滑橇式輸送機(jī)5.5m鏈?zhǔn)絼?dòng)力滾床設(shè)計(jì)【含CAD圖紙、說明書】
滑橇式輸送機(jī)5.5m鏈?zhǔn)絼?dòng)力滾床設(shè)計(jì)【含CAD圖紙、說明書】,含CAD圖紙、說明書,滑橇式,輸送,鏈?zhǔn)?動(dòng)力,設(shè)計(jì),cad,圖紙,說明書,仿單
畢業(yè)設(shè)計(jì)（論文）開題報(bào)告
課題名稱
滑橇式輸送機(jī)5.5m鏈?zhǔn)絼?dòng)力滾床設(shè)計(jì)
院系名稱
專 業(yè)
機(jī)械設(shè)計(jì)制造及其自動(dòng)化
班 級(jí)
學(xué)生姓名
一、 研究本課題的意義：
中國古代的高轉(zhuǎn)筒車和提水的翻車，是現(xiàn)代斗式提升機(jī)和刮板輸送機(jī)的雛形；17世紀(jì)中，開始應(yīng)用架空索道輸送散狀物料；19世紀(jì)中葉，各種現(xiàn)代結(jié)構(gòu)的輸送機(jī)相繼出現(xiàn)。
1868年，在英國出現(xiàn)了帶式輸送機(jī)；1887年，在美國出現(xiàn)了螺旋輸送機(jī)；1905年，在瑞士出現(xiàn)了鋼帶式輸送機(jī)；1906年，在英國和德國出現(xiàn)了慣性輸送機(jī)。此后，螺旋輸送機(jī)受到機(jī)械制造、電機(jī)、化工和冶金工業(yè)技術(shù)進(jìn)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(yùn)，成為物料搬運(yùn)系統(tǒng)機(jī)械化和自動(dòng)化不可缺少的組成部分。
輸送機(jī)是指在一定的線路上連續(xù)輸送物料的物料搬運(yùn)機(jī)械，又稱連續(xù)輸送機(jī)。輸送機(jī)可進(jìn)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(jī)輸送能力大，運(yùn)距長，還可在輸送過程中同時(shí)完成若干工藝操作，所以應(yīng)用十分廣泛?？梢詥闻_(tái)輸送，也可多臺(tái)組成或與其他輸送設(shè)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(shè)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(jìn)技術(shù)和國外二手設(shè)備的再利用，使得輸送設(shè)備更提升了一個(gè)檔次。汽車行業(yè)的輸送設(shè)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(shè)備之一是汽車總裝線。隨著轎車技術(shù)的引進(jìn)，我國汽車總裝線所采用的輸送設(shè)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(diǎn)，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(jī)組成，一類是高架空中懸掛式輸送機(jī)，另一類是地面輸送機(jī)。空中懸掛式輸送機(jī)主要型式有普通懸掛輸送機(jī)、積放式懸掛輸送機(jī)和自行葫蘆輸送機(jī)。地面輸送機(jī)主要型式有地面板式輸送機(jī)、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(dòng)態(tài)：
滑橇輸送系統(tǒng)（見圖1）目前是各個(gè)汽車制造廠普遍采用的輸送設(shè)備，滑橇式輸送機(jī)由動(dòng)力滾床、平移滾床、旋轉(zhuǎn)臺(tái)、舉升臺(tái)、平移機(jī)和鏈?zhǔn)捷斒剿蜋C(jī)等各種獨(dú)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(dú)立執(zhí)行某一個(gè)或多個(gè)動(dòng)作（如傳送車身、旋轉(zhuǎn)、平移和升降等），設(shè)備的驅(qū)動(dòng)裝置為帶有減速器的三相380V交流電機(jī)。和傳統(tǒng)的懸掛積放鏈、地推鏈等輸送設(shè)備相比，具有機(jī)動(dòng)靈活、組合方便、運(yùn)行平穩(wěn)、可靠性高以及便于維護(hù)等顯著優(yōu)點(diǎn)。系統(tǒng)現(xiàn)場(chǎng)安裝如圖2所示。
圖1? 滑橇式輸送系統(tǒng)
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圖2? 系統(tǒng)現(xiàn)場(chǎng)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(dòng)力滾床(見圖3，圖4)它是滑橇式輸送機(jī)最基本的輸送單元。其主要用途是用于橇體的儲(chǔ)存，定位和輸送。動(dòng)力滾床由主框架、動(dòng)力輥?zhàn)?、傳?dòng)構(gòu)件、傳動(dòng)裝置和張緊裝置等主要部分組成。動(dòng)力輥?zhàn)影匆欢ㄓ?jì)算間隔均勻布置。動(dòng)力輥?zhàn)佑砂惭b在一根通軸上的兩個(gè)滾子組成。其中一個(gè)滾子為“U形”帶導(dǎo)向邊沿的動(dòng)力滾，另一個(gè)為平直的從動(dòng)滾。動(dòng)力滾床可以實(shí)現(xiàn)雙向運(yùn)行。并有雙速變頻可選。配置定位裝置可實(shí)現(xiàn)橇體精確定位。按傳動(dòng)構(gòu)件形式不同，動(dòng)力滾床分皮帶式動(dòng)力滾床和鏈?zhǔn)絼?dòng)力滾床兩種。
本次設(shè)計(jì)主要設(shè)計(jì)的是鏈?zhǔn)降?.5m動(dòng)力滾床。
（1） 總體方案的擬定。
（2） 減速電機(jī)的選型和結(jié)構(gòu)的設(shè)計(jì)。
（3） 動(dòng)力輥?zhàn)拥脑O(shè)計(jì)。
（4） 傳動(dòng)構(gòu)件、傳動(dòng)裝置的設(shè)計(jì)。
（5） 張緊裝置的設(shè)計(jì)。
（6） 軸承的選型與校驗(yàn)。
（7） 動(dòng)力滾床主框架的設(shè)計(jì)。
圖3 動(dòng)力滾床（1）
圖4 動(dòng)力滾床（2）
2.研究的步驟：
（1）、明確此動(dòng)力滾床的使用要求，進(jìn)行負(fù)載特性分析。
（2）、設(shè)計(jì)動(dòng)力滾床的設(shè)備方案。
（3）、計(jì)算整個(gè)動(dòng)力滾床中各零、部件的參數(shù)。
（4）、繪制動(dòng)力滾床的工作原理簡圖。
（5）、進(jìn)行運(yùn)動(dòng)學(xué)和動(dòng)力學(xué)分析。
（6）、驗(yàn)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(jī)械設(shè)計(jì)資料完成相應(yīng)部分的計(jì)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(chǎng)信息搜集、計(jì)算機(jī)輔助設(shè)計(jì)、計(jì)算機(jī)輔助分析等完成本次設(shè)計(jì)。
五、參考文獻(xiàn)：
[1]范祖堯.現(xiàn)代機(jī)械設(shè)備設(shè)計(jì)手冊(cè)[M].北京:機(jī)械工業(yè)出版社,1996
[2]吉林工業(yè)大學(xué) 蘇州鏈條廠.鏈傳動(dòng)設(shè)計(jì)與應(yīng)用手冊(cè)[M].北京:機(jī)械工業(yè)出版社,1992
[3]鄭志風(fēng).鏈傳動(dòng)[M].北京:機(jī)械工業(yè)出版社,1984
[4]東北工學(xué)院<機(jī)械零件設(shè)計(jì)手冊(cè)>編寫組.機(jī)械零件設(shè)計(jì)手冊(cè)(第2版)[M].北京:冶金工業(yè)出版社,1989
[5]宋學(xué)義.袖珍液壓氣動(dòng)手冊(cè)[M].北京：機(jī)械工業(yè)出版社,1995
[6]成大先.機(jī)械設(shè)計(jì)手冊(cè)—第5版[M].北京：化學(xué)工業(yè)出版社，2008
[7]黃悠調(diào),趙松年. 機(jī)電一體化技術(shù)基礎(chǔ)及應(yīng)用[M]. 北京:機(jī)械工業(yè)出版社, 2002.
[8]濮良貴、紀(jì)名剛.機(jī)械設(shè)計(jì)（第七版）[M].北京：高等教育出版社，2001
[9]鄞丈緯. 機(jī)械原理[M]．北京：高等教育出版社．1997
[10]胨立周. 機(jī)械優(yōu)化設(shè)計(jì)[M]上海：上海科學(xué)技術(shù)出版杜，1982
[11]郭芝俊、張林芳. 機(jī)械設(shè)計(jì)便覽[M].天津：天津科學(xué)技術(shù)出版社1988
[12]楊廷力，機(jī)械系統(tǒng)基本理論，北京：機(jī)械工業(yè)出版社，1996。
指導(dǎo)教師簽名：
年 月 日
滑橇式輸送機(jī)5.5m鏈?zhǔn)絼?dòng)力滾床設(shè)計(jì),指導(dǎo)人員：,畢業(yè)設(shè)計(jì)的主要內(nèi)容,a 根據(jù)任務(wù)書要求進(jìn)行總體設(shè)計(jì)(大概的布局） b 相關(guān)的設(shè)計(jì)計(jì)算 (1)減速電機(jī)的選型、轉(zhuǎn)矩，轉(zhuǎn)速一些相關(guān)計(jì)算。。 (2)動(dòng)力輥?zhàn)虞S的相關(guān)計(jì)算。 (3)傳動(dòng)部件的相關(guān)計(jì)算。 (4)軸承的選擇及計(jì)算等。 c 繪制5.5m鏈?zhǔn)絼?dòng)力滾床的裝配圖，零件圖。,動(dòng)力滾床的相關(guān)圖片,,,,整體設(shè)計(jì)參數(shù)要求,主參數(shù)： 動(dòng)力電源：AC380V/350Hz 控制電源：DC24V 軌 距：1000mm 滾輪直徑：136mm 運(yùn)行速度：12m/min 額定荷載：900kg,動(dòng)力滾床主要部件設(shè)計(jì),總體傳動(dòng)系統(tǒng)方案的擬定 減速電機(jī)的選型及計(jì)算 動(dòng)力輥?zhàn)拥脑O(shè)計(jì) 套筒的設(shè)計(jì) 鏈傳動(dòng)設(shè)計(jì) 滾子的設(shè)計(jì) 軸承的選型及校驗(yàn),一、總體傳動(dòng)系統(tǒng)方案的擬定,傳動(dòng)方案設(shè)計(jì)： 合理的傳動(dòng)方案，首先應(yīng)滿足工作機(jī)的功能要求，其次還應(yīng)該滿足工作可靠、傳動(dòng)效率高、結(jié)構(gòu)簡單、尺寸緊湊、重量輕、成本低廉、工藝性好、 使用和維護(hù)方便等要求。任何一個(gè)方案，要滿足上述所有要求是十分困難的，設(shè)計(jì)時(shí)要統(tǒng)籌兼顧，滿足最主要的和最基本的要求。 擬定的傳動(dòng)方案：,,主框架的設(shè)計(jì),,,,,,,負(fù)載轉(zhuǎn)矩的計(jì)算 ： 得到 T=122.4N*m 轉(zhuǎn)速的計(jì)算 ： 得到N=28.104r/min 減速電機(jī)的選型 ： （1）減速電機(jī)型號(hào)：R37DT71D4BMG （2）電機(jī) 功率：0.37kw （3）電機(jī) 級(jí)數(shù)：4 （4）輸出 轉(zhuǎn)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(jī)的選型及計(jì)算,三、動(dòng)力輥?zhàn)拥脑O(shè)計(jì),,,,,,,心軸的計(jì)算 ：確定軸端直徑d=25mm 心軸的結(jié)構(gòu)設(shè)計(jì) ：,套筒的作用： 實(shí)際上在本次設(shè)計(jì)中，套筒也起著軸的作用，套筒充當(dāng)?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(jié)構(gòu)和尺寸,四、套筒的設(shè)計(jì),五、鏈傳動(dòng)的設(shè)計(jì),滾子鏈鏈輪的設(shè)計(jì) （1）驅(qū)動(dòng)單鏈輪的結(jié)構(gòu)尺寸,雙鏈輪的結(jié)構(gòu)尺寸 : 張緊鏈輪的結(jié)構(gòu)尺寸: | V ,六、鏈的張緊裝置,鏈傳動(dòng)的布置 （1）常見合理布置形式參見下表,,a.本次設(shè)計(jì)的驅(qū)動(dòng)鏈輪的布置，采用的是兩輪軸線不 在同一水平面，松邊應(yīng)在下面。選擇的是第二種布置方案。 b.傳動(dòng)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(dòng)的張緊 一般的張緊方式：,本次設(shè)計(jì)的張緊裝置如下圖：,七、滾動(dòng)軸承的選擇及計(jì)算,滾動(dòng)軸承的工作特點(diǎn)： 與滑動(dòng)軸承相比，滾動(dòng)軸承具有下列優(yōu)點(diǎn)： （）應(yīng)用設(shè)計(jì)簡單，產(chǎn)品已標(biāo)準(zhǔn)化，并由專業(yè)生產(chǎn)廠家進(jìn) 行大批量生產(chǎn)，具有優(yōu)良的互換性和通用性。（）起動(dòng)摩擦力矩低，功率損耗小，滾動(dòng)軸承效率（0.980.99）比混合潤滑軸承高。 （）負(fù)荷、轉(zhuǎn)速和工作溫度的適應(yīng)范圍寬，工況條件的少量變化對(duì)軸承性能影響不大。（）大多數(shù)類型的軸承能同時(shí)承受徑向和軸向載荷，軸向尺寸較小。（）易于潤滑、維護(hù)及保養(yǎng)。 滾動(dòng)軸承也有下列缺點(diǎn)： 大多數(shù)滾動(dòng)軸承徑向尺寸較大。 在高速、重載荷條件下工作時(shí)，壽命短。 振動(dòng)及噪音較大。,滾動(dòng)軸承的選擇,,,再次謝謝各位評(píng)判老師！,
外文資料
The Two-Dimensional Dynamic Behavior of Conveyor Belts
Ir. G. Lodewijks, Delft University of Technology, The Netherlands
1. SUMMARY
1--------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. INTRODUCTION
2--------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 belt's longitudinal and transverse response to starting and stopping procedures and it's motion during steady state operation. It's 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 SYSTEMS
6--------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 systems
Many 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 resistance's 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 curves
The 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 BELT
A 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 inertia's 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 belt's 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 resistance's 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 belt's tensile member, G represents the belt's variable longitudinal geometric stiffness produced by the vertical acting forces on the belt's cross section between two idlers, V represent the belts velocity dependent resistance's.
Figure 1: Five element composite model [9].
3.1.1 NON LINEAR TRUSS ELEMENT
If 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 describes
Figure 2: Definition of the displacements of a truss element
the change of length of the axis of the truss element [7]:
ε1 = D1(x) = ∫1 o
ds2 - ds2o
dξ ???????? ????(2)
2ds2o
where dso is the length of the undeformed element, ds the length of the deformed element and ξ a dimensionless length coordinate along the axis of the element.
Figure 3: Static sag of a tensioned belt
Although 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 = δ/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]:
εs = 8/3 K2s ?????????????(4)
which yields the total longitudinal deformation of the non linear truss element:
3.1.2 BEAM ELEMENT
Figure 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, ε1, and two bending deformation parameters, ε2 and ε3.
Figure 5: The bending deformations of a beam element
The bending deformation parameters of the beam element can be defined with the component vector of the beam element (see Figure 4):
xT = [up vp μp uq vq μq] ???????? (5)
and the deformed configuration as shown in Figure 5:
ε2 = D2(x) =
e2p1pq
?????? ??(6)
1o
ε3 = D3(x) =
-eq21pq
1o
3.2 THE MOVEMENT OF THE BELT OVER IDLERS AND PULLEYS
The 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 ξ, 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, ε1, ε2 and ε3, determine the deformation of the belt and are already given in 3.1. The remaining two, ε4 and ε5, 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:
ε4 = D4(x) = (rξ + u ξ)e2 - rid.e2 = 0
ε5 = D5(x) = (r ξ + uξ)e1 - rid.e1 = 0 ?????????????? (7)
If during simulation ε4 > 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 RESISTANCE
In 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 ?2u
?Fzb ???t2
fb =
????Mf????
??Fzbri
where 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 BELT'S DRIVE SYSTEM
To 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, μp and μq, one rigid body motion (rotation) and therefore one deformation parameter:
εred = Dred(x) = iμp + μq = 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 + ωsGi + L ?i/?t ???? ????????????? (11)
In eq. (11) i is the vector of phase currents, R the matrix of phase resistance's, C the matrix of inductive phase resistance's, L the matrix of phase inductance's and ωs 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 = Iij
?2?j
+ Cik
??k
??Kil? ???? ????????????(13)
?t2
?t
where 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 axis's.
To simulate a controlled start or stop procedure a feedback routine can be added to the model of the belt's drive system in order to control the drive torque.
3.5 THE EQUATIONS OF MOTION
The equations of motion of the total belt conveyor model can be derived with the principle of virtual power which leads to [7]:
fk - Mkl ?2x1 / ?t2 = σ1Dik ???????????????(14)
where f is the vector of resistance forces, M the mass matrix and σ the vector of multipliers of Lagrange which may be interpret as the vector of stresses dual to the vector of strains ε. 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 EXAMPLE
Application 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 it's natural frequency, otherwise the belt's 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
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