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Lapping
is a machining operation, in which two surfaces are rubbed together
with an abrasive between them, by hand movement or by way of a machine. This
can take two forms. The first type of lapping (traditionally called
grinding), typically involves rubbing a brittle material such as glass
against a surface such as iron or glass itself (also known as the "lap"
or grinding tool) with an abrasive such as aluminum oxide, emery,
silicon carbide, diamond, etc., in between them. This produces
microscopic conchoidal fractures as the abrasive rolls about between
the two surfaces and removes material from both.
The other form
of lapping involves a softer material for the lap, which is "charged"
with the abrasive. The lap is then used to cut a harder material—the
workpiece. The abrasive embeds within the softer material which holds
it and permits it to score across and cut the harder material. Taken to
the finer limit, this will produce a polished surface such as a
polishing cloth on an automobile, or a polishing cloth or polishing
pitch upon glass or steel.
Taken to the ultimate limit, with the
aid of accurate interferometry and specialized polishing machines,
lensmakers can produce surfaces that are flat to better than 30
nanometers. This is one twentieth of the wavelength of light from a
commonly-used source, 632.8 nm. Surfaces this flat can be molecularly
bonded (optically contacted) by bringing them together under the right
conditions. (This is not the same as the wringing effect of Johansson
blocks, although it is similar).
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A jig grinder is a machine tool used for grinding complex shapes and holes where the highest degrees of accuracy and finish are required.
The
jig grinder is very similar to a jig borer, in that the table
positioning and spindles are very accurate (far more so than a manual
milling machine or lathe).
It is almost exclusively used by tool and die makers in the creation of
jigs or mating holes and pegs on dies. There are usually many
peripheral elements to a large jig grinder, including separate
hydraulic motors, air compressors, and various cooling systems for both
the hydraulic circuit and supplying coolant to the work and machine
itself.
The machine operates by a high speed air spindle
rotating a grinding bit. The air spindles are removable and
interchangeable to achieve varying surface speeds. Some spindles are
fixed speed (60000 rpm), others are adjustable (30000-50000 rpm), and
still others are very high speed (175000 rpm). The machines have a
standard X-Y table with the notable exception of knee travel. All axes
are indexed to .0001" via a vernier scale on the handwheels, with
higher accuracy available with the use of measuring bars. The machine
head has two vertical travels, one rough head adjustment and the other
a precise spindle adjustment. The spindle to which the detachable air
spindle mounts also rotates at a variable speed and can typically
outfeed .100" while running, again with an accuracy of .0001" on the
handwheel or greater, for very precise hole, peg and surface grinding.
A well-kept jig grinder will reliably position work to a higher degree
of accuracy than is possible with handwheels alone. These features are
all critical in positioning a hole and peg system a precise distance
from a reference surface or edge.
The most important factor on a
jig grinder is the dual-spindle configuration. The main spindle is
roughly positioned with between 1" or 2" of travel for setup, and then
the .100" of outfeed is used during machine operation to outfeed into
the work. A spacer bar may be used between the grinder and main
spindle, allowing large (9" radius or larger) work to be completed. The
main spindle has a wide range of speeds to ensure proper grinder feed
rates are maintained.
Hypoid gears resemble spiral bevel gears,
except that the shaft axes are offset, not intersecting. The pitch
surfaces appear conical but, to compensate for the offset shaft, are in
fact hyperboloids of revolution.16
Hypoid gears are almost always designed to operate with shafts at 90
degrees. Depending on which side the shaft is offset to, relative to
the angling of the teeth, contact between hypoid gear teeth may be even
smoother and more gradual than with spiral bevel gear teeth. Also, the
pinion can be designed with fewer teeth than a spiral bevel pinion,
with the result that gear ratios of 60:1 and higher are "entirely
feasible" using a single set of hypoid gears
A worm is a gear that resembles a screw.
It is a species of helical gear, but its helix angle is usually
somewhat large(ie., somewhat close to 90 degrees) and its body is
usually fairly long in the axial direction; and it is these attributes
which give it its screw like qualities. A worm is usually meshed with
an ordinary looking, disk-shaped gear, which is called the "gear", the
"wheel", the "worm gear", or the "worm wheel". The prime feature of a
worm-and-gear set is that it allows the attainment of a high gear ratio
with few parts, in a small space. Helical gears are, in practice,
limited to gear ratios of 10:1 and under; worm gear sets commonly have
gear ratios between 10:1 and 100:1, and occasionally 500:1.24
In worm-and-gear sets, because the worm's helix angle is large, the
sliding action between teeth is considerable, and the resulting
frictional loss causes the efficiency of the drive to be usually less
than 90 percent, sometimes less than 50 percent.so comparing to other
gears it gives very less efficiency27
The distinction between a worm and a helical gear is made when at
least one tooth persists for a full 360 degree turn around the helix.
If this occurrs, it is a 'worm'; if not, it is a 'helical gear'. A worm
may have as few as one tooth. If that tooth persists for several turns
around the helix, the worm will appear, superficially, to have more
than one tooth, but what one in fact sees is the same tooth reappearing
at intervals along the length of the worm. The usual screw nomenclature
applies: a one-toothed worm is called "single thread" or "single
start"; a worm with more than one tooth is called "multiple thread" or
"multiple start".
We should note that the helix angle of a worm is not usually
specified. Instead, the lead angle, which is equal to 90 degrees minus
the helix angle, is given.
In a worm-and-gear set, the worm can always drive the gear. However,
if the gear attempts to drive the worm, it may or may not succeed.
Particularly if the lead angle is small, the gear's teeth may simply
lock against the worm's teeth, because the force component
circumferential to the worm is not sufficient to overcome friction.
Whether this will happen depends on a function of several parameters;
however, an approximate rule is that if the tangent of the lead angle
is greater than the coefficient of friction, the gear will not lock.32
Worm-and-gear sets that do lock in the above manner are called "self
locking". The self locking feature can be an advantage, as for instance
when it is desired to set the position of a mechanism by turning the
worm and then have the mechanism hold that position. Tuning gears on
stringed musical instruments work that way.
If the gear in a worm-and-gear set is an ordinary helical gear only point contact between teeth will be achieved.36
If medium to high power transmission is desired, the tooth shape of the
gear is modified to achieve more intimate contact with the worm thread.
A noticeable feature of most such gears is that the tooth tops are
concave, so that the gear partly envelopes the worm. A further
development is to make the worm concave (viewed from the side,
perpendicular to its axis) so that it partly envelopes the gear as
well; this is called a cone-drive or Hindley worm.40
Helical and Worm Hand,
A right hand helical gear or right hand worm is one in which the
teeth twist clockwise as they recede from an observer looking along the
axis. The designations, right hand and left hand, are the same as in
the long established practice for screw threads, both external and
internal. Two external helical gears operating on parallel axes must be
of opposite hand. An internal helical gear and its pinion must be of
the same hand.
A left hand helical gear or left hand worm is one in which the teeth
twist counterclockwise as they recede from an observer looking along
the axis
Bevel gears are essentially conically shaped, although the actual
gear does not extend all the way to the vertex (tip) of the cone that
bounds it. With two bevel gears in mesh, the vertices of their two
cones lie on a single point, and the shaft axes also intersect at that
point. The angle between the shafts can be anything except zero or 180
degrees. Bevel gears with equal numbers of teeth and shaft axes at 90
degrees are called miter gears.
The teeth of a bevel gear may be straight-cut as with spur gears, or they may be cut in a variety of other shapes. 'Spiral bevel gears'
have teeth that are both curved along their (the tooth's) length; and
set at an angle, analogously to the way helical gear teeth are set at
an angle compared to spur gear teeth. 'Zero bevel gears' have
teeth which are curved along their length, but not angled. Spiral bevel
gears have the same advantages and disadvantages relative to their
straight-cut cousins as helical gears do to spur gears. Straight bevel
gears are generally used only at speeds below 5 m/s (1000 ft/min), or,
for small gears, 1000 r.p.m.
Crown gear
A crown gear
A crown gear or contrate gear is a particular form of bevel gear
whose teeth project at right angles to the plane of the wheel; in their
orientation the teeth resemble the points on a crown. A crown gear can
only mesh accurately with another bevel gear, although crown gears are
sometimes seen meshing with spur gears. A crown gear is also sometimes
meshed with an escapement such as found in mechanical clocks
Double helical gears, invented by André Citroën
and also known as herringbone gears, overcome the problem of axial
thrust presented by 'single' helical gears by having teeth that set in
a 'V' shape. Each gear in a double helical gear can be thought of as
two standard, but mirror image, helical gears stacked. This cancels out
the thrust since each half of the gear thrusts in the opposite
direction. They can be directly interchanged with spur gears without
any need for different bearings.
Where the oppositely angled teeth meet in the middle of a
herringbone gear, the alignment may be such that tooth tip meets tooth
tip, or the alignment may be staggered, so that tooth tip meets tooth
trough. The latter type of alignment results in what is known as a Wuest type herringbone gear.
With the older method of fabrication, herringbone gears had a
central channel separating the two oppositely-angled courses of teeth.
This was necessary to permit the shaving tool to run out of the groove.
The development of the Sykes gear shaper now makes it possible to have continuous teeth, with no central gap.
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