崔龍飛,薛新宇,丁素明,喬白羽,樂飛翔
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大型噴桿及其擺式懸架減振系統(tǒng)動力學特性分析與試驗
崔龍飛1,2,薛新宇1※,丁素明1,喬白羽1,樂飛翔1
(1. 農(nóng)業(yè)部南京農(nóng)業(yè)機械化研究所,南京 210014; 2. 江蘇大學農(nóng)業(yè)工程研究院,鎮(zhèn)江 212013)
針對擺式懸架減振系統(tǒng)對噴桿動力學行為影響機理的復雜性,利用第二類拉格朗日方法建立了描述噴桿-懸架系統(tǒng)傾斜運動、垂向運動的數(shù)學模型。在MATLAB/Simulink中進行了瞬態(tài)響應分析、頻率響應分析,研究了動力參數(shù)對其特性的影響。在此基礎上,以某大型噴桿及其擺式減振懸架為試驗對象,通過六自由度運動模擬平臺輸出翻滾和垂向運動激勵,采用超聲波距離傳感器、LVDT位移傳感器等進行數(shù)據(jù)采樣分析,測得噴桿瞬態(tài)動力學響應及頻率響應特性,并與模型預測進行對比,驗證了數(shù)學模型的準確性。最后通過掃頻振動試驗確定了系統(tǒng)的頻率響應峰值及對應頻率,著重分析了阻尼、剛度系數(shù)對噴桿振動特性的影響規(guī)律:在一定范圍內(nèi)增加阻尼可以減弱系統(tǒng)振蕩,增加剛度有利于提高懸架響應速度。研究為大型噴桿懸架參數(shù)優(yōu)化配置提供理論依據(jù)與試驗方法,有利于中國大型噴桿(大于12 m)動力學特性試驗方法、檢測標準的完善。
機械化;模型;試驗;噴桿噴霧機;噴桿運動;擺式懸架;動力學特性
噴桿式噴霧機作為大田植保的主要機具之一,由于田間不平地面的激勵導致噴桿的傾斜、振蕩等不規(guī)律運動(undesired motion),極大的影響噴霧分布形態(tài),降低農(nóng)藥化肥的作用效果[1-4]。在噴桿與車體之間增設懸架系統(tǒng)是提高噴桿穩(wěn)定性與防治效果的重要途徑[4-8]。擺式懸架在12~28 m進口噴桿噴霧機上使用較多,利用阻尼彈簧擺的原理,使噴桿能夠隨著機身的低頻擺動而擺動,以適應長波段的地形起伏,隔離由于短波段地表不平度造成的高頻振動,使噴桿保持相對穩(wěn)定。
噴桿懸架系統(tǒng)動力學特性方面的研究,英國農(nóng)業(yè)工程研究院、魯汶大學農(nóng)業(yè)工程與經(jīng)濟系等開展較早,Nation等[9]對多種噴霧機田間作業(yè)時的動力學特性分別進行了測試,研究了噴桿末梢垂直、水平方向振動,認為噴桿懸架設計時應重點考慮衰減來自噴霧機的翻滾運動。Frost等[10]對雙連桿懸架系統(tǒng)的動力學特性進行了數(shù)學建模和試驗驗證。Anthonis等[11-13]針對John Deere 39 m噴桿噴霧機進行研究,用數(shù)學模型描述噴桿的滾轉(zhuǎn)動力學行為,對懸架上彈簧緩沖器的安裝位置提出了優(yōu)化方案,并通過田間試驗驗證優(yōu)化方案的可行性。Kennes等[14-16]通過噴霧機整機有限元分析的方法,對不同懸架結(jié)構(gòu)下噴桿的動力學響應特性進行了對比。Ooms等[17-20]提出了基于多傳感器信息融合的噴桿運動特性測量方法。張際先[21-22]對“Patriot”噴霧機的雙連桿懸架性能和優(yōu)化曾進行過初步探索;Sun等[23-24]建立了寬幅4彈簧阻尼器型懸架-噴桿系統(tǒng)模型,研究了不同(脈沖、階躍、正弦)激勵下噴桿的動力學特性,發(fā)現(xiàn)車體翻滾運動對噴桿的影響遠大于平移運動的影響;邱白晶等[25-27]研究了當路面激勵相繼作用于噴霧機前、后輪時的噴桿運動響應的提取方法,并用于噴桿運動響應特性分析。
目前擺式懸架動力參數(shù)的對噴桿動力學行為影響的研究較少,本文針對擺式懸架減振系統(tǒng)的翻滾運動、垂向運動分別進行建模仿真,并借助Stewart六自由度運動模擬平臺進行樣機動力學特性測試,研究懸架阻尼系數(shù)、彈簧剛度等動力參數(shù)對噴桿瞬態(tài)響應特性、振動傳遞特性的影響規(guī)律,為大型噴桿懸架參數(shù)配置提供參考。
1.1 基本結(jié)構(gòu)
噴桿與機體之間安裝懸架的主要目的:一方面可以減小噴桿與機架間的機械應力;另一方面可以衰減噴霧機機體的晃動干擾,提供一個可以均勻噴霧的平臺。
彈簧擺式懸架結(jié)構(gòu)如圖1所示,支架1用來承擔噴桿系統(tǒng)的重力及慣性負載,鐘擺機構(gòu)通過吊環(huán)與支架在點鉸接,擺式懸架機構(gòu)由擺桿2、中心架3、托架4、垂向減振器5、側(cè)傾減振器6、噴桿7等組成。設點為整個噴桿(左噴桿、中心架、右噴桿)的質(zhì)心,中心架3可以沿擺桿滑動,托架與擺桿固連。2個彈簧減振器一端與托架固連,另一端支撐中心架。中心架連接左右噴桿,由于導向機構(gòu)的約束,噴桿在豎直平面的運動主要表現(xiàn)為繞轉(zhuǎn)軸的轉(zhuǎn)動、沿著鐘擺長度方向的平動,2種運動相互耦合。
1.支架 2.單擺機構(gòu) 3.浮動架 4.托架 5.垂向減振器 6.側(cè)傾減振器 7.噴桿
1.Bracket 2.Pendulum mechanism 3.Floating frame 4.Carrier fame 5.Vertical vibration damper 6. Roll vibration damper 7. Spray boom
注:表示噴桿質(zhì)心位置,表示單擺機構(gòu)的轉(zhuǎn)動中心。
Note:is centroid position of spray boom;is rotation center of pendulum mechanism.
圖1 噴桿及懸架裝置
Fig.1 Spray boom and suspension device
1.2 工作原理
彈簧擺式減振懸架利用單擺原理,噴桿運動過程中質(zhì)心常處于過點豎直線的左邊或者右邊,設擺桿與豎直線的夾角為,噴桿及中心架總質(zhì)量為,噴桿質(zhì)心由于受到重力和彈簧提供的回復力在平衡位置往復擺動,可調(diào)式液壓減振器安裝于機架與鐘擺之間,噴桿的動能經(jīng)阻尼器、摩擦等消耗,噴桿最終回到平衡位置。在垂直擺桿方向則使用2個大螺旋彈簧及阻尼器直接衰減來自地面的起伏運動。
2.1 模型描述
如圖2所示懸架系統(tǒng)原理圖。噴桿12通過滑動副與擺桿連接,噴桿質(zhì)心可以沿滑動,噴桿12與擺桿上的點通過彈簧和阻尼器連接,擺桿與在點鉸接。圖中3表示傾斜的地面,車體的側(cè)傾運動簡化為繞的擺動,多數(shù)噴霧機使用拖拉機作為運載車輛,研究噴桿滾轉(zhuǎn)運動暫不考慮輪胎的剛度、阻尼的影響。噴桿與擺式懸架減振系統(tǒng)即簡化為三自由度剛性桿-彈簧擺模型,3個自由度分別指連桿繞點的轉(zhuǎn)動、連桿繞點的轉(zhuǎn)動和噴桿(沿方向)的平動,三者之間相互耦合。
1.噴桿 2.彈簧擺懸架 3.地面 4.輪胎和機架
1.Spray room 2.Spring pendulum suspension 3.Ground 4.Tire and frame of vehicle
注:為地面坡度,rad;為噴桿與水平面的夾角,rad;為擺桿與機架的夾角,rad;1為噴桿旋轉(zhuǎn)剛度系數(shù),m·N·rad-1;2為垂向彈簧的剛度系數(shù),N·m-1;1為噴桿旋轉(zhuǎn)阻尼系數(shù),m·s N·rad-1;2垂向滑動阻尼器的阻尼系數(shù),N·s·m-1。
Note:is inclination angle of ground to horizontal, rad;isinclination angle of spray boom to horizontal, rad;is included angle between pendulum link () and link (), rad;1is rotational stiffness coefficient of spray boom, m·N·rad-1;2is stiffness coefficient of vertical spring, N·m-1;1 isrotational damping coefficient of spray boom, m·s N·rad-1;2 isdamping coefficient of vertical damper, N·s·m-1.
圖2 噴桿噴霧機及其擺式懸架減振系統(tǒng)
Fig1 Boom sprayer and pendulum suspension damping system
2.2 動力學方程與頻響函數(shù)
噴桿與擺桿的端點通過減振彈簧、阻尼器連接,擺桿可繞機架上點轉(zhuǎn)動,與機架之間裝有旋轉(zhuǎn)阻尼緩沖器。設地面坡度,不考慮輪胎變形,則車體與重力方向的夾角大小也為,噴桿與水平面的夾角,擺桿相對機架的夾角為。以點為重力勢能零點。噴桿的運動用拉格朗日方程描述
式中T為總動能,N·m;V為系統(tǒng)的勢能,N·m;D為瑞利耗散能,N·m·rad/s。
噴桿懸架原理圖2中噴桿的質(zhì)心在到轉(zhuǎn)軸點的距離為,機架上距離地面瞬時擺動中心的距離為,以為坐標原點,設噴桿重心的縱坐標=cos-cos(+),重心的橫坐標=-sin+sin(+)。
系統(tǒng)的勢能V
式中為噴桿的質(zhì)量,kg;為重力加速度,m/s2。
系統(tǒng)的總動能T
式中為繞質(zhì)心的轉(zhuǎn)動慣量,kg·m2。
設轉(zhuǎn)軸處的摩擦力矩為1(N·m),系統(tǒng)瑞利耗散函數(shù)D
對于被動懸架系統(tǒng),無外界動力源,所以廣義力=0。將式(2)-(4)代入式(1),即可得到系統(tǒng)的動力學方程組,由于田間作業(yè)時地面坡度、噴桿水平傾角都非常小,假設sin(+)≈+,cos(+)≈1,忽略二階小量,將動力學方程組化簡
(5)
通過以上方程(5)描述噴桿在車體擾動輸入下的動力學行為,懸架各關節(jié)運動副潤滑良好的情況下,≈0。
式中為拉普拉斯算子,表示復數(shù)頻率;同理可得噴桿水平傾角與地面坡度角的傳遞函數(shù)
(7)
被動懸架系統(tǒng)屬于二階系統(tǒng),系統(tǒng)的特征方程
系統(tǒng)的懸架翻滾運動阻尼比1為
(9)
系統(tǒng)固有頻率ω
系統(tǒng)的有阻尼頻率為ω
(11)
令=,為虛數(shù),為頻率,rad/s;代入傳遞函數(shù)(7)中,系統(tǒng)頻率響應函數(shù)表達式
(13)
在運載車輛屬性卻確定的情況下,噴桿的翻滾運動(roll movement)特性主要由等效回轉(zhuǎn)半徑l、噴桿旋轉(zhuǎn)阻尼系數(shù)1、噴桿旋轉(zhuǎn)剛度系數(shù)1、擺長和決定。
在研究豎直激勵作用下噴桿振動情況時,噴桿懸架系統(tǒng)可簡化為質(zhì)量-彈簧-阻尼系統(tǒng),該二階系統(tǒng)動力學方程為
對方程(14)兩端進行拉氏變換,可得系統(tǒng)傳遞函數(shù)
(15)
由式(15)可以推導出垂向振動幅頻特性函數(shù),也即位移傳遞函數(shù)
通過傳遞函數(shù)對輸入激勵進行運算就可以得出系統(tǒng)的響應,在MATLAB/Simulink環(huán)境中對懸架數(shù)學模型進行瞬態(tài)響應分析、頻率響應分析,對噴桿懸架系統(tǒng)動力學參數(shù)如噴桿旋轉(zhuǎn)阻尼系數(shù)1、垂向滑動阻尼器的阻尼系數(shù)2、噴桿旋轉(zhuǎn)剛度系數(shù)1垂向彈簧剛度系數(shù)2進行研究,并進行臺架試驗驗證,以期達到提升懸架減振效果及噴桿的穩(wěn)定性的目的。
試驗時設計分體式液壓阻尼器(阻尼調(diào)節(jié)采用插裝式電磁節(jié)流閥)抑制噴桿橫滾運動,且節(jié)流閥開度可調(diào),在疊加套管內(nèi)置復位彈簧。通過機電伺服萬能試驗機測得試阻尼器的拉(壓)力F(N)及對應的伸(縮)速度v(m/s),通過對試驗數(shù)據(jù)擬合如圖3a所示,線性擬合方程F11 389.7v,決定系數(shù)2=0.921,即得緩沖器伸縮阻尼系數(shù)11 389.7 N·s/m,根據(jù)單擺機構(gòu)幾何關系折算出噴桿旋轉(zhuǎn)阻尼系數(shù)1為25 758 N·m·s/rad;同理測得垂向滑動阻尼器的阻尼系數(shù)2為5.11 N·s/m。
彈簧剛度系數(shù)也使用萬能試驗機測試,勻速壓縮彈簧,測得力與變形關系曲線如圖3b所示,圖中斜線的斜率即剛度系數(shù)阻尼器內(nèi)置彈簧剛度系數(shù)26 320 N/m,根據(jù)幾何關系折算出噴桿旋轉(zhuǎn)剛度系數(shù)1為51 521 N·m/rad;同理測得垂向彈簧剛度系數(shù)2為13 350 N/m。
噴桿整體質(zhì)量通過行吊上的電子磅測得,為922.6 kg。利用SolidWorks三維模型測得噴桿繞質(zhì)心慣量2為3.27×104kg·m2。懸架主要參數(shù)測試、換算之后如表1所示。
表1 懸架參數(shù)
懸架的動力學特性通常從時域和頻域2個方面分別采用瞬態(tài)響應法和頻率響應法來分析,在時域內(nèi)研究懸架響應特性時,采用階躍輸入研究懸架的時域瞬態(tài)響應,表征參數(shù)為峰值時間、超調(diào)量等[28-30];采用正弦激勵信號研究傳感器的頻域動力學特性時,常用幅頻特性(位移傳遞率)來描述懸架動力學特性。本文通過模型仿真和試驗相結(jié)合的方法分析懸架的瞬態(tài)響應特性和頻率響應特性,通過阻尼系數(shù)、彈簧剛度等參數(shù)對動力學特性的影響規(guī)律,指導懸架參數(shù)合理配置。
4.1 試驗裝置與數(shù)據(jù)采集
Stewart六自由度運動平臺即由動平臺、鉸支座、驅(qū)動腿和固定平臺組成6UPU并聯(lián)機構(gòu),如圖4a所示。動平臺和固定平臺通過虎克鉸與驅(qū)動腿相連,通過控制驅(qū)動腿的長度即可改變動平臺的位置和姿態(tài),伺服電機進行驅(qū)動,具有剛度大、體積小、運動精度高、動力性能好等優(yōu)點[31-32]。在控制臺輸入動平臺的運動指令,接著運動控制計算機進行位姿反解,得到各驅(qū)動支路的驅(qū)動信號,控制各個電動缸運動,進而帶動上平臺和噴桿運動,伺服電機的運動信息通過旋轉(zhuǎn)編碼器和脈沖計數(shù)器反饋至主控計算機,計算機將脈沖數(shù)據(jù)轉(zhuǎn)換為電動絲杠位移量,形成位置閉環(huán)控制。
六自由度平臺主要參數(shù):轉(zhuǎn)動幅值10°平動幅值0.4 m,頻率范圍0.01~35 Hz,靜載荷2 t,可以進行正弦掃頻振動、激勵譜(路面譜、海浪譜等)復現(xiàn)。試驗對象為圖4a中的28 m桁架式噴桿及其擺式懸架,懸架機構(gòu)如圖2原理圖所示,帶有兩對彈簧、阻尼的擺式懸架,擺桿長度1.1 m,噴桿兩側(cè)噴臂由兩段組成:內(nèi)臂質(zhì)量248.6 kg,長度6.3 m;外臂質(zhì)量125.7 kg,長度6.83 m,內(nèi)、外噴臂通過液壓缸進行折疊/展開。通過安裝夾具將懸架支座固定于Stewart六自由度運動模擬平臺上,以動平臺的運動模擬噴霧機車體的擾動激勵,動平臺運動姿態(tài)(平動、轉(zhuǎn)動)實時反饋給工控機,圖4b為噴桿動力學模擬分析軟件。
如圖5所示噴桿的傾角(繞X軸)通過2個高精度超聲波傳感器(Banner,U-GAGE U45Q)測算,響應時間可調(diào)節(jié)范圍為40~1 280 ms,最高響應頻率為25 Hz,滿足懸架動力學測試頻響要求。噴桿的相對擺桿PQ滑動位移使用頂桿式線位移傳感器(linear variable differential transformer,LVDT)位移傳感器測得,分體式阻尼器(bosch rexroth)的動行程使用分體式LVDT位移傳感器(soway,SDVG20-250)測得,使用東華測試的DH5902無線動力學采集系統(tǒng)進行數(shù)據(jù)采集。
4.2 瞬態(tài)響應仿真與驗證
ANTHONIS等采用提拉法對噴桿纜繩懸架進行瞬態(tài)響應試驗,并以此驗證懸架數(shù)學模型準確性[12]。噴桿擺振提拉法試驗具體方法:在噴桿展開狀態(tài)下,利用行車提拉噴桿一側(cè),將噴桿傾斜至5.7°,自由釋放噴桿,同時使用超聲波高度傳感器,記錄噴桿兩端測點高度變化,計算得到噴桿側(cè)傾角隨時間衰減歷程,瞬態(tài)響應的峰值時間為2.25 s,超調(diào)量為2.24°,到達3.36 s時刻噴桿傾角衰減到初始值的10%以內(nèi)。在Matlab中采用四五階龍格—庫卡塔算法求解二階微分方程5,得到仿真曲線與曲線如圖6a虛線所示,二者變化趨勢一致,均方根誤差為0.072,可知描述噴桿翻滾運動的數(shù)學模型精度較高,可以用于系統(tǒng)動力學特性的分析。
在Matlab環(huán)境中,改變懸架旋轉(zhuǎn)阻尼系數(shù)進行3組仿真分析,噴桿傾角變化如圖6b,可以看出阻尼系數(shù)對動力學響應的峰值影響比較大,增大阻尼,系統(tǒng)振蕩性能減弱,即最大超調(diào)量和振蕩次數(shù)都減小。但阻尼系數(shù)過大,懸架峰值時間增加,響應速度變慢。改變懸架旋轉(zhuǎn)剛度系數(shù)進行3組數(shù)值分析,噴桿傾角變化如圖6c,可知彈簧剛度對響應峰值影響相對較小,剛度系數(shù)越大,懸架的瞬態(tài)響應峰值越大,峰值時間越小,系統(tǒng)的響應越快。
噴桿垂向振動提拉法試驗具體方法:通過門式行車提拉噴桿中心位置,將噴桿整體提升0.1 m,自由釋放噴桿,使用超聲波高度傳感器,記錄噴桿垂向高度變化歷程如圖7a所示,峰值時間0.69 s,超調(diào)量為0.018 m,2.2 s之后噴桿回到平衡位置。在Matlab中求解微分方程14,得到仿真曲線與試驗曲線如圖7a虛線所示,仿真曲線與試驗曲線的均方根誤差為0.046,可知描述噴桿垂向運動的數(shù)學模型精度較高,可以用于系統(tǒng)垂向動力學特性的分析。由圖7b和7c可知阻尼系數(shù)和剛度系數(shù)對垂直方向瞬態(tài)動力學特性影響規(guī)律與翻滾方向一致。
4.3 翻滾運動頻響特性分析
噴桿翻滾運動的頻響特性試驗:使Stewart動平臺繞軸按指定頻率輸出正弦往復擺動,多次試驗發(fā)現(xiàn)激勵頻率大于2 Hz后噴桿運動幅值非常小,隨著頻率增大,測得的噴桿傾角與動平臺傾角的幅值比迅速衰減一個穩(wěn)定值,同時,從式(13)和(16)所述的頻響函數(shù)也可以看出,該擺式懸架屬二階系統(tǒng),對輸入激勵起到二階低通濾波的作用,隨著頻率增大,幅值比存在極限值。因此,試驗過程中縮小了測試頻率范圍,在包含共振區(qū)的低頻段0.01~2.4 Hz取18個頻率點,依次進行試驗,記錄噴桿達到穩(wěn)態(tài)后的傾角幅值,計算出每個試驗頻率對應的幅值比(噴桿傾角幅值與動平臺傾角幅值之比),繪制角位移頻響曲線如圖8a所示,采用對數(shù)坐標系,試驗曲線與數(shù)學模型仿真進行比對,兩者的變化趨勢一致,試驗值與預測值的均方根誤差為0.146。當激勵頻率小于0.07 Hz時,測得側(cè)傾角的幅值比接近水平且保持在0.87左右,說明噴桿能夠隨機架的低頻擺動而擺動,適應長波段的地形變化。當激勵頻率為0.22 Hz時,幅值比最大為1.74,可知當頻率大于0.3 Hz時,進入隔振區(qū),振動幅值比小于1,并逐漸減小,頻率為1.2 Hz(截止頻率)時,幅值比衰減到極小值0.135 6,懸架的截止頻率越低,從機身傳遞到噴桿的高頻振動越少。
從圖8b不同阻尼系數(shù)懸架幅頻曲線可以看出:峰值頻率與阻尼無關,幅頻曲線的峰值受阻尼變化影響較大,阻尼愈小峰值處的幅值比越大,懸架將來自車體的振動進行了放大。從圖8c不同彈簧剛度系數(shù)下幅頻曲線可以看出:彈簧剛度對幅值比峰值影響相對較小,剛度系數(shù)越大,懸架的幅頻特性峰值越大,同時固有頻率增大,系統(tǒng)響應的快速性越好。
通過調(diào)節(jié)阻尼器上節(jié)流閥的開度,調(diào)節(jié)螺釘從最外側(cè)依次旋入2圈,阻尼由小增大,幅頻特性曲線如圖9所示,阻尼小對應節(jié)流閥完全打開;阻尼中對應阻尼調(diào)節(jié)螺釘旋入2圈,阻尼大對應阻尼調(diào)節(jié)螺釘旋入4圈,調(diào)節(jié)螺釘旋入6圈阻時尼器鎖死;幅頻特性受系統(tǒng)阻尼系數(shù)影響下的變化規(guī)律與圖8b模型預測一致。
4.4 垂向振動頻響特性分析
噴桿垂向振動頻響特性試驗:利用六自由度平臺模擬作業(yè)時噴霧機上下起伏運動,使動平臺沿軸輸出正弦往復運動,頻率在0.01~18 Hz范圍內(nèi)取18個頻率點,依次進行試驗,將位移傳感器測得的噴桿相對位移與動平臺位移疊加,即噴桿絕對位移。記錄噴桿運動達到穩(wěn)態(tài)后的幅值,計算出每個試驗頻率對應的幅值比(噴桿運動幅值與動平臺運動幅值之比),繪制幅頻曲線如圖10a中所示,在Matlab中建立公式(14)~(16)所述數(shù)學模型,分析垂向頻響特性,模型預測值與試驗值的均方根誤差為0.203。當激勵頻率為0.59 Hz時,幅值比最大為1.50。當激勵在0.1至1.04 Hz之間為懸架系統(tǒng)的共振區(qū),位移傳遞率大于1;當激勵頻率大于1.05 Hz時為隔振區(qū),隨之頻率增加傳遞率減小。從圖10b和10c可以看出阻尼系數(shù)和剛度系數(shù)對垂直方向瞬態(tài)動力學行為影響規(guī)律與噴桿翻滾運動幅頻特性一致。
1)對大型噴桿擺式減振懸架的基本結(jié)構(gòu)和減振原理進行了分析,建立了描述噴桿-懸架系統(tǒng)翻滾運動、垂向運動的數(shù)學模型,并在MATLAB環(huán)境中進行了瞬態(tài)響應分析、頻率響應分析。
2)以某大型噴桿-擺式懸架為試驗對象,通過六自由度運動模擬平臺分別產(chǎn)生垂向、翻滾運動激勵,采用超聲波距離傳感器、LVDT位移傳感器等進行數(shù)據(jù)分析,測得噴桿瞬態(tài)動力學響應及頻率響應特性,驗證了數(shù)學模型的精度,其中翻滾運動頻響特性模型預測值與試驗值均方根誤差為0.146,垂向頻響特性均方根誤差為0.203。
3)通過振動頻響試驗確定了被測擺式懸架減振系統(tǒng)的頻率響應峰值及共振頻率,研究表明擺式懸架可以有效隔離源于地表不平度造成的高頻振動;阻尼系數(shù)愈小頻響特性特性曲線峰值越大;剛度系數(shù)越大懸架的頻響特性曲線峰值越大。
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Analysis and test of dynamic characteristics of large spraying boom and pendulum suspension damping system
Cui Longfei1,2, Xue Xinyu1※, Ding Suming1, Qiao Baiyu1, Le Feixiang1
(1.210014,;2.212013,)
To increase the yield in agriculture, plants must be protected against diseases and need to be provided with fertilizers. One of the most important methods to spread agro-chemicals is by using spray booms. The efficiency of the chemicals is highly correlated with the uniformity of the spray distribution pattern, and as spray boom motions play a dominant role on the spray distribution pattern, spray boom stability is important. Moreover, with the stable boom, the distance between the nozzles and the target can be reduced, and then the drift losses are less important. Boom movements are due to ground irregularities that are transformed and more or less amplified depending on the mechanics features of the boom suspension. In order to reduce the unevenness in spray deposit, the majority of current agricultural sprayers are equipped with a suspension system to attenuate the roll of the boom. The suspension tries to keep the boom at right angles by isolating the boom from vibrations of the tractor or trailer which are induced by unevenness of the ground. Therefore, the suspension system should act as a system that attenuates undesired machine movement. The most important vibration, affecting the spray distribution pattern, is rolling (rotational motion around an axis along the driving direction) that causes spray boom motions in the vertical plane. However, the correlation between the dynamic behavior of the spray boom and suspension parameters are still unclear and the design principles and methods of the pendulum boom suspension are also missing or imperfect, which restrict the improvement of spray quality and operation efficiency. In order to understand the effect of the dynamic parameters of pendulum suspension system on the dynamic behavior of the spray boom, an analytical mathematical model of this pendulum suspension is established by using the second kind of Lagrange equations and the necessary transfer function. The dynamic characteristics of the pendulum suspension are derived, and the behavior such as the rolling movement and vertical movement of the passive suspension can be most conveniently described by its complex frequency response function. Transient response analysis and frequency response analysis are carried out in MATLAB/Simulink, and the effects of dynamic parameters on the characteristics of the suspension are studied. On the basis of this, taking a large spray boom and its pendulum suspension as the test object, the boom rolling movement and vertical movement excitations were outputted by using the six degrees of freedom motion simulation platform, and the boom suspension was instrumented with ultrasonic distance sensor, LVDT (linear variable differential transformer) displacement sensor, and so on. The transient dynamic response and frequency response characteristics of spray boom were measured, and then the accuracy of the mathematical model was verified. The root mean square error between the mathematical model predictive value and test value was 0.146 for rolling frequency response, and 0.203 for vertical oscillation frequency response. Peak value of the amplitude frequency curve and the corresponding frequency were determined by the sweep frequency vibration test, and the influence of damping and stiffness coefficients on the vibration characteristics of the boom was analyzed. In a certain range, increasing the damping could reduce the system oscillation and increase the stiffness, which was beneficial to increase the response speed and natural frequency of the suspension, but natural frequency could not be too high since beyond this frequency the suspension started to suppress the disturbances. Through research, we get to know that this kind of pendulum suspension with springs and dampers can enable the boom to follow low frequency ground undulations so remaining parallel to the ground beneath it, while providing isolation from the rapid motion of the spray vehicle as it travels over rough terrain. This study also provides a theoretical basis and test method for the parameters configuration of large boom, and it is beneficial to perfect the test method and test standard of the dynamic characteristics of large scale spraying boom (over 12 m) in China.
mechanization; models; experiments; boom sprayer; spray boom movement; pendulum suspension; dynamic characteristics
10.11975/j.issn.1002-6819.2017.09.008
S49
A
1002-6819(2017)-09-0061-08
2016-10-14
2017-04-08
國家自然科學基金資助項目(51605236);國家重點研發(fā)計劃:地面與航空高工效施藥技術及智能化裝備(2016YFD0200700);江蘇省農(nóng)業(yè)科技自主創(chuàng)新資金(CX(16)1043);
崔龍飛,男(漢族),河南鞏義人,助理研究員,博士生,主要從事機械系統(tǒng)動力學研究。南京 農(nóng)業(yè)部南京農(nóng)業(yè)機械化研究所,210014。Email:cuilong.fei@163.com
薛新宇,女(漢族),江蘇蘇州人,研究員,博士,博士生導師,主要從事植保機械技術研究。南京 農(nóng)業(yè)部南京農(nóng)業(yè)機械化研究所,210014。Email:735178312@qq.com
崔龍飛,薛新宇,丁素明,喬白羽,樂飛翔. 大型噴桿及其擺式懸架減振系統(tǒng)動力學特性分析與試驗[J]. 農(nóng)業(yè)工程學報,2017,33(9):61-68. doi:10.11975/j.issn.1002-6819.2017.09.008 http://www.tcsae.org
Cui Longfei, Xue Xinyu, Ding Suming, Qiao Baiyu, Le Feixiang. Analysis and test of dynamic characteristics of large spraying boom and pendulum suspension damping system[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(9): 61-68. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2017.09.008 http://www.tcsae.org