The involute gear is very popular in
industry. In this gear design article, we will define the involute gear and
will discuss the design, applications, and advantages of the involute gear.
Based upon the profile of the spur
gear teeth, gear can be classified in two major categories: involute gear and
cycloidal gear.
Geometrically an involute curve can
be generated by the locus of the endpoint of a virtual taut string unwinding
from its circular roll. Another way of visualizing the involute curve is
visualizing the locus of the end point of a stick, moving around the periphery
of a wheel without slipping. The involute curve generating process we have just
discussed will create a curve like below:
Using AutoCAD or any of the 2D CAD
package you can create involute gear teeth. Before going further, let’s assume
the following data:
○ Root circle diameter (R1) = 14 mm
○ Base circle diameter (R2) = 15.34 mm
○ Pitch circle diameter (R3) = 15.87 mm
○ Outside diameter (R4) = 17.46 mm
○ Number of teeth (N) = 18
Now, let’s go to the actual procedure:
○ Draw the root circle, base circle, pitch circle
and the outside diameter with common centre.
○ Draw a horizontal line (ACB) passing through the
centre and touching the outside diameter.
○ Trim the left side of the line after the centre.
Now the line becomes AC.
○ Draw a small perpendicular line (AD) to the line
AC and at the point A. The length of the line AD is equal to 1/40 times the
diameter of the base circle or equals to 0.38 mm.
○ Now, calculate:
θ = 360/ (Π* 40) Degree
= 2.86 Degree
This θ will be
used later in the process of the involute curve generation.
○ Radially copy the lines AD and AC fourteen times
with spacing between them of 2.86 degrees.
○ Number the lines by 0, 1 …..14.
○ Now, you have to increase the lengths of the
small lines (AD). How long? Multiply the original length of each line with its
index. So, the length of the 0th line will be 0, the length of the 1st line
will be 0.38mm, the length of the 2nd line will be 0.76mm and
so on. Similarly the length of the 14th line will be 5.32 mm.
○ Join the endpoints of the each line by smooth
curve and you will get a curve (AI) involute like below:
○ Now, trim the involute curve beyond the outside
diameter.
○ Draw a line (EA) joining the intersecting point
of the involute curve and the centre. Radially, copy the line by ¼ times the
angular pitch. For us the angular pitch is 180. So we will copy the line by
4.50. Now mirror the line EA and the involute curve AI.
○ Now trim the unnecessary lines and you can see one involute gear tooth. Copy the tooth radially 18 times and you will see the involute gear.
Involute gears are manufactured by
gear hobbing process. The cutting tool is called hob. The hob looks
somewhat like a worm gear with non-continuous and hard threads.
Imagine you have a steel made worm
gear engaged with a thick wax disk and axis of the worm gear and the wax disk
is perpendicular to each other. Now, if you rotate the worm gear you
will see gear teeth are being generated to the wax disk. The hobbing process is
exactly similar to this. You will have a single thread cutter (hob) engaged
with a blank (tooth less gear), the angle between the axis of blank and that of
hob depends upon the helix angle of the spur gear to be generated.
Look at the typical hobbing machine
arrangement is below:
○ The contact between two mating involute gear
tooth moves along a fixed plane of contact irrespective of the centre to centre
distance of the gears. Thus involute gears can handle centre shifts or you will
get greater assembly flexibility.
○ Contact surface is always perpendicular to the
plane of contact, this helps reducing torque variation and thus involute gear
gives silent operation.
○ Manufacturing fairly accurate gears of this type
are quite easier by hobbing process.
○ Not suitable for lesser numbers of teeth.
○ Undercut or interference between the teeth may
occur for this gear in case addendum modifications are not performed properly.
○ Proper lubrication is required for avoiding the
high localized stress.
Except very small gears (used in
watches, toys, and electronics instruments), almost all the gears you will see
in automobiles, earthmoving equipment, and production machines are of involute
gear.
The involute gear is one of the most
widely used gears in industry. Ease of manufacturing, silent
operation, and ease of assembly are the major advantage of using involute
gears. However, the involute gear has a problem of undercut and overheating.
So, while doing gearbox design you must see if an involute gear is really suits
your application or not.