Geometric error compensation for multi-axis CNC machines based on differential transformation
Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece co...
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| Autor*in: |
Chen, Jianxiong [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag London 2013 |
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| Übergeordnetes Werk: |
Enthalten in: The international journal of advanced manufacturing technology - Springer London, 1985, 71(2013), 1-4 vom: 05. Dez., Seite 635-642 |
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| Übergeordnetes Werk: |
volume:71 ; year:2013 ; number:1-4 ; day:05 ; month:12 ; pages:635-642 |
| Links: |
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| DOI / URN: |
10.1007/s00170-013-5487-7 |
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| Katalog-ID: |
OLC2026058385 |
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| 520 | |a Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. | ||
| 650 | 4 | |a CNC machine tool | |
| 650 | 4 | |a Geometric errors | |
| 650 | 4 | |a Differential transformation | |
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| 700 | 1 | |a Lin, Shuwen |4 aut | |
| 700 | 1 | |a He, Bingwei |4 aut | |
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10.1007/s00170-013-5487-7 doi (DE-627)OLC2026058385 (DE-He213)s00170-013-5487-7-p DE-627 ger DE-627 rakwb eng 670 VZ Chen, Jianxiong verfasserin aut Geometric error compensation for multi-axis CNC machines based on differential transformation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2013 Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. CNC machine tool Geometric errors Differential transformation Automatic modeling Lin, Shuwen aut He, Bingwei aut Enthalten in The international journal of advanced manufacturing technology Springer London, 1985 71(2013), 1-4 vom: 05. Dez., Seite 635-642 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:71 year:2013 number:1-4 day:05 month:12 pages:635-642 https://doi.org/10.1007/s00170-013-5487-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2018 GBV_ILN_2333 GBV_ILN_4046 AR 71 2013 1-4 05 12 635-642 |
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10.1007/s00170-013-5487-7 doi (DE-627)OLC2026058385 (DE-He213)s00170-013-5487-7-p DE-627 ger DE-627 rakwb eng 670 VZ Chen, Jianxiong verfasserin aut Geometric error compensation for multi-axis CNC machines based on differential transformation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2013 Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. CNC machine tool Geometric errors Differential transformation Automatic modeling Lin, Shuwen aut He, Bingwei aut Enthalten in The international journal of advanced manufacturing technology Springer London, 1985 71(2013), 1-4 vom: 05. Dez., Seite 635-642 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:71 year:2013 number:1-4 day:05 month:12 pages:635-642 https://doi.org/10.1007/s00170-013-5487-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2018 GBV_ILN_2333 GBV_ILN_4046 AR 71 2013 1-4 05 12 635-642 |
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10.1007/s00170-013-5487-7 doi (DE-627)OLC2026058385 (DE-He213)s00170-013-5487-7-p DE-627 ger DE-627 rakwb eng 670 VZ Chen, Jianxiong verfasserin aut Geometric error compensation for multi-axis CNC machines based on differential transformation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2013 Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. CNC machine tool Geometric errors Differential transformation Automatic modeling Lin, Shuwen aut He, Bingwei aut Enthalten in The international journal of advanced manufacturing technology Springer London, 1985 71(2013), 1-4 vom: 05. Dez., Seite 635-642 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:71 year:2013 number:1-4 day:05 month:12 pages:635-642 https://doi.org/10.1007/s00170-013-5487-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2018 GBV_ILN_2333 GBV_ILN_4046 AR 71 2013 1-4 05 12 635-642 |
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10.1007/s00170-013-5487-7 doi (DE-627)OLC2026058385 (DE-He213)s00170-013-5487-7-p DE-627 ger DE-627 rakwb eng 670 VZ Chen, Jianxiong verfasserin aut Geometric error compensation for multi-axis CNC machines based on differential transformation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2013 Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. CNC machine tool Geometric errors Differential transformation Automatic modeling Lin, Shuwen aut He, Bingwei aut Enthalten in The international journal of advanced manufacturing technology Springer London, 1985 71(2013), 1-4 vom: 05. Dez., Seite 635-642 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:71 year:2013 number:1-4 day:05 month:12 pages:635-642 https://doi.org/10.1007/s00170-013-5487-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2018 GBV_ILN_2333 GBV_ILN_4046 AR 71 2013 1-4 05 12 635-642 |
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10.1007/s00170-013-5487-7 doi (DE-627)OLC2026058385 (DE-He213)s00170-013-5487-7-p DE-627 ger DE-627 rakwb eng 670 VZ Chen, Jianxiong verfasserin aut Geometric error compensation for multi-axis CNC machines based on differential transformation 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag London 2013 Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. CNC machine tool Geometric errors Differential transformation Automatic modeling Lin, Shuwen aut He, Bingwei aut Enthalten in The international journal of advanced manufacturing technology Springer London, 1985 71(2013), 1-4 vom: 05. Dez., Seite 635-642 (DE-627)129185299 (DE-600)52651-4 (DE-576)014456192 0268-3768 nnns volume:71 year:2013 number:1-4 day:05 month:12 pages:635-642 https://doi.org/10.1007/s00170-013-5487-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_20 GBV_ILN_70 GBV_ILN_150 GBV_ILN_2018 GBV_ILN_2333 GBV_ILN_4046 AR 71 2013 1-4 05 12 635-642 |
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Geometric error compensation for multi-axis CNC machines based on differential transformation |
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Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. © Springer-Verlag London 2013 |
| abstractGer |
Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. © Springer-Verlag London 2013 |
| abstract_unstemmed |
Abstract As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path. © Springer-Verlag London 2013 |
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Geometric error compensation for multi-axis CNC machines based on differential transformation |
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