Dénes Takács

Experiments on Quasiperiodic Wheel Shimmy

The lateral vibration of towed wheels―so-called shimmy―is one of the most exciting phenomena of vehicle dynamics. We give a brief description of a simple rig of elastic tire that was constructed for laboratory measurements. A full report is given on the experimental investigation of this rig from the identification of system parameters to the validation of stability boundaries and vibration frequencies of shimmy motion. The experimental results confirm the validity of those tire models that include delay effects. A peculiar quasiperiodic oscillation detected during the experiments is explained by numerical simulations of the nonlinear time-delayed mathematical model.

Contact patch memory of tyres leading to lateral vibrations of four-wheeled vehicles.

It has been shown recently that the shimmy motion of towed wheels can be predicted in a wide range of parameters by means of the so-called memory effect of tyres. This delay effect is related to the existence of a travelling-wave-like motion of the tyre points in contact with the ground relative to the wheel. This study shows that the dynamics within the small-scale contact patch can have an essential effect on the global dynamics of a four-wheeled automobile on a large scale. The stability charts identify narrow parameter regions of increased fuel consumption and tyre noise with the help of the delay models that are effective tools in dynamical problems through multiple scales.

Micro-shimmy of towed structures in experimentally uncharted unstable parameter domain

In this paper, the lateral instability of towed structures (trailers, caravans and articulated buses) is investigated with special attention to the small amplitude lateral vibration that leads to a higher energy consumption in certain parameter domains. A low degree-of-freedom mechanical model of a shimmying towed tyre is used that describes the dynamics of the tyre–ground contact patch by the time delayed differential equation. Stability charts are calculated and the theoretically predicted linear unstable islands of small amplitude shimmy motions are validated by laboratory experiments. A tyre is towed by a relatively long caster, and its temperature and the input current of the conveyor belt are measured in order to show the increased value of the rolling resistance.

Experiments on Quasi-Periodic Wheel Shimmy

The lateral vibration of towed wheels — so-called shimmy — is one of the most exciting phenomena of vehicle dynamics. We give a brief description of a low degree of freedom rig of elastic tyre that was constructed for laboratory measurements. A full report is given on the experimental investigation of this rig from the identification of system parameters to the validation of stability boundaries and vibration frequencies of shimmy motion. The experimental results confirm the validity of those tyre models that include delay effects. A peculiar quasi-periodic oscillation detected during the experiments is explained by numerical simulations of the nonlinear time-delayed mathematical model.© 2007 ASME

Stabilizing skateboard speed-wobble with reflex delay

A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

Experimental Fitting of Rotor Models by Using a Special Three-Node Beam Element

In this paper, a special type of beam element is developed with three nodes and with only translational degrees-of-freedom (DOFs) at each node. This element can be used effectively to build low degree-of-freedom models of rotors. The initial model from the Bernoulli theory is fitted to experimental results by nonlinear optimization. This way, we can avoid the complex modeling of contact problems between the parts of squirrel cage rotors. The procedure is demonstrated on the modeling of a machine tool spindle.

Stability of Damped Skateboards Under Human Control

A simple mechanical model of the skateboard–skater system is analyzed, in which a linear proportional-derivative (PD) controller with delay is included to mimic the effect of human control. The equations of motion of the nonholonomic system are derived with the help of the Gibbs–Appell method. The linear stability analysis of the rectilinear motion is carried out analytically in closed form. It is shown that how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as functions of the speed, position of the skater on the board, and damping of the skateboard suspension system. Based on these, an explanation is given for the experimentally observed dynamic behavior of the skateboard–skater system at high speed. [DOI: 10.1115/1.4036482]

Skateboard: A Human Controlled Non-Holonomic System

A simple mechanical model of the skateboard-skater system is analyzed, in which a linear PD controller with delay is included to mimic the effect of human control. The equations of motion of the non-holonomic system are derived with the help of the Gibbs-Appell method. The linear stability analysis of rectilinear motion is carried out analytically using the D-subdivision method. It is shown how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as a function of the speed and the fore-aft location of the skater on the board. Based on these, an explanation is given for the well-known instability of the skateboard-skater system at high speed.Copyright

Nonlinear Oscillations at Critical Shimmy Parameters: Experiments and Numerics

Brief description of a low degree of freedom shimmying wheel model is presented where the time delay effect is in the focus of the corresponding stretched-string-like tyre model. The stability charts obtained by linear stability analysis present various bifurcation phenomena. These are checked by experiments on a test rig and also by numerical simulations that involve the partial sliding of the tyre contact region as a nonlinear effect. The sense of the Hopf bifurcations are compared to various shimmy models including the classical single-contact-point ones. Double Hopf bifurcations leading to quasi-periodic oscillations are also investigated. The applied numerical methods are optimized for convergence and also for possible application in real-time control strategies.Copyright

Comparison of time delayed tyre models

Abstract This paper investigates a low degree-of-freedom mechanical model of the well-known phenomenon wheel shimmy. The applied model considers the elasticity of the tyre and describes the motion of the towed tyre by time delay differential equation, where the memory effect is originated in the contact patch. The stability charts of the towed tyre are presented for different types of tyre models.