FREIGHT CAR WHEEL

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.