Profile error evaluation of free-form surface using sequential quadratic programming algorithm
•A mathematical model for the evaluation of free-form profile error is built.•STL model based point-to-surface distance Calculation method is proposed.•Evaluation algorithm for the calculation of free-form profile error is proposed. Profile error of free-form surface is evaluated in this paper based...
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| Vydáno v: | Precision engineering Ročník 47; s. 344 - 352 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.01.2017
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| ISSN: | 0141-6359, 1873-2372 |
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| Abstract | •A mathematical model for the evaluation of free-form profile error is built.•STL model based point-to-surface distance Calculation method is proposed.•Evaluation algorithm for the calculation of free-form profile error is proposed.
Profile error of free-form surface is evaluated in this paper based on sequential quadratic programming (SQP) algorithm. The optimal localization model is established with the minimum zone criterion firstly. Subsequently, the surface subdivision method or STL (STeror Lithography) model is used to compute the point-to-surface distance and the approximate linear differential movement model of signed distance is deduced to simplify the updating process of alignment parameters. Finally, the optimization model on profile error evaluation of free-form surface is solved with SQP algorithm. Simulation examples indicate that the results acquired by SQP method are closer to the ideal results than the other algorithms in the problem of solving transformation parameters. In addition, real part experiments show that the maximum distance between the measurement points and their corresponding closest points on the design model is shorter by using SQP-based algorithm. Lastly, the results obtained in the experiment of the workpiece with S form illustrate that the SQP-based profile error evaluation algorithm can dramatically reduce the iterations and keep the precision of result simultaneously. Furthermore, a simulation is conducted to test the robustness of the proposed method. In a word, this study purposes a new algorithm which is of high accuracy and less time-consuming. |
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| AbstractList | •A mathematical model for the evaluation of free-form profile error is built.•STL model based point-to-surface distance Calculation method is proposed.•Evaluation algorithm for the calculation of free-form profile error is proposed.
Profile error of free-form surface is evaluated in this paper based on sequential quadratic programming (SQP) algorithm. The optimal localization model is established with the minimum zone criterion firstly. Subsequently, the surface subdivision method or STL (STeror Lithography) model is used to compute the point-to-surface distance and the approximate linear differential movement model of signed distance is deduced to simplify the updating process of alignment parameters. Finally, the optimization model on profile error evaluation of free-form surface is solved with SQP algorithm. Simulation examples indicate that the results acquired by SQP method are closer to the ideal results than the other algorithms in the problem of solving transformation parameters. In addition, real part experiments show that the maximum distance between the measurement points and their corresponding closest points on the design model is shorter by using SQP-based algorithm. Lastly, the results obtained in the experiment of the workpiece with S form illustrate that the SQP-based profile error evaluation algorithm can dramatically reduce the iterations and keep the precision of result simultaneously. Furthermore, a simulation is conducted to test the robustness of the proposed method. In a word, this study purposes a new algorithm which is of high accuracy and less time-consuming. |
| Author | Lang, Ailei Song, Zhanjie Sang, Yicun He, Gaiyun |
| Author_xml | – sequence: 1 givenname: Ailei orcidid: 0000-0003-2595-4153 surname: Lang fullname: Lang, Ailei organization: School of Science, Tianjin University, Tianjin 300350, China – sequence: 2 givenname: Zhanjie surname: Song fullname: Song, Zhanjie organization: School of Science, Tianjin University, Tianjin 300350, China – sequence: 3 givenname: Gaiyun surname: He fullname: He, Gaiyun email: hegaiyun@tju.edu.cn organization: Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300350, China – sequence: 4 givenname: Yicun surname: Sang fullname: Sang, Yicun organization: Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300350, China |
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| Cites_doi | 10.1007/BF01427149 10.1016/j.acme.2015.06.008 10.1109/34.121791 10.1016/j.cad.2015.02.004 10.1016/S0278-6125(08)00007-1 10.1007/s11431-011-4660-1 10.1016/S0010-4485(02)00205-1 10.1115/1.1763186 10.1007/s00170-008-1673-4 10.1016/j.cad.2004.02.009 10.1007/s11740-016-0660-0 10.1016/S0890-6955(03)00105-6 10.1016/j.measurement.2013.11.002 10.3901/JME.2010.10.001 10.1115/1.3510588 10.1007/s11263-006-5167-2 10.1007/s00170-013-5075-x 10.1007/s00170-006-0430-9 10.1049/iet-cvi.2009.0032 10.3901/CJME.2013.02.406 10.1088/0957-0233/24/8/085008 |
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| Keywords | Signed distance function Surface subdivision Sequential quadratic programming Free-form surface profile error STL model |
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| SubjectTerms | Free-form surface profile error Sequential quadratic programming Signed distance function STL model Surface subdivision |
| Title | Profile error evaluation of free-form surface using sequential quadratic programming algorithm |
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