The analysis focuses on a lightweight tandem bicycle frame engineered to withstand a natural resonant frequency above 30Hz, ensuring a smoother ride. Durability was paramount, with the frame designed to last at least 10 years or 1 million loading cycles. Finite Element Analysis simulations evaluated fatigue life and frequency, while frames made from Aluminium 7075-T6 and Titanium Grade 9 were compared to determine the optimal construction material.

Analysis Context

Tandem bicycles, designed for two riders, present unique challenges in terms of design and performance. They require a robust and lightweight frame to ensure optimal performance and durability. The report focuses on designing such a frame that not only meets the size constraints but also achieves a high resonant frequency and long lifespan. These factors are crucial in ensuring the bicycle’s performance and the comfort of the riders. The study assumes ideal conditions, including perfect joints and no material damage due to external effects. While these assumptions may not hold in real-world scenarios, they provide a baseline for understanding the performance of the frame under optimal conditions.

Methodology

The design process for the lightweight tandem bicycle frame began with the lightest frame possible, with an average wall thickness for aluminium bike tubing around 0.8 - 1mm and an average diameter of the tubes around 38mm. These dimensions were chosen to minimize the weight of the frame while ensuring its structural integrity. The second iteration of the design aimed to increase the resonant frequency by 20% compared to the initial design. This was done by adjusting the dimensions and geometry of the frame.

The study assumes ideal conditions, including perfect joints and no material damage due to external effects. While these assumptions may not hold in real-world scenarios, they provide a baseline for understanding the performance of the frame under optimal conditions. The boundary conditions for the simulations were set to mimic real-world conditions as closely as possible. The frame was fixed at the points where it would connect to the wheels, and the loads were applied at the points where the riders would be exerting force. The magnitude of the loads was based on the weight and force exerted by an average rider.

A fatigue simulation was conducted to evaluate the lifespan of the frame. The frame was subjected to 1 million loading cycles, which is equivalent to 10 years of use. The simulation provided insights into how the frame would perform over time and under various loading conditions. The frequency simulation was conducted to evaluate the resonant frequency of the frame. The goal was to design a frame that could withstand a natural resonant frequency of over 30Hz. This frequency is significant as it ensures the frame will not resonate with the pedalling frequency of the riders, thus providing a smoother ride.

Results

This section delves into a comprehensive analysis of the tandem bicycle frame design, encompassing mesh refinement, original and iterated design outcomes, and sanity checks. Initially, the study explored mesh refinement, transitioning from a standard mesh, which proved ineffective for sizes larger than 7mm, to a blended curved mesh tailored to the model's geometry, facilitating quicker simulations. Optimal mesh parameters were established, with a maximum size of 5mm and a minimum of 1mm, showcasing minimal stress changes at smaller sizes.

Original design assessments revealed an aluminium frame weighing 3.82kg with a wall thickness of 0.8mm and an external diameter of 38mm. The resonance frequency study showcased a mode shape 1 value of 49.51Hz, well above the required 30Hz threshold. Additionally, the fatigue study indicated a lifespan of 40 million cycles, with stress concentrations primarily around the seat joints. Iterated design modifications, featuring a thicker wall of 1mm and an added diagonal member, resulted in a weight increase to 5.40kg but enhanced the resonant frequency to 60.63Hz, marking a 22% improvement. Despite these adjustments, the fatigue study reiterated a maximum lifespan of 40 million cycles, with increased damage likely occurring on the main diagonal bar. Validation of the studies encompassed static studies for stress verification, comparisons with existing tandem frame data for frequency and fatigue results, and visual simulations conforming to Finite Element Analysis principles. Additionally, the custom S-N curve for titanium underwent rigorous validation through cross-referencing multiple sources.

Figure 1. CAD model of a tandem frame tested with FEA.

Discussion

While the results are promising, it's important to note that they are based on an ideal scenario mathematical model. This means that the actual performance of the frame may vary in real-world conditions. The large number of nodes in the model and the lack of random imperfections may affect the accuracy of the results. However, these limitations do not diminish the value of the study. Instead, they highlight areas for further research and refinement of the design. The study provides valuable insights into the design of lightweight tandem bicycle frames and sets the stage for further research and development in this field. Future studies could explore the impact of various factors not considered in this study, such as the effect of imperfect joints and material damage due to external effects.