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Abstract This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.
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Cosine Error-Free Metrology Tool Path Planning for Thickness Profile Measurements
Abstract This paper presents a novel thickness profile measuring system that measures double-sided thin pipe wall surfaces in a non-contact, continuous, cosine error-free, and fast manner. The surface metrology tool path was developed to align the displacement sensors always normal to the double-sided surfaces to remove cosine error. A pair of capacitive-type sensors that were placed on the rotary and linear axes simultaneously scans the inner and outer surfaces of thin walls. Because the rotational error of the rotary axis can severely affect the accuracy in thickness profile measurement, such error was initially characterized by a reversal method. It was compensated for along the rotational direction while measuring the measurement target. Two measurement targets (circular and elliptical metal pipe-type thin walls) were prepared to validate the developed measurement method and system. Not only inner and outer surface profiles but also thin-wall thickness profiles were measured simultaneously. Based on the output data, the circularity and wall thickness variation were calculated. The thickness profile results showed a good agreement with those obtained by a contact-type micrometer (1-µm resolution) at every 6-deg interval. The uncertainty budget for this measuring system with metrology tool path planning was estimated at approximately 1.4 µm.
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- Award ID(s):
- 1902697
- PAR ID:
- 10217881
- Date Published:
- Journal Name:
- Journal of Manufacturing Science and Engineering
- Volume:
- 143
- Issue:
- 4
- ISSN:
- 1087-1357
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4048433
