A method for simulating the process of shooting a rotating shaft to create and test algorithms for calculating its geometric errors based on machine vision data

For the development and verification of algorithms for calculating geometric errors of inspected shafts using machine vision data, reference data is required on the coordinates of the visible boundaries of the shaft in the image, with known parameters of form deviations and positional deviations of the shaft journals, generated during the image acquisition process. To solve this problem, a method for simulating the imaging process of a rotating shaft is proposed.

A mathematical model has been developed that takes into account both the ideal shaft geometry and its actual deviations (runout, ovality, waviness, roughness), as well as the positioning errors of the shaft relative to a digital camera, which converts the optical image into an array of digital data for subsequent processing. The simulation includes generating the shaft profile, projecting three-dimensional coordinates onto a two-dimensional image considering camera parameters, and determining the coordinates of the visible shaft boundaries during its rotation. Computational experiments were performed for a shaft with a diameter of 10 mm, ovality of 0.1 mm, and a ten-point profile roughness height ( Rz ) of 50 μ m. The influence of the tilt angles of the shaft rotation axis on the image of its boundaries was analyzed. The results of calculating the coordinates of the visible boundaries of a rotating shaft during simulation of the imaging process show that the proposed method makes it possible to generate realistic data for testing algorithms, evaluate the influence of various errors, and optimize the parameters of the measurement system. It is shown that simulation is an effective tool for debugging and validating non contact methods for shaft geometry inspection. The proposed simulation method can be useful for developers of machine vision algorithms and methods for non contact inspection of shaft geometry when debugging vision systems without the need for physical reference standards, as well as for specialists in technical measurements and quality control in mechanical engineering engaged in automating shaft geometry inspection (e.g., in automotive, machine tool, and aircraft engine manufacturing). 

1. Taatali A., Sadaoui S. E., Louar M. A., Mahiddini B. On-machine dimensional inspection: machine vision-based approach. The International Journal of Advanced Manufacturing Technology, 131, 393–407 (2024). https://doi.org/10.1007/s00170-023-12298-6

2. Tan Y. S., Zhang W. B., Wang J., Li X. Y., Chen H. Error Correction Method for Rotating Axis of Large Rotating Machinery Based on Machine Vision. In: Multimedia Technology and Enhanced Learning. ICMTEL 2021. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol. 387. Cham, Springer (2021). https://doi.org/10.1007/978-3-030-82562-1_4

3. Stepanov D. N. Mathematical models of stereo image acquisition from two-mirror catadioptric systems taking into account lens distortion. Computer Optics, 43(1), 105–114 (2019). (In Russ.) https://doi.org/10.18287/2412-6179-2019-43-1-105-114

4. Stepanov D. N., Tishchenko I. P. Mathematical modeling and study of the optimal configuration of an optical stereo system consisting of two plane mirrors. Program Systems: Theory and Applications, 15(3), 23–52 (2024). (In Russ.) https://doi.org/10.25209/2079-3316-2024-15-3-23-52

5. Dorenskiy A. A., Pronin S. P., Zryumov E. A. Control of quality of PAT-bottle on digital representation. Instruments and Systems: Monitoring, Control, and Diagnostics, (5), 22–28 (2023). (In Russ.) https://www.elibrary.ru/kytmsl

6. Yuan K., Fu H., Li R., Wang L., Zhang X. Research on sub-pixel detection and evaluation of roundness error of shaft workpiece based on machine vision. Journal of Mechanical Science and Technology, 39, 2041–2049 (2025). https://doi.org/10.1007/s12206-025-0329-8

7. Cao Y., Hou Y. L., Zhang S. C., Liu Y., Li W. Evaluation of crankshaft roundness error based on computational geometry. Manufacturing Technology & Machine Tool, (8), 174–179 (2023). https://doi.org/10.19287/j.mtmt.1005-2402.2023.08.025

8. Gordevich D. A., Bogush R. P. Analysis of methods for determining real geometric dimensions of objects and distances using computer vision. In: Information and Communication Technologies: Achievements, Problems, Innovations (ICT-2024). Polotsk, Polotsk State University of Euphrosyne of Polotsk Publ., рр. 159–163 (2024). (In Russ.) https://www.elibrary.ru/ahgcva

9. Chertov A. N., Khokhlov D. D. Modern optical methods of non-contact geometric measurements and reconstruction of object 3D surface shape: a review. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 24(6), 923–935 (2024). (In Russ.) https://doi.org/10.17586/2226-1494-2024-24-6-923-935

10. Mironenko V. V., Belousov A. R. Preparation of a machine vision system for analyzing the geometry of parts. Kuznechno-shtampovochnoe proizvodstvo. Obrabotka materialov davleniem, (6), 35–40 (2022). (In Russ.) https://www.elibrary.ru/zgnxjf

11. Stepanov P. P., Mironov S. V. Simulation modeling in the development of technical vision systems. Computer Optics, 46(3), 412–419 (2022). (In Russ.) https://doi.org/10.18287/2412-6179-CO-1065