dvanced Materials Research Online: 2012-04-12 ISSN: 1662-8985, Vols. 503-504, pp 923-926 doi:10.4028/www.scientific.net/mr.503-504.923 2012 Trans Tech ublications, Switzerland Kinematics and Luffing Moment of Lemniscate Type Crane with Boom Driving Keqin Li 1,a, Junning Li 2,b 1 School of Mechanical Engineering, Hubei University of Technology, Wuhan,430068,China 2 No.1 Middle School ffiliated To Central China Normal University, Wuhan,430223,China a leekeqin@163.com, b lijunning2010@sina.com Keywords: Kinematics analysis, Luffing moment, Lemniscate type crane with boom driving, Luffing mechanism, Inverse design bstract. The lemniscate type crane is fabricated by Figee B.V. of the Netherlands. There are great differences in outward appearance, geometric shape, luffing performance between lemniscate type crane and ordinary double-link type crane. Lemniscate type crane has some advantages, i.e. lower centre of weight, practical and reasonable structure, strongly anti-wind and easy operation. Based on inverse design and theory of mechanism, instant centers of velocity, luffing locus and moment of lemniscate type crane is studied and solved. The equations of kinematics and luffing moment are obtained. Introduction The lemniscate type crane is specially designed and manufactured by Kenz-Figee B V of the Netherlands. It has 16, 25, 36 or 50 tons grab duty, outreach designed for handling anamax and Capesize vessels, transshipment up to 25,000 tons/day [1]. There are great differences in outward appearance, geometric shape, luffing performance between lemniscate type crane and ordinary double-link type crane. Lemniscate type crane has some advantages, i.e. lower centre of weight, practical and reasonable structure, strongly anti-wind and easy operation. Loading and unloading on-stream as well as at sea, the crane can handle both ship-to-ship and ship-to-shore operations swiftly and efficiently. Flexibility, reliability and progressive performance under all circumstances make the crane stand out from other floating and harbour grab cranes [2,3]. Luffing mechanism of lemniscate type crane consists of boom, flying jib, back-rocker and crane base. Lemniscate type crane with back-rocker driving is former product. Now, Lemniscate type crane with boom-rocker driving is developed and patented [4]. Based on theory of mechanism, kinematics analysis and luffing moment of double-link luffing mechanism of lemniscate type crane with boom driving is studied and realized on MTLB. ll rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech ublications, www.ttp.net. (ID: 130.203.136.75, ennsylvania State University, University ark, US-06/03/16,21:54:24)
924 Frontiers of Manufacturing Science and Measuring Technology II Fig. 1 Lemniscate floating crane (with boom driving) made by Kenz-Figee company Kinematics analysis of double-link luffing mechanism of lemniscate type crane Instant centre of velocity. In Fig.2, Elongated boom and back-rocker, we can get a cross-point. The point is instant center of velocity, thus velocity of point is zero. Because the luffing mechanism with boom driving is moved widely, then the point is changed widely too. The point is changed up and down to horizontal line. To discuss conveniently, we gives two cases, one case is θ 1 less than 90 (θ 1 < 90 ), θ 1 - θ 3 > 0, the point is up to horizontal line; another case is θ 1 more than 90 (θ 1 > 90 ), θ 1 - θ 3 < 0, the point is down to horizontal line. Fluctuation of instant center of double-link luffing mechanism with boom driving is distinctive feature. ω β F ly in g jib B a c k - r o c k e r C X 3 X 2 X 7 B X 4 α D V X V Q O 3 θ 3 X 1 ω 1 B o o m X6 θ 1 c e n tr a l lin e o f r o ta r y X 8 O 1 R X 5 Fig. 2 Schematic diagram of double-link luffing mechanism of lemniscate type crane (with boom driving) The distance between joint O 3 and point is solved by law of sines. ( ) 1 1 3 > O1 = X 56 3+ 0 1 1 θ < 90, θ θ 0, sin( θ θ )/ sin( θ -θ ) X = X + X ; θ = arctan( X / X ) 2 2 56 5 6 0 6 5 3 (1) ( ) 3 O1 X 56 3 0 3 2 θ > 90, θ θ < 0, = sin( θ + θ )/ sin( θ - θ1) (2)
dvanced Materials Research Vols. 503-504 925 Relationship between θ 1 and θ 3. Because θ 1 is input variable, then θ 3 is function relationship of θ 1. To solve locus of point, we must get value of θ 3. To solve equation, we can get θ = a cos(( X + L X ) / (2 X L)) + a cos(( X + L X ) / (2 X L))-θ 2 2 2 2 2 2 3 3 2 3 56 1 56 0 L= X +X -2X X cos( π -θ - θ ) 2 2 56 1 56 0 Locus equation of point. Luffing performance is locus of point approximate level line. Tolerance of locus is more little, then luffing performance is more better. We can use vertical coordinate value of point to indicate luffing path. Coordinate system is located at central line of rotary, then we can solve the locus equation of point. X = X1 cosθ1+ X 4 cosα+ X 8 Y = X1 sinθ1+ X 4 sinα (4) (3) By geometry relationship of point B, we can get value of angle α. α = π + θ γ β 1 0 β = acos( X / X ) + acos( X / X ) 0 7 2 7 4 γ =acos(( X +L - X )/2X L)+acos(( X +L - X )/2X L) 2 2 2 2 2 2 1 56 1 2 3 2 (5) Horizontal direction velocity of point. Horizontal direction velocity of point is influence on luffing operation violently, leading to hoisting freight swing. By velocity consistency of point B, we can get V = ω O B= ω B B ω = ω O B / B (6) By geometry relationship, we can solve velocity of point (V ) and horizontal direction velocity of point (V X ) X = O B, cos β = D / V V = V cos β = ω X D / B X = ω Luffing Moment by lift capacity. Lift capacity Q is applied to double-link luffing mechanism of lemniscate floating crane on the point. Then, luffing moment can be gotted. Let angle of θ 1 coming little define as positive. M = Q D O B / B=Q X D / B (8) Q Calculation and analysis of double-link luffing mechanism of lemniscate type crane with boom driving We can get some information from the book of theory of machines and mechanisms [5], as follows: X 1 =19.3m, X 2 =6.5m, X 3 =14.7m, X 4 =16m, X 5 =6.4m, X 6 =5.3m, C=22.3m. Lift capacity Q=160kN. The maximum outreach from central line of rotary is 30m, corresponding to θ 3 =49. The minimum outreach is 10.5m at θ 3 =132 (lemniscate type crane with back-rocker driving). (7)
926 Frontiers of Manufacturing Science and Measuring Technology II Because geometric shape of lemniscate type crane with boom driving is similar to that lemniscate type crane with back-rocker driving, then we can reference to it [5], suppose to get θ 1 =60~120. Using MTLB program, we can calculate, analysis and plot. The results include, locus of instant centre of velocity, locus of point, diagram of relationship between θ 1 and θ 3, path of horizontal direction velocity of point, luffing moment M Q. 6000 22.3 Y (m ) 4000 2000 0 Y (m) 22.2 22.1 22 21.9-2000 21.8 Fig. 3 Locus of instant centre Fig. 4 Locus of point 140 θ1 θ3 ( ) 120 100 80 θ1 θ3 60 40 Fig. 5 Diagram of relationship between θ 1 and θ 3 VX (m/s) 22 20 18 16 14 12 MQ (kn.m) 300 200 100 0-100 -200-300 Fig. 6 ath of horizontal direction Fig. 7 Diagram of luffing moment M Q velocity of point (suppose ω 1 =1) Conclusions Luffing mechanism with boom driving has distinctive features, as follows: (1) operations of luffing are swift and efficient. (2) it has very good luffing performance, absolute tolerance is 0.41m. (3) process of luffing is safety and reliability. References [1] Kenz-Figee : Brochure of Kenz-Figee: Offshore & Harbour Cranes, http://www.kenz-figee.com/, (2011). [2] Jenny Beechener: ractice proves floating transfer flexibility. International Bulk Journal, Vol. 5(1986): p. 41-49. [3] H.H.Schipper, R.W.Verhoosel: Floating cranes design advantages. International Bulk Journal, Vol. 2(1989): p. 63-65. [4] Nieuwenhuis Gijsbert, Dorresteijn Jacob Jan: Crane. E10486061, European patent, (2000). [5] J.E.Shigley, J.J.Uicker: Theory of machines and mechanisms. (McGraw- Hill Book Company, New York, 1980).
Frontiers of Manufacturing Science and Measuring Technology II 10.4028/www.scientific.net/MR.503-504 Kinematics and Luffing Moment of Lemniscate Type Crane with Boom Driving 10.4028/www.scientific.net/MR.503-504.923