Transcript Slide 1

Gears their designs & uses
Andrei Lozzi 2012
When two gears make contact at
the Pitch Point, the areas of
contact on the face of each gear
will have the same instantaneous
tangential velocity Vt.
The smaller gear (the pinion) has a
smaller radius but a higher angular
velocity, that will match the larger
gear radius but lower angular
velocity.
Hence there is no sliding between
the involutes at the Pitch Point.
P
As the point of contact between the gear
teeth moves away from the Pitch Point P
the tangential velocities of the points on
each gear will change in magnitudes and
direction Vt1 & Vt2.
P
Since instantaneously the two points
shared the same location in space there
must have been an additional relative
velocity Vs that when added (or
subtracted) to one of those tangential
velocity would give the other.
This additional velocity is parallel to the
involutes at the point of contact and
hence represents pure sliding.
The further from the pitch point the
greater will be the sliding
Tooth size, strength & friction
A tooth may be viewed as a short beam subjected to bending, on the surface of which,
the normal stress due to bending will vary inversely with the square of the tooth
thickness. Bigger teeth are therefore stronger, but bigger i.e. is longer teeth, while in
contact with each other, will undergo relatively more sliding.
We may conclude that although big teeth will be disproportionally stronger than smaller
teeth, they will be less efficient due to frictional losses. The most efficient practical spur
gears may have about 2% loss, the worse 5%.
Regions of High stress
There are 4 regions of relatively high stress in each gear pair, 2 in the pinion (the
smaller dia gear) and 2 in the gear (larger dia gear).
To have a balanced designed gear pair, the factor of safety should be very nearly the
same at these 4 locations. The highest stresses are assumed to take place when the
gears make contact at the pitch point, only for high quality gears. For average gears,
the highest stresses are calculated, when the teeth first make contact, at their tip.
Each variable shown
here is a function of
other variables.
There are 2 sets of
such equations one
for each gear
In a gear box there
are many such sets,
and in an industrial
plant there may be
many such boxes
Typical industrial multi stage gear box with large shaft diameters and broad
face widths. For gear reduction of 1:6 or more the gear box will be lighter and
usually cheaper if it incorporates 2 or more stages.
A computer controlled
digitizing machine, measuring
the surface of a helical gear.
CCD machines can have
programs which guide the
sensor tip around any profile,
or just move until the sensor
touched something.
These machines though quite
dear are the only practical
means of determining the
accuracy of a tooth profile
A coal pulveriser as used in modern coal fired power station. A very high
final gear ratio is used here because of the convenience of being able to
use the pulveriser drum as the final gear stage
The pulveriser drive includes a traditional gear box just after the drive motor.
Another example of a supposedly rare high ratio gear pair. Here used to drive
a deep cable drum on an off-shore oil rig service vessel. The power comes
from a hydraulic low speed high torque motor, seen at left.
A herringbone or double helical gear box driving the propeller on a
commercial vessel. The opposing helical gears balance the axial
thrust generated by each gear. The cost of making double gears
must payoff in reduced bearing loads and gearbox mass
A herringbone gear set driving the propeller on a naval vessel. Note the
difference in teeth sizes to the previous gears, indicating quieter more
efficient operation, but certainly not cheaper construction.
A typical heavy duty shaft mounted gear box set. Such
installation may be capable of transmitting 2 MW. The weight
of the assembly is used to partly balance the torque being
transmitted. Note the separate lubrication system needed to
provide high pressure temperature controlled oil.
A rare example of hot
generated large gear
wheels.
The tools steel wheels
at right and left, are
impressed on the
circular gear blank in
the centre, while
rotating to form a
finished gear with
favorable grain flow
and very fine surface
finish
It is possible to have too few a number of teeth on a gear. For any particular pressure
angle, If teeth number become too small, when the teeth are cut there will
discontinuities in the generation of the involute profile, either done by a rack or hob.
In the last few decades cycloidal teeth have almost fallen out of use, possibly
because of the difficulty in generating them. Today with accurate NC machine they
may return, because they allow the use of very few teeth, that is strong teeth and
high gear ratios in single gear pair. Note that Rootes blowers and screw
compressors using 2, 3 or 4 teeth are cycloidal in profile. Cycloids are also used in
mechanical clocks.
Rootes blowers (gear wheels) and their casing from a
GM uniflow engine as used by main line locomotives.
Note that educated well-bred
engineers refer to ‘inter-coolers’ as
the heat exchangers that are used
in between supercharging stages,
not for the exchangers used
between a compressor and the
engine, those are after-coolers !