PSI - Issue 68

Emanuele Vincenzo Arcieri et al. / Procedia Structural Integrity 68 (2025) 969–973 E.V. Arcieri and S. Baragetti / Structural Integrity Procedia 00 (2025) 000–000

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low production costs but innovative materials offer greater energy efficiency as their application, combined with advanced manufacturing technologies, enables the development of optimized geometries (Maleque and Dyuti, 2010; Amiri et al., 2017; Lin et al., 2017; Tomaszewski, 2021; Regenwetter et al., 2023). Enhanced mechanical properties, weight reduction and extended service life are key concepts for the evolution and improvement of mechanical systems in a sustainable way. Improved mechanical properties reduce the amount of material needed for the production of components and weight reduction leads to decreased inertia of mechanical systems. This implies lower fuel consumption in cars and other motor vehicles, decreased electricity demand in battery-powered vehicles and lower human energy expenditure for bicycles. Furthermore, the extension of the service life of products leads to the reduction of waste over time. These strategies contribute to eco-sustainability. Producing safer, lighter, less polluting and longer lasting products, with equal or superior resistance, represents one of the main challenges of contemporary engineering. Many solutions are already present in pioneering sectors such as aerospace. The present duty is therefore to adapt these solutions to other sectors. Thanks to the development of innovative manufacturing technologies, high-performance materials and sophisticated design methodologies, bicycles are undergoing an evolution never seen before. Among the various components of a bicycle, the frame plays a central and fundamental role. It is the load-bearing structure to which the other components are fixed and guarantees the proper functioning of the entire assembly. In addition to maintaining the components in their designated positions, the frame has the aim to absorb the energy deriving from the various forces acting on the bicycles, including those imposed by the rider and caused by the ground irregularities. This work analyses the stress state of a bicycle frame made of titanium using the finite element method. The loading condition consists in a tensile force applied at the front axle of the bicycle. The most stressed frame parts result to be the top and down tubes, in the areas close to the head tube.

Nomenclature E Ti elastic modulus of titanium Ti E steel elastic modulus of steel steel Poisson’s coefficient of steel F applied force ultimate tensile strength Poisson’s coefficient of titanium UTS

2. Finite element analysis of the bicycle frame The investigated bicycle frame geometry is based on one provided by Nevi s.r.l. (nevi-titanio.com). The frame was made of titanium alloys, with titanium Grade 9 used to manufacture all the tubular parts and Grade 5 for the derailleur hangers. The stresses in the frame were assessed for a loading condition derived from one of the experimental test methods reported in the BS EN ISO 4210-6 standard (2015). A tensile force F of 1200 N was applied at the front axle of the bicycle, as shown in Fig.1a. A static load was applied in order to identify the most stressed areas of the frame. The magnitude of the applied force is the maximum value for the fatigue test as reported in the standard. The frame was modeled using 2D finite elements. To reproduce the boundary conditions defined in the BS standard, a rear pin and a dummy fork made of steel were inserted and modeled with 1D elements (Fig. 1b). The cross-sectional size of the dummy fork was determined to satisfy the stiffness requirements specified in the standard. The parts of the assembly were connected using a multi-point constraint type beam (Fig. 1c). The materials of the bicycle frame, dummy fork and pin were assumed to be isotropic, homogeneous and linear elastic, with a Young’s modulus E Ti =110000 MPa and a Poisson’s coefficient Ti =0.34 for titanium and E steel =206000 MPa and steel =0.3 for steel (matweb.com). The created mesh for the whole assembly consists of 117201 elements (Fig. 1d) and was obtained after a mesh convergence study conducted by assessing the maximum and minimum stresses in the entire model.