Optimized design for a MacPherson strut suspension with side load springs

Undesired lateral force inevitably exists in a MacPherson suspension system, which is liable to damper rod’s side wear and promotes the damper’s inner friction decreasing the ride performance from the suspension system. Substituting a new side load spring with curved centerline for the conventional coil spring has been proven able to solve these problems and Multi-body Dynamics combining with Finite Elements Analysis may be an efficient method in optimizing its design. Therefore, taking a passenger car as example, a detailed multi-body dynamics model for the suspension system is built to simulate forces exerted on the damper and the minimization of its lateral component is selected as the design target for the spring. When the structure optimization of the side load spring is performed using FEA software ANSYS, its vertical and lateral elastic characteristics, supported by test data, are analyzed. After importing FEA results back to the suspension system, the dynamics simulation can be performed to validate the optimization result.     

麦弗逊悬架侧载螺旋弹簧优化设计

以某轿车为例,建立了麦弗逊悬架多体动力学模型,将减振器侧向力仿真结果作为侧载弹簧设计目标,应用有限元方法进行结构优化设计,并进行了试验验证。研究结果表明,采用优化设计的侧载螺旋弹簧后可显著降低悬架侧载,为悬架系统及其元件的优化提供了一种参考方法。     

虚拟样机技术在三轴板簧平衡悬架结构改进中的应用

应用机械系统分析软件ADAMS建立了板簧的离散梁动力学模型,对板簧的刚度特性进行了仿真模拟;在此基础上建立了上置式板簧平衡悬架系统的垂向振动分析模型,并对车辆在极限运动状况下行驶时出现的滑板式板簧的不正常接触问题进行了仿真分析,最后提出了结构改进措施。     

客车少片钢板弹簧的异响及解决方法

钢板弹簧是悬架系统中比较传统的弹性元件。悬架系统中的异响大部分是由钢板弹簧引起的,直到今天都未完全解决。本文分析客车钢板弹簧产生异响的原因,探讨解决异响的方法。     

Robust design optimization of suspension system by using target cascading method

This study presents the robust design optimization process of suspension system for improving vehicle dynamic performance (ride comfort, handling stability). The proposed design method is so called target cascading method where the design target of the system is cascaded from a vehicle level to a suspension system level. To formalize the proposed method in the view of design process, the design problem structure of suspension system is defined as a (hierarchical) multilevel design optimization, and the design problem for each level is solved using the robust design optimization technique based on a meta-model. Then, In order to verify the proposed design concept, it designed suspension system. For the vehicle level, 44 random variables with 3% of coefficient of variance (COV) were selected and the proposed design process solved the problem by using only 88 exact analyses that included 49 analyses for the initial meta-model and 39 analyses for SAO. For the suspension level, 54 random variables with 10% of COV were selected and the optimal designs solved the problem by using only 168 exact analyses for the front suspension system. Furthermore, 73 random variables with 10% of COV were selected and optimal designs solved the problem by using only 252 exact analyses for the rear suspension system. In order to compare the vehicle dynamic performance between the optimal design model and the initial design model, the ride comfort and the handling stability was analyzed and found to be improved by 16% and by 37%, respectively. This result proves that the suggested design method of suspension system is effective and systematic.     

Sequential Approximate Optimization of MacPherson Strut Suspension for Minimizing Side Load by Using Progressive Meta-Model Method

In a MacPherson strut suspension, the side load is inevitably generated and it causes friction at the damper reducing riding comfort. In this paper, to solve this problem, progressive meta-model based sequential approximate optimization (SAO) is performed to minimize the side load. To calculate the side load, a wheel travel analysis is performed by using flexible multi-body dynamics (FMBD) model of suspension, which can consider both finite element method (FEM) and multi-body dynamics (MBD). In the optimal design process, meta-model is generated by using extracted sampling points and radial basis function (RBF) method. As a result of optimal design, spring setting positions that minimize the side load are obtained and by using optimal spring setting positions, the suspension FMBD model was constructed.     

对客车转向杆系与悬架系统运动干涉的探讨

针对客车常见的纵置钢板弹簧悬架结构,提出了一种计算转向传动杆系与悬架系统之间的运动干涉量的数学方法.     

浅谈空气悬架

作为汽车的重要组成系统,悬架在汽车的操纵稳定性与舒适性方面起着举足轻重的作用。传统的钢板弹簧与空气悬架有着怎样的区别？空气悬架的市场前景又是如何？     

Designing H∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H_∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H_∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H_∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H_∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H_∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

滑板式钢板弹簧悬架变刚度计算方法的研究

建立了重型载货汽车广泛采用的滑板式钢板弹簧悬架变接触点动力学模型，提出了一类弹性体变接触点约束问题的求解方法。对这种悬架进行了动力学仿真分析，得到了动刚度的变化特性，仿真分析结果与试验结果吻合。     

基于预紧弹簧系统的桥梁挠度冲击系数量测方法

为了提高桥梁挠度及冲击系数测试的稳定性,在传统悬锤法基础上,基于弹簧预紧效应,提出了预紧弹簧法。首先依据车-桥耦合振动理论,以简支梁桥为对象推导了车辆-桥梁-预紧弹簧耦合振动方程,进行了室内试验和系统数值验证;在此基础上分别建立了车辆-桥梁-悬锤系统和车辆-桥梁-预紧弹簧系统的有限元模型,利用数值解法分析了横向风荷载对悬锤法和预紧弹簧法测量主梁挠度及冲击系数的影响;根据建立的车辆-桥梁-预紧弹簧耦合振动系统,研究了影响该方法精度的关键性因素,并给出系统参数选型优化经验公式。最后,以一座30 m预制装配式简支箱梁桥为例,在随机车载激励下,进行支架法、悬锤法和预紧弹簧法3种方法的对比试验。研究结果表明：预紧弹簧法与传统悬锤法相比,冲击系数受风荷载影响较小;无风环境下,预紧弹簧法易受铁丝抗拉刚度、弹簧刚度和悬挂长度的影响,而与初始预紧力值无关;通过合理选用参数,预紧弹簧法能够实现主梁与系统同相位振动;工程实例表明该方法与支架法挠度冲击系数平均误差为6.1%,精度高于悬锤法测量结果,该方法也可为桥梁结构静动载大位移测试提供借鉴。     

Linear matrix inequality based control of vehicle active suspension system

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.     

Motorcycle suspension design using matrix inequalities and passivity constraints

This paper presents a design methodology for the suspension system of a novel aerodynamically efficient motorcycle. Since the machine’s layout and the rider’s seating position are unconventional, several aspects of the machine design, including the suspension, must be reviewed afresh. The design process is based on matrix inequalities that are used to optimise a road-grip objective function – others could be used equally well. The design problem is cast as the minimisation of an H ₂ cost with passivity constraints imposed on the suspension transference. The resulting bilinear matrix inequality problem is solved using a locally optimal iterative algorithm. The matrix inequality-type characterisation of positive real functions permits the optimisation of the suspension system over an entire class of passive admittances. Torsional springs, dampers and inerters are then used to construct networks corresponding to the optimal (positive real) admittances. Networks of first, second, third and fourth orders are considered, and an argument based on the compromise between complexity and improved grip is made for the most suitable suspension configuration. Finally, the effects of improved road grip on the stability of the vehicle’s lateral dynamics are analysed.     

多刚体系统动力学在转向系和悬架运动学分析中的应用

本文介绍了利用自然坐标对多刚体系统进行运动学和动力学分析的方法,并用这一方法模拟了某货车转向系运动学特性、转向轮侧倾转向特性及某轿车麦克弗森式悬架运动学特性,研究了某货车板簧悬架与转向系在直线行驶和弯道行驶时的垂直干涉与制动干涉。     

钢板弹簧悬架系统设计与优化(1)

悬架系统作为整车重要系统之一,对整车承载能力及舒适性有着重要的影响。钢板弹簧系统设计与优化,涉及板簧系统的整车布置、钢板弹簧本体结构的分析与优化、钢板弹簧材料的选择以及钢板弹簧本体设计等。     

钢板弹簧悬架系统运动分析

钢板弹簧在整车上的布置情况，不仅影响整车的平顺性，而且也影响其操纵稳定性。本文将板簧和吊耳看成一体加以考虑，分析板簧系统关键点轨迹和关键角的变化，并用最小二乘法求出关键点轨迹的曲率中心和曲率半径，并举例与“SAE圆弧”法的结果作了比较。     

影响板簧主片断裂的因素及校核方法研究

针对某款10米客车少片簧主片异常断裂故障,提出了板簧悬架力学图解分析方法、扭转角刚度计算方法和适用各种工况的主片应力计算校核方法.相比常规校核方法,增加吊耳摆角、板簧弧高、板簧座位置、板簧扭转角刚度、离心力等因素的影响分析,从而了解主片断裂的机理,完善校核方法.     

Designing H ∞/GH 2 static-output feedback controller for vehicle suspensions using linear matrix inequalities and genetic algorithms

This paper presents an approach to design the H _∞/GH ₂ static-output feedback controller for vehicle suspensions by using linear matrix inequalities (LMIs) and genetic algorithms (GAs). Three main performance requirements for an advanced vehicle suspension are considered in this paper. Among these requirements, the ride-comfort performance is optimized by minimizing the H _∞ norm of the transfer function from the road disturbance to the sprung mass acceleration, while the road-holding performance and the suspension deflection limitation are guaranteed by constraining the generalized H ₂ (GH ₂) norms of the transfer functions from the road disturbance to the dynamic tyre load and the suspension deflection to be less than their hard limits, respectively. At the same time, the controller saturation problem is considered by constraining its peak response output to be less than a given limit using the GH ₂ norm as well. A four-degree-of-freedom half-car model with active suspension system is applied in this paper. Several kinds of H _∞/GH ₂ static-output feedback controllers, which use the available sprung mass velocities or the suspension deflections as feedback signals, are obtained by using the GAs to search for the possible control gain matrices and then resolving the LMIs together with the minimization optimization problem. These designed H _∞/GH ₂ static-output feedback controllers are validated by numerical simulations on both the bump and the random road responses which show that the designed H _∞/GH ₂ static-output feedback controllers can achieve similar or even better active suspension performances compared with the state-feedback control case in spite of their simplicities.     

Pole location control design of an active suspension system with uncertain parameters

This paper addresses the problem of robust control design for an active suspension quarter-car model by means of state feedback gains. Specifically, the design of controllers that assure robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are presented as linear matrix inequalities: (i) the quadratic stability based gain; (ii) a recently published condition that uses an augmented space and has been here modified to cope with the pole location specification; (iii) a condition that uses an extended number of equations and yields a parameter-dependent state feedback gain. Unlike other parameter-dependent strategies, neither extensive gridding nor approximations are needed. In the suspension model, the sprung mass, the damper coefficient and the spring constant are considered as uncertain parameters belonging to a known interval (polytope type uncertainty). It is shown that the parameter-dependent gain proposed allows one to impose the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.     

Pole location control design of an active suspension system with uncertain parameters

This paper addresses the problem of robust control design for an active suspension quarter-car model by means of state feedback gains. Specifically, the design of controllers that assure robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are presented as linear matrix inequalities: (i) the quadratic stability based gain; (ii) a recently published condition that uses an augmented space and has been here modified to cope with the pole location specification; (iii) a condition that uses an extended number of equations and yields a parameter-dependent state feedback gain. Unlike other parameter-dependent strategies, neither extensive gridding nor approximations are needed. In the suspension model, the sprung mass, the damper coefficient and the spring constant are considered as uncertain parameters belonging to a known interval (polytope type uncertainty). It is shown that the parameter-dependent gain proposed allows one to impose the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.