recoil there is no resistance to the fluid flow, the kinetic energy of the counter recoiling mass when it first contacts the buffer is:

And the approximate recoil velocity is

Buffer Force:The buffer force should be such that is should provide the weapon stability .The buffer force is based on the kinetic energy of the recoiling parts, the static resistance and the recuperator force.

=

Design of Recoil mechanism components.

Recoil piston rod :Material selected: EN36B, =1000MpaThe diameter of the piston is determined by the fluid pressure required to be withstand by the recoil system.

Fillet radius of the rod----2mmDiameter of the of the rod 50mmDiameter of the stepped rod 30mm

From the stress concentration table we have Kt =1.9

From the above equation the diameter of the piston can be found out

A=

Design of the recoil cylinder

is the maximum fluid pressure is the proof pressure.

is the radial stress

is the hoop stress of the cylinder

Now the yield strength of the cylinder can be estimated as