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Least squares evaluations for form and profile errors of ellipse using coordinate data

  • Precision Measurement and Signal Processing
  • Published:
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Abstract

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.

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Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Fei Liu, Guanghua Xu, Lin Liang, Qing Zhang & Dan Liu

  2. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710054, China

    Guanghua Xu

  3. Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an, 710049, China

    Lin Liang, Qing Zhang & Dan Liu

Authors
  1. Fei Liu
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  2. Guanghua Xu
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  3. Lin Liang
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  4. Qing Zhang
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  5. Dan Liu
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Corresponding author

Correspondence to Lin Liang.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51575438)

LIU Fei, born in 1979, is currently a PhD candidate at School of Mechanical Engineering, Xi’an Jiaotong University, China. He received his master degree from Henan University of Science and Technology, China, in 2008. His research interests include precision measurement technology and mechanical fault diagnosis.

XU Guanghua born in 1964, is currently a professor at State Key Laboratory for Manufacturing Systems Engineering and School of Mechanical Engineering, Xi’an Jiaotong University, China. He received his PhD degree from Xi’an Jiaotong University, China, in 1998. His research interests include mechanical fault diagnosis and brain-computer interface technology.

LIANG Lin born in 1972, is currently an associate professor at Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University, China. He received his PhD degree from Xi’an Jiaotong University, China, in 2007. His research interests include mechanical fault diagnosis, test and detection technology.

ZHANG Qing born in 1975, is currently an associate professor at Xi’an Jiaotong University, China. He received his PhD degree from Xi’an Jiaotong University, China, in 2007. His research interests include mechanical fault diagnosis, mechatronics technology.

LIU Dan born in 1978, is currently a lecturer at Xi’an Jiaotong University, China. He received his PhD degree from Xi’an Jiaotong University, China, in 2007. His research interests include mechanical fault diagnosis and information network.

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Liu, F., Xu, G., Liang, L. et al. Least squares evaluations for form and profile errors of ellipse using coordinate data. Chin. J. Mech. Eng. 29, 1020–1028 (2016). https://doi.org/10.3901/CJME.2016.0205.022

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  • DOI: https://doi.org/10.3901/CJME.2016.0205.022

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