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For a portable rail measuring device, a leveling bar is usu- 3.3 WHEEL/RAIL PROFILE ASSESSMENT
ally used to measure rail gage and hold the measurement
device in the correct orientation relative to the track plane. If How measured wheel and rail profiles are assessed should
there is no mechanism for holding the device in the correct be based on the objectives of the analysis. They are generally
orientation, then a direct measurement of the rail cant angle related to the following issues:
should also be made.
The automated measurement systems generally require · Making maintenance decisions
more complicated calibrations, as well as additional mathe- · Studying wear processes and wear rates
matical smoothing and filtering. · Studying contact conditions
· Studying wheel/rail interactions
3.2.3 Documentation of Measurement Often, in maintenance decisions, not only the profile
shapes are considered but also the surface conditions. In
Good documentation of measured profiles is useful for transit operations, flat spots on the wheel surface are one of
obtaining a system view of wheel/rail profile conditions, the common reasons for wheel re-profiling. Corrugation
combined with the geometry and contact analysis results. It and surface defects due to rolling contact fatigue are among
is especially helpful for tracking profile changes to determine common reasons for rail grinding. In this section, only
the wear patterns and wear rates, tracking the variations of those assessments related to wheel/rail profiles are dis-
contact situations to determine the maintenance need, and cussed.
identifying the performance trends in vehicle types or track
sites.
3.3.1 Dimension Assessment
Depending on the purpose for making the profile
measurements, other information related to the measure- 3.3.1.1 Wheel Flange Height and Flange Thickness
ments may also need to be recorded, such as surface
conditions (shells, spalls, and head checking), lubrication Wheel flange height is defined as the distance from the
conditions, tie/fastener conditions at the measurement site flange tip to the wheel tread taping line (see Figure 3.9). It
for rails, and vehicle condition for wheels. Tables 3.1 and is an indicator of tread wear and could also be used as an
3.2 give examples of documenting wheel and rail mea- indicator of rim thickness. Wheel flange thickness is defined
surements. More columns can be added for additional as the flange width at a specific height above the taping line.
information. It gives an indicator of flange wear. The minimum flange
TABLE 3.1 Recording example of wheel measurements
Record of Wheel Measurements
Measurement Mileage
Measurement File Name of Vehicle Axle Left/ Date Last Designed
Location Since Last Observations
Date Measurement Number Number Right Turned Profile
Shop/Line Profiled
04102004- Surface
4/10/04 Shop1/Green 708932 3 L 2/25/02 50,000 ST1
0010.whl Shelling
TABLE 3.2 Recording example of rail measurements
Record of Rail Measurements
Number of
Measurement Date Last
Measurement File Name of Curvature High/ Gage Axle Passes Designed
Location Ground/ Observations
Date Measurement (degree) Low (in.) since Last Profile
MP/Line Laid
Grinding/Laid
Head
checking on
04102004-
4/10/04 18.6/Green 5 H 56.6 6/22/03 30,000 115 RE rail gage.
0010.rai Poor
lubrication
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3.3.1.3 Rail Head/Gage Metal Loss
The limit of rail head/gage area loss defines the minimum
rail cross sectional area allowed in service. This limit ensures
rail has sufficient strength under load and provides adequate
guidance for wheels running along the track. The limiting
loss of area should be specified based on the vehicle load,
track curvature, and track condition.
The head or gage losses measured by the gage in Figure
3.5 are indicated by the graduations on the pins. Using the
profile contour measurement device, it is convenient to over-
Figure 3.9. Definitions of flange height and flange lay the worn profile with the new and to compute the area
thickness. (L is the distance from wheel back to the tape loss, as shown in Figure 3.11.
line [or datum line], D is the position where the flange Most profile contour measurement devices now have soft-
thickness is measured.) ware that can quickly process a large group of measured
wheels and provide results for wheel flange height, flange
thickness, tread hollowing, and other geometry parameters
thickness limit ensures the bending strength of the flange on a spreadsheet.
when subjected to dynamic forces. There are different The rail head material loss computation requires that the
designs of wheels adopted in transit operations with differ- measured rail profiles have a correct orientation relative to the
ent dimensions. Each type of wheel should have specifica- new rail template; previous measurements at the same location
tions on the limiting values of flange height and thickness. can be used to confirm the accuracy of the computation.
These specifications should be followed for conducting
maintenance.
3.3.2 Wheel/Rail Contact Assessment
3.3.1.2 Wheel Tread Hollowness Wheel/rail contact assessment is generally performed to
study the effects of wheel/rail interaction on vehicle perfor-
The wheel tread hollowness is defined by placing a hori- mance or wheel/rail wear. Depending on its objectives, the
zontal line at the highest point of the end of the wheel tread. analysis can be either static or dynamic.
The maximum height from the tread to this line is the value Static analysis only concerns wheel and rail shapes and
of hollowness (see Figure 3.10). Hollow-worn wheels can their relative positions under a specified loading condition
have very negative effects on vehicle performance (5, 6). without regard to the vehicle or its motion. The results from
Although rules for removing hollow-worn wheels are still in static analysis are normal contact stress and parameters of the
the process of being established, North American inter- wheel/rail contact constraints. Dynamic assessment is
change freight service now has a general aim to eventually usually performed using vehicle simulation software, which
remove wheels with tread hollowing greater than 3 mm. provides detailed information on wheel/rail interaction,
Transit operations should have a smaller allowed tread hol- including normal forces, tangential forces, creepages, dis-
low limit than freight service not only for operational safety placements, velocities, accelerations, and other dynamic
but also for ride quality. parameters for wheel and rail contact patches. Contact pa-
rameters resulting from dynamic assessment are not only
related to wheel/rail shapes and relative positions but are also
New Rail
Worn Rail
Figure 3.10. Definition of wheel tread hollow. Figure 3.11. Rail head cross sectional area loss.
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influenced by speed, car/truck characteristics, and track The parameters produced from the wheel/rail profile
geometry. The research team has developed a static analysis analysis are described in detail below.
software program (6) and a dynamic analysis program (7).
The static analysis software can analyze contact situations
of many wheelsets against a measured pair of rails or many 3.3.2.1 Maximum Contact Angle
rails against a measured pair of wheels. This method pro-
vides a comprehensive view of wheel/rail contact at a system The maximum wheel/rail contact angle depends on the max-
level. For example, thousands of wheels with different pro- imum wheel flange angle and the maximum angle of the rail
files (due to different levels of wear or resulting from differ- gage face. A wheel profile with a higher flange angle can reduce
ent truck performance) could contact a section of rail at dif- the risk of flange climb derailment and can have much better
ferent positions and, therefore, could produce different compatibility with any new design of vehicle/truck that may be
contact patterns and different levels of contact stress. The introduced in the future compared to wheels with lower flange
performance of the majority of wheel/rail pairs is therefore angles. Also, with a higher L/V ratio limit (according to the
the focus of the assessment. Nadal flange climb criterion), high flange angles will tolerate
The distribution of contact parameters can be used to predict greater levels of unexpected track irregularity.
likely vehicle performance, wheel/rail wear, and contact Figure 3.12 shows two examples of undesirable relation-
fatigue. For example, consider a group of measured wheels ships between wheel flange angles and the preferred rela-
contacting a pair of rails measured on a curve. If the rails are tionship. If rails are worn into a lower gage angle than that of
judged to have unsuitable profiles due to resulting high contact the wheel flange angle or if newly designed wheels have a
stress and undesirable contact patterns, then appropriate action higher flange angle than existing wheels, a point contact
can be taken. If only a small number of wheels give unwanted would occur on the wheel flange, and this would result in a
wheel/rail interaction, then it might be best to remove those maximum wheel/rail contact angle less than the maximum
wheels from service. Alternatively, if many wheels cause prob- wheel flange angle. The contact situation is likely to be as
lems, then it might be best to re-profile the rail by grinding. shown in the left illustration of Figure 3.12 as wheel flang-
Dynamic assessment is generally performed to study the ing. If the wheel flange angle is lower than the rail gage
wheel/rail interaction for specific vehicle/track conditions. angle, the contact situation is likely to be as shown in the
Therefore, using wheels on the vehicles being studied would middle illustration of Figure 3.12. The right illustration
more accurately predict their performance. The contact tan- shows the desirable flanging condition where wheel flange
gential forces and creepages produced from dynamic simu- and rail gage face wear to similar angles.
lation can provide more detailed information for the analysis
of wear and rolling contact fatigue. A large number of simu-
lations would need to be conducted if a detailed analysis of a 3.3.2.2 Contact Positions
large group of wheel profiles was required, such as was
needed for the derailment study performed for this report. Wheel and rail contact have a direct effect on vehicle per-
In summary, the analysis of a large number of profiles is formance and wheel/rail wear. Contact positions are closely
useful for wheel/rail system monitoring and evaluation. A sta- related to wheel/rail profile shapes and influenced by vehicle
tic analysis generally can produce the required results and track condition. The three typical contact conditions
quickly. Dynamic simulation can provide more detailed infor- shown in Figure 3.12 are likely to produce different curving
mation related to wheel/rail interaction under specific condi- forces and rolling resistances. Distribution of contact posi-
tions. The method that should be selected for the wheel/rail tions on a pair of rails from contacting a population of wheels
profile analysis depends on the assessment objectives. gives indications of the likely performance trend.
Figure 3.12. Three types of contact related to wheel flange/rail gage angles.
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Figure 3.13 shows an output example from the static In Figure 3.13, the low rail experienced contact stress
analysis software with 112 wheelsets, which were measured toward the field side that was much higher than the criterion
on trains that had passed over a pair of rails measured on a 7 and should be corrected. The high rail experienced accept-
degree curve. A wheelset lateral shift between 0.3 and 0.5 in. able contact stress toward the gage side, but high stress at the
was assumed for the computation. That is the lateral shift gage corner because of the very small contact radius. High
range for wheel flanging on this degree of curve. The dots in contact stresses in this area combined with the tangential
the figure show the distribution of contact positions on the forces can cause the metal to either wear off before microc-
rails from those 112 axles and the level of contact stress. The racks develop to a size that causes concern or else form head
high rail showed a trend of conformal contact indicated by checking rolling contact fatigue (RCF) or other defects.
the relatively even distribution of dots and the number of Whether wear or RCF occurs depends on the lubrication con-
wheels contacted at each band. While wheels were flanging ditions, tangential forces at the contact patch, and the hard-
on the high rail, the low rail showed highly concentrated con- ness of the wheel and rail steels.
tacts toward the field side. Of the 112 wheelsets, 87 contacted
at a distance only about 0.5 in. from the field side and pro-
duced high contact stress. In this situation, rail grinding was 3.3.2.4 Effective Conicity on Tangent Track
suggested to correct the low rail shape. Removing metal at
the field side of rail can shift contact positions to the rail Lateral instability is more likely to occur when there is high
crown region and reduce contact stress. wheelset conicity (the ratio of RRD between the left and right
By varying the wheel lateral shift range, the distribution of wheel over the wheelset lateral displacement). In this circum-
contact positions of leading and trailing axles can be sepa- stance, as speed is increased, the lateral movement of the
rately investigated, as well as the distributions on different wheelsets, as well as the associated bogie and carbody
degrees of curves. motion, can cause oscillations with a large amplitude and a
well-defined wavelength. The lateral movements are limited
only by the contact of wheel flanges with rail. The high lateral
3.3.2.3 Contact-Stress Level force induced from hunting may cause wheel flange climbing,
gage widening, rail rollover, track panel shift, or combina-
Contact-stress level is one of many factors that affect tions of these. Vehicle lateral stability on tangent track is
rolling contact fatigue and wear at contact surfaces. Com- especially important for high speed transit operation. With a
bined with the distribution of contact positions, the distribu- properly designed vehicle suspension and the modest maxi-
tion of contact stress provides an indication of likely wear mum speeds of most transit operations, high wheelset conic-
patterns and the risk of rolling contact fatigue. ity should not cause vehicle instability, although it can occur.
Good wheel/rail profile designs should produce lower con- The effective conicity of wheel/rail contact has considerable
tact stress and less locally concentrated contact. Although influence on the vehicle hunting speed. As wheelset conicity
there are arguments about the critical level of contact stress, increases, the onset critical speed of hunting decreases. The
the generally accepted level is in the range of 220 to 290 ksi effective conicity is defined by Equation 3.1 (9):
in the rail crown area, and about 480 ksi in the gage face area
when considering the effect of lubrication and strain harden- RRD
Effective Conicity = (3.1)
ing for commonly used rail steels. 2y
Figure 3.13. Distribution of contact positions and contact stress.
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5 30
Rolling radius difference, RRD
R o lli n g r a d i u s d if f e r e n c e , m m
20
2.5
(rR - rL) mm
10
0 0
-15 -10 -5 0 5 10 15
-30 -20 -10 0 10 20 30
-10
-2.5
-20
-5 -30
Wheelset shift, mm (L-R)
Wheelset shift, mm
Figure 3.14. RRD versus lateral shift.
where y is wheelset lateral shift relative to rail. The left dia- wheelset is defined as the RRD, as illustrated in Figure 3.15.
gram of Figure 3.14 shows an example of RRD versus lateral Without adequate RRD, wheelsets can experience higher
shift for new wheel contacting new rail. The slope of the AOAs and higher lateral forces (before reaching saturation).
straight section before reaching flange is used to compute the As a result, both wheel and rail can experience higher rates
effective conicity, which is usually a constant. The right dia- of wear. Note that for trucks with independently rotating
gram of Figure 3.14 shows two examples of worn wheels wheels, RRD has no effect on vehicle curving.
contacting worn rails. Under worn wheel/rail conditions, the Equation 3.2 computes the required RRD (rs) between
effective conicity is no longer a constant. Equation 3.1 two wheels in a solid axle under a pure rolling condition.
should be used for each specified wheel lateral shift value
and corresponding RRD. R+a
The critical hunting speed is highly dependent on the vehi- rs = r0 - 1 (3.2)
cle suspension characteristics and the effective conicity of R-a
the wheel/rail profiles. The maximum conicity that can be
tolerated is critically dependent on the vehicle suspension where
design. As discussed, large wheelset RRD (which can be r0 = the nominal wheel radius,
obtained with high effective conicity) is beneficial to truck R = the curve radius measured to the track center, and
curving ability. In comparison, high effective conicity can a = half the lateral spacing of the two rails.
cause lateral instability in a poor vehicle suspension design,
thus limiting maximum operating speed. The wheelset effec- Figure 3.16 gives examples of the required RRD under a
tive conicity should be carefully selected along with the vehi- pure rolling condition (a wheelset without constraints) for
cle suspension design to give the optimum compromise three different wheels. The values are related to track curve
between lateral stability and curving performance for each radius, wheel diameter, and track gage. A gage of 56.5 in.
transit system. Although the critical value can be varied by was used in this calculation. Note that the curve radius has
vehicle types, generally the effective conicity should be no been converted to curvature in degrees in this figure.
higher than 0.3. Note however that RRD and wheelset conic- Equation 3.2 and Figure 3.16 show that a large rolling
ity has no effect on the hunting speed of trucks equipped with radius (high effective conicity) provides for improved vehi-
independently rotating wheels. cle steering and reduced wheel/rail wear. In Section 3.3.2.4,
Dynamic analysis and track tests are especially important
in introducing new vehicles and/or new profiles into a system
to ensure that, for a specific vehicle/track system, the critical
hunting speed is above the operating speed.
r L
r R
3.3.2.5 RRD for Curving y 0
For a wheelset with a rigid axle to properly negotiate a 0 0
curve, the wheel contacting the outer rail requires a larger
rolling radius than the wheel contacting the inner rail. The
difference in rolling radius between the two wheels of a Figure 3.15. RRD (rl versus rR).
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0.16 the tread taper. When the wheel is worn, the rolling radius
Required Rolling Difference
0.14 would not be linearly varying with the wheelset lateral shift.
0.12 Take an example of a 33-in. diameter wheelset with a 1:40
0.1 taper (0.025 conicity). By assuming that a 0.3-in. wheelset
(inch)
0.08 lateral shift relative to the track will nearly cause wheel
0.06 flanging for this wheel and that the 1:40 taper is maintained
0.04 in this lateral shift range, an RRD of 0.015 in. will be
0.02 obtained. Figure 3.16 shows that this level of RRD will
0 achieve pure rolling on a 1-degree curve. If the wheel has a
0 2 4 6 8 10 12 1:20 taper (0.05 conicity) for the same lateral shift, pure
Curvature (degree)
rolling can be achieved on a 2-degree curve with an RRD of
36 in wheel 33 in wheel 26 in wheel
0.03 in. On large radius curves, free rolling generally can be
achieved with adequate RRD.
Figure 3.16. Required RRD for pure rolling. Note that the RRD only from the wheel taper is limited by
the lateral clearance allowed between the wheel and rail
(which limits the lateral shift). When the clearance is used
it was shown that a low effective conicity could reduce the up, the RRD depends on the shape of the wheel flange throat
tendency for a wheelset to hunt. However, the hunting of a or flange. The rail shape can also influence the RRD. In
vehicle is also critically affected by the vehicle primary lon- Figure 3.18 (shown in an exaggerated way), the low rail B
gitudinal and lateral suspension stiffness. Most transit sys- would produce bigger RRD than rail A by taking advantage
tems operating in North America have relative high primary of wheel taper, assuming the high rail is maintained in the
suspension stiffness, which reduces the tendency to hunt. area close to the wheel throat.
For the majority of the time, many transit systems operate
at relatively low speeds (below 50 mph) and have many RRD on small radius curves (higher degrees of curva-
curves. Therefore, curving and consequent wheel and rail ture). On curves with a radius smaller than 2,000 ft, wheels
wear is likely to be more important than vehicle hunting. on the high rail are likely to be in flange contact. Depending
RRD and wheel/rail conicity should be optimized for each on the wheel/rail profiles, the contact on the outer wheel/rail
system based on the suspension parameters for the particular can be one-point, two-point, or conformal, as illustrated in
vehicles on each system, standard operating speeds, and the Figure 3.12. The rolling radius at the wheel flange root (or
mix of straight and curved track for the system. Different rail slightly down the flange) can be 0.2 to 0.5 in. larger than that
profiles can be designed for curved and straight track and the on the wheel tread depending on the flange height and wheel
wheel profile designed to optimize performance with those shape. For example, according to Figure 3.16, a 0.3-in. RRD
profiles. Analyses of curving and hunting performance using can provide free rolling on curves of about 20 degrees (with
vehicle dynamic computer models is recommended. a curve radius of about 300 ft and a gage of 56.5 in.).
Again, the clearance between wheel and rail also limits the
RRD on large radius curves (low degrees of curva- maximum RRD that can be reached due to limited lateral
ture). For curves with a radius larger than 2,000 ft (close to shift allowed. For example, consider a railroad that only
3 degrees of curvature), there is not likely to be hard wheel allows 0.08 in. (2 mm) of wheel and rail clearance. The RRD
flange contact. The RRD is mainly dependent on the slope in this situation would be considerably smaller because both
of the wheel tread and the flange throat region before flang- wheels are possibly contacting the rails in the flange throat
ing. Figure 3.17 illustrates the rolling radius varying with and on the flange faces.
r1 r2
Taper
Figure 3.18. RRD affected by low rail shapes. (r is the
Figure 3.17. Rolling radius varying with wheel tread radius difference caused by rail contacting a wheel at
taper. different positions.)
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However, on small radius curves, free rolling generally Conformal and close conformal contacts are desirable on
cannot be achieved. The major influences come from truck curves for producing lower lateral forces and rolling resis-
primary yaw stiffness and clearance between truck frame and tance. Nonconformal contact is shown in Figure 3.19, d
axle bearing adapters. The wheel/rail lubrication condition being 1.2 mm, which is severe two-point contact.
can also influence the possibility of free rolling. Therefore, In a system, if severe two-point contact is the trend of
the RRD to avoid flange contact as computed by Equation 3.2 wheel/rail contact in curving, the wheel- and rail-wear rate is
can only be considered as the base requirement from wheel likely to be high due to high creepages and creep forces at the
and rail profiles. contact surfaces. In sharp curves, the risk of rolling contact
In transit operations, especially in urban areas, some fatigue could also be higher than that of a conformal contact
curves have very tight radii. As a result, it is not possible to situation.
achieve the required RRD from the wheel and rail geome- Although severe two-point contact is to be avoided, too
tries. Wheel sliding and higher wear rates become common much conformality, such as that which occurs with very
in those sections. A softer primary suspension and lubrica- worn wheels and rails, can also have drawbacks. Wide bands
tion may improve the situation. of conformal contact between the wheel and rail in the region
In curving, if there is only one-point contact on the outer of the gage shoulder have been implicated as a potential con-
wheels, the contact RRD is relatively easy to determine. tributor to RCF (rail gage corner cracking), especially in
However, if there is two-point contact, especially where shallow curves where the wheels are not running in flange
this condition is severe on the outer wheel, the evaluation contact (10). Current hypotheses suggest that this occurs for
of vehicle curving ability from the view of wheel/rail vehicles with relatively stiff primary suspension in both lat-
profiles is more complicated. This condition is discussed in eral and longitudinal directions.
the next section. Although research is ongoing in this area, potential meth-
It can be seen from the above discussion that requirements ods for controlling this form of RCF may include the fol-
of RRD for curving and lateral stability are conflicting. lowing:
Proper curving requires higher RRD, which results from
higher effective conicity, and lateral stability requires lower · Optimizing wheel/rail profiles to improve vehicle steer-
effective conicity. The required compromise has to be ing by
achieved by adequately designed wheel profile and ground Reducing the width of the contact band in the rail
rail profiles. Note that wheels run over all sections of rail in gage shoulder or
a specified system while rail is locally stationed. Therefore, Increasing the wheel conicity in the flange root area,
adjusting rail profiles based on the local operational empha- which gives a smoother transition of contact from rail
sis can improve both curving and lateral stability. This issue head to the gage shoulder;
will be further discussed in the section of ground rail design. · Optimizing vehicle suspension stiffness to improve
vehicle steering;
· Applying friction modifiers and/or lubricants to the rail
head to reduce wheel rail forces; and
3.3.2.6 Effects of Two-Point Contact · Using harder rail steels.
Two-point contact is defined as a wheel contacting the rail
Hence, compatible wheel and rail profiles are critical for a
at two clearly separated locations. Severe two-point contact
system to reach desirable contact patterns. Figure 3.20 gives
usually has one contact point on the wheel tread and the other
an example of gap distribution for a group of measured
on the flange. As discussed in Section 4.5.1 of Appendix A,
wheels contacting a pair of measured worn rails in the same
severe two-point contact is not desirable in curving since it
system. Conformal contact was reached for these combina-
reduces the wheelset's steering ability because the longitudi-
tions for the majority of values below 0.4 mm.
nal creep forces generated at these two points can act in
opposite directions.
The size of the gap between wheel and rail during flang-
ing, d, can be used as an indicator of the severity of two-point
contact. The larger this gap, the more severe will be the two-
point contact (that is, the two contact points will be farther d
apart and the wear-in period will be longer). The National
Research Council, Canada, defines the nature of the contact
according to the size of the gap:
· If d is 0.1 mm or less--close conformal contact,
· If d is 0.1 mm to 0.4 mm--conformal contact, and Figure 3.19. Illustration of gap between wheel flange root
· If d is 0.4 mm or larger--nonconformal contact. and rail gage.
