1. RAIL WHEEL INTERACTION - Nilmani, Prof. Track

2. 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

3. EFFECT OF VEHICLE ON TRACK
LARGE DYNAMIC FORCES
DETERIORATION OF TRACK GEOMETRY
TRACK COMPONENT WEAR & DAMAGE
NOISE

4. EFFECT OF TRACK ON VEHICLE
SAFETY
RIDING COMFORT
COMPONENT WEAR & DAMAGE

5. NEED FOR UNDERSTANDING
REDUCE SAFETY RISK
IMPROVE RIDING COMFORT
REDUCE DETERIORATION OF TRACK GEOMETRY
MINIMISE WEAR
REDUCE NOISE AND VIBRATIONS IN VEHICLE

6. 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

7. SELF CENTRALIZING CONED WHEELS

8. Sinusoidal motion of wheelset

9. SINUSOIDAL MOTION OF VEHICLE

11. 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

12. Mean Position
Typical (Asymmetrical) Position
Extreme Position

13. 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 =

14. KLINGEL’S FORMULA (1883) Wave Length 0 of a Single wheel 0 =
0 =
G = Dynamic Gauge
r = Dynamic Wheel Radius
 = Conicity
0 
;Frequency  

15. 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

18. EFFECT OF PLAY As conicity increases Lateral Acceleration Increases
acc  a  /2 play
As play increases Lateral Acceleration Increases

19. 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

20. Wheel-set on Curve

21. THE PROCESS OF FLANGE CLIMBING DERAILMENT

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

23. ZERO ANGULARITY (PLAN)

24. POSITIVE ANGULARITY (PLAN)

25. NEGATIVE ANGULARITY (PLAN)

26. EXAMPLES OF WHEEL SET COFIGURATION WITH POSITIVE ANGULARITY

27. ZERO ANGULARITY (ELEVATION)

28. POSITIVE ANGULARITY (ELEVATION)

29. NEGATIVE ANGULARITY (ELEVATION)

30. FORCES AT RAIL-WHEEL CONTACT AT MOMENT OF INCIPIENT DERAILMENT

31. 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 ) 

32. Nadal’s Equation (1908)
For Safety: LHS has to be small. RHS has to be large
Y  Low
Q  High
 Low
tan   Large

34. 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

35. 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.

36. 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

37. FACTORS AFFECTING SAFETY
Flange slope
With wear  increases, but results in greater biting action, hence increase in .

38. 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

39. 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.

40. 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.

41. 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

42. 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

43. DESIGNED ANGULARITY WHILE NEGOTIATING CURVE
PLAY HELPS THE WHEEL NEGOTIATE CURVE

44. 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)

45. 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

46. 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

47. 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

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

49. DIRECTION OF SLIDING FRICTION AT TREAD OF NON-DERAILING WHEEL

50. CHARTET’S FORMULA K2 = 2(’+  )
 = Angle of coning of wheel  = 1/20 = 0.05
 = K1 = K2  0.7

51. 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

52. EFFECT OF TWIST ON VEHICLE

55. 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.

56. 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.

57. 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)

58. 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

59. 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

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

62. 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.

64. 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

65. EFFECT OF STIFFNESS OF SPRINGS
Larger ‘f’ i.e. deflection per unit, better from off loading point of view

66. LOADED / EMPTY CONDITION OF VEHICLE
Larger the ‘T’, Better it is
An empty wagon is more prone for derailment

67. G/a RATIO - should be Large
Overhang should be less
G/a ratio less for MG than BG

68. VARIATIONS IN SPRING STIFFNESSES
One spring
Zs = x/2 (G/a)
x  Defect in one spring
Diagonally opposite springs
Zs = x (G/a) = 2Zs

69. 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

70. 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

71. 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)

72. Motions of Vehicle
(a) Linear oscillation; (b) rotational oscillation

73. Motions of Vehicle
HUNTING: COMBINED ROLLING + NOSING (VIOLENT MOTION)

74. 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

75. 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

76. 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

77. EFFECT OF CYCLIC TRACK IRREGULARITY ON VEHICLE

78. 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

79. 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.

80. 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

81. FOUR TYPES OF FREE OSCILLATIONS FOR SAKE OF COMPARISON

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

83. PRIMARY HUNTING
WHEN THE BODY OSCILLATIONS ARE HIGH WHILE THE BOGIE IS RELATIVELY STABLE
EXPERIENCED AT LOW SPEEDS
MAINLY AFFECTS RIDING COMFORT

84. SECONDARY HUNTING
WHEN THE BODY OSCILLATIONS ARE RELATIVELY LESS. WHILE THE BOGIE OSCILATIONS ARE HIGH
EXPERINCED AT HIGH SPEEDS
AFFECTS VEHICLES STABILITY

85. 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.

86. 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

87. LATERAL STABILITY OF TRACK
LATERAL TRACK DISTROTION DUE TO
LESS LATERAL STRENGTH
EXCESSIVE LATERAL FORCES BY VEHICLE

88. LATERAL STABILITY OF TRACK
THIS STUDY IS IMPORTANT FOR
ASSESSMENT OF STABILITY OF ROLLING STOCK
INVESTIGATION OF DERAILMENTS

89. 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

90. 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

91. 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

92. 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

93. THANKS !!