IV. Technical Background
The basis for this bulletin is the commonly accepted use of the Nadal formula which
considers the influence of wheel flange angle, wheel/rail coefficient of friction and
wheel/rail forces on the possibility of wheel climb derailment. This principle is
expressed in the following Nadal formulation:
L/V=(tand -m )/(1+m tan(d ))
The relationships of these factors are presented in figure #2:
Figure 2
L=wheel/rail lateral force
V=wheel/rail vertical force
L/V=ratio of wheel/rail forces*
*in the context of the figure above L/V ratios greater than the upper bound are provide
potential for derailment
m (Coefficient of Friction) = ratio of tangential
to normal wheel/rail force at which slippage occurs.
It is beyond the scope of this bulletin to address all of the issues to be considered
when specifying wheel profiles. Rather, this technical bulletin stipulates a boundary
value for one parameter, flange angle, that is critical in preventing wheel climb
derailments. It is strongly recommended that individuals and organizations adopt or
develop wheel profiles practices that assure the minimum sustained flange angle of 72°.
As shown in figure 1, a wheel profile that incorporates a flange angle of 72° provides a significant margin of safety compared to profiles in
which the maximum flange angle is approximately 68° to 70°.
V. Suggested Actions
The Task Group strongly suggests that operators of passenger rolling stock consider a
quality inspection program to insure that the minimum flange angle discussed above is
achieved. This inspection program should consist of the following actions.
- inspection of all check and go/no-go gages for new and recontoured wheels check for
wear and distortion due to excessive use and damage
- check wheel contouring machinery:
For lathes:
a) inspect set-up for slop, backlash and evidence of improper operation, e.g., badly
worn cutting tools
b) ensure that templates are appropriate for design and are installed properly ,e.g.,
no improper tilt
For milling tools:
a) inspect cutting heads for tool breakage or wear
Periodic verification of the accuracy of wheel profiles should be based on a sample of
newly manufactured and remachined profiles with a verifiable measuring tool such as a
"Mini Prof" device, which has a traceable
calibration and a process for routine checking of known machined surfaces.
This audit then should demonstrate conformance to the flange angle minimum described
above. The criteria for the audit should be established by the owning authority and
traceable records kept. It is recommended that routine repetition of this quality
inspection should be conducted by the owning authority.
VI. References
1. Shust, W. C., Thompson, R., and Elkins, J. A., 1998, "Controlled
Wheel Climb Derailment Tests Using a Force Measuring Wheelset and AAR's Track Loading
Vehicle," Proceedings of 12th International Wheelset Congress, Qingdao, China
2. Shust, W. C., Elkins, J. A., Kalay, S., and ElSibaie, M., 1997, "Wheel Climb
Derailment Test Using AAR's Track Loading Vehicle," AAR report R-910, Pueblo, CO.
3. Blade. F .B., 1990, A Review of Literature and Methodology in the Study of
Derailments Caused by Excessive Force at Wheel/Rail Interface." AAR Report R-717
4. Weinstock, H., 1984 "Wheel Climb Derailment Criteria For Evaluation of Rail
Vehicle Safety," Proceedings of the ASME Winter Annual Meeting, 84-WA/RT-1
5. Sweet, L. M., Karmel, A., and Moy, P., 1980, Wheel Climb Derailment Criteria under
Steady Rolling And Dynamic Loading Conditions," Proceedings of 6th IAVSD Symposium on
Vehicle Systems Dynamics, Berlin, Swetes, and Zeitlinger B. V., Lisse
6. Gilchrist, A. O., and Brickle, B. V., 1976, "A Re-examination of the Proneness
to Derailment of a Railway Wheelset," Journal of Mechanical Engineering Science, Vol.
18, No. 3, pp. 134-141.
7. Nadal, M. J., 1896, "Theore de la Stabilite des Locomotives, part 2,"
Movement de Lacet, Annales des Mines, 10, 232
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