Properties of Non-Linear Two-Force Elements Used in Vehicle Dynamic Systems under Stationary Stochastic Excitation. Part 1 - Ideal Elements

Non-linear two-force elements (springs, dampers, etc.) are commonly found in vehicle dynamic systems. Their mathematical idealization by expressing their force-excitation relation by a real function is called to be an ideal element. Excitation of these elements can be often considered as being stationary stochastic. Their general properties under such excitation are discussed and computation of the stochastic properties of the output force for known excitation are shown in this paper. Transfer functions of the elements, i.e. output force - input relations in the frequency domain, under the given excitational conditions form the base for the evaluation.     

Properties of Non-Linear Two-Force Elements Used in Vehicle Dynamic Systems under Stationary Stochastic Excitation. Part 2 - Realistic Complex Elements

SUMMARY

Realistic two-force elements used in vehicle dynamic systems have very often complex output force -inputs relations. Determination of their properties under stationary stochastic excitation must be therefore carried out experimentally for every excitational case. Evaluation of the measurements of one type of a passenger car telescopic hydraulic suspension damper and of one type of a heavy duty truck leaf spring is shown in this part of the paper. Transfers of the discussed elements, representing the frequency responses of the elements to the input deflectional process and defined in the first part of this paper, form the base for the evaluation.     

Properties of Non-Linear Two-Force Elements Used in Vehicle Dynamic Systems under Stationary Stochastic Excitation. Part 2 - Realistic Complex Elements

Realistic two-force elements used in vehicle dynamic systems have very often complex output force -inputs relations. Determination of their properties under stationary stochastic excitation must be therefore carried out experimentally for every excitational case. Evaluation of the measurements of one type of a passenger car telescopic hydraulic suspension damper and of one type of a heavy duty truck leaf spring is shown in this part of the paper. Transfers of the discussed elements, representing the frequency responses of the elements to the input deflectional process and defined in the first part of this paper, form the base for the evaluation.     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

SUMMARY

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

Remarks on the Theory of Vehicle Vibrational Analysis Based on the On-the-Road Measurements

SUMMARY

Basic relation between input spectral density matrix and output spectral density matrix of a linear stochastically excited dynamic system is indicated. General conclusions regarding the output processes spectral densities, coherences and phase angles in respect to the input processes stochastic properties are drawn. The possibility of the determination of the system's transfer functions when input and output spectral density matrices are known is discussed. Applications of the obtained results in vehicle vibrational analysis when the vehicle is considered as one-input, two-input or multiinput system are shown.     

Small Vibrations of Nonlinear Dynamic Systems Containing Non-Rigid Bodies Excited by Stationary Stochastic Processes

From a vibrational point of view, real vehicles form dynamic systems containing non-rigid bodies and nonlinear two-force elements, often excited by stationary random processes. Their theoretical investigation in a broader frequency range is practically possible in the frequency domain only. In the treatment of nonlinearities second-order stochastical linearization methods can be used advantageously. The amount of necessary computations can be vastly reduced by using known receptance matrices of all bodies in the system in its equations of motion after Fourier transformation. The article describes the receptance properties of non-rigid bodies, their use for the determination of the dynamic system's transfer functions and the determination of the output processes' spectral density matrix under stationary random external excitation using stochastical second-order linearization of the nonlinearities.     

基于ANSYS二次开发的实体单元模型内力图的实现

当依据规范对结构承载能力极限状态和正常使用极限状态进行设计验算时,需掌握其内力状态.有限单元法对复杂结构进行内力分析有时需要采用空间实体单元,而ANSYS软件不能直接输出实体单元模型的内力图,需另行开发.文中介绍了利用软件后处理中的面操作,通过面积分和矩阵运算并编制APDL宏程序求实体单元模型内力图的方法.给出了4种不同截面形式的连续梁求内力图示例,并对实体单元模型的有限元解与采用三弯矩方程求得的理论解进行了比较.结果表明,文中所述方法可以方便地求得实体单元模型的内力图.     

Force Control of a Semi-Active Damper

SUMMARY

Two strategies are investigated for controlling a semi-active damper to track a prescribed force demand signal: (i) ‘open loop’ control, using a model of the damping force versus velocity characteristics; and (ii) force feedback (closed loop) control.

The damping characteristics and switching transients of a prototype damper were measured, and used to develop a mathematical model of the dynamics of the damper. The two control strategies were investigated using an idealised (constant velocity) test. Their performance was also simulated and measured under realistic operating conditions using the Hardware-in-the-Loop testing method.

Open loop damper control was generally found to give superior performance to force feedback control, due to its smaller phase lag at high frequencies.     

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.     

Random Vehicle Vibrations as Effected by Dry Friction in Wheel Suspensions

SUMMARY

The changes of vibration comfort and stability of vehicles as effected by the value of frictional force generated in laminated springs are discussed and the probability of departure of the tyres from the ground is described.

A partly automated analogue computer simulation being equivalent to a great number of highway experiments was applied in the study.

The computer model was excited by several stochastic roadprofile - analogue signals generated by filters from the wide-band random signal of a digital noise generator.     

Investigation of Features of Tyre Rolling at Non-Small Velocities on the Basis of a Simple Tyre Model with Distributed Mass Periphery

SUMMARY

On the basis of the brush-type tyre model the paper considers the interaction between steady-state rolling deformable wheel and flat road surface as well as corresponding force and moment characteristics of the wheel.

At least two zones of sliding, anisotropic dry friction, sliding friction coefficient speed-dependent and instantaneous leap of the friction coefficient when transition from sliding to adhesion zone occurs, have been taken into account, as well as distributed peripheral mass of tyre, elasticity, pseudo-dry friction and damping properties in radial, tangential and lateral directions of the elements at the wheel periphery, including a visco-elastic belt. Vertical force distribution in the contact area is not supposed to be known in advance and follows from the calculation. As a result, sliding zone lengths, distributed forces in contact area, six components of generalized road reaction reduced to the wheel center, and rolling resistance moment are found as functions of vertical load, movement velocity, longitudinal and side slip, friction in contact area with road, stiffnesses, dry friction and damping in the tyre model elements and of distributed peripheral mass.

A computer program developed in Fortran and results of calculations are of particular interest for qualitative analysis including steady rolling of studded tyre and also racing car and aircraft tyres which peripheral mass shows itself in a special way because of great movement velocities.     

Force Generation in Semi-Active Suspensions Using Modulated Dissipative Elements

ABSTRACT

Large control forces in vehicle suspension systems or other vibration control systems may often be generated effectively by modulating the dissipation characteristics of an element using only modest control power. Most of the systems proposed in the past have involved hydraulic dampers, but a variety of other resistive elements can also be used. What is required is an efficient transducer from mechanical power to another form of power and a means to modulate a generalized resistor in the energy domain in question. Using bond graphs, it is shown that designs in the hydraulic domain can be transferred to other domains with possible benefits in certain cases.     

Optimization of Vehicles Elasto-Damping Elements Characteristics from the Aspect of Ride Comfort

SUMMARY

Spatial random vibrations of a vehicle that arise during driving represent an important factor in functioning of a dynamic system: Driver - Vehicle - Environment. They carry certain information for driver and also cause fatigue of driver and passenger.

This is the reason why the tendency is towards the minimization of vibratory loads, what in practice can be achieved by optimization of characteristics of elasto - damping elements of a vehicle.

In this paper for optimization of elasto - damping elements of a vehicle we used a complex nonlinear model of a driver and a vehicle during the straight - line motion of the vehicle on a rough road. Optimization was performed by application of the Hooke - Jeeves method and by use of outside penalty functions as well as the objective function that enabled simultaneous optimization of vertical vibrations of the driver's seat, vibrations of the steering wheel, and normal reactions in the contact surface of the tyre and road. The optimization was performed with application of the computer HP 9000/800 SE on the example of a medium passenger car.     

Linearization of Non-Linear Stochastically Excited Dynamic Systems by a Modified Second-Order Procedure

An enhanced second-order linearization method for linearization of non-linear dynamic systems excited by stationary stochastic input processes is outlined in the paper. Noise force components originating when deflecting any non-linear two-force element are used as internal excitations of the dynamic system considered. They are noncoherent mutually and with all external excitations. This enables a better approximation of the system's responses under given external excitation as well as a reasonably accurate determination of the coherences of all processes taking place in the system.     

Optimal Linear Active Suspensions with Vibration Absorbers and Integral Output Feedback Control

SUMMARY

The bandwidth of the body response to a road input in an active suspension may be considerably reduced if the axle motions are independently controlled and if, at the same time, the effects of static and dynamic loads are counteracted by integral action in the body force control system. The paper presents a further application of the Ferguson-Rekasius method, leading to optimal output control with incomplete state feedback. To achieve narrow bandwidth body response the support springs are replaced by hydraulic actuators, and vibration absorbers or active wheel dampers are employed for the control of the axle motions. Active wheel damping is the more effective and gives good results. Proportional-plus-integral control action is shown to reduce the transient body displacements due to external forces.     

High Speed Railway: Collecting Pantographs Active Control and Overhead Lines Diagnostic Solutions

SUMMARY

The catenary-pantograph system and its dynamic behaviour play a decisive role for high speed trains from the power collecting point of view. The decisive criterion for assessing the contact quality is to reduce the contact force variability as far as possible. In this paper active pantograph elements are introduced in order to improve the system performance. The control strategy is based on Extended Kalman Filter technique, used to get a contact force estimation available for control feedback. The same estimation procedure based on the Extended Kalman Filter is also used to obtain some information useful to overhead line diagnostic purposes.     

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.     

Identification of the characteristics of motorcycle and scooter tyres in the presence of large variations in inflation pressure

Stability and safety of road vehicles are largely affected by tyre properties. Single-track vehicles are characterised by weakly damped modes of vibration (weave and wobble) and therefore this phenomenon is even more important. This article focuses on the study of both steady-state and transient properties of motorcycle and scooter tyres in the presence of very low and very high inflation pressures. The steady-state properties are defined as lateral forces (side-slip and camber forces) and yaw torques (self-aligning and twisting). The transient properties are described in terms of relaxation length, which represents the distance needed to reach a certain percentage of the steady-state value of the tyre force. Experimental tests are carried out on a specific rotating disk machine. Three sets of tyres are analysed. Steady-state properties are measured by increasing step by step the values of camber and side-slip angles. Transient properties are studied carrying out tests with harmonic side-slip excitation and measuring the phase lag between the excitation (input) and the tyre force (output). Experimental results show important variations in tyre properties with inflation pressure with general trends of all the tested tyres and particular features related to the tyre's geometry. After the analysis and discussion of experimental results, the measured data are fitted by means of a specific version of the Magic Formula. The dependence of the Magic Formula's coefficients on inflation pressure is analysed and interpolation curves are given.