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 Track report lead locos pusher locos loaded coal cars time displacement

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) locowagon track wagon

Steady motion uphill Locomotives pulling forward more; more traction pushes track backwards more Wagons still rolling forward; drag pulls track forward as before loco wagon track wagon

Braking Locomotives and wagons all retarded by braked wheels; track pushed forwards at all wheel contacts. locowagon track wagon

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 combined track long. stiffness Rail stiffness F1F1 F2F2

Representation (2) Series of elements joined at nodes

Representation (3) Special element at ends (takes to infinity) k LH k RH

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) track loco wagon

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 frontmiddleback (4) 5.6 (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 force- deflection relationship

FE: summary results Conditions for residual displacement

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?