Effect of passing trains on
longitudinal stresses and creep of
rails
Robin Ford
A N Abd Manap, K Hartono Putra
School of Mechanical and
Manufacturing Engineering
The University of New South Wales
My topic
Reports that intrigued me
1. Al Reinschmidt of AAR
2. Paper at the 1989
HH Conf
3. Article in Pandrol
lead locos
Track report
pusher locos
time
displacement
loaded coal cars
What’s been done?
Devised an analysis and tested it
Coursework masters student re-coded it and
did a parametric study
Honours student looked at finite element
solutions for comparison
What didn’t I do?
• No lateral loads
(longitudinal loads only)
• No temperature effects
(longitudinal traction forces only)
What’s been done before (1)
Markine/Esveld analysis (LONGIN)
• Braking
• Accelerating
• Lateral forces
• Temperature
• Uniformly distributed loading
(ie not loads at wheel locations)
What’s been done before (2)
Pandrol analysis (PROLIS)
• Analysed two systems:
- conventional
- Vanguard
• Investigated thermal effects
Preview: next possibilities
• Extend from stationary to passing trains
• Scale model tests
• Extend to include temperature and lateral
effects
• Find out practical usefulness
Steady motion on the level
• Locomotives pulling forward; traction
pushes track backwards
• Wagons rolling forward; drag pulls track
forward (a bit)
wagon
wagon
wagon
track
loco
Steady motion uphill
• Locomotives pulling forward more; more
traction pushes track backwards more
• Wagons still rolling forward; drag pulls
track forward as before
Braking
• Locomotives and wagons all retarded by
braked wheels; track pushed forwards at all
wheel contacts.
wagon
wagon
wagon
track
loco
Questions
• How much does the rail move under these
longitudinal forces?
• How much of the movement is permanent?
Model 1
• Rail stretches under longitudinal loads
Model 1
• Rail stretches under longitudinal loads
• Railpads allow “elastic” longitudinal movement
Model 1
• Rail stretches under longitudinal loads
• Railpads allow “elastic” longitudinal movement
• Ballast allows “elastic” longitudinal movement
Model 1
• Rail stretches under longitudinal loads
• Railpads allow “elastic” longitudinal movement
• Ballast allows “elastic” longitudinal movement
• “elastic” => no permanent deformation
Representation (1)
Basic element represents one sleeper bay with
rail and sleeper
F1
Rail stiffness
F2
combined track
long. stiffness
Representation (2)
Series of elements joined at nodes
Representation (3)
Special element at ends (takes to infinity)
kLH
kRH
Representation (4)
Wheel forces aligned with nodes (ie multiples
of sleeper spacing)
Calculations
1. Simple code in BASIC: elastic
no permanent set
2. MATLAB code: elastic
no permanent set
3. Finite element code (STRAND 7):
includes inelastic behaviour
includes permanent set
Simple code in BASIC
• Like a model train set – keep it simple
(1 locomotive, five wagons)
• Level track
• Use superposition (elastic behaviour only)
wagon
wagon
wagon
track
wagon
wagon
loco
Results for train set
Displacement
Sleeper position
MATLAB code?
Why? Because it can handle:
• Long trains
• Multiple locomotives; various positions
• Level, uphill, braking
• Parametric studies
MATLAB code: check
Close agreement with Markine/Esveld results
Displacement
Sleeper position
MATLAB results (1)
Braking: max displacement 6.9mm
Displacement
Sleeper position
MATLAB results (2)
Uphill; 4 locomotives at the front:
max displacement 5.6mm
Displacement
Sleeper position
MATLAB results (3)
Uphill; 2 locos at front, 2 in middle:
max displacement 3.5mm
Displacement
Sleeper position
MATLAB results (4)
Uphill; 2 locos front, 1 loco mid, 1 loco back:
max displacement 3.5mm
Displacement
Sleeper position
MATLAB results (5)
Detail of elastic displacements under wagons
remote from locos.
Displacement
Sleeper position
MATLAB results (6)
Detail of elastic displacement under 4 locos
pulling 200 wagons (max 5.6mm)
Displacement
Sleeper position
MATLAB results (7)
Detail of elastic displacement under 1 loco
pulling 50 wagons (max 1.8mm ie >5.6/4)
Displacement
Sleeper position
Parametric studies
loco position
(number of locos) rail displt, mm
front
middle
back
(4) 5.6
(2) 3.5
(2) 3.5
(2) 3.5
(1) 1.8
(2) 3.5
(1) 1.8
(2) 3.5
Conclusions from parametric
study
1. Largest deflections were for braking
2. Smallest deflections under freely rolling wagons
3. Effects of driven axles of locos limited to the
region around the locos
4. Distributed locos produce lower maximum
deflections
5. Linearity assumption => scalability, but no
permanent set
Finite Element Analysis
• Basic model as before
• Permits non-linear analysis
- permanent slip through rail fasteners
Finite Element Analysis
• Basic model as before
• Permits non-linear analysis
- permanent slip through rail fasteners
Finite Element Analysis
• Basic model as before
• Permits non-linear analysis
- permanent slip through rail fasteners
- permanent slip through ballast
Finite Element Analysis
• Basic model as before
• Permits non-linear analysis
- permanent slip through rail fasteners
- permanent slip through ballast
FE: modelling the forcedeflection relationship
Weak vs. Moderate. vs. Strong Track Resistance
12000
Weak Track
Resistance
10000
Moderate
Track
Resistance
Force (N)
8000
6000
Strong
Track
Resistance
4000
2000
0
0
0.005
0.01
0.015
Displacement (m)
0.02
0.025
FE: summary results
Conditions for residual displacement
Track Arrangement
Track Resistance
Weak Moderate Strong
Level

X
X
Braking

X
X
Uphill
Uphill (3 front and 2
middle locos)


X

X
X
FE: displacement under load
Level Track – Weak Track Resistance
Max 1mm
FE: residual displacement
Level Track – Weak Track Resistance
Max 0.06mm
FE: displacement under load
Uphill Track – Moderate Track Resistance
Max 3mm
FE: residual displacement
Uphill Track – Moderate Track Resistance
Max 0.34mm
FE: displacement under load
Uphill Track – Weak Track Resistance
(3 locos at the front and 2 in the middle)
FE: residual displacement
• Uphill Track – Weak Track Resistance
(3 locos at the front and 2 in the middle)
Next steps (1)
Non-linear with moving train
Do the wheels move the ruckle (wrinkle)
along the carpet, or the bubble under the
GRP lay-up?
Next steps (2)
Effect of weight on the propensity to slip
How does the load on the sleeper (pushing
down or lifting up) affect permanent
sliding?
Next steps (3)
All the other complications:
1. Temperature
2. Lateral loads
3. Loads between sleepers
Next steps (4)
Usefulness
• Good for students
• Is it useful for those running railways?