HeylandCircle: A Computational Framework for the Geometric Reconstruction of the Heyland Circle Diagram
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917165643333632 |
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| author | Gupta, Anubhav Gupta, Abhinav |
| author_facet | Gupta, Anubhav Gupta, Abhinav |
| contents | The Heyland circle diagram is a classical graphical tool for representing the steady-state behavior of induction machines using no-load and blocked-rotor test data. While widely used in alternating-current machinery texts, the diagram is typically presented as a hand-constructed aid and lacks a standardized computational formulation. This paper presents HeylandCircle, a computational framework that reconstructs the classical Heyland circle diagram directly from standard test parameters. The framework formalizes the traditional geometric construction as a deterministic, reproducible sequence of geometric operations, establishing a clear mapping between measured data, fixed geometric objects, and steady-state operating points. Quantities such as power factor, slip, output power, torque, and efficiency are obtained through explicit geometric relationships on the constructed diagram. Validation using a representative textbook example demonstrates close agreement with classical results. The framework provides a computational realization of the traditional Heyland diagram suitable for instruction, analysis, and systematic extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | HeylandCircle: A Computational Framework for the Geometric Reconstruction of the Heyland Circle Diagram Gupta, Anubhav Gupta, Abhinav Systems and Control Mathematical Software The Heyland circle diagram is a classical graphical tool for representing the steady-state behavior of induction machines using no-load and blocked-rotor test data. While widely used in alternating-current machinery texts, the diagram is typically presented as a hand-constructed aid and lacks a standardized computational formulation. This paper presents HeylandCircle, a computational framework that reconstructs the classical Heyland circle diagram directly from standard test parameters. The framework formalizes the traditional geometric construction as a deterministic, reproducible sequence of geometric operations, establishing a clear mapping between measured data, fixed geometric objects, and steady-state operating points. Quantities such as power factor, slip, output power, torque, and efficiency are obtained through explicit geometric relationships on the constructed diagram. Validation using a representative textbook example demonstrates close agreement with classical results. The framework provides a computational realization of the traditional Heyland diagram suitable for instruction, analysis, and systematic extension. |
| title | HeylandCircle: A Computational Framework for the Geometric Reconstruction of the Heyland Circle Diagram |
| topic | Systems and Control Mathematical Software |
| url | https://arxiv.org/abs/2512.20015 |