Vehicle Shimmy Modeling With Pacejka's Magic Formula and the Delayed Tire Model

Tian, Mi; Stépàn, Gábor; Takács, Dénes; Chen, Nan

doi:10.1115/1.4045943

Cited by 10 publications

(6 citation statements)

References 15 publications

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“…Here, 3-DOF (degree of freedom) inclusive of the shimmy angle of the left front wheel θ 1 and right front wheels θ 2 , and the rolling angle ϕ of the dependent suspension, are considered in the modelling of the steering system dynamics as shown in Figure 2. A similar model for wheel shimmy can also be referenced in Mi et al (2020) and Li and Lin (2006). Three assumptions are made to simplify and neglect non-key factors as follows:1.…”

Section: Dynamic Modellingmentioning

confidence: 99%

“…Shimmy in the ground vehicle is typically referred to the generation of self-excited vibrations of the front wheel, where the shimmy energy is continuously absorbed from the longitudinal motions of the vehicle to sustain the lateral oscillation (Sharp and Jones, 1980). According to the different longitudinal speed range, low-speed shimmy (30–70 km/h) around 6 Hz and high-speed shimmy (>100 km/h) around 10 Hz can be separated (Zhang et al, 2017; Mi et al, 2020). The low-speed shimmy mostly comes from multiple factors such as the tyre-ground interaction, the damping and stiffness parameters of steering and suspension systems, and even the wear of long in-service period, in which certain degrees of swinging motions of the vehicle body can be observed.…”

Section: Introductionmentioning

confidence: 99%

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On the non-linear dynamics of vehicle shimmy coupled with handling motions: modelling, bifurcation analysis, and validations

Wei

et al. 2022

Journal of Vibration and Control

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A novel vehicle dynamic model considering the coupling mechanism between the front wheel shimmy and the vehicle lateral handling motions is established to investigate the interacting effect between the steering shimmy instability and the general motion instability, that focuses especially on the influence of the tyre force saturation induced by lateral-longitudinal coupling when different degrees and allocation strategy of braking force are applied. The typical 3-degree-of-freedom front wheel shimmy structure of dependent suspension is dynamically modelled by using the Lagrange method, alongside the equations for plane vehicle handling motions introduced. The stretched-string-based tyre kinematic equations, that describe the transient tyre-road contact status, are proposed by analytically deriving the coupling relations between the angular shimmy variables and vehicle motion status. A theoretically approximated linear tyre model, based on the coupling between vertical, longitudinal, and lateral directional forces, is analytically derived for stability analysis. Meanwhile, a complete PAC-2002 tyre model, with experimentally identified parameters, is employed for simulation verification. The stability chart of linear stability analysis shows the variation of the system bifurcation curves and stable parameter region under different parametric configurations, which gives that the degrees and allocations of braking force largely affect the stable parameter domain and the global stability. The variations of the system characteristic roots indicate that both Hopf and S-N bifurcation could happen due to shimmy oscillations and destabilization of motion, respectively, and their co-existence at certain parameter domains make the dynamic behaviour further unpredictable and complex. Numerical simulation verifies the dynamical characteristics of shimmy, and further analysis shows that three types of vehicle motion instability which coexisted with shimmy instability could be triggered by the coupling effect. In addition, the variation law of limit-cycle amplitude under varying vehicle driving inputs is summarized, and finally, a preliminary experiment is conducted for validations.

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Section: Dynamic Modellingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the non-linear dynamics of vehicle shimmy coupled with handling motions: modelling, bifurcation analysis, and validations

Wei

et al. 2022

Journal of Vibration and Control

View full text Add to dashboard Cite

show abstract

“…Classical vehicles that are equipped with steeringlinkage or tie-rod connection have focused on the shimmy problems in the early stages of the design and development of the steering system, by revising and matching the structural parameters such as length or angles, and increasing the damping or stiffness within the steering column [26], the shimmy can be effectively prevented when coming into production. Nevertheless, shimmy could still reappear after a long mileage of services resulting from increased clearance of the steering rod [22], dry frictions [41], and loss of damping [24]. In advanced by-wire chassis, with the incorporation of novel unsprung structures and In-Wheel-Motor drive, each wheel subsystem forms up an individual domain with steering, driving torque, and suspension controlled locally to the high-level by-wire signals, thus making no mechanical connections between each other.…”

Section: Introductionmentioning

confidence: 99%

Application of nonlinear energy sink in suppressing wheel shimmy for advanced vehicle chassis design under independent wheel subsystems

Lu,

Habib,

et al. 2024

Preprint

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Novel structures in vehicle control-by-wire chassis have re-emphasized the problem of wheel shimmy. Proper suppression of shimmy in the independent wheel subsystems would significantly improve the performance of the steer-by-wire control. In this paper, a wheel shimmy suppression method using a nonlinear energy sink is proposed. Compared with traditional methods of increasing steering damping, NES seldom interferes with the designed steering dynamics of the vehicle due to its particularly small mass and volume, thus reserving availability for in-service or after-designed vehicles. By installing NES in the wheel frame, a single towed wheel model with NES is constructed. Although NES has almost no effect on the linear stability characteristics, an excellent effect on suppressing vibration amplitudes is explored where over 90% oscillation amplitude of shimmy is mitigated by NES within a wide range of reasonable parameters. Global optimization for optimal NES set-up in unstable speed ranges is further proposed to handle the speed-dependent nature of shimmy, and the result highlights its effectiveness and parameter robustness. Integration of the single-wheel model into the full vehicle with independent steering structures summarizes that NES could be a favorable way to both suppress the existing shimmy phenomenon and control the coupled lateral oscillations of the vehicle body.

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“…Since the cornering force of the tire is an important nonlinear factor, different tire models have been used to describe the cornering force. Then, the effect of tire mechanics on vehicle shimmy was studied (Beregi et al, 2017; Mi et al, 2020; Ran et al, 2014; Zhuravlev et al, 2013). However, little consideration has been given to the change of the vertical load of the tire in the studies mentioned above.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis and dynamic shimmy behavior of vehicle–road system

Wei

Shi

et al. 2021

Journal of Vibration and Control

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To analyze the influence of the road roughness excitation on vehicle shimmy, a 12 degrees-of-freedom dynamic model of vehicle–road system is developed. The Hopf bifurcation theory is used to study the system stability. On this basis, the natural frequency and modal properties of the vehicle system are elaborated. It can be found that the roll mode plays a crucial role in the vehicle stability. Then, the dynamic shimmy behavior exposed to the sinusoidal and random road roughness excitations is investigated with the help of the modal analysis and the largest Lyapunov exponent. Furthermore, the numerical results are verified through the measurement results, and the influence of the front wheel track on vehicle shimmy is also examined. The results show that the decrease of the front wheel track is an effective way to attenuate vehicle shimmy for different road roughness excitations.

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Vehicle Shimmy Modeling With Pacejka's Magic Formula and the Delayed Tire Model

Cited by 10 publications

References 15 publications

On the non-linear dynamics of vehicle shimmy coupled with handling motions: modelling, bifurcation analysis, and validations

On the non-linear dynamics of vehicle shimmy coupled with handling motions: modelling, bifurcation analysis, and validations

Application of nonlinear energy sink in suppressing wheel shimmy for advanced vehicle chassis design under independent wheel subsystems

Modal analysis and dynamic shimmy behavior of vehicle–road system

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