A review on the gun barrel vibrations and control for a main battle tank

Tolga Dursun,F?rat Büyükcivelek,?ar?han Utlu

Aselsan Inc MGEO Division,CankiriYolu 7.km Akyurt,Ankara 06750,Turkey

A review on the gun barrel vibrations and control for a main battle tank

Tolga Dursun*,F?rat Büyükcivelek,?ar?han Utlu

Aselsan Inc MGEO Division,CankiriYolu 7.km Akyurt,Ankara 06750,Turkey

1.Introduction

Main battle tanks require effective weapon control system and gun system in order to achieve the highest hit probability under all battlefield conditions,in the shortest possible reaction time from a stationary or moving tank to a stationary or moving target.Weapon control system is composed of two main parts.These are fire control system(FCS)and gun control system(GCS).Weapon control systems used in main battle tanks(MBTs)stabilise the line of sight(LOS)and line of fire(LOF)in order to increase the firing accuracy while the MBT is on the move.FCS determines the necessary motions of the gun and the conditions that will achieve the highest first shot hit probability.These are realised by ballistic computation of data obtained from sensors(laser range finder,meteorological sensor,gun and vehicle encoder and inertial measurement units etc.)and the application of fire inhibit algorithms.On the other hand,gun control system implements the gun and turret motion by the help of elevation and azimuth drivers and stabilization algorithms.Controller algorithm designs which are important inachieving higher stabilisation performance have been studied in Refs.[1-5].An efficient control strategy must be employed to ensure precision pointing of the gun according to the gunner's or commander's sighting system.It is important that the gun control system satisfies this performance under the harsh ground vibrations induced due to the movement of the main battle tank along the roughterrain.The main source of vibrationin a main battle tank is the running gear system.This system includes tracks,sprockets,idler wheels and support rollers.Most vibrations are generated by the constant impact of the driving sprockets on the moving tracks when the vehicle is in motion.Interactions between the tracks and the ground,the idler wheels as well as the support rollers also cause vibration.In addition the running engine and transmission are the other sources of vibration in the main battle tanks[6-8].

The performance objective of the classical gun control system is to maintain minimum trunnion-pointing error as measured by the gun-trunnion angular measurement sensor.Since the gun barrel is a long flexible tube,during the MBT is on the move,the gun barrel deflects.Therefore muzzle end points deflected LOF with respect to the trunnion axis(stabilised point).This deflection,caused by the terrain induced vibration of the gun barrel;results in the dispersion of shots on the target leading to the decrease of the effectiveness of the weapon system and reduced first shot hit probability(FSHP).The gun flexibility is notgenerallyconsidered in gun systems which use L44 calibre gun or similar.Since 1990s,the L44 calibre gun was not considered powerful enough to defeat the new generation armours,which led to the development of advanced 120 mm L55 calibre gun.The L55 gun is approximately 1.3 m longer,giving an increased muzzle velocity(from 1600 m/s to 1750 m/s)to the ammunition fired through it.Longer gun barrels,however,are more susceptible to ground induced vibration.This modification in the gun barrel should not decrease the FSHP of the tank while the tank is on the move.

Since the introduction of the L55 calibre guns,researchers have performed many experimental and numerical studies in order to investigate the effect of the longer gun barrel on the firing accuracy of the tank gun and increase the availability of this gun system.Studies on the vibrations of gun barrel can be grouped in five classes such as the determination of the dynamic characteristics of the gun/projectile system,control of the muzzle end deflection using muzzle reference systems,reduction of the muzzle end vibration using vibration absorbers,reduction of the muzzle end vibration with structural modifications in the gun,and last but not least,studies on the muzzle end deflection estimation/prediction using fire control algorithms(coincidence algorithms,which calculate the right time to allow firing)in conjunction with the sensors such as the gun gyros and accelerometers.In this review paper the first four classes of studies are discussed in detail.The last issue will be discussed in detail in future work.

2.Dynamic characteristics of a tank gun/projectile system

The major components of the tank gun system that may have effect on the dynamic characteristics of the gun are(1)barrel with thermal jacket,(2)cradle,(3)cradle tube,(4)bore evacuator,(5)MRS,(6)breech mechanism,(7)elevation mechanism(elevation gear)and(8)recuperator as shown in Fig.1.

Vibration of a gun barrel is composed of two dynamic events.These are the interaction of the projectile with the barrel during firing instant and the vibration of gun barrel due to the motion of the tank over the rough terrain.The last event is discussed in the next section.The motion of the projectile inside the gun tube is affected by the gun/projectile stiffness,clearance between the barrel and the projectile,the gun barrel centerline curvature,the velocity of the projectile,asymmetric gas pressure etc.The centerline of the deflected gun barrel during the motion of the projectile inside the gun barrel evaluated using finite element analysis[9]is shown in Fig.2.In Fig.2 each curve represents the centerline of the deflected shape of the gun barrel at 1 msec intervals during firing instant.

Fig.1.A typical tank gun system.

Fig.2.Centre line of the deflected gun barrel[9].

Dynamics of a moving projectile in a gun barrel can be described by the following equations[10].The total kinetic energy(T)of the projectile/gun barrel system is

where mg,mpare the masses of the gun and the projectile and Ig,Ipare the mass moments of inertia about the centers of gravity of the gun and the projectile.˙xgand˙ygare the translational velocity of the center of gravity of gun,and˙xpand˙ypare the translational velocity of the center of gravity of projectile respectively.Anglesθ andαare shown in Fig.3˙θand˙αare the respective angular velocities of anglesθandα.

The total potential energy(V)of the projectile/gun system is

Fig.3.Gun and projectile displacements[10].

Where kbcis the stiffness of the bourrelet,δbcis the displacement of the projectile into the gun bore,δois the projectile displacement at the obturator,koandrepresent the stiffness of the plastic band and metallic part of the obturator respectively and,Rc1,ois the radial clearance between the obturator and the bore.The last term of equation(2)is a power series due to the foundation moment that occurs as the projectile moves down the gun barrel.

Lagrange's equations can be applied to multi degrees of freedom(mdof)systems to derive the differential equations.According to Hamilton's principle

The Lagrangian is defined as

and if all forces are conservative,Hamilton's principle becomes

Using a theorem of calculus of variations,δLdt=0 if

Equation(6)are called Lagrange's equations and can be applied to derive the differential for conservative mdof systems.Applying Equations(1)and(2)in(6),equation of motion of gun/projectile can be obtained.By performing dynamic analysis jump angle of projectile at the muzzle end can be determined which is input to free flight trajectory analysis.In addition,ballistic dispersion analysis can also be performed including manufacturing tolerances of barrel and projectile.Detailed gun dynamics analyses have been performed recently in Refs.[11-25].Among the presented methods,in one approach,classical finite element method and an equivalent mass element which represent the moving mass are combined and analysed by a method of step-by-step time integration[11-14].The transverse and longitudinal vibrations of the gun barrel are determined fast and in good accuracy considering the non-uniform of the barrel shape,inclination angle of the barrel,inertia,interaction of the barrel and projectile,Coriolis and damping effects of the projectile.

Flexible multi-body dynamics analyses software tools are also useful in determining the dynamic behaviour of the gun systems which include the 3D model of the chassis,suspension,track system,gun/projectile and road path[22].Using this approach structures are modelled as flexible and/or rigid.For different road types and vehicle speeds,firing conditions are analysed in a realistic way.However,this method requires higher computing power and CPU time.

Explicit dynamic finite element modelling[23-25]is another effective method to simulate the firing instant and analyse the interaction between the gun tube and moving projectile.Explicit FE solvers such as LS-DYNA and Abaqus are required to solve the analysis.With this method contact between the barrel and projectile,gun mount,recoil motion,gravity effect and initial flight of the projectile is also modelled.The outputs of the analysis are gun barrel motion,muzzle exit time,muzzle velocity and projectile tipoff angles.But too many details cannot be included into the model since it requires huge computing power and CPU time.

3.Vibration and control of gun barrel due to the tank motion

Fig.4.Standard deviation of muzzle motion in elevation axis[27].

Vibration of gun barrel due to the tank motion has been studied by experimental and analytical methods for several decades.According to the firing tests performed on different length gun barrels,the decrease of shooting accuracy in longer gun barrels while the tank is on the move was linked to the increased length of the gun barrel.This conclusion led to the performation of experimental studies on the longer gun barrels.Experiments[26-28]were performed on different tank guns in order to compare the terrain-induced dynamic characteristics of these guns'barrel deflections under non- firing conditions.The muzzle tip motion of different length tank guns were experimentally investigated on M1A1 tank using dynamic muzzle reference systems while the tank was moving on the rough terrain with variable speeds[27].The results show that,gun with a longer barrel(approximately 1.3 m longer)de flects substantially compared to short one as shown in Fig.4.

Vibration of the gun barrel due to the tank motion is mainly affected by the combination of the first several mode shapes of the gun.The study[28]performed on M256 barrel in an M1A2 tank moving over the RRC-9 bump course at 15mph,showed that the first three mode shapes of the gun barrel are the dominant modes that determine the barrel shape from the tank motion.With the application of modal analysis technique the barrel shape can be determined accurately using the first three mode shapes as given in Equation(7)

where Yi(i=1,2,3)are the normalised barrel mode shapes and qi(i=1,2,3)are the mode shape amplitudes.Ratio of the amplitudes q1:q2:q3was found to be on the order of 25:5:1.

The results of both firing tests and non-firing tests while the tank is on the move require the control of the muzzle tip motion in order to increase the FSHP.In the following sections the methods used to control the muzzle motion are described.

3.1.Control of the muzzle tip motion by muzzle reference systems

Muzzle reference systems(MRS)are used to correct the LOS-LOF misalignments.Muzzle reference systems can be classified as static MRS and dynamic(automatic)MRS.Static MRS consists of a collimator or reflector(mirror)mounted on the muzzle end of the tank gun barrels and a gunner's periscope is placed on the turret to sense the projected reticle of light.The static MRS is shown in Fig.5.Static MRS is used only when the tank is stationary and it takes some time to align both the sight and gun barrel to a prescribed position then measure the offset between the initial(reference)and final position manually.This method is widely used in main battle tanks such as M1A1,M1A2,K1A1,Leopard 2 and Challenger etc.

Fig.5.Static muzzle reference system[29].

Fig.6.Determination of deflection using MRS.

Fig.7.Dynamic muzzle reference system[30].

The gun barrel droop due to uneven heating resulting from firing or environmental conditions can be measured both in azimuth and elevation axes by measuring the offset between the reference reticle(in gunner's sight)and the projected reticle(in MRS)as shown in Fig.6.The measured offset is input to the fire control system in order to correct the LOS and LOF misalignment.Generally,the accuracy of the correction of the LOS-LOF misalignments using the static MRS is on order of 0.1-0.25 mils.

On the other hand static MRS cannot be used while the tank is on the move therefore with this method the gun barrel deflections due to the ground vibration cannot be corrected and cannot be input to the fire control computer.

Dynamic MRS[30]uses a reflector mounted on the muzzle end of the tank gun barrel and laser receiver/transmitter unit on the rotor(cradle).This system automatically and continuously measures the muzzle end angular position both in azimuth and elevation axes with a precision of approximately 5μrad and at a bandwidth of 1 kHz while the tank is stationary or moving as shown in Fig.7.Another version of this method uses a laser beam transmitter located at the muzzle end in place of reflector and receiver unit on the rotor[31].

Dynamic MRS could be used with appropriate prediction algorithms[32](uses Kalman filter),which process the input from Dynamic MRS in conjunction with the mathematical model of the gun and decide the suitable time for shooting instant.Using the gun gyro,accelerometer etc.input the deflected shape of the barrel is obtained according to the mathematical model of the gun system.The muzzle end position of the deformed barrel shape is checked using the input received by the DMRS.When it is predicted that the shape of the barrel will be nearly straight at the exit time of the projectile from the barrel,the projectile is fired.

3.2.Control of the muzzle tip motion by vibration absorbers

As indicated inprevious sections if a longer gun barrel is decided to be used then another solution to control the muzzle end motions is the reduction of deflections by using a vibration absorber.Vibration absorbers can be passive,semi-active or active.For a one degree of freedom(dof)system with a vibration absorber included is shown in Fig.8.

Fig.8.One dof system with a vibration absorber.

In Fig.8,m,c,and k denote mass,damping value,and stiffness of the primary system,respectively and ma,ca,and kadenote mass,damping value,and stiffness of the absorber system,respectively.F0andωare the amplitude and frequency of the exciting force,respectively,x and xaare the displacement of the primary mass and the absorber mass,respectively.The normalised amplitude of the steady-state response of the primary mass is given as analysis showed that a vibration absorber located at the muzzle end with a mass of 4 kg and a damping ratio of 1.5,tuned at 5.6 Hz could decrease the muzzle tip deflection of a L55 calibre gun barrel to a level of L44 calibre gun.

Another type of vibration absorber[42]was introduced in order to reduce the vertical vibrations of 120 mm calibre longer gun(L55 calibre)barrels.In this method,eddy current damping is applied to a tuned mass damper.Vibration absorbers using eddy current damping require less mass compared to traditional ones.

The magnetically tuned mass damper(mTMD)that is applied to the gun barrel is shown in Fig.9.The relative motion between copper ring(conductive material)and permanent magnets generates eddy current.The copper and the magnet function as a viscous damper.According to the experimental results the gun barrel with magnetic tuned mass dampers(TMD),the damping ratio is 6 times of without TMD and,2 times of with traditional TMD.

The main disadvantage of using a vibration absorber is that a moving part(free in the vertical direction)is subject to severe dynamic conditions such as gun fire shock and motion of tank on the very rough terrain.In the open literature,studies on the performance of vibration absorbers under real firing tests are not reached.This topic is open to research.

The studies on the application of vibration absorbers to the gun barrel go back to the end of the 1990s.Since that time both numerical and experimental efforts[33-40]have been applied to study the effectiveness of such systems on the gun shooting accuracy.A dynamically tuned passive vibration absorber was designed with a spring constant of 10 000 N/m and mass of 20 kg in addition to using the original front thermal shroud of the M1A1 tank.The thermal shroud was fixed to the gun barrel using springs.Changing the spring stiffness overall performance of the system was optimised.Also,adding weights to the system,mass of the absorber was adjusted.M1A1 tank equipped with XM291 gun,XM91 autoloader and a dynamic(continuous)muzzle reference system was tested on the bump-course.Dynamic MRS was used to measure the muzzle angles while the tank is on the move.The test results showed that optimised vibration absorber could significantly reduce the vibration amplitude.

A study[41]was performed on the vibrations of L44 and L55 calibre gun barrel.Firstly,vibration data was collected from the L44 calibre gun at the APG course while the tank was moving.Then this data was used in the random vibration finite element analysis to determine the output PSD(power spectral density)from the muzzle end of L44 calibre gun.The same input PSD was also applied in the random vibration finite element analysis of L55 calibre gun to determine the output PSD from the muzzle end.Next,vibration characteristics of two gun barrels were compared and a conceptual damped tuned vibration absorber was designed in order to decrease terrain induced(due to the motion of the tank)the muzzle tip deflections of a L55 calibre gun to a level of L44 calibre gun.The

3.3.Reduction of the gun barrel vibrations by structural modifications

Gun barrel vibrations may be reduced by making suitable structural modifications on the gun barrel and/or cradle tube[43].The gun barrel flexural stiffness can be optimised to the one in the shorter gun barrel by changing the geometry or the material.The steps and wall thicknesses throughout the length of the barrel can be modified in order to obtain optimum solution.Another modiif cation can be made by changing the cradle tube geometry or the positions of the thrust bearings inside the cradle tube.The length of the cradle tube can be increased and made stiffer such that natural frequency of the gun system is increased to the level of shorter(L44)gun system.The structural modifications both in the gun barrel and cradle tube can increase the weight of the system so that,optimisation both in weight and natural frequency of the system should be taken into consideration together.The application of new candidate materials such as composite materials[44,45]should also be considered.Composite materials have higher specific strength and specific stiffness compared to metallic materials and good vibration damping characteristics.The use of high stiffness composite materials increases the natural frequency of the first bending mode of all steel design which results in higher pointing accuracy and approximately 100 kg of weight saving.Although composite materials provide advantage over all steel design because of their anisotropic structure their behaviour to loading is complicated.Therefore the response of composite structures under gun firing loading should be thoroughly analysed and tested.

Fig.9.Schematic of mTMD applied to the tip of the gun barrel[42].

3.4.Active vibration control of gun barrel

Another way of suppressing the gun barrel vibration is the use of the active vibration control technology.The structure used in this approach includes sensor layer,actuating layer and base layer.In this method a multi-input multi-output deflection controller is built to actively suppress the vibration.The sensor detects the vibration signal and transmits it to the controller.The controller analyses and then sends the response signal to the actuator.The actuator reacts accordingly to suppress the vibration and reduce the deflection.This technology can be applied to gun system to reduce the vibration level.In the gun barrel application,using piezoelectric self-sensing actuators bonded at different locations of the barrel,the deflection of a barrel under a moving projectile and while the tank is on the move can be reduced.Adaptive fuzzy control method can be used in the active vibration control for the time-varying system.Several studies[46-48]were performed on the prototype systems and low calibre guns systems and successful results were obtained.

4.Conclusions

High targeting and hitting accuracy for a main battle tank is important in the battlefield while the tank is on the move.This can be achieved by the proper design of both fire control system and the gun system.In order to design an effective gun system,better understanding of the dynamic behaviour of the gun system is required.According to the studies performed on the moving tank scenarios:

1)the gun system having a longer barrel if not controlled properly,may deflect up to 6 times of the one with the short barrel and may result in poor FSHP,

2)experimental and numerical studies show that the use of MRS and vibration absorbers may be effective for the control and the reduction of the muzzle tip deflections,

3)for the existing gun systems without making substantial modifications,DMRS could be useful in controlling the tip deflections of gun barrels with muzzle motion and firing instant prediction algorithms,

4)with the use of optimised vibration absorbers the vibration levels of L55 calibre gun barrels could be reduced to the level of L44 calibre gun barrels,

5)gun system with a longer barrel can be as accurate as the one with a short barrel by the application of appropriate modifications in the mountings of the gun system and gun barrel shapes,

6)the application of new candidate materials such as composite materials in place of steel could be considered in order to reduce the weight and increase the stiffness and natural frequency for higher pointing accuracy.

Moreover,the development of more detailed dynamic models which takes into account the effects of the recoil motion of the barrel,support flexibility and disturbances due to tank motion could help the designers understand more clearly the behaviour of the gun system during firing instant while the tank is on the move and optimise the gun systems accordingly.

Furthermore,the use of advanced composite materials together with the smart structure active vibration control technology in the large calibre gun barrel design could reduce the barrel weight significantly and improve the gun dynamic performance by suppressing the vibration under all battlefield conditions and increase the first shot hit probability while the tank is on the move.To this end,much more attention should be directed to this approach.

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A R T I C L E I N F O

Article history:

1 December 2016

in revised form

7 April 2017

Accepted 19 May 2017

Available online 25 May 2017

Gun dynamics

Vibration control

Muzzle reference system

Vibration absorber

Achieving high hitting accuracy for a main battle tank is challenging while the tank is on the move.This can be reached by proper design of a weapon control and gun system.In order to design an effective gun system while the tank is moving,better understanding of the dynamic behavior of the gun system is required.In this study,the dynamic behaviour of a gun system is discussed in this respect.Both experimental and numerical applications for the determination of the dynamic behaviour of a tank gun system are investigated.Methods such as the use of muzzle reference system(MRS)and vibration absorbers,and active vibration control technology for the control and the reduction of the muzzle tip deflections are also reviewed.For the existing gun systems without making substantial modifications,MRS could be useful in controlling the deflections of gun barrels with estimation/prediction algorithms.The vibration levels could be cut into half by the use of optimised vibration absorbers for an existing gun.A new gun system with a longer barrel can be as accurate as the one with a short barrel with the appropriate structural modifications.

?2017 Published by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail address:tdursun@aselsan.com.tr(T.Dursun).

Peer review under responsibility of China Ordnance Society.