Measurement and Modeling of a Cargo Bicycle Tire for Vehicle Dynamics Simulation

Abstract

In the field of inner-city cargo transportation, solutions such as electrified cargo trailers are increasingly being used. To provide an intelligent drivetrain control system that improves driving dynamics and enables safety, it is necessary to know the characteristics of the trailer system. This includes the behavior of the tires. Existing investigations of bicycle tires focus on camber-angle-dependent models. However, in most trailers, a rigid mounting of the tires without camber is used. For this reason, a bicycle tire model is created within the scope of this study using real measurement data that represent a 20 in tire with typical wheel loads and without camber. The measurements were collected with the mobile tire measurement laboratory of the Bern University of Applied Sciences on an asphalt test site under real conditions. Crosstalk occurring in the measurement hub during the data collection was successfully corrected using a matrix method. With help of the so-called Magic Formula, a tire model was created that can be used for driving dynamics simulations and controller design.

Modeling of a Bicycle Cargo Trailer with Magic Formula Tire Model for Vehicle Dynamics Simulation

“…The model includes a nonlinear tire model based on the not linearized calculations of the slip angles. The normalized tire model is built on the research of Miller et al (2023a) and is used in a lateral vehicle dynamics simulation for the first time. A combined driver model based on a longitudinal and lateral controller has been introduced to follow a reference longitudinal velocity and a lateral trajectory.…”

“…The tire behavior of the bicycle and trailer is modeled using a generic form of the Magic Formula (MF) model according to Pacejka & Besselink (2012) and the results of Miller et al (2023a). This model considers the tire characteristics in the longitudinal and lateral direction as a function of the slip κ as well as the slip angle α of the wheel and F z , but under the assumption that no camber angles occur.…”

“…This model considers the tire characteristics in the longitudinal and lateral direction as a function of the slip κ as well as the slip angle α of the wheel and F z , but under the assumption that no camber angles occur. Regarding the tire model, it is assumed that bicycle and trailer use 20 in wheels with the tires described in Miller et al (2023a). While this is true for the trailer with one axle and two wheels when operated on an even surface, a bicycle can be driven with camber angles ̸ = 0 • .…”

“…At this point, the modeling differs from reality, as the presented three degrees of freedom (3DOF) model allows for motion in the xy plane as well as rotation about the z-axis but does not allow for rotation of the system around the x-or y-axis. In this research, the measured tire data from Miller et al (2023a) is normalized using the F z force. Afterwards, the coefficients of the generic MF are optimized using the non-linear least squares method so that the mathematical model fits the measured data as accurately as possible.…”

“…The model of this research is based on the model presented by Korayem et al (2022), but extended by a longitudinal dynamics model as can be seen in Miller et al (2023b) and a detailed tire model. The tire model is based on a special tire for cargo bicycles measured and modeled according to Miller et al (2023a), which is implemented as a magic formula (MF) model according to Pacejka & Besselink (2012).…”