Theoretical Analysis of a Semi Active Suspension Fitted to an Off-Road Vehicle

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.     

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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.     

多梁式小箱梁桥沿纵向有效宽度的动力识别方法

与传统的有效宽度计算方法不同,在整桥的动力分析结果和弹性支承连续梁法荷载横向分布理论的基础上,通过假定弹性支承连续梁法动力分析模型的面内1阶转动频率与整桥1阶扭转频率相等,提出了一种多梁式小箱梁桥沿纵向有效宽度的动力识别方法。然后利用该方法识别得到的有效宽度计算各主梁的横向分布影响线及横向弯矩,并与空间有限元模型的计算结果进行了对比,结果表明该法具有很高的精度,为此类问题的研究提供了一种新的思路。     

Influence of some vehicle and track parameters on the environmental vibrations induced by railway traffic

A study is performed on the influence of some typical railway vehicle and track parameters on the level of ground vibrations induced in the neighbourhood. The results are obtained from a previously validated simulation framework considering in a first step the vehicle/track subsystem and, in a second step, the response of the soil to the forces resulting from the first analysis. The vehicle is reduced to a simple vertical 3-dof model, corresponding to the superposition of the wheelset, the bogie and the car body. The rail is modelled as a succession of beam elements elastically supported by the sleepers, lying themselves on a flexible foundation representing the ballast and the subgrade. The connection between the wheels and the rails is realised through a non-linear Hertzian contact. The soil motion is obtained from a finite/infinite element model. The investigated vehicle parameters are its type (urban, high speed, freight, etc.) and its speed. For the track, the rail flexural stiffness, the railpad stiffness, the spacing between sleepers and the rail and sleeper masses are considered. In all cases, the parameter value range is defined from a bibliographic browsing. At the end, the paper proposes a table summarising the influence of each studied parameter on three indicators: the vehicle acceleration, the rail velocity and the soil velocity. It namely turns out that the vehicle has a serious influence on the vibration level and should be considered in prediction models.     

拱梁组合式连续梁桥横向分布研究

为了进一步深入研究拱梁组合式连续梁桥的横向分布特性，以龙溪大桥为背景，采用空间有限元的分析方法，对拱梁组合式连续渠桥的横向分布特性及沿纵向的变化规律进行了研究，并与传统计算刚架拱桥的简化弹性支撑连续梁法进行对比。对比分析后认为，两种方法结果吻合很好，在实际设计拱梁组合式连续梁桥时，横向分布系数计算可以采用弹性支承连续梁简化方法。     

考虑弹性支撑边界条件的电动汽车-路面系统机电耦合振动特性分析

轮毂电机驱动电动汽车的簧下质量大导致轮胎动载荷增加,并且电机电磁力和转矩波动对车轮造成电机激励,进一步加剧车轮振动引起垂向振动负效应的问题。鉴于此,考虑电机的电磁激励,建立了电动汽车-路面系统的机电耦合动力学模型,推导了弹性支撑边界条件下路面结构的模态频率和振型表达式,以及路面振动引起的二次激励。计算了简支与弹性支撑边界条件下的路面模态频率,根据频率分布进行了截断阶数选取,并分析了边界条件、电机激励和车速对路面响应的影响。在此基础上,研究了不同行驶速度、路基反应模量及路面不平顺幅值下,激励形式对汽车车身加速度、悬架动挠度和轮胎动载荷的影响。结果表明：路面不平顺幅值越小,弹性支撑对路面响应的影响越大,弹性支撑边界条件下的路面响应较小,电机激励会引起路面响应的增加;弹性支撑边界条件下,路面不平顺幅值和路基反应模量越小,考虑路面不平顺、路面二次激励和电机激励的三重综合激励对电动汽车响应的影响越大,激励形式对轮胎动载荷的影响最大,对车身加速度的影响次之,对悬架动挠度的影响最小;电机激励导致轮胎动载荷增加,对路面破坏和寿命产生的负效应不容忽视。所建电动汽车-路面系统机电耦合模型及研究思路可为电动汽车垂向动力学分析提供参考与理论支持。     

Robustness analysis of bogie suspension components Pareto optimised values

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.     

An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics

This paper considers a method for estimating vehicle handling dynamic states in real-time, using a reduced sensor set; the information is essential for vehicle handling stability control and is also valuable in chassis design evaluation. An extended (nonlinear) Kalman filter is designed to estimate the rapidly varying handling state vector. This employs a low order (4 DOF) handling model which is augmented to include adaptive states (cornering stiffnesses) to compensate for tyre force nonlinearities. The adaptation is driven by steer-induced variations in the longitudinal vehicle acceleration. The observer is compared with an equivalent linear, model-invariant Kalman filter. Both filters are designed and tested against data from a high order source model which simulates six degrees of freedom for the vehicle body, and employs a combined-slip Pacejka tyre model. A performance comparison is presented, which shows promising results for the extended filter, given a sensor set comprising three accelerometers only. The study also presents an insight into the effect of correlated error sources in this application, and it concludes with a discussion of the new observer's practical viability.     

A methodology for vehicle sideslip angle identification: comparison with experimental data

Sideslip angle could provide important information concerning vehicle's stability. Unfortunately direct measurement of sideslip angle requires a complex and expensive experimental set-up, which is not suitable for implementation on ordinary passenger cars; thus, this quantity has to be estimated starting from the measurements of vehicle lateral/longitudinal acceleration, speed, yaw rate and steer angle. According to the proposed methodology, sideslip angle is estimated as a weighted mean of the results provided by a kinematic formulation and those obtained through a state observer based on vehicle single-track model. Kinematical formula is considered reliable for a transient manoeuvre, while the state observer is used in nearly quasi-state condition. The basic idea of the work is to make use of the information provided by the kinematic formulation during a transient manoeuvre to update the single-track model parameters (tires cornering stiffnesses). A fuzzy-logic procedure was implemented to identify steady state or transient conditions.     

Rule-based control of a semi-active suspension for minimal sprung mass acceleration: design and measurement

In this paper, a rule-based controller is developed for the control of a semi-active suspension to achieve minimal vertical acceleration. The rules are derived from the results obtained with a model predictive controller. It is shown that a rule-based controller can be derived that mimics the results of the model predictive controller and minimises vertical acceleration. Besides this, measurements on a test vehicle show that the developed rule-based controller achieves a real-world reduction of the vertical acceleration, which is in agreement with the simulations.     

Comparison of Ride Comfort Criteria for Computer Optimization of Vehicles Travelling on Randomly Profiled Roads

This paper discusses and compares some ride comfort criteria which may be suitable for randomly vibrating vehicles. The criteria consider single-figure measures based on response mean square spectral densities for plane linear combined vehicle-passenger models. Eight different measures divided into three groups are studied. The two vehicle suspension damper stiffnesses are numerically optimized with respect to the eight measures of ride comfort. The results are compared and discussed. Two optimizations with respect to five vehicle parameters are also reported.     

Optimising a Car Chassis

This paper presents a method to optimise a car chassis fitted either with passive or active suspensions. Provided that a full vehicle model is available for accurate simulations of many different driving situations (J-turn, lane-change, power-on/power-off on even/rough, dry/wet roads), the method allows to tune the parameters of the chassis system (suspension elastokinematics, stiffnesses, dampings, actuator gains, tyre pressures...) in order to achieve the desired dynamic behaviour of the car in all of the considered driving situations. According with the Global Approximation approach, the original physical car model is substituted by another purely numerical mathematical model (backpropagating Artificial Neural Network). This reduces the simulation time dramatically and enables the optimisation process to come to successful results. The computation of the Pareto-optimal set is performed by using Genetic Algorithms. The method is validated by optimising the parameters of the suspension system of an actual car.     

Optimising a Car Chassis

This paper presents a method to optimise a car chassis fitted either with passive or active suspensions. Provided that a full vehicle model is available for accurate simulations of many different driving situations (J-turn, lane-change, power-on/power-off on even/rough, dry/wet roads), the method allows to tune the parameters of the chassis system (suspension elastokinematics, stiffnesses, dampings, actuator gains, tyre pressures...) in order to achieve the desired dynamic behaviour of the car in all of the considered driving situations. According with the Global Approximation approach, the original physical car model is substituted by another purely numerical mathematical model (backpropagating Artificial Neural Network). This reduces the simulation time dramatically and enables the optimisation process to come to successful results. The computation of the Pareto-optimal set is performed by using Genetic Algorithms. The method is validated by optimising the parameters of the suspension system of an actual car.     

重型汽车荷载作用下简支梁桥的动力反应分析

基于结构动力学理论，视桥梁与车辆为一个相互作用的整体系统，建立了桥梁在移动车辆荷载作用下振动的计算模式。在分析中，汽车采用2轴模型，桥梁结构模拟为梁单元，统一列出车桥系统的动力方程，编制了计算程序。对实际预应力混凝土简支箱梁桥在重型汽车作用下的动力冲击效应进行了计算，并与轻型汽车荷载作用下产生的动力冲击系数进行了比较。     

梯形多室箱梁横向内力计算方法研究

箱梁横向内力的计算目前还缺乏精确有效的简化方法。在此利用虚拟框架法,获得箱梁截面的位移变形及横向内力,通过反算得到箱梁对虚拟框架的弹性支承刚度,建立梯形多室箱梁的弹性支承框架分析模型。计算示例的分析结果表明:该模型具有较高的精度,误差能够控制在10%以内,荷载作用下的弯矩值计算精度更高,可为箱梁横向内力分析方法的研究提供了新的思路。     

A methodology for vehicle sideslip angle identification: comparison with experimental data

Sideslip angle could provide important information concerning vehicle's stability. Unfortunately direct measurement of sideslip angle requires a complex and expensive experimental set-up, which is not suitable for implementation on ordinary passenger cars; thus, this quantity has to be estimated starting from the measurements of vehicle lateral/longitudinal acceleration, speed, yaw rate and steer angle. According to the proposed methodology, sideslip angle is estimated as a weighted mean of the results provided by a kinematic formulation and those obtained through a state observer based on vehicle single-track model. Kinematical formula is considered reliable for a transient manoeuvre, while the state observer is used in nearly quasi-state condition. The basic idea of the work is to make use of the information provided by the kinematic formulation during a transient manoeuvre to update the single-track model parameters (tires cornering stiffnesses). A fuzzy-logic procedure was implemented to identify steady state or transient conditions.     

Comparison of Ride Comfort Criteria for Computer Optimization of Vehicles Travelling on Randomly Profiled Roads

SUMMARY

This paper discusses and compares some ride comfort criteria which may be suitable for randomly vibrating vehicles. The criteria consider single-figure measures based on response mean square spectral densities for plane linear combined vehicle-passenger models. Eight different measures divided into three groups are studied. The two vehicle suspension damper stiffnesses are numerically optimized with respect to the eight measures of ride comfort. The results are compared and discussed. Two optimizations with respect to five vehicle parameters are also reported.     

Prediction of tire natural frequency with consideration of the enveloping property

A lumped tire model was developed with consideration of the enveloping property in order to predict the natural tire frequency. Tire stiffness was classified into vertical, sidewall, and enveloping stiffnesses, and the tire characteristics were analyzed in detail experimentally and via finite element analysis. In addition, the effective masses of the tire tread and belt were extracted directly from design specifications taking into account the sizes and material properties of different rubber blocks. Using the design parameters of the tires, natural frequencies were calculated from the derived model and were compared with experimental results. Finally, based on good agreement with experimental results, sensitivity analysis was performed to verify the effect of tire stiffnesses on the natural frequencies.     

Optimization of the Lateral Stability of Rail Vehicles

Summary The lateral stability of a rail vehicle is optimized using a combination of multibody dynamics, sequential quadratic programming, and a genetic algorithm. Several steps are taken to validate this integrated approach and to show its effectiveness. First, a hand-derived solution to a 17 degree of freedom linear rail vehicle model is compared to the simulation results from the A'GEM multibody dynamics software. Second, the calculation of the ‘critical speed’ (above which a rail vehicle response becomes unstable) using sequential quadratic programming is validated for a specific example. In the process, the existence of sharply-discontinuous ‘cliffs’ in the plots of critical speed versus suspension stiffnesses are identified. These cliffs, which are due to switching of the least-damped mode in the system, greatly hinder the application of gradient-based optimization methods. Two methods that do not require gradient information, a genetic algorithm and the Nelder-Mead's Simplex algorithm, are used to optimize the critical speed. The two algorithms and their results are compared. In recognition of the cliff phenomenon, the definition of critical speed is generalized to make it a more practical measure of lateral stability.     

Optimization of the Lateral Stability of Rail Vehicles

Summary The lateral stability of a rail vehicle is optimized using a combination of multibody dynamics, sequential quadratic programming, and a genetic algorithm. Several steps are taken to validate this integrated approach and to show its effectiveness. First, a hand-derived solution to a 17 degree of freedom linear rail vehicle model is compared to the simulation results from the A'GEM multibody dynamics software. Second, the calculation of the 'critical speed' (above which a rail vehicle response becomes unstable) using sequential quadratic programming is validated for a specific example. In the process, the existence of sharply-discontinuous 'cliffs' in the plots of critical speed versus suspension stiffnesses are identified. These cliffs, which are due to switching of the least-damped mode in the system, greatly hinder the application of gradient-based optimization methods. Two methods that do not require gradient information, a genetic algorithm and the Nelder-Mead's Simplex algorithm, are used to optimize the critical speed. The two algorithms and their results are compared. In recognition of the cliff phenomenon, the definition of critical speed is generalized to make it a more practical measure of lateral stability.