考虑转向机构间隙与杆件弹性的汽车摆振系统动力学分析
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摘要
汽车摆振是指汽车在平坦的路面上直线行驶时,转向轮以一定的幅度和频率绕主销持续振动的现象。它恶化汽车的操纵性,影响行车安全,并使得汽车的动力性、经济性下降。它不仅危害大,而且很常见,因此引起国内外的普遍关注。
影响汽车摆振的因素很多,如轮胎特性、车身结构参数等等,本课题组的前期工作表明,转向系统中转向梯形的运动副间隙因素对摆振系统动力学响应有很大影响。而间隙会引起较大的碰撞力,这将使得杆件产生不容忽视的弹性变形,对摆振系统动力学产生很大影响,所以研究间隙和弹性因素共同对摆振系统的影响很有必要。
本文将转向梯形简化为平行于汽车坐标平面的四连杆机构,其中左转向节臂和转向横拉杆之间存在间隙,各杆件为弹性杆件,利用matlab/simulink软件建立了仿真模型,研究了杆件的间隙和弹性因素对摆振系统动力学造成的影响。同时分析了其他因素对摆振产生的影响,并提出了相应的减振措施。具体内容如下:
建立了四连杆机构的动力学模型,分析了间隙因素对四连杆机构运动带来的影响,并得到了含间隙弹性四连杆机构的激励项;建立了含间隙弹性四连杆机构的有限元模型,利用matlab/simulink软件进行建模仿真,经比较发现考虑杆件弹性因素后系统的动力学响应有所改善,但是随着间隙的增大,系统最终还是进入了混沌运动状态。
将转向梯形简化为四连杆机构,应用拉格朗日方程建立了含间隙刚性摆振系统的六自由度动力学模型,并结合含间隙弹性曲柄连杆机构的动力学模型,推出了含间隙弹性摆振系统的动力学模型。
基于含间隙刚性、弹性摆振系统的动力学模型,利用matlab/simulink建立了相应的汽车摆振的模型,通过仿真分析,比较了刚性、弹性系统对汽车摆振带来的影响,发现:随着间隙的变化,弹性系统相对不容易使摆振进入混沌的运动状态,并给出了考虑弹性因素时间隙的取值范围。此外,本文还对车速,转向机的阻尼等相关的参数对摆振系统的影响进行了分析,并给出了相应的取值范围。
Front wheel shimmy is defined as the phenomenon when the car driving in the flat straight road, the vibration of the steering wheel vibrating continually around Kingpin in a certain extent and frequency. It is not only harmful for the maneuverability and driving safety, but also performs negative influence on power performance and fuel economy performance. Because of the negative influence and widespread in many model, it cause the common concern in and out the sea.
There are many factors which make impact on the wheel shimmy, such as the tire characteristics and body structure parameters. The previous studies of our team show that the clearance in the steering trapezoid of steering system has a great influence on the response of wheel shimmy. In fact, the impact forces caused by the clearance make the elastic deformation of the bar, the influence of that can not be ignored, so it is necessary to study the combined effect of clearance and flexibility factors made on the wheel shimmy.
In this dissertation, the steering trapezoid set is simplified as a horizontal four-bar linkage, in which the clearance exists between the left steering knuckle arm and steering tie rod, and the bars are all the elastic rod. Simulation model is established using matlab/simulink software. On this basis, the influence of clearance and flexibility factors together on the wheel shimmy system is analyzed, other factors’impact are also studied, and the measures are given in response. Details are as follows.
The dynamic model of rigid four-bar linkage which exist clearance is established, no only the influence of the clearance factor made on the linkage movement is analyzed, but also get the incentive forces of the elastic linkage. On the basis, the dynamic model of the elastic linkage is established using the finite element method, through comparison with the rigid system, the result shows that considering the flexibility the dynamic response of linkage improve, the impact force decrease much, and the clearance causing the chaos increase. But the system eventually comes into chaos status.
The steering trapezoid set is simplified as a horizontal four-bar linkage, then establishing a 6-DOF dynamic model of rigid wheel shimmy considering the clearance, combined the model of elastic four-bar linkage, the 6-DOF dynamic model of elastic wheel shimmy is derived.
According to the dynamic models of the rigid and elastic wheel shimmy system, the corresponding simulation model is established, through simulation and analysis, the comparison was made. The result shows the wheel shimmy system are more stable considering the flexibility factor, flexibility factor can inhibit the harmful impact of clearance, and the rang of clearance is given. The other factors’impact on the wheel shimmy is also studied, such as speed and steering damp, the corresponding range is given.
影响汽车摆振的因素很多,如轮胎特性、车身结构参数等等,本课题组的前期工作表明,转向系统中转向梯形的运动副间隙因素对摆振系统动力学响应有很大影响。而间隙会引起较大的碰撞力,这将使得杆件产生不容忽视的弹性变形,对摆振系统动力学产生很大影响,所以研究间隙和弹性因素共同对摆振系统的影响很有必要。
本文将转向梯形简化为平行于汽车坐标平面的四连杆机构,其中左转向节臂和转向横拉杆之间存在间隙,各杆件为弹性杆件,利用matlab/simulink软件建立了仿真模型,研究了杆件的间隙和弹性因素对摆振系统动力学造成的影响。同时分析了其他因素对摆振产生的影响,并提出了相应的减振措施。具体内容如下:
建立了四连杆机构的动力学模型,分析了间隙因素对四连杆机构运动带来的影响,并得到了含间隙弹性四连杆机构的激励项;建立了含间隙弹性四连杆机构的有限元模型,利用matlab/simulink软件进行建模仿真,经比较发现考虑杆件弹性因素后系统的动力学响应有所改善,但是随着间隙的增大,系统最终还是进入了混沌运动状态。
将转向梯形简化为四连杆机构,应用拉格朗日方程建立了含间隙刚性摆振系统的六自由度动力学模型,并结合含间隙弹性曲柄连杆机构的动力学模型,推出了含间隙弹性摆振系统的动力学模型。
基于含间隙刚性、弹性摆振系统的动力学模型,利用matlab/simulink建立了相应的汽车摆振的模型,通过仿真分析,比较了刚性、弹性系统对汽车摆振带来的影响,发现:随着间隙的变化,弹性系统相对不容易使摆振进入混沌的运动状态,并给出了考虑弹性因素时间隙的取值范围。此外,本文还对车速,转向机的阻尼等相关的参数对摆振系统的影响进行了分析,并给出了相应的取值范围。
Front wheel shimmy is defined as the phenomenon when the car driving in the flat straight road, the vibration of the steering wheel vibrating continually around Kingpin in a certain extent and frequency. It is not only harmful for the maneuverability and driving safety, but also performs negative influence on power performance and fuel economy performance. Because of the negative influence and widespread in many model, it cause the common concern in and out the sea.
There are many factors which make impact on the wheel shimmy, such as the tire characteristics and body structure parameters. The previous studies of our team show that the clearance in the steering trapezoid of steering system has a great influence on the response of wheel shimmy. In fact, the impact forces caused by the clearance make the elastic deformation of the bar, the influence of that can not be ignored, so it is necessary to study the combined effect of clearance and flexibility factors made on the wheel shimmy.
In this dissertation, the steering trapezoid set is simplified as a horizontal four-bar linkage, in which the clearance exists between the left steering knuckle arm and steering tie rod, and the bars are all the elastic rod. Simulation model is established using matlab/simulink software. On this basis, the influence of clearance and flexibility factors together on the wheel shimmy system is analyzed, other factors’impact are also studied, and the measures are given in response. Details are as follows.
The dynamic model of rigid four-bar linkage which exist clearance is established, no only the influence of the clearance factor made on the linkage movement is analyzed, but also get the incentive forces of the elastic linkage. On the basis, the dynamic model of the elastic linkage is established using the finite element method, through comparison with the rigid system, the result shows that considering the flexibility the dynamic response of linkage improve, the impact force decrease much, and the clearance causing the chaos increase. But the system eventually comes into chaos status.
The steering trapezoid set is simplified as a horizontal four-bar linkage, then establishing a 6-DOF dynamic model of rigid wheel shimmy considering the clearance, combined the model of elastic four-bar linkage, the 6-DOF dynamic model of elastic wheel shimmy is derived.
According to the dynamic models of the rigid and elastic wheel shimmy system, the corresponding simulation model is established, through simulation and analysis, the comparison was made. The result shows the wheel shimmy system are more stable considering the flexibility factor, flexibility factor can inhibit the harmful impact of clearance, and the rang of clearance is given. The other factors’impact on the wheel shimmy is also studied, such as speed and steering damp, the corresponding range is given.
引文
[1]李乔非.车辆转向轮摆振原因及控制[J].佳木斯工学院学报,1995,2,23-25
[2]小林明.汽车振动学[M].北京:机械工业出版社,1981:177-188
[3]何俞生,魏克严等.汽车振动学[M].北京:人民交通出版社,1990:218-223
[4] Knothe K,Bohm F.History of Stability of Railway and Road Vehicle System Dynamics[J].1999,31(5):283~323
[5] Demic M. Analysis of influence of design parameters on steered wheels shimmy of heavy vehicle. Vehicle System Dynamic,1996,26 (5):343-362
[6] Kovacs A P.Computational Vibration Analysis of Vehicle Shimmy by a Power-Work Method.Vehicle System Dynamics,1998,29(6):341-364
[7] Kimura T,Hanamura Y,et al.Analysis of steering shimmy accompanied by sprung mass vibration on light duty truck-fundamental mechanism. ISAE Review,1996,17 (3):301-306
[8] Stepan G,Goodwine B. Feedback linearization of shimmy. Proceedings of the Mini Conference on Vehicle System Dynamic,1998:429-436
[9] Stepan G. Chaotic motion of wheels.Vehicle System Dynamic,1991,20(6):341-351
[10]清华大学汽车教研室,南京汽车制造厂设计科.汽车转向轮的摆振以及结构参数对摆振的影响[J].机械工程学报,1979,10:127~137
[11]管迪华等.汽车转向轮摆振的仿真计算研究[J].汽车工程,1982,12(10):33-38
[12]宋健,管迪华.前轮定位参数与轮胎特性对前轮摆振的影响的研究[J].汽车工程,1995,4(3):13-25
[13]李胜,林逸.非独立悬架汽车转向轮自激型摆振的分岔特性分析[J].机械工程学报,2004,40(12):187-191
[14]李欣业,贺丽娟等.非独立悬架载重车辆摆振的仿真研究[J].河北工业大学学报,2005,34(3):26-33
[15]李欣业,贺丽娟等.解放CA10型载货汽车前轮摆振的数值仿真研究[J].汽车工程,2004,26(5):585-587
[16]杜彬.汽车前轮摆振的原因分析及改进措施[J].山西交通科技,2007,4:75-77
[17] Earles S.W.E,et al.Motion Analysis of a Rigid-link Mechanism with Clearance at a Bearing,Using Lagrangian Mechanics and Digital Computation[A].In:Conference and Mechanisms, ME[C],London,England,1972:83-89
[18] Dubowsky S . On Predicting the Dynamic Effects of Clearance in Planar Mechanism[J].Trans.ASME,J.Emg.Ind,1974,94(1):317-323
[19] Mansour W M , et al . Impact Spectra and Intensities for High-speed Menchanisms[J].Journal of Engineering for Industry,1975,97B(2):347-353
[20] Winfrey R C,Anderson R V,Gnilda CW.Analysis of elastic machinery withclearance[J].ASME Journal of Engineering for Industry,1973,95:695-703
[21] Furuhashi H,et al.A Dynamic Analysis of the Plane Crank-and-rocker Mechanisms with Clearance.Bulletin of the JSME,1988,23(177):446-452
[22] Wang Yu.et al.Dynamic Analysis of Flexible Mechanisms with Clearance[J].Journal of Mechanical Design.1996,118:592-594
[23] Feng zhiyou,et al.Kinto-elastodynamic analysis of four-bar linkages incorporating the effects of clearances in kinematic pair[J].Chinese Journal of Mechanical Engineering,1994,4(3)
[24]靳春梅.含间隙机构非线性动态特性、控制及实验研究(博士学位论文)[D].西安:西安交通大学,2001年
[25]李开泰,黄艾香,黄庆怀.有限元方法及其应用[M].北京:科学出版社,2005:1-7
[26]朱伯芳.有限单元法原理及应用[M].北京:中国水利水电出版社,2009:1-3
[27]冷纪桐,赵军,张娅.有限元技术基础[M].北京:化学工业出版社,2007:24-53
[28]何勇,李冬.含间隙机构动力学进展[J].陕西理工学院学报,2006,22(3)
[29]靳春梅.含间隙机构动态特性分析[J].机械科学与技术,2001,20(1):55-57
[30]唐锡宽,金得闻.机械动力学[M].北京:高等教育出版社,1983:214-238
[31]卢剑伟,顾駃,王其东.含间隙连杆机构周期解稳定性分析[J].合肥工业大学学报,2007,30(11):1417-1420
[32]胡海岩.应用非线性动力学[M].北京:航空工业出版社,2000:35~45
[33]薛定宇,陈阳泉.基于MATLAB/Simulink的系统仿真技术与应用[M].北京:清华大学出版社,2006:36-60
[34]合肥工业大学数学与信息科学系.数值计算方法[M].合肥:合肥工业大学出版社,2004:275-281
[35]师汉民.机械振动系统—分析、测试、建模、对策[M].武汉:华中科技大学出版社,2004:158-169
[36]刘秉正.非线性动力学与混沌基础[M].长春:东北师范大学出版社,1994:17-35
[37]郜文文.随机参数弹性连杆机构的可靠性分析(硕士学位论文)[D].西安:西安电子科技大学,2003年
[38]靳春梅,邱阳.含间隙弹性连杆机构的KED分析[J].机构学与机械动力学,2000,10:21-24
[39] Fawcett J N.Maintaining contact bring reward[J].Engineering,1975,215:741-743
[40]李小涛.汽车转向轮摆振的分岔研究(硕士学位论文)[D].天津:天津大学,2007年
[41]刘启佳.汽车前轮摆振动力学建模相关问题的研究(硕士学位论文)[D].吉林:吉林大学,2007年
[42]卢剑伟,顾駃,王其东.含运动副间隙汽车摆振系统非线性动力学建模[J].农业机械学报,2007,38(12):1-3
[43]余志生.汽车理论[M].北京:机械工业出版社,1988:132-145
[44]顾駃.考虑转向系间隙的汽车前轮摆振系统研究(硕士学位论文)[D].合肥:合肥工业大学,2007年
[45]张洪欣.汽车设计[M].北京:机械工业出版社,1988:200-204
[46]陈家瑞.汽车构造[M].北京:机械工业出版社,2005:174-176
[2]小林明.汽车振动学[M].北京:机械工业出版社,1981:177-188
[3]何俞生,魏克严等.汽车振动学[M].北京:人民交通出版社,1990:218-223
[4] Knothe K,Bohm F.History of Stability of Railway and Road Vehicle System Dynamics[J].1999,31(5):283~323
[5] Demic M. Analysis of influence of design parameters on steered wheels shimmy of heavy vehicle. Vehicle System Dynamic,1996,26 (5):343-362
[6] Kovacs A P.Computational Vibration Analysis of Vehicle Shimmy by a Power-Work Method.Vehicle System Dynamics,1998,29(6):341-364
[7] Kimura T,Hanamura Y,et al.Analysis of steering shimmy accompanied by sprung mass vibration on light duty truck-fundamental mechanism. ISAE Review,1996,17 (3):301-306
[8] Stepan G,Goodwine B. Feedback linearization of shimmy. Proceedings of the Mini Conference on Vehicle System Dynamic,1998:429-436
[9] Stepan G. Chaotic motion of wheels.Vehicle System Dynamic,1991,20(6):341-351
[10]清华大学汽车教研室,南京汽车制造厂设计科.汽车转向轮的摆振以及结构参数对摆振的影响[J].机械工程学报,1979,10:127~137
[11]管迪华等.汽车转向轮摆振的仿真计算研究[J].汽车工程,1982,12(10):33-38
[12]宋健,管迪华.前轮定位参数与轮胎特性对前轮摆振的影响的研究[J].汽车工程,1995,4(3):13-25
[13]李胜,林逸.非独立悬架汽车转向轮自激型摆振的分岔特性分析[J].机械工程学报,2004,40(12):187-191
[14]李欣业,贺丽娟等.非独立悬架载重车辆摆振的仿真研究[J].河北工业大学学报,2005,34(3):26-33
[15]李欣业,贺丽娟等.解放CA10型载货汽车前轮摆振的数值仿真研究[J].汽车工程,2004,26(5):585-587
[16]杜彬.汽车前轮摆振的原因分析及改进措施[J].山西交通科技,2007,4:75-77
[17] Earles S.W.E,et al.Motion Analysis of a Rigid-link Mechanism with Clearance at a Bearing,Using Lagrangian Mechanics and Digital Computation[A].In:Conference and Mechanisms, ME[C],London,England,1972:83-89
[18] Dubowsky S . On Predicting the Dynamic Effects of Clearance in Planar Mechanism[J].Trans.ASME,J.Emg.Ind,1974,94(1):317-323
[19] Mansour W M , et al . Impact Spectra and Intensities for High-speed Menchanisms[J].Journal of Engineering for Industry,1975,97B(2):347-353
[20] Winfrey R C,Anderson R V,Gnilda CW.Analysis of elastic machinery withclearance[J].ASME Journal of Engineering for Industry,1973,95:695-703
[21] Furuhashi H,et al.A Dynamic Analysis of the Plane Crank-and-rocker Mechanisms with Clearance.Bulletin of the JSME,1988,23(177):446-452
[22] Wang Yu.et al.Dynamic Analysis of Flexible Mechanisms with Clearance[J].Journal of Mechanical Design.1996,118:592-594
[23] Feng zhiyou,et al.Kinto-elastodynamic analysis of four-bar linkages incorporating the effects of clearances in kinematic pair[J].Chinese Journal of Mechanical Engineering,1994,4(3)
[24]靳春梅.含间隙机构非线性动态特性、控制及实验研究(博士学位论文)[D].西安:西安交通大学,2001年
[25]李开泰,黄艾香,黄庆怀.有限元方法及其应用[M].北京:科学出版社,2005:1-7
[26]朱伯芳.有限单元法原理及应用[M].北京:中国水利水电出版社,2009:1-3
[27]冷纪桐,赵军,张娅.有限元技术基础[M].北京:化学工业出版社,2007:24-53
[28]何勇,李冬.含间隙机构动力学进展[J].陕西理工学院学报,2006,22(3)
[29]靳春梅.含间隙机构动态特性分析[J].机械科学与技术,2001,20(1):55-57
[30]唐锡宽,金得闻.机械动力学[M].北京:高等教育出版社,1983:214-238
[31]卢剑伟,顾駃,王其东.含间隙连杆机构周期解稳定性分析[J].合肥工业大学学报,2007,30(11):1417-1420
[32]胡海岩.应用非线性动力学[M].北京:航空工业出版社,2000:35~45
[33]薛定宇,陈阳泉.基于MATLAB/Simulink的系统仿真技术与应用[M].北京:清华大学出版社,2006:36-60
[34]合肥工业大学数学与信息科学系.数值计算方法[M].合肥:合肥工业大学出版社,2004:275-281
[35]师汉民.机械振动系统—分析、测试、建模、对策[M].武汉:华中科技大学出版社,2004:158-169
[36]刘秉正.非线性动力学与混沌基础[M].长春:东北师范大学出版社,1994:17-35
[37]郜文文.随机参数弹性连杆机构的可靠性分析(硕士学位论文)[D].西安:西安电子科技大学,2003年
[38]靳春梅,邱阳.含间隙弹性连杆机构的KED分析[J].机构学与机械动力学,2000,10:21-24
[39] Fawcett J N.Maintaining contact bring reward[J].Engineering,1975,215:741-743
[40]李小涛.汽车转向轮摆振的分岔研究(硕士学位论文)[D].天津:天津大学,2007年
[41]刘启佳.汽车前轮摆振动力学建模相关问题的研究(硕士学位论文)[D].吉林:吉林大学,2007年
[42]卢剑伟,顾駃,王其东.含运动副间隙汽车摆振系统非线性动力学建模[J].农业机械学报,2007,38(12):1-3
[43]余志生.汽车理论[M].北京:机械工业出版社,1988:132-145
[44]顾駃.考虑转向系间隙的汽车前轮摆振系统研究(硕士学位论文)[D].合肥:合肥工业大学,2007年
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