Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions

The paper derives analytical solutions for the global optimum of the ride comfort and tyre grip performance measures for a quarter-car vehicle model optimised both individually and in combination. The solutions are derived for six simple suspension networks comprising one or two springs, one damper and possibly one inerter. The solutions are functions of four vehicle parameters: the sprung mass, the unsprung mass, the tyre stiffness and the static stiffness, of the suspension.     

An Evaluation of Passive Automotive Suspension Systems with Variable Stiffness and Damping Parameters

Passenger discomfort, suspension working space and dynamic tyre loading parameters are calculated for different combinations of spring stiffness and damping coefficient representing the suspension system in a quarter car model subject to realistic random disturbance inputs from roads of widely differing quality. Sprung and unsprung masses and the tyre vertical stiffness and damping coefficient employed derive from a current production car. Designs which are best for the specific conditions represented are identified and their performance properties in other (off-design) conditions are considered, and conventional design is explained as the inevitable consequence of the need to compromise if fixed suspension parameters are used. Performance improvements possible if variable parameters can be employed are evaluated as a function of the ranges of variability provided, and a stratagem for controlling parameters is proposed.     

An Evaluation of Passive Automotive Suspension Systems with Variable Stiffness and Damping Parameters

SUMMARY

Passenger discomfort, suspension working space and dynamic tyre loading parameters are calculated for different combinations of spring stiffness and damping coefficient representing the suspension system in a quarter car model subject to realistic random disturbance inputs from roads of widely differing quality. Sprung and unsprung masses and the tyre vertical stiffness and damping coefficient employed derive from a current production car. Designs which are best for the specific conditions represented are identified and their performance properties in other (off-design) conditions are considered, and conventional design is explained as the inevitable consequence of the need to compromise if fixed suspension parameters are used. Performance improvements possible if variable parameters can be employed are evaluated as a function of the ranges of variability provided, and a stratagem for controlling parameters is proposed.     

Possibilities to improve the ride and handling performance of delivery trucks by modern mechatronic systems

The ride and handling qualities of conventional delivery trucks are wores compared to modern passenger cars. However this vehicles have the power to drive as fast as passenger cars. Vehicle comfort and driving safety are mostly influenced by vertical accelerations and vehicle movements caused by pitch and roll motions. In the paper “Vehicle Dynamics with Adaptive or Semi-Active Suspension Systems – Demands on Software and Hardware” Wallentowitz and Ridlich have shown at AVEC'94 in which way tyre stiffness, shock absorber characteristics, spring stiffness and unsprung mass have an influence on vehicle comfort and active safety. They achieved these results by the theoretical analysis of a quarter-vehicle-model. Their examinations are extended in this paper on the model of a complete delivery truck. By the use of the multibody-simulation tool SIMPACK the road performance of a delivery truck will be analysed. Therefore a complex model of the vehicle has been built up in SIMPACK. Several computer simulations have been carried out to analyse the vehicle comfort and handling characteristics in different standard driving manoeuvres.Furthermore, the potential of improvements is shown by simulating different driving manoeuvres with the complete vehicle model by varying some vehicle characteristics such as tyre stiffness, shock absorber characteristics, spring stiffness and unsprung mass.In addition to that, simulations with models of unconventional spring- and damper-systems have been carried out to demonstrate the potential of improvements by the use of these systems. Two different controller algorithms for a semiactive and an active suspension system have been used an will be compared in this paper.     

Heavy vehicle pitch dynamics and suspension tuning. Part I: unconnected suspension

The influence of suspension tuning of passenger cars on bounce and pitch ride performance has been explored in a number of studies, while only minimal efforts have been made for establishing similar rules for heavy vehicles. This study aims to explore pitch dynamics and suspension tunings of a two-axle heavy vehicle with unconnected suspension, which could also provide valuable information for heavy vehicles with coupled suspensions. Based on a generalised pitch-plane model of a two-axle heavy vehicle integrating either unconnected or coupled suspension, three dimensionless measures of suspension properties are defined and analysed—namely the pitch margin (PM), pitch stiffness ratio (PSR), and coupled pitch stiffness ratio (CPSR)—for different unconnected suspension tunings and load conditions. Dynamic responses of the vehicle with three different load conditions and five different tunings of the unconnected suspension are obtained under excitations arising from three different random road roughness conditions and a wide range of driving speeds, and braking manoeuvres. The responses are evaluated in terms of performance measures related to vertical and pitch ride, dynamic tyre load, suspension travel, and pitch-attitude control characteristics of the vehicle. Fundamental relationships between the vehicle responses and the proposed suspension measures (PM, PSR, and CPSR) are established, based on which some basic suspension tuning rules for heavy vehicles with unconnected suspensions are also proposed.     

Technical Note: RMS Values for Control Force, Suspension Stroke and Tyre Deflection in an Active Suspension

Expressions are derived for the numerical computation of rms values for control force, suspension stroke and dynamic tyre deflection in a quarter-car vehicle model on a random road of given roughness. A quadratic performance index is employed and the effects of the assumed weighting factors on the rms values and overall static stiffness determined.     

Technical Note: RMS Values for Control Force,Suspension Stroke and Tyre Deflection in an Active Suspension

Expressions are derived for the numerical computation of rms values for control force, suspension stroke and dynamic tyre deflection in a quarter-car vehicle model on a random road of given roughness. A quadratic performance index is employed and the effects of the assumed weighting factors on the rms values and overall static stiffness determined.     

Investigation into untripped rollover of light vehicles in the modified fishhook and the sine manoeuvres,part II: effects of vehicle inertia property,suspension and tyre characteristics

In this paper, as a continuation of part I of [N. Zhang, G.M. Dong, and H.P. Du, Investigation into untripped rollover of light vehicles in the modified fishhook and the sine manoeuvres, part I: vehicle modelling, roll and yaw instability, Veh. Syst. Dyn. 46 (2008), pp. 271–293], detailed parametric studies are conducted and compared between the fishhook and sine manoeuvres using the presented nine-degree-of-freedom vehicle model, in order to understand the rollover resistance capability of a light passenger vehicle with various parameters. First, effects of driving conditions are studied in the two manoeuvres. Secondly, effects of suspension characteristics are studied, in which the influence of suspension spring stiffness and shock absorber damping, anti-roll bar is discussed. Thirdly, effects of vehicle inertia properties, such as moment of inertia of vehicle sprung mass, sprung mass weight and location of centre of gravity, are investigated. Finally, effects of tyre characteristics are also investigated by altering the scaling factor λ _Fz0. An in-depth understanding has been gained on the significant effects of key system parameters on the kinetic performance of vehicles under the fishhook and the sine manoeuvres. Parametric studies show that the combination of step input (fishhook) and frequency input gives a clear indication of the vehicle dynamic stability during cornering.     

基于舒适性和轮胎动载的车辆悬架参数优化

为了改善汽车行驶的舒适性并减小轮胎对路面的动载，以某载货汽车为研究对象，建立了多目标优化模型，并采用统一目标函数法对车辆悬架参数进行优化。优化结果表明：优化后悬架刚度减小而阻尼增大，且前悬架参数变化较小，后悬架参数变化较大；相比于优化前，车身垂直方向加速度均方根值减小了20％，前轮动栽均方根值减小了40％，后轮变化更显著，减小了49％；采用多目标优化设计方法不仅可提高车辆自身的舒适性，而且可减小轮胎对路面的动载。     

A planar quasi-static constraint mode tyre model

The fast-paced, iterative, vehicle design environment demands efficiency when simulating suspension loads. Towards that end, a computationally efficient, linear, planar, quasi-static tyre model is developed in this work that accurately predicts a tyre's lower frequency, reasonably large amplitude, nonlinear stiffness relationship. The axisymmetric, circumferentially isotropic, stiffness equation is discretised into segments, then parameterised by a single stiffness parameter and two shape parameters. The tyre's deformed shape is independent of the overall tyre stiffness and the forces acting on the tyre. Constraint modes capture enveloping and bridging properties and a recursive method yields the set of active constraints at the tyre–road interface. The nonlinear stiffness of a tyre is captured by enforcing unidirectional geometric boundary conditions. The model parameters are identified semi-empirically; simulated cleat test loads match experiments within 7% including nonlinear stiffness when simulating a flat plate test and a discontinuous stiffness when simulating a cleat test.     

Analysis of vehicle rollover dynamics using a high-fidelity model

Recent data show that 35% of fatal crashes in sport utility vehicles included vehicle rollover. At the same time, experimental testing to improve safety is expensive and dangerous. Therefore, multi-body simulation is used in this research to improve the understanding of rollover dynamics. The majority of previous work uses low-fidelity models. Here, a complex and highly nonlinear multi-body model with 165 degrees of freedom is correlated to vehicle kinematic and compliance (K&C) measurements. The Magic Formula tyre model is employed. Design of experiment methodology is used to identify tyre properties affecting vehicle rollover. A novel, statistical approach is used to link suspension K&C characteristics with rollover propensity. Research so far reveals that the tyre properties that have the greatest influence on vehicle rollover are friction coefficient, friction variation with load, camber stiffness and tyre vertical stiffness. Key K&C characteristics affecting rollover propensity are front and rear suspension rate, front roll stiffness, front camber gain, front and rear camber compliance and rear jacking force.     

Roll and pitch independently tuned interconnected suspension: modelling and dynamic analysis

In this paper, a roll and pitch independently tuned hydraulically interconnected passive suspension is presented. Due to decoupling of vibration modes and the improved lateral and longitudinal stability, the stiffness of individual suspension spring can be reduced for improving ride comfort and road grip. A generalised 14 degree-of-freedom nonlinear vehicle model with anti-roll bars is established to investigate the vehicle ride and handling dynamic responses. The nonlinear fluidic model of the hydraulically interconnected suspension is developed and integrated with the full vehicle model to investigate the anti-roll and anti-pitch characteristics. Time domain analysis of the vehicle model with the proposed suspension is conducted under different road excitations and steering/braking manoeuvres. The dynamic responses are compared with conventional suspensions to demonstrate the potential of enhanced ride and handling performance. The results illustrate the model-decoupling property of the hydraulically interconnected system. The anti-roll and anti-pitch performance could be tuned independently by the interconnected systems. With the improved anti-roll and anti-pitch characteristics, the bounce stiffness and ride damping can be optimised for better ride comfort and tyre grip.     

Optimal Performance of Variable Component Suspensions

SUMMARY

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

Root mean square optimization criterion for vibration behaviour of linear quarter car using analytical methods

In this paper, a linear two-degree-of-freedom quarter car model is used to derive a number of analytical formulae describing the dynamic behaviour of passively suspended vehicles running on a harmonically bumped road. The linearity of the system allows us to analytically investigate the steady-state response characteristics. We derive analytical expressions for the root mean square (RMS) of the sprung mass absolute acceleration and relative displacement. This paper demonstrates the shortcomings of existing classical optimization methods. Hence we introduce a new optimization method based on minimizing the absolute acceleration RMS with respect to the relative displacement RMS. The RMS optimization method is applied for the symbolic derivation of analytical formulae featuring the best compromise among conflicting performance indices pertaining to the vehicle suspension system, i.e., sprung mass acceleration and working space. The proposed optimization technique is utilized to find the optimal damping and stiffness curves for the main suspension. The RMS optimal values are used to create design charts for suspension parameters, which are very useful particularly in the presence of physical constraints such as a limit on relative displacement. We introduce a numerical example to illustrate the optimality of the obtained solutions.     

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation.