A novel method for shape pre-optimization of fir-tree couplings in blade-disk connections

• A novel method for shape pre-optimization of fir-tree couplings in blade-disk connections Muzio M. Gola – Farhad Alinejad. • A new method for pre-optimization of the shape of fir-tree junctions in turbomachines, i.e., for better allocation of material volume at blade-root and at the disk-post. • A spring model that captures the essential elements of the interaction between the blade-root and the disc-post. • A method based on uniform distribution of blade centrifugal loads between pairs of engaging teeth or joint lobes. • A method based on average stresses or pressures (indicative stresses or pressures) on critical cross sections. • A solution made possible by the fact that it has been proved that it is sufficient to know the ratios of spring values, instead of knowing their actual values; the ratios are related to simple geometric proportions. • A spring model method validated by verifying its results, very satisfactorily, against those of full FEM models − Detailed examples and verifications for three-, four- and five-tooth joints. This paper presents an innovative approach to the pre-optimization of the blade-disk fir-tree coupling, with the intent of advancing the design and analysis of such connections in turbomachinery. These couplings are subjected to extreme mechanical loads, primarily from centrifugal forces during turbine operation, compounded by aerodynamic and vibrational forces. These conditions pose substantial challenges to ensuring the structural integrity and long-term reliability of the connections. Failure of the blade-disk attachment can lead to catastrophic consequences, making the optimization of these joints crucial. The proposed pre-optimization method addresses this by optimizing the distribution of material between the blade-root, disk-post, and engaging teeth, ensuring uniform load distribution across all teeth. A novel one-dimensional radial spring model is introduced, which simplifies the representation of the joint. The method achieves accurate load-sharing without requiring knowledge of the spring stiffness values, instead relying on stiffness ratios, which in turn are approximated equal to ratios between the areas of throat cross-sections. This approach effectively balances tensile stresses, contact pressures, and, proportionally, local stress peaks, all while streamlining the design process. Validation against finite element models demonstrates the model’s accuracy across different joint configurations with varying numbers of teeth. This method serves as a foundation for more detailed analysis and future optimization efforts, including those targeting specific failure mechanisms such as fretting fatigue and peak stress mitigation. Overall, this work offers a practical and efficient approach to enhancing the performance and reliability of blade-disk connections in turbomachinery.