The document discusses various terms and measurements related to gear teeth. It defines terms like pitch circle, diametral pitch, module, addendum, dedendum, clearance, pressure angle, and helix angle. It also describes common methods for measuring individual elements of gear teeth, such as tooth thickness, pitch, and errors, using instruments like gear tooth calipers, constant chord method, and base tangent method. Sources of errors in gear manufacturing by generating and reproducing methods are also outlined.

1. MEASURMENTS AND TESTING
OF GEARS

2. Terminology of gear tooth
Gear tooth mainly used for transmission of power and motion.

3. Terminology of gear tooth

4. Terminology of gear tooth

5. Terminology of gear tooth
1. Addendum
2. Dedundum
3. Tooth Thickness
4. Pitch
5. Top land
6. Bottom Land
7. Face Width
8. Circular Pitch
9. Pitch Circle
10. Base Radius.

6. Terminology of gear tooth
Base Circle. It is the circle from which involute form is
generated. Only the base circle on a gear is fixed and
unalterable.

7. Terminology of gear tooth
Base Circle. It is the circle from which involute form is
generated. Only the base circle on a gear is fixed and
unalterable.

8. DO-outside diameter, D- pitch diameter, DB- base diameter, DR- root diameter,

9. Terminology of gear tooth
Pitch Circle Diameter (P.C.D.). It is the diameter of a circle
which by pure rolling action would produce the same motion
as the toothed gear wheel. This is the most important
diameter in gears.

11. Terminology of gear tooth
Module. It is defined as the length of the pitch circle diameter
per tooth. Thus if P.C.D. of gear be D and number of teeth N,
then
module (m)=D∕N . It is generally expressed in mm.
Diametral Pitch. It is expressed as the number of teeth per
inch of the P.C.D.
D.P.=D∕N , D expressed in inch.

13. Terminology of gear tooth
Circular Pitch (C.P.). It is the arc distance measured around
the pitch circle from the flank of one tooth to a similar flank in
the next tooth.
.’. C.P. = ∏D∕N=∏m

14. Terminology of gear tooth
Addendum. This is the radial distance from the pitch circle to
the tip of the tooth.
Its value is equal to one module.

16. Terminology of gear tooth
Clearance.
This is the radial distance from the tip of a tooth to the
bottom of a mating tooth space when the teeth are
symmetri­cally engaged. Its standard value is 0.157 m.
Dedendum.
This is the radial distance from the pitch circle to the bottom
of the tooth space.
Dedendum=Addendum+ Clearance
=m+0.157 m=l.157 m.

18. Terminology of gear tooth
Blank Diameter.
This is the diameter of the blank from which gear is a t. It is
equal to P.C.D. plus twice the addenda.
Blank diameter =P.C.D.+2m.
=mN+2m = m(N+2).

21. Terminology of gear tooth
Tooth Thickness. This is the arc distance measured along the
pitch circle from its intercept with one flank to its intercept
with t le other flank of the same tooth.
Normally tooth thickness.
=½ C.P.
=∏m∕2

22. Terminology of gear tooth
Face of Tooth. It is that part of the tooth surface which is
above the pitch surface.
Flank of the Tooth. It is that part of the tooth surface which is
lying below the pitch surface.

23. Terminology of gear tooth
line of action.
The teeth of a pair of gears in mesh, contact each
other along the common tangent to their base circles,
this path is referred to as line of action.

25. Terminology of gear tooth
Pressure angle ø.
The angle between the line of action and the common
tangent to the pitch circles is known as pressure angle ø.
Db=P.C.D × cosø
Db=base circle dia

28. Terminology of gear tooth
Pressure angle ø.
The angle between the line of action and the common
tangent to the pitch circles is known as pressure angle ø.
Db=P.C.D × cosø
Db=base circle dia

29. Terminology of gear tooth
Base Pitch. It is the distance measured around the base circle
from the origin of the involute on the tooth to the origin of a
similar involute on the next tooth.
Base Pitch=Base Circumference/ No. of teeth
=∏×Db/N
=∏×Dp cosø /N=∏mcosø.

30. Terminology of gear tooth
Involute Function.
It is found from the fundamental principle of the involute,
that it is the locus of the end of a thread (imaginary)
unwound from the base circle.
Involute function δ=tan ø—ø
Where ø is the pressure angle.

32. Terminology of gear tooth
Helix Angle : It is the acute angle between the tangent to the
helix and axis of the cylinder on which teeth are cut.

33. Terminology of gear tooth
Lead Angle : It is the acute angle between the tangent to the
helix and plane perpendicular to the axis of cylinder
LEAD ANGLE= 90­helix angle

34. Terminology of gear tooth
Back Lash : The distance through which a gear can be rotated
to bring its non­working flank in contact with the teeth of
mating gear

35. Anti backlash gear

36. Terminology of gear tooth
Helix Angle : It is the acute angle between the tangent to the
helix and axis of the cylinder on which teeth are cut.

38. Sources of Errors in Manufacturing Gears
The gears (gear teeth) are generally
made by one of the following two
methods :
(i) Reproducing method
(ii) Generating method,

39. Sources of Errors in Manufacturing Gears
Generating method, in which the cutting tool (hob forms
the profiles of several teeth simultaneously during
constant relative motion of the tool and blank.

40. Sources of Errors in Manufacturing Gears
Reproducing method, in which the cutting tool is form­ed
involve cutter, which forms the gear teeth profiles by
reproduc­ing the shape of the cutter itself.
In this method, each tooth space is cut independently of
the other tooth spaces,

42. Sources of Errors in Manufacturing Gears
The various sources of errors in the
gear made by reproducing method can
be due to
(i)incorrect profile on the
cutting tool,
(ii) incorrect positioning of the
tool in relation to the work and
(iii) incorrect indexing of the
blank.

43. Sources of Errors in Manufacturing Gears
The sources of error when gears are
made by generating method are :
(i) Errors in the manufacture
of the cutting tool
(ii) errors in positioning the
tool in relation to the work and
(iii) errors in the relative
motion Of the tool and blank
during the generating

44. Measurement of Individual elements
Measurement of tooth thickness
The permissible error or the tolerance on
thickness of tooth is the variation of actual
thickness of tooth from its theoretical value.
The tooth thickness is generally measured at
pitch circle and is therefore, the pitch line
thickness of tooth.
There are various methods of measuring the
gear tooth thickness.
(i) Measurement of tooth thickness by gear
tooth vernier calliper.
(ii) Constant chord method.
(iii) Base tangent method.
(iv) Measurement by dimension over pins.
Gear Tooth Caliper.
w=Nm. sin( 90∕N)
d= = Nm ∕2[1+2∕N− cos(90∕ N)]

45. Measurement of Individual elements
The Constant Chord Method.
c=constant chord=2A C
=∏/ 2 m cos2 ø
d=addendum—PC
=m—∏/ 4 m cos ø sin ø
=m(1­ ∏/ 4 cos ø sin ø )

46. Measurement of Individual elements
Base Pitch Measuring Instrument. This
instrument has three tips. One is the~!TX53
measuring tip, other one is the sensitive tip
whose position can be adjusted by a screw and
the further movement of it is transmitted
through a leverage system to the dial
indicator; and the third tip is the
supplementary adjustable stop which is meant
for the stability of the instrument and its posi­
tion cart also be adjusted by a screw. The
distance between­the
fixed and sensitive tip is set to be equivalent
to the base pitch of the gear with the help of
slip gauges. The properly set­up instrument is
applied to the gear so that all the three tips
contact the tooth profile. The reading on dial
indicator is the error in the base pitch.

47. Measurement of Individual elements
The Base Tangent Method. (‘David Brown’
tangent comparator). In this method, the span
of a convenient number of teeth is measured
with the help of the tangent comparator. This
uses a single vernier calliper
BD=Nm cos ø [tanø –ø −∏ ∕ 2N +∏ S ∕ N ]

48. Measurement of Individual elements