1、During continuous casting,the oscillation guiding mechanism plays a guidance role in the motion of the mould.Only when the mould vibrates along the correct track,the quality of the strand can be ensured.So the strand requires very high guidance accuracy of the oscillation guiding mechanism for the m
2、ould.But for inevitable gap and wear of the bearings,the four-eccentric axes and four-bar linkage oscillation mechanisms widely used in modern casting will cause uncontrolled deviation in motions of the mould,which badly affects the quality of the strand.1Therefore,the semi-and whole-leaf spring mec
3、hanisms are gradually used as guidance mechanisms for the mould in billet and slab continuous casting.2,3In recent years,with further development of the semi-and whole-leaf spring oscilla-tion mechanisms,the cascaded whole-leaf spring oscilla-tion mechanism is developed abroad,4which has a longer li
4、fe,higher lateral rigidity and reliability and so on.However,until now,reports on this oscillation mechanism are few.5,6Its working principle has been proposed by the authors,7based on which design method of the cascaded whole-leaf spring oscillation mechanism is proposed in this paper and its exper
5、i-mental prototype is manufactured.Furthermore,the rigidexible coupling virtual model of the cascaded whole-leaf spring oscillation mechanism is built and its kinematics and dynamics simulations are analysed using many types of software,such as ANSYS.System modes and the forces applied on leaf sprin
6、gs and revolute joints of the mechanism are analysed,which establish the basis for further studies and application of this mechanism.Working principle of cascaded whole-leaf spring guidance mechanismThe structure of the cascaded whole-leaf spring oscilla-tion mechanism is shown in Fig.1.It mainly co
7、nsists of the cascaded leaf spring,vibration table and frame, which can be driven by machinery(Fig.1a,or hydraulics servo(Fig.1b,generating device of sinusoi-dal or non-sinusoidal oscillation.And the cascaded leaf spring is composed of four steel plate springs divided into two sets.All leaf springse
8、xtension lines join to the circular arc centre of the continuous caster and their ends are separately connected to the vibration table and the frame,as shown in Fig.2,and then two sets of leaf springs,the vibration table and the frame form two four-bar linkage guidance devices.During the mould vibra
9、t-ing,exible leaf springs produce elastic deformations, which make two leaf spring four-bar linkage guidance devices alternately play a guidance role in the mould without any interference by the generating device.71The Mechatronics and Information Engineering School,Foshan University,Foshan528000,Ch
10、ina2College of Mechanical Engineering,Yanshan University,Qinhuangdao 066004,China3No.2Research Development Department,Xian Heavy Machinery Research Institute,Xian710032,China*Corresponding author,email zhanglpok2042010Institute of Materials,Minerals and MiningPublished by Maney on behalf of the Inst
11、ituteReceived14November2008;accepted16September2009DOI10.1179/030192309X12573371383677Ironmaking and Steelmaking2010VOL37NO3Design of cascaded whole-leaf spring oscillation mechanismFrom working principle of the cascaded whole-leaf spring oscillation mechanism,it can be seen that two leaf spring fou
12、r-bar linkages carry on the guidance to the mould.If design is unreasonable,the motion of the two leaf spring four-bar linkages will interfere during vibration,which will block the mould.Therefore,how to design these two leaf spring four-bar linkages becomes the key problem.Design method of cascaded
13、 whole-leaf spring oscillation mechanismAccording to the characters of the cascaded whole-leaf spring mechanism developed from the short-arm four-bar linkage,its design method is proposed as following:(ibased on the design principles of the short-armfour-bar linkage simulating arc,8design two rigid
14、four-bar linkages under the same basic para-meters of the mould by optimum design,which fulfil the requirement for guiding accuracy of the mould simulating arc(iifor settling interference of the two four-barlinkages,rigid linkages optimised in step (iare substituted by steel plate springs with elast
15、ic deformation and then form two leaf spring four-bar linkages(iiibased on the basic principles of the short-armfour-bar linkage,arrange two leaf spring four-bar linkages according to Fig.2.That is,end-points A 1,C 1and A 2,C 2are fixed on the frame;endpoints B 1,D 1and B 2,D 2are connected to the v
16、ibration table of the mould.In this way,two leaf spring four-bar linkages are cascaded,so a cascaded whole-leaf spring mechanism is designed.Calculation exampleCalculations of parameters and guidance accuracy of rigid four-bar linkagesAccording to the geometry relations and the movement relationship
17、s of the four-bar linkage guidance devices of the arc caster (see Fig.2,the position of any point on the mould can be calculated during the mould vibration.In this paper,taken the bottom point E on the outer arc of the mould as an example,formulas of the track and the guiding accuracy of point E are
18、 deduced,as listed in Table 1,with only one rigid four-bar linkage guiding for the mould.To calculate conveniently,it is assumed that l 1,l 2,l 3and l 4are respectively the lengths of linkages of A 1C 1,A 1B 1,B 1D 1and C 1D 1,and A 2C 2,A 2B 2,B 2D 2and C 2D 2;S is the amplitude of the mould;D Q is
19、 the swing angle of the linkage of B 1D 1and B 2D 2under the max displace-ment of the mould downward;R is the casters basic radius;R 1and R 2are radius respectively from the arc centre to two endpoints of linkages A 1C 1,B 1D 1,A 2C 2and B 2D 2;H 1and H 2are the heights of both sides to the horizont
20、al centerline of the mould;a is the included angle between OE and the horizontal centreline of the arc caster when the mould is at equilibrium position;h 1,h 2,r 1and r 2are respectively the included angles between linkages of A 1C 1,A 2C 2,B 1D 1,B 2D 2and the horizontal centreline of the caster;D
21、R E is the simulated arc error of the mould.Mathematical model and optimisation of linkagesOscillation parameters of the mould and the installation positions of linkages are the primary designing terms of the guidance mechanism.Taking arc caster for example,outside penalty function optimisation meth
22、od is adopted in optimum design of the two rigid four-bar linkages.In four-bar linkages design,it is the goal that the trajectory error of the mould meets the requirement for guiding accuracy.So the objective function of the optimisation mathematical model can be written by f(x D R E OE R 0:02(1Acco
23、rding to Table 1,it can be seen that the design optimisation variables are x R ,S ,h ,r ,R 1,R 2 T(2By experience,geometric dimensions and installation positions of two four-bar linkages must meet the following constraints2Layout of cascaded whole-leafspringa mechanic driven;b hydraulics servodriven
24、1Cascaded whole-leaf spring oscillation mechanismZhang et al.Cascaded whole-leaf spring oscillation mechanism for mould in continuous castingIronmaking and Steelmaking 2010VOL37NO320530D R 50D 2S j j 10R 1w 0,h w 0R 2w R 1,r w h 0:91R R 2v R 0:82R R 191R(3where D is the thickness of billet;h and r a
25、re included angles between linkages and horizontal centreline of the caster.Based on the objective function (equation (1,optimisation variables (equation (2and constraints established in equation (3,optimisation procedure of outside penalty function is compiled by C language and two four-bar linkage
26、s are separately optimum designed.Optimisation resultsIn optimisation,it is assumed that the mould is arranged symmetrically about its equilibrium position and its height H 1z H 25900mm;the thickness of the billet D 5150mm;the guiding accuracies of two rigid four-bar linkages D R E 50?02mm.Therefore
27、,the geometrical parameters and the guiding accuracies of the two rigid four-bar linkages are optimum designed (Table 2.By the optimised results,rigid linkages are substituted by leaf springs arranged according to Fig.2;then a cascaded whole-leaf spring mechanism is designed.Experimental prototype of cascaded whole-leaf spring oscillation mechanismBased on the optimised results,the experimental proto-type of the cascaded whole-leaf spring oscillation mechan-ism for the mould is manufactured,as shown in Fig.3,in which leaf spring four-bar linkage A 1C 1B 1D 1is composed of leaf springs 1
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