李克勤,姜翠香

(1.湖北工業(yè)大學(xué) 機(jī)械工程學(xué)院,武漢 430068; 2.武漢科技大學(xué) 理學(xué)院,武漢 430065)

臂架驅(qū)動(dòng)雙紐線型起重機(jī)變幅機(jī)構(gòu)的受力分析和實(shí)現(xiàn)

李克勤1,姜翠香2

(1.湖北工業(yè)大學(xué) 機(jī)械工程學(xué)院,武漢 430068; 2.武漢科技大學(xué) 理學(xué)院,武漢 430065)

雙紐線型起重機(jī)因其變幅軌跡近似為雙紐線而得名.雙紐線型起重機(jī)變幅機(jī)構(gòu)的特點(diǎn)為臂架和后搖桿的活動(dòng)范圍大、幾何形態(tài)特殊、整機(jī)重心高度低.運(yùn)用逆向工程、機(jī)構(gòu)學(xué)原理來(lái)分析該雙紐線型起重機(jī)變幅機(jī)構(gòu)的受力特性,經(jīng)實(shí)例分析并在Matlab軟件平臺(tái)上實(shí)現(xiàn),表明了該雙紐線型起重機(jī)變幅機(jī)構(gòu)具有良好的力學(xué)性能,非常適宜帶載變幅作業(yè).

受力分析; 變幅機(jī)構(gòu); 臂架驅(qū)動(dòng); 雙紐線型起重機(jī)

雙紐線型起重機(jī)為荷蘭的Kenz-Figee公司所獨(dú)創(chuàng),現(xiàn)有兩種典型形式,早期為后搖桿驅(qū)動(dòng)型,近期出現(xiàn)了臂架驅(qū)動(dòng)型[1-2].雙紐線型起重機(jī)已經(jīng)形成系列產(chǎn)品,有16 t,25 t,36 t,50 t等系列,用來(lái)轉(zhuǎn)運(yùn)、過(guò)駁礦石和煤炭等散裝物料,作業(yè)效率甚至高達(dá)25 000 t/d.在我國(guó)還沒(méi)有開發(fā)和使用這類雙紐線型起重機(jī),但是,研究人員早已開始關(guān)注和研究它[3-11].本文運(yùn)用逆向工程原理和機(jī)構(gòu)學(xué)理論,對(duì)臂架驅(qū)動(dòng)的雙紐線型起重機(jī)的變幅機(jī)構(gòu)的受力進(jìn)行深入研究,并在Matlab軟件環(huán)境編程實(shí)現(xiàn).

1 臂架驅(qū)動(dòng)雙紐線型起重機(jī)變幅機(jī)構(gòu)的速度瞬心分析

臂架驅(qū)動(dòng)雙紐線型起重機(jī)變幅機(jī)構(gòu)的最大特點(diǎn)是臂架為主動(dòng)件[12-14],且臂架的活動(dòng)范圍很大,可實(shí)現(xiàn)水平平衡變幅作業(yè)操作.圖1為該雙紐線型起重機(jī)變幅機(jī)構(gòu)正在作業(yè)的情形.

圖1 雙紐線型起重機(jī)變幅機(jī)構(gòu)(臂架為主動(dòng)件)Fig.1 Luffing mechanism of lemniscate type crane with boom driving

該雙紐線型起重機(jī)變幅機(jī)構(gòu)的速度瞬心位置變化很大,隨變幅半徑的變化,瞬心有時(shí)在水平線的上方(當(dāng)幅度較大時(shí)),有時(shí)又出現(xiàn)在水平線的下方(當(dāng)幅度較小時(shí)).

圖2為臂架驅(qū)動(dòng)雙紐線型變幅機(jī)構(gòu)運(yùn)動(dòng)簡(jiǎn)圖.圖2中:X1為臂架(主動(dòng)件);X2為象鼻架后部;X3為后搖桿;X4為象鼻架前部;X5為后搖桿下鉸點(diǎn)O3與臂架下鉸點(diǎn)O1之水平距離;X6為后搖桿下鉸點(diǎn)O3與臂架下鉸點(diǎn)O1之鉛垂距離;X7為象鼻架的下沉量;X8為回轉(zhuǎn)中心線與臂架下鉸點(diǎn)O1之水平距離;R為幅度;γ為臂架與象鼻架后部之夾角;θ3為后搖桿與水平線之夾角;θ1為臂架與水平線之夾角(自變量);β為吊點(diǎn)A速度向量與水平線之夾角;β0為象鼻架前部與后部之夾角;α為象鼻架前部與水平線之夾角;ω1為驅(qū)動(dòng)臂架之角速度;Q為起重量(kN).

圖2 臂架驅(qū)動(dòng)雙紐線型起重機(jī)變幅機(jī)構(gòu)運(yùn)動(dòng)簡(jiǎn)圖Fig.2 Schematic diagram of luffing mechanism of lemniscate type crane with boom driving

從圖2可知:雙紐線型變幅機(jī)構(gòu)的工作范圍較大,臂架的活動(dòng)范圍大并且為主動(dòng)件;而常見的剛性四連桿起重機(jī)變幅機(jī)構(gòu)(臂架為主動(dòng)件)的臂架活動(dòng)范圍一般在42°～ 80°間,大拉桿的活動(dòng)范圍均在90°之內(nèi).

由于該雙紐線型變幅機(jī)構(gòu)的活動(dòng)范圍大,因此,其速度瞬心P的變化范圍也大.為方便討論,分兩種情況:①θ1< 90°,θ1-θ3> 0,速度瞬心P在水平線的上方;②θ1≥90°,θ1-θ3<0,速度瞬心P在水平線的下方.

速度瞬心P與臂架下鉸點(diǎn)O1的距離計(jì)算.據(jù)正弦定理不難求得:

(1)θ1<90°時(shí)

(Ⅰ)θ1-θ3>0

(1)

(2)θ1>90°時(shí)

(Ⅱ)θ1-θ3<0

(2)

式中:θ0=arctan(X6/X5).

很顯然,當(dāng)θ3=θ1時(shí),速度瞬心P在無(wú)窮遠(yuǎn)處.速度瞬心P的軌跡如圖3所示.

圖3 速度瞬心P的軌跡Fig.3 Locus of velocity instantaneous center P

而后搖桿與水平線之夾角θ3可由式(3)求得:

(3)

速度瞬心P的坐標(biāo)由式(4)求解得到:

(4)

2 變幅機(jī)構(gòu)的受力分析

2.1 象鼻架的受力分析與求解

該雙紐線型變幅機(jī)構(gòu)中,象鼻架是受力最復(fù)雜的構(gòu)件.由于臂架為主動(dòng)件,所以臂架除軸向壓力外還有附加的彎矩,彎矩由起重載荷Q產(chǎn)生.而此時(shí),后搖桿只是一個(gè)二力構(gòu)件,只有軸向拉力FC.

圖4 象鼻架的受力圖(不計(jì)自重)Fig.4 Force analysis of flying jib(neglect dead-weight)

由象鼻架的力平衡與力矩平衡可以求解得:

FBx=FCcosθ3

FBy=Q+FCsinθ3

FBx(YC-YB)+FBy(XB-XC)=

Q(XA-XC)

(5)

FC=Q(XA-XB)/[cosθ3(YC-YB)+

sinθ3(XB-XC)]

(6)

式中:FC為后搖桿之力值;FBx為臂架之力值的水平分量;FBy為臂架之力值的垂直分量;XB,YB,XC,YC,XA為點(diǎn)B,C,A的坐標(biāo)值.

2.2 后搖桿的受力分析與求解

雙紐線型變幅機(jī)構(gòu)中,因臂架為主動(dòng)件,后搖桿的受力狀況則大為改善.此時(shí),后搖桿僅為二力構(gòu)件,只受軸向的拉力FC.拉力FC由式(6)可求得.

2.3 臂架的受力分析與求解

因該雙紐線型變幅機(jī)構(gòu)的特殊性,臂架驅(qū)動(dòng),臂架除受軸向壓力FB外,還有附加彎矩MQ最終作用于鉸接點(diǎn)O1.MQ值以使幅角變小為正,反之則為負(fù).FBx和FBy的方向?yàn)檠刈鴺?biāo)軸的正向?yàn)檎?反之則為負(fù).FBx和FBy由式(5)可求得,附加彎矩MQ的求解如下:

MQ=FByX1cosθ1-FCxX1sinθ1

(7)

而鉸接點(diǎn)B的作用力可分解為:垂直于臂架軸線的分力FBx1(引起附加彎矩)和沿臂架軸線的軸向分力FBy1

(8)

圖5 臂架的受力圖(不計(jì)自重)Fig.5 Force analysis of boom(neglect dead-weight)

3 實(shí)例分析與實(shí)現(xiàn)

據(jù)文獻(xiàn)[15],后搖桿驅(qū)動(dòng)雙紐線型起重機(jī)變幅機(jī)構(gòu)的已知數(shù)據(jù)有:X1=19.3 m,X2=6.5 m,X3=14.7 m,X4=16.0 m,AC=22.3 m,X5=6.4 m,X6=5.3 m,最大外伸距(從回轉(zhuǎn)中心線算)30 m時(shí)θ3=49°,最小外伸距10.5 m時(shí)θ3=132°.起重量為160 kN(即16 t).但是,臂架驅(qū)動(dòng)雙紐線型起重機(jī)變幅機(jī)構(gòu)沒(méi)有已知數(shù)據(jù)可循,因其外觀和結(jié)構(gòu)形式與后搖桿驅(qū)動(dòng)類型的相似性,只是驅(qū)動(dòng)型式的不同,故幾何尺寸的數(shù)據(jù)可以借用;運(yùn)用逆向工程分析可以得到θ1的活動(dòng)范圍為60°～120°.

利用Matlab軟件平臺(tái)編程,選取角θ1為自變量,能較快得到FC,FBx,FBy,MQ,FBx1和FBy1的值.實(shí)例分析與實(shí)現(xiàn)的結(jié)論如圖6～圖8和表1所示.

圖6 后搖桿之力值FCFig.6 Diagram of force on back-rocker FC

圖7 臂架之力值的軸向分力FBy1Fig.7 Diagram of axial force on boom FBy1

圖8 對(duì)鉸點(diǎn)O1的附加彎矩MQFig.8 Diagram of luffing moment MQ

θ1/(°)R/mFBx/kNFBy/kNFBx1/kNFBy1/kNMQ/(kN·m)FC/kN6029.9766329.2688544.961012.6422636.5132-244.6203506.56976429.0027259.9715535.9311-1.2993595.602824.6245457.06616827.9130207.2169533.2326-7.6429571.9858147.1491426.89747226.7424163.0586533.7726-9.8826557.9975190.4313407.79177625.5121123.6819536.1393-9.7096550.0999187.1298395.95208024.237086.9258539.5517-8.0994546.4158156.0780389.37848422.928451.4050543.4909-5.6985545.8543109.7575386.92088821.595516.1393547.5384-2.9902547.735757.5010387.87439020.9224-1.6376549.4767-1.6482549.444231.6054389.48029220.2458-19.6175551.2867-0.3763551.60277.0626391.77819618.8851-56.4575554.27691.7796557.1080-34.5380398.298510017.5176-94.8419555.94363.1279563.9311-60.5549407.144110416.1458-135.0815555.55933.3237571.6981-64.3266417.988210814.7690-177.2686552.17882.0314579.8914-39.3752430.381711213.3835-221.1515544.5920-1.0485587.737120.0794443.642911611.9805-265.9375531.3101-6.1192594.0686117.9628456.720912010.5448-310.0263510.6354-13.1786597.1822254.2385468.0400

4 結(jié)論

經(jīng)過(guò)嚴(yán)密的機(jī)構(gòu)學(xué)分析和實(shí)例計(jì)算表明,驅(qū)動(dòng)臂架雙紐線型起重機(jī)變幅機(jī)構(gòu)的受力特性有:

(1) 臂架作為驅(qū)動(dòng)件,受力情況復(fù)雜,除受軸向作用壓力外,還要承受附加彎矩;

(2) 后搖桿只受軸向拉力;

(3) 在角θ1為90°附近時(shí)FC,FBy1的值達(dá)到極小,而FBx1,MQ的值出現(xiàn)跳變;

(4) 在最大幅度位置時(shí),受力出現(xiàn)最大值,是最危險(xiǎn)的工況.

[1] GIJSBERT N,JACOB D.Crane,The Netherlands,EP1048606A1[P].2000-11-02.

[2] KENZ-FIGEE B V.Brochure of kenz-figee:offshore & harbour cranes[EB/OL].(2011-02-08)[2017-01-05].http://www.Kenz-Figee.com.

[3] 李克勤,姜翠香.雙紐線型起重機(jī)兩種類型變幅機(jī)構(gòu)的比較[J].中國(guó)工程機(jī)械學(xué)報(bào),2016(1):50-53.

LI K Q,JIANG C X.Comparative study on two luffing mechanisms of lemniscates type crane[J].Chinese Journal of Construction Machinery,2016(1):50-53.

[4] 李克勤.后搖桿驅(qū)動(dòng)臂架型起重機(jī)變幅系統(tǒng)分析與優(yōu)化設(shè)計(jì)的研究[D].武漢:武漢交通科技大學(xué),1993.

LI K Q.Research on analysis and optimal design of luffing system of jib type crane with back-rocker driving[D].Wuhan:Wuhan University of Water Transportation,1993.

[5] 李克勤,姜翠香.后搖桿驅(qū)動(dòng)臂架起重機(jī)的變幅機(jī)構(gòu)反求設(shè)計(jì)[J].起重運(yùn)輸機(jī)械,2002(5):8-9.

LI K Q,JIANG C X.Reverse design of back rocker powered luffing mechanism of jib crane[J].Hoisting and Conveying Machinery,2002(5):8-9.

[6] 李克勤.具有近似水平直線運(yùn)動(dòng)軌跡雙搖桿變幅機(jī)構(gòu)的運(yùn)動(dòng)學(xué)分析與計(jì)算[J].港口裝卸,2002(2):5-7.

LI K Q.The kinematic analysis and calculation of the double swing bar luffing mechanism with approximate level track[J].Port Operation,2002(2):5-7.

[7] 李克勤,姜翠香.一種新型四連桿變幅機(jī)構(gòu)的反求與MATLAB實(shí)現(xiàn)[J].湖北工業(yè)大學(xué)學(xué)報(bào),2008(3):76-77,80.

LI K Q,JIANG C X.An inverse design of a new double-link luff mechanism and realization on MATLAB[J].Journal of Hubei University of Technology,2008(3):76-77,80.

[8] LI K Q,JIANG C X.Inverse design of a new double-link luffing mechanism and realization on MATLAB[C]// Proceedings of the Third International Conference on Mechanical Engineering and Mechanics.[S.l.]:Monmouth Junction Science Press USA Inc.,2009:301-304.

[9] 李克勤,姜翠香.新型后搖桿驅(qū)動(dòng)四連桿變幅機(jī)構(gòu)的傳力特性與變幅力矩分析[J].科學(xué)技術(shù)與工程,2011(35):8723-872,8730.

LI K Q,JIANG C X.Transmission characteristic and luff moment of a new double-link luff mechanism with vack-rocker driving[J].Science Technology and Engineering,2011(35):8723-8725,8730.

[10] 李克勤,姜翠香.新型后搖桿驅(qū)動(dòng)四連桿變幅機(jī)構(gòu)的受力分析與程序?qū)崿F(xiàn)[J].科學(xué)技術(shù)與工程,2012(13):3231-3234.

LI K Q,JIANG C X.Force analysis and implementation of a new double-link luffing mechanism with back-rocker driving[J].Science Technology and Engineering,2012(13):3231-3234.

[11] 李克勤.后搖桿驅(qū)動(dòng)臂架型起重機(jī)的變幅機(jī)構(gòu)運(yùn)動(dòng)學(xué)與受力分析軟件V1.0,2014SR153105[P].2014.

LI K Q.Software for kinematics and force analysis of luffing mechanism of jib type crane with back-rocker driving V1.0,2014SR153105[P].2014.

[12] LI K Q,LI J N.Kinematics and luffing moment of lemniscate type crane with boom driving[J].Advanced Materials Research,2012,503/504:923-926.

[13] LI K Q,LI J N.Force analysis of luffing mechanism of lemniscate type crane with boom driving[J].Advanced Materials Research,2012,538:2618-2621.

[14] 李克勤.雙紐線型起重機(jī)的變幅機(jī)構(gòu)運(yùn)動(dòng)分析軟件V1.0,2015SR026039[P].2015.

LI K Q.Software for kinematics analysis of luffing mechanism of lemniscates type crane V1.0,2015SR026039[P].2015.

[15] UICKER J J,PENNOCK G R,SHIGLEY J E.Theory of machines and mechanisms[M].4th ed.New York:Oxford University Press Inc.,2010.

Force analysis and implementation of a luffing mechanism of lemniscate type crane with boom driving

LIKeqin1,JIANGCuixiang2

(1.School of Mechanical Engineering,Hubei University of Technology,Wuhan 430068, China; 2.College of Science,Wuhan University of Science & Technology,Wuhan 430065, China)

The luffing mechanism of normal double-link type crane is in general use for portal slewing cranes and floating cranes.But,a new luffing mechanism of lemniscate type crane come to light.There are great differences in outward appearance,geometric shape,luffing performance between lemniscate type crane with boom driving and normal double-link type crane.Loading and unloading on-stream as well as at sea,lemniscate type cranes can handle both ship-to-ship and ship-to-shore operations swiftly and efficiently in the Netherlands.It’s applied for European patent.The luffing mechanism of lemniscate type crane consists of boom,flying jib,back-rocker,but boom is driving.Based on theory of reverse engineering and mechanism,force characteristic of the luffing mechanism of lemniscate type crane with boom driving is studied.By sample analysis,the luffing mechanism of lemniscate type crane has good characteristic of force.

force analysis; luffing mechanism; boom driving; lemniscate type crane

李克勤(1965—),男,副教授.E-mail:leekeqin@163.com

TH 218

A

1672-5581(2017)05-0447-05