Measurement
and
Testing of Gears
Gear Terminology
A gear is a component within a transmission device that transmits rotational force to another gear or device.
Pitch Circle
An imaginary circle within the profiles of the teeth of a gear, such that it rotates against a similar circle rotating at the
same rate on a meshing gear.
Pitch Circle Diameter or Pitch Diameter
It is the diameter of the pitch circle. The size of a gear is usually specified by its pitch circle diameter.
Addendum
It is the radial distance of a tooth from the pitch circle to the top of the tooth.
Dedendum
It is the radial distance of a tooth from the pitch circle to the bottom of the tooth.
Addendum Circle ( Outside Circle)
It is the circle that bounds the outer ends of the teeth.
Dedendum Circle ( Root Circle)
It is the circle that bounds the bottom of the teeth.
Whole Depth
Whole depth = Addendum + Dedendum
Working Depth
It is the radial distance from the addendum circle to the working depth circle or clearance circle.
Clearance
It is the radial distance between working depth circle and root circle.
Circular Thickness or Tooth Thickness
It is the width of the tooth measured along the pitch circle.
Width of Space or Tooth Space
It is the space between teeth measured along the pitch circle.
Face Width
It is the length of teeth in an axial direction
Face
The face of the tooth is the surface of the tooth between the pitch cylinder and the addendum cylinder.
Flank
It is the surface of the tooth between pitch and root cylinder.
Module
It is defined as the length of the pitch circle diameter per tooth.
If D is the diameter of pitch circle and N is the number of teeth in gear, then
Module, m = D/N (mm)
Circular Pitch
Circular pitch is the distance from a point on one tooth to the corresponding point
on the adjacent tooth, measured along the pitch circle.
Circular pitch, Pc = πD/ N = πm
Diametral Pitch
It is the ratio of the number of teeth per inch of pitch diameter.
Diametral Pitch, Pd = N/D
Pitch Point
When a pair of gears are operating in mesh, the point of tangency between the two pitch circles is called pitch point.
Pressure Angle (φ)
It describes the direction of the force created by a driving gear acting upon its mesh. It is formed by a line drawn between
centers and a line drawn perpendicular to the “ line of action”, which is tangent to both base circles and includes the pitch
point.
Diameter of base circle = Pitch circle diameter × Cos φ
 When two gears are in mesh, the smaller is called the pinion and
the larger the gear
Velocity Ratio, mw
It is the angular velocity of the driver divided by the angular velocity of the driven gear.
For spur gear, this ratio varies inversely as the pitch diameters and as the tooth number.
mw = ω1/ ω2 = n1/n2 = D2/D1 = N2/N1
Gear Ratio, mg
Gear ratio is the number of teeth in the gear divided by the number of teeth in the pinion.
 When pinion is the driver, mg = mw
[ In case of Spur Gear, for Metric (Module) Gear ]
Involute Curve
Involute curve is a mathematical curve most commonly used for gear tooth profile. It is an arc generated from the base
circle, and described by lines drawn normal from this curve and tangent to the base circle – much like a string being
unwound from a cylinder.
Normal at any point of an involute is a tangent to the circle
Types of Gear
. According to the position of axes of the shafts a.
Parallel shafts
1.Spur Gear
2.Helical Gear
3.Rack and Pinion
b. Intersecting shafts
Bevel Gear
c. Non-intersecting and Non-parallel
Worm and worm gears
Spur Gear
•
Teeth is parallel to axis of rotation
•
Transmit power from one shaft to another parallel shaft
•
Used in Electric screwdriver, oscillating sprinkler, windup alarm clock, washing machine, clothes dryer etc.
Helical Gear
•
The teeth on helical gears are cut at an angle to the face of the gear.
•
This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears.
Herringbone Gear
 To avoid axial thrust, two helical gears of opposite hand can be mounted side by side, to cancel resulting thrust forces
 Herringbone gears are mostly used on heavy machinery.
Rack and Pinion
 Rack and pinion gears are used to convert rotation (from the pinion) into linear motion (of the rack).
 A perfect example of this is the steering system on many cars.
Bevel Gear
 Bevel gears are used to connect intersecting shafts. These are useful when the direction of a shaft's rotation needs to
be changed
 They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well
 The teeth on bevel gears can be straight or spiral
 Applications include locomotives, marine applications, automobiles, printing presses, cooling towers, power plants,
steel plants, railway track inspection machines, etc.
Straight and Spiral Bevel Gear
Worm Gear
 Worm gears are used to transmit power between non-intersecting shafts

Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc.
Measurement of tooth thickness
 Tooth thickness is generally measured at the pitch circle and is therefore, the pitch line thickness of the tooth
 The tooth thickness is defined as the length of an arc, which is difficult to measure directly
 In most of the cases, it is sufficient to measure the chordal thickness i.e, the chord joining the intersection of the tooth
profile with the pitch circle
Methods of measuring the gear tooth thickness
 Measurement of tooth thickness by gear tooth vernier caliper
 Constant chord method
 Base tangent method
 Measurement by dimension over pins
Measurement of tooth thickness by gear tooth vernier caliper
 The tooth thickness can be conveniently measured by a gear tooth vernier
 The gear tooth vernier has two vernier scales and they are set for the width (W) of the tooth and the depth (d) from
the top
Constant chord method
 If an involute tooth is considered symmetrically in close mesh with a basic
rack form, then it will be observed that regardless of the number of teeth
for a given size of tooth (same module), the contact always occurs at two
fixed point A and B. AB is known as constant chord
 The constant chord is defined as the chord joining those points, on opposite
faces of the tooth, which make contact with the mating teeth when the
centre line of the tooth lies on the line of the gear centres
In fig. PD = PF = Arc PF = ¼ × Circular pitch = ¼ × ( π × P. C. D)/ N = ¼ × π × m
Since AP is the line of action, i.e, it is tangential to the base circle , <CAP = ø
In right angled triangle APD, AP = PD Cos ø = (π/4) m Cos ø
In triangle PAC, AC = AP Cos ø = (π/4) m Cos2 ø
C = Constant chord = 2AC = (π/2) m Cos2 ø ,
ø = Pressure angle
For helical gear, constant chord = (π/2) mn Cos2øn
Where mn = normal module and øn = normal pressure angle
Now PC = AP Sin ø = (π/4) m Cos ø Sin ø
Then, d = addendum – PC = m - (π/4) m Cos ø Sin ø = m (1- (π/4) Cos ø Sin ø )
Also height of AB above pitch line = PC = (πm/4) Sin ø Cos ø = (πm/8) Sin 2 ø
Base tangent method
David Brown base tangent comparator
W = Nm Cos ø [ tan ø – ø – ( π/ 2N) + (πS/N)
Where, N = Number of teeth
m = Module
ø = Pressure angle
S = Number of tooth spaces contained in W