Power Spectral Density of Road Profiles

The road profile is usually considered to be a random process x ( d ), where x is the road height and d is the distance along the road. As the vehicle travels along the road with velocity v , the random process x ( d ) is converted to a random process x ( t ) which is input to the vehicle suspension via the tyre. The random process x ( d ) is usually described in terms of its power spectral density as a function of frequency in either radians or cycles per unit distance. However, there are several different ways of defining power spectral density, and this makes it difficult to compare published data without knowing how the power spectral density has been defined. The proper calculation of RMS values of vehicle response for an assumed road power spectral density is explained by an example.     

车辆路面纵向振动信号再现方法研究

基于自回归滑动平均模型(ARMA)的方法,实现了不同车速和路面条件下的随机振动信号的实验室再现。并对某货车的半主动悬架物理模型进行了路面随机振动信号再现和平顺性试验,通过对实际信号和再现信号的统计数据、累积频率分布(CFD)和功率谱密度(PSD)的效果比较,表明其优点是方法简单、准确度高、周期短、费用低。     

Roadway Elevation Profile Generation for Vehicle Simulation

With a simplified approach for creating road surface elevation information for simulation of vehicle vertical response to roadway unevenness, roadways for single and parallel track simulations and averaged roads for variable velocity simulation are developed. Sets of correctly chosen random roadway slopes are averaged appropriately for the variable velocity simulation. The procedure generates approximately “white” slope spectral density roadways in the frequency ranges of interest, and the elevation profiles are representative of average road profiles. The method is simple in practice yet suffices for many parameter studies of suspensions and vehicle dynamics.     

A stochastic quarter-car model for dynamic analysis of vehicles with uncertain parameters

A quarter-car model is used to investigate the vibration response of cars with uncertainty under random road input excitations in this paper. The sprung mass, unsprung mass, suspension damping, suspension stiffness, and tyre stiffness are considered as random variables. The road irregularity is considered a Gaussian random process and modelled by means of a simple exponential power spectral density. The power spectral density, mean value, standard deviation, and variation coefficient of the vehicle's natural frequencies and mode shapes are obtained by using the Monte Carlo simulation method. The computational expressions for the numerical characteristics of the mean square value of the vehicle's random response in the frequency domain are developed by means of the random variable's functional moment method. The influences of the randomness of the vehicle's parameters on the vehicle's dynamic response are investigated in detail using a practical example, and some useful conclusions are obtained.     

Characterization of Longitudinal Road Unevenness in the Light of the International PIARC - EVEN Experiment 1998

The basic model of road pavement unevenness (homogeneous random function with Gaussian distribution function and simple power spectral density function) is generalized to cover real states of roads under traffic conditions, such as: independent characterization of long and short wavelengths unevenness, and consideration of non-homogeneity including appearance of individual large imperfections. The method of estimating relevant parameters is based on the interaction coupling between the traveling vehicle and the road. To justify the need for these generalizations, summarizing results are given of the International PIARC - EVEN experiment conducted in 1998 in three world regions (Arizona, USA, Hokkaido, Japan, and Netherlands / Germany). Total 47 road sections of different technological execution and different unevenness levels were tested using DYNVIA device.     

An Active Suspension with Optimal Linear State Feedback

In this paper modern optimal control theory is applied to the design of an active suspension system for a motor vehicle. The road profile is assumed to be continuous and random with a power spectral density (P.S.D.) which varies inversely with the square of the frequency. The quadratic integral type performance index employed is a weighted sum of the integral squares of body acceleration, dynamic tyre deflection and relative body-to-axle displacement. A solution is obtained for the infinite time case which is both computationally and physically realizable as an active suspension in which the only continuous measurements required are the body absolute velocity and the body displacement relative to the road. The performance is compared with that of a conventional type passive suspension and found to be significantly better in practically all respects.     

An Active Suspension with Optimal Linear State Feedback

SUMMARY

In this paper modern optimal control theory is applied to the design of an active suspension system for a motor vehicle. The road profile is assumed to be continuous and random with a power spectral density (P.S.D.) which varies inversely with the square of the frequency. The quadratic integral type performance index employed is a weighted sum of the integral squares of body acceleration, dynamic tyre deflection and relative body-to-axle displacement. A solution is obtained for the infinite time case which is both computationally and physically realizable as an active suspension in which the only continuous measurements required are the body absolute velocity and the body displacement relative to the road. The performance is compared with that of a conventional type passive suspension and found to be significantly better in practically all respects.     

道路不平程度的评价方法及相互关系研究

通过回归分析的方法对标准分级道路功率谱密度与相应国际平整度指数之间的关系进行了研究.根据标准道路谱再现出随机路面,以此作为输入去激励标准1/4车辆模型,从而获得与标准道路谱相应的国际平整度指数,然后利用回归分析获得了标准道路谱与国际平整度指数之间的关系.     

由路面引起的汽车振动能量耗散特性频域分析

针对行驶过程中由路面引起的汽车振动能量耗散问题，提出了基于汽车振动二自由度单轮模型的能量耗散特性频域分析方法。采用汽车振动二自由度单轮模型推导了模型的频率响应，确定了能量耗散振动响应量及其频率响应。将路面激励功率谱密度与振动响应量的功率谱密度和均方根值相结合，建立了能量耗散振动响应量统计特性和振动能量耗散平均功率的表示。采用Matlab开发了汽车振动二自由度单轮模型的能量耗散特性频域分析仿真程序，通过3种分析方案研究了由路面引起的汽车振动能量耗散特性。结果表明，汽车振动能量耗散平均功率与速度和路面等级相关，受到路面等级的影响较大；在以B级路面为主的国内城市行驶工况下，由路面引起的汽车振动能量耗散平均功率比较低。     

多点虚拟激励法在整车随机振动分析中的应用

建立了9自由度整车模型,从理论上论述了多点虚拟激励法.构造了路面对整车的路面虚拟激励,求取了汽车虚拟振动响应量,并由此算出了汽车真实振动响应量的功率谱密度.结果表明,虚拟激励法在汽车随机振动分析中的应用和傅里叶分析方法同样有效,却简单得多.     

三维路面模型的构建及其在Adams中的验证

根据多功能激光路面检测仪测得的路面信息,提出了利用Delaunay三角剖分与加权函数插值相结合生成三维路面模型的算法,在此算法的基础上根据Adams中的路面格式生成其相应的路面文件,可以直接被Adams调用。同时通过功率谱对比与Adams中仿真分析对生成的路面模型进行了验证。结果表明,此算法可以生成纹理更加清晰、精度较高的路面模型;不同车速下的仿真结果与实测路面结果有较好的一致性,误差相对较小。因此,生成的路面模型能够真实地反映实际路面不平度的特征。     

Random Response of Tractor-Semitrailer System

This work describes an analytical study of the dynamic behaviour of a tractor-semitrailer vehicle. A digital computer simulation was used to describe the longitudinal, vertical, and pitching motions of the vehicle travelling over a stationary random road surface. A man-seat model was also incorporated into the simulation. Vehicle response to road irregularities has been studied by assuming two different roads for loaded and unloaded cases.

Numerical results are presented for vehicle, showing system eigenvalues, power spectral densities and root mean square values of the linear and angular accelerations and displacements. Vehicle acceleration response is compared with the ISO riding comfort standard. All results for the loaded and unloaded cases and for smooth and rough roads indicated that an uncomfortable ride would result from vehicle response.     

Optimal Preview Control of a Two-dof Vehicle Model Using Stochastic Optimal Control Theory

An optimal preview control algorithm is applied to a two degree of freedom(dof) vehicle model travelling with constant velocity on a randomly profiled road. The road roughness is modelled as a homogeneous random process being the output of a linear first order filter to white noise. The input from the road irregularity is assumed to be measured at some distance in front of the vehicle and this measured infonnation is utilized by the active controller to prepare the system for the ensuing input. The preview control algorithm is obtained by minimizing a quadratic performance index and by describing the average behaviour of the system by the covariance matrix of the vehicle response state vector. Results are presented for full state feedback and significant improvements in sprung mass acceleration, suspension working space and road holding are observed.     

桥面平整度对大跨度钢管混凝土拱桥车辆振动的影响

由路面平整度能量谱密度函数得到桥面平整度不规则形状沿纵向分布函数,分析不同等级桥面平整度对大跨度钢管混凝土拱桥的车辆振动的影响。提出一种车—桥振动简化计算方法,该方法在建立桥的有限元模型时,将车辆的动力性能与桥面平整度对桥梁振动的影响加入到外载荷中,简化了振动分析过程,可用于确定不同等级桥面下的汽车荷载冲击系数取值,为大跨度钢管混凝土拱桥的设计和养护提供参考。     

基于小波变换的四轮车辆非平稳振动时频研究

基于8自由度的车辆动力学模型，以四轮相关滤波白噪声路面为系统输入，对四轮车辆的非平稳随机振动过程进行了计算机时域模拟，进而采用谱分析和小波分析技术分析了系统响应，在时频平面内建立了各振级之间的振动联系，考察了振动能量的流动情况，深入揭示了车辆非平稳振动过程的本质。     

Roadway Elevation Profile Generation for Vehicle Simulation

SUMMARY

With a simplified approach for creating road surface elevation information for simulation of vehicle vertical response to roadway unevenness, roadways for single and parallel track simulations and averaged roads for variable velocity simulation are developed. Sets of correctly chosen random roadway slopes are averaged appropriately for the variable velocity simulation. The procedure generates approximately “white” slope spectral density roadways in the frequency ranges of interest, and the elevation profiles are representative of average road profiles. The method is simple in practice yet suffices for many parameter studies of suspensions and vehicle dynamics.     

Random Response of Tractor-Semitrailer System

SUMMARY

This work describes an analytical study of the dynamic behaviour of a tractor-semitrailer vehicle. A digital computer simulation was used to describe the longitudinal, vertical, and pitching motions of the vehicle travelling over a stationary random road surface. A man-seat model was also incorporated into the simulation. Vehicle response to road irregularities has been studied by assuming two different roads for loaded and unloaded cases.

Numerical results are presented for vehicle, showing system eigenvalues, power spectral densities and root mean square values of the linear and angular accelerations and displacements. Vehicle acceleration response is compared with the ISO riding comfort standard. All results for the loaded and unloaded cases and for smooth and rough roads indicated that an uncomfortable ride would result from vehicle response.     

The use of vehicle acceleration measurements to estimate road roughness

Road roughness is a broad term that incorporates everything from potholes and cracks to the random deviations that exist in a profile. To build a roughness index, road irregularities need to be measured first. Existing methods of gauging the roughness are based either on visual inspections or using one of a limited number of instrumented vehicles that can take physical measurements of the road irregularities. This paper proposes the collection of data from accelerometers fixed in a specific vehicle type and the use of this data to estimate the road condition. Although the estimate is approximate, accelerometers are being increasingly used by car manufacturers to improve suspension performance and the proposed method is relatively inexpensive to implement and provide road managers with constantly updated measurements of roughness. This approach is possible due to the relationship between the power spectral densities of road surface and vehicle accelerations via a transfer function. This paper shows how road profiles can be accurately classified using axle and body accelerations from a range of simulated vehicle–road dynamic scenarios.     

刹车状况下桥上随机车流动态演化及车-桥耦合振动分析

为实现刹车时桥上多状态车流并行动态演化的高真实度模拟和时变汽车荷载与桥梁运动状态的时时耦合,首先从宏观和微观上丰富随机车流模拟方法,宏观上沿用交通荷载调查数据中的车辆顺序、车辆基本特性等不变量,以车辆间距为服从正态分布的限幅随机变量,形成深度融合交通荷载调查数据和交通流理论的随机车流高真实度仿真方法;微观上对车辆间距随机变量确定的关键状态-阻塞状态,引入加权速度,实现阻塞密度时车流的走走停停动态描述,采用考虑驾驶人状态的概率分布方法确定车辆时距;实现多密度随机车流的高真实度仿真。其次细化刹车过程模拟,建立车流差异化刹车模型：采用顺次对比方法,筛选桥长范围最不利刹车车流;引入停车视距,考虑驾驶人反应,区分头车和跟驰车辆,精细模拟车辆刹车动态过程和刹车车流演化过程,差异化确定各车辆刹车参数;实现桥上多状态车流并行动态演化模拟。第三建立刹车力学模型,并融入至已有正常车流的车-桥耦合系统,构建可考虑刹车状态的分析系统。最后确定桥梁典型响应和分析指标,以一座大跨斜拉桥为例,对多刹车工况下的桥梁响应进行分析。结果表明：桥上刹车状况一般会产生超过正常行驶状况下的桥梁响应,最不利单车道刹车状况下的塔根弯矩甚至达到跑车工况的2.7倍,简单采用规范冲击系数方法很难实现刹车响应的包络;刹车过程中的桥梁响应最值不仅与采取刹车的车辆数目和桥上车辆保有量有关,还受刹车作用与桥梁原响应趋势的顺逆程度控制;桥梁及桥上刹停车辆的总质量和桥上正常行驶的车辆决定桥梁响应时程曲线趋势振幅;典型桥梁响应的总体趋势,与车流密度和刹车车道数相关性较小,不同时段车流会对梁端顺桥向位移和塔根弯矩产生影响。     

载重车道路多点随机激励输入的时空相关性建模研究

为解决载重车动力学分析和车辆动态设计的道路建模问题,基于对车辆道路随机不平顺性态的分析,结合其在频域内的统计表示方法———功率谱密度函数,导出了载重车六轮激励输入的关于道路高程的功率谱矩阵,进而通过白噪声滤波方程得到了与给定谱特征相对应的道路时延相关性数学模型,提出了一种新的模拟双轮辙的过程和方法。通过应用该方法可以再现随机道路高程的有代表性的时间样本,为载重车线性和非线性平顺性动力学分析、悬架系统优化及整车振动控制提供模型基础。