Residual stresses in a railway wheel: hardening + braking

Railway wheel

Freight rail wheels (picture 1) are the most loaded elements among all other components of a freight car. The wheel must support the weight of the carriage and guide it along the rails. Static load on 36-inch (914 mm) wheel under freight car weight 286000 pounds (130 T) is 35750 pounds (16,2 T). The wheel must withstand a huge amount of stress from thermal and mechanical stresses, which occur during block braking and high dynamic loads.

Picture 1 - Cast wheel CH36 for rail freight car
manufactured by Griffin (USA) [1]

Wheel manufacturing process

Railway wheels are made in two ways: rolling and casting.

Below will be considered the process of manufacturing cast wheels at the factories of the Griffin company. [1]. Heat treatment of rolled and cast railway wheels is similar to.

After casting, the wheels are heated to a temperature 815 ºС to relieve unfavorable residual stresses, which remain in the wheel after their casting. The wheel is kept at a heating temperature for some time to homogenize its microstructure. Then the rim is cooled with water jets over the rolling surface in a hardening machine, the diagram of which is shown in the figure 2.

Picture 2 - Scheme of quenching the wheel rim in the quenching machine

Rim hardening increases the strength of the steel, improves its wear resistance and forms favorable compressive residual circumferential stresses in the rim.

When the water jets cool the hot wheel rim part of the rim, adjacent to the rolling surface, cools and shrinks. However, at this time, the inner part of the rim is still at a high temperature and therefore has a reduced yield strength.. Under the influence of the outer part of the rim in this part of the rim and the adjacent part of the disc, which are compressed, plastic deformation occurs.

After quenching, the wheel is placed for two hours in a tempering furnace at a temperature 510 ºС to reduce the level of residual stresses. During this phase, the temperature of the wheel is equalized. The outer part of the rim is trying to return to its original state, but this is resisted by the inner part of the rim, as well as the adjoining part of the disk. Therefore, tensile residual stresses arise in them., and the outer part of the rim is at residual compressive stresses. Then the wheel cools down to room temperature while maintaining the distribution of residual stresses.

In this way, as a result of the operation of heat treatment of the ear, favorable compressive residual stresses are formed in its rim. Known, that such residual stresses help prevent fatigue cracks in the rim under operating conditions and, thereby, improve their safety.

Temperature loads on the wheel in operation

In operation, the wheel acts as a brake drum in addition to lateral and vertical mechanical loads. When the brake pad is pressed against the rolling surface of the wheel, the rolling surface heats up due to friction. The most severe temperature loads the wheel experiences, when a loaded train descends an incline for a long time. Besides, a malfunction of the brake mechanism can lead to jamming of the pads on the rolling surface of the wheel. In such cases, the wheel rim is heated to a high temperature.. Hot steel on the rolling surface and in the rim near the rolling surface is trying to expand. In the same time, the expansion of the heated part of the rim is prevented by the colder part of the rim and the wheel disc. Therefore, in the warmer part of the rim, compressive temperature stresses arise..

Change of compressive residual stresses in the rim to tensile ones

Steel in the heated part of the wheel rim will have a reduced yield strength and compressive stresses, which are above this yield point. Therefore, plastic deformations will occur in this heated part of the rim.. When the wheel has cooled down after the end of braking, those parts of the rim, who have undergone plastic deformation, will try to return to their previous position. However, this will be hindered by the underlying layers of the rim and the disc.. As a result, in the rolling surface and the adjacent part of the rim, the initial residual compressive stresses, which were formed during the heat treatment of the wheel, give way to tensile residual stresses.

Brittle breakage of the rim

Thermal fatigue of steel in the rolling surface due to repeated braking cycles can lead to the formation and propagation of thermal cracks. The presence of thermal cracks in the wheel with tensile residual stresses in the rim can lead to brittle fracture, which is initiated by a thermal crack. Therefore, it is very important to know not to allow a change in the sign of the residual stresses in the railway wheel..

Finite element model

Computer simulation helps to better understand the processes of formation of residual stresses during wheel hardening and their change during heating in operation. [1].

Finite element modeling includes calculation:

  • temperature stresses in the wheel during quenching
  • hardening residual stresses after heat treatment
  • change in residual stresses in the wheel after prolonged braking.

Finite element mesh

Due to the axisymmetric wheel shape and the applied thermal load, the task is two-dimensional axisymmetric. The same finite element mesh was used for all calculations., which contains 1826 nodes and 1695 elements (picture 3).

Picture 3 - Finite element mesh wheels

Quenching boundary conditions

The boundary conditions for cooling the wheel during quenching were of two types. (picture 4):

  • water cooling along the rolling surface;
  • air cooling on the rest of the surface.

Picture 4 - Boundary conditions for wheel hardening

Braking Heating Simulation

Because the finished wheels are thermally hardened, then its different parts have different thermal and mechanical properties.

These thermal properties include:

  • coefficient of thermal conductivity;
  • heat capacity.

These mechanical properties include:

  • elastic modulus;
  • yield point;
  • shear module;
  • Poisson's ratio;
  • thermal expansion coefficient.

Two options for the thermal properties of wheel steel (picture 5):

  • for disc and hub, which have not been hardened (T1).
  • for thermally hardened rim (T2);

Picture 5 - Options for the thermal properties of wheel steel
thermally hardened railway wheel
for thermal calculations during heating braking

Three options for the mechanical properties of wheel steel (picture 6):

  • steel with little effect of heat treatment (M1);
  • steel with medium effect of heat treatment (M2);
  • heat-hardened steel (M3).

Picture 6 - Variants of the mechanical properties of wheel steel
thermally hardened railway wheel
for calculating its stress state

Class C wheel steel

All calculations used class C wheel steel according to the classification of the American Railways Association. (AAR). This wheel steel has a carbon content of 0,67 to 0,77 % and most wheels in the USA are made from it [1].

All mechanical properties of steel, except Poisson's ratio, used as functions, which depend on temperature.

Elastoplastic model

In mechanical calculations, a model of an elastic-plastic material with bilinear kinematic hardening was used.

Boundary conditions for heating from braking

Dimensions and location of the rolling surface, affected by the brake pad, was accepted according to the AAR S660 standard [1]:

  • width - 86 mm;
  • distance from the center of the section to the rear end of the rim - 87 mm.

The power of the heat flux from the brake shoe to the wheel was taken to be 33 kWh (45 h.p.) [1].

Wheel hardening simulation

The calculated temperature distribution in the wheel at the end of hardening is shown in the figure. 7. The minimum temperature is reached at the rolling surface and is 218 ºS, maximum temperature - in the hub - 784 ºS. The calculated distribution of residual circumferential stresses of a thermally hardened wheel is shown in the figure 8.

Picture 7 - Temperature distribution at the end of wheel hardening

Picture 8 - Distribution of circumferential residual stresses in the wheel
after its thermal hardening

Braking Heating Simulation

Calculations of temperature and circumferential stresses were carried out for different duration of braking.:

  • 20 minutes;
  • 57 minutes;
  • 70 minutes.

On the picture 9 shows the residual circumferential stresses on the rolling surface after braking of various duration. With heat flow 33 kW residual stresses on the rolling surface do not change, if the duration of deceleration does not exceed 50 minutes. When braking more than 50 minutes, residual stresses begin to change rapidly. With duration 57 minutes, there is a transition from compressive to tensile residual stresses.

Picture 9 - Residual circumferential stresses on the rolling surface of the wheel
depending on the duration of the power braking 33 kWh

On the picture 10 shows residual circumferential stresses in a thermally hardened railway wheel after braking heating with power 33 kW during 70 minutes. The maximum tensile residual hoop stresses are 480 MPa.

Picture 10 – Residual hoop stresses
in a thermally hardened railway wheel
after braking heating power 33 kW during 70 minutes.

Residual radial stresses

Note, what's in work [1] only residual hoop stresses are shown. For railway wheel, especially for his drive, residual radial stresses. Radial stresses from mechanical loads are the main contributors to the cyclic loading of the disc.. Cm. more about this here.


  1. Investigation Of Heat Treating Of Railroad Wheels And Its Effect On Braking Using Finite Element Analysis / Kexiu Wang, Richard pilon – Griffin Wheel Company