趙玉霞，林建飛，鄭泉

(1.滁州職業(yè)技術(shù)學(xué)院，安徽滁州 239000；2.安徽農(nóng)業(yè)大學(xué) 工學(xué)院，安徽合肥 230036)

基于多學(xué)科設(shè)計(jì)法的汽車雙橫臂獨(dú)立懸架優(yōu)化設(shè)計(jì)

趙玉霞1，林建飛2，鄭泉2

(1.滁州職業(yè)技術(shù)學(xué)院，安徽滁州 239000；2.安徽農(nóng)業(yè)大學(xué) 工學(xué)院，安徽合肥 230036)

提出一種基于多學(xué)科優(yōu)化設(shè)計(jì)的雙橫臂獨(dú)立懸架優(yōu)化設(shè)計(jì)方法。以某款汽車的雙橫臂獨(dú)立懸架為研究對(duì)象，構(gòu)建主銷后傾角最小、外傾角和前束角變化量最小的多目標(biāo)優(yōu)化函數(shù)；集成ISIGHT和ADAMS/CAR軟件，并對(duì)其進(jìn)行多學(xué)科優(yōu)化設(shè)計(jì)。優(yōu)化結(jié)果表明：優(yōu)化后主銷后傾角相應(yīng)減小2°，外傾角和前束角變化范圍均減少0.45°和0.5°。經(jīng)試驗(yàn)驗(yàn)證，懸架轉(zhuǎn)向輕便性和綜合性能得到改善。

懸架；雙橫臂；遺傳算法；多學(xué)科優(yōu)化

雙橫臂式獨(dú)立懸架廣泛應(yīng)用于現(xiàn)代汽車上，其運(yùn)動(dòng)特性直接影響汽車操縱穩(wěn)定性、轉(zhuǎn)向輕便性和輪胎使用壽命等[1-2]。國內(nèi)外諸多學(xué)者在雙橫臂懸架優(yōu)化設(shè)計(jì)方面進(jìn)行了大量的研究[3-6]，文獻(xiàn)[7]利用多目標(biāo)遺傳算法對(duì)輪胎滑移和傾角的變化進(jìn)行優(yōu)化，得出雙橫臂懸架輪胎滑移和外傾角的變化關(guān)系及其懸架導(dǎo)向桿系參數(shù)；文獻(xiàn)[8]采用統(tǒng)一目標(biāo)法將多目標(biāo)函數(shù)轉(zhuǎn)化為單目標(biāo)函數(shù)，對(duì)前輪定位參數(shù)進(jìn)行了優(yōu)化。

多學(xué)科設(shè)計(jì)優(yōu)化方法(multidisciplinary design optimization，MDO)作為一種新型的優(yōu)化設(shè)計(jì)方法已經(jīng)在多種行業(yè)得到應(yīng)用，該方法是充分利用和探索系統(tǒng)中相互作用的協(xié)同機(jī)制來設(shè)計(jì)復(fù)雜系統(tǒng)和子系統(tǒng)的方法論，充分考慮各子系統(tǒng)間的耦合關(guān)系，并通過協(xié)調(diào)各子系統(tǒng)間的關(guān)系尋求系統(tǒng)級(jí)的整體最優(yōu)解[9-11]。

本文以某款汽車的雙橫臂獨(dú)立懸架為研究對(duì)象，建立主銷后傾角最小、外傾角和前束角變化量最小的目標(biāo)函數(shù)，基于多學(xué)科優(yōu)化設(shè)計(jì)方法，集成ISIGHT、 ADAMS/CAR環(huán)境下構(gòu)建雙橫臂獨(dú)立懸架多學(xué)科優(yōu)化平臺(tái)，對(duì)其進(jìn)行優(yōu)化設(shè)計(jì)。

1 雙橫臂懸架運(yùn)動(dòng)特性分析

圖1 雙橫臂式獨(dú)立懸架空間結(jié)構(gòu)簡圖

雙橫臂式獨(dú)立懸架空間拓?fù)浣Y(jié)構(gòu)如圖1所示，圖中OAB為下擺臂，繞軸線OA轉(zhuǎn)動(dòng)；MNK為上擺臂，繞軸線MN轉(zhuǎn)動(dòng)；K(xK,yK,zK)、B(xB,yB,zB)點(diǎn)分別為上下球節(jié)點(diǎn)，BK為主銷軸線；G(xG,yG,zG)點(diǎn)為車輪中心，車輪軸線GJ交BK于J(xJ,yJ,zJ)點(diǎn)；P(xP,yP,zP)點(diǎn)為輪胎接地點(diǎn)；轉(zhuǎn)向節(jié)臂DF交BK于F點(diǎn)，DF⊥BK；E、D點(diǎn)分別為橫拉桿內(nèi)外球節(jié)點(diǎn)。運(yùn)用空間機(jī)構(gòu)運(yùn)動(dòng)學(xué)原理，對(duì)懸架進(jìn)行運(yùn)動(dòng)學(xué)分析計(jì)算，為懸架運(yùn)動(dòng)軌跡的研究提供理論參照[12-14]。前輪定位參數(shù)表達(dá)式為：主銷內(nèi)傾角α=arctan〔(yK-yB)/(zK-zB)〕，主銷后傾角β=arctan〔(xK-xB)/(zK-zB)〕，前輪外傾角γ=arctan〔(yP-yG)/(zP-zG)〕,前輪前束量Δ=arctan〔(xG-xJ)/(yG-yJ)〕。

2 雙橫臂獨(dú)立懸架多學(xué)科優(yōu)化

2.1 設(shè)計(jì)變量

圖2 雙橫臂懸架運(yùn)動(dòng)學(xué)模型

基于ADAMS/CAR軟件建立雙橫臂懸架運(yùn)動(dòng)學(xué)模型如圖2所示。由于設(shè)計(jì)變量較多(6個(gè)關(guān)鍵點(diǎn)，總共18個(gè)設(shè)計(jì)變量)，基于靈敏度分析方法對(duì)設(shè)計(jì)變量進(jìn)行分析，設(shè)計(jì)變量約束上下變動(dòng)，設(shè)計(jì)響應(yīng)目標(biāo)為主銷后傾角、外傾角和前束角，進(jìn)行512次部分迭代計(jì)算，計(jì)算結(jié)束后，得出靈敏度分析結(jié)果，如表1所示。在K模式下，利用靈敏度分析方法，在模型中依次調(diào)整每個(gè)因素并進(jìn)行仿真分析，結(jié)果表明下擺臂后點(diǎn)(hpl_lca_rear)、上擺臂前點(diǎn)(hpl_uca_front)對(duì)懸架相關(guān)運(yùn)動(dòng)學(xué)參數(shù)的優(yōu)化作用不明顯，故不予考慮。整理表1靈敏度分析結(jié)果得出對(duì)響應(yīng)目標(biāo)變化影響較大的硬點(diǎn)坐標(biāo)為：下擺臂前點(diǎn)(hpl_lca_front)y和z坐標(biāo)；下擺臂外點(diǎn)(hpl_lca_outer)x坐標(biāo)；上擺臂外點(diǎn)(hpl_uca_outer)x、y和z坐標(biāo)；上擺臂后點(diǎn)(hpl_uca_rear)y和z坐標(biāo)，共4個(gè)點(diǎn)的8個(gè)方向坐標(biāo)為設(shè)計(jì)變量。

表1 懸架關(guān)鍵點(diǎn)靈敏度分析表

2.2 目標(biāo)函數(shù)

懸架系統(tǒng)運(yùn)動(dòng)關(guān)系復(fù)雜、子系統(tǒng)之間相互影響，單純基于某一項(xiàng)性能的優(yōu)化往往會(huì)導(dǎo)致另一項(xiàng)性能的降低[15-16]。因此，在要求主銷后傾角減小的同時(shí)，需滿足前束角和外傾角的變化量最小，此時(shí)主銷后傾角、前束角和外傾角的多目標(biāo)優(yōu)化問題，使用以下公式進(jìn)行優(yōu)化：

F1(Xβ)=min{Xβi},X1∈Xβ，

(1)

(2)

(3)

F(X)=ω1F1(Xβ)+ω2F2(XΔ)+ω3F3(Xγ)，

(4)

式中：n為仿真迭代總次數(shù)，n=256；Xβ、XΔ、Xγ分別為主銷后傾角、前束角和外傾角仿真計(jì)算值；X1、X2、X3分別為設(shè)計(jì)狀態(tài)下主銷后傾角、前束角和外傾角初值，X1=5.3、X2=0.1、X3=-1.0；F1(Xβ)、F2(XΔ)、F3(Xγ)分別為主銷后傾角、前束角和外傾角對(duì)應(yīng)目標(biāo)函數(shù)，設(shè)計(jì)狀態(tài)下邊界條件為0≤F1(Xβ)≤10、-1.0≤F2(XΔ)≤10、-3.0≤F3(Xγ)≤-0.5；F(X)為多目標(biāo)優(yōu)化函數(shù)，定義為F(X)函數(shù)值越小越好；ω1、ω2、ω3為權(quán)重系數(shù)，通過引入層次分析法理論[17-19]，在遺傳算法的編碼過程中對(duì)各變量進(jìn)行權(quán)重賦值，使得對(duì)多目標(biāo)優(yōu)化函數(shù)影響較大的目標(biāo)函數(shù)賦予較大的權(quán)重，從而更好地發(fā)揮各組成部分的作用，通過賦值計(jì)算得出ω1=0.4，ω2=ω3=0.3為最優(yōu)權(quán)重系數(shù)。

3 多學(xué)科優(yōu)化設(shè)計(jì)

圖3 ISIGHT集成ADAMS/CAR

利用多目標(biāo)遺傳算法對(duì)相關(guān)硬點(diǎn)空間坐標(biāo)進(jìn)行多學(xué)科優(yōu)化，以雙橫臂獨(dú)立懸架模型為輸入，在ISIGHT軟件中集成ADAMS對(duì)輸入進(jìn)行解析，創(chuàng)建設(shè)計(jì)變量之間的映射關(guān)系，經(jīng)ADAMS求解器計(jì)算分析并生成輸出文件，再經(jīng)ISIGHT解析完成一次循環(huán)[20-22]，如圖3所示。優(yōu)化前后設(shè)計(jì)變量對(duì)比如表2所示，優(yōu)化前后主銷后傾角、前輪外傾角、前束角變化如圖4所示。

表2 硬點(diǎn)坐標(biāo)參數(shù)優(yōu)化前后對(duì)比

a)主銷后傾角隨輪跳變化曲線 b)前束角隨輪跳變化曲線 c)前輪外傾角隨輪跳變化曲線圖4 懸架優(yōu)化前后運(yùn)動(dòng)特性對(duì)比

由表2可知：下擺臂前點(diǎn)右移10 mm,下移10 mm,下擺臂外點(diǎn)后移10 mm,上擺臂外點(diǎn)前移10 mm,左移10 mm,下移10 mm;上擺臂后點(diǎn)右移10 mm,下移10 mm。

優(yōu)化結(jié)果表明：優(yōu)化后主銷后傾角變小，外傾角和前束量變化范圍較優(yōu)化前都有所改善。優(yōu)化前前輪外傾角變化范圍-2.1°～-0.6°，變化量1.5°；優(yōu)化后變化范圍-0.8°～-1.85°，變化量1.05°，變化量減小了0.45°；優(yōu)化前前束角變化范圍-0.15°～0.75°，變化量0.9°；優(yōu)化后變化范圍0°～0.4°，變化量0.4°，變化量減小了0.5°，在輪跳過程中，一般要求前束量變化范圍越小越好；為避免轉(zhuǎn)向沉重，汽車主銷后傾角不宜過大，優(yōu)化后主銷后傾角相應(yīng)減小了2°，變化范圍在2.2°～4.0°。經(jīng)K&C試驗(yàn)臺(tái)驗(yàn)證，如圖5所示，主銷后傾角滿足設(shè)計(jì)需求，懸架轉(zhuǎn)向輕便性得到了有效提高。

a)主銷后傾角隨輪跳變化曲線 b)前束角隨輪跳變化曲線 c)外傾角隨輪跳變化曲線圖5 雙橫臂懸架K&C試驗(yàn)數(shù)據(jù)圖

4 結(jié)語

構(gòu)建了基于多學(xué)科優(yōu)化設(shè)計(jì)方法的雙橫臂式獨(dú)立懸架多目標(biāo)優(yōu)化模型，集成ISIGHT和ADAMS軟件對(duì)其進(jìn)行優(yōu)化設(shè)計(jì)；優(yōu)化后主銷后傾角變小，前束角變化量和外傾角變化量減小并經(jīng)試驗(yàn)驗(yàn)證，提高轉(zhuǎn)向輕便性的同時(shí)改善了懸架綜合性能，實(shí)現(xiàn)了預(yù)期目標(biāo)。

[1]陳家瑞.汽車構(gòu)造(下冊(cè))[M].北京：機(jī)械工業(yè)出版社,2006.

[2]余志生.汽車?yán)碚揫M].3版.北京：機(jī)械工業(yè)出版社,2005.

[3]MAHMOOD-KALEIBAR M,JAVANSHIR I,ADSADI K,et al.Optimization of suspension system of off-road vehicle for vehicle performance improvement[J].Journal of Central South University of Technology,2013,20(4):902-910.

[4]陳黎卿,王啟瑞,陳無畏,等.基于ADAMS的雙橫臂扭桿獨(dú)立懸架操縱穩(wěn)定性分析[J].合肥工業(yè)大學(xué)學(xué)報(bào)(自然科學(xué)版),2005,28(4):341-345. CHEN Liqing,WANG Qirui,CHEN Wuwei,et al.Analysis of handling stability of torsion-bar double wishbone independent suspension based on ADAMS software[J].Journal of Hefei University of Technology(Natural Science),2005,28(4):341-345.

[5]胡芳,陳無畏.基于非線性模型的汽車空氣懸架系統(tǒng)模糊控制研究[J].合肥工業(yè)大學(xué)學(xué)報(bào)(自然科學(xué)版),2005,28(7):772-777. HU Fang,CHEN Wuwei.Fuzzy control research on automotive air suspension system based on the non-linear model[J].Journal of Hefei University of Technology(Natural Science),2005,28(7):772-777.

[6]胡艷云，干年妃，劉良.某轎車的雙橫臂獨(dú)立懸架優(yōu)化設(shè)計(jì)[J].計(jì)算機(jī)仿真，2015，32(1)：174-178,214. HU Yanyun,GAN Nianfei,LIU Liang.Optimization of double wishbone suspension for car[J].Computer Simulation,2015,32(1):174-178，214.

[7]莫旭輝,鐘志華,韓旭,等.基于多目標(biāo)優(yōu)化的菱形車雙橫臂懸架運(yùn)動(dòng)學(xué)分析[J].中國機(jī)械工程,2009(3):374-377. MO Xuhui,ZHONG Zhihua,HAN Xu,et al.Kinematics analysis of double wishbone suspension based on multi-objective optimizaton[J].China Mechanical Engineering,2009(3):374-377.

[8]李瑜婷,趙治國,章桐.基于ADAMS的雙橫臂懸架性能多目標(biāo)優(yōu)化研究[J].機(jī)械設(shè)計(jì)與制造工程,2009,38(17):30-34. LI Yuting，ZHAO Zhiguo,ZHANG Tong.The ADAMS-based multi-objects optimization of double beams vehicle suspension[J].Machine Design and Manufacturing Engineering,2009,38(17):30-34.

[9]王平,鄭松林,吳光強(qiáng).基于協(xié)同優(yōu)化和多目標(biāo)遺傳算法的車身結(jié)構(gòu)多學(xué)科優(yōu)化設(shè)計(jì)[J].機(jī)械工程學(xué)報(bào),2011,47(2):102-108. WANG Ping,ZHENG Songlin,WU Guangqiang.Multi-disciplinary design optimization of vehicle body structure based on collaborative optimization and multi-objective genetic algorithm[J].Journal of Mechanical Engineering,2011,47(2):102-108.

[9]姜武華.多學(xué)科優(yōu)化方法在汽車底盤設(shè)計(jì)中的應(yīng)用研究[D].合肥：合肥工業(yè)大學(xué),2014. JIANG Wuhua.Application of multi-discipline design optimization in automotive chassis[D].Heifei:Hefei University of Technology,2014.

[11]趙婷.汽車轉(zhuǎn)向與懸架集成系統(tǒng)多學(xué)科設(shè)計(jì)方法研究[D].南京：南京航空航天大學(xué),2014. ZHAO Ting.Multidisciplinary design method research of automotive steering and suspension integrated system[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2014.

[12]楊紅強(qiáng),翁建生.雙橫臂獨(dú)立懸架的仿真與優(yōu)化研究[J].機(jī)械科學(xué)與技術(shù),2011,30(10):1683-1687. YANG Hongqiang,WENG Jiansheng.Simulation and optimization of the double wishbone suspension[J].Mechanical Science and Technology for Aerospace Engineering,2011,30(10):1683-1687.

[13]陳黎卿,陳無畏,何欽章.雙橫臂扭桿獨(dú)立懸架多目標(biāo)遺傳優(yōu)化設(shè)計(jì)[J].中國機(jī)械工程,2007,18(17):2122-2125. CHEN Liqing,CHEN Wuwei,HE Qinzhang.Multi-objective heredity optimization design of torsion-bar wishbone suspension[J].China Mechanical Engineering,2007,18(17):2122-2125.

[14]何磊,陳辛波,黃露,等.雙橫臂獨(dú)立懸架導(dǎo)向機(jī)構(gòu)優(yōu)化仿真及參數(shù)化臺(tái)架實(shí)驗(yàn)驗(yàn)證[J].機(jī)械科學(xué)與技術(shù),2015,34(2):282-286. HE Lei,CHEN Xinbo,HUANG Lu,et al.Simulation optimization of double wishbone independent suspension guide mechanism and parametric bench test[J].Mechanical Science and Technology for Aerospace Engineering,2015,34(2):282-286.

[15]王軍,姜青松,任啟豐.基于遺傳算法的客車動(dòng)力性與經(jīng)濟(jì)性的優(yōu)化匹配[J].山東交通學(xué)院學(xué)報(bào),2012,20(4):5-8. WANG Jun,JIANG Qingsong,REN Qifeng.Optimal matching of coach power performance and economy based on genetic algorithm[J].Journal of Shandong Jiaotong University,2012,20(4):5-8.

[16]陳林,蔣德云,李杰,等.某輕型卡車駕駛室翻轉(zhuǎn)機(jī)構(gòu)的結(jié)構(gòu)設(shè)計(jì)與優(yōu)化[J].山東交通學(xué)院學(xué)報(bào),2013,21(2):9-13. CHEN Lin,JIANG Deyun,LI Jie,et al.The design and optimization of the tilting mechanism for the cab of a light truck[J].Journal of Shandong Jiaotong University,2013,21(2):9-13.

[17]廖紅強(qiáng),邱勇,楊俠,等.對(duì)應(yīng)用層次分析法確定權(quán)重系數(shù)的探討[J].機(jī)械工程師,2012(6):22-25. LIAO Hongqiang,QIU Yong,YANG Xia,et al.A Study of weight coefficient computing method based on AHP[J].Mechanical Engineer,2012(6):22-25.

[18]魏代俊,王能發(fā).關(guān)于層次分析法中群體決策權(quán)重系數(shù)確定的探討[J].湖北民族學(xué)院學(xué)報(bào)(自然科學(xué)版),2007,25(2):146-147. WEI Daijun,WANG Nengfa.Study on the determination of weight coefficients in AHP group decision[J].Journal of Hubei University for Nationalities(Natural Sciences Edition),2007,25(2):146-147.

[19]王化吉,宗長富,管欣,等.基于模糊層次分析法的汽車操縱穩(wěn)定性主觀評(píng)價(jià)指標(biāo)權(quán)重確定方法[J].機(jī)械工程學(xué)報(bào),2011,47(24):83-90. WANG Huaji,ZONG Changfu,GUAN Xin,et al.Method of determining weights of subjective evaluation indexes for car handling and stability based on fuzzy analytic hierarchy process[J].Journal of Mechanical Engineering,2011,47(24):83-90.

[20]李仕鋒,黃雪嬌,曹源文.基于ADAMS/Car的客車平順性仿真研究[J].山東交通學(xué)院學(xué)報(bào),2011,19(4):8-11. LI Shifeng,HUANG Xuejiao,CAO Yuanwen.Design of simulation system for estimation of vehicle manipulation stability[J].Journal of Shandong Jiaotong University,2011,19(4):8-11.

[21]常媛媛,段業(yè)廣,雍文亮,等.基于ISIGHT的重型汽車空氣懸架系統(tǒng)多目標(biāo)優(yōu)化設(shè)計(jì)[J].山東交通學(xué)院學(xué)報(bào),2013,21(3):20-25. CHANG Yuanyuan,DUAN Yeguang,YONG Wenliang,et al.Multi-objective optimization design of air suspension system for heavy vehicle based on ISIGHT[J].Journal of Shandong Jiaotong University,2013,21(3):20-25.

[22]程賢福,劉艷軍,林彧群.汽車雙橫臂懸架參數(shù)穩(wěn)健優(yōu)化設(shè)計(jì)[J].機(jī)械科學(xué)與技術(shù),2016(9):1421-1425. CHENG Xianfu,LIU Yanjun,LIN Yuqun.Robust optimization design of double wishbone suspension system for automotive[J].Mechanical Science and Technology for Aerospace Engineering,2016(9):1421-1425.

(責(zé)任編輯：郎偉鋒)

Optimization Design of Double-wishbone Independent Suspension of Car Based on MDO

ZHAOYuxia1,LINJianfei2,ZHENGQuan2

(1.ChuzhouVocationalandTechnicalCollege,Chuzhou239000,China； 2.CollegeofEngineering,AnhuiAgriculturalUniversity,Hefei230036,China.)

An optimum design method of the double wishbone independent suspension based on the multidisciplinary design optimization (MDO) is presented.By taking the double wishbone independent suspension of a car model as the research subject,the multi-objective optimization functions of the minimum caster,camber and toe angle change is constructed and the multidisciplinary design optimization is made based on the integrated ISIGHT and ADAMS / CAR software.The optimization results show that the optimized caster angle decreases by 2° correspondingly,and the range of camber and toe angles decreases by 0.45° and 0.5° respectively.The experiments verify that the steering portability and overall performance of suspension are improved.

suspension；double-wishbone；genetic algorithm；MDO

2016-09-09

安徽省高校自然科學(xué)重點(diǎn)項(xiàng)目(KJ2015A305)

趙玉霞(1965—)，女，安徽淮北人，講師，主要研究方向?yàn)闄C(jī)械設(shè)計(jì)，E-mail: 362770001@qq.com.

10.3969/j.issn.1672-0032.2016.04.003

U463.33

A

1672-0032(2016)04-0012-06