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TERM PAPER
MEC-302
DYNAMICS OF MACHINE
STUDY OF GYROSCOPIC EFFECT ON MILLINGMACHINE (SPINDLE)
SUBMITTED TO: SUBMITTED BY:
Mr. MANDEEP SINGH AMARJEET SINGH
M3R30A18
11111629
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ACKNOWLEDGEMENT
First and foremost, we would like to thank to our course
teacher Mr. Mandeep Singh for the valuable guidance and
advice. He inspired us greatly to work in this Term paper. His
willingness to motivate us contributed tremendously to our
Term paper. We also would like to thank him for showing us
some examples related to the topic of our project.
Besides, we would like to thank the authority of Lovely
Professional University (LPU) for providing us with a good
environment and facilities to complete this Term paper.
Finally, an honorable mention goes to our families and friends
for their understandings and supports on us in completing this
project. Without helps of the particular that mentioned above,we would face many difficulties while doing this project.
AMARJEET SINGH
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Introduction:
Gyroscope is very useful in many applications. To choose the right rate
gyro sensor, some features, such as power consumption, weight,dimension, etc., must be taken into consideration. its play very vital role
in imparting right amount of force in right direction, so in mechanical
industry it s gain ample respect and application. Its uses approx
everywhere but some very specific fields are aerospace, automobile,
manufacturing industry and robots etc. In case of milling machine its play
role in reduce chattering sound and make it more precise.
Gyroscope history:The earliest known gyroscope instrument was made by German
Johann Bohnenberger who first wrote about it in 1817. In 1832,
American Walter R. Johnson developed a similar device that
was based on a rotating disk. The French mathematician Pierre-
Simon Laplace, recommended the machine for use as a
teaching aid, and thus it came to the attention of Leon
Foucault. In 1852, Foucault used it in an experiment involving
the rotation of the Earth. It was Foucault who gave the device
its modern name, in an experiment to see (Greek skope in, to
see) the Earth's rotation (Greek gyros, circle or rotation), which
was visible in the 8 to 10 minutes before friction slowed the
spinning rotor. In the 1860s, electric motors made the concept
feasible, leading to the first prototype gyrocompasses; the first
functional marine gyrocompass was patented in 1908 by
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German inventor Hermann Anschtz-Kaempfe. In the first
several decades of the 20th century, other inventors attempted
(unsuccessfully) to use gyroscopes as the basis for early black x
navigational systems by creating a stable platform from which
accurate acceleration measurements could be performed (in
order to bypass the need for star sightings to calculate
position). Similar principles were later employed in the
development of inertial guidance systems for ballistic missiles.
During World War Two, the gyroscope became the prime
component for aircraft and anti-aircraft gun sights.
What is Gyroscope?
A gyroscope is a device for measuring or maintaining
orientation, based on the principles of conservation of angular
momentum. A mechanical gyroscope is essentially spinning
wheel or disk whose axle is free to take any orientation. This
orientation changes much less in response to a given external
torque than it would without the large angular momentum
associated with the gyroscope's high rate of spin. Since external
torque is minimized by mounting the device in gimbals, its
orientation remains nearly fixed, regardless of any motion of
the platform on which it is mounted. Gyroscopes based on
other operating principles also exist, such as the electronic,
microchip-packaged MEMS gyroscope devices found in
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consumer electronic devices, solid state ring lasers, fiber optic
gyroscopes and the extremely sensitive quantum gyroscope.
Instead of a complete rim, four point masses, A, B, C, D,
represent the areas of the rim that are most important in
visualizing how a gyro works. The bottom axis is held stationary
but can pivot in all directions. When a tilting force is applied to
the top axis, point A is sent in an upward direction and C goes
in a downward direction. FIG 1. Since this gyro is rotating in a
clockwise direction, point A will be where point B was when the
gyro has rotated 90 degrees. The same goes for point C and D.
Point A is still traveling in the upward direction when it is at the
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90 degrees position in FIG 2, and point C will be traveling in the
downward direction. The combined motion of A and C cause
the axis to rotate in the "precession plane" to the right FIG 2.
This is called precession. A gyros axis will move at a right angle
to a rotating motion (In this case to the right). If the gyro were
rotating counterclockwise, the axis would move in the
precession plane to the left. If in the clockwise example the
tilting force was a pull instead of a push, the precession would
be to the left. When the gyro has rotated another 90 degrees
FIG 3, point C is where point A was when the tilting force was
first applied. The downward motion of point C is now
countered by the tilting force and the axis does not rotate in
the "tilting force" plane. The more the tilting force pushes the
axis, the more the rim on the other side pushes the axis back
when the rim revolves around 180 degrees. Actually, the axis
will rotate in the tilting force plane in this example. The axis will
rotate because some of the energy in the upward and
downward motion of A and C is used up in causing the axis to
rotate in the precession plane. Then when points A and C finally
make it around to the opposite sides, the tilting force (being
constant) is more than the upward and downward counter
acting forces. The property of precession of a gyroscope is used
to keep monorail trains straight up and down as it turns
corners. A hydraulic cylinder pushes or pulls, as needed, on one
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axis of a heavy gyro. Sometimes precession is unwanted so two
counter rotating gyros on the same axis are used.
Milling process:Milling is the process of machining flat, curved, or irregular
surfaces by feeding the work piece against a rotating cutter
containing a number of cutting edges. Milling is a process
where material is removed by a spinning tool, which has several
cutting teeth. The main difference between modeling the
milling and the turning process is that the chip thickness in
milling is not constant, but periodic. Some process parameters
are shown:
1. Feed per tooth f,.
2. Axial depth-of-cut up
3. Spindle speed w
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Several types of milling exist:
Up milling, where the entry angle is zero and the exit angle is
non-zero,
Down-milling, where the entry angle is nonzero and the exit
angle is zero,
Face milling, where the entry angle PHI and exit angle PHI of
the milling cutter relative to the work piece are nonzero,
Slotting, where the entry angle is zero and the exit angle is180.
GYROSCOPIC EFFECT ON MILLING MACHINE:
The process of milling is used widely in many sectors of
industry. The milling of large structures is done in e.g. the
airplane building industry, where large amounts of material areremoved. To make the process the most efficient, the speed of
the process should be as high as possible while maintaining a
high quality level. During the milling process chatter can arise at
certain combinations of spindle speed and depth-of-cut. This
behavior is usually undesired, because in such a case a non-
smooth surface of the work piece is caused by heavy vibrationsof the cutter. In addition the machine and cutting tool wear out
rapidly. Several studies have been done to understand and
model the phenomenon chatter. Both linear and nonlinear
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models have been developed, where nonlinearities are
modeled in several different ways. Early studies have shown
that the border between stable and unstable cuts in terms of
the depth-of-cut can be visualized as a function of spindle
speed. This results in a Stability Lobe Diagram (SLD). With the
help of these diagrams it is possible to find the point with a
combination of spindle speed and depth-of-cut which has the
largest metal removal rate while avoiding chatter.
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GYROSCOPIC EFFECT AS A FUNCTION OF SPINDLE
SPEED:
For low spindle speeds (100-400 rpm) a stability analysis is
applied, where the mean chip thickness is measured. The
model is validated by experiments. Experiments and
simulations done are down milling of 30' helix angle end mill set
at an radial depth-of-cut of 1.5 mm and an axial depth of cut of
6,4 mm. In the experiments, three parameters are varied at a
spindle speed of 135 rpm:
Radial depth of cut Number of flutes. The federate per minute is held
constant, so the feed per tooth f, increases if the number
of flutes decreases
Federate per minuteNote that on the vertical axis, the average chip thickness is
shown. Chip thicknesses above the line result in an unstable
cut, whereas chip thicknesses below the line result in a chatter-
free cut.
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Figure shows the limit of stability decreases with an increasing
feed. If the federate is 70mm/min, the chip thickness is above
the stability border. If the federate decreases then chip
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thickness also decreases, this increases the stability of milling
machine spindle.
Gyroscopic couple in case of milling machinespindle:
A new dynamic milling model of a rotating spindle is developed
and the gyroscopic effect of the spindle on the stability
characteristics of the milling system is investigated for the first
time. The results show that although the gyroscopic effect of
the rotating spindle does not change the instability regions in
milling, it increases the real parts of the Eigen values of thesystem or reduces the critical axial depth of cut. In other words,
it makes the stability prediction less conservative. Its pure
application of gyroscopic effect, because when the cutting done
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with help of tool, there are certain force which directly work on
spindle, which bound it to some short of motion, so for
avoiding that, and avoiding such important disturbance which
enhance productivity gyroscopic effect is very important.
For the milling process aided by AMB, shown in Fig. 6, the
cutting force, Fc, is mainly determined by the axial cut depth, a,
feed rate, f, and spindle speed, . However, at normal
operation mode, the spindle speed and feed rate are generally
retained constants. Therefore, the axial cut depth, a, is, in fact,the key factor to determine the pattern of cutting dynamics. In
order to counterbalance the cutting force and regulate the
spindle position deviation, d, the models of the subsystems,
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shown in Fig. 6, are to be constructed by experiments at first. In
Fig. 6a, the lateral force to the spindle, Fm, represents the
magnetic force exerting on the spindle by the AMB while the
cutting process is not engaged at all. The spindle model at idle
operation mode, shown in Fig.6a, is constructed in order to
explore the link of the shaft position deviation, d, against the
corresponding exerted force, i.e., the magnetic force, Fm.
Similarly, the dynamic model shown in Fig. 6b represents the
spindle position deviation, d, against the axial cut depth, a. By
comparison of the two dynamic models in Fig. 6, the resulted
cutting force, due to milling process, can be estimated for a
given axial cut depth and the available measurement of spindle
position.
Conclusion:
Several researchers have studied and modeled the
phenomenon chatter. Chatter is the result of several causes.
Primary chatter is the consequence of friction effects between
the tool and the chip, mode coupling or thermodynamics of the
cutting process. Secondary chatter is caused by regeneration of
waviness of the surface of the work piece. Both linear and
nonlinear models have been developed in different ways. The
friction force can be modeled as a nonlinear function of the
cutting parameters. Partial tool jump-out can be modeled. Also
the gyroscopic effect of the spindle speed has been modeled.
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Experiments are performed to study chatter and to validate the
models. Several researchers conclude that nonlinearities should
be modeled for a more accurate prediction of chatter. They
show that the milling process contains phenomena which
cannot be modeled using linear models. Gyroscope is very
important and powerful arrangement for removing direction a
alignment and for maintain balancing, its device which used in
balance the specimen like milling machine spindle and lots
more.
References:
www.Google.com www.Wikipedia.org Theory of machine by R.S khurmi www.gyroscope.com/Gyroscopes/
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