自激型汽车摆振动态过程的建模和仿真研究
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摘要
众所周知，汽车摆振是某些车辆在一定条件下转向轮绕主销的持续摆动现象。摆振的影响因素众多，机理复杂，很难在车辆设计开发初期对其进行预测和控制，是底盘设计中很难解决的问题之一。
国内外把摆振分为强迫型摆振和自激型摆振，强迫型摆振主要研究外界周期性激励力引起的共振现象，自激型摆振认为是系统中非线性环节所引起的振动现象，如轮胎侧偏非线性、轮胎松弛效应、转向系干摩擦、间隙等。自激型摆振的研究，通常是建立简化的摆振数学模型，计算系统的固有振动模态，或者是利用稳定性判据进行稳定性分析。摆振动态过程的仿真是研究自激型摆振的一个重要途径，可以用于汽车设计开发初期对自激型摆振进行预测和控制，目前国际上有关自激型摆振动态过程仿真的研究比较少。现有的汽车动力学模型缺少影响自激型摆振的关键环节，导致模型不能对自激型摆振的动态过程进行仿真。
基于上述现状，本文在对自激型摆振关键环节研究的基础上，试图应用动态仿真的方法探索自激型摆振的仿真，重点研究了自激型摆振动态过程建模的关键问题、车辆仿真系统的平衡方法、自激型摆振动态过程的仿真及关键影响因素的分析。
第一，自激型摆振动态过程建模的关键问题研究。车辆系统中的一些关键环节对自激型摆振有重要影响，为了使模型自身具备仿真自激型摆振的能力，需要在模型中对这些关键环节进行准确建模。（1）转向系统左右车轮的协调能力对摆振有很大影响，本文建立起转向系统完备动力学模型，左右车轮、转向节、转向横拉杆、齿条组成了一个完整的动力学系统，转向系统阿克曼机构实现力输入，建立起左右车轮间的力学联系，实现了左右车轮的自适应协调；（2）转向系统静摩擦对摆振有一定的抑制能力，干摩擦的静动摩擦状态切换会引起系统特征值和固有频率的变化，借鉴D.Karnopp的摩擦模型，建立起静、动摩擦分离的转向主销干摩擦模型，准确描述了转向系统的静摩擦特性，实现了转向死区的模拟，使转向系模型具备一定的抵抗外界干扰的能力；（3）胎体的弹性特性对摆振有重要影响，本文建立了考虑胎体弹性的车轮模型，将车轮简化为轮辋和胎体，引入胎体弹簧阻尼和胎体动力学，准确描述轮胎的弹性特性，实现了轮心处的力向转向系统的动态输入，准确计算轮胎接地印迹处运动状态；（4）为使模型能在非水平路面仿真，研究了非水平路面的探测算法，建立了适用于非水平路面的探测模型，可以实时探测非水平路面轮胎接地点处的高程和法向量，使模型适用于非水平路面的仿真。
第二，车辆仿真系统的平衡方法研究。初始状态是自激型摆振激发的必要前提，为了确定出正确的车辆模型初始状态，对车辆仿真系统的平衡方法进行了研究，提出了一种适用于全工况的平衡方法。（1）传统平衡方法，仅适用于车轮接地工况，而不能解决车轮离地的特殊工况，本文基于powell方法建立了车轮离地优化算法，把车体垂向位移自由度作为优化目标，实现了车轮离地工况的平衡问题；（2）针对传统非线性迭代算法—牛顿拉斐逊迭代法必须要计算雅克比矩阵解析表达式的特点，本文建立拟牛顿无导数迭代算法，利用替代的方式来求解系统的雅克比矩阵，从而使迭代算法不受雅克比矩阵的解析表达式很难获取的限制；（3）平衡方法把待求变量分为边界条件和初始状态，在外循环用优化方法求边界条件，在内循环用非线性迭代算法求初始状态。
第三，自激型摆振动态过程的仿真研究。建立了整车动力学模型，对模型稳态性能的正确性进行了试验验证。通过典型摆振工况的仿真，验证了模型具备仿真自激型摆振动态过程的能力；分析了一些关键环节的建模对自激型摆振动态过程仿真的重要性；对影响自激型摆振的关键因素进行了仿真分析，包括：外界激励大小、胎体弹性、转向系统惯量、主销后倾角、车速等，得出以下结论：（1）外界激励必须足够大，自激型摆振才可能被激发；（2）胎体的弹性越小，越容易产生自激型摆振；（3）转向系统的惯量越大，越容易产生自激型摆振；（4）转向系统的刚度越大，越不容易产生自激型摆振；（5）主销后倾角越大，越容易产生自激型摆振；（6）自激型摆振有一定的速度区间，当小于或大于这个速度区间时，摆振将不会发生。所得仿真结论与工程经验相吻合，进一步验证了模型能够较为准确的仿真自激型摆振的动态过程。
It is well known that shimmy is the continued swing of front wheels around thekingpin and occurs when certain vehicles run in certain conditions. Shimmy is influenced bymany factors, and its mechanism is very complex. In the early stages of design anddevelopment it is difficult to predict and control shimmy. Shimmy is one of difficultproblems about chassis design.
Shimmy is divided by domestic and foreign experts into compulsive shimmy andself-excited type. For compulsive shimmy, the main research is about the resonancephenomenon caused by external periodic excitation forces. For the self-excited type shimmy,the limit cycle oscillation phenomenon is caused by the nonlinear components in the system,such as tire cornering nonlinear features, tire relaxation effects, steering stem friction,clearance, etc. By shimmy study research found that self-excited type shimmy simplifiedshimmy mathematical model for eigenvalue analysis to identify the natural vibration modesof the system or the stability criterion for stable analysis and the research on self-excitedtype to shimmy dynamic process simulation is relatively small. The existing vehicledynamics models lack the impact of self-excited type shimmy key link, the model cannotsimulate the dynamic process of self-excited type shimmy.
Based on the above-mentioned status quo, on the basis of the key aspects of research onself-excited type shimmy, try to apply dynamic simulation method to explore the self-excitedtype shimmy simulation, focusing on the key issues of self-excited type to shimmy dynamicprocess modeling, the balance of the dynamics simulation system, self-excited shimmy dynamic process simulation and the key factors.
First, the key issues of self-excited type shimmy dynamic process modeling. Some ofthe key aspects of the vehicle systems have important implications for self-excited typeshimmy, in order to make the model have the ability to simulation of self-excited typeshimmy, needing accurate modeling of these key links in the model.(1) The coordinationability of left and right steering wheels has a great impact on shimmy. This paper hasestablished a complete dynamic model of the steering system. Left and right wheels, axles,steering tie rod, rack form a complete dynamical systems. Ackerman agencies achieve theforce input to establish about the mechanical contact between the wheels, adaptivecoordination of left and right wheels.(2) Static friction in steering system has the ability toinhibit shimmy. Dry friction static and dynamic friction state switching can cause changes inthe system eigenvalues and the natural frequency of system. Drawing D.Karnopp the frictionmodel to establish static and dynamic friction separation of steering kingpin dry frictionmodel that accurately describes the static friction characteristics of the steering system andachieve the simulation of the dead zone, so that the steering system model to have a certainability to resist outside interference.(3) The elastic characteristics of the carcass has animportant impact on shimmy. This paper established a wheel model respecting carcassflexibility. Simplifying the wheel rim and carcass, the introduction of the carcass springdamping and carcass dynamics, an accurate description of the elastic characteristics of thetire, achieve the force at the wheel center input to the steering system dynamics andaccurately calculate the tire ground imprinted at the state of motion.(4) In order to modelsimulation in non-level road, non-level road detection algorithm, this paper establishesdetection model for non-level road, real-time detection of the elevation and the normalvector of the point of contact of tire and non-level road, make the model applicable to thesimulation of non-level road.
Second, research the equilibrium method for dynamic simulation system. The initialstate is a necessary prerequisite to stimulate self-excited type shimmy. In order to determinethe correct vehicle model the initial state, the balance of the dynamics simulation system were studied and proposed a balanced approach in full working condition.(1) Traditionalstatic balance method applies only to the wheel ground contact, while the special conditionsthat the wheels are off the ground cannot be solved. On base of the Powell method establishoptimization algorithm about wheels off the ground conditions, body vertical displacementdegrees of freedom are as the optimization objective to achieve the balance of the wheelfrom the ground conditions.(2) Owing to the Jacobian matrix analytic expression must becalculated in the traditional non-linear iterative algorithm-Newton Raphson iterativemethod. This paper established a quasi-Newton non-derivative iteration method, the use ofalternative means to solve the system Jacobian matrix, so that the iterative algorithm is notdifficult to obtain the limit of the analytical expressions of the Jacobian matrix.(3) Balancedapproach divided the unknown variables into the boundary conditions and initial state, theouter loop optimization method for solving the boundary conditions, the Inner loop with anonlinear iterative algorithm for the initial state.
Third, the study of dynamic process simulation for self-excited shimmy. Establishvehicle dynamics model, experimental verification of the correctness of the modelsteady-state performance. Through the simulation of typical operating conditions, verify themodel with the simulation of self-excited type shimmy dynamic process capacity, analyzethe importance of some key aspects of modeling self-excited type shimmy through dynamicprocess simulation, conduct simulation and analysis about the key factors of self-excitedtype shimmy, including: the size of outside incentives, carcass elasticity, inertia of thesteering system, caster angle, vehicle speed, the following conclusions are summed up:(1)Outside incentives must be large enough, the self-excited type shimmy can be excited.(2)The smaller of the elasticity of the carcass is, the more prone to self-excited type shimmy.(3)The greater the inertia of the steering system is, the more prone to self-excited type shimmy.(4) The greater the Kingpin inclination is, the more prone to self-excited type shimmy.(5)Self-excited type shimmy has certain speed range, shimmy will not occur when less than thisspeed range. The obtained simulation conclusions and engineering experience is consistent,further validate the model more accurate simulation of self-excited type shimmy dynamic process.
国内外把摆振分为强迫型摆振和自激型摆振，强迫型摆振主要研究外界周期性激励力引起的共振现象，自激型摆振认为是系统中非线性环节所引起的振动现象，如轮胎侧偏非线性、轮胎松弛效应、转向系干摩擦、间隙等。自激型摆振的研究，通常是建立简化的摆振数学模型，计算系统的固有振动模态，或者是利用稳定性判据进行稳定性分析。摆振动态过程的仿真是研究自激型摆振的一个重要途径，可以用于汽车设计开发初期对自激型摆振进行预测和控制，目前国际上有关自激型摆振动态过程仿真的研究比较少。现有的汽车动力学模型缺少影响自激型摆振的关键环节，导致模型不能对自激型摆振的动态过程进行仿真。
基于上述现状，本文在对自激型摆振关键环节研究的基础上，试图应用动态仿真的方法探索自激型摆振的仿真，重点研究了自激型摆振动态过程建模的关键问题、车辆仿真系统的平衡方法、自激型摆振动态过程的仿真及关键影响因素的分析。
第一，自激型摆振动态过程建模的关键问题研究。车辆系统中的一些关键环节对自激型摆振有重要影响，为了使模型自身具备仿真自激型摆振的能力，需要在模型中对这些关键环节进行准确建模。（1）转向系统左右车轮的协调能力对摆振有很大影响，本文建立起转向系统完备动力学模型，左右车轮、转向节、转向横拉杆、齿条组成了一个完整的动力学系统，转向系统阿克曼机构实现力输入，建立起左右车轮间的力学联系，实现了左右车轮的自适应协调；（2）转向系统静摩擦对摆振有一定的抑制能力，干摩擦的静动摩擦状态切换会引起系统特征值和固有频率的变化，借鉴D.Karnopp的摩擦模型，建立起静、动摩擦分离的转向主销干摩擦模型，准确描述了转向系统的静摩擦特性，实现了转向死区的模拟，使转向系模型具备一定的抵抗外界干扰的能力；（3）胎体的弹性特性对摆振有重要影响，本文建立了考虑胎体弹性的车轮模型，将车轮简化为轮辋和胎体，引入胎体弹簧阻尼和胎体动力学，准确描述轮胎的弹性特性，实现了轮心处的力向转向系统的动态输入，准确计算轮胎接地印迹处运动状态；（4）为使模型能在非水平路面仿真，研究了非水平路面的探测算法，建立了适用于非水平路面的探测模型，可以实时探测非水平路面轮胎接地点处的高程和法向量，使模型适用于非水平路面的仿真。
第二，车辆仿真系统的平衡方法研究。初始状态是自激型摆振激发的必要前提，为了确定出正确的车辆模型初始状态，对车辆仿真系统的平衡方法进行了研究，提出了一种适用于全工况的平衡方法。（1）传统平衡方法，仅适用于车轮接地工况，而不能解决车轮离地的特殊工况，本文基于powell方法建立了车轮离地优化算法，把车体垂向位移自由度作为优化目标，实现了车轮离地工况的平衡问题；（2）针对传统非线性迭代算法—牛顿拉斐逊迭代法必须要计算雅克比矩阵解析表达式的特点，本文建立拟牛顿无导数迭代算法，利用替代的方式来求解系统的雅克比矩阵，从而使迭代算法不受雅克比矩阵的解析表达式很难获取的限制；（3）平衡方法把待求变量分为边界条件和初始状态，在外循环用优化方法求边界条件，在内循环用非线性迭代算法求初始状态。
第三，自激型摆振动态过程的仿真研究。建立了整车动力学模型，对模型稳态性能的正确性进行了试验验证。通过典型摆振工况的仿真，验证了模型具备仿真自激型摆振动态过程的能力；分析了一些关键环节的建模对自激型摆振动态过程仿真的重要性；对影响自激型摆振的关键因素进行了仿真分析，包括：外界激励大小、胎体弹性、转向系统惯量、主销后倾角、车速等，得出以下结论：（1）外界激励必须足够大，自激型摆振才可能被激发；（2）胎体的弹性越小，越容易产生自激型摆振；（3）转向系统的惯量越大，越容易产生自激型摆振；（4）转向系统的刚度越大，越不容易产生自激型摆振；（5）主销后倾角越大，越容易产生自激型摆振；（6）自激型摆振有一定的速度区间，当小于或大于这个速度区间时，摆振将不会发生。所得仿真结论与工程经验相吻合，进一步验证了模型能够较为准确的仿真自激型摆振的动态过程。
It is well known that shimmy is the continued swing of front wheels around thekingpin and occurs when certain vehicles run in certain conditions. Shimmy is influenced bymany factors, and its mechanism is very complex. In the early stages of design anddevelopment it is difficult to predict and control shimmy. Shimmy is one of difficultproblems about chassis design.
Shimmy is divided by domestic and foreign experts into compulsive shimmy andself-excited type. For compulsive shimmy, the main research is about the resonancephenomenon caused by external periodic excitation forces. For the self-excited type shimmy,the limit cycle oscillation phenomenon is caused by the nonlinear components in the system,such as tire cornering nonlinear features, tire relaxation effects, steering stem friction,clearance, etc. By shimmy study research found that self-excited type shimmy simplifiedshimmy mathematical model for eigenvalue analysis to identify the natural vibration modesof the system or the stability criterion for stable analysis and the research on self-excitedtype to shimmy dynamic process simulation is relatively small. The existing vehicledynamics models lack the impact of self-excited type shimmy key link, the model cannotsimulate the dynamic process of self-excited type shimmy.
Based on the above-mentioned status quo, on the basis of the key aspects of research onself-excited type shimmy, try to apply dynamic simulation method to explore the self-excitedtype shimmy simulation, focusing on the key issues of self-excited type to shimmy dynamicprocess modeling, the balance of the dynamics simulation system, self-excited shimmy dynamic process simulation and the key factors.
First, the key issues of self-excited type shimmy dynamic process modeling. Some ofthe key aspects of the vehicle systems have important implications for self-excited typeshimmy, in order to make the model have the ability to simulation of self-excited typeshimmy, needing accurate modeling of these key links in the model.(1) The coordinationability of left and right steering wheels has a great impact on shimmy. This paper hasestablished a complete dynamic model of the steering system. Left and right wheels, axles,steering tie rod, rack form a complete dynamical systems. Ackerman agencies achieve theforce input to establish about the mechanical contact between the wheels, adaptivecoordination of left and right wheels.(2) Static friction in steering system has the ability toinhibit shimmy. Dry friction static and dynamic friction state switching can cause changes inthe system eigenvalues and the natural frequency of system. Drawing D.Karnopp the frictionmodel to establish static and dynamic friction separation of steering kingpin dry frictionmodel that accurately describes the static friction characteristics of the steering system andachieve the simulation of the dead zone, so that the steering system model to have a certainability to resist outside interference.(3) The elastic characteristics of the carcass has animportant impact on shimmy. This paper established a wheel model respecting carcassflexibility. Simplifying the wheel rim and carcass, the introduction of the carcass springdamping and carcass dynamics, an accurate description of the elastic characteristics of thetire, achieve the force at the wheel center input to the steering system dynamics andaccurately calculate the tire ground imprinted at the state of motion.(4) In order to modelsimulation in non-level road, non-level road detection algorithm, this paper establishesdetection model for non-level road, real-time detection of the elevation and the normalvector of the point of contact of tire and non-level road, make the model applicable to thesimulation of non-level road.
Second, research the equilibrium method for dynamic simulation system. The initialstate is a necessary prerequisite to stimulate self-excited type shimmy. In order to determinethe correct vehicle model the initial state, the balance of the dynamics simulation system were studied and proposed a balanced approach in full working condition.(1) Traditionalstatic balance method applies only to the wheel ground contact, while the special conditionsthat the wheels are off the ground cannot be solved. On base of the Powell method establishoptimization algorithm about wheels off the ground conditions, body vertical displacementdegrees of freedom are as the optimization objective to achieve the balance of the wheelfrom the ground conditions.(2) Owing to the Jacobian matrix analytic expression must becalculated in the traditional non-linear iterative algorithm-Newton Raphson iterativemethod. This paper established a quasi-Newton non-derivative iteration method, the use ofalternative means to solve the system Jacobian matrix, so that the iterative algorithm is notdifficult to obtain the limit of the analytical expressions of the Jacobian matrix.(3) Balancedapproach divided the unknown variables into the boundary conditions and initial state, theouter loop optimization method for solving the boundary conditions, the Inner loop with anonlinear iterative algorithm for the initial state.
Third, the study of dynamic process simulation for self-excited shimmy. Establishvehicle dynamics model, experimental verification of the correctness of the modelsteady-state performance. Through the simulation of typical operating conditions, verify themodel with the simulation of self-excited type shimmy dynamic process capacity, analyzethe importance of some key aspects of modeling self-excited type shimmy through dynamicprocess simulation, conduct simulation and analysis about the key factors of self-excitedtype shimmy, including: the size of outside incentives, carcass elasticity, inertia of thesteering system, caster angle, vehicle speed, the following conclusions are summed up:(1)Outside incentives must be large enough, the self-excited type shimmy can be excited.(2)The smaller of the elasticity of the carcass is, the more prone to self-excited type shimmy.(3)The greater the inertia of the steering system is, the more prone to self-excited type shimmy.(4) The greater the Kingpin inclination is, the more prone to self-excited type shimmy.(5)Self-excited type shimmy has certain speed range, shimmy will not occur when less than thisspeed range. The obtained simulation conclusions and engineering experience is consistent,further validate the model more accurate simulation of self-excited type shimmy dynamic process.
引文
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