劉孟楠,周志立,徐立友,,趙靜慧,閆祥海
?
基于多性能目標(biāo)的拖拉機(jī)運(yùn)輸機(jī)組優(yōu)化設(shè)計(jì)
劉孟楠1,周志立2※,徐立友2,3,趙靜慧3,閆祥海2
(1. 西安理工大學(xué)機(jī)械與精密儀器工程學(xué)院,西安 710048;2. 河南科技大學(xué)車輛與交通工程學(xué)院,洛陽 471003;3. 中國一拖集團(tuán)有限公司技術(shù)中心,洛陽471039)
拖拉機(jī)運(yùn)輸機(jī)組總體參數(shù)的設(shè)計(jì)目標(biāo)多元,約束條件復(fù)雜,傳統(tǒng)經(jīng)驗(yàn)法和單目標(biāo)優(yōu)化法難以使機(jī)組綜合性能達(dá)到最優(yōu)。該文以機(jī)組動(dòng)力性、牽引點(diǎn)受力情況、附著性能和經(jīng)濟(jì)性最優(yōu)為目標(biāo)設(shè)計(jì)了目標(biāo)函數(shù);通過分析拖拉機(jī)運(yùn)輸機(jī)組動(dòng)力學(xué)模型,確定了優(yōu)化參數(shù);通過研究拖拉機(jī)運(yùn)輸機(jī)組使用性能,制定了約束模型;采用改進(jìn)型非支配排序遺傳算法,導(dǎo)出了拖拉機(jī)運(yùn)輸機(jī)組總體參數(shù)多目標(biāo)優(yōu)化算法。以東方紅150拖拉機(jī)運(yùn)輸機(jī)組為實(shí)例,優(yōu)化了原有拖拉機(jī)和掛車的重力參數(shù)、質(zhì)心位置和變速器傳動(dòng)比。設(shè)計(jì)試驗(yàn)與已有單目標(biāo)優(yōu)化方案和原始機(jī)組對比,結(jié)果為:運(yùn)輸Ⅰ擋和運(yùn)輸Ⅱ擋下,最大爬坡度分別提高1.35%、1.68%和1.38%、0.57%;牽引點(diǎn)受力分別減少1 222、703和2 792、2 125 N;驅(qū)動(dòng)輪最大滑轉(zhuǎn)率更接近特征滑轉(zhuǎn)率;燃油消耗量分別下降12.9%和15.8%;改善了機(jī)組動(dòng)力性、牽引點(diǎn)受力、附著性能、經(jīng)濟(jì)性,可為拖拉機(jī)運(yùn)輸機(jī)組配重方案和總體參數(shù)設(shè)計(jì)提供參考。
農(nóng)業(yè)機(jī)械;拖拉機(jī);優(yōu)化;性能;運(yùn)輸機(jī)組;參數(shù);多性能目標(biāo)
拖拉機(jī)進(jìn)行農(nóng)業(yè)作業(yè)的同時(shí)還承擔(dān)運(yùn)輸任務(wù),額定功率下,運(yùn)輸機(jī)組的動(dòng)力性和經(jīng)濟(jì)性高度耦合,驅(qū)動(dòng)輪滑轉(zhuǎn)率未達(dá)容許滑轉(zhuǎn)率限時(shí),二者呈非線性反比關(guān)系[1-2]。配重不足會(huì)導(dǎo)致驅(qū)動(dòng)輪滑轉(zhuǎn)現(xiàn)象嚴(yán)重,配重過度會(huì)產(chǎn)生額外的滾動(dòng)阻力,降低運(yùn)輸機(jī)組經(jīng)濟(jì)性,通過優(yōu)化機(jī)組總體參數(shù)可以在提高牽引效率的同時(shí)改善經(jīng)濟(jì)性[3-5]。
拖拉機(jī)制造企業(yè)通常采用類比法和經(jīng)驗(yàn)法解決此類問題,無法有效針對機(jī)組結(jié)構(gòu)和工況特點(diǎn)設(shè)計(jì)參數(shù),導(dǎo)致機(jī)組使用性能無法達(dá)到最佳。國外,拖拉機(jī)運(yùn)輸機(jī)組單軸掛車質(zhì)心位置偏前量通常較大,有益于增加拖拉機(jī)驅(qū)動(dòng)輪載荷,提升附著性能,降低滑轉(zhuǎn)損失;國內(nèi),運(yùn)輸機(jī)組中拖拉機(jī)承重通常較少,有利于改善拖拉機(jī)操縱穩(wěn)定性[6]。加拿大卡爾頓大學(xué)的Wong教授通過研究升力系數(shù)、運(yùn)載效率、傳動(dòng)效率與運(yùn)輸性能之間的關(guān)聯(lián)性,建立了拖拉機(jī)運(yùn)輸機(jī)組運(yùn)輸效率通用模型[7];新加坡國立大學(xué)的Liu等基于MOBPP-2D模型(multi objective 2-dimensional mathematical model for bin packing problems with multiple constraints)對拖拉機(jī)運(yùn)輸機(jī)組的載荷分布進(jìn)行了雙目標(biāo)優(yōu)化[8];Pranav等通過采集拖拉機(jī)作業(yè)時(shí)的土壤、輪胎、農(nóng)機(jī)具等數(shù)據(jù),基于Visual Basic開發(fā)了拖拉機(jī)軸荷計(jì)算系統(tǒng),準(zhǔn)確度達(dá)到88%~96%,用于優(yōu)化拖拉機(jī)機(jī)組配重方案[9];河南科技大學(xué)陳杰平等以運(yùn)輸效率為目標(biāo),基于Delphi作為主開發(fā)系統(tǒng),結(jié)合Fortran、Gt等軟件對拖拉機(jī)運(yùn)輸機(jī)組進(jìn)行了總體參數(shù)優(yōu)化,優(yōu)化后機(jī)組坡道特性達(dá)到理想坡道特性,滑轉(zhuǎn)率未達(dá)到容許滑轉(zhuǎn)率限[10-11]。相關(guān)研究可使機(jī)組特定性能達(dá)到最優(yōu),無法保證綜合使用性能較好。
本文立足于此提出一種基于改進(jìn)非支配排序遺傳算法的拖拉機(jī)運(yùn)輸機(jī)組總體參數(shù)優(yōu)化方法,處理目標(biāo)函數(shù)之間的復(fù)雜耦合關(guān)系,優(yōu)化機(jī)組經(jīng)濟(jì)性、動(dòng)力性,并改善牽引點(diǎn)受力情況和驅(qū)動(dòng)輪附著性能。以期提升拖拉機(jī)運(yùn)輸機(jī)組綜合使用性能。
圖1為后輪驅(qū)動(dòng)拖拉機(jī)運(yùn)輸機(jī)組受力分析。
假設(shè)車輪的滾動(dòng)阻力系數(shù)相同, 導(dǎo)出發(fā)動(dòng)機(jī)輸出轉(zhuǎn)矩為q時(shí)的拖拉機(jī)運(yùn)輸機(jī)組動(dòng)力學(xué)模型為
(2)
;(3)
(5)
(6)
式中為重力加速度,取=9.8 m/s2;為行駛速度,km/h;D為空氣阻力系數(shù);為拖拉機(jī)迎風(fēng)面積,m2;k為變速器傳動(dòng)比;0為中央傳動(dòng)和最終傳動(dòng)總傳動(dòng)比;T為傳動(dòng)效率。
注:Wt、Wg為分別為拖拉機(jī)和掛車的重力,N;V為行駛速度,km·h-1;Fq為驅(qū)動(dòng)力,N;地面對于拖拉機(jī)前輪、后輪和掛車車輪的支持力分別為Zc、Zq和Zg,滾動(dòng)阻力分別為Ffc、Ffq和Ffg,N;滾動(dòng)阻力矩分別為Mfc、Mfq和Mfg,N·m;機(jī)組加速阻力分別Fjt和Fjg,N;加速阻力矩分別為Mjc、Mjq和Mjg,N·m;Fw、Fα分別為機(jī)組的空氣阻力和坡度阻力,N;α為坡度角,rad;L為拖拉機(jī)軸距,m;a為拖拉機(jī)質(zhì)心到驅(qū)動(dòng)輪中心距離,m;rc為拖拉機(jī)從動(dòng)輪半徑,m;rq為拖拉機(jī)驅(qū)動(dòng)輪半徑,m;rg為掛車車輪半徑,m;h為拖拉機(jī)質(zhì)心高度;m;Lg為掛車車輪到牽引點(diǎn)的距離,m;ag為掛車質(zhì)心到掛車車輪中心的水平距離,m;hg為掛車質(zhì)心高度,m;hT為牽引點(diǎn)高度,m;LT為牽引點(diǎn)到驅(qū)動(dòng)輪的水平距離,m;Fx和Fz為牽引力的垂向和縱向分量,N。
根據(jù)式(1)、(2)可知,在發(fā)動(dòng)機(jī)性能一定的情況下,拖拉機(jī)機(jī)組性能主要由c、q和g決定。此外,q的發(fā)揮受到最大附著力ad(N)的限制,為:
在路面、輪胎等條件不變時(shí),可認(rèn)為驅(qū)動(dòng)輪附著系數(shù)不變,ad大小主要取決于q。因此,根據(jù)式(4)~(6)可知,影響運(yùn)輸機(jī)組性能的主要總體參數(shù)為拖拉機(jī)重力及質(zhì)心位置、掛車重力及質(zhì)心位置、拖拉機(jī)軸距、牽引點(diǎn)位置、車輪半徑和傳動(dòng)系傳動(dòng)比。本文選擇對拖拉機(jī)運(yùn)輸機(jī)組中可以通過外載配重調(diào)整的tgg總體參數(shù)進(jìn)行優(yōu)化,并對變速器傳動(dòng)比k進(jìn)行優(yōu)化,提升運(yùn)輸機(jī)組性能。
2 約束條件
受載荷波動(dòng)影響,需保證前輪動(dòng)載荷不能少于整機(jī)使用重力的15%~20%,根據(jù)式(4)導(dǎo)出
將式(5)代入式(8),消去g,則穩(wěn)定性約束為
(9)
運(yùn)輸機(jī)組作業(yè)時(shí),掛車產(chǎn)生縱向振動(dòng),引起牽引點(diǎn)承受沖擊載荷。必須避免牽引點(diǎn)產(chǎn)生負(fù)增重力,導(dǎo)致過大的沖擊載荷[11]。則約束條件為
(11)
驅(qū)動(dòng)輪載荷受到承載能力qlim的限制,根據(jù)式(6)導(dǎo)出約束模型為
將式(5)代入式(12),得
(13)
采用動(dòng)載荷系數(shù)對機(jī)組重力參數(shù)進(jìn)行約束,需預(yù)留起步過程的功率儲(chǔ)備,且應(yīng)大于其最小運(yùn)用載荷系數(shù)
式中ed為發(fā)動(dòng)機(jī)額定轉(zhuǎn)矩,N·m;d為拖拉機(jī)運(yùn)輸機(jī)組動(dòng)載荷系數(shù);y為發(fā)動(dòng)機(jī)最小運(yùn)用載荷系數(shù),取y=0.85d。
當(dāng)驅(qū)動(dòng)輪滑轉(zhuǎn)率超過容許滑轉(zhuǎn)率限permit時(shí),整機(jī)牽引效率明顯下降[12]。優(yōu)化時(shí),需通過約束質(zhì)心位置和機(jī)組重力使驅(qū)動(dòng)輪滑轉(zhuǎn)率符合容許滑轉(zhuǎn)率限要求。根據(jù)文獻(xiàn)[13-14]中的拖拉機(jī)驅(qū)動(dòng)輪滑轉(zhuǎn)率模型和式(7),可得
(16)
(17)
式中*為容許滑轉(zhuǎn)率,%;為最大附著系數(shù)。
根據(jù)文獻(xiàn)[11],導(dǎo)出動(dòng)力性目標(biāo)函數(shù)為
為減少拖拉機(jī)行駛功率消耗,經(jīng)濟(jì)性目標(biāo)為
(19)
根據(jù)式(3),導(dǎo)出牽引點(diǎn)受力目標(biāo)函數(shù)為
根據(jù)式(13),導(dǎo)出附著性能目標(biāo)函數(shù)為
(21)
4.1 算法設(shè)計(jì)
目前常用的多目標(biāo)優(yōu)化算法有:強(qiáng)度帕累托進(jìn)化算法SPEA(strength pareto evolutionary algorithm)、粒子群算法PSO(particle swarm optimization)、非支配遺傳算法NSGA(non-domination sorting genetic algorithms)、改進(jìn)非支配遺傳算法NSGA-Ⅱ(non-domination sorting genetic algorithms-Ⅱ)等[15-17]。相比SPEA, NSGA-Ⅱ具有更好的收斂性、前端分布和多樣性賦存機(jī)理[18];相比PSO,NSGA-Ⅱ具有更好的多樣性[19];相比NSGA,NSGA-Ⅱ通過增加精英策略、密度值估計(jì)策略和快速非支持排序策略,較大程度地降低了算法復(fù)雜度[20-21]。NSGA-Ⅱ算法廣泛應(yīng)用于處理諸如電網(wǎng)系統(tǒng)規(guī)劃[22-23]、路徑優(yōu)化[24-25]、混合動(dòng)力車輛驅(qū)動(dòng)系統(tǒng)匹配[26-27]等工程實(shí)踐中的多目標(biāo)優(yōu)化問題。因此,在MATLAB環(huán)境下,本文采用基于NSGA-Ⅱ算法的gamultiobj函數(shù)處理拖拉機(jī)運(yùn)輸機(jī)組優(yōu)化模型。通過調(diào)用gacommon函數(shù)確定優(yōu)化模型的約束類型,調(diào)用gamultiobjsolve函數(shù)對多個(gè)目標(biāo)函數(shù)進(jìn)行最優(yōu)值求解。
根據(jù)目標(biāo)函數(shù)和約束條件,設(shè)計(jì)拖拉機(jī)運(yùn)輸機(jī)組優(yōu)化算法流程如圖2所示。
圖2 拖拉機(jī)運(yùn)輸機(jī)組優(yōu)化流程
優(yōu)化時(shí),設(shè)置最優(yōu)前端個(gè)體系數(shù)為0.3,種群大小為100,最大進(jìn)化代數(shù)為200,停止代數(shù)為200,適應(yīng)度函數(shù)值偏差為1e-1 000。首先通過gacommon.m處理約束(14);基于gamultiobjsolve.m對目標(biāo)函數(shù)(18)、(19)開展求解,計(jì)算機(jī)組重力參數(shù);其中,初始化種群由gamultiobjsolveMakeState.m隨機(jī)生成初始化種群。然后,根據(jù)式(22)處理穩(wěn)定性約束(9)和驅(qū)動(dòng)輪承載能力約束(13),并以約束的形式建立重力參數(shù)優(yōu)化過程和質(zhì)心位置優(yōu)化過程間的邏輯關(guān)系。根據(jù)式(23)對目標(biāo)函數(shù)(21)進(jìn)行等效變換;再次通過gamultiobjsolve.m求解質(zhì)心位置參數(shù);并在判斷適應(yīng)度函數(shù)偏差之后添加基于約束式(11)、式(17)的判斷。最后,根據(jù)式(1)~(6)計(jì)算對應(yīng)優(yōu)化后運(yùn)輸機(jī)組參數(shù)的拖拉機(jī)傳動(dòng)比。
(23)
式中qcon為穩(wěn)定性約束和承載能力約束的合并約束。
4.2 優(yōu)化實(shí)例
以東方紅150拖拉機(jī)運(yùn)輸機(jī)組為實(shí)例進(jìn)行多目標(biāo)優(yōu)化,原始參數(shù)可見文獻(xiàn)[11]。
圖3為實(shí)例中目標(biāo)函數(shù)Pareto前端個(gè)體分布情況。由圖可知,(t,g)best為27 000 N,(t,g)best為0.421 5;q的優(yōu)化結(jié)果達(dá)到約束邊界,最優(yōu)解集唯一,(g,g)best為1 600,(tgg)best為0。在得到目標(biāo)函數(shù)的前端個(gè)體分布后,MATLAB的Workspace返回對應(yīng)的Pareto解集。
圖3 目標(biāo)函數(shù)Pareto前端個(gè)體分布
結(jié)合已有基于Delphi的單目標(biāo)優(yōu)化方案[10]和優(yōu)化前機(jī)組設(shè)立對照組,3種方案的tgg、k參數(shù)如表1所示?;贜SGA-Ⅱ算法優(yōu)化后的運(yùn)輸機(jī)組重力相較優(yōu)化前下降了6.86%,拖拉機(jī)質(zhì)心位置前移0.074 m,掛車質(zhì)心位置后移0.14 m;機(jī)組重力較基于Delphi的優(yōu)化結(jié)果下降了3.26%,拖拉機(jī)質(zhì)心位置后移0.022 m,掛車質(zhì)心位置后移0.3 m。下文將通過試驗(yàn)分析目標(biāo)性能的提升效果。
表1 優(yōu)化前、Delphi和NSGA-Ⅱ優(yōu)化方案對比
圖4為試驗(yàn)原理及設(shè)備。
注:1為車輛綜合性能測試系統(tǒng);2為RF無線數(shù)傳模塊;3為GPS模塊;4為負(fù)荷傳感器;A~E為試驗(yàn)坡道,最大坡度分別為2%、5%、7%、9%和12%。
選擇地處洛陽的國家拖拉機(jī)試驗(yàn)檢測基地內(nèi)最大坡度為2%、5%、7%、9%和12%的A、B、C、D、E坡道按照表1中參數(shù)和文獻(xiàn)[28]中的拖拉機(jī)質(zhì)心估算模型和調(diào)整方法調(diào)整被試機(jī)組開展試驗(yàn),分析優(yōu)化方法對于拖拉機(jī)運(yùn)輸機(jī)組動(dòng)力性、牽引點(diǎn)受力和附著性能的提升效果[29]。設(shè)計(jì)試驗(yàn)為:測量出發(fā)位置到各坡道變坡線的水平位置,以對照單次試驗(yàn)中測量得到的機(jī)組位置信息,從而對應(yīng)該位置信息下測量的牽引點(diǎn)軸端拉力、實(shí)際車速等信號(hào);單次試驗(yàn)駕駛員保持相同出發(fā)速度,并于開始爬坡時(shí)以最大加速度加速。具體試驗(yàn)方法為:在拖拉機(jī)牽引點(diǎn)軸端添加BLR-1M10T型電阻應(yīng)變拉壓式負(fù)荷傳感器測量牽引點(diǎn)軸端拉力。試驗(yàn)車牽引點(diǎn)軸端與車架之間為鉸接,通過測量運(yùn)輸機(jī)組在測試坡道上的牽引點(diǎn)軸端軸向和車架間的靜態(tài)角度計(jì)算牽引點(diǎn)水平力和法向力。為避免驅(qū)動(dòng)輪滑轉(zhuǎn)對車速測量過程的干擾,通過添加頻率1 575.42 MHz、額定電壓3.0~5.0 V的GPS模塊接收機(jī)組實(shí)際車速和位置信息,并通過洛陽耐歐電氣有限公司開發(fā)的VDM-BS/TL型車輛綜合性能測試系統(tǒng)對單一采樣步長內(nèi)的拉力信號(hào)、位置信號(hào)進(jìn)行處理,得出該采樣步長內(nèi)的牽引點(diǎn)軸端拉力和實(shí)際車速數(shù)值為
式中p為拖拉機(jī)牽引點(diǎn)軸端拉力,N;max為最大采樣次數(shù);為單次采樣計(jì)數(shù)。
由YL-500IW-232型RF無線數(shù)傳模塊將測量數(shù)據(jù)上傳至上位機(jī)端,計(jì)算牽引功率,并配合顯示車速計(jì)算滑轉(zhuǎn)率。數(shù)據(jù)修正后采用最小二乘法多項(xiàng)式對離散試驗(yàn)數(shù)據(jù)進(jìn)行回歸分析,得到連續(xù)的坡道特性對照結(jié)果。
圖5為動(dòng)力性和牽引點(diǎn)受力對比情況。由圖5a可知,運(yùn)輸擋下,基于NSGA-Ⅱ算法優(yōu)化的運(yùn)輸機(jī)組爬坡度情況較基于Delphi的優(yōu)化方案更好。東方紅150拖拉機(jī)單軸掛車運(yùn)輸機(jī)組低速擋和高速擋的最大爬坡度k1max、k2max分別應(yīng)大于5%和2%[11];運(yùn)輸Ⅰ擋下,NSGA-Ⅱ優(yōu)化方案、Delphi優(yōu)化方案和優(yōu)化前的最大爬坡度分別為10.61%、9.26%、8.93%;運(yùn)輸Ⅱ擋下,三者的最大爬坡度分別為4.67%、3.29%、4.10%;符合要求。運(yùn)輸Ⅰ擋下,基于NSGA-Ⅱ算法多目標(biāo)優(yōu)化運(yùn)輸機(jī)組的最大爬坡度比基于Delphi的單目標(biāo)優(yōu)化方案和優(yōu)化前分別提高1.35%和1.68%;運(yùn)輸Ⅱ擋下,分別提高1.38%、0.57%?;贜SGA-Ⅱ的多目標(biāo)優(yōu)化方案具有更好的動(dòng)力性。由圖5b可知,運(yùn)輸Ⅰ擋車速范圍內(nèi),NSGA-Ⅱ優(yōu)化方案、Delphi優(yōu)化方案和優(yōu)化前機(jī)組方案中牽引點(diǎn)縱向力的平均值分別為1 839、1 631、1 575 N;運(yùn)輸Ⅱ擋下車速范圍內(nèi),牽引點(diǎn)縱向力的平均值分別為794、546、695 N,基于NSGA-Ⅱ優(yōu)化方案的拖拉機(jī)牽引點(diǎn)縱向力較大。由圖5c可知,運(yùn)輸Ⅰ擋、Ⅱ擋下基于NSGA-Ⅱ優(yōu)化的運(yùn)輸機(jī)組牽引點(diǎn)平均受力較基于Delphi的優(yōu)化方案和原方案分別下降1 222、703和2 792、2 125 N,牽引點(diǎn)受力情況得到較大改善。
圖5 動(dòng)力性和牽引點(diǎn)受力情況對比
圖6為附著性能對比情況。由圖可知,最大驅(qū)動(dòng)力范圍內(nèi),NSGA-Ⅱ優(yōu)化方案、Delphi優(yōu)化方案和優(yōu)化前機(jī)組方案驅(qū)動(dòng)輪最大滑轉(zhuǎn)率未達(dá)容許滑轉(zhuǎn)率限15%~18%,符合優(yōu)化要求。由于基于Delphi的單目標(biāo)優(yōu)化方案中g(shù)值最大,機(jī)組中z和q最大,驅(qū)動(dòng)輪附著性能最好,驅(qū)動(dòng)輪滑轉(zhuǎn)率最低?;贜SGA-Ⅱ算法的多目標(biāo)優(yōu)化算法中包含以改善牽引點(diǎn)受力的目標(biāo)函數(shù),因此優(yōu)化后運(yùn)輸機(jī)組中拖拉機(jī)驅(qū)動(dòng)輪滑轉(zhuǎn)率較優(yōu)化前有所增加,幅度較小。拖拉機(jī)運(yùn)輸機(jī)組的車速-負(fù)載特性導(dǎo)致驅(qū)動(dòng)輪滑轉(zhuǎn)率未達(dá)容許滑轉(zhuǎn)率限。由于拖拉機(jī)驅(qū)動(dòng)輪滑轉(zhuǎn)率模型具有非線性的單調(diào)遞增性,當(dāng)≧0.632,即≧*時(shí),加速遞增,3種方案的q差異引起的差異將較為明顯;反之,當(dāng)驅(qū)動(dòng)輪滑轉(zhuǎn)率未達(dá)容許滑轉(zhuǎn)率限時(shí),3種方案下拖拉機(jī)運(yùn)輸機(jī)組的驅(qū)動(dòng)輪滑轉(zhuǎn)損失差別較小。因此,本文優(yōu)化方案的牽引功率更大。
根據(jù)前期研究成果[30],以東方紅150拖拉機(jī)配套柴油機(jī)臺(tái)架試驗(yàn)數(shù)據(jù)作為原始數(shù)據(jù);根據(jù)車速范圍,設(shè)計(jì)EUDC_man_tractor工況,對3種方案的經(jīng)濟(jì)性進(jìn)行分析。
圖7為經(jīng)濟(jì)性對比情況。由圖可知,由于機(jī)組重力較小,基于NSGA-Ⅱ算法優(yōu)化的運(yùn)輸機(jī)組燃油消耗率始終最低,平均達(dá)到1.485 L/h;循環(huán)工況內(nèi)燃油消耗量為0.165 L,比基于Delphi的優(yōu)化方案和優(yōu)化前機(jī)組平均降低12.9%和15.8%,經(jīng)濟(jì)性較好。
基于NSGA-Ⅱ進(jìn)行多目標(biāo)優(yōu)化后,東方紅150拖拉機(jī)單軸掛車運(yùn)輸機(jī)組動(dòng)力性和經(jīng)濟(jì)性獲得較大提升;牽引點(diǎn)受力情況得到改善;最大滑轉(zhuǎn)率更接近特征滑轉(zhuǎn)率,附著性能較好。
圖6 附著性能對比
圖7 經(jīng)濟(jì)性對比
1)本研究提出了基于NSGA-Ⅱ算法的拖拉機(jī)運(yùn)輸機(jī)組總體參數(shù)優(yōu)化方法,分別以動(dòng)力性、經(jīng)濟(jì)性、牽引點(diǎn)受力和驅(qū)動(dòng)輪附著性能設(shè)計(jì)了目標(biāo)函數(shù),在拖拉機(jī)使用性能框架內(nèi)制定了約束條件,設(shè)計(jì)了優(yōu)化算法流程。
2)通過設(shè)立對照組,對東方紅150拖拉機(jī)運(yùn)輸機(jī)組總體參數(shù)進(jìn)行了優(yōu)化,優(yōu)化結(jié)果為:基于NSGA-Ⅱ算法的優(yōu)化方案的拖拉機(jī)質(zhì)心位置比基于Delphi的單目標(biāo)優(yōu)化方案后移0.022 m,比優(yōu)化前前移0.074 m;掛車質(zhì)心位置比二者分別后移0.3 m和0.14 m;機(jī)組重力比二者分別下降3.26%和6.86%。
3)分別對比基于Delphi的單目標(biāo)優(yōu)化方案和優(yōu)化前方案,基于NSGA-Ⅱ算法的優(yōu)化方案運(yùn)輸Ⅰ擋最大爬坡度提高了1.35%和1.68%,運(yùn)輸Ⅱ擋最大爬坡度提高了1.38%和0.57%;運(yùn)輸Ⅰ擋牽引點(diǎn)受力下降了1 222、 703 N,運(yùn)輸Ⅱ擋牽引點(diǎn)受力下降了2 792、2 125 N,牽引點(diǎn)縱向力增加;最大滑轉(zhuǎn)率有所增加,更接近特征滑轉(zhuǎn)率;牽引功率較大;EUDC_man_tractor工況下燃油消耗量平均降低12.9%、15.8%,算法達(dá)到優(yōu)化目標(biāo)。
[1] Wong J Y. Theory of Ground Vehicles 4ndEdition[M]. New York: John Wiley, 2008: 320-324.
[2] 趙剡水,楊為民. 農(nóng)業(yè)拖拉機(jī)技術(shù)發(fā)展觀察[J]. 農(nóng)業(yè)機(jī)械學(xué)報(bào),2010,41(6):42-48. Zhao Yanshui, Yang Weimin. Technological development of agricultural tractor[J]. Transactions of the CSAM, 2010, 41(6): 42-48. (in Chinese with English abstract)
[3] Davies D B, Finney J B, Richardson S J. Relative effects of tractor weight and wheel-slip in causing soil compaction[J]. Journal of Soil Science, 1973, 24(3): 399-409.
[4] Mulcahy N L. Bridge response with tractor-trailer vehicle loading[J]. Earthquake Engineering & Structural Dynamics, 1983, 11(5): 649-665.
[5] Tayanovsky G A, Tanas W. Principles and problems of the tractors transport-pull units unitization analysis[J]. Teka Komisji Motoryzacji I Energetyki Rolnictwa, 2004(4): 196-204.
[6] 賈鴻社,周志立,周政. 拖拉機(jī)機(jī)組系統(tǒng)研究現(xiàn)狀及展望[J]. 拖拉機(jī)與農(nóng)用運(yùn)輸車,2000(4):13-17. Jia Hongshe, Zhou Zhili, Zhou Zheng. Study and outlook of tractor unit systems[J]. Tractor & Farm Transpoter, 2000(4):13-17. (in Chinese with English abstract)
[7] Wong J Y. Terramechanics and Off-Road Vehicle Engineering: Terrain Behaviour, Off-Road vehicle Performance and Design 2ndEdition[M]. Oxford: Elsevier Ltd, 2010: 129-149.
[8] Liu D S, Tan K C, Huang S Y, et al. On solving multiobjective bin packing problems using evolutionary particle swarm optimization[J]. European Journal of Operational Research, 2008, 190(2): 357-382.
[9] Pranav P K, Pandey K P. Computer simulation of ballast management for agricultural tractors[J]. Journal of Terramechanics, 2008, 45(6): 185-192.
[10] 陳杰平,周志立,張文春. 拖拉機(jī)機(jī)組系統(tǒng)性能CAD的混合編程[J]. 拖拉機(jī)與農(nóng)用運(yùn)輸車,2002,16(1):86-88. Chen Jieping, Zhou Zhili, Zhang Wenchun. CAD hybrid programming of tractor unit systems character[J]. Tractor & Farm Transpoter, 2002, 16(1): 86-88. (in Chinese with English abstract)
[11] 周志立,方在華. 拖拉機(jī)機(jī)組牽引動(dòng)力學(xué)[M]. 北京:科學(xué)出版社,2010:207-250.
[12] Liu M N, Xu L Y, Zhou Z L. Design of a load torque based control strategy for improving electric tractor motor energy conversion efficiency[J]. Mathematical Problems in Engineering, 2016,2016(5): 1-14.
[13] 周志立,方在華,張文春. 拖拉機(jī)牽引特性的計(jì)算機(jī)輔助分析[J]. 洛陽工學(xué)院學(xué)報(bào),1993,14(1):1-6. Zhou Zhili, Fang Zaihua, Zhang Wenchun. Computer aided analysis on the theoretical tractive characteristics of tractor[J]. Journal of Luoyang Institute of Technology, 1993, 14(1): 1-6. (in Chinese with English abstract)
[14] 徐立友,劉孟楠,周志立. 串聯(lián)式混合動(dòng)力拖拉機(jī)驅(qū)動(dòng)系設(shè)計(jì)[J]. 農(nóng)業(yè)工程學(xué)報(bào),2014,30(9):11-18. Xu Liyou, Liu Mengnan, Zhou Zhili. Design of drive system for series hybrid electric tractor[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2014, 30(9): 11-18. (in Chinese with English abstract)
[15] Zhou A, Qu B Y, Li H, et al. Multiobjective evolutionary algorithms: A survey of the state of the art[J]. Swarm and Evolutionary Computation, 2011, 1(1): 32-49.
[16] Tan K C, Lee T H, Khor E F. Evolutionary algorithms for multi-objective optimization: performance assessments and comparisons[J]. Artificial Intelligence Review, 2002, 17(4): 251-290.
[17] Elbeltagi E, Hegazy T, Grierson D. Comparison among five evolutionary-based optimization algorithms[J]. Advanced Engineering Informatics, 2005, 19(1): 43-53.
[18] Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
[19] Hirano H, Yoshikawa T. A study on two-step search using global-best in PSO for multi-objective optimization problems[C]//2012 Joint 6th International Conference on Soft Computing and Intelligent Systems and 13th International Symposium on Advanced Intelligent Systems. Kobe, IEEE, 2012: 1894-1897.
[20] Deb K, Jain H. Handling many-objective problems using an improved NSGA-II procedure[C]//2012 IEEE Congress on Evolutionary Computation. Brisbane, IEEE, 2012: 1-8.
[21] Deb K, Karthik S. Dynamic multi-objective optimization and decision-making using modified NSGA-II: A case study on hydro-thermal power scheduling[C]//International Conference on Evolutionary Multi-Criterion Optimization, Matsushima, Springer Berlin Heidelberg, 2007: 803-817.
[22] 王茜,張粒子. 采用NSGA-Ⅱ混合智能算法的風(fēng)電場多目標(biāo)電網(wǎng)規(guī)劃[J]. 中國電機(jī)工程學(xué)報(bào),2011,31(19):17–24. Wang Qian, Zhang Lizi. Multi-objective transmission planning associated with wind farms applying NSGA-Ⅱ hybrid intelligent algorithm[J]. Proceedings of the CSEE, 2011, 31(19): 17-24. (in Chinese with English abstract)
[23] 王洪濤,劉玉田. 基于NSGA-Ⅱ的多目標(biāo)輸電網(wǎng)架最優(yōu)重構(gòu)[J]. 電力系統(tǒng)自動(dòng)化,2009,33(23):14-18. Wang Hongtao, Liu Yutian. Multi-objective optimization of power system reconstruction based on NSGA-Ⅱ[J]. Automation of Electric Power Systems, 2009, 33(23): 14-18. (in Chinese with English abstract)
[24] Ahmed F, Deb K. Multi-objective optimal path planning using elitist non-dominated sorting genetic algorithms[J]. Soft Computing, 2013, 17(7): 1283-1299.
[25] 徐慧英,趙建民,張泳,等. 改進(jìn)NSGA-Ⅱ算法在車輛路徑多目標(biāo)優(yōu)化問題中的應(yīng)用[J]. 計(jì)算機(jī)工程與科學(xué),2010,32(10):117-121. Xu Huiying,Zhao Jianmin,Zhang Yong,et al. Application of the improved NSGA-Ⅱ in multi objective optimization for the vehicle routing problem[J]. Computer Engineering & Science, 2010, 32(10): 117-121. (in Chinese with English abstract)
[26] 胡曉林,王仲范,廖連瑩,等.多目標(biāo)演化算法在混合電動(dòng)車設(shè)計(jì)和控制中的應(yīng)用[J]. 武漢理工大學(xué)學(xué)報(bào):交通科學(xué)與工程版,2004,28(3):384-387.Hu Xiaolin, Wang Zhongfan, Liao Lianying, et al. Application of multi-objective evolutionary algorithm in hybrid electric vehicle design and control[J]. Journal of Wuhan University of Technology: Transportation Science & Technology, 2004, 28(3): 384-387. (in Chinese with English abstract)
[27] Buerger S, Lohmann B, Merz M, et al. Multi-objective optimization of hybrid electric vehicles considering fuel consumption and dynamic performance[C]//2010 IEEE Vehicle Power and Propulsion Conference. Lille, IEEE, 2010: 1-6.
[28] 《拖拉機(jī)》編輯部. 拖拉機(jī)設(shè)計(jì)和計(jì)算[M]. 上海:上海科學(xué)技術(shù)文獻(xiàn)出版社,1980:37-39.
[29] 日本自動(dòng)車技術(shù)會(huì),中國汽車工程學(xué)會(huì). 汽車工程手冊6-動(dòng)力傳動(dòng)系統(tǒng)試驗(yàn)評價(jià)篇[M]. 北京:北京理工大學(xué)出版社,2010:37-38.
[30] 劉孟楠,徐立友,周志立,等. 增程式電動(dòng)拖拉機(jī)及其旋耕機(jī)組仿真平臺(tái)開發(fā)[J]. 中國機(jī)械工程,2016,27(3):413--419. Liu Mengnan, Xu Liyou, Zhou Zhili, et al. Establishment of extended range electric tractor and its rotary cultivator’s simulative platforms[J]. China Mechanical Engineering, 2016, 27(3): 413--419. (in Chinese with English abstract)
Multi-objective optimization and design of tractor trailer systems
Liu Mengnan1, Zhou Zhili2※, Xu Liyou2,3, Zhao Jinghui3, Yan Xianghai2
(1.710048,;2.471003,;3.471039,)
Due to that the design aims for structural parameters of semi-trailer tractor are multivariate and the constricted boundary condition of this designing process is complicated, the utilizations of empirical approach and the single objective optimization can’t always promote the comprehensive performance of semi-trailer tractor. Based on non-dominated sorting genetic algorithm II (NSGA-II), a new optimizing method about semi-trailer tractor’s structure parameters was put forward. By analyzing structural and dynamic characteristics of semi-trailer tractor’s 2-DoF (degree of freedom) model, optimizing principles were established. According to the tractor operation performance including the manipulative stability, negative weight addition, limitation of driving wheel’s load, load rate of engine power and adhesive characteristic, the constricted boundary conditions were designed. The optimizing objective functions were formulated, which included fuel economy, power performance and force status of tractive point. YTO-150 tractor and the matched semi-trailer were collected as the investigative and optimized object. According to the theoretical analysis and mathematical modeling of the tractor and trailer dynamic performance, the 4 objective functions were divided into 2 groups which involved contradictory relation. After the multiple mathematic conversions of objective functions and constraint functions, the complicated and coupled relationship between the optimal objects could be simplified. Using NSGA-II two times , the semi-trailer tractor’s structure parameters and the gear ratios of transportation work condition were calculated. And relevant program was redacted. Parameters including the gravity of the tractor and semi-trailer, and the position of each part’s barycenter were optimized. And the transmission ratio of each transportation gear was modified. The figure describing the Pareto front end of each aimed function was plotted. As compared with the primitive semi-trailer tractor, the total weight was declined by 6.86%, the position of the tractor’s barycenter moved forward by 0.074 m, and the position of the trailer’s barycenter moved backward by 0.14 m. As compared with the single objective optimizing result with the way of developing the CAD (computer aided design) systems of Delphi, the total weight was declined by 3.26%, the position of the tractor’s barycenter moved backward by 0.022 m, and the position of the trailer’s barycenter moved backward by 0.3 m. On 5 different gradient test ramps, the climbing performance experiment was performed. And in the climbing tractor and trailer, the velocity and pull force on the traction axle were measured by the GPS (global position system) device and resistance strain pull and pressure sensor. When the tractor was driven under the transportation gearⅠ, the maximum climbing degree was improved by 1.35% and 1.68%, and the average force of the tractive point declined by 1 222 and 703 N, respectively, compared with the single objective optimizing scheme and primitive semi-trailer tractor. When the tractor was driven under the transportation gearⅡ, the maximum climbing degree was improved by 1.38% and 0.57%, and the average force of the tractive point declined by 2 792 and 2 125 N, respectively, compared with the single objective optimizing scheme and primitive semi-trailer tractor. The fuel economy of the tractor trailer systems was simulated by the simulator, which was developed upon the dynamic joint between AVL CRUISE and MATLAB. When the simulation adopted the marked working condition based on EUDC (extra urban driving cycle), the fuel consuming rate of the multi-objective optimized semi-trailer tractor declined by 12.9% and 15.8%, respectively, compared with the single objective optimizing scheme and primitive semi-trailer tractor. To sum up, this optimized method reaches the requirement of the objective functions, and provides the theoretical and technologic foundation for improving tractive vehicle systems.
agricultural machinery; tractors; optimization; perfoemance; trailer system; parameters; multi-objectives
10.11975/j.issn.1002-6819.2017.08.008
S219.0
A
1002-6819(2017)-08-0062-07
2016-07-18
2017-03-31
“十三五”國家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2016YFD0701002);國家自然科學(xué)基金資助項(xiàng)目(51375145);河南省基礎(chǔ)與前沿技術(shù)研究項(xiàng)目(102102210165)
劉孟楠,男,河南洛陽人。博士生,研究方向?yàn)橥侠瓩C(jī)新型驅(qū)動(dòng)系統(tǒng)及控制技術(shù)。西安 西安理工大學(xué)機(jī)械與精密儀器工程學(xué)院,710048。Email:liumengnan27@163.com
周志立,男,河南洛陽人。博士,教授,博士生導(dǎo)師,研究方向?yàn)檐囕v新型傳動(dòng)理論與控制技術(shù),中國農(nóng)業(yè)工程學(xué)會(huì)常務(wù)理事。洛陽 河南科技大學(xué)車輛與交通工程學(xué)院,471003。Email:zzli@haust.edu.cn
劉孟楠,周志立,徐立友,趙靜慧,閆祥海. 基于多性能目標(biāo)的拖拉機(jī)運(yùn)輸機(jī)組優(yōu)化設(shè)計(jì)[J]. 農(nóng)業(yè)工程學(xué)報(bào),2017,33(8):62-68. doi:10.11975/j.issn.1002-6819.2017.08.008 http://www.tcsae.org
Liu Mengnan, Zhou Zhili, Xu Liyou, Zhao Jinghui, Yan Xianghai. Multi-objective optimization and design of tractor trailer systems[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(8): 62-68. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2017.08.008 http://www.tcsae.org