### Untersuchung und Optimierung der Querdynamik von Einspurfahrzeugen - insbesondere Fahrrädern - mit mitlenkender Hinterachse [article]

Benjamin Schmorl, Wolfgang H. Müller, Technische Universität Berlin, Technische Universität Berlin
2016
In this thesis, a model of a bicycle with additional rear steering is derived and examined. The rear steering angle is coupled with the front steering angle. The model is based on the benchmark bicycle [Schwab et al. 2007] which describes a regular bicycle. Main motivation is an increase of self-stability and a reduction of yaw angle in everyday driving maneuvers and in straight-line driving. The equations of motion are derived with the aid of the LAGRANGE function by using the scheme presented
more » ... he scheme presented in [Basu-Mandal 2007]. At first, the model of the regular bicycle is derived. On this basis, the model of the bicycle with coupled rear steering is derived. In the first case, the model has nine degrees of freedom, of which seven are independent. Two degrees of freedom are dependent due to two holonomic-scleronomic constraints. Four non-holonomic constraints reduce the number of independent coordinates in the first and the second time derivative from seven to three. The model with coupled rear steering has ten degrees of freedom, of which seven are independent. Three degrees of freedom are dependent due to three holonomic-scleronomic constraints. Again, four non-holonomic constraints reduce the number of independent coordinates in the first and the second time derivative from seven to three. The derivation of the LAGRANGE equations and the constraints is completely non-linear by the aid of the software environment Maple. By multidimensional TAYLOR series, the very long expressions are linearized and shortened. Two equations of motion result describing the steer angle and the roll angle. The equations of motion are used to examine 33 parameter combinations of the ratio between rear and front steering angle – called Mitlenkfaktor – and the rear fork pitch angle. Validations are carried out by a second simulation model, which is programmed in multibody-simulation environment Simpack. Stability diagrams, in which the forward speed is shown on the abscissa and the eigenvalues of the differential equation system are shown on the [...]