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Gear Tooth Geometry - This is determined primarily by pitch, depth and pressure angle
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Addendum: The radial distance between the top land and the pitch circle.
- Addendum Circle:
The circle defining the outer diameter of the gear.
- Circular Pitch:
The distance along the pitch circle between the corresponding points
of 2 adjacent teeth. Equals to the sum of the tooth thickness and
space width.
- Clearance:
The radial distance between the bottom land and clearance circle.
- Dedendum Circle:
The circle through the bottom lands of a gear.
- Dedendum:
The radial distance between the pitch circle and the dedendum circle.
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Depth: A number which is standardized in terms of pitch. Full
depth teeth have a working depth of 2/DP. For gears with equal
addenda, then the addendum is 1/P.
- Diametral Pitch
(DP): The ratio
of the teeth to the pitch diameter. It is used in the U.S. to indicate
the coarseness of a gear and an index of tooth size expressed in teeth
per inch.
- Pitch:
A standard pitch is typically a whole number when measured as a
diametral pitch (DP). Coarse-pitch gears have DP less than 20.
Fine-pitch gears have DP larger than 20. Involute-tooth gears can be
made with DP as fine as 200, and cycloidal tooth gears can be made
with DP to 350.
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Pitch Circle: Theoretical circle upon which all calculations
are made. This is the circle that rools without slipping with the
pitch circle of the mating gear.
- Pitch Diameter:
The diameter of the pitch circle in inches or metric (mm).
- Pressure Angle:
The angle between the tooth profile and a perpendicular to the pitch
circle, usually at the point where the pitch circle meets the tooth
profile. Standard angles are 20 and 25 degrees. The pressure angle
affects the force that tends to separate mating gears. A high pressure
angle means that higher ratio of teeth not in contact. However, this
allows the teeth to have higher capacity and also allows fewer teeth
without undercutting.
Power Velocity Load
Power is transmitted by one gear exerting a force on the other gear as follows:
F=33000 hp/V where
F= force on the gear tooth (lb)
hp= horsepower transmitted
V= velocity at pitch circle (ft/min) = 0.262*Pitch Diameter(ft)*Rotational Speed(rpm)
Gear Strength
The maximum allowable load on a gear is calculated as follows:
Fs= s*f*Y/P where
Fs= allowable load (lb)
s= allowable stress, psi
f= face width or width of the gear tooth
Y= tooth form factor which can be obtained from engineering handbooks
P= Diametral pitch
The allowable load should be multiplied by a factor K to allow for shock loads and manufacturing imperfections.
The factor K for accurately hobbed gears rotating at less than 4000 ft/min is calculated as follows:
K = 1200/(1200+V)
Backlash
The backlash clearance for most gear applications is approximately 0.04/P. The backlash or force tending to separate two meshing
gears carrying a load is:
S=F*tan α where:
S= separating force (lb)
α= tooth pressure angle
Gear Classification
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Spur Gears: cylindrical gears with teeth that are straight and
parallel to the axis of rotation. Spur Gears are the most common type of gear in use. The spur gear is manufactured
on a cylindrical blank and is used in applications where input and output are in parallel planes, i.e. they
are used to transmit motion between parallel shafts. The teeth generally have full-face contact though
length-wise crowning is possible. Spur gears are used to drive externally where the pinion and gear mating
surfaces are located on the outside diameter or they drive internally where the outside diameter of
one member drives the inside diameter of the other member such as in a planetary system. Spur gears tend to be noisy at higher speeds.
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Helical Gears: cylindrical shape also but their teeth are set
at an angle to the axis. The helix angle on a helical gear was introduced to achieve higher performance
out of parallel axis gear sets. The helical tooth form brings more teeth into mesh than a spur gear
is capable of. This load sharing increases the overall power capability of the gear set and also
allows for quieter, smoother operation at high speeds.
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