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AFD Case Study:
Walking Bearing Problem
- Problem Description:
- A transaxle bearing in the sun gear of a
truck transmission, after some period of use, "walks" out of
place. It is necessary to eliminate this walking.
-
- Primary Useful Function of bearing:
- Provide rotation of sun gear.
-
- Drawback:
- Bearing moves out from its desired
place.
-
- History of the drawback:
- This drawback appeared when the gear box
was used with a more powerful engine.
-
- Changes which resulted in the
drawback:
- Torque and vibration increased.
-
- Mechanism of the drawback:
- Unknown.
![Walking Bearing [Fig-2]](images/cafd2.gif)
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- Formulating the original problem:
- The bearing, after some period of use,
walks out from its position. How does this phenomenon occur?
- Inverting the problem:
- How can we force the bearing to
walk out from its position?
- Amplifying the problem:
- How can we force the bearing to walk out
from its position using available resources only?
Available resources:
Result of undesired phenomena:
Onward movement of the object with rotational torque and vibration.
To find the required phenomena, we should
use the simplest analogies, for example:
- rotation results in onward movement, as
shown below
| |
screw |
sprial |
| |
![Walking Bearing [Fig-3]](images/cafd3.gif) |
 |
- vibration results in onward movement, as
shown below
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vibro-transportation |
reduction of
friction |
| |
![Walking Bearing [Fig-4]](images/cafd5.gif) |
![Walking Bearing [Fig-5]](images/cafd6.gif) |
Thus, we have found the following
phenomena:
Known Phenomena
with Similar Result:
|
Required Resources: |
| Onward
movement of nut along screw |
- screw surface contacts object
- rotational torque
|
| Onward
movement of object if torque is directed along spiral |
- torque directed along spiral
|
| Movement of
object under vibration (vibro-transportation) |
- vibration
- guide for movement of object
|
| Reducing
friction under vibration |
- vibration
- additional force moving the object
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Hypothesis 1: Torque forces the
bearing to move along spiral.
![Walking Bearing [Fig-6]](images/cafd7.gif)
Hypothesis 1a: Torque creates
deformation which results in deflection wave in sun gear. Teeth of gear
have some angle with axle; it results in twisted front of deflection wave.
This wave moves and forces bearing to move along spiral.
![Walking Bearing [Fig-7]](images/cafd8.gif)
Hypothesis 1b: Bearing interacts
with internal surface of sun gear. This surface has spiral marks created
by machining. Under load bearing and spiral marks create a
"screw-nut" pair. Deflection wave rotates bearing and forces it
to move along spiral marks. ![Walking Bearing [Fig-8]](images/cafd9.gif)
Hypothesis 2: Vibration reduces
friction between bearing and central bore; as a result, bearing walk-out
becomes easier.
![Walking Bearing [Fig-9]](images/cafd10.gif)
Hypothesis
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Verification Method
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| torque
creates deflection wave with twisted front |
- test gearbox with teeth directed
along axle of rotation
- test gearbox with opposite angle
of teeth
|
| torque
creates deflection wave; internal surface of sun gear has spiral
marks |
- render analysis of internal
surface of sun gear
- correlate direction of movement of
bearing, possible direction of deflection wave and direction of
movement of cutting tool during machining
|
| vibration
reduces friction between bearing and central bore |
- create vibrations similar to
working ones and measure friction between bearing and central
bore
|
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Mechanism of Drawback
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Directions for
Elimination
|
| deflection wave with
twisted front |
- strengthen sun gear
- reduce forces in gear mesh
- redirect deflection wave
- redirect tensions in sun gear
|
| movement along spiral
marks |
|
| decreasing friction
between bearing and gear |
- increase friction between bearing
and gear
|
|
Direction for
Elimination
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Solution Concept
|
| strengthen sun gear |
increase thickness of sun
gear |
| reduce forces in gear mesh |
increase amount of
satellite gears |
| redirect deflection wave |
change direction of teeth
in gear mesh |
| redirect tensions in sun
gear |
render an additional
groove in the central bore; this groove redistributes tensions and
works like a barrier for walking bearing |
| redirect spiral marks |
change direction of
rotation of machining tool |
| increase friction between
bearing and gear |
use press-fit bushing
produced from material with a higher thermal expansion coefficient |
|
![Walking Bearing [Fig-1]](images/cafd1.gif)