Bicycle frame load estimation using semi-analytical multi-body simulation methods

The design and dimensioning of bicycles have always been a challenging task. It is necessary to solve the conflict between a high level of safety against component failure and the demand for a lightweight and cost-efficient design. The operating loads to which the system components are subjected play a decisive role in this task. However, the determination of these loads is a crucial challenge. Besides the widespread use of multi-body simulation in other vehicle industries, in the design of bicycles, the potential has so far remained largely untapped. The main problems arise in modeling the complex driving tracks and the need for a driver model that accurately represents the complex human behavior. Using a semi-analytical modeling approach, the system excitation is directly applied in the form of measured loads. This opens the possibility of representing the rider, track, and tire behavior in their full complexity within the numerical simulation, without making simplifications in the modeling process. However, replacing constraints between the bicycle and the environment with forces leads to an unconstrained system where imbalances can lead to instabilities in the form of uncontrolled accelerations, making the results unusable. This paper presents and evaluates the accuracies of four simulation methods that allow a semi-analytical simulation of bicycles. These are defined by two variations of a locating-floating bearing of the wheel hubs, constraining at a static reference point and the constraining of the frame to a reference point guided along the original frame trajectory. The input of the semi-analytical simulation is based on synthetic measurement data, conducted in a fully analytical simulation with a passive driver model. In contrast to the previous applications of this approach, it was shown that for bicycles, highly accurate results can be calculated without taking the trajectory of the bicycle into account.