Jounal of matenals processing technology 63 (1997) 881-886 Experiment and study into the axial drifting of the cylinder of a welding rollerbed Fenggang shen ,xide pan ,jin xue Welding research instiute ,xian jiaotong university. Xian .shaanxi province 710049.P.R.china Abstract The basic theory of the axial drifting of the cylinder of a welding roller bed is introduced in the paper,and at the same time experiment and study on the mechanism of the axial drifting of the cylinder have been done on an experimental model of the welding roller bed . It is shown that the main cause of the axial drifting of the cylinder lies in the existence of a spiral angle between the cylinder and the cylinder and the roller . the relative axial motions between the roller and the cylinder are compose of spiral motion,elastic sliding and frictional sliding. The theory of compatible motion and non-compatible motion is put forward for the axial motions of the cylinder .the relative axial motions of the cylinder . The relative axial motion between the rollers and the cylinder is coordinated by elastic sliding and frictional sliding between them Keywords: welding roller bed； cylinder ； roller ； axial motion ； spiral angle 1 Introduction In welding production, the assembly and circular seam welding of rotary workpieces, such as a boiler, a petrochemical pressure vessel and so on, are conducted on ；a welding roller bed. When rotating On a welding roller bed. The cylinde will inevitably produce axial drifting due to manufacturing, assembling tolerance of the welding roller bed and the cylinders surface irregularity (divergiug froman ideal rotary workpiece), thus the welding procedure may not be carried out successfully. It is necessary, therefore, 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 benefit the studying and designing of antidrifting 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 adjusting value. 2. Theoretical analysis 2.1. Welding 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 out In Fig.1, a is the central angle, S is the supporting distance, L is the span of the roller. and V, is the circular linear velocity of the cylinder, also named the welding velocity2. The axis of the cylinder will be not parallel to that of a roller if the roller is deflected by a certain angle from the deal 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 nevitably move along its axis when rotating on a bed the contact of the cylinder and a roller can be cansidered as point contact if cytinders axis and rollers axis do not lie in the same plane. Suppose P is the point of contact. the cylinders normal plane A is defined by the plane on which are the cylinders axis and generatrix n across the point of tangency on the cylinder (shown in fig2) makea cylinders tangent plane B across point P. Thus, plane A is vertical to plane B. lc is a cylinders tangent across P and lies in plane B. Ir is the rollers tangent across the same point P, and lies in plane B also. In general, is defined as the axial deviation angle between the rol!ersaxis and the cylinders axis； is defined as the spiral angle between generatrix n and m . a projective line obtained by projecting the rollers generatrix m across point p on plane B and is defined as the projective angle between n and m , a projective line obtained byprojecting m on plane A. Fig. 3 indicates that the rela- tionship amongst the three angles is tan = tan2 - tan 2 In Fig. 3, SB, S and S, are called the spiral displace-ment vector, the axial deviation displacement vector and the projective displacement vector respectively. their relationship being: Fig. 2 Geometric relationship between the cylinder and an individual roller Fig. 3 Relationship between the angle vector and the displacement vector 2.2.2 relative axial motions relationship (1)spiral motion2. Fig. 4 Component of axial velocity Because the rollers axis is not parallel to the cylin- ders central line, there is a spiral angle between Vr,. and Vc, 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, where Vc is the circular linear velocity of the cylinder. is the cylinders axial component velociry exerted by 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 (where f is the frictionfactor, and Nj is the normal pressure between a single roller and the cylinder), the cylinder will slide elastically over the roller along the axial direction23 The component of the sliding velocity is. where e is the elastic sliding factor for metallic roller. e=O.OOl 0.005. (3) Frictional sliding When Faj is greater than the maximum frictional force fNj, the cylinder will make a frictional sliding over the roller. The sliding resistance is fNj3. The component of the frictional sliding velocity on Cylinder is Vaj 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, above three kinds of motion do not occur simultaneously Ihereforc. the axial drifting velocity of the cylinder is not the algebraic sum of the three components of velocity In the case of elastic sliding, the axial velocity is. 2.3 axial motion of the cylinder on a welding roller bed 2.3.1 Axial compatible motion Under ideal conditions, when spiral angles j between the cylinder and the four rollers are all the same, that is: 1= 2= 3= 4= the cylinder will move its compatible spiral motion. Two categories can be classified to analyze the axial motion of the cylinder: (I) When there does not exist an axial component due to gravity. the cylinders axial drifting velocity is: Va=Vc * tan (2) When there exists an axial component of gravity Ga there exists an axial force on the cylinder. Now, the axial forces exerted on the four rollers have the same directional And magnitude, the value being equal to Ga besues the component of spiral vetocity, there exist component of elastic on the cylinder the cylinders axial drifting velocity is 2.3.2.axial non-compatible motion In general. spiral angles j between the cylinder and the four rollers are not equal to each other in size and direction. i .e. the geometric relationships between the cylinder and the four rollers are all inconsistent Therefore, the components of the cylinders axial velocity against four rollers (i.e Vc *ta j) are not identical to each another. The cylinder will move with axial nompatible motion The axial velocities of the cylinder againsa the four rollers should be the same because the cylinder is considered as a rigid body as a whole and it has only one axial velocity. However. for some roller, Vc . tan j and the cylinders real axial velocity are not likely to be the same, so an axial frictional force almost certainly appears between 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 forces magnitude: (I) When the axial frictional forces erected by each roller and the cylinder are all less than the maximum axial the action of the cylinder against the frictional force the action of the cylinder against the rollers produces elastic sliding The axial motion betweenan individual roller and the cylinder is coordinated by their elastic sliding when the axial velocity of the cylinder is constant, the algebraic sum of cylinders axial forces erected by four rollers should be zero if rhe axial component of gravity is ignored. i.e. and there is little difference amongst Nj, against the four rollers, so that they can be approximately regarded as the same. Thus: according to the above two equations, the axial drifting velocity of the cylinder is. Where 0.25Tant represents the intrinsic attributes of the welding. Other bed under the condition that only the cylinder against all rolls produces elastic sliding this may be called the spiral rate of the cylinders spiral motion (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 is acting on the bearing of the roller, its value being Ffmax=fFNfmax Because of the esistence of this frictional sliding. the Axial motion between an individual roller and the cylinder is not coordinated by their elastic sliding Now the axial non-compatible motion of the cylinder is determined by the relative relationships between the cylinder and the four rollers. It is difficult to write a general compatible equation of the cylinders 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 Arrange ,1 in the order from big to smll and then from posirive to negative, expressed as (j). then 1234 Similarly, the normal force between the cylinder and a roller can be expressed as N(j). and the axial force as FjfNj In general, the axial motion of the cylinder determined by the spiral angle average is definel as the compatible component of the axial motion, is velocity being The axial motion of the cylinder determined by the relative spiral angle j is defined as the non-compatible component of axial motion, its velocity being expressed asVan Analysis shows that Va is determined by the equilibrium condition the four roller axial forces when the cylinder moves along axial direction at a constant velocity. where not taking into account of the function of gravitys axial component. Supposing that the cylinder makes a non-compatible component of axial motion with the maximum relative spiral angle (I). its velocity is Then the four axial forces can not be in equlibrium .i.e F1-(F2+F3+F4) 0 Because there is little difference amongst four normal forces, the four axial farces are also determined by normal force and the friction factor any axial force undoubtedly being less than the sum of the other three forces. Otherwise, if the cylinder makes a non-compatible component of axial motion with the minimum relative spiral angle (4). its velocity is. Va” = Vc * tan(4) Similarly. four axial forces can not be in equilibrium also, i.e. : F(l) + F(2) + F(3) J - F(4) 0 Therefore, the cylinder can only be approximately considered as making a non-compatible component of axial motion with the second or third relative spiral angle, i.e.: In whatever case as expressed above. when the cylinder make a non-compatible component of axial motion, thetwo rollers having a greater velocity are driving rollers,and the other two rollers having a lesser velocity are resistant rollers, the equilibrium condition of axial forces being operative, i.e.: F(1) + 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 factors of load, material, condition of the contact surface, and circumstance, the non-compatible component Va of the axial velocity of the cylinder is undefined. When the cylinder makes a non-compatible axial motion, its axial velocity is composed of a compatible component Va 0 and a non-compatible component Va n i.e Va=Va0+Van Va=Va0+Van 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 beds inherent property. 3. Experiment 3.1. Descriphm of experment The experimental model is shown in Fig 5. Experiments were done to study two factors: the spiral angle and the cylinders circular linear velocity, which affect the axial drifting of the cylinder. In the experimenting process. the axial displacement Sa and the axial drifting velocity Va 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 recorder to record the cylinders axial displacement every 5s. Linearly regressing the plot Sa-t (t expresses time), the average drifting velocity Va , at every deflecting angle can be calculated. Before experimenting. the experimental model is initialised as follows: first. the height of the four rollers is adusted by means of a level to put the centers of the four rollers in the same horizontal plane, and at the four vertexes of the rectangle. then the rollers are deflected so that the rotating cylinder is at the relative equilibrium position. Then the cylinder does not drift over a long time. or periodically drift over a very small axial range 3.2 experiment results and discussion 3.2.1 Effect of spiral angle (I) Fig. 6 shows that change of Va with the variation ofThe testing condition is: positive rotalion, Vc=35m/h L=422mm, =60” The Va -tan 4 curve shows that Va is directly proportional to tan 4 when 4 is relatively small (16c ). The slope of the line being 3. 06 mm/s, Va is no longer direclly proportional to tan 4 when 4, is greater than 6C The curve is an arched curve. i. e . with the increment of 4,.Va , increases. but with the increment of Va gradually becoming smallet Because only one driven roller (roller No. 4) is deflected, i.e 4 can be changed whilst the others remain zero, the cylinder makes a non-compatible motion. When 4 is relatively small, Va is small also. The axial frictional forces between the cylinder and rollers are less than 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 Va is: in the theoretical curve, the slope K can be calculated by the following equation: K=3.06mm/s in the experimental curve. Thus, in taking account of the experimental tolerance, the two slopes can be considered to be approximately equal. When 4 is relatively large, the axial frictional forces between the cylinder and the rollers are larger than the maximum axial frictional Force, and cylinder produces frictional sliding against the rollers Because of Ihe existence of sliding frictional resistance. Va is no longer lincarty increased with the increment of tan 4 With the increment of tan 4 the increment of V a； with gradually become smaller (2) The following three experiments were arranged to study the cylinders non-compatible axial motion further, deflecting positively one roller. two rollers and three rollers by the same spiral angle to measure three curves between Sa and v The experimental results are shown in Fig 7. With the increment in the number of deflected rollers, Va becomes greater. i e Va 3 Va 2 Va1 When the number of driven rollers deflected is varied, the degree of the cylinders non-compatible axial motion will be changed. With the increment of the number of lollers deflected by the same spiral angle. the compatible component becomes greater, but the non-compatible component becomes smaller. In other words, the cylinders axial motion will be transformed from noncompatible motion to compatible motion. Thus, Va becomes greater also, ultimately, being equal to the compatible axial velocity determined by the spiral angle Now. the four rollers have the same spiral anyle . So that Va is: 3.2.2 effect of circular linear velocity 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 Va -Vc curve, which latter indicates that Va is directly proportional to Vc, the slope of the curve being approximately 0.00708 because 4=+2 is too small, the cylinder does not make frictional sliding against each roller. Thus, the relative axial motion between the roller and the cylinder is completely coordinated by their elastic sliding, so that Va is I. e .Va is directly proportional to Ve For the theoretical Curve the slope K * can be calculated by the following equation K”=0.25tan 4= 0.25tan2=0.00873 where K=0.00708mm/s in the experimental curve. Thus, in taking account of the experimental tolerance, the two slopes can be considered to be approximately equal. 4 Conclusions 1. Because of the deviations due to manufacturing and assembling. the cylinders central line and the rollers axis are not parallel. i. e , they are not in the same plane, and there is a spiral angle at thc point of contact between the cylinder and the roller in the circular linear velocity direction. The existence of is the basic reason for the occurrence of axial drifting. The effect of gravity in cylinders axial direction is also one of reasons for 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 sliding 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 sliding, Va is directly proportional to When axial frictional sliding occurs between the cylinder and a roller. the relative asial motion between therollers and the cylinder will be commonly coordinated by elastic sliding and frictional sliding. but Va is not directly proportional to 3 The axial motions of the cylinder can be divided intocompatibleand 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 surfaces of the rollers and the cylinder, when non-compatible motion exists The non-compatible component of the axial motion is undefined however. the cylinders axial velocity is always existent and definable for a particular bed, its magnitude and direction reflecting the beds inherent property. 4 The reasonable adjustment of the axial motion is to make the non-compatible component as small as possible and the compatible component as large as possible. 5 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 component decreases. With the increment of the compatible component, the velocity of axial drifting of the cylinder increases References (1) Z Wang(ed ). teaching material on welding machinery Equipment Gansu university of Technology lanzhou P R china (1992) pp 85-98 (2)Wuhan lnstitulcof Buildins Materials and TechnologyI Tongi Universily. Nanjing Institute of Chemical Engineering, and Huanan Institute of Technology. Cement Producing machinery equipment, Architectural Industrial Publishing House of China, Beijing, (1981) pp, 184-187 (3)J . Halling(ed.). Principles of Trilrology The Macmillan Press, (1975) pp. 174-200 關(guān)于 焊接滾輪架軸向竄動的實驗研究 摘要 文章引入焊接滾輪架軸向竄動的基本理論 ,并同時在焊接滾輪架的實驗?zāi)Ｐ蜕线M行 了試驗研究 . 結(jié)果表明 , 焊接滾輪架軸向竄動的主要原因在于工件的翻轉(zhuǎn)存在著螺旋夾角 . 軸向相對運動產(chǎn)生螺旋運動 ,彈性滑動與摩擦滑動 . 其中有與理論相符的內(nèi)容以及和理論不符合的內(nèi)容 ,文中了軸向運動滾筒 . 他是相對于軸運動的圓筒形工件 . 相對軸的運動包括滾輪與工件相互協(xié)調(diào)的彈性滑動和摩擦滑動 關(guān)鍵詞 :焊接滾輪架 ； 圓筒工件 ； 滾輪 ； 軸向運動 ； 螺旋角 1 介紹 在焊接生產(chǎn)中 ,常會遇到旋轉(zhuǎn)焊接圓形工件的情況。如焊接鍋爐、石油化工壓力容器等 ,就必須用到 焊接滾輪架 . 進行旋轉(zhuǎn)焊接時，由于制造、裝配公差 ，焊接 滾輪和工件的表面平滑與否等因素 (理想的旋轉(zhuǎn)工件表面是平滑的 )，使焊接不可能理想化的進行，工件必然會產(chǎn)生軸向竄動 。研究提供了當(dāng)圓形工件焊接時，軸向竄動的機制 . 這項研究成果將有利于研究與設(shè)計反竄動焊接滾輪架 . 尤其是應(yīng)用于滾輪架之上 , 并確定了制造及滾輪架的裝配公差 ，為通過機械調(diào)節(jié)的方式，避免軸向竄動的方法供理論依據(jù)。調(diào)整模式采用閉環(huán)控制電路 ,并推選有價值的提案 2 理論分析 2.1 焊接滾輪架一般由四個滾輪組成 .由主動滾輪驅(qū)動 ,滾筒勻速繞軸旋轉(zhuǎn) (例 1), 其間放圓形焊接工件（如圖 1） ,其中 ,s 為滾輪支架 距離 ,L 同列兩滾輪距離 . Ve是圓形工件滾動的線速度 ,也被稱為焊接速度 圖 1 焊接滾輪架 同行的滾輪的的軸并不平行 , 從某個角度看 ,滾輪架的四輥所在的頂點組成一個簡單的四邊形 但如果四滾輪所在頂點不在同一平面 或因為制造及裝配滾輪的圓柱是不規(guī)則的圓形 . 那么 . 工件就會在軸轉(zhuǎn)動時竄動。滾輪架的滾輪與工件有一個接觸點 . 假設(shè) P為這個接觸點 . 工件的標準平面的定義是一個平滑的平面 ,平面 A為圓柱母線與軸的切入點組成的平面 ,與工件相切點不在此平面內(nèi) , 一平面垂 直于平面 A切線，過 P和所在平面 B 就是滾輪的切線過相同點 P, 一般說來 , 被定義為滾輪軸和圓柱行工件的軸線的偏斜夾角 ! 定義螺旋夾角母線 N和 M. 如圖 2、圖 3所示，其射影線取得的突出輥母線橫跨點 P 。 B定義為 N 和 M 線的投影夾角。如例 3其中三個角度關(guān)系 tan = tan2 * tan 2 軸向偏差位移矢量和射影位移矢量它們的關(guān)系是 : 圖 2 滾輪和工件幾何關(guān)系 圖 3 個角度矢量和位移矢量的關(guān)系 2.2 軸向相對關(guān)系 (1)螺旋運動 因為滾輪軸線與中線不平行 , 在 Vr 和 Vc 之間 就有一 個螺旋角 存在 ,如圖 2. 當(dāng)輥筒圍繞自己的軸線轉(zhuǎn)動時 ,使在切線上產(chǎn)生摩擦力 . 因為滾輪和工件各個線速度在不同的方向，由于螺旋效應(yīng)也就是竄動就會發(fā)生在點 p-滾輪和工件的接觸點 (圖 4). 式中： VC 是圓柱的線速 . 是工件的軸向分量 , 1.2.3.4, 分別代表四個滾輪 . (2)彈性滑動 由于存在一種螺旋角 ,在工件上產(chǎn)生軸向力 Faj. 當(dāng)力量小于最大軸向摩擦力fnj(其中 f 是摩擦系數(shù) ,單滾和工件正常的壓力 ) 工件會下滑超過滾輪軸 23mm 的下滑速度為 . 式中 e是金屬滾 輪的彈性滑動系數(shù)： e= ool0.005. (3)摩擦滑動時 faj 大于最高摩擦力 fnj, 工件將在滾輪之上做摩擦滑動 . 滑動阻力為 fnj3. 工件的摩擦滑動速度的大小和方向可確定 由環(huán)球關(guān)系工件和四滾輪摩擦滑動導(dǎo)致滾輪表面的磨損 . 這是意料之外的 ,在焊接進行時 ,工件發(fā)生漂移。以上三種運動不同時發(fā)生 。工件的軸向漂移速度不是代數(shù)的三個組成部分的速度 . whilst in the case of frictional sliding, the axial velocity is發(fā)生摩 擦滑動的軸向速度 2.3 工件滾輪的軸向運動 2.3.1 與理論相符的部分 在理想的條件下 , 工件和四滾輪之間的當(dāng)螺旋角 j 都是一樣時 ,即 : 1=2=3=4 工件的運動將與理論值相同 . 可以將兩個范疇對比分析 : (1)由于重力不存在軸向分量 . 工件的軸向竄動速度 : Va=Vc * tan (2)當(dāng)存在一個有重力 Ga 因素，軸向竄動速度存在一個軸力 . 現(xiàn)在 ,四滾輪有相同的方向 與重力 G等效的軸向竄動速度 是： 2.3.2.與理論不同的關(guān)于軸向竄動的內(nèi)容 . 工件與四滾輪之間螺旋角 j 大小和方向不相等 .工件和 四滾輪的幾何關(guān)系也不相同時 ,工件和四滾輪之間的軸向竄動是個不相同的 . 工件與滾輪軸向速度應(yīng)該是同樣的 ,因為工件被作為一個整視為一個剛體體 ,. 然而 . 有些滾輪和工件的實際上軸向速度是不完全相同的 , 所以軸向摩擦力幾乎肯定會出現(xiàn)這種滾輪和 工件之間以下兩類分類討論不同與理論的摩擦力的大小 (一 )當(dāng)軸向摩擦力確保每個滾輪和工件均低于最大軸向所需對摩擦力 滾輪和工件將產(chǎn)生彈性滑動單個滾輪和工件可以協(xié)調(diào)它們的彈性滑動 當(dāng)工件的軸向速度是常量 , 如果忽略重力工件與四個滾輪的軸向竄動的總和將為 0 四個滾輪并 沒有什么差別因此他們大致是相同的 根據(jù)上述兩個方程 ,工件的軸向竄動為： 凡是 0.25 tant 范圍內(nèi) .使用滾輪架的情況下 ,工件只長生產(chǎn)生彈性滑動 ,這可能是所謂工件 螺旋率螺旋問題 (2)當(dāng)工件與滾輪的軸向摩擦力大于最大軸向摩擦力 , 工件與滾輪的圓柱體之間將發(fā)生摩擦滑動 ,這滾那 . 最大軸向力作用于滾輪軸承 Ffmax=fFNfmax 由于這種摩擦滑動的存在 . 單個滾輪與工件之間軸向傳動并不協(xié)調(diào)， 現(xiàn)在，軸向竄動并不完全由滾輪與工件的相對關(guān)系所決定 . 很難寫一個軸向傳動速度的普遍相容方程 ,因為這樣的條 件 很復(fù)雜 . 以下是進一步的分析和討論這一問題時 ,首先 ,為便于分析問題 , 螺旋角定義為 而相對螺旋角度 按由大到小的順序排列 表達為 1 2 3 4 同樣的 ,滾輪與圓形工件的正常的相互作用力為 n(j). 軸向力為 Fj fNj 一般 工件的軸向運動由螺旋角的平均值 決定 工件的軸向竄動 ,由相對螺旋角的定義竄動為不完全的組成部分 , 當(dāng)圓柱體沿著軸向，恒定速度 ，其速度表示分析表明 asVan 是平