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    振動深松機(jī)多組振動深松鏟自平衡性能及仿真分析

    2018-03-09 05:43:49孫亞朋董向前宋建農(nóng)王繼承劉彩玲徐光浩
    農(nóng)業(yè)工程學(xué)報 2018年4期
    關(guān)鍵詞:方根值松土拖拉機(jī)

    孫亞朋,董向前,宋建農(nóng),王繼承,劉彩玲,徐光浩

    ?

    振動深松機(jī)多組振動深松鏟自平衡性能及仿真分析

    孫亞朋,董向前,宋建農(nóng)※,王繼承,劉彩玲,徐光浩

    (中國農(nóng)業(yè)大學(xué)農(nóng)業(yè)部土壤-機(jī)器-植物系統(tǒng)技術(shù)重點實驗室,北京 100083)

    振動深松具有減阻的優(yōu)勢,但振動對拖拉機(jī)及駕駛員的不利影響制約其推廣,該文對振動深松機(jī)多組振動深松鏟進(jìn)行自平衡性能分析。在優(yōu)化試驗中,多組深松鏟振動作業(yè)時的劇烈振動易造成試驗設(shè)備損壞,仿真試驗可避免危險工作環(huán)境下的實車試驗。對拖拉機(jī)-振動深松機(jī)系統(tǒng)進(jìn)行受力分析,并基于ADAMS建立其仿真模型,建模過程包括導(dǎo)入三維模型、定義輪胎與地面之間接觸力和摩擦力等。理論與仿真分析相互驗證,得到拖拉機(jī)后輪所受支持力均值分別為27.8、26.4 kN,誤差為1.4 kN,并且二者主振動曲線變化趨勢一致。采用加權(quán)加速度均方根值評價振動對駕駛員的影響。通過MATLAB編程,利用功率譜密度函數(shù),計算得到駕駛座質(zhì)心總加權(quán)加速度均方根值。利用Design-Expert軟件設(shè)計試驗并優(yōu)化得到6組振動影響較小的四組振動松土鏟作業(yè)初始相位角組合,減振比率超過90%,實現(xiàn)了振動深松機(jī)作業(yè)時的自平衡。

    農(nóng)業(yè)機(jī)械;振動;計算機(jī)仿真;深松;自平衡;ADAMS

    0 引 言

    深松耕作可降低土壤緊實度,促進(jìn)農(nóng)作物根系的生長[1],增加深層根干質(zhì)量、分布比例、比根長及根條數(shù),以及增加根系酶活性,延緩根系的衰老,從而促進(jìn)農(nóng)作物生長,提高產(chǎn)量[2-4]。另一方面,深松作業(yè)牽引阻力大,需配備大馬力拖拉機(jī),增加農(nóng)戶生產(chǎn)成本。相關(guān)研究得出振動作業(yè)減阻效果顯著[5-6],但振動對拖拉機(jī)及駕駛員的不利影響嚴(yán)重制約其推廣。

    對振動深松耕阻、振動進(jìn)行多目標(biāo)優(yōu)化,可實現(xiàn)提高振動深松減阻效果的同時降低振動的目的[7]。另外,交錯振動可實現(xiàn)多組振動松土自平衡[8],但試驗尋優(yōu)過程中多組振動松土鏟作業(yè)的劇烈振動易造成試驗設(shè)備損壞,仿真試驗可避免危險工作環(huán)境下的實車試驗。ADAMS[9]是全球運用最為廣泛的機(jī)械系統(tǒng)仿真軟件,利用ADAMS可進(jìn)行振動松土自平衡研究。

    ADAMS動力學(xué)仿真有較多研究應(yīng)用。尚進(jìn)強(qiáng)[10]結(jié)合MATLAB控制模型與ADAMS機(jī)械系統(tǒng)模型,對直線行駛時的多個工況進(jìn)行穩(wěn)定性控制的聯(lián)合仿真。顧信忠[11]利用ADAMS/CAR對微型車模型進(jìn)行仿真分析并做整車平順性計算。相關(guān)研究局限于單車仿真,在農(nóng)業(yè)機(jī)械領(lǐng)域,拖拉機(jī)掛接農(nóng)機(jī)具作業(yè),需研究拖拉機(jī)-農(nóng)機(jī)具系統(tǒng)仿真技術(shù)。另外,整車仿真試驗的難點之一為輪胎與地面接觸的定義。

    輪胎與土壤接觸是車輛地面力學(xué)中一個重要且復(fù)雜的研究課題。姜其亮[12]通過試驗分析及仿真模擬的方法來研究輪胎的動態(tài)特性及其作用機(jī)理。周兵等[13]針對軟土路面振動特性,通過基于載荷沉陷理論開發(fā)出用于計算彈性輪胎——軟土路面接觸力的ADAMS用戶子程序。張曉陽[14]以汽車地面力學(xué)為基礎(chǔ),綜合考慮輪胎與地面的接觸變形特性,建立輪胎—變形地面接觸模型,并生成Matlab/Simulink仿真模塊。王平超[15]運用沖擊函數(shù)法(Impact)模擬鋼輪與軌道接觸摩擦。倫佳琪等[16]通過對輪胎與農(nóng)田土壤接觸試驗及有限元模型的研究,獲得輪胎與農(nóng)田土壤在不同工況下的變形規(guī)律。本文在相關(guān)研究基礎(chǔ)上,依據(jù)阻尼系數(shù)-切入深度曲線、附著系數(shù)-滑轉(zhuǎn)率曲線,利用Impact、STEP函數(shù)定義輪胎與土壤之間接觸力、摩擦力。

    本文對拖拉機(jī)-振動深松機(jī)系統(tǒng)進(jìn)行理論力學(xué)分析,并基于ADAMS建立其仿真模型,建模過程包括導(dǎo)入三維模型、添加約束、定義輪胎與地面之間接觸力和摩擦力、加載。根據(jù)GB/T13876-2007標(biāo)準(zhǔn)規(guī)定,采用加權(quán)加速度均方根值評價振動對駕駛員的影響。通過MATLAB編程,利用功率譜密度函數(shù),計算得到駕駛座質(zhì)心各軸向加權(quán)加速度均方根值。設(shè)計試驗并利用Design-Expert軟件優(yōu)化得到振動影響較小的四組振動松土鏟作業(yè)初始相位角組合。

    1 振動深松機(jī)結(jié)構(gòu)及工作原理

    如圖1所示,拖拉機(jī)通過后三點懸掛架掛接振動深松機(jī),拖拉機(jī)動力輸出軸動力通過萬向節(jié)傳遞至振動深松機(jī)變速箱輸入軸,變速箱輸出軸帶動偏心軸轉(zhuǎn)動,進(jìn)而通過連桿使拉桿-松土鏟往復(fù)擺動[7]。其中,激振機(jī)構(gòu)簡圖如圖2所示。

    1.拖拉機(jī) 2.振動深松機(jī) 3.變速箱 4.偏心軸 5.連桿 6.拉桿 7.松土鏟

    1. Tractor 2.Oscillatory subsoiler 3.Gearbox 4.Eccentric shaft 5.Connecting rod 6.Pull rod 7.Break shovel

    圖1 振動深松機(jī)受力簡圖 Fig.1 Force diagrams of oscillatory subsoiler

    注: C為松土鏟質(zhì)心;ωe為偏心軸角速度,rad·s-1;J3J4為連桿長度,mm;J2J3為偏心距,mm;J1J4為拉桿掛接距離,mm。

    本文以江蘇常發(fā)集團(tuán)CF700型拖拉機(jī)[20]為牽引機(jī),其主要參數(shù)如表1所示。

    表1 常發(fā)CF700型拖拉機(jī)參數(shù)表

    圖3 后輪所受支持力時域圖

    2 建立系統(tǒng)仿真模型

    2.1 三維模型的建立與導(dǎo)入

    利用SolidWorks建立拖拉機(jī)-振動深松機(jī)三維裝配體模型(.X_T)導(dǎo)入ADAMS/View,如圖4所示。拖拉機(jī)輪胎材質(zhì)為橡膠,密度為1×10-6kg/mm3,楊氏模量為6.1 N/mm2,泊松比為0.49。地面材質(zhì)為土壤,密度為2×10-9kg/mm3,楊氏模量為1.2 N/mm2,泊松比為0.25。其他零部件材質(zhì)為普通碳鋼,密度為7.801×10-6kg/mm3,楊氏模量為2.07×105N/mm2,泊松比為0.29。

    圖4 拖拉機(jī)-振動深松機(jī)系統(tǒng)仿真模型

    2.2 添加約束

    2.2.1 萬向聯(lián)軸器的簡化

    換向箱輸出軸與偏心軸,以及兩組相鄰偏心軸之間通過雙十字軸可伸縮型萬向聯(lián)軸器實現(xiàn)單自由度約束??紤]到雙十字軸可伸縮型萬向聯(lián)軸器主要作用為傳遞動力,其結(jié)構(gòu)對整機(jī)動力學(xué)分析影響較小,使用垂直約束代替雙十字軸可伸縮型萬向聯(lián)軸器,實現(xiàn)旋轉(zhuǎn)單自由度簡化約束。

    2.2.2 過約束的處理

    拉桿與機(jī)架之間轉(zhuǎn)動副使拉桿繞軸旋轉(zhuǎn),且約束向平動自由度。拉桿與連桿通過球鉸副連接,帶動連桿往復(fù)運動的偏心軸與機(jī)架通過轉(zhuǎn)動副連接,2個連接副同時作用使拉桿無法沿軸平移,即重復(fù)約束拉桿向平動自由度。將拉桿與機(jī)架之間轉(zhuǎn)動副改為圓柱副,移除一個向平動自由度。

    約束后得到一個10自由度拖拉機(jī)-深松機(jī)聯(lián)合仿真模型。拖拉機(jī)主體、、向轉(zhuǎn)動自由度,、、向平動自由度;左前輪向轉(zhuǎn)動自由度,右前輪向轉(zhuǎn)動自由度,后三點懸掛架、向轉(zhuǎn)動自由度。通過添加接觸力和摩擦力的方法進(jìn)一步約束這些自由度。

    2.3 定義輪胎-地面接觸參數(shù)

    2.3.1 定義接觸力

    拖拉機(jī)4個輪子與地面接觸。在ADAMS/View中,采用Impact函數(shù)[21]計算2個構(gòu)件之間的接觸力[15,22]。接觸力包括兩部分:由構(gòu)件相互切入產(chǎn)生的彈性力和由相對速度產(chǎn)生的阻尼力。Impact函數(shù)的表達(dá)式

    當(dāng)≥x1時,兩物體不發(fā)生接觸,力的大小為0;當(dāng)<1時,兩物體發(fā)生接觸。由式(3)可以看出,接觸力分為兩部分:彈性分量,類似于非線性彈簧;阻尼分量,其方向和運動方向相反。阻尼系數(shù)為Step階躍函數(shù)

    根據(jù)聶信天等[23]試驗分析得到導(dǎo)向輪、驅(qū)動輪輪胎徑向剛度、阻尼系數(shù)與輪胎充氣壓力的回歸方程。在140~220 kPa范圍內(nèi),輪胎的變形較小,輪胎阻尼主要是由輪胎橡膠的變形決定,阻尼較穩(wěn)定。在仿真過程中,本文選取輪胎充氣壓力為200 kPa,得到導(dǎo)向輪徑向剛度345 kN/m,阻尼系數(shù)1 772 N/(m/s);驅(qū)動輪徑向剛度419 kN/m,阻尼系數(shù)2 105 N/( m/s)。

    根據(jù)倫佳琪[16]得到定胎壓下輪胎沉陷量擬合方程,計算得到驅(qū)動輪沉陷量24.9 mm,導(dǎo)向輪沉陷量13.2 mm。輪胎沉陷量即拖拉機(jī)行駛過程中輪胎對地面的切入深度。

    表2 車輪-地面接觸參數(shù)表

    2.3.2定義摩擦力

    根據(jù)制附著率-滑轉(zhuǎn)率曲線[24-25],附著率隨滑轉(zhuǎn)率的增加先增加后減小,先后經(jīng)過局部形變滑轉(zhuǎn)和滑動滑轉(zhuǎn)2個階段。附著率峰值一般出現(xiàn)在rat=15%?20%,記為峰值附著系數(shù)adP?;D(zhuǎn)率再增加,附著力系數(shù)下降,直至滑轉(zhuǎn)率為100%。=100%的附著力系數(shù)為滑動附著系數(shù)adS。

    式中為車輪線速度,m/s;為前進(jìn)速度,m/s;Δ為相對滑動速度m/s;s為滑轉(zhuǎn)率。

    2.4 加 載

    Shahgoli G[29]等研究得出,鏟頭上表面作業(yè)時(切削階段),耕作阻力大;鏟頭下表面作業(yè)時(后退階段),耕作阻力小。振動松土過程中,耕作阻力呈正弦曲線規(guī)律變化,變化周期與松土鏟振動周期近似一致。由此得到耕阻的近似表達(dá)式

    式中為幅值,N;為偏距,N;為振動頻率,Hz;為初始相位角,rad,設(shè)定偏心軸軸心位于最高點時,=0,為時間,s。

    將振動深松機(jī)掛接于土槽臺車,進(jìn)行單組松土鏟振動松土作業(yè),如圖5所示,土壤條件如表3所示。通過六分力測量系統(tǒng)測量得到100組受力數(shù)據(jù)[7],每組數(shù)據(jù)包含前進(jìn)(軸)、橫向(軸)、豎直(軸)3個方向的受力值。通過SPSS統(tǒng)計分析得到各向受力值的極大、極小值及均值,如表4所示。

    圖5 單組振動深松鏟土槽作業(yè)

    式中F為前進(jìn)方向阻力,N;F為豎直方向阻力,N。

    表3 試驗土壤條件

    表4 各向受力統(tǒng)計值

    綜合以上建模過程,系統(tǒng)仿真模型構(gòu)建與試驗流程如圖6所示。

    圖6 系統(tǒng)仿真模型構(gòu)建與試驗流程圖

    3 仿真過程

    經(jīng)過上述約束與定義,得到拖拉機(jī)-振動深松機(jī)系統(tǒng)仿真模型。設(shè)置仿真時間為10 s,仿真步數(shù)為2 000,運行仿真,分別進(jìn)行單組鏟、四組鏟振動作業(yè)仿真試驗。

    3.1 仿真數(shù)據(jù)處理

    在ADAMS后處理模塊,調(diào)出駕駛座質(zhì)心位置、、共3個方向的加速度曲線以及后輪豎直方向接觸力曲線。仿真開始階段,軟件仿真啟動慣性力較大,加速度上下波動劇烈。實際作業(yè)中,拖拉機(jī)動力輸出軸轉(zhuǎn)動加速較平穩(wěn)。因此,舍棄0~5 s仿真數(shù)據(jù),以5~10 s仿真數(shù)據(jù)作為分析對象。

    如圖7所示,對單組鏟振動作業(yè)仿真試驗豎直方向接觸力曲線進(jìn)行頻譜分析得到幅值譜,因作傅里葉變換為點投影累加,且有一半能量到負(fù)頻率區(qū)域,故要真實反應(yīng)信號幅值,離散傅里葉變換應(yīng)乘以幅值譜系數(shù)2/(≠0)、1/(=0)[30],由此得到接觸力均值為26.4 kN,與理論計算相差1.4 kN。幅值譜圖中2個幅值較高的主振動(如圖7b所示),振頻分別為4、15.2 Hz。4 Hz由松土鏟振動產(chǎn)生,15.2 Hz由拖拉機(jī)前進(jìn)時輪胎與地面接觸點的變化產(chǎn)生。由幅值譜得到實際幅值分別為3.5、4.0 kN,并由相位譜得到初始相位分別為1.842、?1.978,由此得到二者疊加振動的時域圖。對比圖3可知,二者變化趨勢一致。綜合以上分析,理論計算與仿真結(jié)果可相互驗證。

    圖7 后輪與地面接觸力(豎直方向)頻譜分析

    3.2 舒適性評價

    加權(quán)加速度均方根值是按振動方向,根據(jù)人體對振動頻率的敏感程度而進(jìn)行加權(quán)計算的,是人體振動評價指標(biāo)。加權(quán)加速度均方根值a[31-32]計算公式為

    式中G()為功率譜密度,()為加權(quán)函數(shù)

    總加權(quán)加速度均方根值根值

    式中a、aa為加權(quán)加速度均方根值、、向分量,m/s2。

    3.3 MATLAB編程計算

    ADAMS可將駕駛座質(zhì)心位置加速度時間歷程曲線輸出為表格數(shù)據(jù)(.tab)格式。利用Microsoft Excel將“.tab”格式數(shù)據(jù)轉(zhuǎn)換為“.xlsx”格式數(shù)據(jù),MATLAB的“xlread”函數(shù)可讀取該格式數(shù)據(jù)。

    在MATLAB軟件中,利用“pwelch”函數(shù)對加速度時間歷程信號進(jìn)行功率譜估計得到加速度功率譜密度,利用公式(8)、(9),計算得到總加權(quán)加速度均方根值,MATLAB編程計算過程如圖8所示。

    圖8 仿真數(shù)據(jù)分析及試驗優(yōu)化流程圖

    4 優(yōu)化試驗設(shè)計與分析

    各組鏟初始相位角的相對變化影響駕駛座振動大小。因此,對四組鏟振動,固定松土鏟Ⅰ的初始相位角為0°,其他三組松土鏟初始相位角變化范圍為0~360°,進(jìn)行三因素試驗,既可減少試驗因素,減少試驗次數(shù),又可考察四組鏟初始相位角的相對變化對駕駛座振動的影響。試驗因素、指標(biāo)如表5所示。

    考察三因素交互作用,至少需要三次項,通過預(yù)試驗得出四次多項式回歸擬合優(yōu)度較好,利用Design-Expert優(yōu)化響應(yīng)面設(shè)計,得到試驗方案,如表6所示,其中0°可替換為360°。通過回歸分析得到方差分析表7,決定系數(shù)、預(yù)測決定系數(shù)、修正決定系數(shù)分別為0.894 8、0.841 1、0.765,回歸模型擬合優(yōu)度良好。

    表5 試驗因素及指標(biāo)

    表6 試驗設(shè)計與結(jié)果

    表7 方差分析表

    利用回歸模型,以總加權(quán)加速度均方根值最小為優(yōu)化目標(biāo),通過Design-Expert得出優(yōu)化結(jié)果,如表8所示,回歸模型預(yù)測結(jié)果與仿真試驗結(jié)果近似一致。其中,以初始相位角組合0°、225°、315°、180°為最優(yōu),仿真驗證試驗得到其減振比率達(dá)94%。

    表8 初始相位角組合仿真優(yōu)化結(jié)果

    根據(jù)農(nóng)業(yè)輪式拖拉機(jī)駕駛員全身振動的評價指標(biāo)(GB/T13876-2007)[33],輪式拖拉機(jī)駕駛員全身振動總加權(quán)加速度a應(yīng)不大于3 m/s2,仿真試驗優(yōu)化結(jié)果滿足該要求。

    5 結(jié) 論

    1)對拖拉機(jī)-振動深松機(jī)系統(tǒng)進(jìn)行受力分析,設(shè)定振動深松機(jī)振頻為4 Hz,列出系統(tǒng)平衡方程,計算得到拖拉機(jī)后輪所受支持力變化曲線,變化頻率為4 Hz,變化幅值為5.1 kN,均值為27.8 kN。

    2)基于ADAMS建立拖拉機(jī)-振動深松機(jī)系統(tǒng)仿真模型,包括導(dǎo)入三維模型、定義輪胎與地面之間接觸力和摩擦力等。仿真分析得到后輪所受支持力變化曲線,得到2個幅值較高的主振動,振頻分別為4、15.2 Hz,對應(yīng)幅值分別為3.5、4.0 kN,二者疊加振動曲線與理論計算結(jié)果曲線變化趨勢一致。仿真分析得到后輪所受支持力均值為26.4 kN,與理論計算相比,誤差為1.4 kN。理論與仿真分析相互驗證。

    3)采用加權(quán)加速度均方根值評價振動對駕駛員的影響。通過MATLAB編程,利用功率譜密度函數(shù),計算得到駕駛座質(zhì)心總加權(quán)加速度均方根值。

    4)利用Design-Expert軟件設(shè)計試驗并優(yōu)化得到6組振動影響較小的四組振動松土鏟作業(yè)初始相位角組合,回歸模型預(yù)測結(jié)果與仿真試驗結(jié)果近似一致。仿真優(yōu)化試驗避免了危險工作環(huán)境下的實車試驗。與未優(yōu)化組合相比,減振比率超過90%,實現(xiàn)了振動深松機(jī)作業(yè)時的自平衡。

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    Self-balancing performance and simulation analysis of multi-group vibrating sholvels of oscillatory subsoiler

    Sun Yapeng, Dong Xiangqian, Song Jiannong※, Wang Jicheng, Liu Cailing, Xu Guanghao

    (,,,100083,)

    Oscillation tillage could reduce the drag resistance and power consumption during tillage. But the oscillation has a bad effect on tractor driver. In order to do vibration analysis, a four-tine oscillatory subsoiler and a tractor model were designed using 3D modeling software in this study. In the process of oscillation tillage, the tillage forces and inertia force were unbalanced, these force transferred to the tractor and driver, and negatively impact them to some extent. These vibrations prevent the spreading use of oscillatory subsoiler. Therefore, it is necessary to conduct a vibration optimization test. The simulation optimization test could avoid the real car test in the dangerous working environment. A simulation model of the tractor-subsoiler system was established based on ADAMS. The modeling process had four parts, including introduction of 3D model, adding constraints, loading, defining the contact force and friction between tire and ground. During the contact force definition part, on the basis of the wheel damping coefficient-cut depth curve and the adhesion coefficient-slip rate curve of a running tractor, the contact force and friction force between tire and soil was defined by using the STEP function. This could improve the accuracy of the simulation model. During the contact force definition part, related research had shown that the maximum draft occurred during the period tine had their top face active (cutting) and the minimum draft occurred during the period tine had their underside active (backward). The statistical results showed that a sinusoidal force relationship was between these two peaks. In order to get the actual draft force of the tine during oscillation tillage, a single group tine oscillation tillage test was carried out in the soil bin, and the single tine draft force curve was obtained using statistical software. After that, the optimization tests were started. During the tests, the experimental index was the vibrations at the tractor driver’s seat. The working parameters to be considered were each tine’s initial phase angle of oscillation. The tests result showed that the theoretical and simulation analysis verifies each other. The mean value of the supporting force in the rear wheel of the tractor was 27.8 kN, 26.4 kN, respectively, the error was 1.4kN, and the tendency of the main vibration curve was consistent. The optimization goal was to reduce the root mean square of weighed acceleration on the tractor seat. According to the evaluation index of whole body vibration of agricultural wheeled tractor driver (GB/T13876-2007), the influence of vibration on the driver was evaluated by using the mean square root of weighted acceleration. By using the power spectral density function in MATLAB, the mean square root of the total weighted acceleration of the driving seat was calculated. Related research showed that the relative changes of the initial phase angle of the various groups affected the vibration size of the seat. During the test of four-group vibrating shovels of oscillatory subsoiler, we fixed one of the break shovel initial phase angle of 0°. The other three groups break shovel initial phase angle range of 0-360°. The relative changes of multi-group vibrating shovels’ initial phase angle can influence seat's vibration. The test for three factors can be used to consider the influence of four-group initial phase angles. As such, the test could reduce the test factors and test times. Using optimal design in Design-Expert software, the quartic order regression model was founded. According to the regression analysis, the variance analysis was obtained, and the R-squared, Adj R-squared, Pred R-squared were 0.8948, 0.8411, and 0.765, respectively, and the regression model was good. Six groups for the optimal solution of initial phase angle combination were obtained by using the regression model. Compared with the un-optimized combination, the vibration reduction ratio was over 90%, and the self-balance of the oscillatory subsoiler was realized.

    agricultural machinery; vibrations; computer simulation; subsoiling; self-balancing; ADAMS

    2017-08-17

    2018-01-10

    國家重點研發(fā)計劃(2016YFD0700302/2016YFD0701605),教育部創(chuàng)新團(tuán)隊發(fā)展計劃項目(IRT13039),中央高?;究蒲袠I(yè)務(wù)費專項資金資助項目(2015GX003/2016TC007)

    孫亞朋,博士生,主要從事農(nóng)業(yè)機(jī)械與農(nóng)業(yè)裝備研究。Email:sunypotter@qq.com

    宋建農(nóng),教授,主要從事農(nóng)業(yè)機(jī)械與農(nóng)業(yè)裝備研究。Email:songjn@cau.edu.cn

    10.11975/j.issn.1002-6819.2018.04.011

    S222.1

    A

    1002-6819(2018)-04-0092-08

    孫亞朋,董向前,宋建農(nóng),王繼承,劉彩玲,徐光浩. 振動深松機(jī)多組振動深松鏟自平衡性能及仿真分析[J]. 農(nóng)業(yè)工程學(xué)報,2018,34(4):92-99.doi:10.11975/j.issn.1002-6819.2018.04.011 http://www.tcsae.org

    Sun Yapeng, Dong Xiangqian, Song Jiannong, Wang Jicheng, Liu Cailing, Xu Guanghao. Self-balancing performance and simulation analysis of multi-group vibrating sholvels of oscillatory subsoiler[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(4): 92-99. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2018.04.011 http://www.tcsae.org

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