滑橇式輸送機5.5m鏈式動力滾床設計【含CAD圖紙、說明書】

滑橇式輸送機5.5m鏈式動力滾床設計【含CAD圖紙、說明書】,含CAD圖紙、說明書,滑橇式,輸送,鏈式,動力,設計,cad,圖紙,說明書,仿單 畢業(yè)設計（論文）開題報告課題名稱滑橇式輸送機5.5m鏈式動力滾床設計院系名稱專 業(yè)機械設計制造及其自動化班 級學生姓名 一、 研究本課題的意義：中國古代的高轉筒車和提水的翻車，是現(xiàn)代斗式提升機和刮板輸送機的雛形；17世紀中，開始應用架空索道輸送散狀物料；19世紀中葉，各種現(xiàn)代結構的輸送機相繼出現(xiàn)。 1868年，在英國出現(xiàn)了帶式輸送機；1887年，在美國出現(xiàn)了螺旋輸送機；1905年，在瑞士出現(xiàn)了鋼帶式輸送機；1906年，在英國和德國出現(xiàn)了慣性輸送機。此后，螺旋輸送機受到機械制造、電機、化工和冶金工業(yè)技術進步的影響，不斷完善，逐步由完成車間內(nèi)部的輸送，發(fā)展到完成在企業(yè)內(nèi)部、企業(yè)之間甚至城市之間的物料搬運，成為物料搬運系統(tǒng)機械化和自動化不可缺少的組成部分。 輸送機是指在一定的線路上連續(xù)輸送物料的物料搬運機械，又稱連續(xù)輸送機。輸送機可進行水平、傾斜和垂直輸送，也可組成空間輸送線路，輸送線路一般是固定的。輸送機輸送能力大，運距長，還可在輸送過程中同時完成若干工藝操作，所以應用十分廣泛?？梢詥闻_輸送，也可多臺組成或與其他輸送設備組成水平或傾斜的輸送系統(tǒng)，以滿足不同布置形式的作業(yè)線需要。中國現(xiàn)代的輸送設備發(fā)展更是空前的，隨著中國汽車工業(yè)的發(fā)展，特別是引進技術和國外二手設備的再利用，使得輸送設備更提升了一個檔次。汽車行業(yè)的輸送設備主要用于總裝配線、各總成分裝線以及大總成上線的輸送。完成汽車裝配生產(chǎn)過程最重要的設備之一是汽車總裝線。隨著轎車技術的引進，我國汽車總裝線所采用的輸送設備也由原來的剛性輸送發(fā)展到現(xiàn)在的柔性輸送。根據(jù)車身承載方式的不同，采用的裝配線的型式也有所不同，國內(nèi)用于非承載車身的汽車(一般為載貨汽車、部分面包車)裝配線的型式有以下幾種：雙鏈橋架式；雙鏈橋架式+地面板式；帶隨行支架的地面板式：單鏈牽引地面軌道小車式； 帶隨行小車的地面板式+地面單板式等。 轎車及部分微型車為承載式車身或半承載式車身，根據(jù)其裝配工藝特點，既有車身內(nèi)外裝配也有車下底盤部件裝配，因此轎車總裝配線，通常由二類輸送機組成，一類是高架空中懸掛式輸送機，另一類是地面輸送機?？罩袘覓焓捷斔蜋C主要型式有普通懸掛輸送機、積放式懸掛輸送機和自行葫蘆輸送機。地面輸送機主要型式有地面板式輸送機、地面單鏈牽引軌道小車式和滑橇式輸送系統(tǒng)。二、國內(nèi)外研究動態(tài)：滑橇輸送系統(tǒng)（見圖1）目前是各個汽車制造廠普遍采用的輸送設備，滑橇式輸送機由動力滾床、平移滾床、旋轉臺、舉升臺、平移機和鏈式輸式送機等各種獨立輸送單元所組成的組合式輸送系統(tǒng)，每種輸送單元可以獨立執(zhí)行某一個或多個動作（如傳送車身、旋轉、平移和升降等），設備的驅動裝置為帶有減速器的三相380V交流電機。和傳統(tǒng)的懸掛積放鏈、地推鏈等輸送設備相比，具有機動靈活、組合方便、運行平穩(wěn)、可靠性高以及便于維護等顯著優(yōu)點。系統(tǒng)現(xiàn)場安裝如圖2所示。圖1 滑橇式輸送系統(tǒng)圖2 系統(tǒng)現(xiàn)場安裝二、 本課題的研究內(nèi)容與研究步驟1.研究的內(nèi)容：本課題主要研究的是動力滾床(見圖3，圖4)它是滑橇式輸送機最基本的輸送單元。其主要用途是用于橇體的儲存，定位和輸送。動力滾床由主框架、動力輥子、傳動構件、傳動裝置和張緊裝置等主要部分組成。動力輥子按一定計算間隔均勻布置。動力輥子由安裝在一根通軸上的兩個滾子組成。其中一個滾子為“U形”帶導向邊沿的動力滾，另一個為平直的從動滾。動力滾床可以實現(xiàn)雙向運行。并有雙速變頻可選。配置定位裝置可實現(xiàn)橇體精確定位。按傳動構件形式不同，動力滾床分皮帶式動力滾床和鏈式動力滾床兩種。本次設計主要設計的是鏈式的5.5m動力滾床。（1） 總體方案的擬定。（2） 減速電機的選型和結構的設計。（3） 動力輥子的設計。（4） 傳動構件、傳動裝置的設計。（5） 張緊裝置的設計。（6） 軸承的選型與校驗。（7） 動力滾床主框架的設計。 圖3 動力滾床（1） 圖4 動力滾床（2）2.研究的步驟： （1）、明確此動力滾床的使用要求，進行負載特性分析。 （2）、設計動力滾床的設備方案。 （3）、計算整個動力滾床中各零、部件的參數(shù)。 （4）、繪制動力滾床的工作原理簡圖。 （5）、進行運動學和動力學分析。 （6）、驗算是否滿足工作條件。 （7）、繪制二維零、部件的CAD圖形。 （9）、撰寫畢業(yè)論文。四、研究方法和手段通過各種機械設計資料完成相應部分的計算，并用CAD繪圖軟件完成總裝配圖及部分裝配圖以及其部件的零件圖，采用現(xiàn)場信息搜集、計算機輔助設計、計算機輔助分析等完成本次設計。五、參考文獻：1范祖堯.現(xiàn)代機械設備設計手冊M.北京:機械工業(yè)出版社,19962吉林工業(yè)大學 蘇州鏈條廠.鏈傳動設計與應用手冊M.北京:機械工業(yè)出版社,19923鄭志風.鏈傳動M.北京:機械工業(yè)出版社,19844東北工學院編寫組.機械零件設計手冊(第2版)M.北京:冶金工業(yè)出版社,19895宋學義.袖珍液壓氣動手冊M.北京：機械工業(yè)出版社,19956成大先.機械設計手冊第5版M.北京：化學工業(yè)出版社，20087黃悠調(diào),趙松年. 機電一體化技術基礎及應用M. 北京:機械工業(yè)出版社, 2002.8濮良貴、紀名剛.機械設計（第七版）M.北京：高等教育出版社，20019鄞丈緯. 機械原理M北京：高等教育出版社199710胨立周. 機械優(yōu)化設計M上海：上?？茖W技術出版杜，198211郭芝俊、張林芳. 機械設計便覽M.天津：天津科學技術出版社198812楊廷力，機械系統(tǒng)基本理論，北京：機械工業(yè)出版社，1996。指導教師簽名： 年 月 日 滑橇式輸送機5.5m鏈式動力滾床設計,指導人員：,畢業(yè)設計的主要內(nèi)容,a 根據(jù)任務書要求進行總體設計(大概的布局） b 相關的設計計算 (1)減速電機的選型、轉矩，轉速一些相關計算。 (2)動力輥子軸的相關計算。 (3)傳動部件的相關計算。 (4)軸承的選擇及計算等。 c 繪制5.5m鏈式動力滾床的裝配圖，零件圖。,動力滾床的相關圖片,整體設計參數(shù)要求,主參數(shù)： 動力電源：AC380V/350Hz 控制電源：DC24V 軌 距：1000mm 滾輪直徑：136mm 運行速度：12m/min 額定荷載：900kg,動力滾床主要部件設計,總體傳動系統(tǒng)方案的擬定 減速電機的選型及計算 動力輥子的設計 套筒的設計 鏈傳動設計 滾子的設計 軸承的選型及校驗,一、總體傳動系統(tǒng)方案的擬定,傳動方案設計： 合理的傳動方案，首先應滿足工作機的功能要求，其次還應該滿足工作可靠、傳動效率高、結構簡單、尺寸緊湊、重量輕、成本低廉、工藝性好、 使用和維護方便等要求。任何一個方案，要滿足上述所有要求是十分困難的，設計時要統(tǒng)籌兼顧，滿足最主要的和最基本的要求。 擬定的傳動方案：,主框架的設計,負載轉矩的計算 ： 得到 T=122.4N*m 轉速的計算 ： 得到N=28.104r/min 減速電機的選型 ： （1）減速電機型號：R37DT71D4BMG （2）電機 功率：0.37kw （3）電機 級數(shù)：4 （4）輸出 轉速：29r/min （5）輸出 扭矩：123N*m （6）總 重 量：16kg （7）輸出軸許用徑向載荷：5590N,二、減速電機的選型及計算,三、動力輥子的設計,心軸的計算 ：確定軸端直徑d=25mm 心軸的結構設計 ：,套筒的作用： 實際上在本次設計中，套筒也起著軸的作用，套筒充當?shù)氖强招妮S，所起的作用是傳遞扭矩。 確定套筒的內(nèi)徑和外徑 套筒的內(nèi)徑取d1=30mm，套筒的外徑d2=42mm 套筒的結構和尺寸,四、套筒的設計,五、鏈傳動的設計,滾子鏈鏈輪的設計 （1）驅動單鏈輪的結構尺寸,雙鏈輪的結構尺寸 : 張緊鏈輪的結構尺寸: | V ,六、鏈的張緊裝置,鏈傳動的布置 （1）常見合理布置形式參見下表,a.本次設計的驅動鏈輪的布置，采用的是兩輪軸線不 在同一水平面，松邊應在下面。選擇的是第二種布置方案。 b.傳動鏈輪的布置，采用的是兩輪軸線在同一水平面，松邊在下面，選擇的是第三種布置方案。 鏈傳動的張緊 一般的張緊方式：,本次設計的張緊裝置如下圖：,七、滾動軸承的選擇及計算,滾動軸承的工作特點： 與滑動軸承相比，滾動軸承具有下列優(yōu)點： （）應用設計簡單，產(chǎn)品已標準化，并由專業(yè)生產(chǎn)廠家進 行大批量生產(chǎn)，具有優(yōu)良的互換性和通用性。（）起動摩擦力矩低，功率損耗小，滾動軸承效率（0.980.99）比混合潤滑軸承高。 （）負荷、轉速和工作溫度的適應范圍寬，工況條件的少量變化對軸承性能影響不大。（）大多數(shù)類型的軸承能同時承受徑向和軸向載荷，軸向尺寸較小。（）易于潤滑、維護及保養(yǎng)。 滾動軸承也有下列缺點： 大多數(shù)滾動軸承徑向尺寸較大。 在高速、重載荷條件下工作時，壽命短。 振動及噪音較大。,滾動軸承的選擇,再次謝謝各位評判老師！,外文資料The Two-Dimensional Dynamic Behavior of Conveyor BeltsIr. G. Lodewijks, Delft University of Technology, The Netherlands1. SUMMARY1-In this paper a new finite element model of a belt-conveyor system will be introduced. This model has been developed in order to be able to simulate both the longitudinal and transverse dynamic response of the belt during starting and stopping. Application of the model in the design stage of long overland belt-conveyor systems enables the engineer, for example, to design proper belt-conveyor curves by detecting premature lifting of the belt off the idlers. It also enables the design of optimal idler spacing and troughing configuration in order to ensure resonance free belt motion by determining (standing) longitudinal and transverse belt vibrations. Application of feed-back control techniques enables the design of optimal starting and stopping procedures whereas an optimal belt can be selected by taking the dynamic properties of the belt into account.2. INTRODUCTION2-The Netherlands has long been recognised as a country in which transport and transhipment play a major role in the economy. The port of Rotterdam, in particular is known as the gateway to Europe and claims to have the largest harbour system in the world. Besides the large numbers of containers, a large volume of bulk goods also passes through this port. Not all these goods are intended for the Dutch market, many have other destinations and are transhipped in Rotterdam. Good examples of typical bulk goods that are transhipped are coal and iron ore, a significant part of which is intended for the German market. In order to handle the bulk materials a wide range of different mechanical conveyors including belt-conveyors is used.3-The length of most belt-conveyor systems erected in the Netherlands is relatively small, since they are mainly used for in-plant movement of bulk materials. The longest belt-conveyor system, which is about 2 km long, is situated on the Maasvlakte, part of the port of Rotterdam, where it is used to transport coal from a bulk terminal to an electricity power station. In addition to domestic projects, an increasing number of Dutch engineering consultancies participates in international projects for the development of large overland belt-conveyor systems. This demands the understanding of typical difficulties encountered during the development of these systems, which are studied in the Department of Transport Technology of the Faculty of Mechanical Engineering, Delft University of Technology, one of the three Dutch Universities of Technology.4-The interaction between the conveyor belt properties, the bulk solids properties, the belt conveyor configuration and the environment all influence the level to which the conveyor-system meets its predefined requirements. Some interactions cause troublesome phenomena so research is initiated into those phenomena which cause practical problems, 1. One way to classify these problems is to divide them into the category which indicate their underlying causes in relation to the description of belt conveyors.5-The two most important dynamic considerations in the description of belt conveyors are the reduction of transient stresses in non-stationary moving belts and the design of belt-conveyor lay-outs for resonance-free operation, 2. In this paper a new finite element model of a belt-conveyor system will be presented which enables the simulation of the belts longitudinal and transverse response to starting and stopping procedures and its motion during steady state operation. Its beyond the scope of this paper to discuss the results of the simulation of a start-up procedure of a belt-conveyor system, therefore an example will be given which show some possibilities of the model。3. FINITE ELEMENT MODELS OF BELT-CONVEYOR SYSTEMS6-If the total power supply, needed to drive a belt-conveyor system, is calculated with design standards like DIN 22101 then the belt is assumed to be an inextensible body. This implies that the forces exerted on the belt during starting and stopping can be derived from Newtonian rigid body dynamics which yields the belt stress. With this belt stress the maximum extension of the belt can be calculated. This way of determining the elastic response of the belt is called the quasi-static (design) approach. For small belt-conveyor systems this leads to an acceptable design and acceptable operational behavior of the belt. For long belt-conveyor systems, however, this may lead to a poor design, high maintenance costs, short conveyor-component life and well known operational problems like : excessive large displacement of the weight of the gravity take-up device premature collapse of the belt, mostly due to the failure of the splices destruction of the pulleys and major damage of the idlers lifting of the belt off the idlers which can result in spillage of bulk material damage and malfunctioning of (hydrokinetic) drive systemsMany researchers developed models in which the elastic response of the belt is taken into account in order to determine the phenomena responsible for these problems. In most models the belt-conveyor model consists of finite elements in order to account for the variations of the resistances and forces exerted on the belt. The global elastic response of the belt is made up by the elastic response of all its elements. These finite element models have been applied in computer software which can be used in the design stage of long belt-conveyor systems. This is called the dynamic (design)approach Verification of the results of simulation has shown that software programs based on these kind of belt-models are quite successful in predicting the elastic response of the belt during starting and stopping, see for example 3 and 4.The finite element models as mentioned above determine only the longitudinal elastic response of the belt. Therefore they fail in the accurate determination of: the motion of the belt over the idlers and the pulleys the dynamic drive phenomena the bending resistance of the belt the development of (shock) stress waves the interaction between the belt sag and the propagation of longitudinal stress waves the interaction between the idler and the belt the influence of the belt speed on the stability of motion of the belt the dynamic stresses in the belt during. passage of the belt over a (driven) pulley the influence of parametric resonance of the belt due to the interaction between vibrations of the take up mass or eccentricities of the idlers and the transverse displacements of the belt the development of standing transverse waves the influence of the damping caused by bulk material and by the deformation of the cross- sectional area of the belt and bulk material during, passage of an idler the lifting of the belt off the idlers in convex and concave curvesThe transverse elastic response of the belt is often the cause of breakdowns in long belt-conveyor systems and should therefore be taken into account. The transverse response of a belt can be determined with special models as proposed in 5 and 6, but it is more convenient to extend the present finite element models with special elements which take this response into account.3.1 THE BELTA typical belt-conveyor geometry consisting of a drive pulley, a tail pulley, a vertical gravity take-up, a number of idlers and a plate support is shown in Figure 1. This geometry is taken as an example to illustrate how a finite element model of a belt conveyor can be developed when only the longitudinal elastic response of the belt is of interest.Since the length of the belt part between the drive pulley and the take-up pulley, Is, is negligible compared to the length of the total belt, L, these pulleys can mathematically be combined to one pulley as long as the mass inertias of the pulleys of the take-up system are accounted for. Since the resistance forces encountered by the belt during motion vary from place to place depending on the exact local (maintenance) conditions and geometry of the belt conveyor, these forces are distributed along the length of the belt. In order to be able to determine the influence of these distributed forces on the motion of the belt, the belt is divided into a number of finite elements and the forces which act on that specific part of the belt are allocated to the corresponding, element. If the interest is in the longitudinal elastic response of the belt only then the belt is not discredited on those places where it is supported by a pulley which does not force its motion (slip possible). The last step in building, the model is to replace the belts drive and tensioning system by two forces which represent the drive characteristic and the tension forces.The exact interpretation of the finite elements depends on which resistances and influences of the interaction between the belt and its supporting structure are taken into account and the mathematical description of the constitutive behavior of the belt material. Depending on this interpretation, the elements can be represented by a system of masses, springs and dashpots as is shown in Figure 1, 9, where such a system is given for one finite element with nodal points c and c+ 1. The springs K and dashpot H represent the visco-elastic behavior of the belts tensile member, G represents the belts variable longitudinal geometric stiffness produced by the vertical acting forces on the belts cross section between two idlers, V represent the belts velocity dependent resistances.Figure 1: Five element composite model 9.3.1.1 NON LINEAR TRUSS ELEMENTIf only the longitudinal deformation of the belt is of interest then a truss element can be used to model the elastic response of the belt. A truss element as shown in Figure 2 has two nodal points, p and q, and four displacement parameters which determine the component vector x:xT = up vp uq vq (1)For the in-plane motion of the truss element there are three independent rigid body motions therefore one deformation parameter remains which describesFigure 2: Definition of the displacements of a truss elementthe change of length of the axis of the truss element 7:1 = D1(x) = ods - dsod (2)2dsowhere dso is the length of the undeformed element, ds the length of the deformed element and a dimensionless length coordinate along the axis of the element.Figure 3: Static sag of a tensioned beltAlthough bending, deformations are not included in the truss element, it is possible to take the static influence of small values of the belt sag into account. The static belt sag ratio is defined by (see Figure 3):K1 = /1 = q1/8T (3)where q is the distributed vertical load exerted on the belt by the weight of the belt and the bulk material, 1 the idler space and T the belt tension. The effect of the belt sag on the longitudinal deformation is determined by 7:s = 8/3 Ks (4)which yields the total longitudinal deformation of the non linear truss element:3.1.2 BEAM ELEMENTFigure 4: Definition of the nodal point displacements and rotations of a beam element.If the transverse displacement of the belt is being of interest then the belt can be modelled by a beam element. Also for the in-plane motion of a beam element, which has six displacement parameters, there are three independent rigid body motions. Therefore three deformation parameters remain: the longitudinal deformation parameter, 1, and two bending deformation parameters, 2 and 3.Figure 5: The bending deformations of a beam elementThe bending deformation parameters of the beam element can be defined with the component vector of the beam element (see Figure 4):xT = up vp p uq vq q (5)and the deformed configuration as shown in Figure 5:2 = D2(x) =e2p1pq (6)1o3 = D3(x) =-eq21pq1o3.2 THE MOVEMENT OF THE BELT OVER IDLERS AND PULLEYSThe movement of a belt is constrained when it moves over an idler or a pulley. In order to account for these constraints, constraint (boundary) conditions have to be added to the finite element description of the belt. This can be done by using multi-body dynamics. The classic description of the dynamics of multi-body mechanisms is developed for rigid bodies or rigid links which are connected by several constraint conditions. In a finite element description of a (deformable) conveyor belt, where the belt is discretised in a number of finite elements, the links between the elements are deformable. The finite elements are connected by nodal points and therefore share displacement parameters. To determine the movement of the belt, the rigid body modes are eliminated from the deformation modes. If a belt moves over an idler then the length coordinate , which determines the position of the belt on the idler, see Figure 6, is added to the component vector, e.g. (6), thus resulting in a vector of seven displacement parameters.Figure 6: Belt supported by an idler.There are two independent rigid body motions for an in-plane supported beam element therefore five deformation parameters remain. Three of them, 1, 2 and 3, determine the deformation of the belt and are already given in 3.1. The remaining two, 4 and 5, determine the interaction between the belt and the idler, see Figure 7.Figure 7: FEM beam element with two constraint conditions.These deformation parameters can be imagined as springs of infinite stiffness. This implies that:4 = D4(x) = (r + u )e2 - rid.e2 = 0 5 = D5(x) = (r + u)e1 - rid.e1 = 0 (7)If during simulation 4 0 then the belt is lifted off the idler and the constraint conditions are removed from the finite element description of the belt.3.3 THE ROLLING RESISTANCEIn order to enable application of a model for the rolling resistance in the finite element model of the belt conveyor an approximate formulation for this resistance has been developed, 8. Components of the total rolling resistance which is exerted on a belt during motion three parts that account for the major part of the dissipated energy, can be distinguished including: the indentation rolling resistance, the inertia of the idlers (acceleration rolling resistance) and the resistance of the bearings to rotation (bearing resistance). Parameters which determine the rolling resistance factor include the diameter and material of the idlers, belt parameters such as speed, width, material, tension, the ambient temperature, lateral belt load, the idler spacing and trough angle. The total rolling resistance factor that expresses the ratio between the total rolling resistance and the vertical belt load can be defined by:ft = fi + fa + fb (8)where fi is the indentation rolling resistance factor, fa the acceleration resistance factor and fb the bearings resistance factor. These components are defined by:Fi = CFznzh nhD-nD VbnvK-nk NTnT(9)fa =Mred uFzb tfb =MfFzbriwhere Fz is distributed vertical belt and bulk material load, h the thickness of the belt cover, D the idler diameter, Vb the belt speed, KN the nominal percent belt load, T the ambient temperature, mered the reduced mass of an idler, b the belt width, u the longitudinal displacement of the belt, Mf the total bearing resistance moment and ri the internal bearing radius.The dynamic and mechanic properties of the belt and belt cover material play an important role in the calculation of the rolling resistance. This enables the selection of belt and belt cover material which minimise the energy dissipated by the rolling resistance.3.4 THE BELTS DRIVE SYSTEMTo enable the determination of the influence of the rotation of the components of the drive system of a belt conveyor, on the stability of motion of the belt, a model of the drive system is included in the total model of the belt conveyor. The transition elements of the drive system, as for example the reduction box, are modelled with constraint conditions as described in section 3.2. A reduction box with reduction ratio i can be modelled by a reduction box element with two displacement parameters, p and q, one rigid body motion (rotation) and therefore one deformation parameter:red = Dred(x) = ip + q = 0 (10)To determine the electrical torque of an induction machine, the so-called two axis representation of an electrical machine is adapted. The vector of phase voltages v can be obtained from: v = Ri + sGi + L i/t (11)In eq. (11) i is the vector of phase currents, R the matrix of phase resistances, C the matrix of inductive phase resistances, L the matrix of phase inductances and s the electrical angular velocity of the rotor. The electromagnetic torque is equal to:Tc = iTGi (12)The connection of the motor model and the mechanical components of the drive system is given by the equations of motion of the drive system:Ti = Iijj+ CikkKil (13)ttwhere T is the torque vector, I the inertia matrix, C the damping matrix, K the stiffness matrix and the angle of rotation of the drive component axiss.To simulate a controlled start or stop procedure a feedback routine can be added to the model of the belts drive system in order to control the drive torque.3.5 THE EQUATIONS OF MOTIONThe equations of motion of the total belt conveyor model can be derived with the principle of virtual power which leads to 7:fk - Mkl x1 / t = 1Dik (14)where f is the vector of resistance forces, M the mass matrix and the vector of multipliers of Lagrange which may be interpret as the vector of stresses dual to the vector of strains . To arrive at the solution for x from this set of equations, integration is necessary. However the results of the integration have to satisfy the constraint conditions. If the zero prescribed strain components of for example e.g. (8) have a residual value then the results of the integration have to be corrected, also see 7. It is possible to use the feedback option of the model for example to restrict the vertical movement of the take-up mass. This inverse dynamic problem can be formulated as follows. Given the model of the belt and its drive system, the motion of the take-up system known, determine the motion of the remaining elements in terms of the degrees of freedom of the system and its rates. It is beyond the scope of this paper to discuss all the details of this option.3.6 EXAMPLEApplication of the FEM in the desian stage of long belt conveyor systems enables its proper design. The selected belt strength, for example, can be minimised by minimising, the maximum belt tension using the simulation results of the model. As an example of the features of the finite element model, the transverse vibration of a span of a stationary moving belt between two idler stations will be considered. This should be determined in the design stage of the conveyor in order to ensure resonance free belt support.The effect of the interaction between idlers and a moving belt is important in belt-conveyor design. Geometric imperfections of idlers and pulleys cause the belt on top of these supports to be displaced, yielding a transverse vibration of the belt between the supports. This imposes an alternating axial stress component in the belt. If this component is small compared to the prestress of the belt then the belt will vibrate in its natural frequency, otherwise the belts vibration will follow the imposed excitation. The belt can for example be excitated by an eccentricity of the idlers. This kind of vibrations is particularly noticea