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Department of Mechanical Engineering
JSS Academy of Technical Education, Bangalore-560060
MECHANICAL MEASUREMENTS AND METROLOGY
(Course Code:18ME36B)
TEXT BOOKS
• Mechanical Measurements, Beckwith Marangoni and Lienhard, Pearson Education, 6th Ed., 2006.
• Instrumentation, Measurement and Analysis, B C Nakra, K K Chaudhry, 4th Edition, McGraw Hill.
• Engineering Metrology, R.K. Jain, Khanna Publishers, Delhi, 2009
REFERENCE BOOKS:
• Engineering Metrology and Measurements, N.V.Raghavendra and L.Krishnamurthy, Oxford
University Press..
Further Reference:
 National Programme on Technology Enhanced Learning (NPTEL)
http://nptel.ac.in/courses/112104121/1
MECHANICAL MEASUREMENTS AND METROLOGY
CHAPTER 6: Measurement of Gear Tooth
Learning Objectives
To understand basic principle of measurement of Gear tooth parameters.
Module 2
Gear tooth Measurements
Tooth thickness measurement using;
• Constant chord method
• Base tangent method
Measurement of pitch, Concentricity, Run out and Involute profile.
• Gear roll tester for composite error.
Gear Tooth Measurements
• Gears are toothed wheels
• Used to transmit motion / power between two shafts with constant angular velocity ratio
• + Drives
Gear Tooth Measurements
Classification of Gears
A. Spur gears
B. Helical gears
C. Herringbone gears
D. Worm and worm gears
E. Bevel gears
• Base circle
• Outside circle
• Pitch circle
• Root circle
• Addendum
• Dedendum
• Module
• Circular pitch
• Tooth thickness
• Face
• Flank
• A basic understanding of the errors in spur gears during manufacturing is
required before measurement of different elements of gears.
ERRORS IN SPUR GEARS
1. Gear blank runout errors
2. Gear tooth profile errors
3. Gear tooth errors
4. Pitch errors
5. Runout errors
6. Lead errors
7. Assembly errors
L6 measurement of gear tooth
ERRORS IN SPUR GEARS
1. Gear blank runout errors: have radial runout on its OD surface, due to
machining.
2. Gear tooth profile errors: Deviation of the actual tooth profile from the ideal tooth
profile.
3. Gear tooth errors: Error in form of tooth thickness.
4. Runout errors: Runout of the pitch circle
ERRORS IN SPUR GEARS
Pitch errors: Single pitch error or Accumulated pitch error.
• Single pitch error: Actual measured pitch value
• Accumulated pitch error: Difference between theoretical summation over any
no. of teeth intervals and summation of actual pitch measurement over the
same interval of teeth.
Lead errors: Deviation of the actual advance of the gear tooth profile from the
ideal position.
MEASUREMENT OF GEAR ELEMENTS
The following elements of gears are important for analytical inspection:
1. Runout
2. Pitch
3. Profile
4. Lead
5. Backlash
6. Tooth thickness
MEASUREMENT OF GEAR ELEMENTS
Measurement of Runout
• Runout : Radial runout on the OD surface
• Runout is measured by a specified probe such as a cylinder, ball, cone, rack, or
gear teeth.
• Measurement is made perpendicular to the surface of revolution.
MEASUREMENT OF GEAR ELEMENTS
Measurement of Runout
• A common method of runout inspection, is by
a single-probe check, shown in Fig.
• Uses an indicator with a single probe whose
diameter makes contact with the flanks of
adjacent teeth in the area of the pitch circle.
Single-probe check
Measurement of Pitch
Two types of instruments are used for checking the pitch.
• Pitch-measuring Instruments
• Pitch-checking Instrument
Measurement of Pitch
Pitch-measuring Instrument
• Measurement of chordal pitch.
• Instrument comprises fixed finger and movable
finger.
• The fingers can be set at two identical points on
adjacent teeth along the pitch circle.
• Pitch variation is displayed on dial indicator.
Limitation
• Readings are influenced by profile variations &
runout of the gear
Measurement of Pitch
Pitch-checking Instrument / dividing head
fixed (anvil)
movable
Probe-1
Probe-2
Measurement of Pitch
Pitch-checking Instrument
• A pitch-checking instrument is a dividing head, used to measure pitch variations.
• Has two probes - One fixed (anvil)
Other movable (measuring feeler). Connected to dial indicator through levers
• The instrument is held by two adjacent support on the crests of the teeth.
• Tooth flank is held between the fixed anvil and the locating support.
• Measuring feeler (probe 2) senses the next corresponding flank.
• Instrument is used as a comparator, provides calculation of adjacent pitch error, actual pitch,
and accumulated pitch error.
PARKINSON’S GEAR TESTER
The gear being inspected is meshed with a standard gear, and a dial indicator is
used to capture radial errors.
PARKINSON’S GEAR TESTER
• Standard gear is mounted on a fixed frame, the gear being inspected is fixed to a sliding
carriage.
• Dial indicator primarily measure irregularities in the gear under inspection.
• A dial indicator of high resolution is used to measure the composite error, errors due to runout,
tooth-to-tooth spacing, and profile variations.
PARKINSON’S GEAR TESTER
• A Vernier scale enables measurement of the centre distance up to 25 μm.
• The dial indicator is set to zero
• Gear under inspection is rotated. Radial variations are indicated by the dial indicator.
• This variation is plotted on a graph sheet, which indicates the radial variations in the gear for one
complete rotation.
Tooth thickness measurement by Gear tooth Vernier
N = No. of teeth
M= Module
Pitch circle radius = rp =
𝑁𝑚
2
𝜃 =
360
4×𝑁
=
90
𝑁
To find w (width)
w = AC = AB+BC (since AB=BC)
w= AC= 2AB
From triangle OAB sin 𝜃 =
𝐴𝐵
0𝐴
(since OA = rp )
AB = rp x Sinθ
w = AC = 2AB = N M Sin (
90
𝑁
)
rp
θ
Tooth thickness measurement by Gear tooth Vernier
To find h (height)
h = OE - OB Eq.(1)
OE = OD+DE
OE= rp x m (m = addendum)
OE =
𝑁𝑚
2
+ m Eq.(2)
From triangle OAB COS 𝜃 =
𝑂𝐵
0𝐴
(since OA = rp )
OB = rp x Cosθ
OB=
𝑁𝑚
2
Cos (
90
𝑁
) Eq.(3)
Substitute (2) & (3) in (1) & simplifying
h =
𝑁𝑚
2
[ 1+
2
𝑁
- Cos (
90
𝑁
)]
rp
E
D
Chordal thickness and chordal height
θ
Base Tangent Method / Measurement over multiple teeth
Base Tangent Method
• In this method, the span of a convenient No. of teeth is measured by David
brown tangent comparator.
• The anvils of the comparator are first set of the base tangent length with the
help of slip gauges .
• Then, slip gauges are replaced by the gear which is to be measured.
• Reading are taken by the comparator.
End of Module

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SATELITE COMMUNICATION UNIT 1 CEC352 REGULATION 2021 PPT BASICS OF SATELITE ....
 

L6 measurement of gear tooth

  • 1. Department of Mechanical Engineering JSS Academy of Technical Education, Bangalore-560060 MECHANICAL MEASUREMENTS AND METROLOGY (Course Code:18ME36B)
  • 2. TEXT BOOKS • Mechanical Measurements, Beckwith Marangoni and Lienhard, Pearson Education, 6th Ed., 2006. • Instrumentation, Measurement and Analysis, B C Nakra, K K Chaudhry, 4th Edition, McGraw Hill. • Engineering Metrology, R.K. Jain, Khanna Publishers, Delhi, 2009 REFERENCE BOOKS: • Engineering Metrology and Measurements, N.V.Raghavendra and L.Krishnamurthy, Oxford University Press.. Further Reference:  National Programme on Technology Enhanced Learning (NPTEL) http://nptel.ac.in/courses/112104121/1
  • 3. MECHANICAL MEASUREMENTS AND METROLOGY CHAPTER 6: Measurement of Gear Tooth
  • 4. Learning Objectives To understand basic principle of measurement of Gear tooth parameters.
  • 5. Module 2 Gear tooth Measurements Tooth thickness measurement using; • Constant chord method • Base tangent method Measurement of pitch, Concentricity, Run out and Involute profile. • Gear roll tester for composite error.
  • 6. Gear Tooth Measurements • Gears are toothed wheels • Used to transmit motion / power between two shafts with constant angular velocity ratio • + Drives
  • 7. Gear Tooth Measurements Classification of Gears A. Spur gears B. Helical gears C. Herringbone gears D. Worm and worm gears E. Bevel gears
  • 8. • Base circle • Outside circle • Pitch circle • Root circle • Addendum • Dedendum • Module • Circular pitch • Tooth thickness • Face • Flank
  • 9. • A basic understanding of the errors in spur gears during manufacturing is required before measurement of different elements of gears. ERRORS IN SPUR GEARS 1. Gear blank runout errors 2. Gear tooth profile errors 3. Gear tooth errors 4. Pitch errors 5. Runout errors 6. Lead errors 7. Assembly errors
  • 11. ERRORS IN SPUR GEARS 1. Gear blank runout errors: have radial runout on its OD surface, due to machining. 2. Gear tooth profile errors: Deviation of the actual tooth profile from the ideal tooth profile. 3. Gear tooth errors: Error in form of tooth thickness. 4. Runout errors: Runout of the pitch circle
  • 12. ERRORS IN SPUR GEARS Pitch errors: Single pitch error or Accumulated pitch error. • Single pitch error: Actual measured pitch value • Accumulated pitch error: Difference between theoretical summation over any no. of teeth intervals and summation of actual pitch measurement over the same interval of teeth. Lead errors: Deviation of the actual advance of the gear tooth profile from the ideal position.
  • 13. MEASUREMENT OF GEAR ELEMENTS The following elements of gears are important for analytical inspection: 1. Runout 2. Pitch 3. Profile 4. Lead 5. Backlash 6. Tooth thickness
  • 14. MEASUREMENT OF GEAR ELEMENTS Measurement of Runout • Runout : Radial runout on the OD surface • Runout is measured by a specified probe such as a cylinder, ball, cone, rack, or gear teeth. • Measurement is made perpendicular to the surface of revolution.
  • 15. MEASUREMENT OF GEAR ELEMENTS Measurement of Runout • A common method of runout inspection, is by a single-probe check, shown in Fig. • Uses an indicator with a single probe whose diameter makes contact with the flanks of adjacent teeth in the area of the pitch circle. Single-probe check
  • 16. Measurement of Pitch Two types of instruments are used for checking the pitch. • Pitch-measuring Instruments • Pitch-checking Instrument
  • 17. Measurement of Pitch Pitch-measuring Instrument • Measurement of chordal pitch. • Instrument comprises fixed finger and movable finger. • The fingers can be set at two identical points on adjacent teeth along the pitch circle. • Pitch variation is displayed on dial indicator. Limitation • Readings are influenced by profile variations & runout of the gear
  • 18. Measurement of Pitch Pitch-checking Instrument / dividing head fixed (anvil) movable Probe-1 Probe-2
  • 19. Measurement of Pitch Pitch-checking Instrument • A pitch-checking instrument is a dividing head, used to measure pitch variations. • Has two probes - One fixed (anvil) Other movable (measuring feeler). Connected to dial indicator through levers • The instrument is held by two adjacent support on the crests of the teeth. • Tooth flank is held between the fixed anvil and the locating support. • Measuring feeler (probe 2) senses the next corresponding flank. • Instrument is used as a comparator, provides calculation of adjacent pitch error, actual pitch, and accumulated pitch error.
  • 20. PARKINSON’S GEAR TESTER The gear being inspected is meshed with a standard gear, and a dial indicator is used to capture radial errors.
  • 21. PARKINSON’S GEAR TESTER • Standard gear is mounted on a fixed frame, the gear being inspected is fixed to a sliding carriage. • Dial indicator primarily measure irregularities in the gear under inspection. • A dial indicator of high resolution is used to measure the composite error, errors due to runout, tooth-to-tooth spacing, and profile variations.
  • 22. PARKINSON’S GEAR TESTER • A Vernier scale enables measurement of the centre distance up to 25 μm. • The dial indicator is set to zero • Gear under inspection is rotated. Radial variations are indicated by the dial indicator. • This variation is plotted on a graph sheet, which indicates the radial variations in the gear for one complete rotation.
  • 23. Tooth thickness measurement by Gear tooth Vernier N = No. of teeth M= Module Pitch circle radius = rp = 𝑁𝑚 2 𝜃 = 360 4×𝑁 = 90 𝑁 To find w (width) w = AC = AB+BC (since AB=BC) w= AC= 2AB From triangle OAB sin 𝜃 = 𝐴𝐵 0𝐴 (since OA = rp ) AB = rp x Sinθ w = AC = 2AB = N M Sin ( 90 𝑁 ) rp θ
  • 24. Tooth thickness measurement by Gear tooth Vernier To find h (height) h = OE - OB Eq.(1) OE = OD+DE OE= rp x m (m = addendum) OE = 𝑁𝑚 2 + m Eq.(2) From triangle OAB COS 𝜃 = 𝑂𝐵 0𝐴 (since OA = rp ) OB = rp x Cosθ OB= 𝑁𝑚 2 Cos ( 90 𝑁 ) Eq.(3) Substitute (2) & (3) in (1) & simplifying h = 𝑁𝑚 2 [ 1+ 2 𝑁 - Cos ( 90 𝑁 )] rp E D Chordal thickness and chordal height θ
  • 25. Base Tangent Method / Measurement over multiple teeth
  • 26. Base Tangent Method • In this method, the span of a convenient No. of teeth is measured by David brown tangent comparator. • The anvils of the comparator are first set of the base tangent length with the help of slip gauges . • Then, slip gauges are replaced by the gear which is to be measured. • Reading are taken by the comparator.