PSI - Issue 81

Igor Stoiko et al. / Procedia Structural Integrity 81 (2026) 447–454

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SolidWorks Simulation environment on a purpose-built CAD model of the axle. The overall geometry of the model and the reference designations applied in subsequent calculations are shown in Fig. 9. The finite-element discretisation employed a mixed curvature mesh (Fig. 10) with a maximum element size of 3 mm, as illustrated further in Fig. 11. Based on the simulation results, graphical dependencies describing the variation of static stress, displacement, and the factor of safety were obtained and are presented in Figs. 12 – 14. The assessment of the stress – strain state of the curved axle provides a basis for improving locating reliability, selecting appropriate machining allowances, defining inspection requirements, and ensuring the robustness of the associated tooling. Collectively, these outcomes help eliminate the shortcomings previously observed in the manufacturing technology of curved axles.

Fig. 9. 3D model of the curved axle

Fig. 10. Finite element mesh

Fig. 11. Curved axle model with the applied loading

Fig. 12. Von Mises equivalent stress distribution

Fig. 13. Maximum displacements at the axle ends

Fig. 14. Factor of safety distribution

4. Conclusions Analytical calculations for all three locating methods for curved axes demonstrate that the most accurate locating approach is the method using parallel-offset, angular and axial centers (variant 1). The precision of the resulting angle of intersection of geometric axes for this locating variant can be achieved within Δγ=±5′ – 13′ . Locating CA using variants 2 and 3, namely using two perpendicularly offset and axial centers ( Δγ≤±25′ ) and using two centers in the plane of symmetry and axial center ( Δγ≤22′ ), can be applied to ensure appropriate accuracy depending on the technical requirements of the part drawing. References Aurrekoetxea M, Llanos I, Zelaieta O, López de Lacalle LN (2022). Towards advanced prediction and control of machining distortion: a comprehensive review. International Journal of Advanced Manufacturing Technology , 122, 2823–2848. https://doi.org/10.1007/s00170-022-10087-5 Chen J, Lin S, Zhou X (2016). A comprehensive error analysis method for the geometric error of multi-axis machine tool. International Journal of Machine Tools and Manufacture , 106, 56–66. https://doi.org/10.1016/j.ijmachtools.2016.04.001 Jian-Hua Y, Zhi-Tong C, Jiang ZP (2016). A control process for machining distortion by using an adaptive dual-sphere fixture. I nternational Journal of Advanced Manufacturing Technology , 86(9–12), 3463–3470. https://doi.org/10.1007/s00170-016-8470-2 Li B, Melkote SN (2001). Fixture clamping force optimisation and its impact on workpiece location accuracy. I nternational Journal of Advanced Manufacturing Technology , 17(2),104–113. https://doi.org/10.1007/s001700170198 Meshreki M, Kövecses J, Attia H, Tounsi N (2008) Dynamics modeling and analysis of thin-walled aerospace structures for fixture design in multiaxis milling. Journal of Manufacturing Science and Engineering , 130(3), 031011. https://doi.org/10.1115/1.2927444 Paulo Davim J (2008). Machining: fundamentals and recent adavnces. Springer. ISBN: 978-1-84800-212-8 Paulo Davin J (2016). Metal cutting technologies progress and current trends. DE Gruyter . ISBN: 978-3-11-044942-6 Rahman M, Heikkala J, Lappalainen K (2000). Modeling, measurement and error compensation of multi-axis machine tools. Part I: theory. International Journal of Machine Tools and Manufacture, 40(10), 1535–1546. https://doi.org/10.1016/S0890-6955(99)00101-7 Wang T, Zha J, Jia Q, Chen Y (2016). Application of low-melting alloy in the fixture for machining aeronautical thin-walled component. I nternational Journal of Advanced Manufacturing Technology, 87(9–12), 2797–2807. https://doi.org/10.1007/s00170-016-8654-9 Yang H, Huang X, Ding S, Yu C, Yang Y (2018). Identification and compensation of 11 position-independent geometric errors on five-axis machine tools with a tilting head. I nternational Journal of Advanced Manufacturing Technology , 94(1), 533–544. https://doi.org/10.1007/s00170-017-0826-8 Zha J, Wang T, Li L, Chen Y (2020). Volumetric error compensation of machine tool using laser tracer and machining verification. I nternational Journal of Advanced Manufacturing Technology , 108(7), 2467–2481. https://doi.org/10.1007/s00170-020-05556-8 Zha, J., Villarrazo, N., Martínez de Pisson, G. et al. (2023). An accuracy evolution method applied to five-axis machining of curved surfaces. International Journal of Advanced Manufacturing Technology , 125, 3475–3487. https://doi.org/10.1007/s00170-023-10864-w