Gears

   

Gears are machine elements, which are used for power transmission between shafts, separated by small distance. Irrespective of the type, each gear is provided with projections called teeth and intermediate depressions called tooth spaces. While two gears are meshing, the teeth of one gear enter the spaces of the other. Thus, the drive is positive and when one gear rotates, the other also rotates; transmitting power from one shaft to the other.

Gears are classified on the basis of the shape of the tooth profile and the relative position of the shafts between which, power transmission takes place. The pictorial views of some of the most commonly used gear trains, are shown in Fig.



   

Gear Nomenculature

Figure shows the parts of a spur gear



 
 Fig shows two spur gears in mesh; indicating all the terms associated with the gearing. These terms are also applicable to all types of gears.A number of curves may be used for the tooth profile. However, from a commercial stand point, cycloidal and involute curves are used. Of these two, involute form is extensively used because  of its advantages from manufacturing and operational points of view.





 
Involute is a curve traced by a point on a straight line when it rolls without slipping, on the
circumference of a circle. Figure 13.6 shows the stages in drawing the involute tooth of a gear.
 

The following are the steps involved in the construction.

   

 




 1. With O as centre and radius equal to the pitch circle radius, draw an arc.
2. At any point P on it, drawn a line T-T, tangential to the above arc.
3. Through the point P, draw the line of action N-N, making an angle equal to the pressure angle φ,
with the tangent line T-T.
4. From the centre O, draw the line OQ, perpendicular to the line of action (it will make an angle φ
with OP).
5. With O as centre and radius equal to OQ, draw an arc, representing the base circle.
6. With O as centre, draw arcs, representing addendum and dedendum circles.
7. Starting from any point on the base circle, construct an involute curve, as shown at X.
8. Trace the curve and a part of the base circle, on a piece of tracing paper, as shown at Y.
9. On the pitch circle, mark points 1, 2, 3, 4, etc., separated by a distance equal to half of the
circular pitch.
10. Place the tracing paper, such that the arc AB coincides with the base circle and the curve passes
through the point 1.
11. Prick a few points on the curve, lying between the addendum and base circles.
12. Join these points by a smooth curve.
13. Draw a radial line below the base circle and join it with the bottom land, by means of fillet of
radius r, which may be taken as 0.125 pc.
14. Reverse the tracing paper, follow the steps 11 to 13 and complete the curve through the point 2;
obtaining one tooth profile.
15. Repeat the steps 11 to 14 and construct the other tooth profiles.

Approximate construction of tooth profiles

Often it is necessary to draw the teeth on a pair of meshing gears, to understand the problems
involved in the meshing of the mating teeth. Further, the drawings are not used for producing
the teeth in the shop. Hence, approximate constructions may be followed to draw the tooth
profiles. The following are the steps involved in the construction:

 Case 1 Number of teeth is 30 and above (Fig.13.7)

1. With O as centre, draw arcs representing dedendum, pitch and addendum circles.
2. At any point on the pitch circle, mark a point P.
3. With OP as diameter, draw a semi-circle.
4. With centre P and radius equal to 0.125× pitch circle diameter (D), draw an arc, intersecting the
semi-circle at Q.
5. With O as centre and radius OQ, draw an arc. The centres of arcs for the tooth profiles, lie on this
arc and the radius for the arc is 0.125D.
6. On the pitch circle, mark points 1, 2, 3, 4, etc., separated by a distance equal to half the circular
pitch.


 

7. With each of these points as centres, and radius equal to 0.125D, locate the centres 1′, 2′, 3′, 4′,
etc., for arcs, on the circle for centres (passing through Q).
8. With 1′, 2′, 3′, 4′, etc., as centres and radius equal to R, draw arcs, passing through the points 1,
2, 3, 4, etc.
9. Add the top lands and join the arcs with the bottom land, by a fillet of radius r, equal to
0.125 pc.

Case 2 Number of teeth is less than 30

1. Follow the steps 1 to 8 as described above.
2. From O, draw lines, tangential to the above arcs.
3. Add the top lands and join the above lines with the bottom land, by a fillet of radius equal
to 0.125 pc.



Approximate construction of tooth profile (number of teeth less than 30)