The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Richard W. Topping - One of the best experts on this subject based on the ideXlab platform.
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Understeer Concepts with Extensions to Four-Wheel Steer, Active Steer, and Time Transients
SAE International Journal of Passenger Cars - Electronic and Electrical Systems, 2012Co-Authors: Richard W. ToppingAbstract:An overview of existing and alternative forms of vehicle Understeer/oversteer expressions is presented. New forms are derived consistent with conceptual extensions to the configurations of the vehicle's steering system, the driving mode - steady-state or transient, and the responses - path curvature or yaw velocity. Derivation of all Understeer expressions is presented with a consistent use of the Ackermann reference case and the related "Ackermann vehicle" construct. The vehicle is otherwise represented in a traditional manner as a bicycle model operating in the linear range consistent with small angle approximations. The vehicle's steering system is assumed to be more generally configured with four-wheel steer and active or steer-by-wire actuation at both axles. The actuation is assumed to allow the introduction of significant speed sensitivity to the effective overall steering ratios. Discussion is devoted to the significance of this speed sensitivity on test results and the determination of the mean reference steer angles. Expressions for Understeer gradient associated with this generally configured vehicle are simplified for the more familiar case of a front-wheel steer vehicle with a passive steering system having a fixed overall steering ratio. The driving mode can be either steady-state, as is traditionally assumed, or transient. The transients are assumed to be the result of steering transients or speed changes. Understeer expressions are presented using traditional variables, included reference steer angle and included Ackermann steer angle, and less frequently used variables, axle reference sideslip angles and cornering compliances. Context is given with a brief history of the development of Understeer concepts, both traditional steady-state and transient, and usage of the terms "Understeer" and "oversteer". Language: en
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Understeer Concepts with Extensions to Four-Wheel Steer, Active Steer, and Time Transients
SAE International Journal of Passenger Cars - Electronic and Electrical Systems, 2012Co-Authors: Richard W. ToppingAbstract:An overview of existing and alternative forms of vehicle Understeer/oversteer expressions is presented. New forms are derived consistent with conceptual extensions to the configurations of the vehicle's steering system, the driving mode - steady-state or transient, and the responses - path curvature or yaw velocity. Derivation of all Understeer expressions is presented with a consistent use of the Ackermann reference case and the related "Ackermann vehicle" construct. The vehicle is otherwise represented in a traditional manner as a bicycle model operating in the linear range consistent with small angle approximations. The vehicle's steering system is assumed to be more generally configured with four-wheel steer and active or steer-by-wire actuation at both axles. The actuation is assumed to allow the introduction of significant speed sensitivity to the effective overall steering ratios. Discussion is devoted to the significance of this speed sensitivity on test results and the determination of the mean reference steer angles. Expressions for Understeer gradient associated with this generally configured vehicle are simplified for the more familiar case of a front-wheel steer vehicle with a passive steering system having a fixed overall steering ratio. The driving mode can be either steady-state, as is traditionally assumed, or transient. The transients are assumed to be the result of steering transients or speed changes. Understeer expressions are presented using traditional variables, included reference steer angle and included Ackermann steer angle, and less frequently used variables, axle reference sideslip angles and cornering compliances. Context is given with a brief history of the development of Understeer concepts, both traditional steady-state and transient, and usage of the terms "Understeer" and "oversteer". Language: en
Francesco Frendo - One of the best experts on this subject based on the ideXlab platform.
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On the handling performance of a vehicle with different front-to-rear wheel torque distributions
Vehicle System Dynamics, 2018Co-Authors: Basilio Lenzo, Aldo Sorniotti, Francesco Bucchi, Francesco FrendoAbstract:The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the Understeer coefficient in quasi-steady-state maneuvers. In this paper, ex...
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A New Formulation of the Understeer Coefficient to Relate Yaw Torque and Vehicle Handling
Vehicle System Dynamics, 2016Co-Authors: Francesco Bucchi, Francesco FrendoAbstract:ABSTRACTThe handling behaviour of vehicles is an important property for its relation to performance and safety. In 1970s, Pacejka did the groundwork for an objective analysis introducing the handling diagram and the Understeer coefficient. In more recent years, the Understeer concept is still mentioned but the handling is actively managed by direct yaw control (DYC). In this paper an accurate analysis of the vehicle handling is carried out, considering also the effect of drive forces. This analysis brings to a new formulation of the Understeer coefficient, which is almost equivalent to the classical one, but it can be obtained by quasi-steady-state manoeuvres. In addition, it relates the vehicle yaw torque to the Understeer coefficient, filling up the gap between the classical handling approach and DYC. A multibody model of a Formula SAE car is then used to perform quasi-steady-state simulations in order to verify the effectiveness of the new formulation. Some vehicle set-ups and wheel drive arrangements ...
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The handling surface: a new perspective in vehicle dynamics
Vehicle System Dynamics, 2007Co-Authors: Francesco Frendo, G. Greco, Massimo Guiggiani, Antonio SponzielloAbstract:The problem of describing the Understeer–oversteer behaviour of a general vehicle, such as one with locked differential or tandem rear axle, is addressed taking a new perspective. The well-known handling diagram and the associated classical Understeer gradient may be inadequate, mainly because they are no longer unique. The new concept of handling surface and a new definition of Understeer gradient, which is indeed the gradient of the handling surface and hence a vector, are presented. It is also shown how the new concepts relate to and generalize the classical ones. Finally, a procedure for the experimental measure of the new Understeer gradient is outlined.
Matthijs Klomp - One of the best experts on this subject based on the ideXlab platform.
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On optimal recovery from terminal Understeer
Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering, 2014Co-Authors: Matthijs Klomp, Mathias R Lidberg, Timothy GordonAbstract:This paper addresses the problem of terminal Understeer and its mitigation via integrated brake control. The scenario considered is when a vehicle enters a curve at a speed that is too high for the tyre-road friction limits and an optimal combination of braking and cornering forces is required to slow the vehicle down and to negotiate the curve. Here, the driver commands a step steering input, from which a circular arc reference path is inferred. An optimal control problem is formulated with an objective to minimize the maximum off-tracking from the reference path, and two optimal control solutions are obtained. The first is an explicit analytical solution for a friction-limited particle; the second is a numerically derived open-loop brake control sequence for a nonlinear vehicle model. The particle solution is found to be a classical parabolic trajectory associated with a constant acceleration vector of the global mass center. The independent numerical optimization for the vehicle model is found to approximate closely the kinematics of the parabolic path reference strategy obtained for the particle. Using the parabolic path reference strategy, a closed-loop controller is formulated and verified against the solution from numerical optimization. The results are further compared with Understeer mitigation by yaw control, and the parabolic path reference controller is found to give significant improvement over yaw control for this scenario.
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Experimental verification of Understeer compensation by four wheel braking
2014Co-Authors: Timothy Gordon, Matthijs Klomp, Mathias R LidbergAbstract:This study is designed to validate a new approach to Understeer mitigation chassis control, based on a particle motion reference: parabolic path reference (PPR). Considering the scenario of excess entry speed into a curve, related to run-off-road crashes, the aim is that automatic braking minimizes lateral deviation from the target path by using an optimal combination of deceleration, cornering forces and yaw moments. Previous simulation studies showed that four-wheel braking can achieve this much better than a conventional form of yaw moment control (DYC). The aim of this work is to verify this on a test track with an experimental vehicle, and to compare performance with DYC and an uncontrolled vehicle. Experiments were performed with a front-wheel-drive passenger vehicle equipped with an additional four identical brake callipers controlled via an electro-hydraulic brake (EHB) system, enabling individual brake control. Minimizing the maximum deviation from the intended curve radius is the control objective. Feedback to the controller consists of the available steering wheel angle, wheel speeds, yaw rate and lateral acceleration sensors in the vehicle. Additional to these variables, also the vehicle position was logged using a GPS system. It was found that PPR is superior to DYC in reducing the maximum deviation from the intended path, confirming the trends previously found in simulations. Furthermore, the PPR concept is found to be inherently more stable than DYC since more brake force is applied to the outer wheels than the inner wheels throughout the manoeuvre. The experiments involve a first implementation of a PPR control which is not a fully closed-loop control intervention and tuned to a step steer (transition from straight to fixed-radius curve. This is the first study to explicitly and systematically evaluate this new approach to Understeer mitigation. The approach is fundamentally different from common DYC and suggests the potential for a new generation of controllers based on trajectory control via chassis actuators.
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Optimal path recovery from terminal Understeer
2011Co-Authors: Arman Nozad, Mathias R Lidberg, Timothy Gordon, Matthijs KlompAbstract:This paper presents methods to control vehicle path in the case of limit Understeer. Longitudinal forces are applied to overcome inherent vehicle Understeer, and reduce speed to overcome friction limits. Desired path curvature is derived from the driver’s steering input. Optimization is applied separately to three types of model: (a) particle model with isotropic friction limits; (b) two-track model with idealized tire force constraints (c) another two-track model using more realistic tire force limits. Optimal path tracking for the particle model has a rigorous solution, in the form of a parabolic trajectory – the vehicle decelerates to a point of maximum path curvature. The parabolic reference depend on vehicle speed, mean surface friction and desired curvature inferred from the driver steering input. Overall the optimization results are found to be consistent between the three approaches.
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Influence of Drive Force Distribution on the Lateral Grip and Understeer
2008Co-Authors: Matthijs Klomp, Robert ThomsonAbstract:The increased freedom of control, when compared to traditional driveline configurations, enables the vehicle for instance to maintain characteristics from the linear tire operating range up to the grip limit. However, based on the review of the current state of the art and the importance of factors such as lateral grip and Understeer, the authors see a need for improved (graphical) methods and theory describing the influence of drive force distribution on these said factors. In this work the results used to compute the lateral grip margin for a general drive force distribution was developed for four special cases; front-wheel drive; rear-wheel drive; all-wheel drive with synchronous front- and rear differentials; and finally, an optimal front/rear drive force distribution. From these results, graphical methods of the so-called dynamic square are connected to the classic g-g diagrams. Further the dynamic square is further developed to also show the influence of lef/right drive force distribution and the influence on the Understeer of the vehicle.
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On Drive Force Distribution and Road Vehicle Handling - A Study of Understeer and Lateral Grip
2007Co-Authors: Matthijs KlompAbstract:Computer controlled vehicle sub-systems aimed to support drivers in various driving situations are rapidly increasing in number and sophistication. These systems have evolved from anti-lock braking and traction control systems, to electronic stability control. Recent developments include active steering, suspension, and – of interest in this work – computer controlled drive force distribution. These systems are known to have the potential improve a vehicle’s handling, defined as the relationship between driver input and vehicle output, over a wide range of operating conditions. The focus of past and present research in this field has been on the interaction between combined lateral and longitudinal forces on a tire level. Nonetheless, the influence of the drive force and drive force distribution on vehicle level handling characteristics – of interest for this work – have been unsatisfactory described in the reviewed literature. Based on this fact, and the relevance of this needed knowledge for this study, these shortcomings are being addressed in this work. In the field of vehicle handling, two main aspects are; the Understeer, i.e. how the turning radius changes with speed given a fixed steering input; and the lateral grip, which is defined by the maximum possible steady-state lateral acceleration. One objective of this study is to show how the drive force distribution can be optimized for maximum lateral grip and constant Understeer. For this purpose the existing theory and methods are developed with the aim to show the influence of the drive force distribution on the Understeer and lateral grip. Finally, by means of computer simulations, the developed theory was verified and the influence of effects which should be included in future development of the presented theory was identified. Overall, this present work has successfully expanded the knowledge in the field of combined acceleration and cornering, from tire level properties to vehicle level characteristics.
Mathias R Lidberg - One of the best experts on this subject based on the ideXlab platform.
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A flexible control allocation method for terminal Understeer mitigation
2016 International Conference for Students on Applied Engineering (ISCAE), 2016Co-Authors: Yangyan Gao, Timothy Gordon, Mathias R LidbergAbstract:This paper addresses the problem of terminal Understeer of a road vehicle. The scenario is considered when a vehicle enters a curve with excessive speed and the aim is to apply automatic chassis control to prevent the vehicle from drifting out of the lane. In a previous study, the optimization problem is formulated as the minimization of maximum path off-tracking and the optimal response of a particle model is in the form of a parabolic path recovery (PPR) where the acceleration vector is fixed in the global frame. A recently developed model based control method the Modified Hamiltonian Algorithm (MHA) uses this acceleration information as a reference for control allocation to each wheel. The controller is developed using a simplified 3DOF vehicle model in Matlab and Simulink environment. In this paper, we consider using a high fidelity model in CarMaker to verify the control performance. It is of particular interest to see how well the chassis control can deal with the inherent Understeer and oversteer qualities of the vehicle. Hence in this paper we evaluate the ability of an active safety system to overcome the mechanical limitations of the vehicle.
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On optimal recovery from terminal Understeer
Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering, 2014Co-Authors: Matthijs Klomp, Mathias R Lidberg, Timothy GordonAbstract:This paper addresses the problem of terminal Understeer and its mitigation via integrated brake control. The scenario considered is when a vehicle enters a curve at a speed that is too high for the tyre-road friction limits and an optimal combination of braking and cornering forces is required to slow the vehicle down and to negotiate the curve. Here, the driver commands a step steering input, from which a circular arc reference path is inferred. An optimal control problem is formulated with an objective to minimize the maximum off-tracking from the reference path, and two optimal control solutions are obtained. The first is an explicit analytical solution for a friction-limited particle; the second is a numerically derived open-loop brake control sequence for a nonlinear vehicle model. The particle solution is found to be a classical parabolic trajectory associated with a constant acceleration vector of the global mass center. The independent numerical optimization for the vehicle model is found to approximate closely the kinematics of the parabolic path reference strategy obtained for the particle. Using the parabolic path reference strategy, a closed-loop controller is formulated and verified against the solution from numerical optimization. The results are further compared with Understeer mitigation by yaw control, and the parabolic path reference controller is found to give significant improvement over yaw control for this scenario.
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Experimental verification of Understeer compensation by four wheel braking
2014Co-Authors: Timothy Gordon, Matthijs Klomp, Mathias R LidbergAbstract:This study is designed to validate a new approach to Understeer mitigation chassis control, based on a particle motion reference: parabolic path reference (PPR). Considering the scenario of excess entry speed into a curve, related to run-off-road crashes, the aim is that automatic braking minimizes lateral deviation from the target path by using an optimal combination of deceleration, cornering forces and yaw moments. Previous simulation studies showed that four-wheel braking can achieve this much better than a conventional form of yaw moment control (DYC). The aim of this work is to verify this on a test track with an experimental vehicle, and to compare performance with DYC and an uncontrolled vehicle. Experiments were performed with a front-wheel-drive passenger vehicle equipped with an additional four identical brake callipers controlled via an electro-hydraulic brake (EHB) system, enabling individual brake control. Minimizing the maximum deviation from the intended curve radius is the control objective. Feedback to the controller consists of the available steering wheel angle, wheel speeds, yaw rate and lateral acceleration sensors in the vehicle. Additional to these variables, also the vehicle position was logged using a GPS system. It was found that PPR is superior to DYC in reducing the maximum deviation from the intended path, confirming the trends previously found in simulations. Furthermore, the PPR concept is found to be inherently more stable than DYC since more brake force is applied to the outer wheels than the inner wheels throughout the manoeuvre. The experiments involve a first implementation of a PPR control which is not a fully closed-loop control intervention and tuned to a step steer (transition from straight to fixed-radius curve. This is the first study to explicitly and systematically evaluate this new approach to Understeer mitigation. The approach is fundamentally different from common DYC and suggests the potential for a new generation of controllers based on trajectory control via chassis actuators.
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Optimal path recovery from terminal Understeer
2011Co-Authors: Arman Nozad, Mathias R Lidberg, Timothy Gordon, Matthijs KlompAbstract:This paper presents methods to control vehicle path in the case of limit Understeer. Longitudinal forces are applied to overcome inherent vehicle Understeer, and reduce speed to overcome friction limits. Desired path curvature is derived from the driver’s steering input. Optimization is applied separately to three types of model: (a) particle model with isotropic friction limits; (b) two-track model with idealized tire force constraints (c) another two-track model using more realistic tire force limits. Optimal path tracking for the particle model has a rigorous solution, in the form of a parabolic trajectory – the vehicle decelerates to a point of maximum path curvature. The parabolic reference depend on vehicle speed, mean surface friction and desired curvature inferred from the driver steering input. Overall the optimization results are found to be consistent between the three approaches.
Frendo Francesco - One of the best experts on this subject based on the ideXlab platform.
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On the handling performance of a vehicle with different front-to-rear wheel torque distributions
'Informa UK Limited', 2018Co-Authors: Lenzo Basilio, Bucchi Francesco, Sorniotti Aldo, Frendo FrancescoAbstract:The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the Understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the Understeer coefficient, and allow to infer a relationship between the Understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most Understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle
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Handling performance of a vehicle with different front-to-rear wheel torque distribution
'Informa UK Limited', 2018Co-Authors: Lenzo Basilio, Bucchi Francesco, Sorniotti Aldo, Frendo FrancescoAbstract:The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied through the analysis of the Understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. More specifically, the study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is then performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the Understeer coefficient, and allow to infer a relationship between the Understeer coefficient and the yaw moment analysis. The handling characteristics for the considered maneuvers vary with the vehicle speed and front-to-rear wheel torque distribution. In particular, an apparently surprising result arises at low speed, where the RWD architecture is the most Understeering configuration. This outcome is discussed through the yaw moment analysis, highlighting the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle
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On the handling performance of a vehicle with different front-to-rear wheel torque distributions
'Informa UK Limited', 2018Co-Authors: Lenzo Basilio, Bucchi Francesco, Sorniotti Aldo, Frendo FrancescoAbstract:The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied through the analysis of the Understeer coe�cient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent mo- tors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. More speci�cally, the study presents a pro- cedure to compute the longitudinal and lateral tire forces, which is based on a �rst estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is then performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the un- dersteer coe�cient, and allow to infer a relationship between the Understeer coe�cient and the yaw moment analysis. The handling characteristics for the considered maneuvers vary with the vehicle speed and front-to-rear wheel torque distribution. In particular, an apparently surprising result arises at low speed, where the RWD architecture is the most Understeering con�guration. This outcome is discussed through the yaw moment analysis, highlighting the yaw moment caused by the longitudinal forces of the front tires, which is signi�cant for high values of lateral acceleration and steering angle
