The Three Parts of Gears - Cloud Object Storage | … · –Profile (tooth form tip to root) –Lead ... • Measure of Gear Tooth Profile ... is the angular error or the deviation

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AGMA Webinar: How To Read and Interpret A Gear Inspection Report: Slide 1

How To Read and InterpretA Gear Inspection Report

AGMA WebinarCopyrighted 2016

William M. McVea, Ph.D., P.E.President and Principal Engineer

KBE+, Inc.


The Three Parts of Gears

• The Form

• The Tooth

• The Teeth



• The Form

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• The Form

• The Tooth



• The Form

• The Tooth

• The Teeth


Definition of an Involute

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Base Circle


Involute Helicoid

• Paper Cut as Parallelogram Shape


Involute Helicoid

2pr

H

Cylinder

Axis

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Involute Helicoid


• Wrapped Around Base Cylinder


Involute

Helicoid

H

r

l

Helix

Helix

Tangent


Involute Helicoid


• Wrapped Around Base Cylinder

• Unwrapped as to Generate Involute

• Paper Edge Defines Involute Helicoid

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Involute Helicoid


Involute

Helicoid Involute

Curves

rb

r


So What Are We Trying To Do Here

• Determine the amount of deviation from

a perfect gear tooth form, both;

– Profile (tooth form tip to root)

– Lead (tooth face one end to the other)

• Compare ‘actual’ form to required form

as defined by standard;

– AGMA

– ISO

– Etc.

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Line of Action and Transmission Error

Point of Contact Between Driver and Driven As They Roll Through Mesh


Issues Caused By TE

• This ‘off-axis’ motion causes vibration

as it tries to accelerate / decelerate the load

• This manifests itself as;

– Vibration, which becomes ‘noise’

– Parasitic losses / inefficiencies

– This ‘lost energy’ goes into the lubricant and structure as heat

– And finally it is one of the main sources of wear


Polling Question #1

• What causes transmission error?

– A. Tooth form (profile) deviations

– B. Lead variations

– C. Surface finish (worse than required by quality standards)

– D. Lubricant failure (oxidation, debris entrainment, etc.)

– E. All of the above

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Involute Measurement

• Measure of Gear Tooth Profile

• Rolling Gear on Base Circle

• Produces Contact Traces of Profile

• Relation Between Roll Angle / Profile

• Variations in Tooth Geometry

– Deviations from Straight Line on Chart

• Run Out / Gear Wobble Effect Trace

• Measure at Several Axial Positions


Involute Chart

0o 6

o 12o

18o


Involute

Chart

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Red Liner

• Double Flank Tester

• Master Gear


Red LinerSchematic of Gear Rolling Device


Red Liner


• Master Gear

• Motion of Center of Test Gear

– Recorded (Trace)

– During Roll with Master

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Red LinerTypical Chart


Red Liner


• Master Gear

• Motion of Center of Test Gear

– Recorded (Trace)

– During Roll with Master

• Measures Variation of Test Gear

– Composite Test & Master Gear Error

– Master Variation Assumed to be Negligible


Red Liner Data

• Total Composite Error

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Red Liner Data


• Tooth to Tooth Composite Error

• Tooth to Tooth Error



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Red Liner Data


• Tooth to Tooth Composite Error

• Tooth to Tooth Error

• Run-out




Red Liner Limitations

• Test Run with Zero Backlash

– Not at Operating Pitch Diameter

• Test Run with No-Load

• Both Flanks are Engaged

• Can Not Differentiate Between

– Involute Errors

– Lead Errors

– Profile Modification Errors

– Combination of Errors

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Single Flank Gear Tester

• Measures Similar Parameters

– With Backlash

– On Operating Pitch Diameters



Schematic



• Measures Similar Parameters

– With Backlash

– On Operating Pitch Diameters

• Measures Transmission Error

• More Accurate Representation of Error

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Polling Question #2

• Which measurement system predicts a more

accurate representation of ‘real-world’ operation?

– A. Red-liner (Double flank tester)

– B. Single flank

– C. No difference between the two


CMM: Coordinate Measurement Machine

GMM: Gear Measurement Machine

• Index Variation

• Lead Variation

• Involute Variation

• Topological Plots

• Generates Surface of Actual Tooth Form


Charts: Profile Inspection

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Charts: Profile Inspection

• Profile inspection is a view of the tooth from root to tip

(or tip to root)

• A straight vertical line indicates a prefect involute

– As defined and ‘old school’ measure by the profile check


Profile Chart: General Information

Which part of the chart you are reviewing

Client data

Remarks specific to the job (i.e. orientation)

Inspection machine / system used

Inspection operator



Job specific data (i.e. gear tooth profile, etc.)

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Type of measure profile (i.e. external or internal)

Units of measure

Type and size of probe used



Diametral position of probe (referenced to tooth diameter)

Ratio between horizontal and vertical measurements

Axial grid measure (linear / chordal measure across tooth)

Chart magnification factor



Side of tooth being inspected

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Profile Chart: Tooth Height

Root to Tip


Profile Chart: Active Profile

Start of Active Profile (SAP) to

End of Active Profile (EAP)

OR;

Length / Area of Tooth of Interest


Profile Chart: Measured / Inspected Teeth

Specific teeth designated for identification purposes

Either specifically designated by the client

Or selected equally spaced (typically) around the shaft

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Profile Chart: Measured / Inspected Quantities

Measurement Results:

Fa is the composite error of both angular and form deviations

ffa is the form error or essentially the waviness of the line

fHa is the angular error or the deviation of the assumed straight line from vertical


Profile Chart: Deviation from True Involute







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Profile Chart: Deviation from Tooth Form Position




Profile Chart: Deviation from Tooth Form Position



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Profile Chart: Composite View of Total Error




Profile Chart: Composite View of Total Error




Profile Chart: Results Relative to Quality Number

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Polling Question #3

• This is an extension question; meaning, we did not

specifically cover it in the preceding material, but let’s

expand our thinking a bit . . .

• What is the ‘non-measured’ attribute that also must

be taken into consideration and can be seen on the

previous charts?

– A. Waviness

– B. Tooth spacing (relative position of one tooth to the next)

– C. Consistency (or lack thereof) in error / deviation


Lead on a Helical Gear

Note: Spur gear is the degenerate

form of a helical gear, with a

helix angle of: 0.00°


Charts: Lead Check

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Lead Chart: General Information

Diametral position of probe (referenced to top of tooth)

Ratio between horizontal and vertical measurements

Axial grid measure (linear / chordal measure across tooth)

Chart magnification factor


Lead Chart: General Information



Lead Chart: Tooth Height

Root to Tip

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Lead Chart: Active Profile

Length of tooth face to be inspected

Or of interest


Lead Chart: Measured / Inspected Quantities


FB is the composite error of both lead curvature and form deviations

ffB is the form error or essentially the waviness of the line

fHB is the lead curvature error or the deviation of the assumed straight line from vertical


Lead Chart: Deviation from True Lead



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Lead Chart: Deviation or Curvature of Lead



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Lead Chart: Deviation or Curvature of Lead




Lead Chart: Composite View of Total Error




Lead Chart: Composite View of Total Error



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Lead Chart: Results Relative to Quality Number


Charts: Pitch Inspection


Pitch Chart: General Information

Scale used on chart

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Pitch Chart: General Information



Pitch Chart: Measured / Inspected Quantities


fp is the composite tooth to tooth spacing error

fu is the single highest deviation of pitch spacing

fup is the individual tooth to tooth spacing error


Charts: Run-Out Inspection

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Run-Out Chart: General Information

Scale and side of tooth being measured (right)

Scale and side of tooth being measured (left)

Scale and composite measurement of tooth



Perfect Circles



Representation of Composite

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Reference List

1. “Gear Handbook” by Darle W. Dudley. First Edition, McGraw-Hill, Inc. 1962.

2. “Dudley’s Gear Handbook, Second Edition” by Dennis P. Townsend. McGraw-Hill, Inc. 1992. (ISBN: 0-07-017903-4)

3. “Spur Gears” by Earle Buckingham. First Edition, McGraw-Hill, Inc. 1928.

4. “Handbook of Practical Gear Design” by Darle W. Dudley. First Edition, Technomic Publication,

Inc. 1994. (ISBN: 1-56676-218-9)

5. “A Treatise of Gear Wheels” by George B. Grant. Twenty-First Edition, Philadelphia GEAR

Works Inc. 1899. Reprinted 1980.

6. “Gear Geometry and Applied Theory” by Faydor Litvin. First Ed, Prentice-Hall, Inc. 1994.(ISBN: 0-13-211095-4)

7. “The Internal Gear”, by The Fellows Corporation. Seventh Ed, Fellows Corporation. 1978.

8. “Encyclopedic Dictionary of Gears and Gearing” by D.W. South and R.H. Ewert. McGraw-Hill,

Inc., New York, New York. 1994. (ISBN: 0-07-059795-0)

9. “MAAG Gear Book” by MAAG Gear Company Ltd. 1990.

10. “Gleason Fachworter” by The Gleason Works. Alfred Wentzky & Co. 1967.


Reference List

11. “Mechanical Engineers Reference Handbook” by Edward H. Smith. Twelfth Edition, Society of

Automotive Engineers, Inc. 1994. (ISBN: 1-56091-450-5)

12. “Machinery’s Handbook” by Erik Oberg, Franklin Jones, and Holbrook Horton. Twenty-third

Edition, Industrial Press, Inc. 1914. Revised 1989. (ISBN: 0-8311-1200-X)

13. “Engineering Unit Conversions” by Micheal Lindeburg. Professional Publications, Inc. 1988.

(ISBN: 0-932276-89-X)

14. “Mechanics of Materials” by E. P. Popov. Second Edition, Prentice-Hall, Inc. 1976.

15. “Formulas for Stress and Strain” by Raymond Roark and Warren Young. Fifth Edition,

McGraw-Hill, Inc. 1975. (ISBN: 0-07-053031-9)

16. “Mechanical Engineering Design” by Joseph Shigley. Third Edition, McGraw-Hill, Inc. 1977.(ISBN: 0-07-056881-2)

17. “Mechanical Designs and Systems Handbook”, by Harold Rothbart. Second Edition, McGraw-

Hill Inc. 1985. (ISBN: 0-07-054020-9)

18. “Mark’s Standard Handbook for Mechanical Engineers ” by Eugene Avallone and Theodore

Baumeister. McGraw-Hill Inc. 1978. (ISBN:0-07-004127-X)


Reference List

19. “Rules of Thumb for Mechanical Engineers” by J. Edward Pope. Gulf Publishing Company.

1997.

20. “Mechanisms and Mechanical Devices Sourcebook” by Nicholas Chironis and Neil Sclater.

Second Edition, McGraw-Hill, Inc. 1996. (ISBN: 0-07-011256-4)

21. “Stress Concentration Factors” by R. E. Peterson. John Wiley and Sons, Inc. 1974.

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Reference List – URL Information 1. http://www.flying-pig.co.uk/mechanisms/pages/crank.htm

2. http://www.arrowgear.com/products/zerol_bevel_gears.htm

3. http://en.wikipedia.org/wiki/Spiral_bevel_gear

4. http://materialhandling.globalspec.com/LearnMore/Motion_Controls/Power_Transmission/Gears/

Worms_Worm_Gears

5. http://www.mekanizmalar.com/worm_gear.shtml

6. http://www.flying-pig.co.uk/mechanisms/pages/worm.html

7. http://en.wikipedia.org/wiki/Hypoid_Gear

8. http://en.wikipedia.org/wiki/Involute_gear

9. http://upload.wikimedia.org/wikipedia/commons/c/c2/Involute_wheel.gif

10. http://www.qtcgears.com/Q410/QTC/Q410P342.htm

11. http://www.gears-manufacturers.com/cycloidal-gears.html

12. http://www.csparks.com/watchmaking/CycloidalGears/index.jhtml

13. http://www.youtube.com/watch?v=UayBAHJQE_k

14. http://upload.wikimedia.org/wikipedia/commons/a/a0/CycloidAnim04.gif


Reference List – URL Information 15. http://www.engineeringletters.com/issues_v15/issue_1/EL_15_1_4.pdf

16. http://www.zakgear.com/WN.html

17. http://www.gearsolutionsonline.com/article/detail/5393/title/william-crosher-tooth-tips

18. http://gltrs.grc.nasa.gov/reports/2007/TM-2007-215032.pdf

19. http://upload.wikimedia.org/wikipedia/commons/c/c2/Involute_wheel.gif

20. http://upload.wikimedia.org/wikipedia/commons/4/4e/Hertz_contact_animated.gif

21. http://www.toolingu.com/definition-560100-25038-helical-gear.html

22. http://www.rushgears.com/Gear_Types/helicalGears.php

23. http://en.wikipedia.org/wiki/Face_gear

24. http://www.gears-manufacturers.com/face-gear.html

Documents

The Three Parts of Gears - Cloud Object Storage | … · –Profile (tooth form tip to root) –Lead ... • Measure of Gear Tooth Profile ... is the angular error or the deviation