Gears Terminologies, Standards, Design, and Inspections

Gear Design
Terminologies, Standards, Gear Design,
Gear Inspections

Table of
Contents
Basic Gear
Terminologies
Gear
Designing
Gear
Drawings
• Drawing Formats
• AGMA Quality
Requirements
Gear
Inspection
• Introduction
• Definitions &
Nomenclature
References
• Tooth Design
• Designing Steps
• Design parameters
• Formulas & Dimension Sheets
• Gear Types &
Measurement
Methods
• Measurement
Process

Basic Gear
Terminologies
• Introduction
• Definitions &
Nomenclature

Introduction
Basic Gear Terminologies
Gears are machine parts / components that transmit
power between rotating shafts. The shafts can be parallel or non parallel.
• Gears are categorized on various basis, e.g.:
 Power to be transmitted
 Transmission direction (parallel, non-parallel, etc.)
 Torque
 Shaft Thrusts
 Transmission Ratio
 Costs, Noise, Smoothness of flow required

Introduction
• Some major gear types are as under:
External
Spur
Gears
Internal
Spur
Gears
Helical
Gears
Crossed
Helical
Gears
Straight
Bevel
Gears

Introduction
Spiral
Bevel
Gears
Hypoid
Bevel
Gears
Zerol
Bevel
Gears
Worm
Gears
• Some major gear types are as under:

Introduction
Following is a chronologically ordered list of basic terms used in gearing:
Specific terms used in designing & tolerancing are given in respective chapters.
• Pinion • Helical Gears • Face Width
• Ratio • External / Internal Gears • Clearance
• Diametral Pitch • Bevel Gears • Chordal Thickness
• Module • Worm Gears • Chordal Adendem
• Circular Pitch • Face Gears • Center Distance
• Pitch Diameter • Spiroid Gears • Lead Angle
• Adendum • Transverse Section • Base & Normal Pitch
• Deddendum • Axial Section • Axial Pitch
• Whole Depth • Normal Section • Root Diameter
• Pressure Angle • Base Circle • Backlash
• Helix Angle • Outside Diameter • Lead
• Spur Gears • Working Depth • Throat Diameter

Definitions & Nomenclature
• Pinion
• When two gears mesh together, the smaller of the two is called the pinion. The larger is
called the gear
• Ratio
• Ratio is an abbreviation for gear tooth ratio, which is the number of teeth on the gear
divided by the number of teeth on its mating pinion.
• Diametral Pitch
• A measure of tooth size in the English system. In units, it is the number of teeth per inch
of pitch diameter. As the tooth size increases, the diametral pitch decreases. Diametral
pitches usually range from 25 to 1.

• Module
• A measure of tooth size in the metric system. In units, it is millimeters of pitch diameter per
tooth. As the tooth size increases, the module also increases. Modules usually range from 1
to 25.

• Circular Pitch
• The circular distance from a point on one gear tooth to a like point on the next tooth, taken along
the pitch circle. Two gears must have the same circular pitch to mesh with each other. As they
mesh, their circles will be a tangent to one another.
• Pitch Diameter
• The diameter of the pitch circle of a gear.

• Addendum
• The radial height of a gear tooth above the pitch circle.
• Dedendum
• The radial height of a gear tooth below the pitch circle.
• Whole Depth
• The total radial height of a gear tooth (whole depth = addendum + dedendum).
• Pressure Angle
• It is the angle between a tooth profile and a radial line at its pitch point. In involute teeth, the
pressure angle is often described as the angle between the line of action and the line tangent
to the pitch circle.

• Spur Gears

• Helix Angle
• The inclination of the tooth in a lengthwise direction. (If the helix angle is , the tooth is
parallel to the axis of the gear and is really a spur-gear tooth.)
• Spur Gears
• Gears with teeth straight and parallel to the axis of rotation.
• Helical Gears
• Gears with teeth that spiral around the body of the gear.
• External / Internal Gears
• Gears with teeth on the outside of a cylinder are external gears.
• Gears with teeth on the inside of a hollow cylinder.

• Helical Gears

• Bevel Gears
• Gears with teeth on the outside of a conical-shaped body (normally used on  axes).
• Worm Gears
• Gear sets in which one member of the pair has teeth wrapped around a cylindrical body like screw
threads. (Normally this gear, called the worm, has its axis at  to the worm gear axis.)
• Face Gears
• Gears with teeth on the end of the cylinder.

• Bevel Gears

• Worm Gears

• Face Gears

• Sprioid Gears
• A family of gears in which the tooth design is in an intermediate zone between bevel, worm,
and face gear design. The Sprioid design is patented by the Sprioid division of Illinois
Tool Works, Chicago, Illinois.
• Transverse Section
• A section through a gear perpendicular to the axis of the gear.
• Axial Section
• A section through a gear in a lengthwise direction that contains the axis of the gear

• Sprioid Gears

• Transverse Section
• Axial Section
• Normal Section

• Normal Section
• A section through the gear that is perpendicular to the tooth at the pitch circle. (For spur gears, a
normal section is also a transverse section.)
• Base Circle
• A circle from which the involute tooth curve is generated or developed.
• Outside Diameter
• A diameter that contains the tops of the teeth of the external gears.

• Working Depth
• It is the depth of the engagement of two gears, or the sum of their addendums. The standard
working depth is the depth to which a tooth extends into the tooth space of a mating gear,
when center distance is standard.
• Face Width
• Dimension of the tooth face width that makes contact with the mating gear
• Clearance
• It is the radial distance between the top of the tooth and the bottom of a mating tooth
space, or the amount by dededum of a gear exceeds the adendem of the mating gear

• Chordal Thickness
• It is the length of the chord subtended by the circular thickness arc. The dimension
obtained when a gear tooth caliper is used to measure the tooth thickness at the pitch
circle.
• Chordal Adendem
• It is the radial distance from the circular thickness chord to the top of the tooth.
• Center Distance
• Shortest Distance between the non intersecting axis of the mating gears, or parallel axis
of spur gears and parallel helical gears, or the crossed axis of crossed helical gears or
worm gears.

• Lead Angle
• It is the angle between a tangent to the helix and a plane perpendicular to the axis. Lead
angle is  to the helix angle between the helical tooth face and an equivalent spur tooth
face. For the same lead, the lead angle is larger for smaller gear diameters.
• Base & Normal Pitch
• Circular pitch taken on the circumference of the base circles, or the distance between the
line of action between two successive and corresponding involute tooth profiles. The
normal base pitch is in the normal plane and the axial base pitch is in the axial plane.

Lead Angle

• Axial Pitch
• It is the distance parallel to the axis of the between corresponding sides of adjacent teeth.
• Root Diameter
• It is the diameter of the circle that contains the roots or bottoms of the tooth spaces.
• Backlash
• It is the shortest distance between the non driving surfaces of adjacent teeth when the
working flanks are in contact.

• Axial Pitch

• Backlash

• Throat Diameter
• The throat diameter is the diameter of the addendum circle at the central plane of a wormgear
or of a double-enveloping wormgear.
• Lead
• Lead is the axial advance of a helix / worm gear tooth during one complete turn (36), that
is, the Lead is the axial travel (length along the axle) for one single complete helical / worm
revolution about the pitch diameter of the gear.

• Throat Diameter
• Lead

Gear
Designing
• Tooth Design
• Designing Steps
• Design parameters
• Formulas & Dimension Sheets

Gear Designing
Basics
In this chapter we will look at gear designing from the following perspectives:
1
43
2
BASIC GEAR
TOOTH DESIGN BASIC GEAR
DESIGN STEPS
FORMULAS &
DIMENSION
SHEETS
GEAR DESIGN
PARAMETERS

Gear Designing
Tooth Design
The things that should be considered during tooth design are illustrated below.
Note: Some definitions of the above parameters have been discussed. While others are self explanatory.

Gear Designing
Tooth Design
Gear teeth are a series of cam surfaces that contact similar surfaces on a mating gear in an orderly
fashion. To drive in a given direction and to transmit power or motion smoothly and with a minimum
loss of energy, the contacting cam surface on mating gears must have the following properties:
• The height and the lengthwise shape of the active profiles of the teeth (cam surfaces) must
be such that, before one pair of teeth goes out of contact during mesh, a second pair will
have picked up its share of the load. This is called continuity of action.
• The shape of the contacting surfaces of the teeth (active profiles) must be such that the
angular velocity of the driving member of the pair is smoothly imparted to the driven member
in the proper ratio. The most widely used shape for active profiles of spur gears and
helical gears that meets these requirements is the involute curve. There are many other
specialized curves, each with specific advantages in certain applications.
Basic Considerations

Gear Designing
Tooth Design
• The spacing between the successive teeth must be such that a second pair of tooth
contacting surfaces (active profiles) is in the proper position to receive the load before
the frrst leave mesh.
Basic Considerations

Gear Designing
Tooth Design
Continuity of Action
Control of continuity of action is achieved in spur gears by varying:
• The slope of line of action (Or the operating pressure angle)
• The outside diameters of pinion and gear
• The shape of the active profile
• The relative sizes of the limit diameter and undercut diameter circles (limit circle must be
larger)
In case of helical gears the control is maintained by above mentioned parameters along the
transverse plane along with:
• The lead of tooth (In axial plane)
• The length of tooth (In axial plane)

Gear Designing
Tooth Design
To assure continuity of action, the portion of the line of action bounded by the outside
diameter circles (the straight-line segment ab) must be somewhat longer than the base pitch.

Gear Designing
Tooth Design

Gear Designing
Tooth Design
Continuity of action is checked by calculating the contact ratio. It is numerically calculated by
dividing the length of line of action by the base pitch of the teeth. This is called contact ratio.
mp. AGMA recommends that the contact ratio for spur gears not be less than 1.2:
mp =
La
Pb
⩾ 1.2

Gear Designing
Tooth Design
Equations of Contact Ratios are as follows:

Gear Designing
Tooth Design
Conjugate Action
Many different shapes of surfaces can be used on the teeth to produce uniform transmission
of motion. Curves that act on each other with a resulting smooth driving action and with a
constant driving ratios are called conjugate curves. The fundamental requirements governing the
shapes that any pair of these curves must have are summarized in Willis Basic Law of
Gearing (1841) which states that:
“Normals to the profiles of mating teeth must, at all points of contact, pass through a fixed
point located on the line of centers.”
This requirement is satisfied by involute and cycloidal family of curves. Now-a-days only
involute curves are used for spur and helical gears. For Worm gears, the teeth are made
conjugate to the worm.

Gear Designing
Tooth Design
Pitch Diameters
Pitch Diameters are the starting points of most tooth designs. It is related to base circle
which is the fundamental circle, by the relationships that follow.
Standard Pitch Diameter:
D=
N
Pd
D = Dia of Standard Pitch Circle
Pd = Diametral Pitch of basic rack
N = No. of teeth in gear

Gear Designing
Tooth Design
Pitch Diameters
Operating Pitch Diameter:

Gear Designing
Tooth Design
Involute Gear Tooth Development

Gear Designing
Tooth Design
Pointed Teeth
Gear Cutters are “Fed in” or “Held out” to produce pointed teeth or gears with long
addendum. It is usually done to achieve higher tooth thickness while maintaining the continuity.

Gear Designing
Tooth Design
Undercut
It is given for manufacturers ease as different cutters produce different amounts of undercuts
In some cases, it is used to control tip clearance of meshing gears.

Gear Designing
Tooth Design
Long and Short Addendum Gear Design
Modification of addendum of the pinion serves the following purposes:
• Meshes in which the pinion has a few teeth
• Meshes operating on non standard center distances because of limitations on ratio or
center distances
• Meshes of speed-increasing drives
• Meshes designed to carry maximum power for the given weight allowance.
• Meshes in which an absolute minimum of energy loss through friction is to be achieved.

Gear Designing
Tooth Design
Long and Short Addendum Gear Design
Modification of addendum of the pinion serves the following purposes:

Gear Designing
Tooth Design
Special Considerations
Factors to be considered during the evolution of the gear design:
• Interchangeability
• Tooth Thickness
• Tooth Profile Modifications
• Allowances for errors of gear manufacturer
• Allowances for deflection under load
• Axial Modifications (Crowning)
• Root Fillets (Fatigue Strength)
• Effective Outside Diameter
• Width of Tip of tooth
• Pointed tooth Diameters

Gear Designing
Tooth Design
Purpose of Backlash
Backlash is the lost motion between mating gear teeth. It may be measured along the line of
action or on the pitch cylinder of the gears (transverse backlash). In case of helical gears,
normal to the teeth. Establishment of backlash requirements of gearing needs following
considerations:
• Min and Max Center Distances
• Tooth Thicknesses

Gear Designing
Tooth Design
Standard Tooth Proportions (Spur)

Gear Designing
Decide which
Pressure Angle to
use.
Get application requirements:
• Ratios
• Input Speed
• Kind of duty (Power
Transmission or transfer
of motion
1
2
3
4 5
6
Pick Aprox. No. of teeth
Determine Aprox Center
Distance and Face Width
On basis of pinion teeth
and center distance
determine aprox. Pitch.
(Use standard and adjust
teeth and center distances)
Determine whole depth of
pinion and gear
Tooth Design Steps

Gear Designing
Determine operating
circular pitch
Determine Addendum of
pinion and gear. Use long
addendum to avoid undercut
7
8
9
10 11
12
Determine Design Tooth
Thickness
Recheck Design load
capacity using design
proportions obtained.
If power gearing determine:
• Root fillet radius
• Form dia
• Modification profile
• Dia over pins
Determine some general
dimensions:
• Outside Dia
• Root Dia
• Face Width
• Chordal
Addendum &
Chordal
Thickness
Tooth Design Steps

Gear Designing
In unusual Designs these may
calculated as well:
• Dia at which teeth
become pointed
• Width of top land
• Effective Contact
Ratio
• Undercut Dia
It may be necessary to
calculate:
• Tip Round
• Edge Round
• Roll Angle
• Base Radius
13
14
Tooth Design Steps

Gear Designing
Gear Design Steps
1
2
3
4
5
6
7
8
1. Design of Gear
Parts
4. Design of
Lubrication Systems
2. Design of
Casing Structures
3. Design of
Bearings
8. Definition of acceptable
or unacceptable results
5. Design of
Seals, Bolts, Dwell
Pins etc
7. Specs of gear
running test procedures
6. Specs. Of assembly
procedures

Gear Designing
Gear Design Parameters
• No. of pinion Teeth
More Teeth means:
- Less Noise
- Better Resistance to wear
Less Teeth Means:
- Increased tooth strength
- Lower cutting costs
- Larger tooth dimensions
Durability must be balanced with strength
when deciding about no. of teeth

Gear Designing
• Hunting Teeth • Hunting is required in low
hardness gears
• One member contacts all the
teeth of the mating member
• This equalizes wear and
improves spacing accuracy
• There should be no common
factor b/w mating gears

Gear Designing
• Long Addendum Gears
A pinion
in which
the
addendum
is longer
than that
of mating
gear
Greater than 1.m design
Mate with short addendum gears
The amount of elongation is same as the shortening of gear
addendum
Avoids undercut which is harmful in gear design as it is a low strength
and wear design with increased risks of interference
Highest sliding velocity and max. compressive strength occurs at the
bottom of the tooth, this can be avoided by using a long addendum
pinion which allows active involute to start farther from base circle

Gear Designing
• Backlash
Generous
backlash
in power
gearing
should be
used
Enough to turn the gears freely at
shortest center distance
Should enable gearing in worst
condition of temperature and tooth error

• Spur Gears
Gear Design Formulas & Dimension Sheets
Gear Designing

• Helical Gears
Gear Designing

• Internal Spur Gear
Gear Designing

• Worm Gear
Gear Designing

• Double Enveloping Worm Gear
Gear Designing

Gear Designing

Gear
Drawings
• Drawing Formats
• AGMA Quality
Requirements

Gear Drawings
Standard Formats
• Spur and Helical

Gear Drawings
Standard Formats
• Straight Bevel Gears

Gear Drawings
Standard Formats
• Spiral Bevel Gears

Gear Drawings
Standard Formats
• Single Enveloping Worm Gears

Gear Drawings
Standard Formats
• Double Enveloping Worm Gears

Gear Drawings
Standard Formats
• Symbols and terms for specifying form, runout and center distance tolerances

Gear Drawings
Standard Formats
• Specifying Datum Axis

Gear Drawings
Standard Formats
• Specifying Form Tolerances for datums and mounting surfaces

Gear Drawings
Standard Formats
• Specifying runout Tolerances for mounting surfaces

Gear Drawings
Standard Formats
• Specifying shaft parallelism tolerances

Gear Drawings
AGMA Quality Requirements
Definitions
1
2
34
5
1. Cumulative pitch deviation, total (Fp)
• The largest algebraic difference
between the index deviation values
for a specified flank.
4. Gear Form Filter Cutoff
• Wavelength at which
either involute profile or
helix measurement data
are segregated by low
pas filter
2. Design Helix and Design
Profile
• Helix and Profile specified by
the designer, if not specified it
is an unmodified helix & involute
3. Functional Profile and its
length
• Portion of tooth flank
between profile control
diameter and start of tip
break
5. Helix Deviation
• Amount by which a
measured helix deviates
from the design helix

Gear Drawings
Definitions
6
7
89
10
6. Helix Deviation, Total (Fβ)
• Distance between two helix lines
which enclose the actual helix trace
over the evaluation range Lβ
. Helix Length of trace
• full facewidth is limited toward the
ends of the teeth by the end faces or,
if present, the start of end chamfers,
rounds, or other modification
intended to exclude that portion of
the tooth from engagement.
7. Helix evaluation range (Lβ)
• Helix length of trace shortened
at each end by the smaller of
the two values; 5% of helix
length of trace, length equal to
one module
8. Helix form deviation (ffβ)
• Distance between facsimiles of
mean helix line, which are each
placed at constant separation
from mean helix line, so as to
enclose the actual helix trace
over evaluation range
1. Helix Slope Deviation, fHβ
• Distance between two design
helix lines which intersect at
the mean helix line at the end
points of evaluation range

Gear Drawings
Definitions 11. Index Deviation
• Displacement of any tooth flank
relative from its theoretical position,
relative to a datum tooth flank
14. Profile Control Diameter
• A specified dia of the circle beyond
which the tooth profile must conform
to the specified involute curve
12. Mean Helix Line
• A line or a curve that has the
same shape as the design helix,
but aligned with the measured
trace
13. Mean Profile Line
• A line or a curve that has the
same shape as the design
profile, but aligned with the
measured trace
15. Profile Deviation
• Amount by which a measured
profile deviates from the
design profile.
11
12
1314
15

Gear Drawings
Definitions 16. Profile Deviation, Total (Fα)
• Distance between two profile lines
which enclose the actual profile trace
over the functional profile length Lαc
1. Profile Slope Deviation (fHα)
• Distance between two design profile
lines which intersect at the mean
profile line at the end points of
functional profile length.
17. Profile Evaluation Range
• The profile is evaluated over
the specified functional profile
length
18. Profile form deviation (ffα)
• Distance between facsimiles of
mean profile line, which are each
placed at constant separation
from mean profile line, so as to
enclose the actual profile trace
over functional profile length
2. Roll Path Length
• The linear distance between
along a base tangent line from
its intersection with the base
circle to the given point on the
involute curve in the transverse
plane
16
17
1819
20

Gear Drawings
Definitions
21. Single flank composite test (SFCT)
• A test of transmission error,
performed where mating gears are
rolled together, at their proper center
distance, with backlash, and with only
the driving and driven flanks in
contact
24. Single pitch deviation (fpt)
• The displacement of any tooth flank
from its theoretical position relative
to the corresponding flank of an
adjacent tooth
22. Single flank composite
deviation, tooth--to--tooth
(filtered), (fis)
• The value of greatest single
flank composite deviation over
any one pitch after removal of
long term component, SFCT
when the gear is moved one
revolution
23. 3. Single flank composite
deviation, total (Fis)
• The maximum measured
transmission error range during
a SFCT, when the gear is
moved through one revolution
25. Tolerance diameter dT
• The diameter located one
normal module below the
design outside diameter
21
22
23
24
25
26
26. Start of tip break
• Minimum specified diameter at
which the tip break can occur.
Ref: 112-F

Gear Drawings
AGMA Quality Grade

Gear Drawings
AGMA Quality Grade
• The grading system designates numbers from 2 to 11 in decreasing order of accuracy
• To find the tolerance grades a factor, Sqrt (2), can be multiplied or divided
• The tolerances are applicable for the following ranges:
• Accuracy grades A2 through A11:
0.5 ≤ mn ≤ 50
5 ≤ z ≤ 1000 or 10 000/mn whichever is less
5 ≤ dT ≤ 10 000 mm

Gear Drawings
Tolerances
Tolerance Parameter Tolerance Equations
1. Cumulative pitch deviation
tolerance, total FpT
2. Helix form tolerance ffβT
3. Helix slope tolerance fHβT
4. Helix tolerance, total FβT
5. Profile form tolerance ffαT

Gear Drawings
Tolerances
Tolerance Parameter Tolerance Equations
6. Profile slope tolerance fHαT
7. Profile tolerance, total FαT
8. Single flank composite tolerance,
tooth--to--tooth fisT
. Single flank composite tolerance,
total FisT
10. Single pitch deviation tolerance fptT

Gear
Inspection
• Gear Types &
Measurement
Methods
• Measurement
Process

Accuracy
Group
Grade
Designator
Minimum Acceptable Parameters Alternative
Method
Low (L) A1-A-11 • Cumulative Pitch Deviation, Total (FP)
• Single Pitch Deviation (fpt)
• Tooth Thickness, s
Group M,
Group H
Medium (M) A6-A • Cumulative Pitch Deviation, Total (FP)
• Profile Deviation, total (Fα)
• Helix Deviation, total (Fβ)
Group H
High (H) A2-A5 • Cumulative Pitch Deviation, Total (FP)
• Profile Deviation, total (Fα)
• Helix Deviation, total (Fβ)
• Profile Form Tolerance (ffα)
• Profile Slope Tolerance (fHα)
• Helix Form Tolerance (ffβ)
• Helix Slope Tolerance (fHβ)
cp,, Fis, fis, s
Gear Inspection
Gear Types and Measurement Methods

Gear Inspection
Gear Types and Measurement Methods

Gear Inspection
Measurement Process
Measurement
Methods
Single Probe (indexing pitch method)
Two Probe
Generative Profile Measurement
Coordinate Profile Measurement
Portable Involute Measurement
Projection method of profile Measurement
Measurement over or between pins, and wires
Multiple chordal thickness Measurement
Measurements of Helix Deviations
Single and Double Flank Measurements

Gear Inspection
Measurement Process
• Measurement of Pitch Deviations
• Single Pitch (fpt) and Cumulative Pitch (FP) are elemental parameters relating to
the accuracy of the tooth locations around a gear. There measurements are made:
• Relative to the datum axis of the gear
• At the tolerance diameter dT
• In the specified tolerancing direction (within the transverse plane along the arc of
tolerance diameter)
• The measurements are made by either single probe or two probe methods

Gear Inspection
Measurement Process
• Single Probe (Indexing Pitch Method)
• It uses an indexing apparatus (Index Plate, circle divider, optical encoder, polygon
and auto collimator) to precisely rotate the gear by an angular increment equal to its
pitch.
Single Probe Method

Gear Inspection
Measurement Process
• Subtraction of each successive pair of index values produces a the plus and minus
values of single pitch deviation
Single Probe Method

Gear Inspection
Measurement Process
• The total cumulative pitch deviation is equal to the difference between the most
positive and the most negative index value for the complete gear
Single Probe Method

Gear Inspection
Measurement Process
• Single Probe Method
• Hypothetical table constructed by the application of single probe method
Two Probe Method

Gear Inspection
Measurement Process
• Two Probe Method
• Two probe devices are hand held or mechanized, probes are oriented to contact the
adjacent tooth flanks at the tolerance diameter. One probe establishes reference
flank, the other probe is fitted with an indicator to measure variations from the first
Two Probe Method

Gear Inspection
Measurement Process
• The values obtained from comparator method do not indicate single pitch deviation
until adjusted to true position pitch pm (Value obtained after dividing the average of
tooth pair measurements by the no. of teeth)
• The measurements are made in normal plane for the this method
• Single pitch deviation for each pair is obtained by subtracting tooth pair
measurement from pm resulting in plus and minus values of single pitch deviations
• Index values and cumulative pitch deviation value is measured as described in the
single probe method
Two Probe Method

Gear Inspection
Measurement Process
• Hypothetical table constructed by the application of two probe method
Two Probe Method

Gear Inspection
Measurement Process
• Two Probe Method for Normal Base Pitch Measurement
• It is a localized composite observation of gear tooth flank accuracy. Localized, as
the observation is made on a single point on the tooth flank, composite, as it
combines the effects of involute, profile, helix and pitch into a single measurement
• It directly relates to the gears ability to achieve smooth, conjugate meshing action
with its mate
Two Probe Method

Gear Inspection
Measurement Process
• The theoretical normal base pitch can be calculated as follows:
• pbn = mn cos αn
• pbn = Theoretical Normal Base Pitch
• mn = Normal Module
• α n = Normal Pressure Angle
Two Probe Method

Gear Inspection
Measurement Process
• Using this method allows us to calculate a variety of quality related parameters
including:
Two Probe Method

Gear Inspection
Measurement Process
• Measurement of Profile Deviations
• Profile is the shape of the tooth flank from its root to its tip. While, the functional
profile is the operating portion, which is in actual contact during tooth mesh, and
cannot extend below the base cylinder
• Profile deviation is the difference between the specified and measured profile of
the gear. The deviations are recorded in transverse plane

Gear Inspection
Measurement Process
• Generative Profile Measurement Method
• It requires tangential movement of a measurement probe, within the plane tangent to
the base cylinder of the given gear, together with a rotational movement of the gear
mounted on the instrument spindle.
• Linear movement is equal to the distance along the circumference of the base circle
diameter associated with the rotational movement
Generative Profile Method

Gear Inspection
Measurement Process
• Generative Profile Measurement Method
• The instruments employ a master involute cam or master base circle. CNC
electronic drive system is also used to generate a nominal involute curve
• The measurements are always relative to the datum axis of the gear
Generative Profile Method

Gear Inspection
Measurement Process
• Portable Involute Profile Measurement Method
• These are portable measurement machines that measure profiles by accurately
mounting gears on centers. They operate on a variety of generative and non
generative methodologies.
Portable Involute Profile Method

Gear Inspection
Measurement Process
• Profile Diagram
• Amplified traces of profile inspection results graduated for rolling path lengths or
degrees of roll
• Excess material is a plus deviation and insufficient material a minus deviation
Profile Diagram

Gear Inspection
Measurement Process
Profile Diagram

Gear Inspection
Measurement Process
Profile Diagram
• Evaluation of Profile Diagram
• The total profile deviation can be calculated directly while for other measurements it
may be necessary to superpose mean profile line onto the profile diagram and
measure all the necessary parameters

Gear Inspection
Measurement Process
Projection Method
• Projection Method
• Shadow of gear tooth under inspection may be magnified and directly projected for
profile comparisons to a large scale layout of a specific profile. It is normally
applied to fine pitch gears

Gear Inspection
Measurement Process
Indirect Profile Inspection
• Multiple thickness measurement
• The chordal tooth thickness and associated addendum depth for several positions
on a tooth may be computed for a gear tooth caliper. Comparison with computed
values indicate profile accuracy

Gear Inspection
Measurement Process
• Auxiliary Gaging Elements
• The theoretical position of wires, rolls, pins or balls of several different diameters
placed in a tooth space may be computed and compared to actual measurements

Gear Inspection
Measurement Process
• Limitations
• These methods cannot indicate the specific profile which has errors, since two
flanks of a measured tooth are contacted at the same time
• They do not indicate deviations that cancel each other, such as those caused by a
form cutter, which has been offset from a true radial position

Gear Inspection
Measurement Process
• Measurement of Helix Deviations
• Helix is the lengthwise shape of the tooth flank across the face from one end to the
other
• The theoretical helix of a spur gear is a straight line parallel to its rotating axis. It
does not include edge rounds or chamfers
• Lead is the axial advance of a helix for one complete turn of the gear. It is therefore,
infinite
• Helix deviation is difference between specified and measured helix of the gear
• The direction of helix deviation has to be within transverse plane, tangent to base
circle

Gear Inspection
Measurement Process
Generative Helix Method
• It is the most common method, it compares the generated helix with a nominal helix
• It requires axial movement of measurement probe together with a rotational movement of
the gear mounted on instrument spindle. These movements are synchronized. In spur
gears rotational movement is eliminated
• The method may apply usage of master disk driven by a straight edge, which in turn is
driven by axial movement of probe slide. Or it can use CNC helix generator, or master
lead screw bar.

Gear Inspection
Measurement Process
Generative Helix Method

Gear Inspection
Measurement Process
Coordinate & Portable Helix Measurements
• These methods are similar to profile measurements

Gear Inspection
Measurement Process
Helix Diagram

Gear Inspection
Measurement Process
Helix Diagram
• Mean Helix Slope Deviation
• In addition to eccentricity, tilt also plays role in slope deviations. It may be due to
mis-orientation gear tooth relative to the datum axis. This will lead to rocking of
center of contact pressure on each turn of the gear

Gear Inspection
Measurement Process
Helix Diagram
• Mean Helix Slope Deviation
• Following parameters can be calculated from mean helix slope deviation:

Gear Inspection
Measurement Process
Single flank composite deviations
• For this measurement two gears are mounted rotatably in mesh at an appropriate center
distance. The gears are mounted with backlash so that contact occurs only on one set of
corresponding flanks
• A device rotates with the meshed gears synchronously, measuring angular motion

Gear Inspection
Measurement Process
• One gear acts as a driver, while the other is driven
• During rotation, angular positions of both gears is calculated through ratioing of the
signals from the two sensing devices using analog or digital encoders
• The angular measurements are converted to linear values at specified tolerance diameter
• These measurements are taken with tooth flank contact maintained, under very light load,
and with low angular velocities
• Tooth to tooth single flank composite deviation fis is the value of greatest measured
transmission error over any one pitch (36/z) after removal of long term component,
when the gear is moved through one complete rotation

Gear Inspection
Measurement Process

Gear Inspection
Measurement Process
• Single flank composite measurement with a master gear
• The quality of master gear is at least 4 accuracy grades better than the required
grade of the product gear
• The results of comparisons yield information regarding the influence of:
• Profile Deviations
• Pitch deviations
• Helix deviations
• Contact ratio
• The interpretation and diagnostic of results reveals gear defects

References
• 2nd Ed, Dudley’s Handbook of Practical Gear Design & Manufacture
• 3th Ed, Industrial Press Machinery’s Handbook
• AGMA 215-1-A1
• AGMA 15-1-A2
• AGMA 15-2-A5
• AGMA 15-3-A
• AGMA 112-F

Gears Terminologies, Standards, Design, and Inspections

Gears Terminologies, Standards, Design, and Inspections

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