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C-1
APPENDIX C:
Investigation of Wheel Flange Climb
Derailment Criteria for Transit Vehicles
(Phase II Report)
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C-3
INVESTIGATION OF WHEEL FLANGE CLIMB
DERAILMENT CRITERIA FOR TRANSIT VEHICLES
(PHASE II REPORT)
SUMMARY This research investigated wheel flange climb derailment to develop a general
flange-climb-distance criterion for transit vehicles in Phase II of the project. The inves-
tigations used computer simulations of single wheelsets and representative transit vehi-
cles. The Phase I work investigated the relationships between flange angle, flange
length, axle AOA, and distance to climb. Based on these simulations flange-climb-
distance equations were developed for some specific wheel profiles.
Based on single wheelset simulation results, Phase II proposed a general flange-
climb-distance criterion for transit vehicle wheelsets. The general flange-climb-
distance criterion was validated by the flange-climb-distance equations in the Phase I
report for each of the wheel profiles with different flange parameters.
Phase II also proposed a biparameter flange-climb-distance criterion for vehicles with an
AAR-1B wheel/136-pound rail profile combination. The bilinear characteristics between
the transformed climb distance and the two parameters, AOA and lateral-over-vertical
(L/V) ratio, were obtained through a nonlinear transformation. The accuracy of the fitting
formula was further improved by using a gradual linearization methodology. The bipa-
rameter distance criterion based on the simulation results was validated by comparison with
the research team's TLV test data. The application to two AAR Chapter XI performance
acceptance tests and limitations of the biparameter distance criterion are also presented.
The following conclusions were drawn from the Phase II work:
· A general flange-climb-distance criterion taking the AOA, the maximum flange
angle, and flange length as parameters is proposed for transit vehicles:
A * B * Len
D<
AOA + B * Len
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C-4
where AOA is in mrad and A and B are coefficients that are functions of the max-
imum flange angle Ang (degrees) and flange length Len (in.):
100
A = + 3.1 *
-1.9128 Ang + 146.56
1
Len - + 1.23
-0.0092( Ang) + 1.2152 Ang - 39.031
2
B = + 0.05 * Ang +
10 10
-5
-21.157 Len + 2.1052 0.2688 Len - 0.0266
· The general flange-climb-distance criterion is validated by the flange-climb-
distance equations in the Phase I report (Appendix B) for each of the wheel pro-
files with different flange parameters.
· Application of the general flange-climb-distance criterion to a test of a passenger
car with an H-frame truck undergoing Chapter XI tests shows that the criterion is
less conservative than the Chapter XI and the 50-msec criteria.
· A biparameter flange-climb-distance criterion, which takes the AOA and the L/V
ratio as parameters, was proposed for vehicles with AAR-1B wheel/136-pound rail
profile:
1
D <
0.001411 * AOA + (0.0118 * AOA + 0.1155) * L/V - 0.0671
where AOA is in mrad.
· A study of the flange-climb-distance criterion, which takes the friction coefficient
as another parameter besides the L/V ratio and the AOA, is recommended for
future work.
· The biparameter distance criterion is validated by comparison with TLV test data.
Since the running speed of the TLV test was only 0.25 mph, its validation for the
biparameter distance criterion is limited. A trial test for validation is recommended.
· Application of the biparameter distance criterion to a test of a passenger car with an
H-frame truck undergoing Chapter XI tests shows that the biparameter distance crite-
rion is less conservative than the Chapter XI criteria, including the 50-msec criterion.
· Application of the biparameter distance criterion to an empty tank car derailment
test results show that the biparameter distance criterion can be used as a criterion
for the safety evaluation of wheel flange climb derailment.
Application limitations of the biparameter distance criterion include the following:
· The L/V ratio in the biparameter distance criterion must be higher than the L/V
limit ratio corresponding to the AOA. No flange climb can occur if the L/V ratio
is lower than the limit ratio.
· The biparameter distance criterion is obtained by fitting in the bilinear data range
where AOA is larger than 5 mrad. It is conservative at AOA less than 5 mrad due
to the nonlinear characteristic.
· The biparameter distance criterion was derived based on the simulation results for
the AAR-1B wheel on AREMA 136-pound rail. It is only valid for vehicles with
this combination of wheel and rail profiles.
· For each of the different wheel profiles listed in Table B-2 of the Phase I report,
individual biparameter flange-climb-distance criteria need to be derived based on
the simulation results for each wheel and rail profile combination.
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C-5
CHAPTER 1
A GENERAL FLANGE-CLIMB-DISTANCE CRITERION
The research team investigated wheel flange climb derail- TABLE C-1 Wheel Profiles Designed by AutoCAD
ment to develop a general flange-climb-distance criterion for Length of Maximum Flange
transit vehicles in Phase II of the project. The investigations Angle FaceL0 (in.)
0.252 0.352 0.452 0.552
used computer simulations of single wheelsets and represen- Maximum
Flange Angle Ang (degrees)
tative transit vehicles. The Phase I work investigated the rela- 63 degrees W1 W2 W3 W4
tionships between flange angle, flange length, axle AOA, and 68 degrees W5 W6 W7 W8
distance to climb. Based on these simulations, flange-climb- 7 2 degrees W9 W10 W11 W12
distance equations were developed for some specific wheel 7 5 degrees W13 W14 W15 W16
profiles.
Based on single wheelset simulation results, Phase II pro-
posed a general flange-climb-distance criterion for transit flange root and flange tip were kept the same shape with no
vehicle wheelsets. The general flange-climb-distance crite- restrictions on flange height and thickness.
rion was validated by the flange-climb-distance equations in As shown in Figure C-1, the flange length is defined as the
Appendix B, the Phase I report, for each of the wheel profiles sum of the maximum flange angle length and the flange tip
with different flange parameters. arc length from the maximum flange angle to 26.6 degrees.
Flange-climb-distance criteria were developed for each of Figure C-2 shows the simulation results of these 16 wheel
the rail/wheel profiles, as published in Table B-2 of Appen- profiles on 115-pound AREMA rail profiles experiencing lat-
dix B, the Phase I report. Since the wheel and rail profiles eral and vertical forces, which produce an applied L/V ratio
vary widely within transit systems, it was desirable to of about 1.99. Results are similar to the test (1) and simula-
develop a general flange-climb-distance criterion with the tion results in the Phase I report and show that the flange-
maximum flange angle and flange length as parameters for climb distance decreases with increasing AOA. Results also
different wheel profiles. show that the relationship between climb distance D and
The effects of the maximum flange angle and flange length AOA is nonlinear, with climb distances converging asymp-
on climb distance were further analyzed through single totically to similar values for large AOA.
wheelset simulations by using 16 wheel profiles with differ- To develop a general flange-climb-distance criterion with
ent maximum flange angle and flange length combinations, multiple parameters, a methodology was adopted in which
as listed in Table C-1. The wheel maximum flange angle and the nonlinear relationship between the climb distance and
flange length were deliberately varied using AutoCAD. The parameters was linearized. This was achieved by using the
35
30
Climb Distance (feet)
25
20
Flange Length Len 15
10
5
0
0 2 4 6 8 10 12
Maximum Flange Angle Length L0
AOA (mrad)
75° W1 W2 W3 W4 W5 W6
W7 W8 W9 W10 W11 W12
W13 W14 W15 W16
Figure C-1. Definition of the flange length and maximum Figure C-2. Effect of AOA on flange-climb distance for
flange angle length. different wheel profiles.
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C-6
following nonlinear transformation function to transform the ing nonlinear fitting result shown in Figure C-3 can be writ-
AOA and distance (D) in Figure C-3 to (x, y) as shown in ten in the following form:
Figure C-4 for wheelset W1:
m
{ X = AOA D = (C-3)
(C-1) AOA + n
Y = 1/D
where the two coefficients m and n can be calculated as:
The transformed simulation results in Figure C-4 were
then fit with high accuracy (R2 of 0.998) in linear form, 1 b
shown as "fit" in Figure C-4. The linear fit was then trans- m = , n =
a a
formed back and plotted in Figure C-3.
It is clearly shown in Figure C-4 that the relationship
The highly accurate fitting Equation C-3 is obtained, as
between 1/D and AOA is linear after the nonlinear transfor-
shown in Figure C-3, due to the benefit of the linear rela-
mation of Equation C-1. The linear fitting result can be writ-
tionship through the transformation.
ten in the following form:
By using this methodology, 16 formulas were obtained
through high accuracy fitting (R2 > 0.97) based on the simu-
y = ax + b (C-2)
lation data at an L/V ratio of 1.99 for each of these wheel pro-
files listed in Table C-1. Correlation analysis between the
The coefficients a and b for the W1 profile are shown in
two coefficients m and n and the maximum flange angle and
Figure C-4; i.e., a = 0.0427 and b = 0.3859. The correspond-
flange length were conducted to generate a general function
expression.
3
The coefficient n is decomposed as:
n = B * Len
2.5
Climb Distance (feet)
2
1.5
where Len is defined as the flange length (in.) from the
maximum flange angle Ang to 26.6 degrees as shown in
1
Figure C-1, and B is a coefficient.
0.5 Correlation analysis shows that the relation between the
0 coefficient B and the maximum flange angle parameter Ang
0 2 4 6 8 10 12 is roughly linear, as shown in Figure C-5.
AOA (mrad) Based on the relationship shown in Figure C-5, coefficient
Simulation fit B can be expressed in a linear form:
Figure C-3. Effect of AOA on climb distance, B = KB * Ang + CB
W1 profile, 1.99 L/V ratio.
30
0.9
y = 0.0427x + 0.3859 25
0.8
R2 = 0.998
0.7 20
Coefficient B
0.6
1/D (1/feet)
0.5 15
0.4
10
0.3
0.2 5
0.1
0
0
62 64 66 68 70 72 74 76
0 2 4 6 8 10 12
Maximum Flange Angle (Degree)
AOA (mrad)
L0=0.252 L0=0.352 L0=0.452 L0=0.552
Simulation fit
Figure C-5. Effect of maximum flange angle on
Figure C-4. Linear relation between 1/D and AOA, coefficient B for different wheel profiles, maximum flange
W1 profile, 1.99 L/V ratio. angle length L0 in Table 1.
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C-7
Coefficient KB and CB are obtained through linear fitting Coefficient m was decomposed as:
of the lines in Figure C-5. As shown in Figure C-6, the rela-
tionship between KB and the flange length Len is nonlinear. m = A * B * Len
To get a highly accurate fitting result, the linearization
methodology is applied again at this step. First, the nonlinear where B is another coefficient.
relationship must be transformed to a linear one. However, no Correlation analysis shows that the relation between the
general method was found to construct a transformation func- coefficient A and the flange angle parameter Len is roughly
tion; therefore, a trial and error method was used in this report. linear, as shown in Figure C-8.
This resulted in the following transformation function: The linearization methodology is used to obtain an expres-
sion between the coefficient A and flange parameters Ang, Len.
{Y
X = Len
= 10/(KB - 0.05)
(C-4)
Based on the above analysis of the coefficients, a general
flange-climb-distance formula with the following AOA and
flange parameters is proposed:
A linear relationship was generated by using this nonlin-
ear transformation function to transform the (Len, KB) in A * B * Len
D = (C-5)
Figure C-6 to X, Y. See Figure C-7. AOA + B * Len
The same methodology is applied to the coefficient CB to
obtain a linear expression between CB and the flange length where A and B are coefficients that are functions of maxi-
parameter Len. mum flange angle Ang (degrees) and flange length Len (in.):
100
A = + 3.1 *
-1.9128 Ang + 146.56
0
-0.2 1
Len - + 1.23
-0.4 -0.0092( Ang) + 1.2152 Ang - 39.031
2
Coefficient KB
-0.6
-0.8
B = + 0.05 *
10
-1 -21.157 Len + 2.1052
-1.2
-1.4 10
Ang + -5
-1.6 0.2688 Len - 0.0266
-1.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
The corresponding general flange-climb-distance criterion
Flange Length (inch)
is proposed as:
Simulation
A * B * Len
Figure C-6. Nonlinear relationship between KB and the D<
AOA + B * Len
flange length.
12
0 10
Coefficient 10/(KB-0.05)
-2
8
Coefficient A
y = -21.157x + 2.1052
-4 2
R =1
6
-6
-8 4
-10
2
-12
-14 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flange Length (inch) Flange Length (inch)
Simulation Linear (Simulation) Ang=63Deg Ang=68Deg Ang=72Deg Ang=75Deg
Figure C-7. Linear relationship between the transformed Figure C-8. Effect of flange length on coefficient A for
KB and flange length. different wheel profiles.
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C-8
The general criterion was derived from simulation results that at lower AOA of 5 mrad, the limiting flange-climb dis-
of the 16-wheel profiles listed in Table C-1. The general tance increases as the wheel flange angle and flange length
equations presented above are considered to be conservative do. At higher AOA of 10 mrad, flange length has more effect
and adequate for use for wheel profiles with flange angles in on the distance limit than flange angle.
the normal range of 60 to 75 degrees. In summary, considering that flange climb generally occurs
Table C-2 lists a range of limiting flange-climb-distance at a higher AOA, increasing wheel flange angle can increase the
values computed using Equation C-5 for a specified range of wheel L/V ratio limit required for flange climb, and increasing
flange angles, flange lengths, and AOAs. Table C-2 indicates flange length can increase the limiting flange climb distance.
TABLE C-2 Limiting flange-climb distance computed using Equation C-5
AOA = 5 mrad AOA = 10 mrad
Flane Angle deg 63 deg 68 deg 72 deg 75 deg 63 deg 68 deg 72 deg 75 deg
Flange Length (inch)
0.4 inch 2.0 2.2 2.4 2.3 1.5 1.5 1.5 1.9
0.52 inch 2.4 2.6 2.9 2.8 1.8 1.8 1.8 2.1
0.75 inch 3.2 3.5 3.7 4.3 2.3 2.3 2.2 2.4
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C-9
CHAPTER 2
VALIDATION OF THE GENERAL FLANGE-CLIMB-DISTANCE CRITERION
Six different wheel profiles from several transit systems
25
were analyzed in the Phase I report. Using the maximum
flange angle and flange length from these wheels, the rela- Wheel 1: D=5/(0.13*AOAe+1)
20
Climb Distance (feet)
Wheel 2: D=4.1/(0.16*AOAe+1)
tionship between climb distance and AOA was derived from
Wheel 3: D=4.2/(0.136*AOAe+1)
the general Equation C-5 and plotted in Figure C-9. The cor- 15
Wheel 4/5: D=28/(2*AOAe+1.5)
responding climb distance formulas for each wheel profile
10 Wheel 6: D=49/(2*AOAe+2 2)
are shown in the figure.
In the Phase I report, flange climb formulas were devel- 5
oped for these same wheels based on an AOAe for various
degrees of curvature. Results were shown in Figure B-32 of 0
0 2 4 6 8 10
the Phase I report and are repeated here in Figure C-10. The
Curve Curvature (degrees)
shapes of the curves are very similar in nature, with climb
distances converging asymptotically to similar values at high Wheel 1 Wheel 2 Wheel 3
AOAs and increasingly sharp curves. The AOAe for transit Wheel 4/5 Wheel 6 Freight Car[3]
Figure C-10. Climb distance for different wheel profiles.
25
and passenger vehicles in curves was derived from the curve
Wheel 1: D=39.17944/(AOA+6.941152)
radius, based on an assumption that these vehicles do not
Climb Distance (feet)
20
Wheel 2: D=29.8701/(AOA+8.365168)
have significant wheelset misalignments within their trucks
Wheel 3: D=38.0625/(AOA+8.713917)
15 and do not have significant wheelset steering angles.
Wheel 4/5: D=22.18793/(AOA+1.71472)
Equation C-5 is derived based on the simulation results
10 Wheel
l 6: D=26.32589/(AOA+1.20198)
when the wheelset was experiencing a 1.99 L/V ratio. As
5 shown in Chapter 7 of this appendix, the average 1.99 L/V
ratio (not the peak value) lasting for more than 1 foot is rare
0 according to practical test results. Compared with the mea-
0 2 4 6 8 10
sured L/V ratio in practice, the L/V ratio of 1.99 is consid-
AOA (mrad)
ered to be conservative enough for transit cars.
Wheel 1 Wheel 2 Wheel 3 Wheel 4/5 Wheel 6 The general flange-climb-distance criterion is recom-
mended for use with transit and commuter cars. It is conser-
Figure C-9. Climb distance generated from Equation C-5 vative at a lower L/V ratio (< 1.99) and less conservative
for different wheel profiles. when the L/V ratio is close to 1.99.
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C-10
CHAPTER 3
A BIPARAMETER DISTANCE CRITERION FOR
FLANGE CLIMB DERAILMENT
The flange-climb-distance criterion proposed in the research
14
team's previous research work (2, 3) for freight cars was based
Climb Distance D (feet)
12
on single-wheelset simulations at a 2.7 L/V ratio for a range of
different AOAs. An L/V ratio of 2.7 was considered conserva- 10
tive for freight cars. The general flange-climb-distance criterion 8
in Chapter 2 of this appendix was derived from simulation 6
results at a fixed L/V ratio of 1.99 for different AOAs, which 4
was considered conservative for transit cars. Both criteria were 2
conservative at low L/V ratios, but not conservative enough at 0
L/V ratios higher than the fixed L/V ratio used in the simula- 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1
tions, although the chance of encountering sustained L/V ratios Wheel L/V Ratio
this high is rare in practice. To avoid this dilemma, it is desir- AOA=0mrad AOA=2.5mrad AOA=5mrad
able to include the L/V ratio as a variable parameter in the AOA=10mrad AOA=20mrad
flange-climb-distance criterion.
Results from testing (1) and simulations in the Phase I Figure C-11. Effect of L/V ratio at different AOA,
report show the flange-climb distance decreases with increas- 75-degree, AAR-1B wheel, 136-pound rail.
ing L/V ratio. No flange climb happens (the climb distance is
infinite) if the L/V ratio is lower than Nadal's value. Since the wheel L/V ratios varied with the AOA as shown in the fol-
L/V ratio is another important factor affecting flange climb lowing tabulations:
besides the AOA, a criterion including the L/V ratio and AOA
is expected to reveal more about the physical nature of flange AOA(mrad) L/V Ratio (Average value during climb)
climb and produce more accurate results, although the multi-
variables fit is more complicated than that of a single variable. 0 2.87
2.5 2.82
5 2.78
10 2.73
3.1 THE BILINEAR CHARACTERISTIC 20 2.61
BETWEEN 1/D AND THE PARAMETER'S
AOA AND L/V RATIO
0.9
In the following section, a combination of AAR-1B wheels 0.8
and AREMA 136-pound rail profiles were used in simulations 0.7
to develop a multivariable fit formula. Figure C-11 shows the 0.6
1/D (1/feet)
simulation results of a single wheelset climbing at different 0.5
L/V ratios and AOAs. 0.4
Figure C-11 shows that the relationship between the climb 0.3
distance D and the L/V ratio is nonlinear. Through a nonlin- 0.2
ear transformation similar to that described in Chapter 1, a 0.1
linear relationship between 1/D and the L/V ratio was devel- 0
oped (Figure C-12). 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1
Whee l L/V Ratio
Due to the effect of AOA on the creep force, the wheel L/V
ratios shown in Figures C-11 and 12 were not the same value AOA=0mrad AOA=2.5mrad AOA=5mrad
for different AOAs even though the same group of lateral and AOA=10mrad AOA=20mrad
vertical forces was applied to the wheelset. For example,
when a 21,700-pound lateral force and 6,000-pound vertical Figure C-12. The linear relationship between 1/D and
force were applied to the wheelset at different AOAs, the L/V ratio, AAR-1B wheel, 136-pound rail.
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C-11
The average L/V ratio for a wheelset being subjected to the
0.9
same group of lateral and vertical forces at different AOAs,
0.8
L/Va, for this example is calculated as follows:
0.7
L/Va = (2.87+2.82+2.78+2.73+2.61)/5 = 2.76 0.6
1/D (1/feet)
0.5
The L/Va ratio was used to further describe the relationship 0.4
between climb distance and AOA for different L/V ratios. 0.3
The relationship between the climb distance D and the 0.2
AOA is nonlinear, as shown in Figure C-13. Again, a similar 0.1
nonlinear transformation was performed, as described in 0
Chapter 1, with results shown in Figure C-14. The figure 0 5 10 15 20 25
shows that there is an approximately linear relationship AOA (mrad)
between 1/D and the AOA higher than 5 mrad. However, it L/Va=1.54 L/Va=1.67 L/Va=1.86 L/Va=1.97 L/Va=2.76
can be seen that the relationship between 1/D and the AOA
lower than 5 mrad is nonlinear. Figure C-14. Linear relation between 1/D and AOA,
AAR-1B, 136-pound rail.
3.2 THE BIPARAMETER CLIMB DISTANCE
FORMULA AND CRITERION
The fitting accuracy of Equation C-6 may not be satisfac-
Due to the bilinear characteristics between the function of tory depending on the simulation model, wheel/rail profile,
1/D and the two variables shown in Figures C-13 and C-14, a and the data fitting range. To improve the fitting accuracy, a
gradual linearization methodology including two steps refinement through further linearization corresponding to the
described below was developed to obtain an accurate fitting gradual linearization methodology is used in the second step.
formula. First, the least squares fitting method for two vari- The wheelset AOA was kept constant by constraining the axle
ables was used to fit the simulation result. Since the relation- yaw motions in the simulation. However, the L/V ratio varied
during flange climb. The average L/V ratio during flange climb
ship between the function of 1/D and the L/V ratio is linear for
was used in the fitting process. Therefore, in Equation C-6, the
all L/V ratios in the simulations (shown in Figure C-12), the
coefficient a1 is less accurate than a2 due to the variation of the
fitting data range for the L/V ratio is the whole data range. But
L/V ratio. Further transformation is performed as follows:
the fitting data range for AOAs is from 5 mrad to 20 mrad to
cut off the nonlinear relationship at lower AOAs (< 5 mrad), Y = 1/D - a2*AOA (C-7)
as shown in Figure C-14. The fitting formula is thus conserv-
ative for those AOAs less than 5 mrad, which have a steeper The simulation results were collected as different groups,
slope than that of the fitting range (5 mrad
C-12
was proposed for vehicles with AAR-1B wheel/136-pound rail TABLE C-3 Fitting errors of Equation C-6 and Equation C-11
profile: Gradual
Fitting Error of Linearization
AOA Equation C-6
1 Cases L/VRatio (mrad) Fitting Error
D< (%)
(Equation C-11)
[0.001411 * AOA (%)
+ (0.0118 * AOA + 0.1155) * L/V - 0.0671] 1 1.69 5 20.70 1.58
2 1.87 5 1.68 1.23
3 1.98 5 -8.12 1.31
where AOA is in mrad.
4 1.67 10 16.91 -1.24
5 1.83 10 1.82 -0.89
Table C-3 shows the comparison of fitting errors between 6 1.94 10 -6.64 -1.01
Equation C-6 and Equation C-11. The fitting accuracy was 7 1.63 20 19.31 0.92
greatly improved through the "gradual linearization" 8 1.79 20 4.76 -0.20
9 1.89 20 -1.38 0.97
methodology. The fitting error in Table C-3 is defined as:
Formula Value - Simulation Value
Fitting Error =
Simulation Value
5 mrad. It is conservative at AOA less than 5 mrad due
Based on the above derivation process, some application to the nonlinear characteristic.
limitations of the biparameter distance criterion are as · The biparameter distance criterion was derived based
follows: on the simulation results for the AAR-1B wheel on
136-pound rail. It is only valid for vehicles with this
· The L/V ratio in the criterion must be higher than the combination of wheel and rail profiles.
L/V limit ratio corresponding to the AOA, because no · For each of the different wheel profiles listed in
flange climb can occur if the L/V ratio is lower than the Table B-2 of the Phase I report, individual biparame-
limit ratio. ter flange-climb-distance criteria need to be derived
· The biparameter distance criterion is obtained by fitting based on the simulation results for each wheel and rail
in the bilinear data range where AOA is larger than profile combination.
C-13
CHAPTER 4
COMPARISON BETWEEN THE SIMULATION DATA AND THE
BIPARAMETER FORMULA
The comparison between the simulation data and Equa- Figures C-16 and C-17 show that Equation C-11 is conser-
tion C-11 for all L/V ratios at different AOA is shown in vative for AOA less than 5 mrad, with calculated climb
Figure C-15. Overall, the results are consistent, especially at distance shorter than the corresponding values from the
AOA greater than 5 mrad. simulations. Above 5 mrad AOA, the simulations and
Figures C-16 through C-20 compare the simulation Equation C-11 match very closely.
results with results of Equation C-11 for a range of AOA.
14 14
12 12
Climb Distance (feet)
Climb Distance (feet)
10 10
8
8
6
6
4
4
2
2
0
0 5 10 15 20 25 0
AOA (mrad) 0 0.5 1 1.5 2 2.5 3 3.5 4
Wheel L/V Ratio
Simulation Formula
Simulation Formula
Figure C-15. Comparison between the simulation and
equation C-11 for all L/V ratios. Figure C-17. Comparison between the simulation and
equation C-11, AOA = 2.5 mrad.
10
25
9
Climb Distance (feet)
8
20
Climb Distance (feet)
7
6
15
5
4
10
3
5 2
1
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
Wheel L/V Ratio Wheel L/V Ratio
Simulation Formula Simulation Formula
Figure C-16. Comparison between the simulation and Figure C-18. Comparison between the simulation and
equation C-11, AOA = 0 mrad. equation C-11, AOA = 5 mrad.
C-14
6 3.5
5 3
Climb Distance (feet)
Climb Distance (feet)
2.5
4
2
3
1.5
2
1
1 0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
Wheel L/V Ratio Wheel L/V Ratio
Simulation Formula Simulation Formula
Figure C-19. Comparison between the simulation and Figure C-20. Comparison between the simulation and
equation C-11, AOA = 10 mrad. equation C-11, AOA = 20 mrad.
C-15
CHAPTER 5
VALIDATION THROUGH TLV TEST
The biparameter flange-climb-distance criterion was vali-
25
dated with flange-climb test data from the TLV test on August
Climb Distance (feet)
25, 1997 (1). The test was conducted on new rails. Since the 20
climb distance is sensitive to AOA, the AOA values were cal-
15
culated from the test data by the longitudinal displacements
(channel ARR and ARL) of sensors installed on the right and 10
left side of the wheelset by using the following equation:
5
ARR + ARL
AOA = (C-12) 0
93.5 0 0.5 1 1.5 2 2.5 3 3.5 4
Wheel L/V Ratio
where AOA is in mrad and ARL and ARR are in inches. The TLV Test Formula
distance between the right and left sensor was 93.5 in.
Figure C-21 shows the overall comparison between the test Figure C-22. Comparison between the TLV test and
data and Equation C-11 for all L/V ratios at different AOA. Equation C-11, AOA = -2.8 mrad.
Figures C-21 through C-25 compare the TLV test data
with results from Equation C-11 for several of the controlled
AOAs. Results of Equation C-11 are more consistent with coefficients during test varied from 0.29 to 0.54 for the dry
the test data at higher AOA than at lower AOA. flange face of the new rail.
The difference between the TLV test and Equation C-11, To demonstrate these differences, three TLV test cases at
as shown in Figures C-22 through C-25, is due to two main 32 mrad AOA were simulated by using the single-wheelset
factors: the wheel/rail friction coefficients and the running flange climb model. The friction coefficients in these simula-
speed. Equation C-11 was derived based on simulations of a tions were derived from the instrumented wheelset L/V ratios.
single wheelset with 0.5 friction coefficient at 5 mph running Simulation results show the L/V ratio converges to Nadal's
speed. The TLV test was conducted at an average 0.25 mph value when AOA is larger than 10 mrad. For these runs (runs
running speed, and the test data (1) show that the friction 30, 31, and 32), the L/V ratio just before the wheel climb is
16 10
9
14
Climb Distance (feet)
8
Climb Distance (feet)
12 7
10 6
8 5
6 4
3
4
2
2 1
0 0
-5 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 3 3.5 4
AOA (mrad) Wheel L/V Ratio
Formula TLV test TLV Test Formula
Figure C-21. Comparison between the TLV test and Figure C-23. Comparison between the TLV test and
Equation C-11 for all L/V ratios. Equation C-11, AOA = 4.4 mrad.
C-16
6 2.5
5
Climb Distance (feet)
Climb Distance (feet)
2
4
1.5
3
1
2
0.5
1
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4
Wheel L/V Ratio Wheel L/V Ratio
TLV test Formula TLV Test Formula Simulation of TLV Test
Figure C-24. Comparison between the TLV test and Figure C-25. Comparison between the TLV test and
Equation C-11, AOA = 11 mrad. Equation C-11, AOA = 32 mrad.
1.57. The instrumented wheel profile is the 75-degree AAR- Corresponding to these two situations, the effects of flang-
1B wheel profile. The friction coefficient between wheel and ing friction coefficients differ:
rail is thus calculated as 0.32, according to Nadal's formula.
As can be seen in Figure C-25, the simulations with 0.32 fric- · For AOA greater than 5 mrad, the climb distance
tion coefficient and 0.25-mph running speed show a good decreases with a decreasing flanging friction coeffi-
agreement between the simulation results and test data. cient µ because the lateral creep force changes direc-
Considering the running speed in practice, it is reasonable tion on the flange tip to resist the derailment. If µ is
to use a 5-mph simulation speed rather than the actual smaller, then the resisting force is smaller; thus, the
0.25-mph test speed for developing the flange climb criteria. wheelset derails faster than that with a higher friction
A trend evident in Figures C-22 through C-25 was that the coefficient.
climb distance in the TLV test is shorter than that of Equa- · For AOA less than or equal to 5 mrad, the climb dis-
tion C-11 with the increase of AOA. Besides the effect of the tance increased with a decreasing flanging friction coef-
lower test speed and the lower friction coefficients in the runs ficient µ. The lateral creep force helped the wheel to
of TLV, the effect of friction coefficients at different AOAs climb on the flange face and took less time to climb on
must be considered. In the Phase I report, simulation results the tip. In total, it took more time to derail than that with
show the following: a higher friction coefficient.
· For AOAs greater than 5 mrad, the wheel climbed The effect of friction coefficients is much more compli-
quickly over the maximum flange angle face and took cated than that of the L/V ratio and the AOA. A study of the
most of the time to climb on the flange tip. flange-climb-distance criterion, which takes the friction coef-
· For AOAs less than 5 mrad, the wheelset took most of ficient as another parameter besides the L/V ratio and the
the time to climb on the maximum flange angle. AOA, is recommended for future work.
C-17
CHAPTER 6
ESTIMATION OF AOA
Fixed AOA was used in the single-wheelset flange climb
18
simulations and the TLV test in order to investigate the
effect of AOA on flange climb. Both the single-wheelset 16
flange climb simulations and the TLV test have shown that
AOAe (mrad)
14
the flange-climb distance is sensitive to AOA. However,
the wheelset was not kept at a constant AOA but varied 12
during the climb, as shown in the vehicle simulations. In 10
most practical applications, measurement of instantaneous
AOA is not possible. Therefore, to evaluate flange climb 8
potential, an equivalent AOA (AOAe) has to be estimated 6
on the basis of available information (e.g., vehicle type, 0.4 0.6 0.8 1 1.2 1.4 1.6
track geometry, perturbation, suspension parameters) in Longitudinal Primary Suspension Stiffness Ratio
order to use the biparameter flange-climb-distance crite-
LRV1 LRV2 HRV
rion in practice.
In the Phase I report, three kinds of representative vehicles
corresponding to the Light Rail Vehicle Model 1 (LRV1), Figure C-26. Effect of longitudinal suspension stiffness
Light Rail Model 2 (LRV2), and Heavy Rail Vehicle (HRV) on AOAe.
were evaluated. Further simulations, including a freight car
with three-piece bogies, were made for these vehicles run-
ning on a 10-degree curve, with 4 in. superelevation, and not climb on the rail due to improved steering resulting from
with the AAR Chapter XI Dynamic Curve perturbation. Sim- the new profile having a larger RRD on the tread than that of
ulation results were used to estimate the AOAe during the worn profile.
wheelset flange climb. In the Phase I report, an equivalent AOAe formula for
Five running speeds of 12, 19, 24, 28, and 32 mph--cor- the leading axle of a two-axle truck, based on the geometric
responding to a 3- and 1.5-in. underbalance and balance analysis of the truck geometry in a curve, was derived as
(respectively) and a 1.5- and 3-in. overbalance speed--were
simulated to find the worst flange climb cases with the
longest climb distances.
Longitudinal primary suspension stiffness of the passenger 22
trucks can have a significant effect on axle steering and axle 20
AOA. Therefore, for each of these vehicles, two stiffness vari-
18
ations, which were 50 percent lower and 150 percent higher
AOAe (mrad)
than that of the designed longitudinal primary stiffness, were 16
used to investigate the effect of suspension parameters on 14
flange climb. 12
Figure C-26 shows the effect of longitudinal primary sus- 10
pension stiffness on AOAe, which was calculated as the
8
average AOA during the flange climb.
The warp stiffness of three-piece bogies has an important 6
4.00E-01 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07
influence on the AOAe. As shown in Figure C-27, for the
Warp Stiffness (in-lb/rad)
worn AAR-1B wheel/136-pound rail profiles, the average
AOA during climb decreased with increasing warp stiffness New Profile Wron Profile
corresponding to the worn truck, new truck, and stiff
H-frame truck. For the new wheel/rail profile, the wheel did Figure C-27. Effect of warp stiffness on AOAe.
C-18
TABLE C-4 Estimation of AOAe based on the simulation result of the maximum AOAe and
Maximum AOAe Axle Spacing Distance
axle spacing distance for each of them.
Vehicle Type Constant c
(mrad) (in.) Due to the track perturbations and the degrading of
LRV1 16.8 74.8 3.08 wheelset steering capability, the practical wheelset AOA
LRV2 15.6 75 2.86
could be higher than the value calculated by Equation 2.5.
HRV 12.1 82 2.04
The following AOAe, which were considered conservative
Freight Car with Three-
Piece Bogies 12.7 70 2.5 enough according to the simulation results and test data, were
(New Bogie) recommended in Table C-5 and shown in Figure C-28.
Freight Car with Three- When the vehicle runs on a curve with the curvature lower
Piece Bogies 20.7 70 4.0
than 10 degrees and not listed in Table C-5, it is recom-
(Worn Bogie)
mended that a linear interpolation value between the segment
points in Table C-5 be used in the criterion, as shown in
Figure C-28. Also, it is recommended that AOA statistical
Equation C-6. Table C-4 lists the constant c in Equation B-6 data from the wayside monitoring system be used in the cri-
of Phase I report (Appendix B) for these four kinds of repre- terion to take into account the many factors affecting AOAe
sentative vehicles (LRV1, LRV2, HRV, Three-Piece Bogie) if such systems are available.
TABLE C-5 Conservative AOAe for practical use
Straight 5-Degree 10 Degree Above 10
Vehicle and Truck Type Lines Curves Curves Degree Curves
Vehicle with Independent Equation C-6
Rolling Wheel or Worn 10 15 20 (Appendix B)
Three-Piece Bogies +10
Equation C-6
Others 5 10 15
(Appendix B) +5
30
25
AOAe (mrad)
20
15
10
5
0
0 2 4 6 8 10 12
Curvature (degree)
IRW Solid Wheelset
Figure C-28. Recommended conservative AOAe for
practical use.
C-19
CHAPTER 7
APPLICATION TO VEHICLE DYNAMIC PERFORMANCE
ACCEPTANCE TESTS
7.1 APPLICATION TO A PASSENGER CAR TEST general flange climb criterion, the flange criterion for the
AAR-1B wheel profile is as follows:
The general flange climb criterion (Equation C-5) and the
biparameter distance criterion (Equation C-11) were applied 26.33
to a passenger car with an H-frame truck undergoing D<
AOAe + 1.2
dynamic performance tests at the FRA's Transportation
Technology Center, Pueblo, Colorado, on July 28, 1997. The The axle spacing distance for this passenger car is 102 in.,
car was running at 20 mph through a 5-degree curve with 2.04 was adopted for the constant c since the vehicle
2-in. vertical dips on the outside rail of the curve. The L/V and truck design is similar to the heavy rail vehicle in Table
ratios were calculated from vertical and lateral forces mea- C-4. According to Equation B-6 published in the Phase I
sured from the instrumented wheelsets on the car. Table C-6 report (Appendix B), the AOAe is about 7.6 mrad for this
lists the five runs with L/V ratios higher than 1.0, exceeding passenger H-frame truck on a 5-degree curve. By substitut-
the AAR Chapter XI flange-climb safety criterion. The rails ing the AOAe into the above criteria, the safe climb distance
during the tests were dry, with an estimated friction coeffi- without derailment is 3 ft. According to Table C-5, the con-
cient of 0.6. The wheel flange angle was 75 degrees, result- servative AOAe for a 5 degree curve should be 10 mrad. The
ing in a corresponding Nadal value of 1.0. conservative safe climb distance without derailment is
The climb distance and average L/V ratio (L/V ave) in 2.4 ft; however, the climb distance according to the 50-ms
Table C-6 were calculated for each run from the point where criterion is 1.4 ft.
the L/V ratio exceeded 1.0. Figure C-29 compares the climb The wheel, which climbed a 2 ft distance in the run (rn046)
distances to the corresponding distances that are equivalent with a 1.01 average L/V ratio (maximum L/V ratio 1.06), was
to a 50-msec time duration. As can be seen, all the climb dis- running safely without threat of derailment according to the
tances exceeded the 50-msec duration. However, there does criterion. The other four runs were unsafe because their
not appear to be a direct correlation between test speed and climb distances exceeded the criterion.
climb duration.
7.1.2 Application of Biparameters Distance
7.1.1 Application of General Flange Climb Criterion
Criterion
Equation C-11 was used to calculate a climb distance
The instrumented wheelset has the AAR-1B wheel profile criterion for each run, based on the measured L/V ratios,
with a 75.13-degree maximum flange angle and 0.62 in. flange angle, and flange length from the test wheels. Because
flange length. By substituting these two parameters into the AOA was not measured during the test, the Equation C-11
TABLE C-6 Passenger car test results: climb distance and average L/V (L/V ave)
measured from the point where the L/V ratio exceeded 1.0 for friction coefficient of 0.6
Runs Speed L/V Maximum Average L/V Climb Distance
rn023 20.39 mph 1.79 1.37 6.2 ft
rn025 19.83 mph 2.00 1.43 7 ft
rn045 19.27 mph 1.32 1.10 4 ft
rn046 20.07 mph 1.06 1.01 2 ft
rn047 21.45 mph 1.85 1.47 5.7 ft
C-20
8 9
8
7
Climb Distance (feet)
7
Climb Distance (feet)
6 6
5
5
4
4 3
2
3
1
2 0
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
1
Average L/V Ratio during Climb
0
19 19.5 20 20.5 21 21.5 22 Measured Formula, 7.6 mrad AOA
Running Speed (mph) Formula, 10 mrad AOA Formula, 13 mrad AOA
Formula, 20 mrad AOA 50 msec Criteria at 20mph
Measured 50 msec Criterion
Figure C-30. Comparison of new criterion (Equation
Figure C-29. Application of 50-msec climb-distance C-11) to the 50-msec criterion, 0.6 friction coefficient.
criterion.
calculation was made for several values of AOA. Results are mum 1.32 L/V ratio would be acceptable since the climb dis-
compared to the 50-msec duration in Figure C-30. tance was well below the 20-mrad AOAe criterion, as shown
According to the biparameter distance criterion, the run in Figure C-31. The other three runs would be considered
with a 1.01 average L/V ratio (maximum L/V ratio 1.06) was unacceptable because their climb distances exceeded the
acceptable even for the 20-mrad average AOA, which is an 7.6-mrad AOAe criterion line.
unlikely occurrence for an H-frame truck in a 5-degree curve. The same conclusion can also be drawn if the conservative
The run with a 1.1 average L/V ratio (maximum L/V ratio AOAe (10 mrad) in Table C-5 is used.
1.32) was acceptable according to the new criterion, as This passenger car test shows that Nadal's value, the AAR
shown in Figure C-30. It would be unacceptable if the AOAe Chapter XI criterion, and the 50-msec time-based criterion
was greater than 13 mrad. This result also means the bipara- are more conservative than the new distance-based criterion
meter distance criterion is less conservative than the general for speeds of around 20 mph. This means that critical L/V
flange-climb-distance criterion. values would be permitted for longer distances under the
The other three test runs were unacceptable since they distance-based criterion at low speeds.
exceeded the new criterion for AOA greater than 7.6 mrad. The
same conclusion can also be drawn by applying the criterion 7.2 APPLICATION TO AN EMPTY TANK CAR
with a conservative 10-mrad AOA, according to Table C-5. As FLANGE CLIMB DERAILMENT
noted before, all the test runs exceed the 50-msec criterion.
If a friction coefficient of 0.5 is assumed instead of 0.6, the The biparameter distance criterion was applied to an empty
corresponding climb distances, measured at an L/V ratio tank car flange climb derailment that occurred during dynamic
higher than Nadal's value of 1.13, are listed in Table C-7. performance testing at TTCI on September 29, 1998. The car
The run with the maximum L/V ratio 1.06 would then be was running at 15 mph through the exit spiral of a 12-degree
acceptable because no climb was calculated when the L/V curve. The L/V ratios and wheel/rail contact positions on the
ratio was lower than Nadal's value. The run with the maxi- tread, measured from the instrumented wheelsets on the car, are
TABLE C-7 Passenger car test results: distance measured from the L/V ratio higher
than 1.13 for friction coefficient of 0.5
Average
Runs Speed L/V Maximum Climb Distance
L/V Ratio
rn023 20.39 mph 1.79 1.39 5.8 ft
rn025 19.83 mph 2.00 1.45 6.3 ft
rn045 19.27 mph 1.32 1.23 0.7 ft
rn047 21.45 mph 1.85 1.52 5 ft
C-21
Wheel B Contact Position (inches)
9 3
2.5
8
2
7
Climb Distance (feet)
1.5
6 1
0.5
5
0
4 -0.5
3 -1
-1.5
2
-2
1 -2.5
0 944 994 1044 1094 1144
1.1 1.2 1.3 1.4 1.5 1.6 Distance (feet)
Average L/V Ratio during Climb
Measured Formula,7.6 mrad AOA Figure C-34. Contact position on tread of wheel B.
Formula, 10 mrad AOA Formula, 20 mrad AOA
Figure C-31. Application of the new criterion (Equation 2
1.8
C-11) for a friction coefficient of 0.5. 1.6
Wheel B L/V Ratio
1.4
shown in Figures C-32 through C-35. Positive contact positions 1.2
indicate contact on the outside of the wheel taping line, while 1
negative values indicate contact on the flange side of the taping 0.8
line. Negative values approaching -2.0 indicate hard flange 0.6
0.4
contact. This is shown for Wheel B, which derailed. 0.2
0
944 994 1044 1094 1144
Wheel A Contact Position (inches)
3
Distance (feet)
2.5
2
1.5
1
Figure C-35. L/V ratio of wheel B.
0.5
0 The climb distance measured when the L/V ratio was greater
-0.5
-1
than 1.13 (Nadal's value for a 75-degree flange angle and a 0.5
-1.5 friction coefficient) is 17.9 ft, as shown in Figure C-35. The
-2 average L/V ratio is 1.43 during the 17.9 ft climb distance.
-2.5
944 994 1044 1094 1144
The data shown is for an instrumented wheelset that was in
Distance (feet)
the leading position of the truck. The curvature of the spiral
during the climb is about 9 degrees. The axle spacing distance
for this tank car is 70 in. The constant c was adopted as 2.5,
Figure C-32. Contact position on tread of wheel A. which represents a new bogie in Table C-4. According to
Equation B-6 in the Phase I report, the AOAe is about 11 mrad
for the three-piece bogie at this location in the spiral curve.
2
1.8
According to Equation C-11, the climb distance is 3.3 ft
1.6 for the 11-mrad AOAe. The corresponding 50-msec distance
Wheel A L/V Ratio
1.4 at 15 mph would be 1.1 ft. Since the measured climb distance
1.2 exceeded the value of the biparameter distance criterion, the
1 vehicle was running unsafely at that moment.
0.8
Wheel B started climbing at 1,054.6 ft and derailed at
0.6
0.4 1,164 ft. Therefore, the actual flange-climb distance is longer
0.2 than 17.9 ft. As shown in Figure C-35, the wheel climbed a
0 longer distance on the flange tip, and the L/V ratio decreased
944 994 1044 1094 1144
due to the lower flange angle on the tip.
Distance (feet)
The empty tank car derailment test results show that the
biparameter distance criterion can be used as a criterion for
Figure C-33. L/V ratio of wheel A. the safety evaluation of wheel flange climb derailment.
C-22
CHAPTER 8
CONCLUSION
The following findings were made: · A study of the flange-climb-distance criterion that
takes the friction coefficients as other parameters
· A general flange-climb-distance criterion that uses the besides the L/V ratio and the AOA is recommended for
AOA, maximum flange angle, and flange length as pa- future work.
rameters is proposed for transit vehicles: · The biparameter distance criterion has been validated
by the TTCI TLV test data. Since the running speed of
A * B * Len the TLV test was only 0.25 mph, one test's validation
D<
AOA + B * Len for the biparameter distance criterion is limited. A trial
test to validate the biparameter distance criterion is
where AOA is in mrad and A and B are coefficients that recommended.
are functions of maximum flange angle Ang (degrees) · Application of the biparameter distance criterion to
and flange length Len (in.): a test of a passenger car with an H-frame truck under-
going Chapter XI tests shows that the criterion is
100 less conservative than the Chapter XI and 50-msec
A = + 3.1 *
-1.9128 Ang + 146.56 criteria.
· Application of the biparameter distance criterion to an
1
Len - + 1.23 empty tank car derailment test results showed that the
-0.0092( Ang) 2 + 1.2152 Ang - 39.031 criterion can be used in the safety evaluation on the
wheel flange climb derailment.
B = + 0.05 *
10
-21.157 Len + 2.1052
10 Application limitations of the biparameter distance crite-
Ang + -5 rion include the following:
0.2688 Len - 0.0266
· The general flange-climb-distance criterion is validated
by the flange-climb-distance equations in the Phase I · The L/V ratio in the biparameter distance criterion must
report for each of the wheel profiles with different be higher than the L/V limit ratio corresponding to the
flange parameters. AOA, because no flange climb can occur if the L/V ratio
· Application of the general flange-climb-distance criterion is lower than the limit ratio.
to a test of a passenger car with an H-frame truck under- · The biparameter distance criterion is obtained by fitting
going Chapter XI tests shows that the criterion is less con- in the bilinear data range where AOA is larger than
servative than the Chapter XI and the 50-msec criteria. 5 mrad. It is conservative at AOAs less than 5 mrad
· A biparameter flange-climb-distance criterion, which due to the nonlinear characteristic.
uses the AOA and the L/V ratio as parameters, was pro- · The biparameter distance criterion was derived based on
posed for vehicles with AAR-1B wheel and AREMA the simulation results for the AAR-1B wheel on
136-pound rail profiles: AREMA 136-pound rail. It is only valid for vehicles
with this combination of wheel and rail profiles.
1 · For each of the different wheel profiles listed in Table
D<
[0.001411 * AOA B-2 of the Phase I report, individual biparameter
+ (0.0118 * AOA + 0.1155) * L/V - 0.0671] flange-climb-distance criteria must be derived based
on the simulation results for each wheel and rail pro-
where AOA is in mrad. file combination.
C-23
REFERENCES
1. Shust, W.C., Elkins, J., Kalay, S., and EI-Sibaie, M., "Wheel- 3. Elkins, J., and Wu, H., "New Criteria for Flange Climb Derail-
Climb Derailment Tests Using AAR's Track Loading Vehicle," ment," Proceedings, IEEE/ASME Joint Railroad Conference,
Report R-910, Association of American Railroads, Washington, Newark, New Jersey, 2000.
D.C., December 1997.
2. Wu, H., and Elkins, J., "Investigation of Wheel Flange Climb
Derailment Criteria," Report R-931, Association of American
Railroads, Washington, D.C., July 1999.
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