Kineto-dynamic design optimisation for vehicle-specific seat-suspension systems

Designs and analyses of seat-suspension systems are invariably performed considering effective vertical spring rate and damping properties, while neglecting important contributions due to kinematics of the widely used cross-linkage mechanism. In this study, a kineto-dynamic model of a seat-suspension is formulated to obtain relations for effective vertical suspension stiffness and damping characteristics as functions of those of the air spring and the hydraulic damper, respectively. The proposed relations are verified through simulations of the multi-body dynamic model of the cross-linkage seat-suspension in the ADAMS platform. The validity of the kineto-dynamic model is also demonstrated through comparisons of its vibration transmission response with the experimental data. The model is used to identify optimal air spring coordinates to attain nearly constant natural frequency of the suspension, irrespective of the seated body mass and seated height. A methodology is further proposed to identify optimal damping requirements for vehicle-specific suspension designs to achieve minimal seat effective amplitude transmissibility (SEAT) and vibration dose value (VDV) considering vibration spectra of different classes of earthmoving vehicles. The shock and vibration isolation performance potentials of the optimal designs are evaluated under selected vehicle vibration superimposed with shock motions. Results show that the vehicle-specific optimal designs could provide substantial reductions in the SEAT and VDV values for the vehicle classes considered.     

Active Control of Non-stationary Response of Vehicles with Nonlinear Suspensions

SUMMARY

Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.     

I. Minutes of the IAVSD Board Meetings

SUMMARY

A theoretical analysis is presented to model a hydromechanical, semi-active suspension system, first as a single wheel station and then as fitted to each wheel of an off-road vehicle. Predicted results show that two benefits are obtained by comparison with the equivalent passive system. First, vehicle attitude is controlled for changes in body forces arising from static loads or braking/cornering inputs. Second, a significant improvement in ride comfort is obtained because low suspension stiffnesses can be used.     

Development of a generalised equivalent estimation approach for multi-axle vehicle handling dynamics

This paper devotes analytical effort in developing the 2M equivalent approach to analyse both the effect of vehicle body roll and n-axle handling on vehicle dynamics. The 1M equivalent vehicle 2DOF equation including an equivalent roll effect was derived from the conventional two-axle 3DOF vehicle model. And the 1M equivalent dynamics concepts were calculated to evaluate the steady-state steering, frequency characteristics, and root locus of the two-axle vehicle with only the effect of body roll. This 1M equivalent approach is extended to a three-axle 3DOF model to derive similar 1M equivalent mathematical identities including an equivalent roll effect. The 1M equivalent wheelbases and stability factor with the effect of the third axle or body roll, and 2M equivalent wheelbase and stability factor including both the effect of body roll and the third-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the three-axle vehicle. By using the recursive method, the generalised 1M equivalent wheelbase and stability factor with the effect of n-axle handling and 2M equivalent generalised wheelbase and stability factor including both the effect of body roll and n-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the n-axle vehicle. The 2M equivalent approach and developed generalised mathematical handling concepts were validated to be useful and could serve as an important tool for estimating both the effect of vehicle body roll and n-axle handling on multi-axle vehicle dynamics.     

A Full-Car Roll Model of a Vehicle with Controlled Suspension

SUMMARY

The full-car roll model of a vehicle suspension with static and dynamic control (using wheel, body and seat) is described by means of vertical and lateral input for both static and dynamic states. It is shown that the control deteriorates the static performance of the vertical response and improves the performance of the lateral response.     

A Procedure for Optimization of Truck Suspensions

SUMMARY

The purpose of this paper is to develop a procedure based on covariance analysis and nonlinear programming techniques which can be used for the parameter selection of optimum truck suspensions. The procedure is applied to explore the differences in parameter selection caused by the changes in the frequency content of the road input or by changes in the criteria for optimization. The equations of motion for a tractor-semitrailer truck are cast in state space form. The road excitations are represented by the output of a white noise excited shaping filter taking into consideration the time delays between the different vehicle axles. Shape filters to represent human perception of vibration in both the vertical and longitudinal directions in the time domain are presented and realized in terms of state variables. The suspension parameters of the road-vehicle-human body system are optimized using a direct search algorithm.     

Discomfort of vertical whole-body shock-type vibration in the frequency range of 0.5 to 16 Hz

Shock-type vibrations are frequently experienced in vehicles excited by impulsive input, such as bumps in the road, and cause discomfort. Current national and international standard weightings were primarily developed for assessing exposure to sinusoidal or random vibrations and not impulsive excitations or shocks. In this experimental study, various shock signals were systematically produced using the response of a one degree-of-freedom vibration model to hanning-windowed half-sine force input. The fundamental frequency of the shock was varied from 0.5 to 16 Hz at a step of 1/3 of an octave. The magnitude estimation method was used for fifteen subjects to compare the discomfort of shocks with various unweighted vibration dose values between 0.35 ms^−1.75 and 2.89 ms^−1.75 at each frequency. The equivalent comfort magnitude of shock showed greater sensitivity at frequencies less than 0.63 Hz and at the resonance frequency of the human body between 5.0 Hz and 6.3 Hz. The frequency weighting constructed by using both the equivalent comfort magnitude and the growth rate of discomfort obtained in this study was compared with the current standard weightings, W_b of BS 6841 and W_k of ISO 2631. The derived weightings for shock were applied to the acceleration of the shocks, and an enhanced correlation was proved between the magnitude estimations and the weighted physical magnitude of shock.     

Shear Force Development by Pneumatic Tyres in Steady State Conditions: A Review of Modelling Aspects

SUMMARY

Modelling of the generation of shear forces by pneumatic tyres under steady state conditions is reviewed. The review is placed in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer. It will be of interest also to the student of rolling contact problems.

The subject is divided into sections, covering physically founded models which require computation for their solution, physically based models which are sufficiently simplified to allow analytical solutions and formula based, empirical models. The classes are more nearly continuous than this strict division would imply, since approximations in obtaining analytical solutions may be made, empirical correction factors may be applied to analytical results and formula based methods may take into account tyre mechanical principles. Such matters are discussed in the relevant sections. Attention is given to the important matter of choosing model parameters to best represent the behaviour of a particular tyre.

Conclusions relate to the structural and frictional mechanisms present in the shear force generation process, the contributions of carcass and tread elastic properties and of geometrical and frictional factors to the determination of the distributions of force through the contact region, the relationship between accuracy and computational load and the selection of methods for modelling tyre forces in a road vehicle dynamics context. Reference to the most pertinent literature in the field is made and possibilities for the further development of the state of the art are mentioned.     

DISCUSSION NOTE on Karnopp's article “Active Damping in Road Vehicle Suspension Systems”

SUMMARY

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.     

Straight-ahead running of road vehicles – analytical formulae including full tyre characteristics

ABSTRACT

During straight-ahead running, the longitudinal axis of road vehicles, notably cars, is not parallel to road axis. This occurrence is general and is due both to road cross slope (road banking) and to tyre characteristics, particularly ply-steer and conicity. In order to describe such a phenomenon, the paper develops a new and relatively simple analytical model. Despite the model is linear, the solution which is provided is exact, since straight-ahead motion occurs with small angles and both the elastokinematics of suspension system and tyre characteristics can be modelled by linearised equations. The Handling Diagram theory is updated and completed by introducing the actual shifts of tyre characteristics. The validation of the analytical expressions is performed by using a MSC Adams^TM full model of a car. A subjective-objective experimental test campaign provides preliminary substantiation of the ability of the derived formulae to describe tyre performance. By means of the unreferenced analytical formulae developed in the paper, we allow, given the vehicle, the proper tyre design specification and vice-versa. In particular, a formula is given to make null the steering torque during straight-ahead driving. The derived analytical formulae may provide a sound understanding of the straight-ahead running of road vehicles.     

An inverse railway wagon model and its applications

An inverse wagon model was developed to estimate wheel–rail contact forces using only measurements of wagon body responses as inputs. The purpose of this work was to provide mathematical modelling to embed in low-cost devices that can be mounted on each freight wagon in a large wagon fleet. To minimize cost, complication, and the maintenance inconvenience of these devices, the constraint is imposed that transducers and connections are limited to locations on the wagon body. Inputs to the inverse model developed include only vertical and lateral translational accelerations and angular accelerations of roll, pitch, and yaw of the wagon body. The model combines the integration and partial modal matrix (PMM) techniques together to form an IPMM method. Besides wheel–rail contact forces some motion quantities such as the lateral and yaw displacements of wheelset are also predicted. Results from the inverse model were compared with data from full scale laboratory suspension tests for vertical suspension excitations. The inverse model was also compared with results from simulations completed in VAMPIRE^® for more complicated track input profiles. The model results and the applications of the model are discussed.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Model Development,Validation and Comparison

SUMMARY

Recent research on autonomous highway vehicles has begun to focus on lateral control strategies. The initial work has focused on vehicle control during low-g maneuvers at constant vehicle speed, typical of lane merging and normal highway driving. In this paper, and its companion paper, to follow, the lateral control of vehicles during high-g emergency maneuvers is addressed. Models of the vehicle dynamics are developed, showing the accuracy of the different models under low and high-g conditions. Specifically, body roll, tire and drive-train dynamics, tire force saturation, and tire side force lag are shown to be important effects to include in models for emergency maneuvers. Current controllers, designed for low-g maneuvers only, neglect these effects. The follow on paper demonstrates the performance of lateral controllers during high-g lateral emergency maneuvers using these vehicle models.     

Black-box modelling of nonlinear railway vehicle dynamics for track geometry assessment using neural networks

ABSTRACT

The use of vehicle dynamics simulation for the track geometry assessment gives rise to new demands. In order to analyse the responses of the vehicles to the measured track geometry defects, the integration of the simulation process in the measurement chain of the track geometry recording car is envisaged. Fast and reliable simulation results are required. This work studies the use of black-box modelling approaches as an alternative to multi-body simulation. The performances of different linear and nonlinear black-box models for the simulation of the vertical and lateral bogie accelerations are compared. While linear transfer function models give good results for the simulation of the vertical responses, their use is not suitable for the highly nonlinear lateral vehicle dynamics. The lateral accelerations are best represented by recurrent neural networks. For the training and validation on high-speed lines using measured vehicle responses, the performance of the black-box simulation outperforms the multi-body simulation. Due to the larger variability of track design and track quality conditions on conventional lines, the model performance degrades and depends significantly on the analysed vehicle type and the track characteristics.     

Development and Evaluation of Vehicle Simulation Models for a 4WS Application

SUMMARY

In the scope of the European Prometheus project a passenger car with active rear wheel steering was developed by TNO in cooperation with PSA. During development and engineering of the rear wheel steering system simulation tools have been used to reduce development costs. This paper describes the evaluation of different simulation models, from simple to complex, with results of full vehicle driving tests. The optimal balance for model complexity and accuracy was achieved with a 2-dimensional model with an added roll degree of freedom. The results show that validation using time responses can give ambiguous and inaccurate results, and that frequency response functions are much more usable in validation.     

Flexible Bodies in Multibody System Codes

SUMMARY

Multibody codes are'efficient tools to simulate nonlinear dynamic behaviour of rigid and flexible multibody systems undergoing large overall motions overlaid by small elastic deformation. This paper gives an overview of common approaches for the equations of motion of flexible body models and presents a general way to prepare the required data including geometric stiffening terms. In particularly, for the nodal approach the data are derived using standard results of a finite element analysis of the body. The computation of coefficient matrices describing the equations of motion is done outside the finite element code by matrix manipulations only. The data are stored in a standardised object-oriented structure. Consequently, the data set is independent of the formulation of the multibody system code.     

A new method of identification of equivalent suspension and damping rates of full-vehicle model

ABSTRACT

The equivalent spring and damper are often used to simplify the dynamic analysis of a nonlinear full-vehicle model. Clearly, those rates are strongly influenced by the kinematics of a suspension mechanism. This paper presents a new approach to the identification of the equivalent suspension and damping rates. The suspension is considered as a 1-degree-of-freedom (DOF) spatial parallel mechanism. The instantaneous kinestatic relations of the 1-DOF spatial parallel mechanism can be described using the theory of screws. The process of identification of the rates involves three steps: first, the joint positions of the suspension are found from the displacement analysis of the suspension mechanism. Second, the motion of each wheel of four suspension mechanisms is represented by the corresponding instantaneous screw at any instant. Third, the equivalent suspension and damping rates are determined from the kinestatic relations of the instantaneous screw. These rates are used for the dynamic analysis of the nonlinear full-vehicle model consisting of two pairs of the front (double-wishbone) and rear (multi-link) suspensions. Two dynamic behaviours of a car are analysed and compared with the simulation utilising the Adams/View software.     

Active Roll Control for Passenger Cars

SUMMARY

The development of a mathematical model of a limited bandwidth hydro-pneumatic suspension that is incorporated into a vehicle handling model is described. The combined model is used to evaluate a suitable control strategy for eliminating body roll during a cornering manoeuvre. The philosophy behind the roll control strategy has been to use feedback measurements of the body motions which do not compromise the ride control. A study of the influence of the position of the body motion feedback transducer on the effectiveness of the system to reduce the body roll is presented. Non-linear modelling of the suspension components for a 0.8g cornering manoeuvre has revealed performance limitations. Conclusions are drawn as to the effectiveness of the control scheme.     

Dynamic model for automotive side impact crashes

A rigid body model to represent a side impact crash is constructed using five degrees-of-freedom (dof) for the vehicle and three dof for each occupant in the vehicle. Nonlinear stiffness and damping elements and the presence of physical gaps between several components make the model highly nonlinear. The model is validated using experimental crash test data from a National Highway Traffic Safety Administration (NHTSA) database. To simplify the parameter identification process and reduce the number of parameters to be identified at each stage, a two-step process is adopted in which the vehicle is first assumed to be unaffected by the presence of the occupants, and its model parameters are identified. Subsequently, the parameters in the occupant models are identified.

The active set method with a performance index that includes both the L₂ and L_∞ norms is used for parameter identification. A challenge is posed by the fact that the optimisation problem involved is non-convex. To overcome this challenge, a large set of random initial values of parameter estimates is generated and the optimisation method is applied with all these initial conditions. The values of parameters that provide the minimal performance index from the entire set of initial conditions are then chosen as the best parameter values. The optimal parameters values thus identified are shown to significantly improve the match between the model responses and the experimentally measured sensor signals from the NHTSA crash test.