Steering and Stability of Single-track Vehicles

1951 ◽  
Vol 5 (1) ◽  
pp. 191-213 ◽  
Author(s):  
R. A. Wilson-Jones
Keyword(s):  
Lateral Force ◽  
Front Wheel ◽  
Slip Angle ◽  
Single Track ◽  
Motor Cycle ◽  
Low Mass ◽  
Low Speeds ◽  
The Stability ◽  
Straight Ahead

The author briefly states the elementary principles of equilibrium and claims that the stability of the conventional bicycle or motor cycle is automatic except at very low speeds. This is because the steering automatically turns in the direction in which the machine is leaning and returns to the straight ahead position when the machine is restored to the vertical. The achievement of these effects is largely due to the “trail” of the front wheel. The causes of “steering roll” and “steering wobble” and the purpose of the inclination of the steering head, are examined, as are the effects of high and low mass centres and of the rider leaning with and against the machine. It is shown how the elementary principles of steering apply to various types of vehicle, including single-track vehicles in which the necessary lateral force comes mainly from camber thrust rather than slip angle. The results are given of experiments on varying amounts of “trail”, and a method of measuring slip angles is described which is applicable to motor cycles. Finally, a method of indicating the direction of the torque applied to the handlebars when entering, holding, and leaving a bend is described.

Bifurcation analysis of vehicle shimmy system exposed to road roughness excitation

2021 ◽  
pp. 107754632098779
Author(s):  
Heng Wei ◽  
Jian-Wei Lu ◽  
Sheng-Yong Ye ◽  
Hang-Yu Lu
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Averaging Method ◽  
Lagrange Equation ◽  
Response Characteristic ◽  
Lateral Force ◽  
Front Wheel ◽  
The Road ◽  
Road Roughness ◽  
The Stability

The vertical load of the tire has a significant influence on the lateral force, so the influence of the dynamic load on vehicle shimmy should be taken into account. Based on the dynamic model of a quarter vehicle, a three-degrees-of-freedom dynamic model of the shimmy system with consideration of the road roughness excitation is established by applying the second Lagrange equation. The response characteristic of the system is investigated by the numerical simulations. Moreover, the complexification-averaging method is used to obtain the analytical expression of the shimmy angle of the front wheel, and then, the stability of periodic solutions of the system is evaluated based on the bifurcation theory. Finally, the saddle-node bifurcation and Hopf bifurcation of the shimmy system are studied. The influence of the system parameters on the bifurcation characteristic of the system is also investigated, and the results obtained by using the complexification-averaging method are compared with the numerical examples.

The Effect of Plate Length on the Behaviour of Free-to-Rotate VIV Suppressors With Parallel Plates

2012 ◽  
Author(s):  
Gustavo R. S. Assi ◽  
Julia R. H. Rodrigues ◽  
Cesar M. Freire
Keyword(s):  
Reynolds Number ◽  
Cross Flow ◽  
Lateral Force ◽  
High Amplitude ◽  
Parallel Plates ◽  
Number Range ◽  
Plate Length ◽  
Low Mass ◽  
The Stability ◽  
Vibration Suppressor

Experiments have been carried out on free-to-rotate parallel plates fitted to a rigid section of circular cylinder to investigate the effect of plate length on the stability of this type of VIV (vortex-induced vibration) suppressor. Measurements of the dynamic response and trajectories are presented for models with low mass and damping which are free to respond in the cross-flow and streamwise directions. It is shown that, depending on a combination of geometric and strucutral parameters, parallel plates might not be able to completely suppress VIV for the whole range of reduced velocities investigated. Plates with length between 1.0 and 2.0 diameters showed instabilities and induced high-amplitude vibrations for some specific reduced velocities. Rotational friction was increased for a second run and all plates stabilised and suppressed VIV for the whole range of reduced velocities tested. An undesirable steady lateral force was also observed to occur for all configurations. Experiments with a plain cylinder in the Reynolds number range from 1,000 to 20,000 have been performed to serve as reference.

Experimental Investigation on the Stability of Parallel and Oblique Plates as Suppressors of Vortex-Induced Vibration

2013 ◽  
Author(s):  
Gustavo R. S. Assi ◽  
Guilherme S. Franco
Keyword(s):  
Cross Flow ◽  
Lateral Force ◽  
High Amplitude ◽  
Parallel Plates ◽  
Number Range ◽  
Vortex Induced Vibration ◽  
Plate Length ◽  
Low Mass ◽  
The Stability ◽  
Vibration Suppressor

Experiments have been carried out on models of free-to-rotate parallel and oblique plates fitted to a rigid section of circular cylinder to investigate the effect of plate length and oblique angle on the stability of this type of VIV (vortex-induced vibration) suppressor. Measurements of the dynamic response and trajectories of motion are presented for models with low mass and damping which are free to respond in the cross-flow and streamwise directions. It is shown that, depending on a combination of geometric parameters — such as plate length, plate angle and gap between plates and cylinder — devices might not be able to completely suppress VIV for the whole range of reduced velocities investigated. Plates with larger oblique angles turned to be less stable than parallel plates and induced high-amplitude vibrations for some specific reduced velocities. An undesirable steady lateral force was also observed to occur for all configurations and might be related to the existence of a large gap and oblique angles. Systems may present streamwise vibration due to strong flow separation and reattachment on the outer surface of plates with large oblique angles. Large angles may also increase drag. Experiments with a plain cylinder in the Reynolds number range from 3,000 to 20,000 have been performed to serve as reference. Reduced velocity was varied between 2 and 13.

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

Normalization of Tire Force and Moment Data

1993 ◽  
Vol 21 (2) ◽  
pp. 91-119 ◽  
Author(s):  
H. S. Radt ◽  
D. A. Glemming
Keyword(s):  
Surface Water ◽  
Lateral Force ◽  
Slip Angle ◽  
Inflation Pressure ◽  
Slip Ratio ◽  
Tire Force ◽  
Camber Angle ◽  
Potential Benefits ◽  
Overturning Moment ◽  
Semi Empirical

Abstract Semi-empirical theories of tire mechanics are employed to determine appropriate means to normalize forces, moments, angles, and slip ratios. Force and moment measurements on a P195/70R 14 tire were normalized to show that data at different loads could then be superimposed, yielding close to one normalized curve. Included are lateral force, self-aligning torque, and overturning moment as a function of slip angle, inclination angle, slip ratio, and combinations. It is shown that, by proper normalization of the data, one need only determine one normalized force function that applies to combinations of slip angle, camber angle, and load or slip angle, slip ratio, and load. Normalized curves are compared for the effects of inflation pressure and surface water thickness. Potential benefits as well as limitations and deficiencies of the approach are presented.

Simplified Prediction of Ply Steer in Radial Tires

1980 ◽  
Vol 8 (1) ◽  
pp. 3-9 ◽  
Author(s):  
C. W. Bert
Keyword(s):  
Composite Laminate ◽  
Ground Plane ◽  
Lateral Force ◽  
Rolling Contact ◽  
Slip Angle ◽  
Uniform Stress ◽  
Rubber Composite ◽  
Laminate Theory ◽  
Contact Models ◽  
Uniform Stress State

Abstract Ply steer is a rolling contact phenomenon which manifests itself as a lateral force acting at the ground plane of a tire constrained in yaw or a change in slip angle of a tire free to yaw. It has long been known that radial tires generally exhibit greater ply steer than do bias tires. However, the only previously published quantitative analysis of this phenomenon considered the multi-layer cord-rubber composite by means of netting analysis, which is not very accurate at cord angles typical of radial tire belts. A simple, explicit expression is developed herein by combining modern composite laminate theory with two very simple, uniform-stress-state tire-road contact models. The ply-steer results predicted by the resulting expressions are compared with some experimental results and the agreement is found to be reasonably satisfactory.

A novel path tracking approach considering safety of the intended functionality for autonomous vehicles

2021 ◽  
pp. 095440702110205
Author(s):  
Huiran Wang ◽  
Qidong Wang ◽  
Wuwei Chen ◽  
Linfeng Zhao ◽  
Dongkui Tan
Keyword(s):  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
Coordinated Control ◽  
Steering System ◽  
Front Wheel ◽  
Path Tracking ◽  
Hierarchical Architecture ◽  
Automatic Steering ◽  
The Stability ◽  
Control Layer

To reduce the adverse effect of the functional insufficiency of the steering system on the accuracy of path tracking, a path tracking approach considering safety of the intended functionality is proposed by coordinating automatic steering and differential braking in this paper. The proposed method adopts a hierarchical architecture consisting of a coordinated control layer and an execution control layer. In coordinated control layer, an extension controller considering functional insufficiency of the steering system, tire force characteristics and vehicle driving stability is proposed to determine the weight coefficients of automatic steering and the differential braking, and a model predictive controller is designed to calculate the desired front wheel angle and additional yaw moment. In execution control layer, a H∞ steering angle controller considering external disturbances and parameter uncertainty is designed to track desired front wheel angle, and a braking force distribution module is used to determine the wheel cylinder pressure of the controlled wheels. Both simulation and experiment results show that the proposed method can overcome the functional insufficiency of the steering system and improve the accuracy of path tracking while maintaining the stability of the autonomous vehicle.

scholarly journals STUDY OF A STRUCTURE SUSPENDED FROM A SYSTEM OF STEEL COLUMNS AND TRUSSES (SYSTEM AND STABILITY)

2020 ◽  
Vol 9 (9) ◽  
pp. 43-54
Keyword(s):  
Reinforced Concrete ◽  
Lateral Force ◽  
Concrete Slabs ◽  
Structural Constraints ◽  
Steel Columns ◽  
Force Method ◽  
Reinforced Concrete Slabs ◽  
The Stability

Throughout history, men always wanted to build structures that are each more impressive than the next, while rising higher in the air. In this process, men were not satisfied with making sure that these structures were beautiful, impressive and majestic, but that they could also be very useful, that they fulfilled a function, and that they were able to resist the various structural constraints that will be imposed on it, or that could be imposed on it. With this in mind, we thought of creating a structure that could both inspire this side of wonder and structural beauty, while being useful and resistant to the loads imposed on it. In this work, we are going to talk about a building suspended to its foundation, in the sense that the building does not rest directly on the ground, but is suspended nearly eight meters from the ground by each of the three columns which support the said building by a system of trusses. The structure is made of steel with reinforced concrete slabs, which gives it a significant advantage in terms of weight. Another advantage is that it reacts quite well to earthquakes, showing only very small deflections using the equivalent lateral force method. In this work we will focus on the stability of the members of the system that carries the building and the stability of the building in general.

scholarly journals Adhesion state estimation based on improved tire brush model

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774770
Author(s):  
Bei Shaoyi ◽  
Li Bo ◽  
Zhu Yanyan
Keyword(s):  
Lateral Force ◽  
Longitudinal Force ◽  
Lateral Acceleration ◽  
Stable Range ◽  
The Road ◽  
Nonlinear Compensation ◽  
The Stability ◽  
Standard Calculation ◽  
Double Nonlinear ◽  
Brush Model

On the basis of calculating the longitudinal force using the original brush model, we simplify the tire structure and consider the lateral force generated by the lateral elasticity of the tread. At the same time, the boundary conditions between the adhesion area and the slip zone in the contact area of the tire are fully discussed. By establishing an improved tire brush model, the error caused by neglecting the sideslip characteristics is avoided, and the adaptability of the tire model is improved. A double nonlinear compensation method based on the lateral acceleration deviation and the yaw rate deviation is employed to estimate the road adhesion coefficient, which is closer to the actual attachment situation than the standard calculation. Based on this model, the vehicle stability coefficient k is defined and calculated to describe the stability of the vehicle during the driving process. The modeling results show that the value of k is always in the stable range of [0, 1]. Therefore, the vehicle that utilizes the improved tire brush model is always within the controllable range in the driving process, which verifies the effectiveness of the model.

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