汽车钢板弹簧计算的一种新模型及其静动态特性研究
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摘要
钢板弹簧作为汽车悬架系统中的弹性元件,因其结构简单、技术成熟,获得了广泛的应用。它是重要的高负荷安全部件,在汽车的生产应用中有着重要的地位。因此,合理地设计钢板弹簧的性能指标以及结构参数是决定整车设计水平的关键因素之一,对提高其使用寿命及改善汽车行驶的平顺性和安全性都具有重要意义。在汽车钢板弹簧设计的传统计算方法中,一般的计算模型都是将钢板弹簧看成是直梁,然后基于一定的假设来进行分析计算,这与钢板弹簧的实际结构、受力和变形情况等有不小的差距,因而其计算结果往往不够精确。因此,寻求一种高精度的半解析法来解决钢板弹簧计算精度差、效率低的问题相当有必要。
论文首先介绍了钢板弹簧现有的一些计算方法,并对这些方法进行了分析比较。然后系统介绍了曲梁理论和精细积分算法,并基此提出了汽车钢板弹簧设计的一种新模型——层叠曲线梁模型。
随后,文中分别建立了忽略片间摩擦和考虑片间摩擦的多片等截面式钢板弹簧的两种层叠曲线梁模型,运用MATLAB软件对这两种模型进行了编程计算,分析研究了板簧的静动态特性,并将计算结果与CAE有限元法和传统的钢板弹簧设计方法的结果相比较,有力的证明了文中所建立的层叠曲线梁模型的正确性,且通过考虑簧片间的摩擦情况,钢板弹簧计算模型的精度得到了进一步提高。
另外,还建立了少片变截面式钢板弹簧的层叠曲线梁模型,并分析研究了少片变截面式钢板弹簧的静动态特性,同样将计算结果与CAE有限元法和传统计算方法的结果相比较,显示了模型的精确性和方法的优越性。
最后,针对钢板弹簧在工作过程中存在大变形问题(几何非线性),文中采用线性模型逐步逼近的方法,对多片等截面式钢板弹簧的刚度进行了讨论分析,为实际工程应用设计提供了一定的理论参考。
The leaf spring is an elastic part of the suspension, which is widely used for its simple structure and mature technology. It is an important safety component burdening high load and plays an important role in automobile production and application. So that, it is one of the key factors for vehicle design to determine the performance and structural parameters of the leaf spring rationally. This is of great significance to increasing the service life of a vehicle and improving its ride comfort and safety. In traditional methods of the leaf spring, it is usually considered as a straight beam. Their analyses are based on some assumptions. But there is a bigger gap between the assumptions and the actual force and deformation of the leaf spring. Thus, the accuracy of their analyses is not high. For this reason, the search for a precise semi-analytical method to solve the poor precision and low efficiency issues of the leaf spring is necessary.
Firstly, this paper introduced the traditional calculation methods of the leaf spring, and analyzed and compared them simply. Then the curved beam theory and precise integration method were introduced systematically. Based on them, a new model– the layered curve beam model of the leaf-spring was constructed.
After that, by neglecting or considering interleaf friction, two layered curve beam models of the multi-leaf spring with equal section were established. On the basis of above models, the static and dynamic characteristics of the multi-leaf spring were analyzed by the MATLAB software. The comparisons between the results of present method and the CAE finite element method and the traditional calculation methods verified the accuracy of the proposed method strangely. By considering the interleaf friction, the precision of the spring computation model was further enhanced.
In addition, the layered curve beam model of a few-leaf-spring with variable section was built and their static and dynamic characteristics were analyzed. The paper also compared with the results of present method and the CAE finite element method and the traditional calculation method. It shows the accuracy and advantages of the present model.
For the big deformation problem of the leaf spring (geometric nonlinear) in the work process, a gradual approximation method based on the linear model is adopted to analyze and discuss the stiffness of the multi-leaf spring with equal section. It provides a certain theoretical reference for the practical application.
论文首先介绍了钢板弹簧现有的一些计算方法,并对这些方法进行了分析比较。然后系统介绍了曲梁理论和精细积分算法,并基此提出了汽车钢板弹簧设计的一种新模型——层叠曲线梁模型。
随后,文中分别建立了忽略片间摩擦和考虑片间摩擦的多片等截面式钢板弹簧的两种层叠曲线梁模型,运用MATLAB软件对这两种模型进行了编程计算,分析研究了板簧的静动态特性,并将计算结果与CAE有限元法和传统的钢板弹簧设计方法的结果相比较,有力的证明了文中所建立的层叠曲线梁模型的正确性,且通过考虑簧片间的摩擦情况,钢板弹簧计算模型的精度得到了进一步提高。
另外,还建立了少片变截面式钢板弹簧的层叠曲线梁模型,并分析研究了少片变截面式钢板弹簧的静动态特性,同样将计算结果与CAE有限元法和传统计算方法的结果相比较,显示了模型的精确性和方法的优越性。
最后,针对钢板弹簧在工作过程中存在大变形问题(几何非线性),文中采用线性模型逐步逼近的方法,对多片等截面式钢板弹簧的刚度进行了讨论分析,为实际工程应用设计提供了一定的理论参考。
The leaf spring is an elastic part of the suspension, which is widely used for its simple structure and mature technology. It is an important safety component burdening high load and plays an important role in automobile production and application. So that, it is one of the key factors for vehicle design to determine the performance and structural parameters of the leaf spring rationally. This is of great significance to increasing the service life of a vehicle and improving its ride comfort and safety. In traditional methods of the leaf spring, it is usually considered as a straight beam. Their analyses are based on some assumptions. But there is a bigger gap between the assumptions and the actual force and deformation of the leaf spring. Thus, the accuracy of their analyses is not high. For this reason, the search for a precise semi-analytical method to solve the poor precision and low efficiency issues of the leaf spring is necessary.
Firstly, this paper introduced the traditional calculation methods of the leaf spring, and analyzed and compared them simply. Then the curved beam theory and precise integration method were introduced systematically. Based on them, a new model– the layered curve beam model of the leaf-spring was constructed.
After that, by neglecting or considering interleaf friction, two layered curve beam models of the multi-leaf spring with equal section were established. On the basis of above models, the static and dynamic characteristics of the multi-leaf spring were analyzed by the MATLAB software. The comparisons between the results of present method and the CAE finite element method and the traditional calculation methods verified the accuracy of the proposed method strangely. By considering the interleaf friction, the precision of the spring computation model was further enhanced.
In addition, the layered curve beam model of a few-leaf-spring with variable section was built and their static and dynamic characteristics were analyzed. The paper also compared with the results of present method and the CAE finite element method and the traditional calculation method. It shows the accuracy and advantages of the present model.
For the big deformation problem of the leaf spring (geometric nonlinear) in the work process, a gradual approximation method based on the linear model is adopted to analyze and discuss the stiffness of the multi-leaf spring with equal section. It provides a certain theoretical reference for the practical application.
引文
[1]刘惟信.汽车设计[M].北京:清华大学出版社,2001.431-483.
[2]王望予.汽车设计[M].北京:机械工业出版社,2002.133-148.
[3]小林明.汽车工程手册.第二分册[M].北京:机械工业出版社,1984.359-366.
[4]江浩斌,周孔亢.农用运输车钢板弹簧选型与计算机辅助参数设计[J].江苏理工大学学报(自然科学版),2000,21(1):19-23.
[5]肖军.汽车钢板弹簧的应用及其发展趋势[J].城市车辆,2007,(11):54-57.
[6]杨宗孟.汽车钢板弹簧的设计与计算[J].汽车技术,1979,(1):12-28.
[7]郭孔辉.钢板弹簧刚度计算的主片分析法[J].汽车工程,1984,(2):22-28.
[8]刘广宽.汽车钢板弹簧计算模型的研究[J].当代汽车,1986,(4).
[9]林金木.有限单元法解钢板弹簧[J].汽车工程,1984,(4):20-36.
[10]郑贤中,蒙培生,黄延恩等.受力钢板弹簧的有限元三维数值模拟[J].机械设计与研究,1998,(3):41-42.
[11]邹海荣,黄其柏.基于非线性的汽车钢板弹簧断裂问题分析[J].华中科技大学学报(自然科学版),2003,31(3):96-98.
[12]胡玉梅,邓兆祥,王欣等.汽车后悬架的非线性有限元分析[J] .重庆大学学报,2003,26(4):38-41.
[13]丁能根,马建军.钢板弹簧迟滞特性的有限元分析[J].汽车工程,2003,25(1):12-24.
[14]王其东.基于多体理论的汽车悬架系统分析、设计与控制研究[D]:合肥:合肥工业大学,2002.
[15]郑银环.汽车钢板弹簧计算模型研究[D]:武汉:武汉理工大学,2005.
[16] Erol Sancaktar ,Mathieu Gratton. Design ,analysis,and optimization of composite leaf springs for light vehicle applications[J]. Composite Structures,44(1999) .195-204.
[17] M.A.Osipenko,Yu.I.Nyashin,R.N.Rudakov. A contact problem in the theory of leaf spring bending[J].International Journal of Solids and Structures,40(2003) .3129-3136.
[18] I. Rajendran,S .Vijayarangan. Optimal design of a composite leaf spring using genetic algorithms[J].Computers and Structures,79(2001).1121-1129.
[19] A.E.Baumal,J.J.Mcphee,P.H.Calamai. Application of genetic algorithms to the design optimization of an active vehicle suspension system[J].Computer methods in applied mechanics and engineering,163(1998).87-94.
[20] H. A. Al-Aureshi. Automobile leaf springs from composite materials[J].Journal of materials Processing technology,118(2001).58-61.
[21] Mahmood M. Shokrieh,and Davood Rezaei. Analysis and optimization of a composite leaf spring[J]. Composite Structures,60(2003).317-325.
[22] Winkler B C,Hagan M,A test facility for the measurement of heavy vehicle suspension parameters[J].SAE Trans.800906,1980:2754-2782.
[23] Cebon D.Simulation of response of leaf springs to broad band random excitation[J].Vehicle System Dynamics,1986,15:375-390.
[24] Apetaur M. Brief note On D. Carbon’s paper[J] .Vehicle System Dynamics,1986,15:391-392
[25] A.E.Baumal,J.J , Mcphee,P.H.Calamai. Application of genetic algorithms to the design optimization of an active vehicle suspension system [J].Computer methods in applied mechanics and engineering,163(1998).87-94.
[26] Kim S,Moon W,Yoo Y.An efficient method for calculating the nonlinear stiffness of progressive multi-leaf springs [J].International Journal of Vehicle Design,2002,29(4):403-422.
[27] Ekici B.Multi-response optimization in a three-link leaf-spring model [J].International Journal of Vehicle Design,2005,38(4):326-346.
[28] K.F.帕尔希洛夫斯基,宁开平译.汽车的钢板弹簧[M].北京:人民交通出版社,1959.
[29] Zahavi.E.. Analysis of a contact problem in leaf springs[J].Mechanics Research Communications,1992,19(1).
[30] Toshio Hamano.Koichiro Kawashima,Hirotake Kato. Analysis of Hysteresis Behavior of Leaf Springs with FEM:1st Report,Basic Formulation of a Special Contact Element for the Beam-element-models.日本机械学会论文集,A辑.1998,64(622).
[31] Toshio Hamano.Koichiro KawashInIa,Hirotake Kato.Analysis of Hysteresis Behavior of Leaf Springs with FEM(2nd Report,Application of Special Contact Element to Multi- leaf Spring Modeled by Beam Element).日本机械学会论文集,A辑.1998,64(625).
[32] Zadeh A Ghazi. Neuro-leaf Spring [J].Heavy Vehicle Systems,2000,7(4).
[33]刘鸿文.高等材料力学[M].北京:高等教育出版社,1985.
[34]王金明.工形截面薄壁圆弧曲梁的稳定性分析[D]:哈尔滨:哈尔滨工程大学,2000.
[35] Lin Jiahao,Zhong Wanxie,Zhang Wenshou. Precise integration of the variance matrix of structural non-stationary random responses [J].Journal of Vibration Engineering,1999,12(1):1-8.
[36] Moler C,Loan C V. Nineteen dubious ways to compute the exponential of a matrix[J].SIAM Review,1978,20(4):801-836.
[37]王跃先,周钢等.齐次扩容精细算法[J].计算力学学报,2001,18(3):339-344.
[38]向宇,黄玉盈.精细时程积分法的误差分析与精度设计[J].计算力学学报,2003,19(3):276-280.
[39]向宇,黄玉盈.一种新型齐次扩容精细积分法[J] .华中科技大学学报,2002,14(2):31-36.
[40]于安和,桂良进.钢板弹簧刚度特性的有限元分析[J].汽车技术,2007,10(2):26-29.
[41]胡国友,夏品奇,杨劲松.渐变刚度钢板弹簧刚度特性计算的曲率一载荷混合法[J].南京航空航天大学学报,2008,40(1):46-50.
[42]王庆五,徐人平,杨晓光.用传递矩阵法求解变截面钢板弹簧的固有频率[J] .拖拉机与农用运输车,2004,10(5):32-34.
[43]李世荣,宋曦,周又和.弹性曲梁几何非线性精确模型及其数值解[J] .2004,21(2):129-133.
[2]王望予.汽车设计[M].北京:机械工业出版社,2002.133-148.
[3]小林明.汽车工程手册.第二分册[M].北京:机械工业出版社,1984.359-366.
[4]江浩斌,周孔亢.农用运输车钢板弹簧选型与计算机辅助参数设计[J].江苏理工大学学报(自然科学版),2000,21(1):19-23.
[5]肖军.汽车钢板弹簧的应用及其发展趋势[J].城市车辆,2007,(11):54-57.
[6]杨宗孟.汽车钢板弹簧的设计与计算[J].汽车技术,1979,(1):12-28.
[7]郭孔辉.钢板弹簧刚度计算的主片分析法[J].汽车工程,1984,(2):22-28.
[8]刘广宽.汽车钢板弹簧计算模型的研究[J].当代汽车,1986,(4).
[9]林金木.有限单元法解钢板弹簧[J].汽车工程,1984,(4):20-36.
[10]郑贤中,蒙培生,黄延恩等.受力钢板弹簧的有限元三维数值模拟[J].机械设计与研究,1998,(3):41-42.
[11]邹海荣,黄其柏.基于非线性的汽车钢板弹簧断裂问题分析[J].华中科技大学学报(自然科学版),2003,31(3):96-98.
[12]胡玉梅,邓兆祥,王欣等.汽车后悬架的非线性有限元分析[J] .重庆大学学报,2003,26(4):38-41.
[13]丁能根,马建军.钢板弹簧迟滞特性的有限元分析[J].汽车工程,2003,25(1):12-24.
[14]王其东.基于多体理论的汽车悬架系统分析、设计与控制研究[D]:合肥:合肥工业大学,2002.
[15]郑银环.汽车钢板弹簧计算模型研究[D]:武汉:武汉理工大学,2005.
[16] Erol Sancaktar ,Mathieu Gratton. Design ,analysis,and optimization of composite leaf springs for light vehicle applications[J]. Composite Structures,44(1999) .195-204.
[17] M.A.Osipenko,Yu.I.Nyashin,R.N.Rudakov. A contact problem in the theory of leaf spring bending[J].International Journal of Solids and Structures,40(2003) .3129-3136.
[18] I. Rajendran,S .Vijayarangan. Optimal design of a composite leaf spring using genetic algorithms[J].Computers and Structures,79(2001).1121-1129.
[19] A.E.Baumal,J.J.Mcphee,P.H.Calamai. Application of genetic algorithms to the design optimization of an active vehicle suspension system[J].Computer methods in applied mechanics and engineering,163(1998).87-94.
[20] H. A. Al-Aureshi. Automobile leaf springs from composite materials[J].Journal of materials Processing technology,118(2001).58-61.
[21] Mahmood M. Shokrieh,and Davood Rezaei. Analysis and optimization of a composite leaf spring[J]. Composite Structures,60(2003).317-325.
[22] Winkler B C,Hagan M,A test facility for the measurement of heavy vehicle suspension parameters[J].SAE Trans.800906,1980:2754-2782.
[23] Cebon D.Simulation of response of leaf springs to broad band random excitation[J].Vehicle System Dynamics,1986,15:375-390.
[24] Apetaur M. Brief note On D. Carbon’s paper[J] .Vehicle System Dynamics,1986,15:391-392
[25] A.E.Baumal,J.J , Mcphee,P.H.Calamai. Application of genetic algorithms to the design optimization of an active vehicle suspension system [J].Computer methods in applied mechanics and engineering,163(1998).87-94.
[26] Kim S,Moon W,Yoo Y.An efficient method for calculating the nonlinear stiffness of progressive multi-leaf springs [J].International Journal of Vehicle Design,2002,29(4):403-422.
[27] Ekici B.Multi-response optimization in a three-link leaf-spring model [J].International Journal of Vehicle Design,2005,38(4):326-346.
[28] K.F.帕尔希洛夫斯基,宁开平译.汽车的钢板弹簧[M].北京:人民交通出版社,1959.
[29] Zahavi.E.. Analysis of a contact problem in leaf springs[J].Mechanics Research Communications,1992,19(1).
[30] Toshio Hamano.Koichiro Kawashima,Hirotake Kato. Analysis of Hysteresis Behavior of Leaf Springs with FEM:1st Report,Basic Formulation of a Special Contact Element for the Beam-element-models.日本机械学会论文集,A辑.1998,64(622).
[31] Toshio Hamano.Koichiro KawashInIa,Hirotake Kato.Analysis of Hysteresis Behavior of Leaf Springs with FEM(2nd Report,Application of Special Contact Element to Multi- leaf Spring Modeled by Beam Element).日本机械学会论文集,A辑.1998,64(625).
[32] Zadeh A Ghazi. Neuro-leaf Spring [J].Heavy Vehicle Systems,2000,7(4).
[33]刘鸿文.高等材料力学[M].北京:高等教育出版社,1985.
[34]王金明.工形截面薄壁圆弧曲梁的稳定性分析[D]:哈尔滨:哈尔滨工程大学,2000.
[35] Lin Jiahao,Zhong Wanxie,Zhang Wenshou. Precise integration of the variance matrix of structural non-stationary random responses [J].Journal of Vibration Engineering,1999,12(1):1-8.
[36] Moler C,Loan C V. Nineteen dubious ways to compute the exponential of a matrix[J].SIAM Review,1978,20(4):801-836.
[37]王跃先,周钢等.齐次扩容精细算法[J].计算力学学报,2001,18(3):339-344.
[38]向宇,黄玉盈.精细时程积分法的误差分析与精度设计[J].计算力学学报,2003,19(3):276-280.
[39]向宇,黄玉盈.一种新型齐次扩容精细积分法[J] .华中科技大学学报,2002,14(2):31-36.
[40]于安和,桂良进.钢板弹簧刚度特性的有限元分析[J].汽车技术,2007,10(2):26-29.
[41]胡国友,夏品奇,杨劲松.渐变刚度钢板弹簧刚度特性计算的曲率一载荷混合法[J].南京航空航天大学学报,2008,40(1):46-50.
[42]王庆五,徐人平,杨晓光.用传递矩阵法求解变截面钢板弹簧的固有频率[J] .拖拉机与农用运输车,2004,10(5):32-34.
[43]李世荣,宋曦,周又和.弹性曲梁几何非线性精确模型及其数值解[J] .2004,21(2):129-133.