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Research Papers

Design and Error Analysis of Multiball Artifact Composed of Simple Features to Evaluate Pitch Measurement Accuracy

[+] Author and Article Information
Masaharu Komori

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

Haixiang Li, Fumi Takeoka, Takashi Kiten, Daisuke Shirasaki

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

Sonko Osawa

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

Osamu Sato

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

Yohan Kondo

Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8550, Japankondou.y@aist.go.jp

J. Mech. Des 131(4), 041006 (Mar 23, 2009) (11 pages) doi:10.1115/1.3087535 History: Received August 20, 2008; Revised December 02, 2008; Published March 23, 2009

The strength and vibration/noise of gears are influenced by the pitch deviation of micrometer order and therefore, advanced quality control is needed in gear manufacturing processes using measuring instruments. The accuracy of the pitch measuring instrument is verified using a master gear or artifact, but their accuracy is not sufficiently high. An artifact with higher accuracy for the evaluation and calibration of the pitch measurement is necessary in order to respond to the requirement of gear accuracy. In this research, the multiball artifact, a novel high-precision pitch artifact, is proposed for use in the evaluation of pitch measuring instruments. The multiball artifact is composed of balls, a cylinder, and a plane, where the center cylinder or center ball is surrounded by the balls on the plane. The positions of those elements are decided automatically by the contact among those elements. Balls, cylinders, and planes can be manufactured with accuracy on the order of several tens of nanometers. Therefore, this artifact can realize high accuracy. In addition, this artifact does not need advanced techniques in manufacturing and assembly. This leads to the reduction in manufacturing cost. In this report, the concept and structure of the multiball artifact are proposed, and theoretical analysis on the measurement of the artifact is carried out. Feasible angular pitch is analyzed theoretically. For a cylinder-centered artifact, it is easy to realize the target angular pitch by adjusting the cylinder diameter. Ball-centered types suffer from the limitation of the variation in ball diameter if standard balls are used, but an angular pitch close to the target pitch is possible through the selection of an appropriate combination of balls. The effects of the dimensional deviation of the diameter of the center cylinder, the inclination of the center cylinder, the dimensional deviation of the surrounding ball diameters, the sphericity of balls, and the flatness of the base plane are analyzed. Deviations in the cylinder have a comparatively large effect on angular pitch. On the other hand, the effect of the deviation of the ball or base plane is smaller. The feasible angular pitch is clarified, and it is verified that the concept and structure of the multiball artifact are effective. The effects of deviations in the form and dimension of the composing elements are analyzed, and it is clarified that the accuracy of the cylinder is important.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Cylinders
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References

Figures

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Figure 1

Previously proposed pitch artifact with gauge blocks (18)

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Figure 2

Structure of multiball artifact

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Figure 3

Contact point of stylus tip in the measurement of angular pitch of multiball artifact

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Figure 4

Structure of cylinder-centered multiball artifact with the surrounding balls of different diameters

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Figure 5

Structures of multiball artifacts with different angular pitches

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Figure 6

Condition of interference and gap between the surrounding balls (cross section including the center of surrounding balls)

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Figure 7

Histogram of feasible angular pitch of multiball artifact

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Figure 8

Definition of elements and parameters of cylinder-centered multiball artifact (SK2L)

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Figure 9

Relationship between diameter of center cylinder and angular pitch

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Figure 10

Multiball artifact whose centered cylinder is inclined

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Figure 11

xyz coordinates and xcyczc coordinates of multiball artifact whose centered cylinder axis is inclined

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Figure 12

Contacting condition between balls and cylinder

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Figure 13

Position of rotational axis of artifact in pitch measurement

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Figure 14

Effect of inclination of cylinder

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Figure 15

Position of balls under two different conditions of φ that have the difference of 180 deg

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Figure 16

Probability density based on Gaussian distribution for diameter of surrounding balls (mean value is 12.7 mm and standard deviation is 0.13/6 μm)

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Figure 17

Results of analysis where a dimensional deviation in the diameter of the surrounding balls exist

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Figure 18

Results of analysis considering sphericity of surrounding balls

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Figure 19

Results of analysis on the effect of unevenness of the base plane

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