Rakenteiden Mekaniikka (Journal of Structural Mechanics)Vol. 44, No 4, 2011, pp. 309-329Force, pressure and strain measurements fortraditional heavy mortar launch cycleJuha Toivola, Seppo Moilanen and Henna-Riitta JussilaSummary. The measurement applications of pressure, forces and strains for traditional heavymortar launch cycle are presented. Especially the processing method of measured strain data forlaunch loading determination is discussed. The chamber pressure estimates calculated frommeasured tube strains are evaluated and the pressure calculation method includingcompensation of thermal stress proved to be relevant for the case of traditional mortar launchcycle. The transversal component of socket force proved to be insignificant compared to theaxial force component. The ground base type had negligible effect on measured socket forcesand on extreme base plate strains in this study.Key words: mortars, mortar tubes, mortar base plates, strain gages, force measurement,pressure measurement, strain measurement, test firingsIntroductionThe definitions of pressure terms and their relationship for large caliber weapon systemsare presented in standard [1]. The main component of mortar launch loading is a gaspressure of burning propellant charge during internal ballistic cycle of shot.Traditional methods of gas pressure measurement of heavy guns are mechanicalcrusher gauge and piezoelectric pressure transducer [2]. The crusher method is based onthe measurement of the deformation of copper element due to the pressure resultantforce on the piston of crusher gauge. The crusher method gives an estimate of peak gaspressure of shot in gun chamber. The accuracy of estimated crusher pressure value is afunction of the shape of pressure curve p(t), the type of used crusher gauge and dynamical material properties of crusher element. Some tailored calibration methods have tobe used to guarantee the required accuracy of measurement results for crusher method,as shown in Refs. [3] and [4]. Also the construction of the weapon can cause differencesin the results of crusher pressures due to the chamber volume, tube dimensions and theireffects on the burning rate of propellant charge and the dynamical deformation ofcrusher element, as shown in Ref. [7].The piezoelectric pressure transducer gives a pressure vs. time curve p(t). Highsampling rate and reliability of calibration of transducer can guarantee the high accuracyof pressure peak determination for launch pressure [9] and [10]. The pressures measuredby piezoelectric transducers are supposed to be exact values of pressure, but someaccuracy problems in calibration still exist especially in cases of high pressure levelsand pressure wave determination in gun applications, as discussed in Ref. [8]. The309

drawback of piezoelectric transducer is that some kind of mechanical housing (drillingand tapping) for transducer should be machined into the weapon, which cause structuralweaknesses and prevent the service use of pressure test weapons. The third pressuremeasurement method is a combination of crusher and piezoelectric methods. The piezoelectric transducer and its electronics are installed in cylindrical metallic body, whichcan be put into gun chamber and used like a traditional crusher gauge. Nowadays thesizes of piezoelectric crusher gauges allow their use also in mortar chambers as pressuremeasurement sensors [11].The measurement of gun tube strains and strain data analysis offer a reliablecomparison method for ballistic pressure measurement. Because the gun tubes are thickwall cylinders with high manufacturing quality (small tolerances in dimensions) and thegeometrical changes of shape are usually smooth, the traditional equations of elasticityapply well for deformation vs. pressure load applications [7], [12], [13], [14] and [15].Special application of tube strain measurement is an evaluation of rotating band loadingon gun tubes, which is important for rifled cannon tubes. The application details of bandpressure measurements and calculations are discussed in Refs. [16], [17] and [18] and intheir sub-references.During mortar launch cycle the pressure force presses the breech piece towards thebase plate and the ground. The value of socket force can be estimated as a resultantforce of chamber pressure, but dynamic effects of structures and the stiffness of groundbase can cause disturbances on reaction force values. The results of test firing forcesand strain measurements can be used as a base of structural designing [19], designingand evaluation of mechanical fatigue laboratory tests and the laboratory acceptance testsof mortar base plate [20].The modern mortar ammunition can cause higher pressure and force loads due to theincreased weight of projectile and higher muzzle velocity than earlier versions of mortarammunition. The requirements of low weight of weapon construction and good launchstability together with the overall usability of the weapon in all types of ground basesare more or less in conflict with each other.Measurement configuration in mortar test firingThe purpose of mortar test firing discussed in this paper was to evaluate the socketforces and strains in base plate structure when different kinds of ammunition were fired.Some results of earlier test firings were available in the research report [6], when thebase plate was positioned in extreme soft sandy soil or a rigid concrete bed without baseplate was used. In this study the ground bases were realistic service cases: Base plate ingravel soil and in sandy soil. The sandy soil ground was created by digging a largecavity in gravel soil and then filling it with sand.Axial and hoop strains of outside surface of tube chamber section were measured byusing biaxial 0o/90o strain gage rosette. The chamber pressure was calculated from themeasured strain data. Direct pressure measurement method was aimed to be used foroverpressure rounds by using piezoelectric pressure transducer, but the measurementfailed.310

Special breech piece with dog-bone geometry was used for socket forcemeasurement, when service rounds or equivalent rounds were fired. The cylindrical partof the breech piece body was instrumented as a force transducer by tri-axial strain gagerosettes as shown in figure 1. Finally the base plate was also instrumented by straingages. The positions of strain gages are shown in figure 2.Figure 1. Special breech piece for socket force measurement. Strain gage instrumentation [5]and real structure.Figure 2. Strain gage positions on base plate311

Figure 3. Socket forces acting on instrumented breech piece, base plate is not shown. Straingage rosette for pressure measurement located on chamber section of tube, distance of 350 mmfrom tube base end.Test weapon and ammunitionsTest weapon was Finnish 120 KRH 92 mortar (Patria 120 mm long range mortar) withspecial force measurement breech piece. The projectiles used in tests were traditional120 mm HE mortar shell (projectile mass mp 13 kg) and 120 mm ballistic slug(projectile mass range mp (15.20) kg). Different charge zones from low pressures upto overpressure levels were used. The weapon and examples of used ammunition typesare shown in figures 4 and 5, respectively.Totally 34 rounds were fired in test including: 4 4 2 10 warmers and base plate stabilizing rounds 3 5 8 16 service rounds 3 5 8 pressure control and overpressure rounds on sandy soil.312

Figure 4. Traditional muzzle loaded 120 KRH 92 mortar on gravel soil before firing. The maincomponents of mortar are: Base plate, special breech piece for socket force measurements, tube,sight unit and bipod assembly.Figure 5. Traditional 120 mm HE shells (left) and ballistic slugs (right) with charge modules.Measurement hardwareThe hardware of measurements was: Strain gages on base plate and tube;o Kyowa KFG-5-120-C1-11L3MR, k 2.10, uniaxialo Kyowa KFG-2-120-D16-11L5M3S, k 2.06, biaxial 0o/90o rosetteo Kyowa KFG-5-120-D16-11L5M3S, k 2.06, biaxial 0o/90o rosette. Strain gages on force measurement breech piece;o HBM RY31 6/120, k 1.93, tri-axial 0o/45o/90o rosette. Kistler piezoelectric pressure transducer K 6215 (used for overpressure rounds) PCB charge amplifier 422D13/A (used for overpressure rounds)313

IOTech Wavebook Data Acquisition UnitIOTech WBK 16 Strain Gage Signal ConditionerLapTop PC ComputerWeibel W-700M Velocity AnalyzerCitius C10 and C100 Centurio high speed video camerasZwick/Z250 tensile test machine for calibrating of axial force of breech piece forsocket force measurement Tamtron MCS 0-6300 kg electronic scale for calibrating of transversal socketforces of breech piece.Sampling rate fs 40 kHz was used in measurements and totally 20 channels wereused for strain and force measurements: 5 channels for socket forces measurements;o 1 full bridge for axial force Fxo 2 full bridges for transversal forces Fy and Fz (shear deformation)o 2 half bridges for transversal forces Fy and Fz (bending deformation). 15 channels for strain measurement (¼ bridges);o 2 channels of tube strains for pressure measuremento 13 channels for base plate strain measurement.One channel was used for direct chamber pressure measurement by piezoelectrictransducer for overpressure rounds, when standard pressure measurement breech piecewas used instead of special force measurement breech piece. The later one wasoriginally designed for measurements of the loading level of service round firing.Data analysis softwareThe measured data was stored and analysed by using Matlab software.Computation of pressure estimates from measured dataTheoretical basis of pressure computation from strains of tube wallAxial and hoop strains were measured at outer surface of tube where axial and hoopstresses arise from following phenomena:Axial stress: tube bending (including bending vibration) axial rigid body acceleration (including rigid body vibration of the tube) axial elastic vibration axial loading by friction between projectile and inner surface of the tube(insignificant in presented case) inner surface radial pressure loading variation in axial direction (insignificantin presented case) thermal stress due to nonlinear temperature distribution.Hoop stress: inner surface radial loading by projectile (insignificant in presented case) inner surface radial loading by gas pressure thermal stress due to nonlinear temperature distribution.314

Axial stress is denoted as(1) a aB aA ap aT ,where aB is bending stress, aA axial stress arising from purely axial phenomena (axialacceleration, vibration and loading), ap axial stress caused by inner surface radialloading variation in axial direction and aT axial stress due to nonlinear temperaturedistribution. Similarly hoop stress is decomposed as p T ,(2)where p is hoop stress caused by inner surface radial loadings and T hoop stress dueto nonlinear temperature distribution. Generalised Hooke's law for plane stress state is1 a TE1(3) a a TE T T ,where E is Young’s modulus, Poisson’s factor, temperature expansion coefficient, , a and T are hoop, axial and thermal strain respectively and T change of temperature.During internal ballistic cycle lasting for some milliseconds, temperature change atouter surface is small. For this reason thermal strain T T is neglected in thesequel. For longer measurement time this naturally does not hold and strain gageresponse curve for thermal strain is needed if this term is kept in analysis (for ideallytemperature compensated strain gages response to thermal strain is zero) andtemperature should be measured or thermal strain should be compensated by anothermeans.According to Ref. [21] for stationary case of long axially free cylinder underaxisymmetric axially uniform thermal loading it can be shown that axial and hoopstresses at outer surface are equal. In Ref. [21] it has been shown that thermally inducedvibrations are prominent for slender beams and thin plates. Based on these classicalresults, it is assumed that thermally induced vibrations are insignificant and axial andhoop thermal stresses at outer surface are equal, i.e. aT T T.Outer surface hoop stress for long open-ended thick wall cylinder under internaluniform pressure is2p,(4) 2 1where p is the internal pressure, D / d the wall ratio, D the outer diameter of thecylinder and d the inner diameter of the cylinder. Although assumptions behindequation (4) are not completely fulfilled in the case of gun tube, results andinterpretations based on this approach have been found useful.In order to cancel out some unwanted phenomena from computed results, weightedsum of strain components is written as315

1 1 22 p 1 aA aB ap 1 1 1 T .(5)EE 1 EIt can be seen that by choosing weighting factor 1 cancels out thermal stress, butaxial phenomena remains. Choosing axial phenomena can be cancelled out, butthermal stress remains. Solving internal pressure for these cases results a 2 2 1 E a 1 aA aB ap 2 1 22 1 E 2 1 a : p T .2 1 22 1 : p (6)(7)From equations (6) and (7) it is seen, that some error is unavoidable. Choice should bemade according to which error seems to be smaller, error caused by thermal stress orerror caused by axial phenomena.According to analysis presented above internal pressure estimates are 2 1 E a 1 : p1 2 1 2 1 E : p2 a .2 1 2(8)(9)When left hand side pressures in equations (6) and (7) are taken as real gas pressure,using equations (8) and (9) results 2 1 aA aB ap p1 p (10)2 2 1(11)p2 p T ,2where p is a real gas pressure. Because thermal stress T is positive at the outer surface,estimate p2 always overestimates the real pressure.In the absence of axial phenomena it is possible to estimate thermal stress T atouter surface. Using weighting factor 1/ in equation (5) and solving for thermalstress yieldsE a aA aB ap .(12) T 1 2Thermal stress estimate isE a (13) T ,est 1 2and it’s relationship to true thermal stress T T ,est T aA aB ap .316(14)

Other pressure estimatesIn actual measurements pressure estimate from direct pressure measurement wasdenoted as p3 for overpressure rounds. Because the direct pressure measurements usingpiezoelectric pressure transducer failed, the results of them are not presented.In this study fourth possibility to estimate tube pressure is to compute it from socketaxial force Fx measurement:Fp4 x ,(15)Awhere A is a pressurized area of tube cross section.When socket axial force is assumed to be positive for compressive force andacceleration a is assumed to be positive towards the rear end of the tube, the equation ofmotion for the tube assembly is(16)pA Fx ma ,where p is a real gas pressure at the bottom of the tube and m is the mass of tube andbreech piece. Combining equations (15) and (16) it is seen thatmap4 p .(17)AAssuming that axial stress in equation (10) is due to rigid body acceleration, aA mt a At , and using numerical values for a particular case in hand it is found thatma 2 1 A mt map1 p p 0.35,(18)A2 At m Awhere At is the cross sectional area of tube wall at strain measurement point on the tubeand mt is the partial mass of the tube from the strain gage position to muzzle end.At the beginning of the internal ballistic cycle acceleration is positive and bothestimates p1 and p4 underestimate the true pressure. Comparing equations (17) and (18)it is readily seen that error caused by axial rigid body acceleration a is clearly smaller inestimate p1 than in estimate p4 and thus at the beginning of the internal ballistic cycleestimate p1 should exceed estimate p4.Choice for chamber pressure estimateFor overpressure rounds pressure was intended to be measured using piezoelectrictransducer, and strain gages were meant to be a backup pressure sensor if direct pressuremeasurement fails. Unfortunately this was what happened because of poor chargeamplifier action. Therefore direct pressure measurement results for these rounds weredoubtful. For service rounds strain gages on the tube surface were intended to act onlyas pressure measurement sensor, because special force measurement breech piece wasused and direct pressure measurement was impossible. This situation necessitatedanalysis and comparison of different pressure estimators and a choice between them inthis study. The comparison of direct pressures with strain pressures is discussed shortlyin Ref. [7].Choice between pressure estimates p1 and p2 must be based on measured data andtype of weapon. Experience from several measurements of recoiling cannon has shownthat acceleration of recoil movement and muzzle brake force is clearly visible in tube317

strain measurements and so axial effects need to be compensated. Also rotating bandpressure creates axial stress when it passes measurement point as shown in Refs. [16],[17] and [18]. For a traditional smooth bore mortar there is no recoil mechanism, nomuzzle brake and no rotating band passing present. Based on these considerations bothof pressure estimates (p1, p2) can be chosen for traditional mortar firing.In figure 6 measured hoop and axial strains are presented for a typical mortar shot.As can be seen there is no significant axial or bending vibration visible after internalballistic cycle and hence it can be assumed that elastic vibrations are absent.Considering axial effects, only rigid body acceleration and thermal stress could bepresent. Effect of thermal stress is visible in figure 6 after internal ballistic cycle, whereboth axial and hoop strain settles rapidly to approximate level of 50 m/m corresponding to thermal stress of 15 MPa at outer surface. This also proves experimentally,that after internal ballistic cycle both axial and hoop strains and stresses are equalalthough temperature field is non-stationary.Axial strainHoop strain100600500Strain (10-6)4000300200100-500-1001. (s)22.22.4-1001. (s)Figure 6. Axial and hoop strain of tube for typical mortar shot.140p1p2120p4100Pressure (MPa)Strain (10-6)508060402001.661.6621.6641.6661.668Time (s)1.671.6721.674Figure 7. Pressure estimates p1, p2 and p4.3181.67622.22.4

Pressure estimates p1, p2 and p4 are shown in figure 7 for a typical service roundwhen the soil base has been compacted by previous rounds. There are several issuesvisible: Estimate p2, which is known to overestimate real pressure, always exceedsestimate p1. Estimate p1, which underestimates real pressure less than p4 when acceleration ispositive, exceeds estimate p4 almost to the pressure peak. When estimates p1 andp4 coincide, acceleration changes sign (within the measurement and analysisaccuracy). Thermal stress, which is the only error source for estimate p2, developes veryrapidly and has almost reached it’s final value at pressure peak. Estimate p2 clearly overestimates pressure peak value. For this round estimate p1 probably slightly overestimates pressure peak value. For this round estimate p4 apparently overestimates pressure peak value, becauseacceleration has changed sign before peak and estimate p4 (and p1) overestimatesthe real pressure under negative acceleration (after crossing of estimates p1 andp4).Based on the observations above, estimate p1 seems to be the best choice. Pressurepeak value is an important result parameter. Because estimate p2 always overestimatesthe real pressure, pressure peak value and also gas impulse computation will beerroneous. For estimate p4 it is not known in advance whether it overestimates orunderestimates pressure peak value because acceleration could change sign before orafter pressure peak depending on the characteristics of the soil base.Thermal stress of tubeIn figure 8 typical result for estimated thermal stress together with pressure estimates p1and p2 is shown. After internal ballistic cycle thermal stress rapidly settles toapproximate level of 27 MPa for this round. During internal ballistic cycle thermalstress estimate rises almost immediately up to the final level and then drops beforeclimbing up to the final level again. This is because axial acceleration effect issuperimposed into the estimate. At the beginning of internal ballistic cycle axialacceleration is positive and hence thermal stress estimate overestimates the real thermalstress (Eq. 14). However, thermal stress builds up very rapidly. At the beginning of theinternal ballistic cycle propellant gas temperature is higher due to burning and heattransfer into the tube is efficient. At later part of the cycle propellant gas expands andcools therefore reducing heat transfer.ResultsSocket forces vs. pressureThe socket forces vs. time t curves together with the pressure p1(t) and tube straincurves for service round fired on sandy soil are presented in figure 9. The maximums offorce components occurred at the same time as the maximum of gas pressure. Thedirections of “vertical” transversal force component Fy are opposite between the319

140p1p2120Pressure, stress (MPa) T1008060402001.661.6651.671.6751.68Time (s)1.6851.691.6951.7Figure 8. Thermal stress estimate and pressure estimates p1 and p2.measurement methods (shear or bending). This is supposed to be a consequence of nonsymmetric contact between the socket ball of breech piece and socket cup of base plate.Because the maximum values of axial force Fx are (30.100) times higher thanmaximums of transversal force components, the small eccentricity in the contact withthe socket can cause bending moment due to the axial force. Based on theseconsiderations measurement results relying on shear deformation of dog bone rod wereassumed to be a better choice for transversal force estimations.The maximum value of axial socket force Fx vs. maximum gas pressure p ispresented in figure 10 for different types of ground and gas pressure range (25.125)MPa. The rounds of earlier work were fired on the extremely soft sandy soil with baseplate and on the fixed socket cup on concrete bed without base plate. Previously thespecial pressure measurement tube had been used and gas pressure had been measuredusing a piezoelectric pressure sensor mounted on tube wall. The results presented inprevious report [6] are included in figure 10.In earlier work [6] it was shown that: The force results of soft sandy soil case were clearly lower than theoreticalgas pressure resultant force value max Fx max p A The effect of compaction of soft sandy soil base due to firing can be seen.Stabilising rounds (index A, marker ) have lowest force value compared topressure. The forces increased towards to the theoretical line, when the nextseries (index B and C, marker ) were fired. The force values are evenhigher for series C (fired after B series round) at lower gas pressure than forthe rounds of stabilising series A with higher gas pressure maximums The maximum axial forces were 30 % higher than theoretical gas pressureresultant force when the rounds were fired on fixed socket cup (marker ).320

Tube axial strainTube hoop strain20025002000strain [µm/m]strain [µm/m]0-200-4001500100050001.91.92Tube pressure p1-5001.9415001001000force [kN]150501.881.91.92Force Fz (shear)-5001.94252020151510501.881.91.92Force Fy (shear)1.941.881.91.921.94Force Fz (bending)1.881.91.921.94Force Fy (bending)105-51.9450force [kN]force [kN]1.92Force Fx0500-501.9025-51.885000-50force [kN]1.88force [kN]pressure [MPa]-6001.881.91.92Time (s)0-501.941.881.91.92Time (s)1.94Figure 9. Axial and hoop strain components of tube wall, pressure calculated from strainsp1( x, ) and socket forces of the round fired on sandy soil: Axial force Fx, transversal forces Fzand Fy measured by shear and bending deformations.321

Figure 10. Maximums of axial socket force vs. gas pressure, when the rounds were fired on thedifferent types of ground base.In this study the measured axial force values on both of gravel and sandy soil werepositioned near the theoretical gas pressure force value, relative differences were - 5%.The force maximums of low and middle pressure p (25.60) MPa stabilising roundswere a little bit lower and the forces of high pressure service rounds (up to p 120 MPa)were a little higher than the theoretical maximum value of the gas pressure resultant inboth cases.Base plate strains during launch cycleTube strains, pressure estimates p1 and p2 and base plate strains at strain measurementpoint 4 are presented for two rounds on gravel soil and sandy soil in figure 11. Thesesoil bases do not significantly affect tube internal pressures estimated from tube strains.Strain gage V41 shows typical base plate strain measurement result where no significantdependence on soil base is visible. An example of few exceptions of this behaviour is322

shown in results of strain gage V42 where strain history is clearly different for sandyand gravel soil base.Tube strainsTube strains20002000 a a1500 Strain (10-6)Strain (10-6)150010005000-5001.58 100050001.591.6Pressure estimates-5001.611502.082.09Pressure estimates2.1150p1p2100Pressure (MPa)Pressure (MPa)p15001.591.6Base plate strain ase plate strain V412.082.092.1Base plate strain V424002001.591.6Base plate strain 200-2501.582.080Strain (10-6)Strain (10-6)500Strain (10-6)Strain (10-6)1.58p21001.591.6Time (s)1.61-2502.082.09Time (s)2.1Figure 11. Left column gravel soil, right column sandy soil, service rounds.323

Tube strainsTube strains40004000 a a3000 Strain (10-6)Strain (10-6)300020001000200010000-1000 01.861.871.88Pressure estimates-10001.892001.75 1.755 1.76 1.765 1.77 1.775Pressure estimates200p1p2100500501.891.75 1.755 1.76 1.765 1.77 1.775Base plate strain V412000200015001500Strain (10-6)Strain (10-6)1.871.88Base plate strain V4110005000100050001.861.871.88Base plate strain V42-5001.8910010000Strain (10-6)Strain (10-6)10001.86-500-100-200-300-400p2150Pressure (MPa)150Pressure (MPa)p11.75 1.755 1.76 1.765 1.77 1.775Base plate strain V42-100-200-3001.861.871.88Time (s)1.89-4001.75 1.755 1.76 1.765 1.77 1.775Time (s)Figure 12. Left column low pressure round, right column overpressure round.324

In figure 12 tube strains, pressure estimates p1 and p2, base plate strains V41 andV42 are presented for two extreme rounds, one with low pressure charge and anotherfor overpressure charge. Both rounds were fired on sandy soil. Comparing pressureestimates and base plate strain V41 it is seen that maximum values of base plate strainand tube internal pressure do not follow linear dependence. This is more pronouncedlyvisible in the results for strain gage V42 where strain response to low pressure round islow but to overpressure round both maximum strain level and overall behaviour ofstrain history are completely different.Figure 13. Base plate after service rounds firing on gravel soil (left) and on sandy soil (right).Table 1. Number of fired rounds in series, pressure estimate p1, socket force component Fx andmajor limit value of base plate strains for the rounds fired on the gravel base. The mean andstandard deviation values are presented for the series including many rounds.No 423122631127761083513534rds.Base plate strains µm/m ( 10-6)Triggering signal missed, measured data was not available for this round.Remarks:§Measured signals of meridional strain component V81 on side of base plate cone were noisy.§§Measured signals of tangential strain component V42 were unsettled for low pressure rounds,see figure 12.*Stabilizing rounds.325

Table 2. Number of fired rounds in series, pressure estimate p1, socket force component Fx andmajor limit value of base plate strains on sandy base for service round and overpressure roundfiring cases. Mean and standard deviation values are presented for the series including manyrounds.No 3-1786533-6MPakN(2)*28.2305119-20950151N/A§§Base plate strains µm/m ( 10 535477216915276527Pressure measurement breech piece was used after these rounds, socket force measurements were not emarks:§Measured signals of meridional strain component V81 on side of base plate cone were noisy.§§Measured signals of tangential strain component V42 were unsettled for low pressure rounds,see figure 12.*Stabilizing rounds.&Pressure control and adjusting rounds for overpressure series.The radial strains of inner trunk plate (V1, V3) were tension in forward and sidedirections and radial strain V2 was compression on the rear gauge. The tangentialstrains (Vx2) of trunk cone were compression in all locations due to ground pressure onthe outside surfaces of the tr

The piezoelectric pressure transducer gives a pressure vs. time curve p(t). High sampling rate and reliability of calibration of transducer can guarantee the high accuracy of pressure peak determination for launch pressure [9] and [10]. The pressures measured by piezoelectric transducers are supposed