4T焊接滾輪架機械設計【含13張CAD圖紙】
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ucfion, the assembly and circular seam welding of rotary workpieces, such as a boiler, a petro- vessel and so on, are conducted on ;i welding roller bed. When ifOtiNtitky On a welding roller bed. the cylinder will inevitably produce axial dl-ifting due to manufacturing, assembling tolerance ot” the welding roller bed and the cylinder s surface irrcgtjlalty (divcrgiug from an ideal rotary workpiece), thus the welding procedure may rmt be carried out successfully. It is necessary, thcc- fore, to study the mechanism of the axial drifting of the cylinder to solve the problem of the axial drifting of the cylinder in circumferential welding. The results of the research will benefjt the studying and designing of nnti- drifting welding roller bed. especially the analysis of the applied forces on the bed, and lead to determining the manufacturing and assembling tolerance of the bed, and providing the basis of theory for the mechanical adjusting mode to avoid axial drifting, the adjusting mode of closed circuit in the control circuit, and the selection of the ad- justing value. 2. Theoretical analysis 2. I. Wevelding roller bed and cylinder A welding roller bed is generally composed of four rollers. Driven by the driving roller, the cylinder makes a rotary uniform motion around its axis(shown in Fig. I), during which the circumferential welding procedure is carried outt l. In Fig.1, co is the central angle, S is the supportirg distance, I, is the span of the roller. and V, is the circular linear velocity of the cylinder, also named the 0924-0136/97/$15.00 6%) 1997 Elswier Science S.k All ri* reserved PII SO924-0136(96)02743-4 The axis of the cylinder will be not parallel to thaw of a roller if the roller is deflected by a certain angle from the ideal position, or if the centers of the four rollers lie in the vertices of a simple quadrilateral, or if the centers of the four rollers are not on the same plane, or if the circu- larity of the cylinder is irregular because of deviation in manufacturing and assembling. Thus. the cylinder will inevitably move along its axis when rotating on a bed The contact of the cylinder and a roller can be cansidered as point contact if cytinder s axis and roller s axis do not lie in the same plane. Suppose P is the point of contact. The cylinder s normal plane A is defined by the plane on which are the cylinder s axis and eaeratrix IP across the point of tangency on the cylinder (shown in a cylinder s tangent plane E across point P. Thus, plane A is vertical to plane &. I, is a cylinder s tangent acrOss P. and lies in plane B. I, is the roller s tangent across the same point P, and lies in plane B also. In general, 0 k defined as the axial deviation angle between the rol!er s axis and the cylinder s axis; p is defined as the spiral angle between generatrix 8 and JJJ . a projective line obtained by projecting the roller s generatris II? across point I on plane H. and y is defined as the projective angle between JJ and JJI- , a projective line obtained by projecting JJJ on plane A. Fig. 5 indicates that the rela- tionship amongst the three angles is tan . p = tan 8 - tan y In Fig. 3, SB, Se and S, are called the spiral displace- ment vector, the axial deviation displacement vector and the projective displacement vector respectively. their relationship being: q$=$+s; Fig. 2 Geometric relationship bej. een the cylinder and an individual roller Fig. 3 Relationship hctwcen the ;rnglc vector and the displacement vector , . i . 2. #C/trti * CJXid JJJOti0JJ.S J diJtiOlJShi (1) Spiral motion Rolier Cylinder Fig. 4 Component of axial velocity Because the roller s axis is not parallel to the cylin- der s central line, there is a spiral angle p between /,. and 1, on the point of contact (shown in Fig. 2). When the roller and cylinder rotate synchronistically around their own axes, driven by tangential frictional force. a spiral effect will occur because of the different linear velocity direction between the roller and the cylinder at point P of contact The cylinder has a component of axial velocity, 1: (shown in Fig 4). pi PO, = 1,: . tan /I, where I , is the circular linear velocity of the cylinder. lzfis the cylinder s axial component velociry exerted b) a single roller, and j can be 1. 2, 3, 4, representing the four rollers, respectively. (2) Elastic sliding Because of the existence of a spiral angle, an axial force Faj acts on cylinder. When the force IS less than the maximum axial frictional force fNj (whereI is the friction factor, and Ni is the normal pressure between a single roller and the cylinder), the cylinder will slide elastically over the roller along the axial directioni2 “ 1. The compo- nent of the sliding velocity is. eF,V, va;: = - I where e is the elastic sliding factor for metallic roller. e=O.OOl - 0.005. (3) Frictional sliding When F.j is greater than the maximum frictional force fNj, the cylinder will make a frictional sliding over the roller. The sliding resistance is fNj”I. The component of the frictional sliding velocity on Cylinder is Vi;, the magnitude and direction of which can be determined by the universal relationship between the cylinder and the four rollers Frictional sliding will lead to the wear and tear of the surface of the cylinder and the rollers. which is unexpected in welding production When the cylinder drifts, ahovc three kinds of motion do not occur simultaneously I hereforc. the axial drifting velocity ot the cylinder is no1 the algebraic sum of the three components of vclociry In the case of elastic slid- ing, the axial velocity is. VW. = y; -I- i$ whils! in the case of frictional sliding, the axial velocity is 2.3.1. Axial COJJJJalibk JJJCJtiOtJ Under ideal conditions, when spiral angles fij between the cylinder and the four rollers are all the same, that is: the cylinder will move with compatible spiral motion. Two categories can be classified to analyze the axial mo- tion of the cylinder: (I) When there does not exist an axial component due to gravity. the cylinder s axial drifting velocity is: (2) When there exists an axial component of gravity G, there exists an axial force on the cylinder. Now, the axial forces exerted on the four rollers have the same direction especially, when ,L?=O: In general. spiral angles p, between th cylinder and the four rollers are not equal to each otlwr in size and direction. i e. the geometric relationships between the cylinder and the four rollers are ali inconsislent Thcrc*- fore, the compowepts of the cylinder s axial velocity against four rollers (i.e iYC .ta ,) are not identtcal to each another. The cylinder move with axial non- compatible motion The axial velocities of the cylinder againsa the four rollers should be the same because the cylinder is consid- ered as a rigid body as a whols and it has o velocity. However. for some roller, VC . tM cylinder s real axial velocity are nat likely to be the same, so an axial frictional force almost certainly appears be- tween this roller and the cylinder The following two categories can be classified to discuss the non-compatible axial motion of the cylinder according to Ihe frictional force s magnitude: (I) When the axial frictional forces erected by each roller and the cylinder are ali less than the mahimuni axial frictional force, :hc action of the cylinder against the rollers produces elastic sliding The axial motion between an individual roller and Ihe cylinder is coordinated hv their elastic sliding when the axial velocity of the cylinder is c.onstant, the algebraic sum of cylinder s axial forces erected !y four rollers should be zero if rhe axial component of gravity is ignored. i.e.: 1 c Fj = 0 )=I and there is little difference amongst N, against the foul rollers, so that they can be approximately regarded as the same. Thus: FIIJ =o according to the above two equations, the axial drifting velocity of the cylinder is. (2) When the axial frictional force erected by some roller and the cylinder is greater than the maximum axial frictional force, frictional sliding occurs between the cylinder and this roller Then. the maximum axial force ig acting on the bearing of the roller, its value being Because of the esistence of this frictional sliding. the axial motion between an individual roller and rhe cylinder is not coordinated by their elastic sliding Now the axial non-compatible motion of the cylinder is determined b) the relative relationships between the cylinder and the four rollers. It is difficult to write a general compatible equation of the cylinder s axial drifting velocity because this kind of condition is very complex. The following is further analysis and discussion of the problem At first, for ease in analyzing problem, the spiral angle average is defined as and the relative spiral angle as .P: = P, -a Arrange ,L?l in the order from his to smll and thm f1onl posirive to negative, expressed as /J(j). then Similarly, the normal force between the cylinder and a roller can h: expressed as N(j). and the axial force ;I WI :l;Ci) In general, the axial motion of the cylinder dcter- - mined by the spiral angle avcragep is dcfinwl as the compatible component uf the axial motion, i:s velocity being. The axial motion of the cylinder determined by the rcla- tive spiral angle /3(i) is defined as the non-compatible component of axial motion, iis velocity being expressed as r; Analysis shows that y: is determined by the equilibrium condition I the four rollers axial furces when the cylinder moves along axial direction at a con- stant velocity. where not taking into account of the func- lion of gravity s axial component. Supposing tnat the cylinder makes a non-compatible component of axial motion with the maximum relative spiral angle j?(I). its velocity is Jfy = v,. . tan p( 1) then the four axial forces can not be in equilibrium, i e F(l) - /F(2) + F(J) + r;(J) J 0 Therefore, the cylinder can only be approximately con- sidered as making a non-compatible component of axial motion with the second or third relative spiral angle, i.e.: If N(I) + N(2) N(3) + N(J) y,” = v, + tanp(2) or: If N(I) + N(2) N(3) + N(J) r = V, m/3(3) In whatever case as expressed above. when the cylinder make a non-compatible component of axial motion, the two rollers having a greater velocity arc driving rollers, and the other two rollers having a lesser velocity are resistant rollers, the equilibrium condition of axial forces being cpart!ive, i.e.: F(i) + F(2) = F(3) + F(4) According to the analysis above, and because of the unstability of friction factor f that is affected by the fac- tors of load, material, condition of the contact surface, and circumstance, the patible component vi of the axial velocity of the cylinder is undefined. When the cylinder makes a nan-compatible axial mo- tion, its axial velocity is composed uf a compatible com- ponent vOo and a non-compatible component I:, i.e The most optimal adjustment of the axial motion is to make the non-compatible component as small as possible according to the stability of adjustment and decrease in axial force. No matter whether the cylinder makes compatible or non-compatible motion, supposing that the cylinder is ideal, its axial velocity is always existent and definable for a particular bed, its magnitude and direction reflecting the bed s inherent property. 3. Experiment 3.1. Descriphm of experrmertr The experimental model is shown in Fig 5. Experiments were done to study two factors: the spiral angle and the cylinder s circular linear velocity, which affect the axial drifting of the cylinder. In the experimenting process. the axial displacement S, and the axial driftin? velociiy V. of the cylinder were measured by the variation of the two factors described above. The measuring method is shown in Fig. 5, and is carried out by means of bringing an axial displacement sensor into contact with one end of the cylinder. with the sensor being connected to an X-Y re- corder to record the cylinder s axial displacement every 5 s. Linearly regressing the plot S.-r (t expresses time), - the average drifting velocity vC, at every deflecting angle can be calculated. Before experimenting. the experimental model is initial- ised as follows: first. the height of the four rollers is ad- justed by means of a level to put the ccntcrs of the four r- I s I Back MI: Driving device of driving roller Mz: Lifting device of driven roller M,: Deflecting device of driven roller M,: Displacement sensor MI: X-Y recorder I -Driving roller No. I 2-Lifted driven roller No. 2 3-Driven roller No. 3 4-Deflected driven roller No. 4 1 I F&t _* daflection +s, L Fig. 5 Sketch of the experimental model oilers in the same horizontal plane, and at the QW vcr- texes of the rectangle. then the rollers are deFgected so that the rotating cylinder is ill tilt? KlrPliW UiPikrGUI position. Then. the cylinder does not drift over a long time. or periodically drift over a very small axial range (I) Fig. 6 shows that change of V. with the variation of The testing condition is: positive rotalion, I C=j5mlh, =422mm, a=60” Fig 6 Esperinlental curve of I C,-tan/l, The I ,-tan& curve shows that I, is directly propor- tional 10 tan/Y, when ,#, is rrlativcly small (1 u 6” ). the slope of the line being 3 06 mm/s, I;, is no longer direclly proportional to tan& when /I, ;s greater than 6” The curve is an arched curve. i e . with the increment of /II,. I“ , incrsases. but with the increment of I , gradually be- coming smallet Because only one driven roller (roller No. 4) is de- flected, i.e., /3, can be changed whilst the others remain zero, the cylinder makes a non-compatible motion. When /3, is relatively small, I C, is small also. The axial frictional forces between the cylinder and rolEers are less thorn the maximum axial frictional force, and the cylinder produces an elastic sliding against rollers. Axial motion between each roller and the cylinder is coordinated by elastic sliding. thus I , is: V” +$tanp, = I-1 i.e. V, a tan/?, In the theoretical curve. the following equation: iVc tan/?, the slope K can be calculated by where K=X06mm/s in the experimental curve. Thus, in taking account of the experimental tolerance, the Iwo slopes can be considered to be approximately equal. When /?, is relatively large, the axial frictional forces betwee the q:inJer and the rollers are larger than the wnximum axial friotlonaP Force, and cylinder produces hxional sliding agains t the voPlers Because of Ihe enis- Uence of sliding PricIionai resisrance. E , is no longer ?ine- arty increased with the increment of tanf14 With the in- crement of tan/I, the increment of a; wile gradually be- come smaller I- p.,- ” c I I , When the number of driven rollers deflecred is varted, the degree of the cylinder s non-compatible axial motion will be changed. With the incremenr of the number of lollers dellected by Ihe same spiral angle. the compatible component becomes greater, but the non-compatible component becomes smaller. In other words, the cylin- der s axial motion will be transformed from non- compatible motion to compatible motion. Thus, V# be- comes greater also, ultimately, being equal to the com- patible axial velocity determined by the spiral angle p Now. the four rollers have the same spiral anyle fl. SO that V, is: Deflecting driven roller No 4 to a spiral angle of +2” from the equilibrium position, the cylinder will suffer axial drifting, Fig. 8 shows the l C,-L C curve, which latter indicates that V, is directly proportional to L =, the slope of the curve being approximately O.QO iOB. Eecause /?,=+2” is too small, the cylinder does not make frictional sliding against each roller. Thus, the rela- tive axial motion between the roller and the cylinder is completely coordinated by their elastic sliding, so that I;, is- i.e: I , is directly proportional to 1“ For the theoretical curve, the slope K * can be calculated by the following equation K” =+p, = $tan2=z0.00873 where K=O.O0708mm/s in the experimental curve. Thus, in taking account of the experimental tolerance, the two slopes can be considered to be approximately equal. 25 f Fig. 8 Experimental curve of V,-I , 4 Conclusiuns I Because of the dcviaions due to manufacturing and assembling. the cylinder s central line and the roller s asis arc nol parallel. i c , tlrcy nrc ilot in the same plane, and thcrc is a spiral angle 11 at hc point of con- tacl between the cylinder and lhe roller in the circular linear velocity direction. The wistoncc of /? is the ba- sic reason fw the occurrence uf axial drifting. The ef- t&t of gravity in cylinder s axial direction is also one of reasons tdr drifting. 2. The relative axial motions between an individual roller and the cylinder are composed of spiral motion. elastic sliding and frictional sliding When axial frictional slid- ing does not occur between the cylinder and a single roller, the relative axial motion between the rollers and the cylinder is completely coordinated by their elastic 4 sliding, I , is directly proportional IO & i tan p , J-I When axial frictional slidins occurs between the cylin- der and a roller. the relative asial motion between the rollers and the cylinder will be commonly coordinated by elastic sliding and frictional sliding. but I ., is not directly proportional to r;&lllp, J=I The axial motions of the cylinder can be divided into compatible and non-compatible motion There will be large axial forces acting on the bearings of the rollers, which will cause the wear and tear of the contact sur- faces of the rollers and the cylinder, when non- compatible motion exists The non-compatible compo- nent of the axial motion is undefined tiowever. the cylinder s axial velocity is always existent and defin- able for a particular bed, its magnitude and direction reflecting the bed s inherent property. The reasonable adjustment of the axial motion is to make the non-compatible component as small as possi- ble and the compatible component as large as possible. With the increment of the number of rollers deflected by the same value of /, the compatible component of axial velocity increases, but the non-compatible com- ponent decreases. With the increment of the compati- ble component, the velocity of axial drifting of the cyl- inder increases Rel rrcnccs L Wang(ed ). 7ktrchrrrp ,4lrrk*rrtrl 011 ll eldir/g J V!O- L./Iw I: qrrrpwrr/. Gansu Universit! of Technolqqy. I.anzhou. 1 R China, (I 992) pp 85-98 Wuhan lnstitulc of Buildins Materials and Technol- ogyI Tongi Universily. Nanjing Institute of Chemical Engineering, and Huanan Institute of Technology. ( cmott Prodrrcittg Machtwry I: cpipnwnl, Architec- tural Industrial Publishing House of China, Beijing, (I981) pp, 184-187 J . Halling(ed.). Prittciples of Trilrolog.v, The Mac- millan Press, (1975) pp. 174-200
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