Optimization method of frictional braking force distribution for integrated system of electromagnetic and frictional braking of car
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摘要: 分析了轿车电磁与摩擦制动集成系统的结构与工作原理, 推导了轿车前后轴利用附着系数的计算公式。以ECE R13制动法规与电磁制动器设计要求为约束条件, 以轿车前后轴实际利用附着系数与理想状态制动强度差值的平方和最小为目标函数, 以MATLAB优化工具箱为计算工具, 建立了轿车电磁与摩擦制动集成系统摩擦制动力分配优化方法, 计算了不同工况下的摩擦制动力分配最优值。计算结果表明: 当制动强度分别为0.1、0.2、0.3、0.4、0.5、0.6、0.7、0.8时, 优化前的目标函数值分别为0.03、0.05、0.07、0.07、0.08、0.07、0.06、0.04, 优化后的的目标函数值分别为0.00、0.00、0.00、0.00、0.00、0.00、0.01、0.01, 优化后, 目标函数值明显减小, 轿车前后轴利用附着系数曲线更靠近理想曲线, 且均在ECE R13制动法规控制曲线的下方, 因此, 提出的优化方法满足ECE R13制动法规的要求, 轿车制动稳定性得到提高。Abstract: The structure and working principle of integrated system of the electromagnetic and frictional braking for car were analyzed.The calculation formula of utilization adhesion coefficient for front and rear axles was derived.The ECE R13 braking regulation and the design requirement of electromagnetic braking were taken as constraint conditions, the minimum square sum of differences between the actual curve of utilization adhesion coefficient and the braking strength of ideal condition for front and rear axles was taken as objective function, MATLAB optimization toolbox was employed, the optimization method of frictional braking force distribution for the integrated system of electromagnetic and frictional braking was established, and the optimal values of frictional braking force distribution under different conditions were calculated.Calculation result indicates when the braking strength is 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8respectively, the value of objective function before optimization is 0.03, 0.05, 0.07, 0.07, 0.08, 0.07, 0.06, 0.04 respectively, while the value of objective function after optimization is 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.01, 0.01 respectively.After optimization, the values of objective function reduce obviously, the curve of utilization adhesion coefficient for front and rearaxles is close to the ideal curve and is below the control curve of ECE R13 braking regulation, so the proposed optimization method satisfies the requirement of ECE R13 braking regulation, and the braking stability of car also improves.
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表 1 技术参数
Table 1. Technological parameters
表 2 优化前后K值的对比
Table 2. Comparison between original and optimized K values
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[1] 赵迎生, 何仁, 王永涛, 等. 利用电涡流缓速器调节车辆制动稳定性[J]. 江苏大学学报: 自然科学版, 2007, 28(4): 309-311. doi: 10.3969/j.issn.1671-7775.2007.04.009ZHAO Ying-sheng, HE Ren, WANG Yong-tao, et al. Adjusting vehicle's braking stability using eddy current retarder[J]. Journal of Jiangsu University: Natural Science Edition, 2007, 28(4): 309-311. (in Chinese) doi: 10.3969/j.issn.1671-7775.2007.04.009 [2] 何仁, 刘存香. 摩擦式制动器与非接触轮边缓速器集成系统仿真分析[J]. 南京理工大学学报, 2011, 35(5): 590-594. doi: 10.3969/j.issn.1005-9830.2011.05.002HE Ren, LIU Cun-xiang. Simulation of integrated system of frictional brake and contactless wheel retarder[J]. Journal of Nanjing University of Science and Technology, 2011, 35(5): 590-594. (in Chinese) doi: 10.3969/j.issn.1005-9830.2011.05.002 [3] 何仁, 衣丰艳. 电涡流缓速器性能特性评价方法[J]. 中国公路学报, 2006, 19(5): 114-118. doi: 10.3321/j.issn:1001-7372.2006.05.021HE Ren, YI Feng-yan. Evaluation method of performance characteristic of eddy current retarder[J]. China Journal of Highway and Transport, 2006, 19(5): 114-118. (in Chinese) doi: 10.3321/j.issn:1001-7372.2006.05.021 [4] ANWAR S. Predictive yaw stability control of a brake-by-wire equipped vehicle via eddy current braking[C]∥IEEE. Proceedings of the 2007 American Control Conference. New York: IEEE, 2007: 2308-2313. [5] ANWAR S. Generalized predictive control of yaw dynamics of a hybrid brake-by-wire equipped vehicle[J]. Mechatronics, 2005, 15(9): 1089-1108. doi: 10.1016/j.mechatronics.2005.06.006 [6] 张永辉, 于良耀, 宋健, 等. 基于减速度参数的电子制动力分配控制算法[J]. 江苏大学学报: 自然科学版, 2010, 31(6): 645-650. https://www.cnki.com.cn/Article/CJFDTOTAL-JSLG201006008.htmZHANG Yong-hui, YU Liang-yao, SONG Jian, et al. Control algorithm of electronic braking force distribution based on deceleration parameters[J]. Journal of Jiangsu University: Natural Science Edition, 2010, 31(6): 645-650. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSLG201006008.htm [7] 何仁, 陈庆樟. 汽车制动能量再生系统制动力分配研究[J]. 兵工学报, 2009, 30(2): 205-208. doi: 10.3321/j.issn:1000-1093.2009.02.016HE Ren, CHEN Qing-zhang. Research on braking force distribution of regenerative braking system of car[J]. Acta Armamentarii, 2009, 30(2): 205-208. (in Chinese) doi: 10.3321/j.issn:1000-1093.2009.02.016 [8] 许沧粟, 于洪波. 铰接车辆电涡流缓速器联合制动系统研究[J]. 汽车工程, 2006, 28(4): 366-369. doi: 10.3321/j.issn:1000-680X.2006.04.012XU Cang-su, YU Hong-bo. A research on associated braking system for articulated vehicles with eddy retarder[J]. Automotive Engineering, 2006, 28(4): 366-369. (in Chinese) doi: 10.3321/j.issn:1000-680X.2006.04.012 [9] 何仁, 何建清. 装用电涡流缓速器的汽车制动性能分析[J]. 江苏大学学报: 自然科学版, 2004, 25(1): 29-32. doi: 10.3969/j.issn.1671-7775.2004.01.008HE Ren, HE Jian-qing. Analysis on braking ability of automobile equipped with eddy current retarder[J]. Journal of Jiangsu University: Natural Science Edition, 2004, 25(1): 29-32. (in Chinese) doi: 10.3969/j.issn.1671-7775.2004.01.008 [10] 张焱, 刘成晔, 何仁, 等. 电涡流缓速器对汽车制动力利用率的影响[J]. 交通运输工程学报, 2011, 11(6): 62-67. http://transport.chd.edu.cn/article/id/201106010ZHANG Yan, LIU Cheng-ye, HE Ren, et al. Influence of eddy current retarder on vehicle braking force utilization[J]. Journal of Traffic and Transportation Engineering, 2011, 11(6): 62-67. (in Chinese) http://transport.chd.edu.cn/article/id/201106010 [11] 赵迎生, 何仁, 王永涛. 恒速下坡汽车联合制动系统的制动力模糊分配[J]. 中国机械工程, 2008, 19(8): 1003-1007. doi: 10.3321/j.issn:1004-132X.2008.08.028ZHAO Ying-sheng, HE Ren, WANG Yong-tao. Fuzzy distribution of braking forces in united braking system of downhill automobile at constant speed[J]. China Mechanical Engineering, 2008, 19(8): 1003-1007. (in Chinese) doi: 10.3321/j.issn:1004-132X.2008.08.028 [12] 杨莉玲. 液压盘式制动器建模与仿真分析[D]. 武汉: 武汉理工大学, 2009.YANG Li-ling. Modeling and simulation of the hydraulic disk brake[D]. Wuhan: Wuhan University of Technology, 2009. (in Chinese) [13] 刘存香, 何仁. 电磁制动与摩擦制动集成系统测试台架设计及试验研究[J]. 汽车技术, 2012(1): 51-55. doi: 10.3969/j.issn.1000-3703.2012.01.013LIU Cun-xiang, HE Ren. Test bench design and experimental study of integrated system of electromagnetic braking and friction braking[J]. Automobile Technology, 2012(1): 51-55. (in Chinese) doi: 10.3969/j.issn.1000-3703.2012.01.013 [14] 余强, 陈荫三, 马建, 等. 发动机制动、排气制动与缓速器联合作用时的非连续线性控制系统的研究[J]. 中国公路学报, 2005, 18(1): 117-121. doi: 10.3321/j.issn:1001-7372.2005.01.024YU Qiang, CHEN Yin-san, MA Jian, et al. Study of non-continuous linear control system of combining action with engine brake, exhaust brake and retarder[J]. China Journal of Highway and Transport, 2005, 18(1): 117-121. (in Chinese) doi: 10.3321/j.issn:1001-7372.2005.01.024 [15] 马建, 陈荫三, 余强, 等. 缓速器在汽车高速行驶状况下的应用研究[J]. 中国公路学报, 1999, 12(3): 105-111. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL199903015.htmMA Jian, CHEN Yin-san, YU Qiang, et al. Application research on retarder used in automobile at high speed[J]. China Journal of Highway and Transport, 1999, 12(3): 105-111. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL199903015.htm [16] GAY S E. Contactless magnetic brake for automotive applications[D]. Houston: Texas College of Agriculture and Mechanics, 2005. [17] EDWARDS J D, JAYAWANT B V, DAWSON W R C, et al. Permanent-magnet linear eddy-current brake with a nonmagnetic reaction plate[J]. IEE Proceedings-Electric Power Applications, 1999, 146(6): 627-631. doi: 10.1049/ip-epa:19990574 [18] 余强, 陈荫三, 马建, 等. 客车发动机制动与缓速器联合作用的制动能力[J]. 长安大学学报: 自然科学版, 2004, 24(2): 87-90. doi: 10.3321/j.issn:1671-8879.2004.02.021YU Qiang, CHEN Yin-san, MA Jian, et al. Braking ability of engine brake and retarder brake when bus downhill[J]. Journal of Chang'an University: Natural Science Edition, 2004, 24(2): 87-90. (in Chinese) doi: 10.3321/j.issn:1671-8879.2004.02.021 [19] 王亚晴, 张代胜, 沈国清. 汽车制动力分配比的优化设计与仿真计算[J]. 合肥工业大学学报: 自然科学版, 2005, 28(11): 1493-1496. https://www.cnki.com.cn/Article/CJFDTOTAL-HEFE200511008.htmWANG Ya-qing, ZHANG Dai-sheng, SHEN Guo-qing. Optimizing design and simulative calculation of braking force distribution ratio of vehicles[J]. Journal of Hefei University of Technology: Natural Science, 2005, 28(11): 1493-1496. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HEFE200511008.htm [20] 吕奉阳. 纯电动客车再生制动与气压制动协调控制策略研究[D]. 长春: 吉林大学, 2009.LU Feng-yang. Study on coordinating control strategy of regenerative braking and pneumatic braking for electric bus[D]. Changchun: Jilin University, 2009. (in Chinese) [21] 陈一鸣. 混合动力电动汽车(HEV)再生制动与ABS控制策略研究[D]. 沈阳: 东北大学, 2008.CHEN Yi-ming. Study on control strategy of hybrid electric vehicle and anti-lock braking system[D]. Shenyang: Northeastern University, 2008. (in Chinese) [22] 何仁, 俞剑波, 王润才. 电动汽车混合制动系统控制策略的改进[J]. 江苏大学学报: 自然科学版, 2013, 34(2): 125-130. doi: 10.3969/j.issn.1671-7775.2013.02.001HE Ren, YU Jian-bo, WANG Run-cai. Improvement of control strategy in hybrid brake system of electric vehicle[J]. Journal of Jiangsu University: Natural Science Edition, 2013, 34(2): 125-130. (in Chinese) doi: 10.3969/j.issn.1671-7775.2013.02.001 [23] 刘志强, 过学迅. 纯电动汽车电液复合再生制动控制[J]. 中南大学学报: 自然科学版, 2011, 42(9): 2687-2691. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201109026.htmLIU Zhi-qiang, GUO Xue-xun. Electronic-hydraulic-compound regenerativev braking control for electric vehicles[J]. Journal of Central South University: Science and Technolgy, 2011, 42(9): 2687-2691. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201109026.htm [24] 赵国柱. 电动汽车再生制动稳定性研究[D]. 南京: 南京航空航天大学, 2006.ZHAO Guo-zhu. Research on braking stability of regenerative braking system in EV and HEV[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2006. (in Chinese) [25] 何仁, 刘存香, 李楠. 轿车电磁制动与摩擦制动集成系统的模糊控制[J]. 机械工程学报, 2010, 46(24): 83-87. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201024014.htmHE Ren, LIU Cun-xiang, LI Nan. Fuzzy control of the integrated system of electromagnetic brake and friction brake of car[J]. Journal of Mechanical Engineering, 2010, 46(24): 83-87. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201024014.htm [26] 何仁, 胡东海, 张端军. 汽车电磁制动技术的研究与进展[J]. 汽车安全与节能学报, 2013, 4(3): 202-214. doi: 10.3969/j.issn.1674-8484.2013.03.002HE Ren, HU Dong-hai, ZHANG Duan-jun. Research and development of automobile electromagnetic brake technology for commercial vehicles[J]. Journal of Automotive Safety and Energy, 2013, 4(3): 202-214. (in Chinese) doi: 10.3969/j.issn.1674-8484.2013.03.002 [27] 龚贤武, 张丽君, 马建, 等. 基于制动稳定性要求的电动汽车制动力分配[J]. 长安大学学报: 自然科学版, 2014, 34(1): 103-108. https://www.cnki.com.cn/Article/CJFDTOTAL-XAGL201401018.htmGONG Xian-wu, ZHANG Li-jun, MA Jian, et al. Braking force distribution of electric vehicles based on braking stability[J]. Journal of Chang'an University: Natural Science Edition, 2014, 34(1): 103-108. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XAGL201401018.htm [28] JANG S M, LEE S H, JEONG S S. Characteristic analysis of eddy-current brake system using the linear Halbach array[J]. IEEE Transactions on Magnetics, 2002, 38(5): 2994-2996. doi: 10.1109/TMAG.2002.803191 [29] SHARIF S, FAIZ J, SHARIF K. Performance analysis of a cylindrical eddy current brake[J]. IET Eelctric Power Application, 2012, 6(9): 661-668. doi: 10.1049/iet-epa.2012.0006 [30] 马建, 陈荫三, 余强, 等. 基于缓速器制动的汽车停车距离控制研究[J]. 中国公路学报, 2003, 16(1): 108-112. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL200301026.htmMA Jian, CHEN Yin-san, YU Qiang, et al. Distance control for automotive's stopping with retarder[J]. China Journal of Highway and Transport, 2003, 16(1): 108-112. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL200301026.htm [31] 赵迎生, 赵又群, 魏超. 汽车联合制动系统制动力分配系数优化[J]. 农业机械学报, 2009, 40(10): 14-17. https://www.cnki.com.cn/Article/CJFDTOTAL-NYJX200910005.htmZHAO Ying-sheng, ZHAO You-qun, WEI Chao. Optimization of braking force distribution parameter of united brake system of automobile[J]. Journal of Agricultural Machinery, 2009, 40(10): 14-17. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-NYJX200910005.htm [32] 何仁, 刘学军, 刘存香. 汽车电磁-液压复合制动技术研究进展[J]. 中国公路学报, 2014, 27(11): 109-119. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201411018.htmHE Ren, LIU Xue-jun, LIU Cun-xiang. Research progress in electromagnetic-hydraulic hybrid brake technology[J]. China Journal of Highway and Transport, 2014, 27(11): 109-119. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201411018.htm [33] 马建, 陈荫三, 余强, 等. 汽车电涡流缓速器供耗电特性研究[J]. 长安大学学报: 自然科学版, 2002, 22(3): 64-66. https://www.cnki.com.cn/Article/CJFDTOTAL-XAGL200203016.htmMA Jian, CHEN Yin-san, YU Qiang, et al. Power characteristics of vehicle eddy-current-retarder[J]. Journal of Chang'an University: Natural Science Edition, 2002, 22(3): 64-66. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XAGL200203016.htm