A predictive method of effective area of rolling lobe air spring for vehicles
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摘要: 空气弹簧帘线-橡胶复合材料结构具有刚度可变、轻量化、高度可调、隔振效果好等优势,在汽车“新四化”的发展趋势下,车用空气弹簧力学成为学术和工程研究热点。但其受力的“有效面积”这一重要参数还未建立完善理论模型。结合复合材料力学特性与几何学特征,提出一种车用膜式空气弹簧有效面积理论分析与预测方法。给出了空气弹簧有效面积理论预测表达式,体现了空气弹簧气囊内压强、空气弹簧高度等因素对有效面积的综合影响。利用力学综合实验台架设计实验,对某型号空气弹簧进行有效面积测量,实验结果与理论分析的对比显示在实验测量的范围内,理论预测的有效面积误差在1%以内,表明了这种理论分析方法的合理性。这种方法对进行有效面积的预测、空气弹簧的准确建模及进一步进行高精度的车高控制具有一定的指导意义。Abstract: Air springs with cord-rubber structure have the advantages of variable stiffness, lightweighting and better isolating effect, which have become the highlights of vehicle research in the current of new developing trends of automobile. However, as an important parameter, the effective area of air spring is lack of thorough predictive theory. A predictive analytical method for effective area of rolling lobe air spring for vehicles was put forward based on composite material mechanics and the geometrical characteristics of air spring bellow. A predictive formula of air spring effective area was given manifesting the influence of various parameters especially pressure inside bellow and air spring height on effective area. Experiments were conducted using mechanical test rig with certain air spring and the results of test fit the theory well. The errors of theoretical prediction can be less than 1% compared with experiment data. The method is useful for effective area prediction and accurate modeling as well as the height control of air suspension.
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表 1 橡胶和帘线力学参数
Table 1. Mechanical parameters of rubber and cord
Parameter Value Ef/MPa 2700 νf 0.3 Cf/% 33.2 Gf/MPa 1038 Em/MPa 2.0 νm 0.497 Cm/% 66.8 Gm/MPa 0.667 Notes: Ef, νf, Cf and Gf —Young’s modulus, Poisson’s ratio, volume fraction and shear modulus of cord material in composite; Em, νm, Cm and Gm—Equivalent Young’s modulus, Poisson’s ratio, volume fraction and shear modulus of rubber material in composite. 表 2 计算得到的帘线-橡胶复合材料表观力学值
Table 2. Apparent mechanical value of cord-rubber composite via computation
Parameter Value E1/MPa 897.7 E2/MPa 2.993 ν21 0.432 ν12 1.439×10−3 G12/MPa 0.998 Q11/MPa 898.3 Q12/MPa 1.293 Q22/MPa 2.995 Q66/MPa 0.998 Notes: E1, E2—Elastic modulus of laminate in 1st and 2nd principle direction; ν21, ν12—Poisson’s ratios of laminate; G12—Shear modulus of laminate in plane; Q11, Q12, Q21, Q22 and Q66—Elements in matrix Q in Eq.(11). 表 3 用于空气弹簧有效面积计算的参数取值
Table 3. Parameter values in effective area computation for air spring
Parameter Value α/(°) 50 R/10−2m 7.50 RD /10−2m 7.32 t/10−3m 2.00 δ 0.8 κ/10−2m −1.069 Δ/m2 0.01383 Notes: R—Bellow radius after pressure variation; RD —Initial bellow radius without obvious radial deformation; δ, κ and Δ—Experimental parameters defined in Eq.(27) and Eq.(29). 表 4 空气弹簧理论预测与实验数据的误差
Table 4. Errors between experimental data and theoretical prediction of air spring
Pressure/
105 Pae23/% e25/% e27/% e29/% 3 0.20 0.11 <0.01 0.39 4 0.04 0.56 0.11 0.03 5 0.31 0.51 0.10 0.16 6 0.18 0.35 0.14 0.29 7 0.22 0.25 <0.01 0.38 8 0.23 0.26 <0.01 0.46 Notes: e23, e25, e27 and e29—Errors between experimental data and theoretical prediction when height of air spring are 230 mm, 250 mm, 270 mm and 290 mm, respectively. -
[1] 郑明军, 林逸, 王海花, 等. 多曲囊式空簧非线性弹性特性研究[J]. 振动与冲击, 2009, 28(8):11-15. doi: 10.3969/j.issn.1000-3835.2009.08.003ZHENG Mingjun, LIN Yi, WANG Haihua, et al. Nonlinear stiffness characteristics of multilayer cystiform air spring[J]. Journal of Vibration and Shock,2009,28(8):11-15(in Chinese). doi: 10.3969/j.issn.1000-3835.2009.08.003 [2] 叶珍霞, 朱海潮, 鲁克明, 等. 囊式空簧刚度特性的非线性有限元法研究[J]. 振动与冲击, 2006(4):94-97. doi: 10.3969/j.issn.1000-3835.2006.04.026YE Zhenxia, ZHU Haichao, LU Keming, et al. Study on stiffness characteristics of air spring with nonlinear finite element method[J]. Journal of Vibration and Shock,2006(4):94-97(in Chinese). doi: 10.3969/j.issn.1000-3835.2006.04.026 [3] 成小霞, 李宝仁, 杨钢, 等. 囊式空簧载荷建模与实验研究[J]. 振动与冲击, 2014, 33(17):80-84.CHENG Xiaoxia, LI Baoren, YANG Gang, et al. Modeling and tests for load of a cystiform air spring[J]. Journal of Vibration and Shock,2014,33(17):80-84(in Chinese). [4] 胡德安, 甘亮亮, 丁飞, 等. 基于活塞形状改变的空簧特性仿真研究[J]. 计算机仿真, 2012, 29(1):331-334. doi: 10.3969/j.issn.1006-9348.2012.01.084HU De’an, GAN Liangliang, DING Fei, et al. Simulation of stiffness character of diaphragm air spring based on change piston contour[J]. Computer Simulation,2012,29(1):331-334(in Chinese). doi: 10.3969/j.issn.1006-9348.2012.01.084 [5] 夏仕朝. 空簧隔振系统载荷分配优化研究[D]. 西安: 西安科技大学, 2008.XIA Shichao. Optimization of load distribution of vibration isolation system of air spring[D]. Xi’an: Xi’an University of Science and Technology, 2008(in Chinese). [6] CHEN J J, YIN Z H, RAKHEJA S, et al. Theoretical modelling and experimental analysis of the vertical stiffness of a convoluted air spring including the effect of the stiffness of the bellows[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering,2018,232(4):547-561. doi: 10.1177/0954407017704589 [7] 杨泽彪. 车用膜式空簧承载特性建模与试验研究[D]. 广州: 华南理工大学, 2018.YANG Zebiao. Research on modeling and testing of bearing characteristics of vehicular rolling lobe air spring[D]. Guangzhou: South China University of Technology, 2018(in Chinese). [8] 冯元元. 半挂车电控空气悬架系统的建模与控制研究[D]. 广州: 华南理工大学, 2011.FENG Yuanyuan. Research on modeling and control of electrically controlled air suspension for semi-trailer[D]. Guangzhou: South China University of Technology, 2011(in Chinese). [9] PRASIL L, KRACIK V, FRYDRYCH D. Shape modelling of air bellows springs[C]//Proceedings of Algoritmy. Bratislava: Publishing House of STU, 2005: 142–149. [10] 罗贤光. 曲囊式橡胶空簧的一些力学问题[J]. 橡胶工业, 1997(4):36-40.LUO Xianguang. Mechanical problems of bellow-type rubber spring[J]. China Rubber Industry,1997(4):36-40(in Chinese). [11] 李滨, 陈无畏. 汽车膜式空簧的分析与计算[J]. 合肥工业大学学报(自然科学版), 2004, 27(10):1191-1195.LI Bin, CHEN Wuwei. Analysis and calculation of diaphragm air spring of an automobile[J]. Journal of Hefei University of Technology (Natural Science),2004,27(10):1191-1195(in Chinese). [12] QUAGLIA G, GUALA A. Evaluation and validation of an air spring analytical model[J]. International Journal of Fluid Power,2003,4(2):43-54. doi: 10.1080/14399776.2003.10781165 [13] LI X B, LI T. Research on vertical stiffness of belted air springs[J]. Vehicle System Dynamics,2013,51(11):1655-1673. doi: 10.1080/00423114.2013.819984 [14] LI X B, HE Y, LIU W Q, et al. Research on the vertical stiffness of a rolling lobe air spring[J]. Proceedings of the Institution of Mechanical Engineers Part F: Journal of Rail & Rapid Transit,2016,230(4):1172-1183. [15] 汪少华. 半主动空气悬架混杂系统的多模式切换控制研究[D]. 镇江: 江苏大学, 2013.WANG Shaohua. Research on multi-mode switching control of semi-active air suspension hybrid system[D]. Zhen-jiang: Jiangsu University, 2013(in Chinese). [16] FOX M N, ROEBUCK R L, CEBON D, et al. Modelling rolling-lobe air springs[J]. International Journal of Heavy Vehicle Systems,2007,14(3):254-270. doi: 10.1504/IJHVS.2007.015603 [17] CHANG F. LU Z H. Air suspension performance analysis using nonlinear geometrical parameters model[J]. SAE Technical Paper,2007,1:9. [18] ZHU H, YANG J, ZHANG Y, et al. Nonlinear dynamic model of air spring with a damper for vehicle ride comfort[J]. Nonlinear Dynamics,2017,89(2):1545-1568. doi: 10.1007/s11071-017-3535-9 [19] QUAGLIA G, SORLI M. Air suspension dimensionless analysis and design procedure[J]. Vehicle System Dynamics,2001,35(6):443-475. doi: 10.1076/vesd.35.6.443.2040 [20] NIETO A J, MORALES A L, GONZÁLEZ A, et al. An analytical model of pneumatic suspensions based on an experimental characterization[J]. Journal of Sound& Vibration,2008,313(1-2):290-307. [21] 曾亮铭. 基于主动悬架的汽车平顺性与操纵稳定性协调控制[D]. 长沙: 湖南大学, 2017.ZENG Liangming. Coordinated control of vehicle ride comfort and handling stability based on active suspension[D]. Changsha: Hunan University, 2017(in Chinese). [22] 沈观林, 胡更开. 复合材料力学[M]. 2版. 北京: 清华大学出版社, 2013.SHEN Guanlin, HU Gengkai. Mechanics of composite materials[M]. 2nd edition. Beijing: Tsinghua University Press, 2013(in Chinese). [23] 徐芝纶. 弹性力学[M]. 5版. 北京: 高等教育出版社, 2016.XU Zhilun. Elasticity[M]. 5th edition. Beijing: Higher Education Press, 2016(in Chinese). [24] 中国国家标准化管理委员会. 锦纶66浸胶帘子布: GB/T 9101—2017[S]. 北京: 中国标准出版社, 2017.Standardization Administration of the People’s Republic of China. Polyamide 66 dipped tyre cord fabric: GB/T 9101—2017[S]. Beijing: China Standards Press, 2017(in Chinese). [25] 李雪冰. 空簧刚度的精确仿真与解析计算研究[D]. 北京: 清华大学, 2020.LI Xuebing. Research on accurate simulation and analytical calculation of air spring stiffness[D]. Beijing: Tsinghua University, 2020(in Chinese). [26] 李雪冰, 曹金凤, 危银涛. 空簧多变过程的有限元模拟[J]. 工程力学, 2019, 36(2):224-228. doi: 10.6052/j.issn.1000-4750.2017.12.0925LI Xuebing, CAO Jinfeng, WEI Yintao. Finite element modelling on polytropic process of air springs[J]. Engineering Mechanics,2019,36(2):224-228(in Chinese). doi: 10.6052/j.issn.1000-4750.2017.12.0925