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Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
21
CASK ROLLER BEARINGS MACHINED BY ELECTRICAL
EROSION
Prof.univ.dr.ing. MARCEL S.POPA, Technical University of Cluj-Napoca
Drd. Ing. IOAN BADIU, Technical University of Cluj-Napoca
ABSTRACT: At low speeds of rotation or heavily loaded bearings in motion analysis of bearing
elements can be neglected dynamic effects. It can be considered as pressure angles of the ball and the two rings
are the same and does not change during operation, in the general case in which both the inner ring and the
outer orbital rotation of the ball rotesc.Intrucat generally occurs in a different plan rolling plane between the
ball and raceway will occur relative pivoting movement will affect vitrzei vector angular position and size of the
ball.
KEY WORDS : angular velocity of the ball, electrical erosion, rotation speed.
1.INTRODUCTION .
Because moments friction pivot ball in
relation to the two runways are unequal, it is
assumed that this will occur only pivoting
movement relative to the tread in contact with
the friction when the pivot is small. As a rule
when the friction at the contact with the inner
path is higher, it means that the ball is rolling
without pivoting on the inner path (which is
said so that you control the movement) and
rolls and pivots relative to the exterior. Due
to the geometrical shape of the rolling
elements moving and elastic deformations,
the contact surface will curve its radius in the
plane perpendicular to the direction of motion
is equal to the harmonic mean of the radii of
curvature in the plan.Because of the curvature
of the linear speeds in the region of the
contact points will be different. Only certain
points will achieve equality condition gear, so
pure rolling.
The other points will be subject to partial slip
before and partly back. Size differential slip
velocities can be determined by calculation.
Considering the contact of the ball with two
horses running in a radial-axial bearing, the
outer ring is fixed to analyze the relative
motion will give the ball to the center related
fix.In conditions remain dry or mixed friction
regime in reality there will be slip differential
on the entire surface contact friction forces
causing a non-slip grip relative to a specific
portion.Adhesion causes tangential tensile
stress in those areas that will help as those in
the differential slip rolling resistant moment
creating, modifying the character wear. By
choosing proper bearing geometric
parameters pate pure rolling lines change
position so that the center of the ellipse of
contact, the contact normal stresses
requested, to enter the area without slip
differential adhesion, thus resulting in a reduce
wear.
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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2.EXPERIMENTAL RESULTS
FROM THE POCESSING OF
ELECTRICAL EROSION
Fig.1.Machine is manufactured by electrical
erosion AF-10
Spherical roller bearings consist of solid
outer rings with spherical raceway, solid
ring with two collars cylindrical or conical
hole and spherical roller cage. With self-
aligning capability, they are particularly
suitable in the radial, axial load capacity is
usually reduced.
Fig.3. Spherical roller bearings SKF Energy
Fig.2. The processing of bearings circular
orbits.
Fig.4. The Timken spherical roller bearings
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig.5. NSK spherical roller bearings.
Fig. 9. The connection between electrical
erosion parameters
Fig. 6. Table containing the values parameters
of electrical erosion
Fig. 10. The graph parameters electrical
erosion
Fig. 7. The graph electrical erosion parameters
Fig. 11. The reporting of electric erosion
productivity parameters
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 8. The electrical erosion parameter values.
Fig. 12. The reporting of electric erosion
productivity parameters
Fig. 13. Table containing the values
parameters of electrical erosion.
Fig. 17. Table containing the values
parameters of electrical erosion.
Fig. 14. The connection between electrical
erosion parameters.
Fig. 18. Table containing the values
parameters of electrical erosion
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 15. The reporting of electric erosion
productivity parameters.
Fig. 19. The shape 3D graphics parameters
electrical erosion.
Fig. 16. The shape 3D graphics parameters
electrical erosion.
Fig. 20. Table containing the values
parameters of electrical erosion
Fig. 21. The shape 3D graphics parameters
electrical erosion.
Fig. 25. The shape 3D graphics parameters
electrical erosion.
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 22. The shape 3D graphics parameters
electrical erosion.
Fig. 26. Table containing the values
parameters of electrical erosion.
Fig. 23. Table containing the values
parameters of electrical erosion.
Fig. 27.The shape 2D electrical erosion
parameters.
Fig. 24. The shape 3D graphics parameters
electrical erosion.
Fig. 28. The shape 2D electrical erosion
parameters.
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 29. The reporting of electric erosion
productivity parameters.
Fig. 33. The shape 2D electrical erosion
parameters.
Fig. 30. Table containing the values
parameters of electrical erosion
Fig. 34. The shape 2D electrical erosion
parameters.
Fig.31. The shape 2D electrical erosion
parameters.
Fig. 35. The shape 2D electrical erosion
parameters.
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 32. Table containing the values
parameters of electrical erosion.
Fig. 36. The shape 2D electrical erosion
parameters.
Fig. 37. The electrical erosion parameter
values.
Fig. 41. 2D representation of the parameters
the electrical erosion.
Fig. 38. Table containing the values
parameters the electrical erosion.
Fig. 42. 2D representation of the parameters
the electrical erosion
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 39. 3D graphical representation of the
parameters the electrical erosion.
Fig. 43. 2D representation of the parameters
the electrical erosion.
Fig. 40. Table containing the values
parameters the electrical erosion
Fig. 44. 2D representation of the electrical
erosion parameters expressed in percentage.
Fig. 45. 2D representation of the parameters
the electrical erosion.
Fig. 46. 2D representation of the electrical
erosion parameters expressed in percentage.
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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Fig. 47. 2D representation of the electrical erosion parameters expressed in percentage.
3.CONCLUSIONS.
If bearing operating at high speeds
due to the action of centrifugal forces, the
down force on the ball at the contact of the
two rings will be different, and therefore,
pressure angles will have different values.
Under the action of gyroscopic moments
there is a tendency of further spins the ball
which, depending on the speed and the
bearing lubrication conditions, there will
always be hampered by the forces of friction.
Arises in this case spin balls with adverse
effects on the bearing friction moment. For a
rigorous analysis will be necessary to
consider the angular velocity vector of the
ball, which has the following components in
the general case after three directions:
ωjx = ω
jb cos β
' cos β
''
ωjy = ω
jb cos β
' sin β
''
ωjz = ω
jb sin β
'
External forces acting on the bearing
are related to the total axial and radial
deformations. Theoretical analysis can be
deepened further by considering the
interaction between the balls and cage, which
is limited due to practical orbital velocity
amplitude variation around the average bead,
ie the angular velocity of the cage. The large
volume of calculations justify complete
analysis only in special cases, as was done,
for example, bearing devices used in
aerospace missions. In particular situations,
simpler, such as radial bearings symmetric
load, the number of unknowns is significantly
reduced.Given that between balls and
raceways there is a dry or mixed friction
regime, it is assumed that the gyroscopic
moment is insufficient to produce rotation of
the ball in the camp charged. Therefore the
angle β will be void ball rotation vector
finding thus in the plane passing through the
bearing and ball Cetra. In addition, if using
the assumption of control of the ball, that ball
is considered rolls and pivots in relation to
the path that controls movement and rolls and
pivots in relation to the other runway will
result in the opposing friction moment gyro
(gyro moment is zero) will act only upon
contact with conductive path.
Analysis of the dynamics and kinematics of
the ball is so much simplificata.In dry friction
conditions hypothesis ball control gives
sufficiently accurate results only for the
orbital velocity of the ball, and pivot about
Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2014
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not really zero in relation to any of
cai.Valorile angles setting for a given load and
speed of the bearing should be determined in
this case by analyzing the position of the ball,
for symmetrical load bearing situation is much
simplified.The ball control by the inner or
outer ring equation results from the analysis
points in the direction perpendicular to the
orbital motion (yaw moments are
components). Non-compliance leads to an
exciting outer ring control.
In the partial-load operation medium is
typically accomplished so ball control will be
provided by the inner ring.
At high speeds, due to the action of
centrifugal force, the force becomes larger
and more than a speed limit control is taken
over by the outer ring. It should be noted
again that in terms of fluid friction, ball
control assumption is no longer valid. To
analyze the kinematics of the bearing
imposing a complex calculation.
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