Parametric study of nonlinear adaptive control algorithm with magneto-rheological suspension systems

This paper describes the details of the simulation analysis of a nonlinear model-based adaptive suspension control system [Song X, Ahmadian M, Southward SC, Miller LR. An adaptive semiactive control algorithm for magneto-rheological suspension systems. ASME J Vibr Acoust, in press; Song X. Design of adaptive vibration control systems with application of magneto-rheological dampers. Dissertation, Virginia Tech, December, 1999]. The numerical aspect of the simulation study of a seat suspension with application of magneto-rheological dampers will be presented. Magneto-rheological (MR) dampers have strong nonlinearities such as bi-linearity, hysteresis, and saturation related to magnetism, which can be represented by appropriate mathematic functions, respectively. Thus the model-based adaptive algorithm becomes complicated because of involvement of MR damper models. One objective of this study is to investigate the effect of MR damper model simplifications on the adaptive suspension performance. Furthermore, simulation is also applied to do parametric study of adaptive algorithm parameters such as filtering and step size. The numerical results compare the proposed adaptive controller with passive dampers to validate not only its effectiveness but also obtain some guidance information for its experimental implementation.     

The development of hybrid ES-FE-SEA method for mid-frequency vibration analysis of complex built-up structure

The beam-plate structures and its complex composite structures are widely used in practical engineering. Recently, a hybrid FE-SEA method was applied for the vibration analysis of beam-plate structures in mid-frequency regime. However, the accuracy of prediction is still low, due to “overly-stiff” feature of embedded conventional FEM. In this work, a hybrid ES-FE-SEA model of a beam-plate built-up structure is developed for response prediction in vibration testing, in which, the edge-based smoothed technique is applied in the 3D beam structure FEM model to soften the whole system stiffness. Then, combined with SEA, this ES-FEM is embedded to achieve a hybrid ES-FE-SEA framework, to improve the accuracy of mid-frequency response predictions of the complex built-up structure. In hybrid ES-FE-SEA model, the plate structure which has a higher model density is considered as a statistical subsystem and modeled statistically using statistical energy analysis (SEA). The beam structure with a relative lower model density is modeled deterministically using edge-based smooth finite element method (ES-FEM). The coupling between these two different types of subsystems is achieved through the diffuse field reciprocity relation. The acceleration loads are applied to the model. The results obtained by the ES-FE-SEA and FE-SEA are compared. It is found that the hybrid ES-FE-SEA method is reliable for the mid-frequency vibration problems of the beam-plate built-up structure. The proposed ES-FE-SEA is verified by various numerical examples.     

On the oscillations of a thin-walled structure containing a fluid, in the presence of a hydrodynamic damper : PMM vol. 43, no. 6, 1979, pp. 1095–1101

A model of a hydrodynamic oscillation damper is proposed. The model is used to obtain the equations describing longitudinal oscillations of a structure which includes a shell partially filled with fluid, and contains a hydrodynamic damper. It is shown that the use of the damper leads to considerable increase in the damping of the oscillations of specified frequencies within the structure.

In modern technology one encounters various types of problems connected with restricting the amplitudes of the axisymmetric vibrations of shells and of the longitudinal oscillations of structures consisting of shells partially filled with fluid. Various devices have been proposed [1] for solving these problems. All these devices have a common feature, namely an elastic shell filled with gas and placed in the fluid. The natural frequency of oscillations of such a shell in a fluid can be tuned to required frequency. The effect of such a device is analogous to the effect of a dynamic vibration damper in mechanical systems [2]. A part of the fluid contained in the shell serves as the active mass of the dynamic damper, and for this reason we shall call such devices the hydrodynamic vibration dampers.     

A tuning criterion for the inertial tuned damper. Design using phasors in the Argand–Gauss plane

A new approach to the design of a dynamic damper for a monomass oscillator is presented; the design procedure is then applied to control a multimodal oscillator. This new dynamics emerged from an analysis by means of phasors (rotating vectors in the Argand–Gauss plane) which revealed the phase relations between the damper and main oscillator. In particular this work introduces a geometric formalism, based on the use of phasors in the complex plane, for the sizing of inertial dampers applied to multimodal structural oscillators. Their damping effect depends on the fact that the response of the secondary oscillator (the damper) delays the response of the primary mass by 90°, so that the elastic force transmitted by the damper becomes a viscous force on the controlled oscillator. When such condition occurs we say that the damper is “tuned” to the main oscillator; the damping induced by the damper serves to limit the displacement of main oscillator. Our geometrical approach provides a method whose language is close to that of structural mechanics, thus paving the way to the professionals for: (i) sizing the damper parameters and (ii) evaluating the stability to the damped system and its performance limits. The aim of the development is that of exploring the use of dampers to control the response of buildings under horizontal seismic and aerodynamic loads.     

基于车身装配结构优化的改进图分解算法

在考虑车身制造和装配成本的前提下对车身装配结构优化方法进行了研究,提出一种改进的图分解算法将车身装配结构最优地分解为一组部件.以白车身侧围的装配模型为例,将结构的几何图形转化为与之对应的关系拓扑图,再分割该关系拓扑图为一组工程约束下的单连通不交叉子图集,结合遗传算法中的算子操作,利用有限单元法分析并计算得到产品几何图形的最优分割,采用NSGA-Ⅱ算法并实现该装配体综合性能最优的目标.     

On the nonlinear dynamics of a high-speed railway vehicle with nonsmooth elements

A comprehensive lateral mathematical model of a high-speed railway vehicle with 17 degrees of freedom is built to study its nonlinear dynamics on a straight line. The hunting stability is explored by using eigenvalue analysis, bifurcation diagrams and the first Lyapunov coefficient. Due to the non-smoothness in the wheel/rail contact table and the secondary suspension elements such as anti-yaw dampers, bump stops, etc., an event-driven strategy is applied in the integration process of the ODEs. As an example, the nonlinear dynamics of a Chinese Railway High-speed (CRH) vehicle (named CRH2) is investigated. The result shows that the stable equilibrium of the high-speed railway vehicle loses its stability through a supercritical Hopf bifurcation with the increase of the forward speed, and the stable periodic solution loses its stability through a grazing bifurcation with the decrease of the forward speed. The influence of primary system parameters on the hunting stability of the high-speed railway vehicle is also investigated.     

设置黏滞阻尼器的纵飘斜拉桥地震响应简化分析方法

针对纵飘体系斜拉桥现有黏滞阻尼器参数设计方法的不足,提出了更为快捷有效的分析方法.首先基于钟摆原理,采用双质点模型简化模拟纵飘斜拉桥的动力响应特征;然后基于能量耗散等效原理,提出了黏滞阻尼器的等效线性模型;最后基于结构动力学原理,建立了设置黏滞阻尼器的纵飘斜拉桥地震响应简化分析方法.在此基础上,针对某主跨392 m的纵飘斜拉桥建立了全桥分析模型,在正弦波作用下,对比分析了全桥模型、双质点简化模型数值解和解析解的计算误差.结果表明:双质点模型数值解计算结果精度较高,可以代替全桥模型的有限元计算结果;解析解与双质点数值解计算结果吻合良好,验证了双质点模型简化分析方法在理论上的可靠性;在不同地震动特性和体系周期下,三者计算误差均满足工程精度要求,表明该简化分析方法具有良好的适用性,可为阻尼器参数优化提供更简便的模型.     

Optimisation of road vehicle passive suspension systems. Part 2. Qualification and case study

As an aid during the concept design phase, the two-dimensional vehicle simulation programme Vehsim2d has been developed (see part 1 of this paper for the vehicle model). The leap-frog optimisation algorithm for constrained problems (LFOPC) has been linked to the multi-body dynamics simulation code (Vehsim2d) to enable the computationally economic optimisation of certain vehicle and suspension design variables. This paper describes the simulation programme, the qualification of the programme, and gives an example of the application of the Vehsim2d/LFOPC system. In particular it is used to optimise the damper characteristics of an existing 22 ton three axle vehicle, over a typical terrain and at a representative speed. By using this system the optimised damper characteristics with respect to ride comfort for the vehicle are computed. The optimum damper characteristics give a 28.5% improvement in the ride comfort of the vehicle over the specified terrain and prescribed speed. Further optimisation runs were performed considering other terrain and different speed values. From these results final damper characteristics for the vehicle are proposed. Using the proposed characteristics, simulations were performed with the more advanced and proven DADS programme. The results show that the damper suggested by the optimisation study is indeed likely to improve the suspension of the vehicle. This study proves that the Vehsim2d/LFOPC vehicle modelling and optimisation system is indeed a valuable tool for a vehicle design team.     

Shaking table tests of a model-scale building with 2DOF pendulum mass damper

In this paper, the numerical and experimental studies of a tall building's model with 2DOF pendulum mass damper (PMD) are considered. It is assumed that the model excitation is in the form of horizontal and/or torsional motion of the ground caused by earthquake. The construction consists of the main system (tall building's model) and a double pendulum mass damper, which is attuned to the first (bending) and the second (torsional) eigenfrequencies of the main structure. The analysis focuses on reduction of structure vibration caused by horizontal or torsional component of ground motions. Therefore, results presented in this work show efficiency of 2DOF PMD for vibration reduction. The numerical analysis of the problem is performed with using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is carried out on a physical model-scale building with 2DOF PMD. Model consists of twenty five recurrent storeys (height 2.5m) with a PMD located on the highest one. Shaking table device is used to simulate an earthquake excitation in horizontal and torsional component, independently. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gradient-based approximation methods applied to the optimal design of vehicle suspension systems using computational models with severe inherent noise

The principal aim of this paper is to evaluate the feasibility of using gradient-based approximation methods for the optimisation of the spring and damper characteristics of an off-road vehicle, for both ride comfort and handling. The Sequential Quadratic Programming algorithm and the relatively new Dynamic-Q method are the two successive approximation methods used for the optimisation. The determination of the objective function value is performed using computationally expensive numerical simulations that exhibit severe inherent numerical noise. The use of forward finite differences and central finite differences for the determination of the gradients of the objective function within Dynamic-Q is also investigated. This is done in investigating methods for overcoming the difficulties associated with the optimisation of noisy objective functions.A recreational off-road vehicle is modelled in ADAMS, and coupled to MATLAB for the execution of the optimisation process. The full vehicle ADAMS model includes suspension kinematics, a load-dependent tyre model, as well as non-linear springs and dampers. Up to four design variables are considered in modelling the suspension characteristics.It is found that both algorithms perform well in optimising handling. However, difficulties are encountered in obtaining improvements in the design process when ride comfort is considered. Nevertheless, meaningful design configurations are still achievable through the proposed optimisation process, at a relatively low cost in terms of the number of simulations that have to be performed.     

非线性系统动力分析的模态综合技术

各种模态综合方法已广泛应用于线性结构的动力分析,但是,一般都不适用于非线性系统. 本文基于[20][21]提出的方法,将一种模态综合技术推广到非线性系统的动力分析.该法应用于具有连接件耦合的复杂结构系统,以往把连接件简化为线性弹簧和阻尼器.事实上,这些连接件通常具有非线性弹性和非线性阻尼特性.例如,分段线性弹簧、软特性或硬特性弹簧、库伦阻尼、弹塑性滞后阻尼等.但就各部件而言,仍属线性系统.可以通过计算或试验或兼由两者得到一组各部件的独立的自由界面主模态信息,且只保留低阶主模态.通过连接件的非线性耦合力,集合各部件运动方程而建立成总体的非线性振动方程.这样问题就成为缩减了自由度的非线性求解方程,可以达到节省计算机的存贮和运行时间的目的.对于阶次很高的非线性系统,若能缩减足够的自由度,那么问题就可在普通的计算机上得以解决. 由于一般多自由度非线性振动系统的复杂性,一般而言,这种非线性方程很难找到精确解.因此,对于任意激励下系统的瞬态响应,可以采用数值计算方法求解缩减的非线性方程.     

Decomposition approach to model smart suspension struts

Model and simulation study is the starting point for engineering design and development, especially for developing vehicle control systems. This paper presents a methodology to build models for application of smart struts for vehicle suspension control development. The modeling approach is based on decomposition of the testing data. Per the strut functions, the data is dissected according to both control and physical variables. Then the data sets are characterized to represent different aspects of the strut working behaviors. Next different mathematical equations can be built and optimized to best fit the corresponding data sets, respectively. In this way, the model optimization can be facilitated in comparison to a traditional approach to find out a global optimum set of model parameters for a complicated nonlinear model from a series of testing data. Finally, two struts are introduced as examples for this modeling study: magneto-rheological (MR) dampers and compressible fluid (CF) based struts. The model validation shows that this methodology can truly capture macro-behaviors of these struts.     

Feed-forward modelling and fuzzy logic based control strategy for powertrain efficiency improvement in a parallel hybrid electric vehicle

With the stricter limitations on both fuel consumption and air pollution, the advantages of a hybrid electric vehicle are becoming more evident than ever. In the present study, an energy management system for a hybrid electric vehicle is developed. Because the plant under consideration is nonlinear, multi-domain, time-varying, has multiple uncertainties and, in addition, the designed control strategy must be able to obey the driver's commands and achieve the par-internship for a new generation of vehicle regulations, the fuzzy logic approach is chosen. A feed-forward hybrid vehicle simulation model is used to demonstrate the validity and the convenience of the current approach and its results have been compared with the other parallel hybrid electric vehicle control strategies. Simulation results show considerable improvement in the efficiency of the internal combustion engine and, consequently, fuel consumption and acceleration performances.     

Neural network control of seat vibrations of a non-linear full vehicle model using PMSM

In this paper, the dynamic behaviour of a non-linear eight degrees of freedom vehicle model having active suspensions and passenger seat using Permanent Magnet Synchronous Motor (PMSM) controlled by a Neural Network (NN) controller is examined. A robust NN structure is established by using principle design data from the Matlab diagrams of system functions. In the NN structure, Fast Back-Propagation Algorithm (FBA) is employed. The user inputs a set of 16 variables while the output from the NN consists of f₁–f₁₆ non-linear functions. Further, the PMSM controller is also determined using the same NN structure. Various tests of the NN structure demonstrated that the model is able to give highly sensitive outputs for vibration condition, even using a more restricted input data set. The non-linearity occurs due to dry friction on the dampers. The vehicle body and the passenger seat using PMSM are fully controlled at the same time. The time responses of the non-linear vehicle model due to road disturbance and the frequency responses are obtained. Finally, uncontrolled and controlled cases are compared. It is seen that seat vibrations of a non-linear full vehicle model are controlled by a NN-based system with almost zero error between desired and achieved outputs.     

Multi-parametric optimizations for power dissipation characteristics of Stockbridge dampers based on probability distribution of wind speed

Power dissipation characteristics of Stockbridge dampers (SD) is one of the important indexes in anti-vibration work of transmission line. The study focuses on the optimization of the SD's power dissipation characteristics under the effect of multi-structure parameter coupling. The aeolian vibration of overhead transmission lines is uncertain and random in stochastic dynamics. According to Strouhal formula, the relationship between the vibration frequency of transmission lines and wind speed can be found out. Based on the Weibull wind speed probability distribution, the probability density function of the transmission line conductor and damper coupling system vibration frequency is derived. The SD is considered as a typical 2-dimension of stochastic dynamical system. Based on the random process generated by the power dissipation of the SD, the characteristics of power dissipation and SD's resonant frequencies are analyzed when the multi-structure parameters of the SD are coupled. And the diagrams of the power dissipation at various frequencies are obtained.Based on the probability density function of the vibration frequency of the overhead conductor and damper, the objective function, namely the mathematical expectation of power dissipation (E(PD)), of the optimizations for the SD's power dissipation under the coupling of multiple structural parameters is proposed for the first time according to the author's knowledge. Constraint conditions of the optimizations are built by the quantization processing. The energy dissipation characteristics of the dampers can be evaluated by E(PD), and the power dissipation of SD with different coupled dual structure parameters is optimized based on the proposed method. The optimal values or the optimal value intervals of different coupled dual structure parameters are found, which may provide practical data.     

Symmetric and Asymmetric Underplatform Dampers for Turbine Blades

Friction damping devices like underplatform dampers are widely used in turbomachinery applications to reduce vibration amplitudes and to increase lifetime and reliability of the bladed disk. Nowadays, in practical applications, a variety of different underplatform damper geometries is applied. Nevertheless, a detailed study of the in.uence of the geometric and dynamic properties of the damper is still not available. Within this paper the most frequently applied damper types like cylindrical and wedge as well as asymmetrical dampers are investigated and compared to each other with respect to their effectiveness. Especially the in.uence of the damper geometry on the resonance frequency and vibration amplitude is pointed out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental analysis of magnetorheological dampers when subjected to impact and shock loading

The vast majority of the investigations for controllable magnetorheological (MR) dampers have focused on their low velocity and low frequency applications. The extensive work in this area has led to a good understanding of MR fluid properties at low velocities and frequencies. Many of the issues pertaining to MR damper behavior in impact and shock applications are relatively unknown. This study provides an experimental analysis of magnetorheological dampers when they are subjected to impact and shock loading. To this end, a drop-tower is developed to apply impulse loads to the dampers. The drop-tower design uses a guided drop-mass, which is released from variable heights to achieve different impact energies. The nominal drop-mass is 55 lb and additional weight may be added to reach a maximum of 500 lb. The nominal drop-mass of 55 lb is used throughout this study. Five drop-heights are investigated: 12, 24, 48, 72 and 96 in., corresponding to impact velocities of 86, 127, 182, 224 and 260 in./s, respectively. Two MR damper configurations are tested, a damper with a single-stage, double-ended piston and a mono-tube damper with a two-stage piston. The results indicate that the two damper configurations exhibit different force–displacement characteristics during impulse loading. For the single-stage, double-ended damper, the peak force occurs close to the beginning of the impact. Conversely, the two-stage, mono-tube damper does not reach the peak force until after the nitrogen accumulator bottoms out. To verify this behavior, a theoretical model of the accumulator is derived and compared to the experimental data. Additionally, the results show that at large impact velocities, the peak force does not depend on the current supplied to the damper, as is commonly the case at low velocities. This phenomenon is hypothesized to be the result of the fluid inertia preventing the fluid from accelerating fast enough to accommodate the rapid piston displacement. Thus, the peak force is primarily attributed to fluid compression, rather than the flow resistance (“valving”) associated with the fluid passing through the MR valve.     

Search algorithm for optimal damping parameters of transfemoral prosthetic limb

In this paper, we developed a mathematical model to find the parameters of prosthetic damper which will provide a similar trajectory for the prosthetic knee joint. Two popular searching methods namely grid searching and optimization are used to determine the damper's parameters. The proposed model is validated with a simulation process using the data of the able-body individuals. We utilized the ground reaction force of sound limb to determine the values of the damper parameters of a prosthetic knee joint for maximum symmetry. Symmetry between knee moments was also improved in the stance period with optimized parameters. Finally, optimization-based searching was observed to be more computationally efficient than the grid-based searching method. The present study will provide a virtual solution to set the prosthetic dampers parameters based on user needs. In the future, the present method can be used for adjusting damping of microprocessor prosthetic knee joint for symmetrical gait pattern.     

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.