1730_帶式輸送機(jī)的機(jī)械傳動(dòng)裝置

1730_帶式輸送機(jī)的機(jī)械傳動(dòng)裝置,輸送,機(jī)械傳動(dòng),裝置 畢業(yè)設(shè)計(jì)（論文）題目： 帶式輸送機(jī)的機(jī)械傳動(dòng)裝置系 別 航空工程系 專業(yè)名稱 機(jī)械設(shè)計(jì)制造及其自動(dòng)化班級(jí)學(xué)號(hào) 088105429學(xué)生姓名 袁小龍指導(dǎo)教師 賀紅林二 O 一二 年 六 月 畢業(yè)設(shè)計(jì)（論文）任務(wù)書I、畢業(yè)設(shè)計(jì)(論文) 題目：帶式輸送機(jī)的機(jī)械傳動(dòng)裝置設(shè)計(jì)II、畢 業(yè)設(shè)計(jì)(論文)使用的原始資料(數(shù)據(jù))及設(shè)計(jì)技術(shù)要求1）輸送物料為：煤炭顆粒，粒度為 10mm；運(yùn)輸量 Q＝80t/h；2）運(yùn)輸帶速度 =1.5 m/s，帶寬 B=800mm；v3）滾筒直徑 D=400 mm，輸送帶拉力 F=2200N；4）滾筒效率 （包括 軸承與滾筒的效率損失）；96.0?j?5）工作情況：兩班制，連續(xù)單向運(yùn)轉(zhuǎn)， 載荷較平穩(wěn)；6）使用折舊期：8 年；7）工作環(huán)境：室內(nèi)，灰塵較大， 環(huán)境最高溫度 ；C0358）制造條件及生產(chǎn)批量：一般機(jī)械廠制造，小批量生產(chǎn)；9）動(dòng)力來源：電力，三相交流，電壓 380/220v；運(yùn)動(dòng)簡圖（參考）II、畢 業(yè)設(shè)計(jì)( 論文)工作內(nèi)容及完成時(shí)間：（1）查閱相關(guān)資料，外文資料翻譯（6000 字符以上），撰寫開題報(bào)告 4 周（3）擬定帶式輸送機(jī)的機(jī)械傳動(dòng)方案確定 1 周 （4）傳動(dòng)系統(tǒng)的總體設(shè)計(jì)計(jì)算 1 周 （5）帶式輸送機(jī)傳動(dòng)系統(tǒng)三維總體裝圖設(shè)計(jì) 4 周（6）帶式輸送機(jī)主要零（部）件工作圖設(shè)計(jì) 2 周（7）畢業(yè)設(shè)計(jì)說明書（論文）撰寫 3 周（8）畢業(yè)設(shè)計(jì)審查、畢業(yè)答辯 2 周Ⅳ 、主 要參考資料：[1] 美輸送設(shè)備 制造協(xié)會(huì)編. 散狀物料帶式輸送機(jī). 北京：機(jī)械工業(yè)出版社，1984[2] 濮良貴. 機(jī)械設(shè)計(jì)（第8版）. 北京：高等教育出版社，2008[3] 王昆等編 . 機(jī)械設(shè)計(jì)基礎(chǔ)課程設(shè)計(jì). 高等教育出版社，1995[4] 龔桂義. 機(jī)械設(shè)計(jì)課程設(shè)計(jì)圖冊(cè). 北京：高等教育出版社，1989[5] 中國煤炭建 設(shè)協(xié)會(huì). 帶式輸送機(jī)工程設(shè)計(jì)規(guī)范. 北京：中國計(jì)劃出版社，2000[6] M. A. Alspaugh. Latest Developments in Belt Conveyor Technology. MINExpo 2004, Las Vegas, NV, USA[7] Phonix Conveyor Belt. Phoenix Conveyor Belts Design Fundamentals. Hamburg, 2004[8] 芮曉明. 機(jī)械設(shè)計(jì)基礎(chǔ)及電廠金屬材料. 北京：中國電力出版社，2000航空制造工程 學(xué)院 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 專業(yè)類 0881054 班學(xué)生（簽名）： 袁小龍 日期： 自 20 年 月 日 至 20 年 月 日指導(dǎo)教師（簽名）： 助理指導(dǎo)教師(并指出所負(fù)責(zé)的部分)：機(jī)械設(shè)計(jì) 系（室） 主任（簽名）： 附注:任 務(wù)書應(yīng)該附在已完成的畢業(yè)設(shè)計(jì)說明書首頁。學(xué)士學(xué)位論文原創(chuàng)性聲明本人聲明，所呈交的論文是本人在導(dǎo)師的指導(dǎo)下獨(dú)立完成的研究成果。除了文中特別加以標(biāo)注引用的內(nèi)容外，本論文不包含法律意義上已屬于他人的任何形式的研究成果,也不包含本人已用于其他學(xué)位申請(qǐng)的論文或成果。對(duì)本文的研究作出重要貢獻(xiàn)的個(gè)人和集體，均已在文中以明確方式表明。本人完全意識(shí)到本聲明的法律后果由本人承擔(dān)。作者簽名： 日期：學(xué)位論文版權(quán)使用授權(quán)書本學(xué)位論文作者完全了解學(xué)校有關(guān)保留、使用學(xué)位論文的規(guī)定，同意學(xué)校保留并向國家有關(guān)部門或機(jī)構(gòu)送交論文的復(fù)印件和電子版，允許論文被查閱和借閱。本人授權(quán)南昌航空大學(xué)科技學(xué)院可以將本論文的全部或部分內(nèi)容編入有關(guān)數(shù)據(jù)庫進(jìn)行檢索，可以采用影印、縮印或掃描等復(fù)制手段保存和匯編本學(xué)位論文。作者簽名： 日期：導(dǎo)師簽名： 日期：帶式輸送機(jī)的機(jī)械傳動(dòng)裝置設(shè)計(jì)學(xué)生姓名：袁小龍 班級(jí)：0881054指導(dǎo)老師：賀紅林 摘要：帶式輸送機(jī)在煤炭運(yùn)輸、交通、糧食運(yùn)輸、礦石等多個(gè)領(lǐng)域有所運(yùn)用。本文首先介紹了帶式輸送機(jī)傳動(dòng)裝置的研究背景，未來發(fā)展?fàn)顩r及發(fā)展方向。本文為了研究帶式輸送機(jī)傳動(dòng)裝置設(shè)計(jì)，完成了以下工作。（1） 擬定帶式輸送機(jī)的機(jī)械傳動(dòng)方案（2） 傳動(dòng)方案的總體設(shè)計(jì)計(jì)算（3） 帶式輸送機(jī)傳動(dòng)總體狀圖設(shè)計(jì)（4） 帶式輸送機(jī)主要零部件工作圖設(shè)計(jì)（5） 畢業(yè)設(shè)計(jì)說明說的撰寫關(guān)鍵詞 ：電動(dòng)機(jī)；齒輪；軸；帶式輸送機(jī)。指導(dǎo)老師簽名：Design of belt conveyor Student name : Yuan XiaoLong Class : 0881054Supervisor : He HongLinBelt conveyer system is known as an efficient mean of transporting bulk materials, it has a high requirement of reliablity.With the development of mining work conditions, the convery route become more and more complex, and it′s conveyance ability with transport distance is all other transport a machine equipments can't compare to, its structure simple, circulate balance, revolve credibility.This article sums up the feasible scheme of the key technology, aimed at the primitive parameter of the belt conveyor of coal colliery.In the article, through the design calculation of choosing the equipments and the design of some important parts of the belt conveyor, the system can finish the mission safely and dependably on the occasion.The ordinary belt conveyor consists of six main parts: Drive Unit, Jib or Delivery End, Tail Ender Return End, Intermediate Structure, Loop Take-Up and Belt. The article passes the comparison which tenses device merit and shortcoming of main function and a few kinds that the introduction tenses device in going into detail to tense the foundation of the main form of device with domestic currently.We serve the purpose at last.Keywords: Motor, Gear, ShaftSignnature of Supervison:畢業(yè)設(shè)計(jì)（論文）開題報(bào)告題目帶式輸送機(jī)的機(jī)械傳動(dòng)裝置設(shè)計(jì)專 業(yè) 名 稱 機(jī)械設(shè)計(jì)制造及其自動(dòng)化班 級(jí) 學(xué) 號(hào) 0 8 8 1 0 5 4 2 9學(xué) 生 姓 名 袁 小 龍指 導(dǎo) 教 師 賀 紅 林填表日期：2 0 1 2 年 2 月 21 日說 明開題報(bào)告應(yīng)結(jié)合自己課題而作，一般包括：課題依據(jù)及課題的意義、國內(nèi)外研究概況及發(fā)展趨勢(shì)（含文獻(xiàn)綜述） 、研究內(nèi)容及實(shí)驗(yàn)方案、目標(biāo)、主要特色及工作進(jìn)度、參考文獻(xiàn)等內(nèi)容。以下填寫內(nèi)容 各專業(yè) 可根據(jù)具體情況適當(dāng) 修改 。但每個(gè)專業(yè)填寫內(nèi)容應(yīng)保持一致。一、選題的依據(jù)及意義：帶式輸送機(jī)是最重要的現(xiàn)代散狀物料輸送設(shè)備，它廣泛的應(yīng)用電力、糧食、冶金、化工、煤礦、礦山、建材、輕工及交通運(yùn)輸?shù)阮I(lǐng)域。由于帶式輸送機(jī)比較經(jīng)濟(jì)，操作安全、可靠具有多方面的適應(yīng)性及生產(chǎn)能力實(shí)際上不受限制等優(yōu)點(diǎn)。此外，由于帶式輸送機(jī)能完成使物料在各工序之間連續(xù)流動(dòng)的工作，因此具有多種工藝功能。帶式輸送機(jī)在環(huán)境保護(hù)方面是更令人滿意的，它既不污染空氣有沒有噪音。帶式輸送機(jī)也是煤礦最為理想的高效連續(xù)運(yùn)輸設(shè)備，特別是煤礦高產(chǎn)高效現(xiàn)代化的大型礦井，帶式輸送機(jī)己成為煤炭高效開采機(jī)電一體化技術(shù)與裝備的關(guān)鍵設(shè)備。目前，普通帶式運(yùn)輸機(jī)已經(jīng)在礦山得到了普遍的應(yīng)用。但由于目前形成系列化的帶式運(yùn)輸機(jī)運(yùn)輸傾角一般 18°以下，使得帶式輸送機(jī)在生產(chǎn)實(shí)際現(xiàn)場(chǎng)的應(yīng)用受到一定范圍的限制。而近年來發(fā)展起來的各種大傾角帶式輸送機(jī)在露天、地下礦山以及其他場(chǎng)合的使用，都取得了較好的效果。而且大傾角帶式輸送機(jī)在提升高度相 同的情況下，所占地面積和空間都比使用普通帶式輸送機(jī)少，并且具有常規(guī)帶式輸送機(jī)的所有特點(diǎn)，投資成本低，因而在生產(chǎn)運(yùn)輸中越來越受到重視，應(yīng)用前景十分廣闊。二、國內(nèi)外研究概況及發(fā)展趨勢(shì)（含文獻(xiàn)綜述）：1.國外帶式輸送機(jī)技術(shù)的現(xiàn)狀國外帶式輸送機(jī)技術(shù)的發(fā)展很快，其主要表現(xiàn)在 2 個(gè)方面：一方面是帶式輸送機(jī)的功能多元化、應(yīng)用范圍擴(kuò)大化，如高傾角帶輸送機(jī)、管狀帶式輸送機(jī)、空間轉(zhuǎn)彎帶式輸送機(jī)等各種機(jī)型；另一方面是帶式輸送機(jī)本身的技術(shù)與裝備有了巨大的發(fā)展尤其是長距離、大運(yùn)量、高帶速等大型帶式輸送機(jī)已成為發(fā)展 的主要方向，其核心技術(shù)是開發(fā)應(yīng)用于了帶式輸送機(jī)動(dòng)態(tài)分析與監(jiān)控技術(shù)，提高了帶式輸送機(jī)的運(yùn)行性能和可靠性。國外已經(jīng)使用或已經(jīng)進(jìn)行設(shè)計(jì)的幾條典型長距離帶式輸送機(jī)輸送線：1.1 西班牙的西撒哈拉帶式輸送機(jī)線路是世界最長的長距離輸送機(jī)線路，該線路長達(dá) 100km，用來將位于石質(zhì)高原地區(qū)的布·克拉露天礦的磷灰石礦石運(yùn)往艾汾阿雍海港。此線路于兩年半內(nèi)建成，并于 1972 年使用，該系統(tǒng)總投資額為 2 億馬克。服務(wù)年限為30 年，年平均運(yùn)輸量為 1000 萬噸磷灰石礦石(2000t/h)。每噸千米的運(yùn)費(fèi)為 0.026 法郎，整條線路由長為 6.9～11.8km 的 11 臺(tái)輸送機(jī)組成。輸送機(jī)采用寬為 1000mm，強(qiáng)度為3150N/mm 的鋼繩芯輸送帶，帶速為 4.5m/s。輸送帶的安全系數(shù)為 6.7～10。輸送機(jī)設(shè)有頂棚，迎風(fēng)側(cè)裝有護(hù)板。借助聲納檢測(cè)器可以發(fā)現(xiàn)損壞的托輥。1.2 澳大利亞恰那礦 20km 地面帶式輸送機(jī)系統(tǒng)是代表了現(xiàn)代帶式輸送機(jī)發(fā)展水平的一條輸送線。該輸送系統(tǒng)由一條長為 10.3km 的平面轉(zhuǎn)彎帶式輸送機(jī)和一條 10.1km的直線長距離帶式輸送機(jī)構(gòu)成。轉(zhuǎn)彎帶式輸送機(jī)的曲率半徑為 9km，弧長為 4km。兩條輸送機(jī)除線路參數(shù)外，其他參數(shù)相同，運(yùn)輸能力為 2200t/h，帶寬 1050mm，輸送帶抗拉強(qiáng)度為 3000N/mm，安全系數(shù)為 5，拉緊裝置為重錘拉緊。允許行程為 25m，驅(qū)動(dòng)采用 3 臺(tái) 700kw 直流電動(dòng)機(jī)，雙滾筒驅(qū)動(dòng)。該機(jī)在 25℃下每臺(tái)電動(dòng)機(jī)的牽引功率小平330kW，相應(yīng)摩擦系分別為：直線輸送機(jī) 0.00998，轉(zhuǎn)彎輸送機(jī)為 0.011。系統(tǒng)采用了先進(jìn)的托輥制造和安裝技術(shù)、水平轉(zhuǎn)彎技術(shù)和動(dòng)態(tài)分析技術(shù)。1.3 津巴布韋鋼鐵公司(ZISCO)15.6km 水平轉(zhuǎn)彎越野帶式輸送機(jī)于 1996 年投入使用，是世界上單機(jī)最長的帶式輸送機(jī)。該輸送機(jī)將 ZISCO 的 New Ripple Creek 礦的經(jīng)過二次破碎的鐵礦石運(yùn)送到 Redcliff，Zimbabwe 的煉鋼廠附近。輸送量為干礦石500t/h(濕礦石 600t/h)。系統(tǒng)全長為 15.6km，物料提升高度為 90m。輸送帶采用橋石公司的鋼繩芯輸送帶，抗拉強(qiáng)度為 888N/mm，運(yùn)行速度為 4.25m/s。輸送帶的安全系數(shù)為 5.8，當(dāng)環(huán)境溫度為 0℃時(shí)，安全系數(shù)降到 5.5，當(dāng)輸送量增加到 600t/h 時(shí)，輸送帶安全系數(shù)降低到 4.8。為了提高輸送帶的利用率，輸送帶的上、下覆蓋層采用相同的厚度，為 5mm。這樣做的目的是，當(dāng)上覆蓋層磨損超過 2mm 時(shí)，可將輸送帶翻面使用，從而達(dá)到提高輸送帶的使用壽命。輸送機(jī)采用頭部雙滾筒，尾部單滾筒的驅(qū)動(dòng)方案，整個(gè)系統(tǒng)功率為 500kW。目前，在煤礦井下使用的帶式輸送機(jī)其關(guān)鍵技術(shù)與裝備有以下幾個(gè)特點(diǎn)：（1）設(shè)備大型化。其主要技術(shù)參數(shù)與裝備均向著大型化發(fā)展，以滿足年產(chǎn) 300~500萬 t 以上高產(chǎn)高效集約化生產(chǎn)的需要。（2）應(yīng)用動(dòng)態(tài)分析技術(shù)和機(jī)電一體化、計(jì)算機(jī)監(jiān)控 等高新技術(shù)，采用大功率軟起動(dòng)與自動(dòng)張緊技術(shù)，對(duì)輸送機(jī)進(jìn)行動(dòng)態(tài)監(jiān)測(cè)與監(jiān)控， 大大地降低了輸送帶的動(dòng)張力，設(shè)備運(yùn)行性能好，運(yùn)輸效率高。（3）采用多機(jī)驅(qū)動(dòng)與 中間驅(qū)動(dòng)及其功率平衡、輸送機(jī)變向運(yùn)行等技術(shù)，使輸送機(jī)單機(jī)運(yùn)行長度在理論上 已有受限制，并確保了輸送系統(tǒng)設(shè)備的通用性、互換性及其單元驅(qū)動(dòng)的可靠性。（4）新型、高可靠性關(guān)鍵元部件技術(shù)。如包含 CST 等在內(nèi)的各種先進(jìn)的大功率驅(qū)動(dòng)裝置與調(diào)速裝置、高壽命高速托輥、自清式滾筒裝置、高效貯帶裝置、快速自移機(jī)尾等。2 國內(nèi)帶式輸送機(jī)技術(shù)的現(xiàn)狀我國生產(chǎn)制造的帶式輸送機(jī)品種、類型較多。在“八五” 期間，通過國家一條龍“日產(chǎn)萬噸綜采設(shè)備”項(xiàng)目的實(shí)施，帶式輸送機(jī)技術(shù)水平有了很大提高，煤礦井下用大功率、長距離帶式輸送機(jī)關(guān)鍵技術(shù)研究和新產(chǎn)呂開發(fā)都 取得了很大的進(jìn)步。從SDJ、 SSJ、STJ 、DT 等系列發(fā)展到各種多功能特種帶式輸送機(jī)系列，如大傾角長距離帶式輸送機(jī)成套設(shè)備、高產(chǎn)高效工作面順槽可伸縮帶式輸送機(jī)等均填補(bǔ)了國內(nèi)空白，并用動(dòng)態(tài)分析、智能化控制技術(shù)等對(duì)關(guān)鍵設(shè)備進(jìn)行了理論研究和產(chǎn)品開發(fā)，研制成功了多種軟起動(dòng)和制動(dòng)裝置以及以 PLC 為核心的可編程電控裝置，驅(qū)動(dòng)系統(tǒng)采用調(diào)速型液力偶合器和行星齒輪減速器。但是和外國先進(jìn)型相比，國內(nèi)輸送機(jī)機(jī)型一般較小，帶速通常不超過 4m/s，普遍沿用靜態(tài)設(shè)計(jì)法，設(shè)備成本偏高，運(yùn)行的可靠性低。此外，我國尚未形成元部件的大規(guī)模專業(yè)生產(chǎn)廠，設(shè)計(jì)制造水平有待提高。帶式輸送機(jī)通常有機(jī)型（1）固定帶式輸送機(jī)；（2）可伸縮帶式輸送機(jī)；（3）大傾角上、下運(yùn)帶式輸送機(jī)；（4）水平拐彎輸送機(jī)；（5）下運(yùn)帶式輸送機(jī)；（6）垂直提升帶式輸送機(jī)；（7）管狀式帶式輸送機(jī)；（8）壓帶式輸送機(jī)。目前我國用剛性理論來分析研究帶式輸送機(jī)并制訂計(jì)算方法和設(shè)計(jì)規(guī)范，設(shè)計(jì)中對(duì)輸送帶使用了很高的安全系統(tǒng)（一般取 n=10 左右） ，與實(shí)際情況相差很遠(yuǎn)。實(shí)際上輸送帶是粘彈性體，長距離帶式輸送機(jī)其輸送帶對(duì)驅(qū)動(dòng)裝置的起、制動(dòng)力的動(dòng)態(tài)響應(yīng)是一個(gè)非常復(fù)雜的過程，而不能簡單地用剛體力學(xué)來解釋和計(jì)算。已開發(fā)了帶式輸送機(jī)動(dòng)態(tài)設(shè)計(jì)方法和應(yīng)用軟件，在大型輸送機(jī)上對(duì)輸送機(jī)的動(dòng)張力進(jìn)行動(dòng)態(tài)分析與動(dòng)態(tài)監(jiān)測(cè)，確保了輸送機(jī)運(yùn)行的可靠性，從而使大型帶式輸送機(jī)的設(shè)計(jì)達(dá)到了最高水平，并使輸送機(jī)的設(shè)備成本尤其是輸送帶成本大為降低。3 帶式輸送機(jī)的發(fā)展趨勢(shì)3.1 設(shè)備大型化、提高運(yùn)輸能力為了適應(yīng)高產(chǎn)高效集約化生產(chǎn)的需要，帶式輸送機(jī)輸送能力要加大。長距離、高帶速、大運(yùn)量、大功率是今后發(fā)展的必然趨勢(shì)，也是高產(chǎn)高效礦井運(yùn)輸技術(shù)的發(fā)展方向。在今后的 10a 內(nèi)輸送量要提高到 3000～10000 t/h，帶速提高至 5～8m/s，輸送長度對(duì)于可伸縮帶式輸送機(jī)要達(dá)到 6000m。對(duì)于鋼繩芯強(qiáng)力帶式輸送機(jī)需加長至 14000m 以上，單機(jī)驅(qū)動(dòng)功率要求達(dá)到 1000～2500 kW，輸送帶抗拉強(qiáng)度達(dá)到大于 6000 N/mm（鋼繩芯）和 31500 N/mm（整芯） 。尤其是煤礦井下順槽可伸縮輸送技術(shù)的發(fā)展，隨著高產(chǎn)高效工作面的出現(xiàn)及煤炭科技的不斷發(fā)展，原有的可伸縮帶式輸送機(jī)，無論是主參數(shù)，還是運(yùn)行性能都難以適應(yīng)高產(chǎn)高效工作面的要求，煤礦現(xiàn)場(chǎng)急需主參數(shù)更大、技術(shù)更先進(jìn)、性能更可靠的長距離、大運(yùn)量、大功率順槽可伸縮帶式輸送機(jī)，以提高我國帶式輸送機(jī)技術(shù)的設(shè)計(jì)水平，填補(bǔ)國內(nèi)空白，接近并趕上國際先進(jìn)工業(yè)國的技術(shù)水平。其包含 7 個(gè)方面的關(guān)鍵技術(shù)：（1）帶式輸送機(jī)動(dòng)態(tài)分析與監(jiān)控技術(shù)；（2）軟起動(dòng)與功率平衡 技術(shù)；（3）中間驅(qū)動(dòng)技術(shù)（4）自動(dòng)張緊技術(shù)（5）新型高壽命高速托輥技術(shù)；（6）快速自移機(jī)尾技術(shù)；（7）高效儲(chǔ)帶技術(shù)。3.2 提高元部件性能和可靠性設(shè)備開機(jī)率的高與低主要取決于元部件的性能和可靠性。除了進(jìn)一步完善和提高現(xiàn)有元部件的性能和可靠性，還要不斷地開發(fā)研究新的技術(shù)和元部件，如高性能可控軟起動(dòng)技術(shù)、動(dòng)態(tài)分析與監(jiān)控技術(shù)、高效貯帶裝置、快速自移機(jī) 尾、高速托輥等，使帶式輸送機(jī)的性能得到進(jìn)一步的提高。3.3 擴(kuò)大功能，一機(jī)多用化 將帶式輸送機(jī)結(jié)構(gòu)作適當(dāng)修改，拓展運(yùn)人、運(yùn)料或雙向運(yùn)輸?shù)裙δ?，做到一機(jī)多用，使其發(fā)揮最大的經(jīng)濟(jì)效益。3.4 開發(fā)專用機(jī)型我過煤礦的地質(zhì)條件差異很大，為了滿足特殊要求，應(yīng)開發(fā)特殊型帶式輸送機(jī)，如彎曲帶式輸送機(jī)、大傾角或垂直提升輸送機(jī)等。三、研究內(nèi)容： 1 帶式輸送機(jī)系統(tǒng)初步設(shè)計(jì)1.1 帶式輸送機(jī)初步設(shè)計(jì)計(jì)算布置形式的分析確定，帶速的選擇；輸送帶帶寬、類型的選擇確定；輸送帶線質(zhì)量的計(jì)算；物料線質(zhì)量的計(jì)算；托輥旋轉(zhuǎn)部分質(zhì)量的計(jì)算；各直線區(qū)段阻力計(jì)算；局部阻力計(jì)算；輸送帶各點(diǎn)張力計(jì)算及強(qiáng)度校核；變坡段曲率半徑的確定；滾筒牽引力與電機(jī)功率的計(jì)算；拉緊力與拉緊行程的計(jì)算；制動(dòng)力矩的計(jì)算。1.2 機(jī)械裝置的選擇與確定 電動(dòng)機(jī)、減速器、聯(lián)軸器的選擇；軟起動(dòng)裝置或制動(dòng)裝置的選擇；傳動(dòng)滾筒、改向滾筒的選擇與設(shè)計(jì)；采用托輥、托輥組的種類、結(jié)構(gòu)形式及特點(diǎn)；采用拉緊裝置的結(jié)構(gòu)與特點(diǎn)。2 帶式輸送機(jī)的傳動(dòng)裝置的總體設(shè)計(jì)2.1 確定傳動(dòng)方案在進(jìn)行傳動(dòng)系統(tǒng)總體設(shè)計(jì)時(shí)常需要擬定多種方案進(jìn)行比較，以使所設(shè)計(jì)的機(jī)器盡可能具有較高的傳動(dòng)效率，且工作可靠、結(jié)構(gòu)簡單、尺寸緊湊、成本低廉、工藝性好，同時(shí)便于維護(hù)。2.2 傳動(dòng)裝置總傳動(dòng)比的計(jì)算和分配3 傳動(dòng)裝置基本參數(shù)的計(jì)算各軸轉(zhuǎn)數(shù)的計(jì)算、功率的計(jì)算。四、目標(biāo)、主要特色及工作進(jìn)度（1）查閱相關(guān)資料，外文資料翻譯（6000 字符以上） ，撰寫開題報(bào)告 ————————————————————————————————4 周（2）擬定帶式輸送機(jī)的機(jī)械傳動(dòng)方案確定 ————————————————— ————————————————1 周（3）傳動(dòng)系統(tǒng)的總體設(shè)計(jì)計(jì)算 —————————————————————————————————1 周（5）帶式輸送機(jī)傳動(dòng)系統(tǒng)三維總體裝圖設(shè)計(jì) —————————————————— ———————————————2 周（6）帶式輸送機(jī)主要零（部）件工作圖設(shè)計(jì) ——————————————————-———————————————2 周（7）畢業(yè)設(shè)計(jì)說明書（論文）撰寫 —————————————————————————————————3 周（8）畢業(yè)設(shè)計(jì)審查、畢業(yè)答辯 —————————————————————————————————2 周五、參考文獻(xiàn)[1] 美輸送設(shè)備制造協(xié)會(huì)編. 散狀物料帶式輸送機(jī). 北京：機(jī)械工業(yè)出版社，1984[2] 濮良貴. 機(jī)械設(shè)計(jì)（第8版）. 北京：高等教育出版社，2008[3]王昆等編. 機(jī)械設(shè)計(jì)基礎(chǔ)課程設(shè)計(jì). 高等教育出版社，1995[4] 龔桂義. 機(jī)械設(shè)計(jì)課程設(shè)計(jì)圖冊(cè). 北京：高等教育出版社，1989[5]中國煤炭建設(shè)協(xié)會(huì). 帶式輸送機(jī)工程設(shè)計(jì)規(guī)范. 北京：中國計(jì)劃出版社，2000[6]M. A. Alspaugh. Latest Developments in Belt Conveyor Technology. MINExpo 2004, Las Vegas, NV, USA[7] Phonix Conveyor Belt. Phoenix Conveyor Belts Design Fundamentals. Hamburg, 2004[8] 芮曉明. 機(jī)械設(shè)計(jì)基礎(chǔ)及電廠金屬材料. 北京：中國電力出版社，2000輸送帶的二維動(dòng)態(tài)特性3.1.1 非線性梁架（構(gòu)架）元如果只有帶的縱向變形是主要素，那么梁架元就可用于模型的皮帶彈性反應(yīng)。梁架元組成部分有如圖 2 所示的兩個(gè)結(jié)點(diǎn)， P 和 Q ，四個(gè)位移參數(shù)確定部分載體 X：xT = [up vp uq vq] (1)對(duì)平面運(yùn)動(dòng)的梁架元有三個(gè)獨(dú)立的剛體運(yùn)動(dòng)，因此（這公式）仍然是描述一個(gè)變形的參數(shù)。圖 2 ：梁架元的精確位移梁架元軸的長度變化， [ 7 ] ：ds2 - ds2oε1 = D1(x) = ∫1 o2ds2odξ (2)DSO 是限元未變形的長度，DS 是限元變形的長度，ξ 是沿著有限元軸的無量綱長度。圖 3 ：張帶的靜態(tài)凹陷雖然帶呈彎曲狀態(tài)，但梁架元并沒有變形，這可能考慮到帶小數(shù)值凹陷的靜態(tài)影響。靜態(tài)帶凹陷的比率是有定義的（見圖 3 ） ：K1 = δ/1 = q1/8T (3)其中 q 是暴露在外面帶和散裝物料的重量在豎直方向上分布的荷載， 1 是帶輪間距，而 T 是帶的張力。 ，帶凹陷的縱向變形影響取決于[ 7 ] ：εs = 8/3 K2s (4)產(chǎn)生了非線性梁架元總的縱向變形。3.1.2 梁架元圖 4 ：節(jié)點(diǎn)的精確位移和旋轉(zhuǎn)的梁架元。如果帶的橫向位移是主要因素，那么梁架元就可以用來模擬皮帶。同樣對(duì)于擁有六個(gè)位移參數(shù)的梁架元的平面運(yùn)動(dòng)來說，相當(dāng)于三個(gè)獨(dú)立的剛體運(yùn)動(dòng)。因此就剩下三個(gè)變形參數(shù)是：縱向變形參數(shù) ε1 ，兩個(gè)彎曲變形參數(shù) ε2 和ε3 。圖 5 ：梁架元的彎曲變形的梁架元彎曲變形的參數(shù)可以定義為梁架元的組成載體（見圖 4 ） ：xT = [up vp μp uq vq μq] (5)和如圖 5 的變形結(jié)構(gòu)ε2 = D2(x) e2p1pq = 1o-eq21pqε3 = D3(x) = 1o(6)3.2 繞過托輥及帶輪的帶運(yùn)動(dòng)當(dāng)繞過托輥或帶輪的時(shí)候，帶運(yùn)動(dòng)是受到約束的。為了說明（弄清楚）這些制約因素，影響制約因素（邊界）的條件都必須添加到用來代模擬帶的有限元中來。這可以通過使用多體動(dòng)力學(xué)進(jìn)行描述。多體機(jī)置動(dòng)力學(xué)的經(jīng)典描述，建立起由若干約束條件連接起來的剛體或剛性鏈接。在（變形）輸送帶的有限元描述里，帶被分離成多個(gè)有限元，有限元之間的聯(lián)系是可變形的。有限元是由節(jié)點(diǎn)連接的，因此分配了位移參數(shù)。要確定帶的運(yùn)動(dòng)，排除了剛體模型的變形模式。如果一個(gè)帶繞過托輥， ，決定托輥上帶的位置（如見圖 6）的帶長度為ξ，被添加到組件矢量，如：式（6） ，因此產(chǎn)生了 7 個(gè)位移矢量參數(shù)。圖 6 ：由托輥支撐的帶梁架元有兩個(gè)獨(dú)立的剛體運(yùn)動(dòng)，因此依然有五個(gè)變形參數(shù)存在。其中已經(jīng)在 3.1 中給出了 ε1 , ε2 和 ε3 ，確定了帶的變形。剩下 ε4 和 ε5 ，確定帶和托輥之間的相互作用，見圖 7 。圖 7 ：兩個(gè)約束條件的梁架元有限元。這些變形參數(shù)可以假設(shè)成無限剛度的彈性。這意味著：ε4 = D4(x) = (rξ + u ξ)e2 - rid.e2 = 0 ε5 = D5(x) = (r ξ + uξ)e1 - rid.e1 = 0 (7)如果模擬的是 ε4 > 0 的時(shí)候，那么帶將脫離托輥，而描述帶的有限元上的約束條件也將去除。3.3 滾動(dòng)阻力為了使一種模型能應(yīng)用于帶式輸送機(jī)有限元模型的滾動(dòng)阻力，已經(jīng)制定了一種計(jì)算滾動(dòng)阻力的近似公式， [ 8 ] 。帶運(yùn)動(dòng)中，暴露在帶外面的總滾動(dòng)阻力的組成部分，這三部分是耗能的主要部分，可以區(qū)分為包括：壓痕滾動(dòng)阻力，托輥的慣性（加速滾動(dòng)阻力）和軸承滾動(dòng)阻力（軸承阻力） 。確定滾動(dòng)阻力因素的參數(shù)包括直徑和托輥的材料，以及各種帶參數(shù)，如速度，寬度，材料，緊張狀態(tài)，環(huán)境溫度，帶橫向負(fù)荷，托輥間距和槽角?？倽L動(dòng)阻力的因素，可以表示成總滾動(dòng)阻力和帶垂直負(fù)荷之間的比例，定義為：ft = fi + fa + fb (8)Fi 是壓痕滾動(dòng)阻力的系數(shù)，F(xiàn)A 是加速阻力系數(shù)，而 FB 是軸承阻力系數(shù)。這些組成系數(shù)由下面的[9]確定：Fi = CFznzh nhD-nD VbnvK-nk NTnTMred ?2ufa =Fzb ?t2Mf fb =Fzbri(9)FZ 是帶垂直方向上分布的負(fù)載和散裝物料的負(fù)載的總和， H 是帶的覆蓋厚度，D 是托輥的直徑，Vb 是帶速，KN 是帶負(fù)荷的名義百分之比，T 是環(huán)境溫度，Mred 是托輥的折算質(zhì)量，B 是帶的寬度， U 是帶的縱向位移，MF 是總的軸承阻力矩和 RI 是軸承內(nèi)部半徑。在計(jì)算滾動(dòng)阻力中，皮帶的動(dòng)力性能及機(jī)械性能和皮帶上覆蓋的材料發(fā)揮著重要作用。這使得帶的選擇和帶上覆蓋材料，盡量減少由動(dòng)力阻力引起的能源消耗。3.4 帶驅(qū)動(dòng)系統(tǒng)在穩(wěn)定性的帶運(yùn)動(dòng)情況下，為了能夠測(cè)定帶式輸送機(jī)驅(qū)動(dòng)系統(tǒng)的旋轉(zhuǎn)組件的影響，這個(gè)帶式輸送機(jī)的總模型必須是含有驅(qū)動(dòng)系統(tǒng)模型。驅(qū)動(dòng)系統(tǒng)的旋轉(zhuǎn)元件，就像一個(gè)減速箱，參照了 3.2 節(jié)中所述的約束條件。帶有減速比的減速箱，可以用帶兩個(gè)位移參數(shù)的減速元件來代替， μp 和 μq ，像一個(gè)剛體的（旋轉(zhuǎn)）運(yùn)動(dòng)，因此就剩下一個(gè)變形參數(shù)：εred = Dred(x) = iμp + μq = 0 (10)要確定電式扭矩感應(yīng)式電機(jī)，是否適應(yīng)所謂的兩軸式電動(dòng)機(jī)。該相電壓的矢量v 可從（11）獲得：v = Ri + ωsGi + L ?i/? t (11)在（11）式中 I 是相電流矢量，R 是模型的相電阻， c 是模型的相電感抗，L 是模型的相感系數(shù)而 ωs 是電機(jī)轉(zhuǎn)子的角速度。電磁轉(zhuǎn)矩等于：Tc = iTGi (12)電機(jī)模型和驅(qū)動(dòng)系統(tǒng)機(jī)械組件是由驅(qū)動(dòng)系統(tǒng)的運(yùn)動(dòng)方程聯(lián)系著的：?2?j??kTi = Iij?t2+ Cik?tKil? (13)其中 T 是扭矩矢量，I 是模型的慣量，C 是模型的阻尼，K 是矩陣剛度和 ?是電機(jī)旋轉(zhuǎn)軸的角速度。 模擬啟動(dòng)或停止程序控制反饋的程序可以添加到帶式驅(qū)動(dòng)系統(tǒng)模型中，用來控制驅(qū)動(dòng)扭矩。3.5 運(yùn)動(dòng)方程整個(gè)帶式輸送機(jī)模型的運(yùn)動(dòng)方程可以得出潛在功率的原則， [ 7 ] ：fk - Mkl ?2x1 / ?t2 = σ1Dik (14)其中 F 是阻力矢量，M 是模型的質(zhì)量而 σ 是拉格朗日乘數(shù)的矢量，可能解釋為雙重壓力矢量 to 張力矢量 ε 。為了解決帶有 X 這一組方程，方程一體化是必要的。但是一體化的結(jié)果，必須確保滿足約束條件。如果(8)式中應(yīng)變?yōu)榱?，那么必須糾正一體化結(jié)果，如見[ 7 ] 。可以使用模型的反饋選擇，例如限制提升物質(zhì)垂直方向上的運(yùn)動(dòng)。這種違逆動(dòng)力學(xué)的問題可以用下面公式表示。鑒于帶模型及其驅(qū)動(dòng)系統(tǒng)的提升運(yùn)動(dòng)眾所周知，根據(jù)系統(tǒng)自由度和它的比例（速度）可以確定其他元件的運(yùn)動(dòng)。它超出了本文所討論關(guān)于此項(xiàng)的所有細(xì)節(jié)范圍。3.6 實(shí)例為了在長距離帶式輸送機(jī)系統(tǒng)設(shè)計(jì)階段能夠正確設(shè)計(jì)，應(yīng)用了有限元法。例如帶強(qiáng)度的選擇，可以減少的盡量減少，使用模型模擬的結(jié)果確定傳送帶的最大張力。以有限元模型的功能作為例子，應(yīng)該考慮到在兩個(gè)托輥位置范圍之間穩(wěn)定移動(dòng)帶的橫向振動(dòng)。在運(yùn)輸機(jī)的設(shè)計(jì)階段這必須被確定，才得以確?？諑У墓舱?。 對(duì)于皮帶輸送機(jī)的設(shè)計(jì)來說，托輥和移動(dòng)帶間相互作用影響是很重要的。托輥的及帶輪的幾何不完善性，導(dǎo)致帶脫離托輥和帶輪能支撐的位置，在帶和支撐帶輪之間產(chǎn)生一種橫向振動(dòng)。這對(duì)帶施加了一部分的交互軸向應(yīng)力。如果這部分力是比皮帶的預(yù)應(yīng)力小，那么帶將在它的固有頻率中振動(dòng)，否則帶將被迫振動(dòng)。皮帶是會(huì)受迫振動(dòng)的，例如受托輥的偏心率影響。在輸送帶返程中，這種振動(dòng)特別值得注意。由于受迫振動(dòng)的頻率取決于帶輪和托輥的角速度，因此對(duì)于帶的速度，確定在帶輪和托輥之間，帶在自然頻率狀況下，橫向振動(dòng)中帶速影響，這個(gè)是很重要的。如果受迫振動(dòng)的頻率接近于皮帶橫向振動(dòng)的固有頻率，將發(fā)生共振現(xiàn)象。 有限元模型的模擬結(jié)果可用于確定穩(wěn)定移動(dòng)的帶的橫向振動(dòng)頻率范圍。該頻率是利用快速傅立葉技術(shù)從時(shí)域范圍到頻域范圍，帶橫向位移變換后得到的結(jié)果。除了使用有限元模型外也可以運(yùn)用近似分析法。皮帶可以模擬成一個(gè)預(yù)應(yīng)力梁。如果皮帶的彎曲硬度可以被忽略，橫向位移比托輥間距還小，Ks << 1 ，并且?guī)г黾拥拈L度相對(duì)于橫向位移的原始長度來說是微不足道，帶的橫向振動(dòng)可近似為下列線性微分方程，如見圖 15 ：?2v= (c22 - C2b)?2v- 2Vb?2v(15)?t2?x2?x?t其中 V 是皮帶的橫向位移和 C2 是橫向波的波速度，由（16）式定義：c2 = √g1/8Ks (16)首先，圖 5 中帶的橫向固有頻率范圍可從公式（16）獲得，如果假定v(O,t)=v(l,t)=0：1fb =21c2 (1 - ?2) (17)? 是無量綱的速比，由（18）式確定：? = Vb / c2 (18)FB 是不同帶的各自獨(dú)立的頻率范圍，由于輸送帶長度方向上帶張力變化。托輥的受迫振動(dòng)頻率，使托輥產(chǎn)生了一個(gè)偏心率等于：fi = Vb / πD (19)其中 D 是托輥的直徑。為了設(shè)計(jì)一個(gè)在托輥間距中無支撐的共振，這受到以下條件限制：πDL ≠2?(1-?2) (20)由線性微分方程（16）所取得的成果不過是只適用于小數(shù)值的速比 ?。對(duì)于大數(shù)值的速比 ? 來說，如高速運(yùn)輸機(jī)或低的帶張力，在（16）式中所有非線性條件就顯得重要的。因此，數(shù)值模擬的運(yùn)用，有限元模型的開發(fā)，都是為了確定帶橫向振動(dòng)線性和非線性頻率之間的比例范圍。這些關(guān)系已被確定適合不同的數(shù)值的 ?，例如說一個(gè)功能凹陷的比率 Ks。使用快速傅里葉技術(shù)將橫向位移結(jié)果的轉(zhuǎn)化為頻譜。從這些頻譜中獲得的頻率與公式（18）獲得的頻率相比，其產(chǎn)生了圖 8 所顯示的曲線。從這一數(shù)字可見，對(duì)小于 0.3 的 ? 來說，計(jì)算誤差很小。對(duì)于大數(shù)值的 ? 來說，運(yùn)用線性近似值法產(chǎn)生的計(jì)算誤差達(dá)到 10 ％以上。運(yùn)用了皮帶采用非線性梁架元的有限元模型，因此可以準(zhǔn)確地確定大數(shù)值 ? 的橫向振動(dòng)。對(duì)于小數(shù)值 ? 的橫向振動(dòng)的頻率也可以用公式（18）準(zhǔn)確地預(yù)測(cè)。然而，它不能分析，例如帶凹陷和縱向波的傳播之間的相互作用，或者同樣可以看成有限元模型的脫離托輥的皮帶。這決定帶應(yīng)力和橫向振動(dòng)頻率之間的關(guān)系可以用于皮帶張力監(jiān)測(cè)系統(tǒng)。圖 8 ：由兩個(gè)托輥支撐的帶的橫向振動(dòng)線性和非線性頻率之間的比例。4 實(shí)驗(yàn)驗(yàn)證為了使模擬的結(jié)果能夠得到驗(yàn)證，實(shí)驗(yàn)中使用了動(dòng)態(tài)試驗(yàn)設(shè)備，如圖 9 所示。圖 9 ：動(dòng)態(tài)試驗(yàn)設(shè)施使用這試驗(yàn)設(shè)施能夠確定的兩個(gè)托輥的間距和卸荷扁帶的橫向振動(dòng)，例如返程部分的。聲音裝置是用來測(cè)量皮帶的位移。此外，還有在試驗(yàn)中為我們所知的張緊力，帶速，電機(jī)轉(zhuǎn)矩，托輥轉(zhuǎn)子與托輥的距離。5 為例由于最具有成本效益帶式輸送機(jī)的操作條件中出現(xiàn)了寬度范圍為 0.6m- 1.2m[ 2 ] 的各種皮帶 ，可通過變換不同的帶速改變帶的輸送能力， 。然而在帶速度被改變之前，應(yīng)確定帶和托輥之間的相互作用，以確保無支撐的帶的共振。為了說明穩(wěn)定移動(dòng)的帶的橫向位移這一點(diǎn)，測(cè)量了兩個(gè)托輥的間隔。帶的總長度 L 是 52.7m，托輥間距 I 是 3.66m，靜態(tài)凹陷的比例常數(shù)是 2.1 ％ ，?為 0.24 而帶速 Vb 為 3.57m/ s。這個(gè)信號(hào)的后期轉(zhuǎn)化由如圖 5 所示的快速傅里葉技術(shù)頻譜獲得。在圖 5 中 出圖 10 ：帶穩(wěn)定移動(dòng)時(shí)橫向振動(dòng)頻率現(xiàn)了 3 個(gè)頻率。第一頻率是由帶結(jié)合處所引起的：fs = Vb/L = 0.067 Hz第二個(gè)頻率，出現(xiàn)在 1.94 赫茲，是由皮帶的橫向振動(dòng)所造成的。第三個(gè)頻率出現(xiàn)在 10.5Hz，是由托輥的旋轉(zhuǎn)所造成的，從圖 11 所示的數(shù)值模擬獲得。圖 11 ：計(jì)算共振區(qū)的不同托輥的直徑 D.貫穿實(shí)驗(yàn)表明皮帶速度和托輥間距。圖 11 顯示的是拖過帶與托輥互動(dòng)引起的共振區(qū)可以預(yù)測(cè)三個(gè)托輥的直徑。該帶式輸送機(jī)的托輥直徑為 0.108M，從而可以預(yù)測(cè)皮帶速度鄰近 0.64M/S 的共振現(xiàn)象。為了驗(yàn)證結(jié)果，在啟動(dòng)運(yùn)輸機(jī)的時(shí)候測(cè)量了帶的最大橫向位移跨度。圖 12 ：測(cè)量橫向振動(dòng)和帶靜態(tài)凹陷幅度的標(biāo)準(zhǔn)差的比例。在圖 12 中，可以看出橫向振動(dòng)的最大振幅發(fā)生在帶速為 0.64M/S 處，正如有限元模型模擬預(yù)測(cè)的結(jié)果一樣。因此，帶速度不應(yīng)選擇臨近 0.64 米/ s 的。雖然是用扁帶進(jìn)行實(shí)驗(yàn)和理論的驗(yàn)證的，但是這種應(yīng)用技術(shù)也可運(yùn)用于槽型帶中。6．結(jié)論帶式輸送機(jī)有限元模型中梁架元的應(yīng)用，帶橫向位移的模擬，從而使能夠設(shè)計(jì)出帶無支撐的共振。對(duì)于小數(shù)值的 ? 來說，采用梁架元代替線性微分方程預(yù)測(cè)共振現(xiàn)象的優(yōu)勢(shì)是同樣可以預(yù)測(cè)到皮帶縱向和橫向位移的之間的相互作用以及從模擬中預(yù)見皮帶脫離托輥。The Two-Dimensional Dynamic Behavior of Conveyor Belts3.1.1 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]:ds2 - ds2oε1 = D1(x) = ∫1 o2ds2odξ (2)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 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 = 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 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, ε1, and two bending deformation parameters, ε2 and ε3.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 μp uq vq μq] (5)and the deformed configuration as shown in Figure 5:e2p1pqε2 = D2(x) =1o-eq21pqε3 = D3(x) =1o(6)3.2 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 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 = 0ε5 = 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 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 NTnTMred ?2ufa =Fzb ?t2Mf fb =Fzbri(9)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, mred 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 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, 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:?2?j ??kTi = Iij?t2+ Cik?tKil? (13)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 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 ?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 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 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 noticeable on belt conveyor returns. Since the frequency of the imposed excitation depends on the angular speed of the pulleys and idlers, and thus on the belt speed, it is important to determine the influence of the belt speed on the natural frequency of the transverse vibration of the belt between two supports. If the frequency of the imposed excitation approaches the natural frequency of transverse vibration of the belt, resonance phenomena occur.The results of simulation with the finite element model can be used to determine the frequency of transverse vibration of a stationary moving belt span. This frequency is obtained after transformation of the results of the transverse displacement of the belt span from the time domain to the frequency domain using the fast fourier technique. Besides using the finite element model also an analytical approach can be used.The belt can be modelled as a prestressed beam. If the bending stiffness of the belt is neglected, the transverse displacements are small compared to the idler space, Ks << 1, and the increase of the belt length due to the transverse displacement is negligible compared to its initial length, the transverse vibration of the belt can be approximated by the following linear differential equation, also see Figure 5:?2v ?2v ?2v?t2= (c22 - C2b)?x2- 2Vb?x?t(15)where v is the transverse displacement of the belt and c2 the wave speed of the transverse waves defined by, [1]:c2 = √g1/8Ks (16)The first natural transverse frequency of the belt span of Figure 5 can be obtained from eq. (16) if it is assumed that v(O,t)=v(l,t)=0:1 fb =21c2 (1 - ?2) (17)where ? is the dimensionless speed ratio defined by:? = Vb / c2 (18)The frequency fb is different for each individual belt span since the belt tension varies over the length of the conveyor. The excitation frequency of an idler which has a single eccentricity is equal to:fi = Vb / πD (19)where D is the diameter of the idler. In order to design a resonance free belt support the idler space is subjected to the following condition:πDL ≠2?(1-?2) (20)The results obtained with the linear differential equation (16) however are valid only for low values of the ratio ?. For higher values of ?, as is the case for high-speed conveyors or low belt tensions, the non-linear terms in the full form of e.g. (16) become significant. Therefore numerical simulations using, the FEM model have been made in order to determine the ratio between the linear and the non-linear frequency of transverse vibration of a belt span. These relations have been determined for different values of ? as a function of the sag ratio Ks. The results for the transverse displacements were transformed to a frequency spectrum using a fast-fourier technique. The frequencies obtained from these spectra were compared to the frequencies obtained from e.g. (18) which yielded the curves as shown in Figure 8. From this figure it follows that for ? smaller that 0.3 the calculation errors are small. For higher values of ? the calculation error made by a linear approximation is more than 10 %. Application of a finite element model of the belt which uses non-linear beam elements therefore enables an accurate determination of the transverse vibrations for high values of ?.For lower values of ? the frequencies of transverse vibration can also be predicted accurate by e.g. (18). However it is not possible to analyse, for example, the interaction between the belt sag and the propagation of longitudinal waves or the lifting of the belt off the idlers as can be done with the finite element model.The determined relation between the belt stress and the frequency of transverse vibrations can also be used in belt tension monitoring systems.Figure 8: Ratio between the linear and the non-linear frequency of transverse vibration of a belt span supported by two idlers.4. EXPERIMENTAL VERIFICATIONIn order to be able to verificate the results of the simulations, experiments have been carried out with the dynamic test facility shown in Figure 9.Figure 9: Dynamic test facilityWith this test facility the transverse vibration of an unloaded flat belt span between two idlers, as for example a return part, can be determined. An acoustic device is used to measure the displacement of the belt. Besides that, also the tensioning force, belt speed, motor torque, idler rotations and idler space were known during the experiments.5. EXAMPLESince the most cost-effective operation conditions of belt conveyors occur in the range of belt widths 0.6 - 1.2 m [2], the belt's capacity can be varied by varying the belt speed. However before the belt speed is varied the interaction between the belt and the idler should be determined in order to ensure resonance free belt support. To illustrate this the transverse displacement of a stationary moving belt span between two idlers have been measured. The total belt length L was 52.7 m, the idler space I was 3.66 m, the static sag ratio Ks 2.1 %, ? was 0.24 and the belt speed Vb 3.57 m/s. After transformation of this signal by a fast fourier technique the frequency spectrum of Figure 5 was obtained. In Figure 5 three frequencies appear. The first frequency is caused by the passage of the belt splice:fs = Vb/L = 0.067 HzThe second frequency, which appears at 1.94 Hz, is caused by the transverse vibration of the belt.Figure 10: Frequencies of transverse vibration of a stationary moving belt span supported by two idlers.The third frequency which appears at 10.5 Hz is caused by the rotation of the idlers. From the numerical simulations Figure 11 was obtained.Figure 11: Calculated resonance zone's for different idler diameters D. Cross indicates belt speed and idler space during experiment.Figure 11 shows the zone's where resonance caused by the belt/idler interaction may be expected for three idler diameters. The idlers of the belt conveyor had a diameter of 0.108 m thus resonance phenomena may be expected nearby a belt speed of 0.64 m/s. To check this, the maximum transverse displacement of the belt span has been measured during a start-up of the conveyor.Figure 12: Measured ratio of the standard deviation of the amplitude of transverse vibration and the static belt sag.As can be seen in Figure 12 the maximum amplitude of the transverse vibration occur at a belt speed of 0.64 m/s as was predicted by the results of simulation with the finite element model. Therefore the belt speed should not be chosen nearby 0.64 m/s. Although a flat belt is used for the experiments and the theoretical verification, the applied techniques can also be used for troughed belts.6. CONCLUSIONSApplication of beam elements in finite element models of belt conveyors enable the simulation of the transverse displacement of the belt thus enabling the design of resonance free belt supports. The advantage of applying beam elements for small values of ? instead of using a linear differential equation to predict resonance phenomena is that also the interaction between the longitudinal and transverse displacement of the belt and the lifting of the belt off the idlers can be predicted from simulation.