Features of an elastic wheel motion along a curvilinear and rectilinear trajectory with a slip

The results of the study of the motion of an elastic wheel as an integral mechanism along a curvilinear and a rectilinear trajectory with a slip on the ground plane having a high adhesion coefficient are presented. The previous researches analysis has shown that the most complete theory of wheel skidless rolling without slipping on elastic pneumatics was formulated by Keldysh V. M. who proposed the equation for calculating the curvature of the motion trajectory. Due to the difficulty of this equation coefficients determining, its use is currently limited. In this paper, the dependences for determining the components of the equation of the elastic wheel motion trajectory curvature have been proposed. According to the shimmy theory, during an elastic wheel rolling along a curvilinear trajectory, the rim turn and its lateral displacement relative to the tire-ground contact patch occur simultaneously. The rim turn causes tire body torsion, and the lateral displacement causes the elastic wheel moving with a slip angle. It is established that the absolute value of the tire body torsion angle is equal to the slip angle, and their values depend on the trajectory curvature, on the tire-ground contact patch longitudinal axis, and on the existence of traction there. The condition, under which the tire body energy distribution on the rim relative rotation and on its lateral displacement during the movement along a curved trajectory is uniform, has been determined. The experimental confirmation of the hypothesis of uniform distribution of the energy supplied to the elastic wheel during its movement along a curvilinear trajectory on the rim relative turning and its lateral displacement has been obtained. When the elastic wheel moves along a rectilinear trajectory with a slip, only the rim lateral displacement occurs, this displacement is accompanied by a cornering force applied in the center of the tire-ground contact patch and by the tire alining torque relative to the vertical axis passing through the contact patch geometric center. The energy consumption for the rim lateral displacement during the wheel rolling along a rectilinear trajectory with a slip has been also determined. The results of the research can be useful to professionals improving the wheeled vehicles performance characteristics, including maneuverability, handling, and road stability.

Total Variance Approach on Commercial Vehicle Handling Dynamics

The suspension roll motion can produce roll steer, which are functions of roll angle, thus producing extra lateral forces. This paper develops the total variance approach to analyze the effect of suspension roll on commercial vehicle handling dynamics. The side-slip angle unified transfer function, reaction time, transition time, damping ratio and total variance are introduced with the effect of suspension. The vehicle designers could use this approach to get optimization design parameters of vehicle without numerical calculation. For the two-axle commercial vehicles, the total variance approach is useful and could serve as an important tool for evaluating the effect of vehicle suspension roll on commercial vehicle dynamics.

Phase Portrait Trajectory of a 3DOF Vehicular Dynamic Model

This article formulates a front-wheel-drive three-degree-of-freedom (3DOF) four-wheel planar vehicle model with the Magic Formula tire model. The state variables' evolutions of the model, i.e., trajectories of the model under acceleration and deacceleration conditions, are analyzed. The process of evolution is divided into desirable and undesirable phases based on the response characteristics of the vehicle to the driver input during the process. The trajectories are categorized as unsaturated trajectories and saturated trajectories by the existence of saturated tires during these phases. The response of state variables to driver input under acceleration conditions during undesirable phases are zero or even opposite, while the response of undesirable phases under the deacceleration condition is partially positive. Besides, the existing yaw rate safety envelope is recalibrated by using a longitudinal and lateral tire force coupling model. A more accurate yaw rate safety envelope is obtained from the given driver input. Furthermore, a longitudinal speed safety envelope is proposed according to the relationships among slip angle, yaw rate, and longitudinal speed. These safety envelopes are determined by driver input, tire properties, and grip condition. After overlaying yaw rate and longitudinal speed safety envelopes in the state space, the feasibility of using the safety envelope as trajectory classification criteria is discussed.

Integrated Chassis Control and Control Allocation for All Wheel Drive Electric Cars with Rear Wheel Steering

This study investigates a control strategy for torque vectoring (TV) and active rear wheel steering (RWS) using feedforward and feedback control schemes for different circumstances. A comprehensive vehicle and combined slip tire model are used to determine the secondary effect and to generate desired yaw acceleration and side slip angle rate. A model-based feedforward controller is designed to improve handling but not to track an ideal response. A feedback controller based on close loop observation is used to ensure its cornering stability. The fusion of two controllers is used to stabilize a vehicle’s lateral motion. To increase lateral performance, an optimization-based control allocation distributes the wheel torques according to the remaining tire force potential. The simulation results show that a vehicle with the proposed controller exhibits more responsive lateral dynamic behavior and greater maximum lateral acceleration. The cornering safety is also demonstrated using a standard stability test. The driving performance and stability are improved simultaneously by the proposed control strategy and the optimal control allocation scheme.

Modeling and Analysis of the Kinetic Influence of Liquid Sloshing Characteristics on High-Clearance Sprayers

To research the influence of liquid sloshing on the driving stability of high-clearance sprayers, this paper builds an equivalent liquid sloshing mechanical model and obtains the stochastic acceleration excitation of the rectangular spray tank using the Adams kinetic model, thus obtaining the relationship between the impact force, moment, and the stochastic acceleration using Fluent numerical simulation analysis. This paper makes further calculations with MATLAB/Simulink system models, and the result from comparing these two calculations shows that the equivalent strategy proposed in this paper has a better consistency. Based on the consideration of the acting forces of the additional moment due to lateral movement of the center of mass of the liquid and the dynamic pressure due to liquid sloshing in the tank, this paper builds a mathematical model of the sprayer and researches the influence of the filling ratio and vehicle velocity on the vehicle stability through stochastic acceleration excitation. The results show that, in the case of different speeds, the liquid sloshing has a small influence on the overall roll angle; in the case of different filling ratios, the liquid sloshing has a big influence on the overall roll angle, the slip angle of the center of mass, and the yaw angular velocity; the filling ratio k = 0.85 and the speed u = 1 m/s−2 m/s are safe operation parameters of the sprayer. This research provides reference solutions for the stability control and optimization problems of the high-clearance sprayer and semitrailer.

A benchmark study on the model-based estimation of the go-kart side-slip angle

Nowadays, the active safety systems that control the dynamics of passenger cars usually rely on real-time monitoring of vehicle side-slip angle (VSA). The VSA can’t be measured directly on the production vehicles since it requires the employment of high-end and expensive instrumentation. To realiably overcome the VSA estimation problem, different model-based techniques can be adopted. The aim of this work is to compare the performance of different model-based state estimators, evaluating both the estimation accuracy and the computational cost, required by each algorithm. To this purpose Extended Kalman Filters, Unscented Kalman Filters and Particle Filters have been implemented for the vehicle system under analysis. The physical representation of the process is represented by a single-track vehicle model adopting a simplified Pacejka tyre model. The results numerical results are then compared to the experimental data acquired within a specifically designed testing campaign, able to explore the entire vehicle dynamic range. To this aim an electric go-kart has been employed as a vehicle, equipped with steering wheel encoder, wheels angular speed encoder and IMU, while an S-motion has been adopted for the measurement of the experimental VSA quantity.

Direct yaw-moment control of vehicles based on phase plane analysis

In view of the problems related to vehicle-handling stability and the real-time correction of the heading direction, nonlinear analysis of a vehicle steering system was carried out based on phase plane theory. Subsequently, direct yaw-moment control (DYC) of the vehicle was performed. A four-wheel, seven-degree-of-freedom nonlinear dynamic model that included the nonlinear characteristics of the tire was established. The stable and unstable regions of the vehicle phase plane were divided, and the stable boundary model was established by analyzing the side slip angle–yaw rate ([Formula: see text]) and side slip angle–side slip angle rate [Formula: see text] phase planes as functions of the vehicle state variables. In the unstable region of the phase plane, taking the instability degree as the control target, a fuzzy neural network control strategy was utilized to determine the additional yawing moment of the vehicle required for stability restoration, which pulled the vehicle back from an unstable state to the stable region. In the stable region of the phase plane, a fuzzy control strategy was utilized to determine the additional yawing moment so that the actual state variables followed the ideal state variables. In this way, the vehicle responded rapidly and accurately to the steering motion of the driver. A simulation platform was established in MATLAB/Simulink and three working condition was tested, that is, step, sine with dwell, and sine amplification signals. The results showed that the vehicle handling stability and the instantaneous heading-direction adjustment ability were both improved due to the control strategy.

Vehicle Dynamic Control with 4WS, ESC and TVD under Constraint on Front Slip Angles

To enhance vehicle maneuverability and stability, a controller with 4-wheel steering (4WS), electronic stability control (ESC) and a torque vectoring device (TVD) under constraint on the front slip angles is designed in this research. In the controller, the control allocation method is adopted to generate yaw moment via 4WS, ESC and TVD. If the front steering angle is added for generating yaw moment, the steering performance of the vehicle can be further deteriorated. This is because the magnitude of the lateral tire forces are limited and the required yaw moment is insufficient. Constraint is imposed on the magnitude of the front slip angles in order to prevent the lateral tire forces from saturating. The driving simulation is performed by considering the limit of the front slip angle proposed in this study. Compared to the case that uses the existing 4WS, the results of this study are derived from the actuator combination that enhances performance while maintaining stability.

The Use of Crosslinks with Posterior Pedicular Screw Fixation in Lumbar Spondylolisthesis

Background Pedicle screw instrumentation has gained wide popularity for stabilization of spinal fusions. The use of pedicle screw fixation has increased fusion rates. The placement of segmental pedicle screws and cross-links in short segment posterior pedicle screw constructs has been shown to increase the construct stiffness in some planes. Aim of the Work to evaluate addition of crosslinks to posterior pedicular screw fixation as a modality for surgical management of lumbar spondylolisthesis. Patients and Methods This study included 50 patients with lumbar spondylolisthesis divided into two groups according to the surgical approach used in treatment. One group with Posterolateral fixation by transpedicular screws and rods and the other Group had cross-links added to the posterior construct. Results There was no significant difference in postoperative JOA score between both groups, while comparing mean of preoperative and postoperative JOA scores in each group showed a significant rise of the score in each group after surgery. There was no significant difference in the variables of postoperative sagittal alignment between both groups, while comparing mean of preoperative and postoperative sagittal alignment variables in each group revealed a significant reduction of the disc height percent in both groups, and in slip angle and lumbar lordosis angle in group B. Regarding postoperative rate and degree of improvement in the studied groups, there was no significant difference in the rate and degree of improvement between both groups. Conclusion no appreciable benefit from using cross-links was found in short-segment fixation of lumbar spondylolisthesis, where there’s no or little torsional instability encountered.