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英文原文
Mathematical model of electric hydraulic and powered support control system at a plough mining face
ZHANG Wei, HAN Xiao, SUN Jing-jing
School of Mechanical Electronic and Information Engineering, China University of Mining & Technology, Beijing 100083, China
Abstract: Given the actual working of a fully mechanized plough at a mining face, we have proposed a formula for running constraints between powered supports and a coal plough under assumed geological conditions of the coal face and, on this basis, established an automatic control model of powered supports for the coal plough face. We introduced the working principle of the powered support control system of the plough at the mining face. We established three advanced characteristics of this control system: response speed, reliability and easy maintenance of the system. .As well, we briefly introduced, the principal function of primary and subordinate controllers and the realization of the communication system by a Single Bus. Ten controllers were constructed and tested in our laboratorium. The results show that the control model is practical and meets actual conditions. It provides a theoretical basis for designing a computer control system for a powered support system of a plough at a mining face.
Key words: plough mining face; powered supports; constraints; automatic control model
1 Introduction
More than six billion tonnes of thin seam mineable reserves with a shearing height of 0.7–1.3 m, are available in China, which is about 18 percent of the total reserves of our country. With a thin seam shearer, 0.8 m is the lowest mining limit because of its structural restrictions. Furthermore, the shearer is inconvenient for workers to operate and maintain and workers have to work under conditions of extremely low space with this machine[1]. Therefore, coal ploughs become major pieces of equipment for mining thin seams. However, the space of a thin seam is narrow and small. Although workers do not need to work following the coal plough, they still need to operate the powered support system. Not only is there a hidden safety problem, but also the speed of moving the supports artificially falls far short of the speed of the coal plough, seriously restricting the efficiency and output at the mining face[2] .
The powered support system is the support equipment but it is also one of the major pieces of equipment at a fully mechanized coal face. With the development of electronic computers and automatic control technology, the automation of mining equipment is continually improving and simultaneously the electric hydraulic control technology of powered support systems is also developing. The electric hydraulic control system of powered support can not only control the action of the support system automatically, but also realize adjacent or long-range control. Thus the potential of an automated mining face, operated without human hands, may be realized. Therefore, its application to a fully mechanized coal face should be explored for its important implications[3]
2 Automatic control model of powered support system and its constraints on the coal plough
2.1Constraints between powered support system and coal plough
The coal plough and the shearer are two different mining machines. Compared with a shearer, coal ploughs are mainly applied with thin seams. Their structure is simple, the cutting depth is thin and the draught speed is quick. Therefore, the constraints between powered supports and a coal plough, which will be discussed by us, are different from that between powered supports and a shearer. We assume the following geological conditions to prevail at the coal face: the hardness coefficient is below 21°, the dip angle is small and the thin ceiling of the seam is steady[4] .
The following mechanical pieces of cutting equipment are provided for the coal face: a coal plough, a flexible chain conveyor and powered supports. Let the letter “p” represent the cutting depth of the coal plough (100 mm) and “q” the stroke of the cylinder (600 mm) of the support pusher. The constraints among the coal plough, powered supports and the flexible chain conveyor will be discussed under the assumptions listed above.
As shown in Fig. 1, when the coal plough is mining coal by drawing back and forth along the face, the system of two supports push the conveyor behind the plough and each of these supports pushes the conveyor (mm), which is per stroke. The scraper conveyor bends along a certain curve. Supports manage to push the conveyor to the cutting depth p (mm) after having pushed the conveyor two times when the coal plough finishes mining a draught once along the coal face. Supports manage to push the conveyor a distance of half stroke after the plough has mined integer times along face. The supports that have finished a half stroke perform a lower-advance-set operation every other support. The mention above is the constraints between supports and the coal plough.
In order to obtain the constraints between supports and the coal plough, variables and functions are defined as follows:
1）Number powered supports at the mining face from left to right: 1, 2, 3, …, (n–1), n;
2）v: speed of plough, mining coal; x: displacement of plough, i.e., the distance from the left of the face to the center of the plough (see Fig. 1).
The displacement x of the plough is converted into displacement K calculated by support number, which corresponds with the center of the plough. Suppose that t = , and = 0, where v is the speed of the coal plough (m/s); b is the distance between two centers of adjacent supports (m).
3）The direction from left to right is forward and vice versa. The direction of the plough movement is denoted by the variable y:
4）The support acts are denoted by , which can represent a single action, such as setting the leg, lowering the leg, moving and pushing the conveyor and so on; it can also represent a combined action composed of several single acts, such as lower-advance-set. The subscript shows action i (i=1, 2, 3). The symbols of the 3 actions are defined as follows:
f1: act1 (half of a cutting depth is pushed);
f2: act2 (a cutting depth is pushed);
f3: lower-advance-set operation.
5）Define action function. When support M carries out action , we define:
?M (4)
where the symbol “?” means operating.
f1 ? K1: support K1 act1 (half of a cutting depth is pushed);
f2 ? K2: support K2 act2 (a cutting depth is pushed);
f3 ?: support （lowing-advancing-setting;
These 11 actions are expressed in a united way:
where “s” is the moving distance of the plough (mm).
6) The relative distance, calculated by support number, between the support performing action i and the center of the plough is denoted by ?K , where ?Ki=|K–Ki|. ?Ki is related to the position of the center of the plough (confirmed when its position is known). ?Ki is a constant for a certain face. We know from Fig. 2, condition (3) and the definition of ?Ki that:
Eq.(8) is the mathematical expression of the constraints between powered supports and the coal plough. It expresses the relation between action of the supports, the displacement and the moving direction of the coal plough. Support Ki, whose distance to the center of the plough ?Ki never changes, performs 3 different actions fi separately with various displacements x (or K) of the plough while mining coal.
2.2 Constraints between powered supports and scraper conveyor
Every pusher cylinder of a support is connected to a section of the ledge of the conveyor, and the pusher jack makes a move. The conveyor is required to bend according to a certain curvature in order to decrease abrasion at the point of flexure while moving. The conveyor is ensured to be flexible in order to decrease traction resistance after half of a stroke.
2.3 Automatic control model of powered supports
Actually, the Eqs.(7) and (8) are automatic control models of the support location of the plough, which takes the displacement of the plough (x or K) as a variable. The displacement K calculated by the support number (the support number K corresponds to the center of plough pull) changes while the plough is mining coal back and forth. Taking the support K which corresponds with the the center of the plough pull as a benchmark, a set of supports whose locations do not alter relative to support K perform their corresponding actions according to the constraints. By putting i and y into Eq.(8), the automatic control model can be described:
When the plough moves to the right, the support K–?K1 moves 1/p of a stroke; the support K–?K2 moves 2/p of a stroke; the support K–Δperforms lower-advance-set operation (At this point, the supports have accomplished half of a stroke).
When the plough moves to the left, the support K+?K1 moves 1/p of a stroke; the support K+?K2 moves 2/p of a stroke; the support K+Δ performs a lower-advance-set operation (At this point, the supports have accomplished half of a stroke).
K is the support number worked by the key-press operation;
?K1–Δ is the distance calculated by support number between performing support and support K[5–9] .
3 System principle structure
As shown in Fig. 3, every support is controlled by a subordinate controller and forms an electric hydraulic control subordinate system. COM ports of the primary controller and all subordinate controllers are connected to a communication bus, which constitutes the microcomputer distribution system of powered supports at a fully mechanical coal face[5].
Advanced response speed of the system: communication between principal controller and subordinate controllers, or among subordinate controllers is direct because the COM ports of the primary controller and any subordinate controllers are connected to a Single Bus and hence the response speed of control among subordinate controllers is advanced.
Advanced reliability of the system: in a Single communication Bus system, the normal work of the entire system will not be affected if the primary or a subordinate controller has trouble. Only the broken-down controller, either primary or subordinate, is affected and this incidence is remote. The Single communication Bus system is fairly reliable.
Maintenance of the system: after switching off electricity to the primary or subordinate controller, maintenance, can be performed, the hydraulics of the subordinate system can be maintained and components can be replaced. This maintenance does not affect the normal work of the system and is convenient for the system.
4 Function of subordinate and primary controllers and system communication
Every support is equipped with a subordinate controller which is at the heart of the electric hydraulic control system of powered supports. The subordinate controller monitors data about its own powered support, such as running tension, support action and so on, translates and edits these data and sends out control commands to the support[3]
COM ports of the primary and all subordinate controllers at the mining face are connected to a communication bus, which can realize comprehensive management and establishes system control parameters.
The system has adopted a Single Bus, which links the separate subordinate controllers to a network. The subordinate controller monitors and controls the movements of its own support and sends out and receives control signals from the Single Bus to realize controls among subordinate controllers. The primary controller at a mining face initializes the system and sets up parameters and collects signals from the Single Bus to realize centralized inspection and a display of the state of the system.
5 Conclusions
In this study, we have proposed a mathematical expression of the running constraints between powered supports and a coal plough. We established an automatic control model of powered support and introduced the essential principle of an electric hydraulic control system as well as the function of a primary controller and subordinate controllers. Ten sets of subordinate controllers were constructed in our laboratorium and our experiment shows that the control model agrees with practical considerations.
Acknowledgements
Our deepest gratitude goes first and foremost to the Education Bureau, which gives us the chance to do the research. Second, we wish to express our appreciation to many people who have greatly contributed to or helped with the development of this article in their special ways. We are especially grateful to a friend named Tom, who has given us much help in the revision of the article. Our gratefulness also goes to those friends who have given us much inspiration and many constructive suggestions.
中文譯文
長壁工作面液壓支架電液控制系統(tǒng)數(shù)學模型
摘要：根據(jù)綜采工作面實際工作情況，我們提出了采煤工作面液壓支架和刨煤機兩者運行關系的一個公式，并在此基礎上，建立了工作面液壓支架和刨煤機的自動化控制系統(tǒng)。我們介紹了采煤工作面液壓支架控制的系統(tǒng)工作原理。我們歸納了本控制系統(tǒng)的三個參數(shù)：反應速度，可靠性和易維護性。同樣，我們簡要介紹了它的主控制器與附屬控制器和由單總線實現(xiàn)的通信系統(tǒng)。我們實驗室建造和測試了10個控制器。結(jié)果表明，該控制模型是可行的，符合實際情況。它為長壁工作面的液壓支架計算機控制系統(tǒng)的設計提供了理論依據(jù)。
關鍵詞：長壁工作面,液壓支架,參數(shù),自動控制
1. 引言
在我國采高0.7-1.3米的薄煤層可開采的儲量超過6億噸，大約占我國總儲量的百分之十八。因為薄煤層采煤機結(jié)構的限制，0.8米是采煤機最低開采高度，而且，這么低的空間下采煤機也不便于工人操作和維護。因此，刨煤機成為薄煤層開采的主要設備。然而，薄煤層工作面空間狹小。雖然工人不需要在刨煤機后工作，但他們?nèi)匀恍枰僮饕簤褐Ъ芟到y(tǒng)。這不僅是一個安全隱患，而且移架的速度遠未達到的刨煤機速度，嚴重制約著綜采工作面效率和產(chǎn)出 [ 2 ]。
液壓支架不僅是支護設備，但它也是綜采工作面的一個重要設備。隨著電子計算機和自動控制自動化技術的發(fā)展，采礦設備的不斷改善，電液控制技術也將在液壓支架上逐步應用。電液控制系統(tǒng)不僅可以自動控制液壓支架的動作，而且還實現(xiàn)鄰架控制或遠程控制。因此，綜采工作面的自動化，完全無人化，完全可以會實現(xiàn)。所以，綜采工作面的自動化成了應探討的重要問題[ 3 ]。
2. 液壓支架自動化控制系統(tǒng)模型及刨煤機的約束參數(shù)
2.1液壓支架和刨煤機之間的制約關系
在刨煤機和采煤機是兩個不同的采煤設備。同采煤機相比，刨煤機主要適用于薄煤層。其結(jié)構簡單、截深小、牽引速度快。因此，我們將討論不同于采煤機的刨煤機和液壓支架之間的制約關系，我們假定下面的采煤工作面地質(zhì)條件良好：硬度系數(shù)低于21°，傾角小，薄煤層的頂板穩(wěn)定。
下列是為采煤工作面提供的機械設備：刨煤機，刮板鏈式輸送機和液壓支架。字母“ P ”代表刨煤機截割深度（100毫米）和“ q ”是液壓支架的推移距離（600毫米）。上面列出的是討論刨煤機、液壓支架和刮板鏈式輸送機之間的制約關系所做的假設。
圖一表示的是刨煤機在工作面上利用往復運動采煤，兩架液壓支架在刨煤機后推移輸送機，每個支架推移的距離是(mm)，每程是。刮板輸送機沿著某一曲線彎曲。液壓支架推動刮板輸送機兩次后達到切割深度p （毫米）。當刨煤機在工作面完成一次截割。刨煤機在工作面上開采時間后液壓支架能推移刮板輸送機半程的距離。此液壓支架完成比其他沒有推移的支架一半推移行程。
圖一
上文提到的就是液壓支架和刨煤機之間的制約因素。為了獲得液壓支架和刨煤機之間的制約關系，變量和函數(shù)的定義如下：
1) 綜采工作面液壓支架數(shù)在從左至右依次為： 1 ， 2 ， 3 ， ... ， (n–1), n;
2) v：刨煤機速度，采煤速度; x：刨煤機采過距離，即從工作面左側(cè)到刨煤機中心的距離（見圖-1 ） 。
刨煤機采過距離x轉(zhuǎn)化為位移K可用液壓支架數(shù)目來計算，這與刨煤機中心一致。假設t= ，且 = 0 ，其中V是速度的刨煤機（米/秒） ; b是兩個相鄰液壓支架中心之間的距離（米） 。
3) 方向是從左向右前進，反之亦然。刨煤機運動方向由變量y表示：
4) 支架的動作定義為，可以表示單一動作，如升架，降架，移架和推動刮板輸送機等等，它也可以代表由幾個單一動作組成的聯(lián)合動作，如降價，移架，升架，下腳標表示某個動作（i = 1 ， 2 ， 3 ） 。三種動作的符號的定義如下：
f1： 動作1 （推移截深的一半）;
f2： 動作2 （推移一個截深距離）;
f3： 降架--移架--升架
5) 定義的動作功能。當液壓支架M執(zhí)行動作，我們定義如下：
?M (4)
其中，代號為“ ? ”是指操作。
f1 ? K1:：支架K1 動作1 （推移截深的一半） ;
f2 ? K2：支架K2 動作2 （推移一個截深） ;
f3 ?：支架降架-移架-升架
這11個動作統(tǒng)一表示為：
“ S ”的是刨煤機移動的距離（毫米）。
當刨煤機在工作面往返采煤時液壓支架首先執(zhí)行動作f1和f2 ，動作執(zhí)行完成半程后，執(zhí)行動作f3。
6) 相對距離，根據(jù)液壓支架的數(shù)目，執(zhí)行動作的液壓支架Ki，刨煤機的中心ΔK ，?Ki=|K–Ki|。 ΔKi與刨煤機的中心有關（當位置已知）。?Ki對于工作面是一個常量。我們從圖二和條件三和?Ki的定義得到：
從表達式(2)、(5)、(6)我們可以得到：
表達式（8）是液壓支架和刨煤機制約因素之間的數(shù)學關系。它表達液壓支架間的動作的關系，和刨煤機行程，刨煤機運行方向。支架Ki 刨煤機中心的距離沒有變化，當開采時液壓支架分別對應不同的刨煤機運動距離x執(zhí)行3個不同的動作 。
圖二
2.2液壓支架和刮板輸送機之間的制約因素
? 每個液壓支架推移千斤頂與刮板輸送機相連，由推移千斤頂推移刮板輸送機。刮板輸送機按照一定的曲線減少在運動時彎曲點的磨損。刮板輸送機要保持靈活以減少半程的牽引阻力。
2.3液壓支架自動化控制模型
實際上，方程（7）及（8）是支架位置自動化控制模型的表達式，其中刨煤機的行程（ x或K）作為一個變量。由液壓支架數(shù)目計算（支架數(shù)目K相當于刨煤機中心）位移K當刨煤機來回往復可以變化。以與刨煤機中心一致的液壓支架K為基準，一套支架相對支架K的位置不會改變。把i，y帶入公式（8）,自動控模型可以描述為：
1 ）當刨煤機向右運動時，液壓支架K - ΔK1移動1 / P的行程，支架K - ΔK2移動2 / P的行程;液壓支架K-Δ執(zhí)行降架-移架-升架（在這一點上，支架完成了行程的一半） 。
2 ）當刨煤機向左運動時，支架K+ΔK1移動1 / P的行程;支架K+?K2移動2 / P的行程;支架K+Δ執(zhí)行降架-移架-升架（在這一點上，支架完成了行程的一半） 。
K是由按鍵操作的液壓支架的數(shù)目;
ΔK1 -Δ是距正在執(zhí)行動作的支架到支架K的距離[ 5-9 ]
3. 系統(tǒng)的原理結(jié)構
如圖-3所示，每個液壓支架都由附屬控制器控制和形成一套電液控制附屬系統(tǒng)。 COM端口的主要控制器及所有附屬控制器連接到一個通信總線，它構成了綜采工作面液壓支架微機電系統(tǒng) [ 5 ] 。
圖三
1）系統(tǒng)的響應速度迅速：主控制器和附屬控制器之間的通信，或中下級控制器是直接的，因為COM端口的主控制器和任何附屬控制器都連接到單總線，因此從屬控制器之間的響應速度迅速。
2 ）快速系統(tǒng)的可靠性：在一個單總線通信系統(tǒng)，如果主控制器或下級控制器故障整個系統(tǒng)將不會受到影響仍能夠正常工作。除非控制器遭破壞，主控制器或下級控制器才受到影響，這種情況很少發(fā)生。單一通信總線系統(tǒng)是相當可靠的。
3）系統(tǒng)維護：關掉電源后的主控制器或從屬控制器的維修就可以執(zhí)行了，附屬控制器液壓系統(tǒng)的可以維修和部件可以被替換。這種維修不影響系統(tǒng)正常工作，系統(tǒng)維護方便。
4. 主控制器和附屬控制器的功能和系統(tǒng)通信
每臺液壓支架配備的附屬控制器是電液控制系統(tǒng)的核心。附屬控制器監(jiān)測記錄所在液壓支架數(shù)據(jù)，如支架的動作等，翻譯和編輯這些數(shù)據(jù)，并對支架發(fā)送控制命令 [ 3 ]。
綜采工作面COM端口的主控制器和所有附屬控制器連接到通信總線，可實現(xiàn)統(tǒng)一管理，并建立系統(tǒng)的控制參數(shù)。
該系統(tǒng)已通過單總線，連接不同的附屬控制器到網(wǎng)絡。附屬控制器從單一總線發(fā)送和接收控制信號監(jiān)測和控制所在液壓支架的動作和之間實現(xiàn)控制。綜采工作面主控制器初始化系統(tǒng)和設置參數(shù)，并從單一總線收集信號實現(xiàn)集中檢查和系統(tǒng)的距離顯示。
5.結(jié)論
? 在這項研究中，我們已經(jīng)提出了液壓支架和刨煤機之間運行制約因素的一個數(shù)學表達式。我們建立了一個液壓支架的自動控制模型并介紹了電液控制系統(tǒng)的基本原理，以及主控制器及附屬控制器的功能。我們在實驗室建造了十套從屬控制器，實驗表明，該控制模型符合實際要求。
鳴謝
我們首先要感謝教育局，給我們這次研究的機會。第二，我們要感謝以其他的方式極大地幫助和提高本文的人。我們特別感謝朋友湯姆，他在文章修改上給了我們很大幫助。我們感激還要給了我們很多靈感和許多建設性的建議的朋友。