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1、<p> 一組塔式起重機的位置優(yōu)化</p><p> 摘要 計算機模型能使一組塔機位置更加優(yōu)化。合適的位置條件能平衡工作載荷,降低塔機之間碰撞的可能性,提高工作效率。這里對三個子模型進(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)每個塔機的合適位置。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,運用一個單塔起重機優(yōu)化模型去尋找吊鉤運輸時間最短的位置。本文對模型完成的實驗結(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)一個單塔起動機不能全面的完成重要的任務(wù)要求時或者當(dāng)塔機不能完成緊急的建設(shè)任務(wù)時通常是由幾個塔機同時完成任務(wù)。影響塔機的因素很多。從操作效率和安全方面考慮,如果所有計劃的任務(wù)都能執(zhí)行,應(yīng)將塔機盡可能的分開,避免互相干擾和碰撞。然而這種理想的情況在實踐中很難成
3、功,因為工作空間的限制和塔機的耐力有限使塔機的工作區(qū)域重疊是不可避免的。因此,即使起重機的鐵臂在不同的水平工作面也會發(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,通過反復(fù)實驗來決定塔式起重機的合適位置。起重機位置的選擇很復(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> 在過去的20年里,起重機位置模型逐步形成。Warszawski(1973)嘗試盡可能用時間與距離來計算塔機
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)劃動態(tài)模型,但是沒考慮到位置。Gray and Little (1985)在處理不規(guī)則的混凝土建筑物時候,設(shè)置位置優(yōu)化的塔式起動機。然而,Wijesundera and Harris (1986)在處理具體的任務(wù)時減少了操作時間和延長了設(shè)備使用周期時設(shè)計了一種模擬模型。Farrell and Hover (1989)開發(fā)了帶有圖解界面的數(shù)據(jù)庫,來協(xié)助
5、起動機的位置的選擇。Choi and Harris (1991)通過計算運輸所須的全部時間來提出另一種優(yōu)化單塔起重機位置優(yōu)化。Emsley (1992)改進(jìn)了Choi and Harris提出的模型。除了在計算方法相似外,起重機的數(shù)量類型和設(shè)計系統(tǒng)規(guī)則也得以提高</p><p><b> 假設(shè)</b></p><p> 采訪網(wǎng)站管理員關(guān)于他們的公司和觀察到手上的工
6、作電流的方法。另外觀察起重機集中在14個操作站點的運用。(在中國是4個,在英格蘭是6個,在蘇格蘭是4個)。研究設(shè)備放在4個站點時間為6個星期,兩個站點用兩個星期時間。調(diào)查結(jié)果顯示尤其是在全面覆蓋工作領(lǐng)域,沒有干擾,平衡工作載荷和地面情況是決定塔機位置重要的原因。因此,重點在這些因素上(除了地面情況因為站點管理員能明確說明合適的區(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)點和需求點的幾何布局、起重機的類型和數(shù)量。</p><p> 對于每個供應(yīng)點和需求點,運輸需求水平是已知的。例如,起重機的總數(shù)、每組起重機的數(shù)量、最大限度的裝載、延遲卸貨等等。</p><p> 在建設(shè)時期和工作區(qū)域大體相同。</p><p> 只用一個起重機運輸供應(yīng)點與需求點之間的物料。</p><p><b> 模型
8、描述</b></p><p> 決定起重機理想的位置有三個位置條件。首先用位置模型產(chǎn)生一個相似的任務(wù)組,然后用任務(wù)分配模型調(diào)整,最后優(yōu)化模型輪流并運用到每個任務(wù)組中的準(zhǔn)確位置。</p><p><b> 初始位置生成模型</b></p><p> 起重機的起升能力和合適的區(qū)域</p><p> 起重機
9、的升起能力取決于曲線的半徑,負(fù)荷量越大,起重機的操作半徑越小。假設(shè)供應(yīng)點的負(fù)荷量是w,相應(yīng)的起重機半徑是r。一個起重機若不能承受裝載除非它的半徑在圓內(nèi)(圖1)。從供應(yīng)點傳送一個裝載需求點,必須把起重機放在兩個重合的橢圓區(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)點和需求點的距離、負(fù)荷量、起重機的耐力有關(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)的測量</b
10、></p><p> 對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,(a)一個圖與另個圖完全重合(任務(wù)1與2)。(b)兩個區(qū)域部分相交(任務(wù)1與3)。(c)兩個區(qū)域分開(任務(wù)2與3)。如指出的實例a與b,起重機被放在區(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> 然而實例c顯示,任務(wù)2和3距離太遠(yuǎn),一個單獨的起重機在沒有移
11、動位置的情況下不能完成任務(wù),因此,需要多個或起重能力更大的起重機去完成。交疊的區(qū)域可以測量相臨的任務(wù)。例如,任務(wù)2到任務(wù)1的距離比到任務(wù)3的距離近因為任務(wù)1和2交疊區(qū)域比任務(wù)1和3的大。這個概念也可以應(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)組的距離近因為c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,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</b></p><p> 如果兩個合適的區(qū)域不存在重疊的部分,在沒有其它的可選擇的情況下兩個起重機就需要分開來完成任務(wù),例如起重機的舉起能力很大或作用點重新規(guī)劃布局等類似的情況,如果有3個任務(wù)且沒有任何兩個任務(wù)有交疊的區(qū)域情況下需要3個起重機完成任務(wù)。總的來說,合適區(qū)域是孤立的任務(wù)必須分開來完成。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
13、作的第一個成員,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)多種選擇存在時電腦通過篩選作為最初的任務(wù),越少的可行領(lǐng)域任務(wù)就會用越少的操作時間。模型能夠通過展示任務(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,模型通過核對交疊區(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)生一個最新的任務(wù)組。之后,模型會從所有任務(wù)轉(zhuǎn)向下一個任務(wù),直到所有任務(wù)都完成。如果一個任務(wù)分配失敗,系
14、統(tǒng)會顯示出來,更多的起重機被應(yīng)用或改變?nèi)蝿?wù)布局。</p><p><b> 初始起重機的位置</b></p><p> 當(dāng)產(chǎn)生了任務(wù)組,交疊區(qū)域也同時形成了。因此,初始位置自動的變成公共合適區(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,一個起重機任務(wù)較多而其它的卻沒任務(wù)。而且起重機之間會干擾,將任務(wù)分配并用多個起重機同時工作使干擾降低到最小</p><p> 過去三套輸入切實可行的區(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?,考慮到站點的情況如,起重機位置有益的
16、空間和有益機座的地面環(huán)境,站點邊界嚴(yán)格控制。因此,起重機應(yīng)該安放在一個建筑物內(nèi),在這一方面,假如一個攀登起重機可行同時建筑結(jié)構(gòu)也能支持這種起重機,就合理的沖突索引和標(biāo)準(zhǔn)差計算的工作量,裝置4是一個不錯選擇。另外,裝置5有優(yōu)越的固定塔機位置的電梯井,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)劃起重機機組的重
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念基礎(chǔ)上。一個模型能夠改進(jìn)傳統(tǒng)的尋找位置的方法。為了做到這點,突出強調(diào)了三個子模型,首先,通過相近的幾何位置將所有的任務(wù)分類產(chǎn)生一個總體布局。然后,在尋找每個任務(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,運用最佳優(yōu)化原則找到一個在三個層面上的精確的吊鉤位置。實驗結(jié)果表明模型
18、是令人滿意的。除了起重機的安全設(shè)施的改進(jìn)和平均效率的提高,還縮短10-40%的吊鉤的運輸時間。為了找出塔機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,并且兩個真正的數(shù)據(jù)點已經(jīng)被用于測試模型。但是它沒有捕獲所有的專業(yè)知識和現(xiàn)場管理經(jīng)驗。然而其他有關(guān)材料的建筑結(jié)構(gòu)、條件基礎(chǔ)、卸貨場所、無障礙的鄰近樓宇等等因素也是塔機定位的問題所在。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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