Report on Contact

Stresses b/w Wheel

and Rail, & Stresses

due to Surface

Defects.

2010-TE-45

Hafiz Syed Rizwan

Department of Transportation Engineering

& Management, UET, Lahore

Railway Engineering Assignment Group # 2 | 1 P a g e

Hafiz Syed Rizwan 2010-TE-45 DTEM, UET, LHR.

Report on Contact Stresses b/w Wheel

and Rail, & Stresses due to Surface

Defects.

1. Contact Stresses b/w Wheel and Rail:

Since Heinrich Hertz published his contact theory in 1882, it has been extensively

applied In many engineering fields which deal with contact problems. The application

of the Hertz Contact theory (HCT) in rail-wheel contact problems can be found also in

the recent literature.

For example, the HCT is applied in to investigate the growth of shell-type defects in

the Head of a railroad rail. Hertzian contact pressure is applied in a fatigue life model

to describe the damage of wheels in. An approximation of the HCT is used in the

three-dimensional (3D) rail-fatigue model PHOENIX to describe the fatigue initiation

in rail subsurface, etc.

The program CONTACT of the Delft group can be considered as one of the most

prominent programs in Europe for calculating the contact area and the corresponding

deformation and stress state.

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Hafiz Syed Rizwan 2010-TE-45 DTEM, UET, LHR.

However, CONTACT is based on the theory of an elastic half space. Besides the HCT,

a point load iteration method has recently been used to obtain the contact pressure in

order to investigate the state of residual stress in a rail head.

With the development of computational tools, numerical calculations have recently

been extended to every corner of sciatic research. For instance, a self-developed finite

element (FE) code is applied in to analyze rail-rolling contact fatigue cracks. The HCT

leads to an elliptical contact area and a semi-ellipsoid contact pressure distribution in

the contact region. Due to its efficiency and simplicity, this theory has been

extensively applied since its publication. However, as mentioned in there are two

limiting conditions for the applications of the HCT

�The contact between elastic bodies should be frictionless,

�The significant dimensions of the contact area should be much smaller than the

dimensions and the radii of curvature of the bodies in contact.

The maximum contact shear stress at the contact point between the wheel and the rail

is given by the relation:

F=4.13 [P/R]1/2

Where; F= max. Shear stress in kg/mm2

R= radius of fully worn-out wheel in mm

P= static wheel load in kg + 1000kg for on loading on curves

1.1. Contact Pressure for a WDM-2 locomotive:

May be calculated on curves as follows:

Let the static wheel load P= 9400+1000 = 10400 KG

Radius of worn-out wheel (R) for maximum wear of 76mm. (38mm radius reduction

0r 76mm diameter reduction)

R= 1092/2 – 76/2 = 508mm

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F = 4.13 [10400/508]1/2 =18.7 kg/mm2

The maximum value is limited to 21.6 kg/mm2 which is 30% 0f ultimate tensile stress

value (72 kg/mm2) of the rail.

2. Stress due to Surface Defects:

A low spot on the rail or flat on the rim of the wheel causes extra stresses on the rail

section resulting in the failure of the rail such as fracture of the rail. Experiments have

shown that an additional deflection of 1.5 times the depth of low spot of the rail or flat

takes place at a speed of 30 km/h. the value of this additional bending moment is about

3,70,000kg cm for BG Group A with WDM-4 locomotive.

The origins of many forms of rail failures like those originating from manufacturing

defects and damages caused by inappropriate storage, handling and usage of the rail.

However, certain rail defects commonly known as Rolling Contact Fatigue (RCF)

defects cannot be attributed to any metallurgical or manufacturing defects in the rail or

wrong handling and usage during service. These defects are essentially initiated on the

surface or very close to the surface of rail. They develop due to excessive shear

stresses at the wheel-rail contact surface

Some common defects in rails are as follow:

2.1. Rolling Contact Fatigue Defects:

Rolling contact fatigue (RCF) is a group of rail damages which manifest themselves

on the surface or close to surface inside the rails due to overstressing of the rail

material.

The defects may first appear on the rail surface in the form of shelling, squats

and gauge corner cracks or within the subsurface in the form of deep seated shells.

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2.2. Gauge Corner Cracks:

These defects develop on top corner of the gauge face in the form of a series of surface

cracks spaced at about 2-5 mm intervals at a downward angle of 10-30 degrees and

gradually spreading across the rail head. These defects are more prominent on outer

rails of sharp curves and manifest themselves as fish scales.

2.3. Shelling:

Shelling is an internal defect which generally initiates at a depth of 2-8 mm

below the gauge corner of the high rails in curved track. In the initial stages of

development, shelling defects are noticeable as dark spots in the gauge corner

region of the rails. Shelling defects do not appear as regularly along the rail as

gauge corner checking defects.