Bicycle frame load estimation using a controlled semi-analytical simulation of an unconstrained multi-body system

Abstract Semi-analytical simulation methods have the potential to significantly enhance the development of bicycles, as they enable the reproduction of operating loads within the system with high accuracy. To eliminate the need for a numerical model of the human, tires, and track, measured loads are applied to the bicycle structure as excitations in a multi-body simulation. These excitation loads are measured at the connection points between the bicycle system and the environment and replace all constraints of the bicycle structure to the environment in the multi-body simulation, resulting in the simulation of an unconstrained system. The key challenge is to prevent the occurrence of unwanted, motion-dependent loads that potentially compromise the accuracy of the load calculations. To address this, it is crucial to stabilize the simulation and prevent a model drift. Hence, this paper presents the stabilization of an unconstrained bicycle system using existing and newly developed control concepts. It is demonstrated that stabilizing unconstrained multi-body systems with control loads leads to highly accurate system loads. It has been found that for bicycles, a specifically developed $\mathrm{PI}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PI</mml:mi> </mml:math> -control minimizing the angular velocity of the vehicle system is most suitable for accurate reproduction of the operating loads. This approach does not rely on measurement data of the original system trajectory. In adition to the control concepts, a novel method is presented to distribute the control loads over the bicycle system, to increase the accuracy of the calculated component loads and enhance the comparability for elastic multi-body simulations.