Calculation gears are similar,
particularly in the spur gear and helical gear. Therefore, Spur gear
description will focus more on the basis of mechanical gears size calculations,
while for the strength calculation of the gear will be described in more detail
in the calculation of helical gear. (Read more: calculation of helical gear)
The main parameters of the spur
gear is the pitch circle or module, pitch diameter, outside diameter, root
diameter, whole depth, addendum and dedendum as shown in the following figure:
Standard dimension of spur gear
Main dimensions of spur gear is
expressed with a pitch diameter is an imaginary circle that rolls without
slipping as a point of meeting two tooth profile pairs. The tooth size is
expressed by the pitch circle is the distance along the circle of the distance
between two profiles of adjacent teeth. Pitch circle is a circle which has the
radius of half the pitch diameter with its center at the axis of the gear. The
relationship between pitch diameter and pitch circle can be seen by the
following equation:
C = Pitch circle (mm)
D = Pitch
Diameter (mm)
T = Number of Teeth
The tooth size may
be determined from the amount of
pitch circle, because the pitch circle is the
circumference of a pitch divided by the number of tooth. However,
because the pitch circle always contains
π factor used as
a dimension of the tooth is less
convenient. To remedy this, take
a measure called ‘module’ with the M symbol, where:
M = Module
D = Pitch
Diameter (mm)
T = Number of Teeth
Thus, M (module) can be specified as integers and
fractions numbers of 0.5 and 0.25 are more
practical. Therefore π * M = C, the module can be used as size of the tooth.
Selection of the
module will
affect the gear strength,
so election gear module must be in
accordance with the power
requirement and speed of pinion gear. The modules can be selected through the curve selection module below.
In the selection
of modules
recommended to opt for the larger size of the modules obtained in the graphic selection module above.
Other standard dimension
required in the design of the
spur gear is calculated based on the modules, including:
==> Outside diameter, it is the overall diameter of the gear which is
the pitch circle plus two addendums. Its relationship with module can be
described by formula:
Do = Outside diameter (mm)
M
= Module
D
= Pitch diameter (mm)
==> Root diameter, it is the diameter of the root circle that is the
circle formed by the bottoms of the tooth spaces. Its relationship with module
can be described by formula:
Dr
= Root diameter (mm)
M
= module
D
= Pitch diameter (mm)
C
= Clearance
==> Addendum, it is the radial distance between the pitch circle and
the outside diameter or the height or the tooth above the pitch circle. The addendum
is equal to the module by formula:
Ad
= Addendum (mm)
M
= module
==> Dedendum, it is the radial
distance from the pitch circle to the bottom of tooth space. The dedendum is
equal to the module plus the clearance by formula:
Dd
= Dedendum (mm)
M
= module
C
= Clearance
==> Whole depth, it is the
full depth of the tooth or the distance equal to the addendum plus dedendum.
The whole depth is equal to two module plus clearance by formula:
H = Whole depth (mm)
M
= Normal module
C
= Clearance
A spur gear transmission system is connecting the two shafts by gear and pinion.
Pinion and gear must be has the same module, while other
sizes are adjusted according to the
gear ratio. Gear ratio is comparing the speed ratio or the pitch
diameter ratio or the number of
teeth ratio. Gear ratio may be expressed
by the formula:
i
= Gear ratio
n1
= Speed of pinion (rpm)
n2
= Speed of gear (rpm)
T1
= Number of teeth of pinion
T2
= Number of teeth of gear
D1=
Pitch diameter of pinion (mm)
D2
= Pitch diameter of gear (mm)
In the standard of spur gear transmission,
the value of gear ratio can be taken 4 to
5 and can be expanded to 7
to change the profile offset of gear.
In the helical gears and double helical
gear, the ratio could reach 10.
The gears are generally used for the reduction of (i > 1); but
sometimes it is used to speed up of (i < 1). As regards
the construction machines, the gear
ratio is influenced by the center
distance and the pitch diameter
of the pinion and gear that can be
expressed by the following equation:
CD
= Center Distance (mm)
D1=
Pitch diameter of pinion (mm)
D2
= Pitch diameter of gear (mm)
Spur gear strength for deflection and surface pressure
Spur gear will
be damaged such as broken teeth, worn, perforated surface and a scratch due to
the rupture of lubricating oil
membranes. The strength of the tooth that must be considered is the
strength of deflection and surface pressure
and the strength against scratches, especially
for wide loading and high speed gear.
The calculation
of the spur
gear strength for deflection load and surface pressure can be used in the calculation of helical gear formulas.
(Read more: calculation of helical gear)
The only difference is the velocity factor in which for spur gear has its own formula based
on the level of the speed of pinion
gear (V), namely:
==> Low
speed, its speed between V = 0,5 to 10 m/s has velocity factor formula:
==> Middle
speed, its speed between V = 5 to 20 m/s has velocity factor formula:
==> High
speed, its speed between V = 20 to 50 m/s has velocity factor formula:
That is a description about Spur Gear Design: Spur Gear Dimension and Strength. If you find misconceptions in the spur gear formula, please provide the correction in the comment box.
Very Useful , practical and accurate! Many thanks!
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