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Research Papers

Artifact Design and Measurement Error Analysis in the Evaluation of Lead Measurement Accuracy of Helical Gear Using Wedge Artifact

[+] Author and Article Information
Masaharu Komori1

Department of Mechanical Engineering and Science, Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501, Japankomorim@me.kyoto-u.ac.jp

Fumi Takeoka, Aizoh Kubo, Kazuhiko Okamoto

Department of Mechanical Engineering and Science, Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501, Japan

Sonko Osawa, Osamu Sato

Dimensional Standards Section, National Metrology Institute of Japan, AIST, Tsukuba, Ibaraki 305-8563, Japan

Toshiyuki Takatsuji

Dimensional Standards Section, National Metrology Institute of Japan, AIST, Tsukuba, Ibaraki 305-8563, Japantoshiyuki.takatsuji@aist.go.jp

Yohan Kondo

Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japankondo.y.ae@m.titech.ac.jp

1

Corresponding author.

J. Mech. Des 132(7), 071006 (Jun 17, 2010) (11 pages) doi:10.1115/1.4001668 History: Received November 06, 2009; Revised March 15, 2010; Published June 17, 2010; Online June 17, 2010

The reduction in the vibration and noise of gears is an important issue in mechanical devices such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are markedly affected by deviations of the tooth flank form of micrometer order; therefore, strict quality control of the tooth flank form is required. The accuracy of the lead measurement for a gear-measuring instrument is usually evaluated using a helicoid artifact. However, it is difficult to manufacture it with high accuracy because the helix is a complicated geometrical form. To solve this problem, a method of evaluating a gear-measuring instrument using a wedge artifact, which includes a highly precise plane surface, has been proposed. In this research, to put the wedge artifact into practice, a design method of the wedge artifact is developed. In addition, the effects of the measuring condition and the setting error of the wedge artifact on the measurement result are investigated. The uncertainty for the evaluation method using a wedge artifact is assessed by a measurement experiment and simulation.

Copyright © 2010 by American Society of Mechanical Engineers
Topics: Wedges , Errors , Gears
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References

Figures

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Figure 3

Basic posture of the wedge artifact on a gear-measuring instrument (23)

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Figure 4

Effect of the inclination angle of lead measurement plane of the wedge artifact on the theoretical measurement curve and the measurable range

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Figure 5

Relationship between the inclination angle of lead measurement plane and the measurable range in the tooth width direction

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Figure 6

Schematic model of the development surface of a lead measurement cylinder

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Figure 9

Effect of the lead measurement circle radius on the theoretical measurement curve

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Figure 10

Experimental result of the lead measurement of a wedge artifact under different helix angles

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Figure 13

State in basic posture with a setting error and that after rotation of the wedge artifact: (a) cross section at x=rm and (b) cross section at z=za

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Figure 14

Effect of the actual inclination angle on the difference curve between the theoretical measurement curve without an error and that with an error

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Figure 15

Effect of the maximum-inclination direction error on the measurement curve

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Figure 16

Effect of the maximum-inclination direction error on the difference curve between the theoretical measurement curve without an error and that with an error

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Figure 17

Actual measurement curves using the gear-measuring instrument without resetting the wedge artifact (ten measurements)

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Figure 18

Deviation of the actual measurement curve from the mean curve without resetting the wedge artifact (ten measurements): (a) deviation from the mean curve and (b) distribution of deviation of each data point

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Figure 19

Deviation of the actual measurement curve from the mean curve for the case in which the wedge artifact is reset (ten measurements): (a) deviation from the mean curve and (b) distribution of deviation of each data point

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Figure 20

Difference δγ between the calibrated inclination angle and the estimated actual inclination angle for each measurement for the case in which the wedge artifact is reset for each measurement

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Figure 21

Deviation of the actual measurement curve from the mean curve without resetting the helicoid artifact (ten measurements): (a) deviation from the mean curve and (b) distribution of deviation of each data point

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Figure 22

Deviation of the actual measurement curve from the mean curve for the case in which the helicoid artifact is reset (ten measurements): (a) deviation from the mean curve and (b) distribution of deviation of each data point

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Figure 23

Distributions of the total helix deviations and helix slope deviations for the calculated difference curve in the Monte Carlo simulation of the evaluation of the gear-measuring instrument using the wedge artifact: (a) distribution of the calculated total helix deviation and (b) distribution of the calculated helix slope deviation

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Figure 24

Example of the virtually measured difference curve and definition of fluctuation amplitude

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Figure 25

Distribution of fluctuation amplitude

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Figure 1

Definition of the form of the involute helicoid surface (23)

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Figure 2

An example of a wedge artifact (23)

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Figure 7

Optimization of inclination angle of the lead measurement plane to maximize the measurable range under the condition that βm and rm are fixed: (a) optimal inclination angle Φopt of the lead measurement plane, and (b) measurable range in the tooth width direction under Φopt

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Figure 8

Effect of the helix angle on the theoretical measurement curve

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Figure 11

Experimental condition and result of the lead measurement of a wedge artifact under different lead measurement circle radii: (a) measurement conditions and (b) measurement result

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Figure 12

Setting errors of the wedge artifact: (a) actual inclination angle γ of the lead measurement plane of a wedge artifact, and (b) maximum-inclination direction error η

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