臂架驱动双纽线型起重机变幅机构的受力分析和实现

李克勤,姜翠香

(1.湖北工业大学 机械工程学院,武汉 430068; 2.武汉科技大学 理学院,武汉 430065)

臂架驱动双纽线型起重机变幅机构的受力分析和实现

李克勤1,姜翠香2

(1.湖北工业大学 机械工程学院,武汉 430068; 2.武汉科技大学 理学院,武汉 430065)

双纽线型起重机因其变幅轨迹近似为双纽线而得名.双纽线型起重机变幅机构的特点为臂架和后摇杆的活动范围大、几何形态特殊、整机重心高度低.运用逆向工程、机构学原理来分析该双纽线型起重机变幅机构的受力特性,经实例分析并在Matlab软件平台上实现,表明了该双纽线型起重机变幅机构具有良好的力学性能,非常适宜带载变幅作业.

受力分析; 变幅机构; 臂架驱动; 双纽线型起重机

双纽线型起重机为荷兰的Kenz-Figee公司所独创,现有两种典型形式,早期为后摇杆驱动型,近期出现了臂架驱动型[1-2].双纽线型起重机已经形成系列产品,有16 t,25 t,36 t,50 t等系列,用来转运、过驳矿石和煤炭等散装物料,作业效率甚至高达25 000 t/d.在我国还没有开发和使用这类双纽线型起重机,但是,研究人员早已开始关注和研究它[3-11].本文运用逆向工程原理和机构学理论,对臂架驱动的双纽线型起重机的变幅机构的受力进行深入研究,并在Matlab软件环境编程实现.

1 臂架驱动双纽线型起重机变幅机构的速度瞬心分析

臂架驱动双纽线型起重机变幅机构的最大特点是臂架为主动件[12-14],且臂架的活动范围很大,可实现水平平衡变幅作业操作.图1为该双纽线型起重机变幅机构正在作业的情形.

图1 双纽线型起重机变幅机构(臂架为主动件)Fig.1 Luffing mechanism of lemniscate type crane with boom driving

该双纽线型起重机变幅机构的速度瞬心位置变化很大,随变幅半径的变化,瞬心有时在水平线的上方(当幅度较大时),有时又出现在水平线的下方(当幅度较小时).

图2为臂架驱动双纽线型变幅机构运动简图.图2中:X1为臂架(主动件);X2为象鼻架后部;X3为后摇杆;X4为象鼻架前部;X5为后摇杆下铰点O3与臂架下铰点O1之水平距离;X6为后摇杆下铰点O3与臂架下铰点O1之铅垂距离;X7为象鼻架的下沉量;X8为回转中心线与臂架下铰点O1之水平距离;R为幅度;γ为臂架与象鼻架后部之夹角;θ3为后摇杆与水平线之夹角;θ1为臂架与水平线之夹角(自变量);β为吊点A速度向量与水平线之夹角;β0为象鼻架前部与后部之夹角;α为象鼻架前部与水平线之夹角;ω1为驱动臂架之角速度;Q为起重量(kN).

图2 臂架驱动双纽线型起重机变幅机构运动简图Fig.2 Schematic diagram of luffing mechanism of lemniscate type crane with boom driving

从图2可知:双纽线型变幅机构的工作范围较大,臂架的活动范围大并且为主动件;而常见的刚性四连杆起重机变幅机构(臂架为主动件)的臂架活动范围一般在42°～ 80°间,大拉杆的活动范围均在90°之内.

由于该双纽线型变幅机构的活动范围大,因此,其速度瞬心P的变化范围也大.为方便讨论,分两种情况:①θ1< 90°,θ1-θ3> 0,速度瞬心P在水平线的上方;②θ1≥90°,θ1-θ3<0,速度瞬心P在水平线的下方.

速度瞬心P与臂架下铰点O1的距离计算.据正弦定理不难求得:

(1)θ1<90°时

(Ⅰ)θ1-θ3>0

(1)

(2)θ1>90°时

(Ⅱ)θ1-θ3<0

(2)

式中:θ0=arctan(X6/X5).

很显然,当θ3=θ1时,速度瞬心P在无穷远处.速度瞬心P的轨迹如图3所示.

图3 速度瞬心P的轨迹Fig.3 Locus of velocity instantaneous center P

而后摇杆与水平线之夹角θ3可由式(3)求得:

(3)

速度瞬心P的坐标由式(4)求解得到:

(4)

2 变幅机构的受力分析

2.1 象鼻架的受力分析与求解

该双纽线型变幅机构中,象鼻架是受力最复杂的构件.由于臂架为主动件,所以臂架除轴向压力外还有附加的弯矩,弯矩由起重载荷Q产生.而此时,后摇杆只是一个二力构件,只有轴向拉力FC.

图4 象鼻架的受力图(不计自重)Fig.4 Force analysis of flying jib(neglect dead-weight)

由象鼻架的力平衡与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为后摇杆之力值;FBx为臂架之力值的水平分量;FBy为臂架之力值的垂直分量;XB,YB,XC,YC,XA为点B,C,A的坐标值.

2.2 后摇杆的受力分析与求解

双纽线型变幅机构中,因臂架为主动件,后摇杆的受力状况则大为改善.此时,后摇杆仅为二力构件,只受轴向的拉力FC.拉力FC由式(6)可求得.

2.3 臂架的受力分析与求解

因该双纽线型变幅机构的特殊性,臂架驱动,臂架除受轴向压力FB外,还有附加弯矩MQ最终作用于铰接点O1.MQ值以使幅角变小为正,反之则为负.FBx和FBy的方向为沿坐标轴的正向为正,反之则为负.FBx和FBy由式(5)可求得,附加弯矩MQ的求解如下:

MQ=FByX1cosθ1-FCxX1sinθ1

(7)

而铰接点B的作用力可分解为:垂直于臂架轴线的分力FBx1(引起附加弯矩)和沿臂架轴线的轴向分力FBy1

(8)

图5 臂架的受力图(不计自重)Fig.5 Force analysis of boom(neglect dead-weight)

3 实例分析与实现

据文献[15],后摇杆驱动双纽线型起重机变幅机构的已知数据有: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(从回转中心线算)30 m时θ3=49°,最小外伸距10.5 m时θ3=132°.起重量为160 kN(即16 t).但是,臂架驱动双纽线型起重机变幅机构没有已知数据可循,因其外观和结构形式与后摇杆驱动类型的相似性,只是驱动型式的不同,故几何尺寸的数据可以借用;运用逆向工程分析可以得到θ1的活动范围为60°～120°.

利用Matlab软件平台编程,选取角θ1为自变量,能较快得到FC,FBx,FBy,MQ,FBx1和FBy1的值.实例分析与实现的结论如图6～图8和表1所示.

图6 后摇杆之力值FCFig.6 Diagram of force on back-rocker FC

图7 臂架之力值的轴向分力FBy1Fig.7 Diagram of axial force on boom FBy1

图8 对铰点O1的附加弯矩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 结论

经过严密的机构学分析和实例计算表明,驱动臂架双纽线型起重机变幅机构的受力特性有:

(1) 臂架作为驱动件,受力情况复杂,除受轴向作用压力外,还要承受附加弯矩;

(2) 后摇杆只受轴向拉力;

(3) 在角θ1为90°附近时FC,FBy1的值达到极小,而FBx1,MQ的值出现跳变;

(4) 在最大幅度位置时,受力出现最大值,是最危险的工况.

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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