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1、<p> 一組塔式起重機(jī)的位置優(yōu)化</p><p> 摘要 計(jì)算機(jī)模型能使一組塔機(jī)位置更加優(yōu)化。合適的位置條件能平衡工作載荷,降低塔機(jī)之間碰撞的可能性,提高工作效率。這里對(duì)三個(gè)子模型進(jìn)行了介紹。首先,把初始位置模型分組,根據(jù)幾何的相似性,確認(rèn)每個(gè)塔機(jī)的合適位置。然后,調(diào)整前任務(wù)組的平衡工作載荷并降低碰撞的可能性。最后,運(yùn)用一個(gè)單塔起重機(jī)優(yōu)化模型去尋找吊鉤運(yùn)輸時(shí)間最短的位置。本文對(duì)模型完成的實(shí)驗(yàn)結(jié)果和
2、必要的步驟進(jìn)行了討論。</p><p><b> 引言</b></p><p> 在大規(guī)模的建設(shè)工程中特別是當(dāng)一個(gè)單塔起動(dòng)機(jī)不能全面的完成重要的任務(wù)要求時(shí)或者當(dāng)塔機(jī)不能完成緊急的建設(shè)任務(wù)時(shí)通常是由幾個(gè)塔機(jī)同時(shí)完成任務(wù)。影響塔機(jī)的因素很多。從操作效率和安全方面考慮,如果所有計(jì)劃的任務(wù)都能執(zhí)行,應(yīng)將塔機(jī)盡可能的分開(kāi),避免互相干擾和碰撞。然而這種理想的情況在實(shí)踐中很難成
3、功,因?yàn)楣ぷ骺臻g的限制和塔機(jī)的耐力有限使塔機(jī)的工作區(qū)域重疊是不可避免的。因此,即使起重機(jī)的鐵臂在不同的水平工作面也會(huì)發(fā)生互相干擾和碰撞。在地形選址和全面的完成任務(wù)的基礎(chǔ)上,通過(guò)反復(fù)實(shí)驗(yàn)來(lái)決定塔式起重機(jī)的合適位置。起重機(jī)位置的選擇很復(fù)雜,因此,管理人員仍然面臨著多樣的選擇和少量的定量參考。</p><p> 在過(guò)去的20年里,起重機(jī)位置模型逐步形成。Warszawski(1973)嘗試盡可能用時(shí)間與距離來(lái)計(jì)算塔機(jī)
4、的位置。Furusaka and Gray (1984) 提出用目標(biāo)函數(shù)和被雇用成本規(guī)劃動(dòng)態(tài)模型,但是沒(méi)考慮到位置。Gray and Little (1985)在處理不規(guī)則的混凝土建筑物時(shí)候,設(shè)置位置優(yōu)化的塔式起動(dòng)機(jī)。然而,Wijesundera and Harris (1986)在處理具體的任務(wù)時(shí)減少了操作時(shí)間和延長(zhǎng)了設(shè)備使用周期時(shí)設(shè)計(jì)了一種模擬模型。Farrell and Hover (1989)開(kāi)發(fā)了帶有圖解界面的數(shù)據(jù)庫(kù),來(lái)協(xié)助
5、起動(dòng)機(jī)的位置的選擇。Choi and Harris (1991)通過(guò)計(jì)算運(yùn)輸所須的全部時(shí)間來(lái)提出另一種優(yōu)化單塔起重機(jī)位置優(yōu)化。Emsley (1992)改進(jìn)了Choi and Harris提出的模型。除了在計(jì)算方法相似外,起重機(jī)的數(shù)量類(lèi)型和設(shè)計(jì)系統(tǒng)規(guī)則也得以提高</p><p><b> 假設(shè)</b></p><p> 采訪(fǎng)網(wǎng)站管理員關(guān)于他們的公司和觀(guān)察到手上的工
6、作電流的方法。另外觀(guān)察起重機(jī)集中在14個(gè)操作站點(diǎn)的運(yùn)用。(在中國(guó)是4個(gè),在英格蘭是6個(gè),在蘇格蘭是4個(gè))。研究設(shè)備放在4個(gè)站點(diǎn)時(shí)間為6個(gè)星期,兩個(gè)站點(diǎn)用兩個(gè)星期時(shí)間。調(diào)查結(jié)果顯示尤其是在全面覆蓋工作領(lǐng)域,沒(méi)有干擾,平衡工作載荷和地面情況是決定塔機(jī)位置重要的原因。因此,重點(diǎn)在這些因素上(除了地面情況因?yàn)檎军c(diǎn)管理員能明確說(shuō)明合適的區(qū)域位置)。下面4種假設(shè)被應(yīng)用于模型發(fā)展(以后的詳盡)</p><p> 預(yù)先確定所有
7、供應(yīng)點(diǎn)和需求點(diǎn)的幾何布局、起重機(jī)的類(lèi)型和數(shù)量。</p><p> 對(duì)于每個(gè)供應(yīng)點(diǎn)和需求點(diǎn),運(yùn)輸需求水平是已知的。例如,起重機(jī)的總數(shù)、每組起重機(jī)的數(shù)量、最大限度的裝載、延遲卸貨等等。</p><p> 在建設(shè)時(shí)期和工作區(qū)域大體相同。</p><p> 只用一個(gè)起重機(jī)運(yùn)輸供應(yīng)點(diǎn)與需求點(diǎn)之間的物料。</p><p><b> 模型
8、描述</b></p><p> 決定起重機(jī)理想的位置有三個(gè)位置條件。首先用位置模型產(chǎn)生一個(gè)相似的任務(wù)組,然后用任務(wù)分配模型調(diào)整,最后優(yōu)化模型輪流并運(yùn)用到每個(gè)任務(wù)組中的準(zhǔn)確位置。</p><p><b> 初始位置生成模型</b></p><p> 起重機(jī)的起升能力和合適的區(qū)域</p><p> 起重機(jī)
9、的升起能力取決于曲線(xiàn)的半徑,負(fù)荷量越大,起重機(jī)的操作半徑越小。假設(shè)供應(yīng)點(diǎn)的負(fù)荷量是w,相應(yīng)的起重機(jī)半徑是r。一個(gè)起重機(jī)若不能承受裝載除非它的半徑在圓內(nèi)(圖1)。從供應(yīng)點(diǎn)傳送一個(gè)裝載需求點(diǎn),必須把起重機(jī)放在兩個(gè)重合的橢圓區(qū)域,如圖表1(b),這是合適任務(wù)區(qū)域。區(qū)域的大小與供應(yīng)點(diǎn)和需求點(diǎn)的距離、負(fù)荷量、起重機(jī)的耐力有關(guān)。合當(dāng)?shù)膮^(qū)域越大,越容易完成任務(wù)。</p><p><b> 相近任務(wù)的測(cè)量</b
10、></p><p> 對(duì)于任何兩種合適的任務(wù)區(qū)域存在3種幾何關(guān)系,如圖解2.也就是說(shuō),(a)一個(gè)圖與另個(gè)圖完全重合(任務(wù)1與2)。(b)兩個(gè)區(qū)域部分相交(任務(wù)1與3)。(c)兩個(gè)區(qū)域分開(kāi)(任務(wù)2與3)。如指出的實(shí)例a與b,起重機(jī)被放在區(qū)域A中能完成任務(wù)1和任務(wù)2,同樣的,在區(qū)域B中,能完成任務(wù)1和3.</p><p> 然而實(shí)例c顯示,任務(wù)2和3距離太遠(yuǎn),一個(gè)單獨(dú)的起重機(jī)在沒(méi)有移
11、動(dòng)位置的情況下不能完成任務(wù),因此,需要多個(gè)或起重能力更大的起重機(jī)去完成。交疊的區(qū)域可以測(cè)量相臨的任務(wù)。例如,任務(wù)2到任務(wù)1的距離比到任務(wù)3的距離近因?yàn)槿蝿?wù)1和2交疊區(qū)域比任務(wù)1和3的大。這個(gè)概念也可以應(yīng)用在任務(wù)組上。例如,圖表中的區(qū)域c,2(b)是完成3個(gè)任務(wù)的合適區(qū)域,但是任務(wù)5比任務(wù)4到任務(wù)組的距離近因?yàn)閏和d的交疊區(qū)域比c和e的大。如果把任務(wù)5加到任務(wù)組中來(lái),最合適新的任務(wù)組區(qū)域是d,如圖表2(c)所示。</p>&
12、lt;p><b> 將任務(wù)組分類(lèi)</b></p><p> 如果兩個(gè)合適的區(qū)域不存在重疊的部分,在沒(méi)有其它的可選擇的情況下兩個(gè)起重機(jī)就需要分開(kāi)來(lái)完成任務(wù),例如起重機(jī)的舉起能力很大或作用點(diǎn)重新規(guī)劃布局等類(lèi)似的情況,如果有3個(gè)任務(wù)且沒(méi)有任何兩個(gè)任務(wù)有交疊的區(qū)域情況下需要3個(gè)起重機(jī)完成任務(wù)??偟膩?lái)說(shuō),合適區(qū)域是孤立的任務(wù)必須分開(kāi)來(lái)完成。這些起始任務(wù)各自分配到不同的任務(wù)組,工作組作為整體運(yùn)
13、作的第一個(gè)成員,然后把其它相似的任務(wù)集中在一起。很顯然,進(jìn)一步分配任務(wù)給了起始任務(wù)優(yōu)先權(quán),當(dāng)多種選擇存在時(shí)電腦通過(guò)篩選作為最初的任務(wù),越少的可行領(lǐng)域任務(wù)就會(huì)用越少的操作時(shí)間。模型能夠通過(guò)展示任務(wù)的圖形布局和合適區(qū)域大小的列表提供幫助。將起始任務(wù)分組后,模型通過(guò)核對(duì)交疊區(qū)域的大小尋找相近的任務(wù),然后把它們放入同一組找出新的合適區(qū)域相應(yīng)的產(chǎn)生一個(gè)最新的任務(wù)組。之后,模型會(huì)從所有任務(wù)轉(zhuǎn)向下一個(gè)任務(wù),直到所有任務(wù)都完成。如果一個(gè)任務(wù)分配失敗,系
14、統(tǒng)會(huì)顯示出來(lái),更多的起重機(jī)被應(yīng)用或改變?nèi)蝿?wù)布局。</p><p><b> 初始起重機(jī)的位置</b></p><p> 當(dāng)產(chǎn)生了任務(wù)組,交疊區(qū)域也同時(shí)形成了。因此,初始位置自動(dòng)的變成公共合適區(qū)域幾何中心或者是被指定的公共合適區(qū)域。</p><p><b> 任務(wù)分配模型</b></p><p>
15、; 相近的幾何位置決定任務(wù)組的位置。但是,一個(gè)起重機(jī)任務(wù)較多而其它的卻沒(méi)任務(wù)。而且起重機(jī)之間會(huì)干擾,將任務(wù)分配并用多個(gè)起重機(jī)同時(shí)工作使干擾降低到最小</p><p> 過(guò)去三套輸入切實(shí)可行的區(qū)域</p><p> 合適區(qū)域的形狀與大小,圖表9所示。在這一研究中,從數(shù)據(jù)和圖表中看,最佳位置是最好的選擇(平衡工作量,可能小的碰撞,高效率的操作)?;蛘?,考慮到站點(diǎn)的情況如,起重機(jī)位置有益的
16、空間和有益機(jī)座的地面環(huán)境,站點(diǎn)邊界嚴(yán)格控制。因此,起重機(jī)應(yīng)該安放在一個(gè)建筑物內(nèi),在這一方面,假如一個(gè)攀登起重機(jī)可行同時(shí)建筑結(jié)構(gòu)也能支持這種起重機(jī),就合理的沖突索引和標(biāo)準(zhǔn)差計(jì)算的工作量,裝置4是一個(gè)不錯(cuò)選擇。另外,裝置5有優(yōu)越的固定塔機(jī)位置的電梯井,除了干擾和不平衡負(fù)載太大</p><p><b> 結(jié)論</b></p><p> 全面的完成任務(wù)是規(guī)劃起重機(jī)機(jī)組的重
17、要衡量標(biāo)準(zhǔn)。但是這一要求不能決定最佳的位置。還應(yīng)在工作載荷的平衡、盡可能降低干擾和提高工作效率的觀(guān)念基礎(chǔ)上。一個(gè)模型能夠改進(jìn)傳統(tǒng)的尋找位置的方法。為了做到這點(diǎn),突出強(qiáng)調(diào)了三個(gè)子模型,首先,通過(guò)相近的幾何位置將所有的任務(wù)分類(lèi)產(chǎn)生一個(gè)總體布局。然后,在尋找每個(gè)任務(wù)組的合適區(qū)域基礎(chǔ)上重新調(diào)整任務(wù)組,從而產(chǎn)生一個(gè)能夠完成工作載荷,產(chǎn)生最小的碰撞可能性和合適的區(qū)域任務(wù)組。最后,運(yùn)用最佳優(yōu)化原則找到一個(gè)在三個(gè)層面上的精確的吊鉤位置。實(shí)驗(yàn)結(jié)果表明模型
18、是令人滿(mǎn)意的。除了起重機(jī)的安全設(shè)施的改進(jìn)和平均效率的提高,還縮短10-40%的吊鉤的運(yùn)輸時(shí)間。為了找出塔機(jī)合適的位置和在做重要標(biāo)準(zhǔn)的模型這一方面做出了很大努力,并且兩個(gè)真正的數(shù)據(jù)點(diǎn)已經(jīng)被用于測(cè)試模型。但是它沒(méi)有捕獲所有的專(zhuān)業(yè)知識(shí)和現(xiàn)場(chǎng)管理經(jīng)驗(yàn)。然而其他有關(guān)材料的建筑結(jié)構(gòu)、條件基礎(chǔ)、卸貨場(chǎng)所、無(wú)障礙的鄰近樓宇等等因素也是塔機(jī)定位的問(wèn)題所在。因此,最終的決定應(yīng)該與這些因素有關(guān)。</p><p> LOCATION
19、OPTIMIZATION FOR A GROUP OF TOWER CRANES</p><p> ABSTRACT: A computerized model to optimize location of a group of tower cranes is presented. Location criteria are balanced workload, minimum likelihood of c
20、onflicts with each other, and high efficiency of operations. Three submodels are also presented. First, the initial location model classifies tasks into groups and identifies feasible location for each crane according t
21、o geometric ‘‘closeness.’’ Second, the former task groups are adjusted to yield smooth workloads and minimal conflicts. Fin</p><p> INTRODUCTION</p><p> On large construction projects several
22、cranes generally undertake transportation tasks, particularly when a single crane cannot provide overall coverage of all demand and supply points, and/or when its capacity is exceeded by the needs of a tight constructio
23、n schedule. Many factors influence tower crane location. In the interests of safety and efficient operation, cranes should be located as far apart as possible to avoid interference and collisions, on the condition that
24、all planned tasks can</p><p> Crane location models have evolved over the past 20 years. Warszawski (1973) established a time-distance formula by which quantitative evaluation of location was possible. Furu
25、saka and Gray (1984) presented a dynamic programming model with the objective function being hire cost, but without consideration of location. Gray and Little (1985) optimized crane location in irregular-shaped building
26、s while Wijesundera and Harris (1986) designed a simulation model to reconstruct operation times and equ</p><p> Assumptions</p><p> Site managers were interviewed to identify their concerns a
27、nd observe current approaches to the task at hand. Further, operations were observed on 14 sites where cranes were intensively used (four in China, six in England, and four in Scotland). Time studies were carried out o
28、n four sites for six weeks, two sites for two weeks each, and two for one week each. Findings suggested inter alia that full coverage of working area, balanced workload with no interference, and ground conditions are ma
29、j</p><p> Geometric layout of all supply (S) and demand (D) points, together with the type and number of cranes, are predetermined.</p><p> For each S-D pair, demand levels for transportation
30、are known, e.g., total number of lifts, number of lifts for each batch, maximum load, unloading delays, and so on.</p><p> The duration of construction is broadly similar over the working areas.</p>
31、<p> The material transported between an S-D pair is handled by one crane only.</p><p> MODEL DESCRIPTION</p><p> Three steps are involved in determining optimal positions for a crane gr
32、oup. First, a location generation model produces an approximate task group for each crane. This is then adjusted by a task assignment model. Finally, an optimization model is applied to each tower in turn to find an exac
33、t crane location for each task group.</p><p> Initial Location Generation Model</p><p> Lift Capacity and ‘‘Feasible’’ Area</p><p> Crane lift capacity is determined from a radiu
34、s-load curve where the greater the load, the smaller the crane’s operating radius. Assuming a load at supply point (S) with the weight w, its corresponding crane radius is r. A crane is therefore unable to lift a load un
35、less it is located within a circle with radius r[Fig. 1(a)]. To deliver a load from (S) to demand point (D), the crane has to be positioned within an elliptical area</p><p><b> (a)</b></p>
36、<p> FIG.1. Feasible Area of Crane Location for Task</p><p> FIG. 2. Task “Closenness”</p><p> enclosed by two circles, shown in Fig. 1(b). This is called the feasible task area. The s
37、ize of the area is related to the distance between S and D, the weight of the load, and crane capacity. The larger the feasible area, the more easily the task can be handled.</p><p> Measurement of ‘‘Closen
38、ess’’ of Tasks</p><p> Three geometric relationships exist for any two feasible task areas, as illustrated in Fig. 2; namely, (a) one fully enclosed by another (tasks 1 and 2); (b) two areas partly intersec
39、ted (tasks 1 and 3); and (c) two areas separated (tasks 2 and 3). As indicated in cases (a) and (b), by being located in area A, a crane can handle both tasks 1 and 2, and similarly, within B, tasks 1 and 3. However, cas
40、e (c) shows that tasks 2 and 3 are so far from each other that a single tower crane is unable to </p><p> Grouping Tasks into Separated Classes</p><p> If no overlapping exists between feasibl
41、e areas, two cranes are required to handle each task separately if no other</p><p> alternatives—such as cranes with greater lifting capacity or replanning of site layout—are allowed. Similarly, three crane
42、s are required if there are three tasks in which any two have no overlapping areas. Generally, tasks whose feasible areas are isolated must be handled by separate cranes.</p><p> These initial tasks are ass
43、igned respectively to different (crane) task groups as the first member of the group, then all other tasks are clustered according to proximity to them. Obviously, tasks furthest apart are given priority as initial task
44、s. When multiple choices exist, computer running time can be reduced by selecting tasks with smaller feasible areas as initial tasks. The model provides assistance in this respect by displaying graphical layout of tasks
45、 and a list of the size of feasi</p><p> Initial Crane Location</p><p> When task groups have been created, overlapping areas can be formed. Thus, the initial locations are automatically at t
46、he geometric centers of the common feasible areas, or anywhere specified by the user within common feasible areas.</p><p> Task Assignment Model</p><p> Group location is determined by geometr
47、ic ‘‘closeness.’’ However, one crane might be overburdened while others are idle. Furthermore, cranes can often interfere with each other so task assignment is applied to those tasks that can be reached by more than one
48、crane to minimize these possibilities.</p><p> Feasible Areas from Last Three Sets of Input</p><p> shape and size of feasible areas, illustrated in Fig. 9. In this case study, from the data a
49、nd graphic output, the user may become aware that optimal locations led by test sets 1, 2, and 3(Fig. 3) are the best choices (balanced workload, conflict possibility, and efficient operation). Alternatively, in connect
50、ion with site conditions such as availability of space for the crane position and ground conditions for the foundation, site boundaries were restricted. Consequently, one of the cranes had</p><p> CONCLUSIO
51、NS</p><p> Overall coverage of tasks tends to be the major criterion in planning crane group location. However, this requirement may not determine optimal location. The model helps improve conventional loc
52、ation methods, based on the concept that the workload for each crane should be balanced, likelihood of interference minimized, and efficient operation achieved. To do this, three submodels were highlighted. First, by cl
53、assifying all tasks into different task groups according to geometric ‘‘closeness’’ </p><p> Experimental results indicate that the model performs satisfactorily. In addition to the improvement on safety
54、and average efficiency of all cranes, 10–40% savings of total hooks transportation time can be achieved. Effort has been made to model the key criteria for locating a group of tower cranes, and two real site data have b
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