RAIL WHEEL INTERACTION

- Nilmani, Prof. Track

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

EFFECT OF VEHICLE ON TRACK

LARGE DYNAMIC FORCES

– DETERIORATION OF TRACK GEOMETRY

– TRACK COMPONENT WEAR & DAMAGE

– NOISE

EFFECT OF TRACK ON VEHICLE

• SAFETY

• RIDING COMFORT

• COMPONENT WEAR & DAMAGE

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

SELF CENTRALIZING CONED WHEELS

Sinusoidal motion of wheelset

SINUSOIDAL MOTION OF VEHICLE

• 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

PLAY BETWEEN WHEEL SET AND RAILS

• Mean Position

• Typical (Asymmetrical) Position

• Extreme Position

EFFECT OF PLAY

Lateral Displacement Y = a sin wta amplitude = /2 = Play/2Lateral velocity = aw cos wtLateral Acceleration = -aw2 sin wtMax acc = -aw2

Angular Velocity w =

2

2 f

KLINGEL’S FORMULA (1883)

Wave Length 0 of a Single wheel

0 =

G = Dynamic Gauger = Dynamic Wheel Radius = Conicity

0 ;Frequency

22

rG

1

CONCLUSIONS•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

2

1

G

l

EFFECT OF PLAY

•As conicity increases Lateral Acceleration Increases

•acc a /2 play•As play increases Lateral Acceleration Increases

2

224.

v

aacc

2

1acc

CONCLUSIONS

• EXCESSIVE OSCILLATIONS DUE TO– Slack Gauge

– Thin Flange

– Increased Play in bearing & Journal

– Excessive Lateral and Longitudinal Clearances

• Increased Derailment Proneness

Wheel-set on Curve

THE PROCESS OF FLANGE CLIMBING DERAILMENT

SECTIONAL PLAN OF WHEEL FLANGE AT LEVEL OF FLANGE TO RAIL CONTACT

ZERO ANGULARITY (PLAN)

POSITIVE ANGULARITY (PLAN)

NEGATIVE ANGULARITY (PLAN)

EXAMPLES OF WHEEL SET COFIGURATION WITH POSITIVE ANGULARITY

ZERO ANGULARITY (ELEVATION)

POSITIVE ANGULARITY (ELEVATION)

NEGATIVE ANGULARITY (ELEVATION)

FORCES AT RAIL-WHEEL CONTACT AT MOMENT OF INCIPIENT DERAILMENT

• Resolving Along Flange SlopeR= 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 )

)sin(cos

)cos(sin

Q

Y

FORCES AT RAIL-WHEEL CONTACT AT MOMENT OF INCIPIENT DERAILMENT

For Safety: LHS has to be small. RHS has to be large

Y Low

Q High Low

tan Large

tan1

tan

Q

Y

Nadal’s Equation (1908)

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

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.

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

FACTORS AFFECTING SAFETY

Flange slope

• With wear increases, but results in greater biting action, hence increase in .

FACTORS AFFECTING SAFETY

OTHER FACTORS INFLUENCING NADAL’S FORMULA

INCREASES WITH INCREASED ANGULARITY, (PROF. HEUMANN)

(acting upwards for positive angularity)

0.0

0.02

0.0

0.27

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.

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.

FACTORS AFFECTING SAFETY

DEFECTS/FEATURES AFFECTING

1. Rusted rail lying on cess, emergency x-over

2. Newly turned wheel – tool marks

3. Sanding of rails (on steep gradient, curves)

4. Sharp flange (radius of flange tip < 5mm) increases biting action

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

DESIGNED ANGULARITY WHILE NEGOTIATING CURVE

PLAY HELPS THE WHEEL NEGOTIATE CURVE

• DEFECTS / FEATURE FOR INCREASED POSITIVE ECCENTRICITY

• WHEEL FLANGE SLOPE BECOMING STEEPER (THIS DEFECT REDUCES SAFETY DEPTH AS ECCENTRICITY INCREASES)

DEFECTS/FEATURES FOR INCREASED ANGLE OF ATTACK

• 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

DEFECT/FEATURES CAUSING PERSISTENT ANGULAR RUNNING

• Q & Y – Instantaneous values, measurement by MEASURING WHEEL

• Hy = Horizontal force measured at axle box level

• Q = (Vertical) spring deflection x spring constant

STABILITY ANALYSIS

Nadal’s Formula

Dry Rail 0.33Wet Rail 0.25Lubricated Rail 0.13Rusted 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

tan1

tan

Q

Y

STABILITY ANALYSIS

• LIMITING VALUES OF Y/Q RATIO VS TIME DURATION (JAPANESE RAILWAY)

• DIRECTION OF SLIDING FRICTION AT TREAD OF NON-DERAILING WHEEL

CHARTET’S FORMULA

K2 = 2(’+ )

= Angle of coning of wheel = 1/20 = 0.05

= 0.25 K1 = 2 K2 0.7

2'

Q

QoKK

Q

Y21

'

tan1

tan1K

FOR SAFETY

Y >2Q – 0.7Qo

2Q <Y + 0.7Qo

As Y 0 2Q <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

Q

Qo

Q

y7.02

EFFECT OF TWIST ON VEHICLE

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-2e = amount of overhang of spring centre

beyond the wheel rail contact point.

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.

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)

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

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

• By geometry, the above difference implies a difference in the levels of the two rails under the wheel set under consideration, to be

2

22

a

GTf

a

G

a

GTf

• 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. 2

021

2

a

GTfZ

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

EFFECT OF STIFFNESS OF SPRINGS

• Larger ‘f’ i.e. deflection per unit, better from off loading point of view

LOADED / EMPTY CONDITION OF VEHICLE

• Larger the ‘T’, Better it is

• An empty wagon is more prone for derailment

• G/a RATIO - should be Large

• Overhang should be less

• G/a ratio less for MG than BG

VARIATIONS IN SPRING STIFFNESSES

One spring

Zs = x/2 (G/a)

x Defect in one spring

Diagonally opposite springs

Zs = x (G/a) = 2Zs

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

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

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)

• (a) Linear oscillation; (b) rotational oscillation

Motions of Vehicle

Motions of Vehicle

HUNTING: COMBINED ROLLING + NOSING (VIOLENT

MOTION)

TRACK & VEHICLE DEFECTSS CAUSING VARIOUS PARASITIC

MOTIONS

A. TRACK DEFECTS• X-Level• Loose Packing• Low Joint• Alignment• Slack Gauge• Versine Variation

PARASITIC MOTION• Rolling• Bouncing, Rolling• Pitching• Nosing, Lurching• Nosing, Lurching• Nosing, Hunting

VEHICLE DEFECTS CAUSING PARASITC MOTION

A. VEHICLE DEFECT• Coupling• Worn wheel

• Ineffective spring

• Side Bearer Clearance

• In-effective Pivot

PARASITIC MOTION• Shuttling, Nosing• Hunting, Nosing,

Lurching• Bouncing, Pitching,

Rolling• Rolling, Nosing• Nosing

Contd…..

TRACK DEFECT MODE OF OSCILLATIONS

AFFECTS’ VALUE

Low joint Unevenness Loose Packing

Bouncing & Pitching Q

AlignmentGauge Fault

Lurching, Nosing & Rolling

Y

Q

Twist Rolling Q

The above track defects when occurring in cyclic form would cause external excitationHence, Adequate Damping Necessary

EFFECT OF CYCLIC TRACK IRREGULARITY ON VEHICLE

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

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.

m

k

2

1

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

m

k

2

1

• FOUR TYPES OF FREE OSCILLATIONS FOR SAKE OF COMPARISON

• MAGNIFICATION FACTOR VERSUS FREQUENCY RATIO FOR VARIOUS AMOUNTS OF DAMPING FOR SIMPLE SPRING MASS DAMPER SYSTEM SHOWN.

PRIMARY HUNTING• WHEN THE BODY OSCILLATIONS

ARE HIGH WHILE THE BOGIE IS

RELATIVELY STABLE

• EXPERIENCED AT LOW SPEEDS

• MAINLY AFFECTS RIDING

COMFORT

SECONDARY HUNTING

• WHEN THE BODY

OSCILLATIONS ARE

RELATIVELY LESS. WHILE THE

BOGIE OSCILATIONS ARE HIGH

• EXPERINCED AT HIGH SPEEDS

• AFFECTS VEHICLES STABILITY

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.

FACTORS AFFECTING CRITICAL SPEED

1. VEHICLE WHEEL PROFILE

2. RAIL HEAD PROFILE, INCLINATION & GAUGE

3. RAIL WHEEL COEFF. OF FRICTION

4. AXLE LOAD AND DISTRIBUTION OF VEHICLE MASS

5. DESIGN AND CONDITION OF VEHICLE SUSPENSION

LATERAL STABILITY OF TRACK LATERAL TRACK DISTROTION

DUE TO

• LESS LATERAL STRENGTH

• EXCESSIVE LATERAL FORCES BY VEHICLE

LATERAL STABILITY OF TRACK

THIS STUDY IS IMPORTANT FOR

• ASSESSMENT OF STABILITY OF ROLLING STOCK

• INVESTIGATION OF DERAILMENTS

PRUD’HOME’S FORMULA

–Hy > 0.85 (1+P/3)

–Hy> LATERAL FORCE

–P = AXLE LOAD (t)

Allowable Twist in TrackRDSO letter no CRA 501 dtd 29.04.83

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 22 1 in 163

30 24 25 1 in 144

15 33 30 1 in 120

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