DESIGN OPTIMIZATION OF A FREIGHT CAR WHEEL
ABSTRACT
Design optimization of a freight car wheel was
performed employing statistical techniques. A threestep
process was developed to arrive quickly at an
optimum solution that provided lower stresses. At all
stages weight reduction and the ability to manufacture
were considered. The initial criteria were established by
creating and analyzing several designs in which
significant dimensional attributes were varied. During
the second stage, we concentrated on those variables
that resulted in reduced thermal stresses. The third
stage involved final optimization wherein the combined
effects of thermal and mechanical loads were evaluated.
INTRODUCTION
The calculated stresses due to thermal and
mechanical loading of the tread surface were modeled
using non-linear thermal and elastic range mechanical
analysis. We used ANSYS 5.6.1 Finite Element
software for the actual calculation of stress. Advances
in both hardware and software have enabled many
manufacturers to perform FEA in-house, thereby
providing a higher degree of control in the design process.
The evaluation procedure established the
thermal and mechanical inputs and the locations at
which the inputs were made. We used the requirements
of the Association of American Railroads S-660-83.
The geometry limits were obtained fiom Figure 9 of the
same institution’s M- 107/208-84, revised March 1,1998.
It was very apparent after completing the first
three configurations that, to arrive at an optimum
designed wheel, we would have to understand how
modifying the geometry affected the resultant stresses.
One of our option was to modify one feature at a time.
We felt this option was an enormous waste of resources.
And, the lack of an iterative model might lead to
improper design assumptions early in the design
process. Features that may be important in a nonoptimized
model may be unimportant as the design
approaches an optimized configuration. For example,h
establishing a plate position relative to the rim that is
not centered to the tread heat &put zone would result in
twisting stresses at the front and back rim fillets.
Stiffening the contour to prevent twisting would reduce
stresses but might not be important to an optimized
design. In addition, we felt that many more simulations
would be needed to achieve our goals.
Software techniques are available that will
permit optimization of a design given certain geometric
constraints. However, this evaluation process was
considered too complex for employing such a program.
We decided to use simple statistical techniques to
establish trending and not limit the number of features
that could be changed in each configuration. As we
approached an optimum design, we would exclude some
of the prior configurations fiom the statistics so as to
weight the later models appropriately.
INITIAL SET-UP
By reviewing the qualification requirements, we
were able to “guess” what the initial features of the plate
design should be. As noted previously, knowing the
location of the heat input zone on the tread surface led
to the decision to center the plate near the rim within
this area. Our reasoning for this was to reduce twisting
of the rim. By balancing the plate within this zone, the
total heat input would be roughly equal on both sides of .
the plate. Other features were selected based on
manufacturing constraints and past performance. Since
one of our goals was to decrease cost, we tended to
establish values for each feature that would decrease weight.
To reduce the effort in running simulations, we
ran the FEA at the condemning thickness of the wheel
rim. Both temperatures and stresses would be highest in
this state. This approach gave us the most conservative
design for the highest state of stress.
Defining which features to evaluate was fairly
easy. The rim ID and hub OD angles, all of the plate
fillets and radii and plate thicknesses were considered
important. The attachment points of the centerline of
the plate to the rim ID and hub OD were also evaluated
for their effect on stress. Features of the rim greater
than the front or back ID or smaller than the hub ODs
were not correlated to stress. These features were held
constant throughout all simulations.
ESTABLISHING CORRELATIONS
Ascertaining trends from the analytical results
were done using the Pearson Product-Moment
Correlation Coefficient. This function is an integral part
of most Spreadsheet programs.
r = b ( S,/ S,)
where:
r is the Pearson Correlation Coefficient
b = S, / S, ; The slope of the relation X:Y
The Pearson correlation ranges in value from -1
to +l. A value near zero indicates poor correlation. A
value close to -1 or +1 indicates potentially strong
negative or positive correlation. It is possible to get a
number close to -1 or +1, yet not have a true
correlation. If “b”, the slope of the best-fit curve, is
close to zero then no true correlation exists. It is also
important to remember that, although the Correlation
Coefficient is dimensionless, the slope is not. The slope
depends on both the relationship between the variables
“x” (independent) and “Y” (dependent) and their values.
Some features also exhibit interactions and
cross-correlation between one another. In this
evaluation, the mid-plate radius showed such a cross correlation.
Since both the front and backside plate
radii correlated strongly, only one or the other needed to
be correlated to stress. Since we intended to run less
than twenty simulations, the possibility of cross-
Correlation was high. The use of forecasting techniques
helped to minimize the potential for false assumptions.
If a change to a feature resulted in an unexplainable
change in predicted stress, then we would carefully
watch that correlation on subsequent models.
We found that thermal stress and mechanical
stress were analyzed best in separate spreadsheets. It
was important to understand what features were
important to each stress type. The project was divided
into three steps. The first step was to change each
feature in such a way as to give meaningful variation for
correlation. The second step involved reducing thermal
stress without regard to the effect on mechanical stress.
The last step in the process was to reduce mechanical
stress without compromising stress due to the thermal load.
Some feature changes tended to increase
mechanical stress but acted to reduce thermal stress.
The forecasting technique was used in these cases in
order to find the proper direction for moving the feature
to reduce the combined stress.
Features that did not correlate to changes in
stress were used to reduce weight. It seemed at times
that every piece of data was being used to improve the
design. Such “bone picking” would have been difficult
using other technique
Another interesting observation of this project
was the lack of correlation of maximum rim temperature
to end-of-solution stress. It was apparent that the
maximum rim temperature was dependent on rim mass.
As we reduced the weight of the rim, the temperature
increased. But, the geometry changes acted to reduce
stress independent of the maximum rim temperature
CONCLUSIONS
A statistical approach to solving complex
problems is not new. Using statistics to assist in the
design of new parts or improving older versions has
proven to be a time saving technique. Understanding the
use of statistics in the design environment helped us to
complete successfully the optimization of this wheel
design. The lessons learned during the course of this
project should lead to more cost-effective and safer
wheel designs for the future.
