Measurement and Evaluation of the Ellipsoid Deviation in Cartesian Coordinates
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International Journal of Precision Engineering and Manufacturing https://doi.org/10.1007/s12541-020-00408-7
REGULAR PAPER
Measurement and Evaluation of the Ellipsoid Deviation in Cartesian Coordinates Fei Liu1 · Lin Liang1,3 · Guanghua Xu1,2 · Chenggang Hou1,3 · Dan Liu1,3 Received: 1 June 2020 / Revised: 27 July 2020 / Accepted: 13 August 2020 © Korean Society for Precision Engineering 2020
Abstract Ellipsoid part is now increasingly applied to the product manufacturing, while the high-quality ellipsoid part depends not only on the manufacturing and machining techniques, but also on the adopted measurement and evaluation approaches. Based on the typical quadratic surface, an evaluation method of the least squares ellipsoid deviation is proposed in this paper to quantify the form deviation of measured ellipsoid. The method can overcome the weakness of the low measurement adaptability compared with other evaluation methods. With obtaining the coefficients of surface equation to replace the linear superposing of the coordinates of measured points, the measurement error existing in the coordinates of measured points is homogenized and reduced effectively, which prompts to obtain the accurate measurement result. Finally, the results from experimental verifications show that the proposed method is effective for the measurement and evaluation of the ellipsoid deviation in Cartesian coordinates, and the adaptability is also a significant advantage in the measurement and evaluation of geometry deviation. Keywords Ellipsoid deviation · Deviation evaluation · Cartesian coordinates · Least squares method · Coordinate measuring machine
1 Introduction In the past decades, ellipsoid surface machining has been greatly improved with the development of manufacturing technology. Currently, the form and structure of ellipsoid have been applied to the manufacture of precision parts, especially in bearing, optical lens, and flow channel. The high-precision ellipsoid surface is a guarantee of improving the existing performances and obtaining the expected functions for the precision mechanical product. However, the quality control of the ellipsoid surface is dependent not only * Fei Liu [email protected] 1
School of Mechanical Engineering, Xi’an Jiaotong Uni versity, No. 28, Xianning West Road, Xi’an 710049, Shaanxi, People’s Republic of China
2
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710054, People’s Republic of China
3
Key Laboratory of Education Ministry for Modern Design and Rotor‑Bearing System, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
on the advanced design and manufacturing methods, but also on the measurement and evaluation techniques. To meet the requirements of strict tolerance and excellent performance, the measurement and evaluation of form deviation have become the essential for manufacturer to control the basic dimensions of the processed part. It is clear that the ellipsoid surface can be considered as a quadratic surfa
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