非水平路面动态车轮模型建模研究
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摘要
轮胎作为连接车身与路面的惟一单元，除空气作用力外，车辆受到的几乎所有外力都来自于轮胎和路面的接触力。对车辆动力学模型进行精确建模的基础首先是要对轮胎和路面的接触力进行精确建模。传统车轮模型在计算轮胎力时，未考虑轮辋和胎体的弹性连接，从而不能动态计算轮胎接地处的滑移情况，无法反映轮胎胎体弹性对力的传递的影响。另外，为研究非水平路面上的车辆动力学特性而进行车辆模型仿真的前提，是要对非水平路面进行数学表达并建立轮胎接地点位置信息的探测方法。因此，本文以动态计算轮胎的滑移率为出发点，建立了考虑胎体动力学的动态车轮模型，同时建立了非水平路面模型和路面接触探测算法以满足非水平路面车辆动力学模型仿真对路面信息输入的要求。本文的主要工作和相关结论如下：
1.以动态计算轮胎接地点的滑移率为出发点，建立了动态车轮模型。模型通过考虑胎体和轮辋之间的弹性连接并建立胎体六自由度方向的动力学，动态地计算出轮胎接地点的滑移情况，描述了轮胎非稳态工况下的力学特性。具体的建模过程分为两部分：刚性环动力学部分和轮胎静力学部分。刚性环动力学部分将轮胎胎体简化为刚性环模型、将胎侧和充气弹性简化为连接刚性环和轮辋的六向弹簧阻尼器。通过建立刚性环完备六自由度的动力学，动态地计算出了轮胎接地印迹的滑移情况。通过建立六向弹簧阻尼器模型，描述了胎体弹性的滤波效果。轮胎静力学部分建立了轮胎与路面之间的接触模型和摩擦模型，以计算轮胎和地面的接触力。为了仿真车辆低速区行驶和“Stand Still”等工况，摩擦模型建立了动静摩擦分离的算法，建立了对轮胎动、静摩擦状态的判定规则以及动、静摩擦力的求解方法。其中在求解动摩擦力时，建立了稳态插值轮胎模型。
动态车轮模型的参数主要是轮胎胎体的六向刚度。根据轮胎印迹中心的变形及轮胎受力情况，在动态车轮模型的建模假设基础上，推导出模型中轮胎胎体六向刚度的解算公式，并应用悬架K&C试验数据计算出结果。
2.基于“新一代车辆动力学仿真平台”对路面进行表达的要求，建立了非水平路面模型。通过定义了描述路面的“S‐L”坐标系，并建立基于“S‐L”坐标系的存储路面信息的三表结构，将路面离散点划分为三角网格，通过描述每一个三角形平面的位置信息，建立了对道路表面进行连续描述的方法，并研究了获取轮胎接地点位置信息的探测算法，从而建立了非水平路面模型。
3.论文最后对所建立的非水平路面动态车轮模型进行了仿真验证，分别验证了平路面以及非水平路面上动态车轮模型的仿真结果。结果显示：非水平路面动态车轮模型不仅计算效率高，可用于车辆动力学实时仿真，而且对稳态轮胎力学特性的描述精度较高，对动态轮胎力学特性的描述效果较好，对路面的表达也具有较高的精度。
通过本文的研究，完成了对车辆动力学仿真系统中车轮‐地面系统的精确建模。动态车轮模型针对以前的不足，更为准确地计算出了轮胎接地处的滑移情况，描述了非稳态轮胎力学特性，可用于低速行驶区、“Stand Still”等工况的仿真，模型计算精度高，参数少且物理意义明确、易于获取，计算速度快，可应用于车辆动力学实时仿真，提高整车模型的仿真精度。非水平路面模型对地面进行了精确的数学表达，且计算速度快，应用于非水平路面车辆动力学模型实时仿真，提供了路面信息输入。
Tires as the only unit to connect the body with the road, in addition to the air force,almost all the external forces acted on vehicles are from the tire and road contact force. Thefirst is based on accurate modeling of the vehicle dynamics model for accurate modeling ofthe contact force to the tires and the road. Model of the traditional wheel tire forcecalculation does not consider the rim and the matrix of elastic connection, and thus cannot bedynamic calculation of the tire ground at the slip, and can not reflect the flexibility of the tirecasing on the power transfer.
In addition, the premise of research on non-level road vehicle dynamics and the vehiclemodel simulation is a mathematical expression to non-level road and the establishment of thedetection method of the tire ground point location information. Therefore, based on thedynamic calculation of the tire slip rate, build a dynamics model considering the dynamicwheel of the matrix, while creating a model of non-level road and the road surface contactdetection algorithm in order to meet the non-level road vehicle dynamics model simulationon the road information input requirements. The main work and conclusions are as follows:
1. The model of the dynamic wheel based on a ground point to the dynamic calculationof the tire slip rate is established. The model describes the mechanical properties of tirenon-steady state conditions by taking into account the flexibility to connect and establish thedynamics of the six degrees of freedom of the matrix, dynamically calculating the slip of thetire ground between the matrix and rims. The modeling process is divided into two parts: thesystem of rigid ring dynamics and the system of the tire statics. Rigid ring dynamics systemsimplifies the tire carcass as a rigid ring model, and the sidewall and inflatable elastic as thesix spring-dampers which connects the rigid ring and the rim. Through the establishment ofthe dynamics of a rigid ring complete six degrees of freedom; dynamically calculate the slipof the tire ground imprinted is acquired. Through the establishment of six spring-dampers model, describing the filtering effect of the flexibility of the carcass is obtained. Through theestablishment of contact between the tire and the road model and friction model of tirestatics system, calculating the tire and the ground contact force is achieved.
In order to simulate the driving of the low velocity zone and "Stand Still" and otheroperating conditions, the friction model establishes static and dynamic friction separationalgorithm, dividing friction force into friction static friction and dynamic friction accordingto certain rules, as well as adopting different methods of calculation. Among them, the staticfriction force is calculated according to external power (six spring-damping force); whiledynamic friction is obtained by using the steady-state tire model. To calculate the dynamicfriction, the steady-state interpolation tire model is created. The main parameters of thedynamic wheel model are the six stiffness of the tire carcass. This paper presents the solutionmethod of the matrix stiffness, and applies the suspension K&C test data to calculate.
2. Based on the requirements of describing for a new generation of vehicle dynamicssimulation platform on the road, a non-level road model is established. Based on the S-Lcoordinate system and table structure of stored road information, road model is divided intopavement discrete points mesh, the description of the road surface is established, and accessto the tire ground detection algorithm is studied.
3. Finally, the non-level road dynamic wheel model is simulated to verify the results ofthe dynamic wheel model on the flat road surface as well as on a non-level road. The resultsshowed that: the non-level road dynamic wheel model is computationally efficient and canbe used for real-time simulation of vehicle dynamics, and of high precision in describing thesteady-state mechanical properties of the tire, and can better describe the mechanicalproperties of the dynamic tire, and has a higher accuracy on the road surface expression aswell.
Through this research, the model of the tire-ground system for the pre-developmentphase is established. The model is of high accuracy, with few parameters while each with aclear physical meaning, easily obtained, and of high computational efficiency. Therefore, itcan be applied to real-time simulation of vehicle dynamics to improve vehicle modelsimulation accuracy.
1.以动态计算轮胎接地点的滑移率为出发点，建立了动态车轮模型。模型通过考虑胎体和轮辋之间的弹性连接并建立胎体六自由度方向的动力学，动态地计算出轮胎接地点的滑移情况，描述了轮胎非稳态工况下的力学特性。具体的建模过程分为两部分：刚性环动力学部分和轮胎静力学部分。刚性环动力学部分将轮胎胎体简化为刚性环模型、将胎侧和充气弹性简化为连接刚性环和轮辋的六向弹簧阻尼器。通过建立刚性环完备六自由度的动力学，动态地计算出了轮胎接地印迹的滑移情况。通过建立六向弹簧阻尼器模型，描述了胎体弹性的滤波效果。轮胎静力学部分建立了轮胎与路面之间的接触模型和摩擦模型，以计算轮胎和地面的接触力。为了仿真车辆低速区行驶和“Stand Still”等工况，摩擦模型建立了动静摩擦分离的算法，建立了对轮胎动、静摩擦状态的判定规则以及动、静摩擦力的求解方法。其中在求解动摩擦力时，建立了稳态插值轮胎模型。
动态车轮模型的参数主要是轮胎胎体的六向刚度。根据轮胎印迹中心的变形及轮胎受力情况，在动态车轮模型的建模假设基础上，推导出模型中轮胎胎体六向刚度的解算公式，并应用悬架K&C试验数据计算出结果。
2.基于“新一代车辆动力学仿真平台”对路面进行表达的要求，建立了非水平路面模型。通过定义了描述路面的“S‐L”坐标系，并建立基于“S‐L”坐标系的存储路面信息的三表结构，将路面离散点划分为三角网格，通过描述每一个三角形平面的位置信息，建立了对道路表面进行连续描述的方法，并研究了获取轮胎接地点位置信息的探测算法，从而建立了非水平路面模型。
3.论文最后对所建立的非水平路面动态车轮模型进行了仿真验证，分别验证了平路面以及非水平路面上动态车轮模型的仿真结果。结果显示：非水平路面动态车轮模型不仅计算效率高，可用于车辆动力学实时仿真，而且对稳态轮胎力学特性的描述精度较高，对动态轮胎力学特性的描述效果较好，对路面的表达也具有较高的精度。
通过本文的研究，完成了对车辆动力学仿真系统中车轮‐地面系统的精确建模。动态车轮模型针对以前的不足，更为准确地计算出了轮胎接地处的滑移情况，描述了非稳态轮胎力学特性，可用于低速行驶区、“Stand Still”等工况的仿真，模型计算精度高，参数少且物理意义明确、易于获取，计算速度快，可应用于车辆动力学实时仿真，提高整车模型的仿真精度。非水平路面模型对地面进行了精确的数学表达，且计算速度快，应用于非水平路面车辆动力学模型实时仿真，提供了路面信息输入。
Tires as the only unit to connect the body with the road, in addition to the air force,almost all the external forces acted on vehicles are from the tire and road contact force. Thefirst is based on accurate modeling of the vehicle dynamics model for accurate modeling ofthe contact force to the tires and the road. Model of the traditional wheel tire forcecalculation does not consider the rim and the matrix of elastic connection, and thus cannot bedynamic calculation of the tire ground at the slip, and can not reflect the flexibility of the tirecasing on the power transfer.
In addition, the premise of research on non-level road vehicle dynamics and the vehiclemodel simulation is a mathematical expression to non-level road and the establishment of thedetection method of the tire ground point location information. Therefore, based on thedynamic calculation of the tire slip rate, build a dynamics model considering the dynamicwheel of the matrix, while creating a model of non-level road and the road surface contactdetection algorithm in order to meet the non-level road vehicle dynamics model simulationon the road information input requirements. The main work and conclusions are as follows:
1. The model of the dynamic wheel based on a ground point to the dynamic calculationof the tire slip rate is established. The model describes the mechanical properties of tirenon-steady state conditions by taking into account the flexibility to connect and establish thedynamics of the six degrees of freedom of the matrix, dynamically calculating the slip of thetire ground between the matrix and rims. The modeling process is divided into two parts: thesystem of rigid ring dynamics and the system of the tire statics. Rigid ring dynamics systemsimplifies the tire carcass as a rigid ring model, and the sidewall and inflatable elastic as thesix spring-dampers which connects the rigid ring and the rim. Through the establishment ofthe dynamics of a rigid ring complete six degrees of freedom; dynamically calculate the slipof the tire ground imprinted is acquired. Through the establishment of six spring-dampers model, describing the filtering effect of the flexibility of the carcass is obtained. Through theestablishment of contact between the tire and the road model and friction model of tirestatics system, calculating the tire and the ground contact force is achieved.
In order to simulate the driving of the low velocity zone and "Stand Still" and otheroperating conditions, the friction model establishes static and dynamic friction separationalgorithm, dividing friction force into friction static friction and dynamic friction accordingto certain rules, as well as adopting different methods of calculation. Among them, the staticfriction force is calculated according to external power (six spring-damping force); whiledynamic friction is obtained by using the steady-state tire model. To calculate the dynamicfriction, the steady-state interpolation tire model is created. The main parameters of thedynamic wheel model are the six stiffness of the tire carcass. This paper presents the solutionmethod of the matrix stiffness, and applies the suspension K&C test data to calculate.
2. Based on the requirements of describing for a new generation of vehicle dynamicssimulation platform on the road, a non-level road model is established. Based on the S-Lcoordinate system and table structure of stored road information, road model is divided intopavement discrete points mesh, the description of the road surface is established, and accessto the tire ground detection algorithm is studied.
3. Finally, the non-level road dynamic wheel model is simulated to verify the results ofthe dynamic wheel model on the flat road surface as well as on a non-level road. The resultsshowed that: the non-level road dynamic wheel model is computationally efficient and canbe used for real-time simulation of vehicle dynamics, and of high precision in describing thesteady-state mechanical properties of the tire, and can better describe the mechanicalproperties of the dynamic tire, and has a higher accuracy on the road surface expression aswell.
Through this research, the model of the tire-ground system for the pre-developmentphase is established. The model is of high accuracy, with few parameters while each with aclear physical meaning, easily obtained, and of high computational efficiency. Therefore, itcan be applied to real-time simulation of vehicle dynamics to improve vehicle modelsimulation accuracy.
引文
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[3] Bradley J and Allen R F. The behavior of rubber-tyred wheels[J]. AutomotiveEngineer,1931,21.
[4]沈浩.轮胎振动载荷模型建立与仿真前景[D].上海：同济大学，2006.
[5] Fiala E. Seitenkr fte am rollenden luftreifen[J]. Zeitcrift der VDI,1954,96(973):79.
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