【導(dǎo)讀】ofbeltconveyors.thedesignofbelt-conveyorlay-outsforresonance-freeoperation,[2].Inthispapera

　　

【正文】 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 nonlinear frequency of transverse vibration of a belt span supported by two idlers. 4. EXPERIMENTAL VERIFICATION In 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 facility With 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. EXAMPLE Since the most costeffective operation conditions of belt conveyors occur in the range of belt widths m [2], the belt39。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 m, the idler space I was m, the static sag ratio Ks %, 223。 was and the belt speed Vb 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 = Hz The second frequency, which appears at 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 Hz is caused by the rotation of the idlers. From the numerical simulations Figure 11 was obtained. Figure 11: Calculated resonance zone39。s for different idler diameters D. Cross indicates belt speed and idler space during experiment. Figure 11 shows the zone39。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 m thus resonance phenomena may be expected nearby a belt speed of m/s. To check this, the maximum transverse displacement of the belt span has been measured during a startup 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 m/s as was predicted by the results of simulation with the finite element model. Therefore the belt speed should not be chosen nearby 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. CONCLUSIONS Application 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 223。 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. 7. REFERENCES 1. Lodewijks, G. (1995), Present Research at Delft University of Technology, The Netherlands, 1995 5th International Conference on Bulk Material Storage, Handling and transportation, Newcastle, Australia, 1012 July 1995, The Institution of Engineers, Australia Preprints pp. 381394. 2. Roberts, . (1994), Advances in the design of Mechanical Conveyors, Bulk Solids Handling 14, pp. 255281. 3. Nordell, . and Ciozda, . (1984), Transient belt stresses during starting and stopping: Elastic response simulated by finite element methods, Bulk Solids Handling 4, pp. 99104. 4. Funke, A. and K246。nneker, . (1988), Experimental investigations and theory for the design of a longdistance beltconveyor system, Bulk Solids Handling 8, pp. 567579. 5. Harrison, A. (1984), Flexural behaviour of tensioned conveyor belts, Bulk Solids Handling 4 pp. 6771. 6. Lodewijks, G. (1994), Transverse vibrations in flexible belt systems, Delft University of Technology, report no. . 7. Lodewijks, G. (1994), On the Application of Beam Elements in Finite Element Models of Belt Conveyors, Part 1, Bulk Solids Handling 14, pp. 729737. 8. Lodewijks, G. (1995), The Rolling Resistance of Belt Conveyors, Bulk Solids Handling 15, pp. 1522. 9. Nordell, . and Ciozda, . (1984), Transient belt stresses during starting and stopping: Elastic response simulated by finite element methods, Bulk Solid Handling 11, pp. 99104. 輸送帶的二維動(dòng)態(tài)特性 伊 . 基 . 勞德維加克斯， 代爾夫特科技大學(xué)，荷蘭 1 概要 本文將介紹一種新的皮帶輸送系統(tǒng)的有限元模型。該模型被開發(fā)成能用于模擬皮帶在啟動(dòng)和停止時(shí)的縱向和橫向動(dòng)態(tài)響應(yīng)。使工程師能在長(zhǎng)距離陸路皮帶輸送系統(tǒng)的設(shè)計(jì)階段應(yīng)用該模型，例如， 設(shè)計(jì)適當(dāng)?shù)钠л斔蜋C(jī)曲線檢測(cè)元件過早解除皮帶張緊輪。 這也能使張緊輪間距和凹槽輪廓的設(shè)計(jì)最優(yōu)化，以確保無帶運(yùn)動(dòng)的共振和確定縱向和橫向帶振動(dòng)。應(yīng)用反饋控制技術(shù)實(shí)現(xiàn)了啟動(dòng)和停止程序的優(yōu)化設(shè)計(jì)，因而計(jì)算皮帶的動(dòng)態(tài)特性時(shí)可以選擇最理想的皮帶。 2 導(dǎo)言 荷蘭一直以來 被認(rèn)為是一個(gè)運(yùn)輸和轉(zhuǎn)運(yùn)行業(yè)在經(jīng)濟(jì)中扮演重要角色的國(guó)家。特別是被稱為歐洲的門戶的鹿特丹港口，聲稱擁有世界上最大的海港系統(tǒng)。除了數(shù)量龐大的集裝箱，大量的散裝貨物也都是要通過這個(gè)港口的。并非所有這些物品的目的地都是在荷蘭市場(chǎng)，許多要通往其他目的地的貨物轉(zhuǎn)運(yùn)點(diǎn)都是在鹿特丹港口。有個(gè)很好的例子，典型的散裝貨物的轉(zhuǎn)運(yùn) 煤炭和鐵礦石，很大一部分，其目的地是在德國(guó)市場(chǎng)。為了處理大量材料不同地方大范圍的轉(zhuǎn)運(yùn)，使用了機(jī)械運(yùn)輸機(jī)，其中就包括帶式輸送機(jī)。 長(zhǎng)度最長(zhǎng)帶式輸送系統(tǒng)架設(shè)在相對(duì)較小的國(guó)家 荷蘭，因?yàn)樗鼈兪侵饕糜诖罅?原材料的流動(dòng)運(yùn)輸。最長(zhǎng)的帶式輸送系統(tǒng)，其長(zhǎng)度約為 2公里長(zhǎng)，它位于鹿特丹港口的一部分 馬斯弗拉克特，它是用來從批發(fā)油庫運(yùn)輸