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RAIL WHEEL INTERACTION - Nilmani, Prof. Track
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RAIL WHEEL INTERACTION
RUNNING OF A RAILWAY VEHICLE OVER A LENGTH OF TRACK PRODUCES DYNAMIC FORCES BOTH ON THE VEHICLE AND ON THE TRACK THE INTERACTION AFFECTS BOTH TRACK AND RAILWAY VEHICLE – RAIL WHEEL INTERACTION
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EFFECT OF VEHICLE ON TRACK
LARGE DYNAMIC FORCES DETERIORATION OF TRACK GEOMETRY TRACK COMPONENT WEAR & DAMAGE NOISE
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EFFECT OF TRACK ON VEHICLE
SAFETY RIDING COMFORT COMPONENT WEAR & DAMAGE
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NEED FOR UNDERSTANDING
REDUCE SAFETY RISK IMPROVE RIDING COMFORT REDUCE DETERIORATION OF TRACK GEOMETRY MINIMISE WEAR REDUCE NOISE AND VIBRATIONS IN VEHICLE
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UNDERSTANDING RAIL -WHEEL INTERACTION
DERAILMENT BY FLANGE MOUNTING WHEEL CONICITY AND GAUGE PLAY WHEEL OFF-LOADING CYCLIC TRACK IRREGULARITIES- RESONANCE & DAMPING CRITICAL SPEED TRACK / VEHICLE TWIST
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SELF CENTRALIZING CONED WHEELS
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Sinusoidal motion of wheelset
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SINUSOIDAL MOTION OF VEHICLE
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PLAY BETWEEN WHEEL SET AND RAILS
G = Gw + 2 tf + s G is track gauge 1676 mm (BG) Gw is wheel gauge 1600 mm (BG) tf is flange thickness – 28.5 mm new; 16mm worn out s is standard play = 19mm for new wheel = 44mm for worn out wheel
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Mean Position Typical (Asymmetrical) Position Extreme Position
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EFFECT OF PLAY Lateral Displacement Y = a sin wt
a amplitude = /2 = Play/2 Lateral velocity = aw cos wt Lateral Acceleration = -aw2 sin wt Max acc = -aw2 Angular Velocity w =
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KLINGEL’S FORMULA (1883) Wave Length 0 of a Single wheel 0 =
0 = G = Dynamic Gauge r = Dynamic Wheel Radius = Conicity 0 ;Frequency
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CONCLUSIONS l= Rigid wheel base
With increase , 0 reduces, f increases – oscillations increase – instability For high speed – low 1 in 40 on high speed routes Worn out wheel increases – increasing instability For wheel set (MULTIPLE RIGID WHEELS) l= Rigid wheel base
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EFFECT OF PLAY As conicity increases Lateral Acceleration Increases
acc a /2 play As play increases Lateral Acceleration Increases
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EXCESSIVE OSCILLATIONS DUE TO
CONCLUSIONS EXCESSIVE OSCILLATIONS DUE TO Slack Gauge Thin Flange Increased Play in bearing & Journal Excessive Lateral and Longitudinal Clearances Increased Derailment Proneness
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Wheel-set on Curve
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THE PROCESS OF FLANGE CLIMBING DERAILMENT
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SECTIONAL PLAN OF WHEEL FLANGE AT LEVEL OF FLANGE TO RAIL CONTACT
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ZERO ANGULARITY (PLAN)
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POSITIVE ANGULARITY (PLAN)
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NEGATIVE ANGULARITY (PLAN)
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EXAMPLES OF WHEEL SET COFIGURATION WITH POSITIVE ANGULARITY
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ZERO ANGULARITY (ELEVATION)
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POSITIVE ANGULARITY (ELEVATION)
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NEGATIVE ANGULARITY (ELEVATION)
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FORCES AT RAIL-WHEEL CONTACT AT MOMENT OF INCIPIENT DERAILMENT
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FORCES AT RAIL-WHEEL CONTACT AT MOMENT OF INCIPIENT DERAILMENT
Resolving Along Flange Slope R= Q cos + Y sin …. 1. For safety against derailment Derailing forces > stabling forces Y cos + R > Q sin Substituting R from equation 1 Y cos + (Q cos + Y sin ) > Q sin Y (cos + sin ) > Q (sin - cos )
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Nadal’s Equation (1908) For Safety: LHS has to be small. RHS has to be large Y Low Q High Low tan Large
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FACTORS AFFECTING SAFETY
Flange Slope = 90º would indicate higher safety. However, with slight angularity, flange contact shifts to near tip. Safety depth for flange reduces resulting into increase in derailment proneness
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FACTORS AFFECTING SAFETY
Flange Slope ANGULARITY is inherent feature of vehicle movement. If the vehicle has greater angularity, should be less for greater safety depth of flange tip. However, there is a limit to it, as this criterion runs opposite to that indicated by Nadal’s formula.
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FACTORS AFFECTING SAFETY
Flange slope On I.R., for most of rolling stock = 68º 12’ (flange slope 2.5:1) For diesel and electric locos, the outer wheels encounter greater angularity for negotiation of curves and turnouts. For uniformity, same adopted for all wheels. kept as 700 on locos upto 110 kmph kept as 600 on locos beyond 110 kmph
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FACTORS AFFECTING SAFETY
Flange slope With wear increases, but results in greater biting action, hence increase in .
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FACTORS AFFECTING SAFETY
OTHER FACTORS INFLUENCING NADAL’S FORMULA INCREASES WITH INCREASED ANGULARITY, (PROF. HEUMANN) (acting upwards for positive angularity) 0.0 0.02 0.27
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FACTORS AFFECTING SAFETY
OTHER FACTORS INFLUENCING NADAL’S FORMULA Greater eccentricity (positive angularity) increases derailment proneness as flange safety depth reduces. Persistent Angular Running As positive angularity increases derailment proneness, persistent angularity leads to greater chances of derailment.
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FACTORS AFFECTING SAFETY
Not possible to know values of Q, Y, , and eccentricity at instant of derailment. Calculations by NADAL’s formula not to be attempted. Qualitative analysis by studying magnitude of defects in track/vehicle and relative extent to which they contribute to derailment proneness, should be done.
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DEFECTS/FEATURES AFFECTING
Rusted rail lying on cess, emergency x-over Newly turned wheel – tool marks Sanding of rails (on steep gradient, curves) Sharp flange (radius of flange tip < 5mm) increases biting action
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DEFECTS/FEATURES CAUSING INCREASED ANGLE OF ATTACK
Excessive slack gauge Thin flange (<16mm at 13mm from flange tip for BG or MG) Excessive clearance between horn cheek and axle box groove Sharp curves and turnouts Outer axles of multi axle rigid wheel base subject to greater angularity, compared to inner wheel
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DESIGNED ANGULARITY WHILE NEGOTIATING CURVE
PLAY HELPS THE WHEEL NEGOTIATE CURVE
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DEFECTS/FEATURES FOR INCREASED ANGLE OF ATTACK
DEFECTS / FEATURE FOR INCREASED POSITIVE ECCENTRICITY WHEEL FLANGE SLOPE BECOMING STEEPER (THIS DEFECT REDUCES SAFETY DEPTH AS ECCENTRICITY INCREASES)
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DEFECT/FEATURES CAUSING PERSISTENT ANGULAR RUNNING
DIFFERENCE IN WHEEL DIA MEASURED ON SAME AXLE INCORRECT CENTRALISATION & ADJUSTMENT OF BRAKE RIGGING AND BRAKE BLOCKS WEAR IN BRAKE GEARS HOT AXLE HIGHER COEFFICIENT OF FRICTION DIFFERENT BEARING PRESSURES
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STABILITY ANALYSIS Q & Y – Instantaneous values, measurement by MEASURING WHEEL Hy = Horizontal force measured at axle box level Q = (Vertical) spring deflection x spring constant
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STABILITY ANALYSIS Nadal’s Formula for =68º, =0.25
Dry Rail 0.33 Wet Rail 0.25 Lubricated Rail 0.13 Rusted Rail 0.6 for =68º, =0.25 RHS works out to 1.4, rounded off to 1.0 for a factor of safety On I.R. Hy/Q measurement over 0.05 sec. It is one of the criteria for assessing stability of Rolling Stock
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LIMITING VALUES OF Y/Q RATIO VS TIME DURATION (JAPANESE RAILWAY)
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DIRECTION OF SLIDING FRICTION AT TREAD OF NON-DERAILING WHEEL
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CHARTET’S FORMULA K2 = 2(’+ )
= Angle of coning of wheel = 1/20 = 0.05 = K1 = K2 0.7
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For safety, the Q limited to 60 % of Qo
Y >2Q – 0.7Qo 2Q <Y + 0.7Qo As Y Q <0.7Qo Q < 0.35Qo Instantaneous Wheel Load Q should not drop below 35% of nominal wheel load Qo. For safety, the Q limited to 60 % of Qo
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EFFECT OF TWIST ON VEHICLE
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REFERRING TO FIG. a = Distance between centres of the spring A&B bearing on the wheel set PA = Load reaction in spring A PB = Load reaction in spring B G = Dynamic gauge R1 = rail reaction under wheel –1 R2 = rail reaction under wheel-2 e = amount of overhang of spring centre beyond the wheel rail contact point.
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Contd.. Let the rail under wheel-2 be depressed suddenly by an extent ½ Zo, so that the instantaneous value of R2 becomes zero, i.e. the wheel load of wheel-2 drops to zero.
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Contd.. Under effect of lowering of rail, spring B would elongate and load reaction PB would drop Taking moments about spring B PA a+ m (G/2+e) = R1 (G +e) + R2e = R1 (G+e) (since R2 = 0) (i) Taking moments about spring A PB a+ m (G/2+e) = R1e + R2 (G+e) = R1e (since R2 = 0) (ii)
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Contd.. Subtracting (i) from (ii) (PA-PB) a = R1G or PA – PB = R1 G/a
Now, R1 + R2 = T/2 R1 = T/2, since R2 = 0 PA – PB = T/2 *G/a
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Contd.. Difference in deflections of the springs A & B (owing to difference in the load reactions viz PA – PB = f (PA – PB), where f is specific deflection (assuming f to be the same for all the springs) That is, the difference in deflections of the two springs. = f *T/2* G/a
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By geometry, the above difference implies a difference in the levels of the two rails under the wheel set under consideration, to be
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Obviously, this is the extent by which the rail under wheel 2 would required to be depressed to reduce R2 instantaneously to zero. i.e.
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EFFECT OF TRACK AND VEHICLE TWIST
Track Defect that will completely off load the wheel Zo = fT (G/a)2 This equation is given by Kereszty
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EFFECT OF STIFFNESS OF SPRINGS
Larger ‘f’ i.e. deflection per unit, better from off loading point of view
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LOADED / EMPTY CONDITION OF VEHICLE
Larger the ‘T’, Better it is An empty wagon is more prone for derailment
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G/a RATIO - should be Large
Overhang should be less G/a ratio less for MG than BG
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VARIATIONS IN SPRING STIFFNESSES
One spring Zs = x/2 (G/a) x Defect in one spring Diagonally opposite springs Zs = x (G/a) = 2Zs
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TORSIONAL STIFFNESS OF VEHICLE UNDER FRAME
Converted to Equivalent Track Twist Zu = T/4 (G/a)2 Specific deflection of a corner of under frame Torsionally flexible under frame is desirable Riveted under frame desirable as against welded one
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TRANSITION OF A CURVE Track
Cant Gradient should be as flat as possible Effect on vehicle Zb = i.L, i Cant Gradient L = wheel base Longer wheel base is not desirable
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PERMISSIBLE TRACK TWIST
Zperm = 0.65 Zo – Zs + Zu – Zb (If one spring is defective) Zperm = 0.65 Zo – 2Zs + Zu – Zb (If two diagonal springs are defective)
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Motions of Vehicle (a) Linear oscillation; (b) rotational oscillation
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Motions of Vehicle HUNTING: COMBINED ROLLING + NOSING (VIOLENT MOTION)
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TRACK & VEHICLE DEFECTSS CAUSING VARIOUS PARASITIC MOTIONS
TRACK DEFECTS X-Level Loose Packing Low Joint Alignment Slack Gauge Versine Variation PARASITIC MOTION Rolling Bouncing, Rolling Pitching Nosing, Lurching Nosing, Hunting
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VEHICLE DEFECTS CAUSING PARASITC MOTION
Coupling Worn wheel Ineffective spring Side Bearer Clearance In-effective Pivot PARASITIC MOTION Shuttling, Nosing Hunting, Nosing, Lurching Bouncing, Pitching, Rolling Rolling, Nosing Nosing
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Lurching, Nosing & Rolling Y
Contd….. TRACK DEFECT MODE OF OSCILLATIONS AFFECTS’ VALUE Low joint Unevenness Loose Packing Bouncing & Pitching Q Alignment Gauge Fault Lurching, Nosing & Rolling Y Twist Rolling The above track defects when occurring in cyclic form would cause external excitation Hence, Adequate Damping Necessary
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EFFECT OF CYCLIC TRACK IRREGULARITY ON VEHICLE
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Oscillation mode of vehicle will be bouncing and pitching
Contd… Oscillation mode of vehicle will be bouncing and pitching For speed v = 13 m/s, excitation freq. t=13m For speed v = 26 m/s’ excitation freq. = 2 cps, t=13m This is “forcing” frequency, f = v/t
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Contd… “Natural” frequency of a vehicle in a particular mode of oscillation : Frequency of osc. in that mode, when system oscillates freely, after removal of external forcing frequency. For simple spring of stiffness “k” & mass “m” natural freq., fn= For 2 stage suspension system, there would be 2 natural frequencies.
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RESONANCE Natural Frequency = k = Spring Stiffness m = Mass
If frequency caused by external excitation is equal to natural frequency, resonance occurs under no damping condition
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FOUR TYPES OF FREE OSCILLATIONS FOR SAKE OF COMPARISON
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MAGNIFICATION FACTOR VERSUS FREQUENCY RATIO FOR VARIOUS AMOUNTS OF DAMPING FOR SIMPLE SPRING MASS DAMPER SYSTEM SHOWN.
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PRIMARY HUNTING WHEN THE BODY OSCILLATIONS ARE HIGH WHILE THE BOGIE IS RELATIVELY STABLE EXPERIENCED AT LOW SPEEDS MAINLY AFFECTS RIDING COMFORT
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SECONDARY HUNTING WHEN THE BODY OSCILLATIONS ARE RELATIVELY LESS. WHILE THE BOGIE OSCILATIONS ARE HIGH EXPERINCED AT HIGH SPEEDS AFFECTS VEHICLES STABILITY
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CRICITAL SPEED THE SPEED AT THE BOUNDARY CONDTION BETWEEN THE STABLE & UNSTABLE CONDITON IS CALLED AS CRITICAL SPEED OF THE VEHICLE THE SPEED FOR WHICH THE ROLLING STOCK IS CLEARED FOR THE SERVICE IS NORMALLY ABOUT 10 TO 15% LESS THAN THEC RITICAL SPEED AT WHICH THE VEHICLE HAS BEEN TESTED.
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FACTORS AFFECTING CRITICAL SPEED
VEHICLE WHEEL PROFILE RAIL HEAD PROFILE, INCLINATION & GAUGE RAIL WHEEL COEFF. OF FRICTION AXLE LOAD AND DISTRIBUTION OF VEHICLE MASS DESIGN AND CONDITION OF VEHICLE SUSPENSION
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LATERAL STABILITY OF TRACK
LATERAL TRACK DISTROTION DUE TO LESS LATERAL STRENGTH EXCESSIVE LATERAL FORCES BY VEHICLE
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LATERAL STABILITY OF TRACK
THIS STUDY IS IMPORTANT FOR ASSESSMENT OF STABILITY OF ROLLING STOCK INVESTIGATION OF DERAILMENTS
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PRUD’HOME’S FORMULA Hy > 0.85 (1+P/3) Hy> LATERAL FORCE
P = AXLE LOAD (t) Another formula, called blondel formula is there but it gives more values than prud’homme’s formula. Hy= P
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Allowable Twist in Track
RDSO letter no CRA 501 dtd Speed (KMPH) Peak value of UN on 3.6m chord (mm) Peak value of TW on 3.6m chord (mm) Twist (mm/M) 75 14 13 1 in 276 60 16 15 1 in 240 45 22 1 in 163 30 24 25 1 in 144 33 1 in 120
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Allowable Twist in Track
Allowable rate of change of cant actual on curves: Normal 55 mm/sec Exceptional 35 mm/sec With the changing speeds, the time element increases and therefore, the allowable change in the cant actual also increases. The allowable twist in track, therefore, increases with the reduction in speed
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Allowable change in gauge
Maximum gauge variations permitted are not laid down. In any case, the safety tolerances are not laid down in the manual Para 237(8)(a): It is a good practice to maintain uniform gauge over turnouts If there is a derailment over P & Cs, the gauge variation is often a point of controversy. We shall use the allowable variation in versines to check if the gauge variation is within limits
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THANKS !!
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