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How can both the dynamic behaviour and wear of the wheel set be integrated in the design of a wheel profile?

Pieter van Elderen – NedTrain B.V. (Januari - December 2014)

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The wheel-rail interface of a train wheel plays an important role in many aspects like safety, dynamics, wear and costs. After the introduction of a new wheel profile (HIT-1) for the VIRM trains of the Dutch Railways (NS), the trains show reduced dynamic behaviour and a different kind of wear mechanism (Rolling Contact Fatigue instead of sliding wear). Therefore a research is done about the design of a wheel profile with both the dynamic behaviour and wear taken into account.

The research contains an analysis of the dynamic behaviour of a wheel set using Klingel's formula and a Rolling Contact Fatigue (RCF) analysis. This RCF analysis determines the contact area, contact pressure and the stress distribution in the wheel material (Figure 2). With the stress distribution the principal stresses and maximum shear stress is calculated and with the use of the Miner Damage rule is determined if the material is suffering from RCF.

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Figure 1: Bogie of a VIRM train

For the Miner Damage rule, an estimated S/N plot is used but this estimation is not sufficient to give a good representation of the real fatigue occurring in the wheel material. Therefore further research is necessary to define the S/N plot for a steel under compression and in a vacuum condition. Due to this lack of this S/N curve the D-value of the Miner Damage rule for the HIT profile (Figure 3) is reaching a value of almost 6000 where a value of 1 indicates that the lifetime is exceeded.

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Figure 2: Shear stress distribution (HIT profile)

Figure 3: D-value of the Miner Damage rule (HIT profile)

To integrate both the dynamic behaviour and wear in the design of a train wheel profile, the equivalent conicity of the profile should be used to find the optimum between both subjects.


  • The equivalent conicity affects both the dynamic behaviour and the wear of a wheel profile.
    • A higher equivalent conicity leads to a shorter wavelength of the hunting oscillation and therefore a higher hunting frequency. A lower frequency is in case of the VIRM trains interfering with the natural frequency of the carriage.
    • Due to this different frequency, the wheel contact point (WCP) variation will change and the loads can be more distributed over the whole wheel profile.
    • The radius of the wheel profile in y-direction is used to determine the rolling radii difference between the left and right wheel (Figure 4). Therefore the linearized equivalent conicity is higher when the radius is smaller. Since the radius of the wheel profile is used to calculate the contact area and pressure, the equivalent conicity has also in this way influence on the wear of a train wheel.

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Figure 4: Rolling radii difference for the HIT and s1002 wheel profile

  • Contact geometry and pressure between wheel and rail can be determined with the Hertz contact model.
  • The idea behind the HIT-profile (larger contact area and therefore lower contact pressure) seems to be incorrect. A constant area and pressure are more leading in the wear process of a train wheel.