汽车轮胎力学模型研究
摘要
轮胎是汽车系统最具有代表性的非线性部件,其行为十分复杂。作为汽车与路面的支承和传递单元,它的力学特性直接影响汽车的运动性能。汽车操纵稳定性的计算精度很大程度上取决于轮胎力数学模型的精度。多年来人们进行了广泛的研究,建立了许多轮胎模型,每个都有其特殊的作用。这些模型主要用于汽车的动力学分析,但它们不可能包含轮胎的全部非线性因素,这无疑影响到研究精度。
人工神经网络是最近发展起来的十分热门的交叉学科,其本质上是一种接近人的认识过程的计算模型。神经网络系统是一个高度复杂的非线性动力学系统。它由大量的神经元节点组成,尽管每个神经元的结构相对简单和功能有限,但由大量神经元按一定的方式连接成的网络集体工作,按一定的规则来调整神经元间的连接强度,能使系统具有十分强大的功能。这种模型有高度的容错性、联想性和自组织学习等优点,以及可逼近任一非线性函数的能力,对非线性系统具有较强的映射能力。
轮胎力学特性的精确描述是研究汽车的基础,但用传统的数学方法来解决非线性问题较为困难,因而人们开始研究将神经网络理论应用至汽车动力特性的建模及自动控制等方面。本课题主要用BP神经网络对汽车轮胎的力学特性进行建模分析。本课题在第二章中,利用“魔术公式”建立汽车轮胎纯工况力学模型,并将其模型输出值与试验实测值进行比较,模型误差较大。第四章中,利用MATLAB软件中的神经网络工具箱提供的图形用户界面(GUI),首先建立纯工况轮胎力学神经网络模型,选择合适的相关参数对其进行训练,并将训练好后的模型预测值与试验实测值进行比较,模型误差较“魔术公式”模型误差相比减小很多;之后,建立联合工况下轮胎力学神经网络模型,并将训练好后的模型预测值与试验实测值进行比较,误差控制在工程允许范围内,网络模型预测精度高。从而验证这种建模方法的实用性。
The tire is the most representative non-linear part of the automobile system, which behavior is very complicated. As a supporting of automobile and road surface and transmission unit, its dynamics characteristic influences the movement performance of the automobile directly. It depends on the precision of the tire dynamics model to a great extent that the automobile handles the calculation precision of stability. People have carried on extensive research for many years, and have set up a lot of tire models, each one has its special function. Dynamics that these models are used mainly in the automobile is analyzed, but they can' t include all non-linear factors of the tire, which influences precision of studying undoubtedly.An artificial neural networks is a very hot cross discipline developed recently, it is a calculation model of a kind of process of cognition which is close to the person in essence. The neural networks system is a highly complicated nonlinear kinetics system. It is made up of a large number of neuron nodes, though the structure of each neuron is relatively simple, limited with the function, but the networks teamwork joined from a large number of neurons in some way, adjust the connection intensity among the neuron in rule, they can make the system have very strong functions. The model has highly fault-tolerant, imagination and self-organization properties, and can approach any nonlinear function, so on, it have better ability of shining upon to non-linear system.The accurate description of the dynamics characteristic of a tire is a foundation to study dynamics of automobile, but it is comparatively difficult to solve the non-linear problem by traditional mathematics method. Therefore people begin to study and employ neural network theory to respects such as the modeling of the automobile dynamics characteristic and automation control, etc. This subject mainly focuses
on modeling and analyzing the model of the automobile tire with BP neural network. This subject utilizes 'magic formula* to set up dynamics model of automobile tire under purely work condition in chapter two, and compare with the survey result, the model error is relatively lager. Among the chapter four, at first the author utilizes MATLAB interface GUI , that neural network toolbox offered, to set up the neural network model of tire under purely work condition, choose suitable relevant parameters to train it, and the model predicted value after trained is compared with the survey result, the error reduces a lot more than the model error of "magic formula";Later, sets up the neural network model of tire under united work condition, and the model predicted value after training was compared with the survey result, the error is controlled in the range of allowed, the precision is good. It verifies the practicability of this kind of modeling method.
人工神经网络是最近发展起来的十分热门的交叉学科,其本质上是一种接近人的认识过程的计算模型。神经网络系统是一个高度复杂的非线性动力学系统。它由大量的神经元节点组成,尽管每个神经元的结构相对简单和功能有限,但由大量神经元按一定的方式连接成的网络集体工作,按一定的规则来调整神经元间的连接强度,能使系统具有十分强大的功能。这种模型有高度的容错性、联想性和自组织学习等优点,以及可逼近任一非线性函数的能力,对非线性系统具有较强的映射能力。
轮胎力学特性的精确描述是研究汽车的基础,但用传统的数学方法来解决非线性问题较为困难,因而人们开始研究将神经网络理论应用至汽车动力特性的建模及自动控制等方面。本课题主要用BP神经网络对汽车轮胎的力学特性进行建模分析。本课题在第二章中,利用“魔术公式”建立汽车轮胎纯工况力学模型,并将其模型输出值与试验实测值进行比较,模型误差较大。第四章中,利用MATLAB软件中的神经网络工具箱提供的图形用户界面(GUI),首先建立纯工况轮胎力学神经网络模型,选择合适的相关参数对其进行训练,并将训练好后的模型预测值与试验实测值进行比较,模型误差较“魔术公式”模型误差相比减小很多;之后,建立联合工况下轮胎力学神经网络模型,并将训练好后的模型预测值与试验实测值进行比较,误差控制在工程允许范围内,网络模型预测精度高。从而验证这种建模方法的实用性。
The tire is the most representative non-linear part of the automobile system, which behavior is very complicated. As a supporting of automobile and road surface and transmission unit, its dynamics characteristic influences the movement performance of the automobile directly. It depends on the precision of the tire dynamics model to a great extent that the automobile handles the calculation precision of stability. People have carried on extensive research for many years, and have set up a lot of tire models, each one has its special function. Dynamics that these models are used mainly in the automobile is analyzed, but they can' t include all non-linear factors of the tire, which influences precision of studying undoubtedly.An artificial neural networks is a very hot cross discipline developed recently, it is a calculation model of a kind of process of cognition which is close to the person in essence. The neural networks system is a highly complicated nonlinear kinetics system. It is made up of a large number of neuron nodes, though the structure of each neuron is relatively simple, limited with the function, but the networks teamwork joined from a large number of neurons in some way, adjust the connection intensity among the neuron in rule, they can make the system have very strong functions. The model has highly fault-tolerant, imagination and self-organization properties, and can approach any nonlinear function, so on, it have better ability of shining upon to non-linear system.The accurate description of the dynamics characteristic of a tire is a foundation to study dynamics of automobile, but it is comparatively difficult to solve the non-linear problem by traditional mathematics method. Therefore people begin to study and employ neural network theory to respects such as the modeling of the automobile dynamics characteristic and automation control, etc. This subject mainly focuses
on modeling and analyzing the model of the automobile tire with BP neural network. This subject utilizes 'magic formula* to set up dynamics model of automobile tire under purely work condition in chapter two, and compare with the survey result, the model error is relatively lager. Among the chapter four, at first the author utilizes MATLAB interface GUI , that neural network toolbox offered, to set up the neural network model of tire under purely work condition, choose suitable relevant parameters to train it, and the model predicted value after trained is compared with the survey result, the error reduces a lot more than the model error of "magic formula";Later, sets up the neural network model of tire under united work condition, and the model predicted value after training was compared with the survey result, the error is controlled in the range of allowed, the precision is good. It verifies the practicability of this kind of modeling method.
引文
[1] 郭孔辉.汽车操纵动力学[M].长春:吉林科学技术出版社,1991
[2] Clark S. K. Mechanics of Pneumatic Trires. Mono.122[J], National Bureau of Standards. Washington D. C. 1971.34-37
[3] 刘青,郭孔辉.轮胎侧偏特性研究的特点及其发展[J].汽车技术,1997,(10),1-8
[4] 赵又群,郭孔辉.汽车操纵稳定性评价的发展、研究意义与基本问题[J].汽车技术,1998(5):1-5
[5] 安部正人(日),陈辛波(译).汽车的运动和操纵[M].北京:机械工业出版社,1998
[6] Fromn H. Kuzer berichte ueber die geschichte der theoriedes tadflattems[M]. Ber:Ulie-nthal Ges, 1941
[7] Fiala E. Seitenkrafte am Rollenden Luftreifen [J]. ZVDI Nr29, 11,okt,1954:81-92
[8] 庄继德.汽车轮胎学[M].北京:北京理工大学出版社,1996
[9] Frank F. Grundlagen zur Berechnung der Seitenund rungskennlinien von Reifen. Kautschuk unt Gummi, Kunstotuffe [J]. Jar Nr 8z,1965:267-274
[10] Pacejka H B. The Wheel Shimmy Phenomenon [M]. Diss TH Delft,1966
[11] Boehm F. Zur Machanic des Luftreinfens Habilitation schdft[M]. TH Stuttgart,1996
[12] 赵又群,郭孔辉.稳态轮胎偏滑力学的发展与展望[J].汽车技术,1997(3):1-5
[13] Willumeit H P. Theory Unstersuchungen an Eunem Model des Luftreinfens Under Seitenund Umfangsfrafe [M]. Diss. TU Berlin,1969
[14] 孙逢春,李德圣,李晓雷.轮胎侧偏力学的新发展[J].汽车工程,1995,17(2):65—73
[15] 崔胜民.轮胎侧偏特性和汽车操纵稳定性的模拟计算研究[D]:[博士学位论文].北京:北京农业工程大学,1994
[16] Bergman W. Theoretical Prediction of the Effect Traction on Cornering Force [J]. SAE Transactions, 1961,69:614-640
[17] Nordeen D. L. et al.. Force and Moment Characteristics of Rolling Tires[J]. SAE paper. Washington D. C.,1963:30-34
[18] Krempel G.. Experinnenteller Beitrag zu Untersuchungen and Kraftfahrzeifen. TH. [J],Karlsruhe, 1965:7-16
[19] Henker E.. Dynamische Kennlinien von RKW-riefen. Wissenschafilisch technische Veroffentlich ungen aus dem Automobilbau[J].Heft,1968:4-9
[20] Dugoff H. et. al.. An analysis of tire traction properties and their influence vehicle dynamic performance[J]. SAE 700377. Washington D. C., 1978:64-66
[21] 酒井秀男.工学[M1].东京:出版,1987,224-278
[22] Gwanghun G, Nikravesh P E. An analytical model of pneumatic tires for vehicle dynamic simulations. Part 1: pure slips[J]. Int.J. of vehicle Design, 1990(11):6-13
[23] Gwanghun G, Nikravesh P E. An analytical model of pneumatic tires for vehicle dynamic simulations. Part 2: pure slips[J]. Int. J. of vehicle Design, 1991 (12):2-6
[24] 郭孔辉,隋军.轮胎垂直载荷分布与侧向力模型及纵向力之间的关系[J].汽车研究与开发,1995(1):22-25
[25] Szostak H T et al. An interative tire model for driver/vehicle simulation [J]. DOT HS 807271:20-25
[26] Pacejka H B, Rgbert B. Tire modeling for use in vehicle dynamics studies[Z]. SAE paper 870421
[27] 胡守仁等.神经网络导论、实现技术、应用技术(共三册)[M].长沙:国防科技大学出版社,1993、1995
[28] 焦李成.神经网络系统理论、计算、应用与实现(共三册)[M].西安:西安电子科技大学出版社,1990、1992
[29] 王文成.神经网络及其在汽车工程中的应用[M].北京:北京理工大学出版社,1998:2-89
[30] 田久保.利用神经网络系统的驾驶员模型研究[J].自动车技术学会学术演讲论文集.北京,1990:14-17
[31] M.米奇克(德),陈荫三(译).汽车动力学[M].北京:人民交通出版社,1997
[32] Palkvics L., El-Gindy M.. Neutral network representation tire characteristics: the Neuron-Tire. Int. J. of Vehicle Design[J], 1993, 14(5), 563-591
[33] 张子达,赵丁选,刘刚.工程轮胎静力学特性实验研究与参数识别[J].工程机械,2004(07):23-26
[34] Palkvics L., El-Gindy M, Pacejka H. B..Modelling of the cornering characteristics of tire on an uneven road surface: a dynamic version of the "Neuron-Tire" Int. J. of Vehicle Design[J], 1994, 15(1/2).189-215
[35] 赵和平.车辆轮胎动力学的神经网络方法研究[D]:[硕士学位论文].洛阳:洛阳工学院,1998,1-21
[36] 王永骥,涂键编.神经元网络控制[M].北京:机械工业出版社,1998
[37] 张平安等译.神经—模糊和软计算[M].西安:西安交通大学出版社,2000
[38] 张乃尧,阎平凡.神经网络与模糊控制[M].北京:清华大学出版社,1999
[39] 赵振宇.模糊理论和神经网络的基础和应用[M].北京:清华大学出版社,1993:24-31
[40] 陈明.神经网络模型[M].大连:大连理工大学出版社,1995
[41] 何玉彬,李新忠.神经网络控制技术及其应用[M].北京:科学出版社,2000
[42] 周志华,曹存根.神经网络及其应用[M].北京:清华大学出版社,2004
[43] 魏海坤.神经网络结构设计的理论与方法[M].北京:国防工业出版社,2005
[44] 徐丽娜.神经网络控制[M].北京:电子工业出版社,2003
[45] 加卢什金(俄),阎平凡(译)[M].神经网络理论.北京:清华大学出版社,2002
[46] 魏道高等.汽车轮胎侧偏特性研究综述[J].江苏大学学报,2002,23(3):55-59
[47] 宗长富,郭孔辉.汽车操纵稳定性的客观定量评价指标[J].吉林:吉林工业大学自然科学学报,2000(30):13-16
[48] 徐立友等.轮胎在侧向力、纵向力联合工况下的神经网络模型[J].北京:机床与液压.2005,12(4):128-130
[49] Kattan, Peter Issa. MATLAB guide to finite elements: an interactive approach[M]. Bedin, New York :Springer,2003
[50] 飞思科技产品研发中心.MATLAB 7基础与提高[M].北京:电子工业出版社,2005
[51] 飞恩科技产品研发中心.神经网络理论与MATLAB 7实现[M].北京:电子工业出版社,2005
[52] 周开利,康耀红.神经网络模型及其MATLAB仿真程序设计[M].北京:清华大学出版社,2005
[53] 王家文,王皓,刘海.MATLAB 7.0编程基础[M].北京:机械工业出版社,2005
[54] 闻新,周露,李翔.MATLAB神经网络仿真与应用[M].北京:科学出版社,2003
[2] Clark S. K. Mechanics of Pneumatic Trires. Mono.122[J], National Bureau of Standards. Washington D. C. 1971.34-37
[3] 刘青,郭孔辉.轮胎侧偏特性研究的特点及其发展[J].汽车技术,1997,(10),1-8
[4] 赵又群,郭孔辉.汽车操纵稳定性评价的发展、研究意义与基本问题[J].汽车技术,1998(5):1-5
[5] 安部正人(日),陈辛波(译).汽车的运动和操纵[M].北京:机械工业出版社,1998
[6] Fromn H. Kuzer berichte ueber die geschichte der theoriedes tadflattems[M]. Ber:Ulie-nthal Ges, 1941
[7] Fiala E. Seitenkrafte am Rollenden Luftreifen [J]. ZVDI Nr29, 11,okt,1954:81-92
[8] 庄继德.汽车轮胎学[M].北京:北京理工大学出版社,1996
[9] Frank F. Grundlagen zur Berechnung der Seitenund rungskennlinien von Reifen. Kautschuk unt Gummi, Kunstotuffe [J]. Jar Nr 8z,1965:267-274
[10] Pacejka H B. The Wheel Shimmy Phenomenon [M]. Diss TH Delft,1966
[11] Boehm F. Zur Machanic des Luftreinfens Habilitation schdft[M]. TH Stuttgart,1996
[12] 赵又群,郭孔辉.稳态轮胎偏滑力学的发展与展望[J].汽车技术,1997(3):1-5
[13] Willumeit H P. Theory Unstersuchungen an Eunem Model des Luftreinfens Under Seitenund Umfangsfrafe [M]. Diss. TU Berlin,1969
[14] 孙逢春,李德圣,李晓雷.轮胎侧偏力学的新发展[J].汽车工程,1995,17(2):65—73
[15] 崔胜民.轮胎侧偏特性和汽车操纵稳定性的模拟计算研究[D]:[博士学位论文].北京:北京农业工程大学,1994
[16] Bergman W. Theoretical Prediction of the Effect Traction on Cornering Force [J]. SAE Transactions, 1961,69:614-640
[17] Nordeen D. L. et al.. Force and Moment Characteristics of Rolling Tires[J]. SAE paper. Washington D. C.,1963:30-34
[18] Krempel G.. Experinnenteller Beitrag zu Untersuchungen and Kraftfahrzeifen. TH. [J],Karlsruhe, 1965:7-16
[19] Henker E.. Dynamische Kennlinien von RKW-riefen. Wissenschafilisch technische Veroffentlich ungen aus dem Automobilbau[J].Heft,1968:4-9
[20] Dugoff H. et. al.. An analysis of tire traction properties and their influence vehicle dynamic performance[J]. SAE 700377. Washington D. C., 1978:64-66
[21] 酒井秀男.工学[M1].东京:出版,1987,224-278
[22] Gwanghun G, Nikravesh P E. An analytical model of pneumatic tires for vehicle dynamic simulations. Part 1: pure slips[J]. Int.J. of vehicle Design, 1990(11):6-13
[23] Gwanghun G, Nikravesh P E. An analytical model of pneumatic tires for vehicle dynamic simulations. Part 2: pure slips[J]. Int. J. of vehicle Design, 1991 (12):2-6
[24] 郭孔辉,隋军.轮胎垂直载荷分布与侧向力模型及纵向力之间的关系[J].汽车研究与开发,1995(1):22-25
[25] Szostak H T et al. An interative tire model for driver/vehicle simulation [J]. DOT HS 807271:20-25
[26] Pacejka H B, Rgbert B. Tire modeling for use in vehicle dynamics studies[Z]. SAE paper 870421
[27] 胡守仁等.神经网络导论、实现技术、应用技术(共三册)[M].长沙:国防科技大学出版社,1993、1995
[28] 焦李成.神经网络系统理论、计算、应用与实现(共三册)[M].西安:西安电子科技大学出版社,1990、1992
[29] 王文成.神经网络及其在汽车工程中的应用[M].北京:北京理工大学出版社,1998:2-89
[30] 田久保.利用神经网络系统的驾驶员模型研究[J].自动车技术学会学术演讲论文集.北京,1990:14-17
[31] M.米奇克(德),陈荫三(译).汽车动力学[M].北京:人民交通出版社,1997
[32] Palkvics L., El-Gindy M.. Neutral network representation tire characteristics: the Neuron-Tire. Int. J. of Vehicle Design[J], 1993, 14(5), 563-591
[33] 张子达,赵丁选,刘刚.工程轮胎静力学特性实验研究与参数识别[J].工程机械,2004(07):23-26
[34] Palkvics L., El-Gindy M, Pacejka H. B..Modelling of the cornering characteristics of tire on an uneven road surface: a dynamic version of the "Neuron-Tire" Int. J. of Vehicle Design[J], 1994, 15(1/2).189-215
[35] 赵和平.车辆轮胎动力学的神经网络方法研究[D]:[硕士学位论文].洛阳:洛阳工学院,1998,1-21
[36] 王永骥,涂键编.神经元网络控制[M].北京:机械工业出版社,1998
[37] 张平安等译.神经—模糊和软计算[M].西安:西安交通大学出版社,2000
[38] 张乃尧,阎平凡.神经网络与模糊控制[M].北京:清华大学出版社,1999
[39] 赵振宇.模糊理论和神经网络的基础和应用[M].北京:清华大学出版社,1993:24-31
[40] 陈明.神经网络模型[M].大连:大连理工大学出版社,1995
[41] 何玉彬,李新忠.神经网络控制技术及其应用[M].北京:科学出版社,2000
[42] 周志华,曹存根.神经网络及其应用[M].北京:清华大学出版社,2004
[43] 魏海坤.神经网络结构设计的理论与方法[M].北京:国防工业出版社,2005
[44] 徐丽娜.神经网络控制[M].北京:电子工业出版社,2003
[45] 加卢什金(俄),阎平凡(译)[M].神经网络理论.北京:清华大学出版社,2002
[46] 魏道高等.汽车轮胎侧偏特性研究综述[J].江苏大学学报,2002,23(3):55-59
[47] 宗长富,郭孔辉.汽车操纵稳定性的客观定量评价指标[J].吉林:吉林工业大学自然科学学报,2000(30):13-16
[48] 徐立友等.轮胎在侧向力、纵向力联合工况下的神经网络模型[J].北京:机床与液压.2005,12(4):128-130
[49] Kattan, Peter Issa. MATLAB guide to finite elements: an interactive approach[M]. Bedin, New York :Springer,2003
[50] 飞思科技产品研发中心.MATLAB 7基础与提高[M].北京:电子工业出版社,2005
[51] 飞恩科技产品研发中心.神经网络理论与MATLAB 7实现[M].北京:电子工业出版社,2005
[52] 周开利,康耀红.神经网络模型及其MATLAB仿真程序设计[M].北京:清华大学出版社,2005
[53] 王家文,王皓,刘海.MATLAB 7.0编程基础[M].北京:机械工业出版社,2005
[54] 闻新,周露,李翔.MATLAB神经网络仿真与应用[M].北京:科学出版社,2003