Modelbased Investigations of Gyroscopic Effect on the (Elasto-)Kinematics of Suspension Systems

During wheel bumping caused by stochastic road excitation, the wheel performs rotational and translational movements. The bump and rebound wheel velocity leads to significant angular velocities based on the (elasto-)kinematics of the suspension system. Based on the gyroscopic effect, moments arise about the rotating wheel induced by the angular change while bumping. Therefore it leads to undesirable wheel changes and degrades the tire contact and finally decreases the driving stability. A flexible MBS-model of the five-link rear axle system that includes these effects has been built up to allow a detailed investigation of the gyroscopic effect. Using the simulation results, conclusions can be drawn for refining design criteria for the kinematics, elastokinematics and topology of the suspension system to increase the active safety of the vehicle. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of Narrow Tilting Vehicles

Narrow commuter vehicles can address many congestion, parking and pollution issues associated with urban transportation. In making narrow vehicles safe, comfortable and acceptable to the public, active tilt control systems are likely to play a crucial role. This paper concentrates on developing a dynamic model for narrow vehicles that can be used for the design and evaluation of active tilt control systems. The model has four degrees of freedom including lateral and tilt dynamics. The influence of gyroscopic forces due to rotating wheels and the influence of front wheel trail are included but secondary coupling effects are ignored so as to keep the model tractable. The model is used in this paper to understand the influence of vehicle tilt on the steering angle required for cornering, the desired tilt angle for any specified cornering maneuver and the influence of gyroscopic moments on transient tilting/cornering maneuvers. A study of the model equations also provides insight into how narrow vehicles can be designed so as to be self-stabilizing.     

On the influence of design parameters and nonlinearities in vehicle suspensions on road deformation

Among others, two main objectives of modern vehicle design are road friendliness and ride comfort. Both aspects are strongly related since the dynamical tire forces depend on the vertical acceleration of the vehicle. In order to investigate the influence of design and operation parameters, different car models are considered which move with constant velocity on a rippled road. First, a linear half car model is examined and the influence of different design parameters is discussed. Second, nonlinear suspensions with Coulomb friction due to sealings as well as with bilinear shock absorbers are taken into account. The vertical dynamics of the vehicle model and the dynamic tire forces between vehicle and road are calculated using analytical methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of stiffness analysis of rubber material applied in resilient wheel

Resilient wheels are well-known for their contribution to prevent squealing, impact noise and dynamic stresses on unsprung masses. In this study, a FE model is established in ABAQUS to analyze the stiffness of resilient wheels based on the Mooney-Rivlin hyperelastic material theory. The modes of each part in the resilient wheel and the whole wheel are calculated. The static and dynamic stiffness of the resilient wheel are analyzed. The simulation shows that the resilient wheel can reduce the dynamic loads both in the lateral and vertical directions between the vehicle and the track. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of High-Speed Ball Bearings with MSC/ADAMS

High-speed-rotors can be supported by angular ball bearings. Therefore, the nonlinear, time-variant bearing reaction forces are modeled for high revolution rates in this approach. Assuming local deformations, bearing stiffness is modeled with Hertzian contact between balls and races. Centrifugal forces on balls and rings are considered. Under consideration of clearance ratio the contact angle changes due to bearing load, rotational frequency and tilting angle of the inner ring. Since the contact angle determines the direction of reaction force and moment, it is possible to analyze the non-planar inner ring movement. To be able to attach further machinery parts easily to the bearing model, this approach has been done with the multi-body simulation software package MSC/ADAMS. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

多车场多车型车辆调度问题及其遗传算法

研究多车场多车型车辆调度问题,建立了一种基于最小配送费用的数学模型,模型的配送费用在考虑基本运输费的基础上又引入了司机的工资支出,包括基本工资和加班费.在多车场多车型车辆调度模型中,一辆车可以为多个客户服务,但一个客户只能由一辆车提供服务.根据模型的这些特点,提出了一种新的染色体混合编码方案和遗传操作策略,从而借助遗传算法成功实现了模型的求解.数值仿真结果验证了算法的可行性.     

Modelling Flexible Manipulators With Motors at the Joints

A computationally efficient recursive model of a flexible manipulator with motors at the joints is described in this paper. The model adopts a mixed Eulerian and Lagrangian formulation of the equations of a flexible body and exploits the chained structure of the equations for a serial manipulator. The dynamic effects of the motors at the joints, including gyroscopic terms, are fully taken into account. Symbolic manipulation is used in a newly developed package, whose performance in detailed reproduction of the dynamic effects due to the interplay between the motors and the flexible links is assessed through simulation. A comparison between the complete model and a simplified one, where the motors are considered as simple inertias rotating around their own axis, has been carried out, using both a time domain analysis and a frequency domain analysis, in order to show the relevance of gyroscopic effects in modelling flexible robots.     

Vehicle dynamics simulations with coupled multibody and finite element models

With the advent of multibody system simulations (MSS) programs, it has become common practice to use computer modeling to evaluate vehicle dynamics performance. This approach has proved to be very effective for predicting the handling performance of vehicles; however, it has proved less successful for predicting the vehicle response at frequencies that are of interest in ride harshness and durability applications. The lack of correlation between theory and experiment can be partially traced back to tire models that are inadequate for rough road simulation. This paper presents a comprehensive vehicle dynamics model for simulating the dynamic response of ground vehicles on rough surfaces. This approach uses a MSS program to simulate the vehicle and a nonlinear FE program for the tires. Parallel processing of the tire models improves the efficiency of the overall simulation. Applications for this technology include vehicle ride and harshness analysis and durability loads simulation. This paper describes the MSS vehicle model, the tire FE model, and the interface which transfers data between the two simulations. Simulation and experiment results for a single tire without a vehicle encountering an obstacle and for a vehicle with four tires driving across a pot hole are presented. Conclusions and opportunities for further research end the paper.     

On the influence of gyroscopic forces on the stability of steady-state motion : PMM vol. 39, n 6, 1975, pp. 963–973

The question of the influence of gyroscopic forces on the stability of steady-state motion of a holonomic mechanical system when the forces depend upon the velocities of only the position coordinates was answered by the Kelvin-Chetaev theorems [1] on the influence of gyroscopic and dissipative forces on the stability of equilibrium. However, if the gyroscopic forces depend as well on the velocities of the ignorable coordinates, then their influence on the stability of steady-state motions can, as the two problems in [2] show, prove to be entirely different from the influence of gyroscopic forces depending only on the velocities of the position coordinates. In this paper we investigate the influence of gyroscopic forces depending linearly on the velocities of the generalized coordinates, including the ignorable ones, on the stability of the steady-state motion of a holonomic conservative system. We prove that when the gyroscopic forces applied with respect to the ignorable coordinates are given as total time derivatives of certain functions of the position coordinates, the gyroscopic forces can both stabilize as well as destabilize the steady-state motion. Under certain conditions, this influence is also preserved for the action of dissipative forces depending on the velocities of only the position coordinates. In the case of action of dissipative forces depending also on the velocities of the ignorable coordinates, we have indicated the stability and instability conditions of the steady-state motion. Examples are considered. In conclusion, we discuss the conditions under which the application of gyroscopic forces to the system is equivalent to adding terms depending linearly on the generalized velocities to the Lagrange function.     

Computational aero-acoustic analysis of a passenger car with a rear spoiler

This study proposes an effective numerical model based on the Computational Fluid Dynamics (CFD) approach to obtain the flow structure around a passenger car with wing type rear spoiler. The topology of the test vehicle and grid system is constructed by a commercial package, ICEM/CFD. FLUENT is the CFD solver employed in this study. After numerical iterations are completed, the aerodynamic data and detailed complicated flow structure are visualized using commercial packages, Field View and Tecplot. The wind effect on the aerodynamic behavior of a passenger car with and without a rear spoiler and endplate is numerically investigated in the present study. It is found that the installation of a spoiler with an appropriate angle of attack can reduce the aerodynamic lift coefficient. Furthermore, the installation of an endplate can reduce the noise behind the car. It is clear that the vertical stability of a passenger car and its noise elimination can be improved. Finally, the aerodynamics and aero-acoustics of the most suitable design of spoiler is introduced and analyzed.     

Numerical and experimental investigation on stochastic dynamic load of a heavy duty vehicle

Numerical simulation and field test are used to investigate tire dynamic load. Based on multi-body dynamics theory, a nonlinear virtual prototype model of heavy duty vehicle (DFL1250A9) is modeled. The geometric structural parameters of the vehicle system, the nonlinear characteristics of shock absorber and leaf springs are precisely described. The dynamic model is validated by testing the data, including vertical acceleration of driver seat, front wheel, intermediate wheel and rear wheel axle head. The agreement between the response of the virtual vehicle model and the measurements on the test vehicle is satisfactory. Using the reliable model, the effects of vehicle speed, load, road surface roughness and tire stiffness on tire dynamic load and dynamic load coefficient (DLC) are discussed. The results demonstrate that the proposed model can offer efficient and realistic simulation for stochastic dynamic loads, so as to investigate vehicle road-friendliness.     

Gyroscopic stabilization of nonconservative systems

The problem is considered of the stabilization of a mechanical system having only nonconservative positional forces by adding gyroscopic forces. The gyroscopic stabilization is proved to be always realizable in the case of a degenerate matrix of nonconservative forces and even number of coordinates. If the matrix of nonconservative forces is nonsingular then a possibility of the gyroscopic stabilization is established for all systems whose number of coordinates is divisible by four. For a nonautonomous systemwith nonconservative positional forces and dissipative forces with complete dissipation, some sufficient conditions are obtained for stabilization up to the exponential stability by addition of gyroscopic forces.     

Fuzzy-hybrid modelling of an Ackerman steered electric vehicle

Physical system modelling with known parameters together with 2-D or high order look-up tables (obtained from experimental data), have been the preferred method for simulating electric vehicles. The non-linear phenomena which are present at the vehicle tyre patch and ground interface have resulted in a quantitative understanding of this phenomena. However, nowadays, there is a requirement for a deeper understanding of the vehicle sub-models which previously used look-up tables. In this paper the hybrid modelling methodology used for electric vehicle systems offers a two-stage advantage: firstly, the vehicle model retains a comprehensive analytical formulation and secondly, the ‘fuzzy’ element offers, in addition to the quantitative results, a qualitative understanding of specific vehicle sub-models. In the literature several hybrid topologies are reported, sequential, auxiliary, and embedded.In this paper, the hybrid model topology selected is auxiliary and within the same hybrid model, the first paradigm used is the vehicle dynamics together with the actuator/gearbox system. The second paradigm is the non-linear fuzzy tyre model for each wheel. In particular, conventional physical system dynamic modelling has been combined with the fuzzy logic type-II or type-III methodology. The resulting hybrid-fuzzy tyre models were estimated for a-priori number of rules from experimental data. The physical system modelling required the available vehicle parameters such as the overall mass, wheel radius and chassis dimensions. The suggested synergetic fusion of the two methods, (hybrid-fuzzy), allowed the vehicle planar trajectories to be obtained prior to the hardware development of the entire vehicle. The strength of this methodology is that it requires localised system experimental data rather than global system data. The disadvantage in obtaining global experimental data is the requirement for comprehensive testing of a vehicle prototype which is both time consuming process and requires extensive resources. In this paper the authors have proposed the use of existing experimental rigs which are available from the leading automotive manufacturers. Hence, for the ‘hybrid’ modelling, localised data sets were used. In particular, wheel-tyre experimental data were obtained from the University tyre rig experimental facilities. Tyre forces acting on the tyre patch are mainly responsible for the overall electric vehicle motion. In addition, tyre measurement rigs are a well known method for obtaining localised data thus allowing the effective simulation of more detailed mathematical models. These include, firstly, physical system modelling (conventional vehicle dynamics), secondly, fuzzy type II or III modelling (for the tyre characteristics), and thirdly, electric drive modelling within the context of electric vehicles. The proposed hybrid model synthesis has resulted in simulation results which are similar to piece-wise ‘look-up’ table solutions. In addition, the strength of the ‘hybrid’ synthesis is that the analyst has a set of rules which clearly show the reasoning behind the complex development of the vehicle tyre forces. This is due to the inherent transparency of the type II and type III methodologies. Finally, the authors discussed the reasons for selecting a type-III framework. The paper concludes with a plethora of simulation results.     

The stability and stabilization of the motion of non-conservative mechanical systems

Two stability problems are solved. In the first, the stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces (systems of general form) act, is investigated. The stability is considered in the case when the potential energy has a maximum at equilibrium. The condition for asymptotic stability is obtained by constructing Lyapunov's function. In the second problem, the possibility of stabilizing a gyroscopic system with two degrees of freedom up to asymptotic stability using non-linear dissipative and positional non-conservative forces is investigated. Stability of the gyroscopic system is achieved by gyroscopic stabilization. The stability conditions are obtained in terms of the system parameters. Cases when the gyroscopic stabilization is disrupted by these non-linear forces are indicated.     

Dynamic rolling process of tires as layered structures

Due to inner pressure the tire is a prestressed system of cord layers. The cord layers are covered by rubber layers. The whole structure is coated by a wear-resistive thread and a soft side wall coating. Serving as a boundary condition at the cord ends is a steel ring at both sides of the wheel rim. To stiffen the thread the structure has a steel cord belt with a ply angle of ±20° to the circumferential direction. The rolling system works like a spring with changing contact forces, and to compute the car dynamics it is necessary to take into account a high frequency and nonlinear varying contact. The forces between tire and road are limited by friction which gives rise to high frequency friction oscillations. Also the structural dynamics of the tire is nonconservative and self-excited, and an appropriate damping of cords and rubber is needed to stabilize the system dynamically. The computing static equilibrium and equations of motion of a continuum mechanics membrane model are treated, and the discretization to a multi-masspoint model is shown. The resulting nonlinear system of Newtonian equations is solved by using the predictor-corrector integration method in time. The time step of integration is due to the highest frequency of the system, and it is ten times shorter than the minimum of oscillation time in the system. All the nonlinearities, the hysteretic damping, and small bending moments of the rubber layers are taken into account to compute the nonstationary rolling with slip and spin on uneven roads or soft ground.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Berlin Technical University, Berlin, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 824–834, November–December, 1996.     

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method, Part 1: Mathematical modelling

A methodology is proposed for the efficient determination of gradient information, when performing gradient based optimisation of an off-road vehicle’s suspension system. The methodology is applied to a computationally expensive, non-linear vehicle model, that exhibits severe numerical noise. A recreational off-road vehicle is modelled in MSC.ADAMS, and coupled to MATLAB for the execution of the optimisation. The successive approximation method, Dynamic-Q, is used for the optimisation of the spring and damper characteristics. Optimisation is performed for both ride comfort and handling. The determination of the objective function value is performed using computationally expensive numerical simulations.This paper proposes a non-linear pitch-plane model, to be used for the gradient information, when optimising ride comfort. When optimising for handling, a non-linear four wheel model, that includes roll, is used. The gradients of the objective function and constraint functions are obtained through the use of central finite differences, within Dynamic-Q, via numerical simulation using the proposed simplified models. The importance of correctly scaling these simplified models is emphasised. The models are validated against experimental results. The simplified vehicle models exhibit significantly less numerical noise than the full vehicle simulation model, and solve in significantly less computational time.     

Study on numerical simulation methods of the railway vehicle-track dynamic interaction

A very efficient numerical simulation method of the railway vehicle–track dynamic interaction is described. When a vehicle runs at high speed on the railway track, contact forces between a wheel and a rail vary dynamically due to the profile irregularities existing on the surface of the rail. A large variation of contact forces causes undesired deteriorations of a track and its substructures. Therefore these dynamic contact forces are of main concern of the railway engineers. However it is very difficult to measure such dynamic contact forces directly. So it is important to develop an appropriate numerical simulation model and identify structural factors having a large influence on the variation of contact forces. When a contact force is expressed by the linearized Hertzian contact spring model, the equation of motions of the system is expressed as a second–order linear time–variant differential equation which has a time–dependent stiffness coefficient. Applying a well–known Newmark direct integration method, a numerical simulation is reduced to solving iteratively a time–variant, large–scale sparse, symmetric positive–definite linear system. In this study, by defining a special vector named a contact point one, it is shown that this time–variant stiffness coefficient can be expressed simply as a product of the contact point vector and its transpose and so the Sherman–Morrison–Woodbury formula applied for updating the inverse of the coefficient matrix. As a result, the execution of numerical simulation can be carried out very efficiently. A comparison of the computational time is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A reduced beam and joint concept modeling approach to optimize global vehicle body dynamics

Ideally, NVH simulations become available already in the concept phase of vehicle development. The initial computer-aided design (CAD) can then be improved (by already including countermeasures), and the feasibility to balance NVH with other performance attributes is increased. In this early design stage, when exact geometrical information is not or scarcely available, conventional virtual prototyping techniques based on detailed CAD and FE models are not directly applicable. A state-of-the-art overview of concept NVH simulation methods in vehicle industry is given.This paper then presents a “Reduced Beam and Joint Modeling” approach to analyze and optimize the global bending and torsion modes of a vehicle body. Concept modifications in the body beam-like sections and in the joints are analyzed using the body reduced modal model. This small-sized model can be used to quickly and accurately optimize the low-frequency vehicle performance. The modifications are considered with respect to the existing (predecessor) model. Equivalent beam properties are estimated from the body FE model; modifications in the beam-like sections are then implemented with beam elements from a standard FE library. The joint modifications are considered through static superelements: stiffness formulations between the end points of the joint connected to the beam layout. The validity of the approach is first demonstrated on simple example models. An industrial vehicle BIW application case is subsequently presented. A beam and joint layout is created, and used for a fast sensitivity analysis to identify suitable modifications to improve the global modes. Next, two application cases are presented. First, a fast optimization analysis is performed to optimize the global body modes. Subsequently, suitable physical modifications are identified and applied to the full FE model; it is shown that the effect of these physical modifications is accurately predicted with the fast sensitivity analysis.     

基于SD-GM理论的城市交通拥堵收费模型研究

随着中国城市化建设步伐的不断加快,交通拥堵在不断地加剧。同时,因机动车污染物的排放,每年将产生大量的NO_x,从而又会引起严重的大气污染(如“雾霾”污染)。针对这些问题,本文从环境和社会的角度出发,采用系统动力学与灰色系统相结合的方法(SD-GM),构建了城市交通拥堵收费模型,并对模型中主要变量进行动态仿真和决策分析,以此来寻找缓解交通拥堵和减少机动车尾气排放的可行策略。通过现实性测试和敏感性测试,得到拥堵收费的范围不超过100元/天*辆。通过进一步的仿真和结果分析可得到以下结论:(1)在区间[25,40] 内,随着拥堵收费的提高,NO_x存量,机动车出行吸引度和交通拥堵程度都呈下降趋势,而车均道路面积呈上升趋势。(2)但并非拥堵收费越高越好, 超过40 元/天*辆,会产生相反的效果。最后,通过比较分析,得到NO_x存量,机动车出行量,机动车出行吸引度和交通拥堵程度分别下降了约33.76%,39.64%,43.26%,82.25%,而车均道路面积提高了大约65.68%,进而验证了模型的有效性和实用性。