挖掘機的機械學和液壓學畢業(yè)外文翻譯、中英文翻譯、挖掘機的外文文獻翻譯

畢業(yè)設計（論文）報告紙 共 頁 第 1 頁 裝 訂 線 外文原文： Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator Abstract It is demonstrated how to model and simulate an excavator with Modelica and Dymola by using Modelica libraries for multi-body and for hydraulic systems. The hydraulic system is controlled by a “l(fā)oad sensing” controller. Usually, models containing 3-dimensional mechanical and hydraulic components are difficult to simulate. At hand of the excavator it is shown that Modelica is well suited for such kinds of system simulations. 1. Introduction The design of a new product requires a number of decisions in the initial phase that severely affect the success of the finished machine. Today, digital simulation is therefore used in early stages to look at different concepts. The view of this paper is that a new excavator is to be designed and several candidates of hydraulic control systems have to be evaluated. Systems that consist of 3-dimensional mechanical and of hydraulic components like excavators are difficult to simulate. Usually, two different simulation environments have to be coupled. This is often inconvenient, leads to unnecessary numerical problems and has fragile interfaces. In this article it is demonstrated at hand of the model of an excavator that Modelica is well suited for these types of systems. The 3-dimensional components of the excavator are modeled with the new, free Modelica MultiBody library. This allows especially to use an analytic solution of the kinematic loop at the bucket and to take the masses of the hydraulic cylinders, i.e., the “force elements”, directly into account. The hydraulic part is modeled in a detailed way, utilizing pump, valves and cylinders from HyLib, a hydraulics library for Modelica. For the control part a generic “l(fā)oad sensing” control system is used, modeled by a set of simple equations. This approach gives the required results and keeps the time needed for analyzing the problem on a reasonable level. 2. Modeling Choices There are several approaches when simulating a system. Depending on the task it may be necessary to build a very precise model, containing every detail of the system and needing a lot of information, e.g., model parameters. This kind of models is expensive to build up but on the other hand very useful if parameters of a well defined system have to be modified. A typical example is the optimization of parameters of a counterbalance valve in an excavator (Kraft 1996). The other kind of model is needed for a first study of a system. In this case some properties of the pump, cylinders and loads are specified. Required is information about the performance of that system, e.g., the speed of the pistons or the necessary input power at the pump shaft, to make a decision whether this design can be used in principle for the task at hand. This model has therefore to be “cheap”, i.e., it must be possible to build it in a short time without detailed knowledge of particular components. The authors intended to build up a model of the second type, run it and have first results with a minimum amount of time spent. To achieve this goal the modeling language Modelica (Modelica 2002), the Modelica simulation environment Dymola (Dymola 2003), the new Modelica library for 3-dimensional mechanical systems “MultiBody” (Otter et al. 2003) and the Modelica library of hydraulic components HyLib (Beater 2000) was used. The model consists of the 3-dimensional mechanical construction of the excavator, a detailed description of the power hydraulics and a generic “l(fā)oad sensing” controller. This model will be available as a demo in the next version of HyLib. 3. Construction of Excavators In Figure 1 a schematic drawing of a typical excavator under consideration is shown. It consists of a chain track and the hydraulic propel drive which is used to manoeuvre the machine but usually not during a work cycle. On top of that is a carriage where the operator is sitting. It can rotate around a vertical axis with respect to the chain track. It also holds the Diesel engine, the hydraulic pumps and control system. Furthermore, there is a boom, an arm and at the end a bucket which is attached via a planar kinematic loop to the arm. Boom, arm and bucket can be rotated by the appropriate cylinders. 畢業(yè)設計（論文）報告紙 共 頁 第 2 頁 裝 訂 線 Figure 2 shows that the required pressures in the cylinders depend on the position. For the “stretched” situation the pressure in the boom cylinder is 60 % higher than in the retracted position. Not only the position but also the movements have to be taken into account. Figure 3 shows a situation where the arm hangs down. If the carriage does not rotate there is a pulling force required in the cylinder. When rotating excavators can typically rotate with up to 12 revolutions per minute the force in the arm cylinder changes its sign and now a pushing force is needed. This change is very significant because now the “active” chamber of the cylinder switches and that must be taken into account by the control system. Both figures demonstrate that a simulation model must take into account the couplings between the four degrees of freedom this excavator has. A simpler model that uses a constant load for each cylinder and the swivel drive leads to erroneous results 4. Load Sensing System Excavators have typically one Diesel engine, two hydraulic motors and three cylinders. There exist different hydraulic circuits to provide the consumers with the required hydraulic energy. A typical design is a Load Sensing circuit that is energy efficient and user friendly. The idea is to have a flow rate control system for the pump such that it delivers exactly the needed flow rate. As a sensor the pressure drop across an orifice is used. The reference value is the resistance of the orifice. A schematic drawing is shown in figure 4, a good introduction to that topic is given in (anon. 1992). The pump control valve maintains a pressure at the pump port that is typically 15 bar higher than the pressure in the LS line (= Load Sensing line). If the directional valve is closed the pump has therefore a stand-by pressure of 15 bar. If it is open the pump delivers a flow rate that leads to a pressure drop of 15 bar across that directional valve. Note: The directional valve is not used to throttle the pump flow but as a flow meter (pressure drop that is fed back) and as a reference (resistance). The circuit is energy efficient because the pump delivers only the needed flow rate, the throttling losses are small compared to other circuits. If more than one cylinder is used the circuit becomes more complicated, see figure 5. E.g. if the boom requires a pressure of 100 bar and the bucket a pressure of 300 bar the pump pressure must be above 300 bar which would cause an unwanted movement of the boom cylinder. Therefore compensators are used that throttle the oil flow and thus achieve a pressure drop of 15 bar across the particular directional valve. These compensators can be installed upstream or downstream of the directional valves. An additional valve reduces the nominal pressure differential if the maximum pump flow rate or the maximum pressure is reached (see e.g. Nikolaus 1994). 5. Model of Mechanical Part In Figure 6, a Modelica schematic of the mechanical part is shown. The chain track is not modeled, i.e., it is assumed that the chain track does not move. Components “rev1”, ., “rev4” are the 4 revolute joints to move the parts relative to each other. The icons with the long black line are “virtual” rods that are used to mark specific points on a part, especially the mounting points of the hydraulic cylinders. The light blue spheres (b2, b3, b4, b5) are bodies that have mass and an inertia tensor and are used to model the corresponding properties of the excavator parts. The three components “cyl1f”, “cyl2f”, and “cyl3f” are line force components that describe a force interaction along a line between two attachment points. The small green squares at these components represent 1-dimensional translational connectors from theModelica.Mechanics. Translational library. They are used to define the 1- dimensional force law acting between the two attachment points. Here, the hydraulic cylinders described in the next section are directly attached. The small two spheres in the icons of the “cyl1f, cyl2f, cyl3f” components indicate that optionally two point masses are taken into account that are attached at defined distances from the attachment points along the connecting line. This allows to easily model the essential mass properties (mass and center of mass) of the hydraulic cylinders with only a very small computational overhead. The jointRRR component (see right part of Figure 6) is an assembly element consisting of 3 revolute joints that form together a planar loop when connected to the arm. A picture of this part of an excavator, a zoom in the corresponding Modelica schematic and the animation view is shown in Figure 7. When moving revolute joint “rev4” (= the large red cylinder in the lower part of Figure 7； the small red cylinders characterize the 3 revolute joints of the jointRRR assembly component) the position and orientation of the attachment points of the “l(fā)eft” and “right” revolute joints of the jointRRR component 畢業(yè)設計（論文）報告紙 共 頁 第 3 頁 裝 訂 線 are known. There is a non-linear algebraic loop in the jointRRR component to compute the angles of its three revolute joints given the movement of these attachment points. This non-linear system of equations is solved analytically in the jointRRR object, i.e., in a robust and efficient way. For details see In a first step, the mechanical part of the excavator is simulated without the hydraulic system to test this part separatly. This is performed by attaching translational springs with appropriate spring constants instead of the hydraulic cylinders. After the animation looks fine and the forces and torques in the joints have the expected size, the springs are replaced by the hydraulic system described in the next sections. All components of the new MultiBody library have “built-in” animation definitions, i.e., animation properties are mostly deduced by default from the given definition of the multi-body system. For example, a rod connecting two revolute joints is by default visualized as cylinder where the diameter d is a fraction of the cylinder length L (d = L/40) which is in turn given by the distance of the two revolute joints. A revolute joint is by default visualized by a red cylinder directed along the axis of rotation of the joint. The default animation (with only a few minor adaptations) of the excavator is shown if Figure 8. The light blue spheres characterize the center of mass of bodies. The line force elements that visualize the hydraulic cylinders are defined by two cylinders (yellow and grey color) that are moving in each other. As can be seen, the default animation is useful to get, without extra work from the user side, a rough picture of the model that allows to check the most important properties visually, e.g., whether the center of masses or attachment points are at the expected places. For every component the default animation can be switched off via a Boolean flag. Removing appropriate default animations, such as the “centerof- mass spheres”, and adding some components that have pure visual information (all visXXX components in the schematic of Figure 6) gives quickly a nicer animation, as is demonstrated in Figure 9. Also CAD data could be utilized for the animation, but this was not available for the examination of this excavator. 6. The Hydraulics Library HyLib The (commercial) Modelica library HyLib (Beater 2000, HyLib 2003) is used to model the pump, metering orifice, load compensator and cylinder of the hydraulic circuit. All these components are standard components for hydraulic circuits and can be obtained from many manufacturers. Models of all of them are contained in HyLib. These mathematical models include both standard textbook models (e. g. Dransfield 1981, Merrit 1967, Viersma 1980) and the most advanced published models that take the behavior of real components into account (Schulz 1979, Will 1968). An example is the general pump model where the output flow is reduced if pressure at the inlet port falls below atmospheric pressure. Numerical properties were also considered when selecting a model (Beater 1999). One point worth mentioning is the fact that all models can be viewed at source code level and are documented by approx. 100 references from easily available literature. After opening the library, the main window is displayed (Figure 10). A double click on the “pumps” icon opens the selection for all components that are needed to originate or end an oil flow (Figure 11). For the problem at hand, a hydraulic flow source with internal leakage and externally commanded flow rate is used. Similarly the needed models for the valves, cylinders and other components are chosen. All components are modeled hierarchically. Starting with a definition of a connector a port were the oil enters or leaves the component a template for components with two ports is written. This can be inherited for ideal models, e.g., a laminar resistance or a pressure relief valve. While it usually makes sense to use textual input for these basic models most of the main library models were programmed graphically, i.e., composed from basic library models using the graphical user interface. Figure12 gives an example of graphical programming. All mentioned components were chosen from the library and then graphically connected. 7. Library Components in Hydraulics Circuit The composition diagram in Figure 12 shows the graphically composed hydraulics part of the excavator model. The sub models are chosen from the appropriate libraries, connected and the parameters input. Note that the cylinders and the motor from HyLib can be simply connected to the also shown components of the MultiBody library. The input signals, i.e., the reference signals of the driver of the excavator, are given by tables, specifying the diameter of the metering orifice, i.e. the reference value for the flow rate. From the mechanical part of the excavator only the components are shown in 畢業(yè)設計（論文）報告紙 共 頁 第 4 頁 裝 訂 線 Figure 12 that are directly coupled with hydraulic elements, such as line force elements to which the hydraulic cylinders are attached. 8. Model of LS Control For this study the following approach is chosen: Model the mechanics of the excavator, the cylinders and to a certain extent the pump and metering valves in detail because only the parameters of the components will be changed, the general structure is fixed. This means that the diameter of the bucket cylinder may be changed but there will be exactly one cylinder working as shown in Figure 1. That is different for the rest of the hydraulic system. In this paper a Load Sensing system, or LS system for short, using one pump is shown but there are other concepts that have to be evaluated during an initial design phase. For instance the use of two pumps, or a separate pump for the swing. The hydraulic control system can be set up using meshed control loops. As there is (almost) no way to implement phase shifting behavior in purely hydraulic control systems the following generic LS system uses only proportional controllers. A detailed model based on actual components would be much bigger and is usually not available at the begin of an initial design phase. It could be built with the components from the hydraulics library but would require a considerable amount of time that is usually not available at the beginning of a project. In Tables 1 and 2, the implementation of the LS control in form of equations is shown. Usually, it is recommended for Modelica models to either use graphical model decomposition or to define the model by equations, but not to mix both descrip- tion forms on the same model level. For the LS system this is different because it has 17 input signals and 5 output signals. One might built one block with 17 inputs and 5 outputs and connect them to the hydraulic circuit. However, in this case it seems more understandable to provide the equations directly on the same level as the hydraulic circuit above and access the input and output signals directly. For example, ”metOri1.port_A.p” used in table 2 is the measured pressure at port_A of the metering orifice metOri1. The calculated values of the LS controller, e.g., the pump flow rate “pump.inPort.signal1 = .” is the signal at the filled blue rectangle of the “pump” component, see Figure 12). The strong point of Modelica is that a seamless integration of the 3-dimensional mechanical library, the hydraulics library and the non standard, and therefore in no library available, model of the control system is easily done. The library components can be graphically connected in the object diagram and the text based model can access all needed variables. 9. Some Simulation Results The complete model was built using the Modelica modeling and simulation environment Dymola (Dymola 2003), translated, compiled and simulated for 5 s. The simulation time was 17 s using the DASSL integrator with a relative tolerance of 10-6 on a 1.8 GHz notebook, i.e., about 3.4 times slower as real-time. The animation feature in Dymola makes it possible to view the movements in an almost realistic way which helps to explain the results also to non-experts, see Figure 9. Figure 13 gives the reference signals for the three cylinders and the swing, the pump flow rate and pressure. From t = 1.1 s until 1.7 s and from t = 3.6 s until 4.0 s the pump delivers the maximum flow rate. From t = 3.1 s until 3.6 s the maximum allowed pressure is reached. Figure 14 gives the position of the boom and the bucket cylinders and the swing angle. It can be seen that there is no significant change in the piston movement if another movement starts or ends. The control system reduces the couplings between the consumers which are very severe for simple throttling control. Figure 15 shows the operation of the bucket cylinder. The top figure shows the reference trajectory, i. e. the opening of the directional valve. The middle figure shows the conductance of the compensators. With the exception of two spikes it is open from t = 0 s until t = 1 s. This means that in that interval the pump pressure is commanded by that bucket cylinder. After t = 1 s the boom cylinder requires a considerably higher pressure and the bucket compensator therefore increases the resistance (smaller conductance). The bottom figure shows that the flow rate control works fine. Even though there is a severe disturbance (high pump pressure after t = 1 s due to the boom) the commanded flow rate is fed with a small error to the bucket cylinder. 10. Conclusion 畢業(yè)設計（論文）報告紙 共 頁 第 5 頁 裝 訂 線 For the evaluation of different hydraulic circuits a dynamic model of an excavator was built. It consists of a detailed model of the 3 dimensional mechanics of the carriage, including boom, arm and bucket and the standard hydraulic components like pump or cylinder. The control system was not modeled on a component basis but the system was described by a set of nonlinear equations. The system was modeled using the Modelica MultiBody library, the hydraulics library Hylib and a set of application specific equations. With the tool Dymola the system could be build and tested in a short time and it was possible to calculate the required trajectories for evaluation of the control system. The animation feature in Dymola makes it possible to view the movements in an almost realistic way which helps to explain the results also to 畢業(yè)設計（論文）報告紙 共 頁 第 6 頁 裝 訂 線 譯文 ； 多疇模擬：挖掘機的機械學和液壓學 概要： 通 過使用用于多體和液壓系統(tǒng)的 Modelica程序庫，示范通過 Modelica和 Dymola如何模擬和仿真挖掘機。液壓系統(tǒng)由“負載傳感”控制器控制。一般，模型包含難以模擬的三維機械和液壓組件。對于挖掘機將演示 Modelica有效適用于這種系統(tǒng)的仿真。 1 緒論 一種新產(chǎn)品的設計在開始階段需要一系列決定，這些決定對最終產(chǎn)品是否成功產(chǎn)生很大的影響。因此，今天在初始階段使用數(shù)字模擬來檢驗不同的想法。這篇論文的目的是設計一臺新的挖掘機并評估幾個備選的液壓系統(tǒng)。 模擬包含三維機械和液壓組件的系統(tǒng)是很難的，如挖掘機，一般，兩個 不同的模擬環(huán)境必須連結(jié)在一起，這一般很不方便，導致不必要的數(shù)字問題和破碎界面。在這篇文章中，將對挖掘機模型的開始進行演示以證明 Modelica是適合這些系統(tǒng)的。 挖掘機的三維組件由新近的，豐富的 Modelica，聯(lián)合體程序庫來模擬，這使得可以使用鏟斗運動循環(huán)的分析結(jié)論，并直接考慮液壓缸（也就是動力元件）的質(zhì)量。液壓部分以詳細的方法模擬，從一個用于 Modelica的液壓程序庫中使用泵，閥和缸。在控制部分使用一個普通的負載傳感器，由一簡單方程組模擬。這種方法得到要求的結(jié)果，并使得分析問題所需的時間限制在合理的要 求內(nèi)。 2模型選擇 模擬一個系統(tǒng)有幾種方法。根據(jù)任務的需要建立一個很精確的模型，包含系統(tǒng)的每一個細節(jié)，需要許多的信息，比如模型參數(shù)。建立這種模型很麻煩。但另一方面，如果一個定義系統(tǒng)的參數(shù)需要修正，建立這種模型是很有效的。挖掘機上平衡閥參數(shù)的優(yōu)化就是一個特殊的例子。 對一個系統(tǒng)的初步研究需要另外一個模型，在這種情況下，泵，閥和負載的容量是具體的，需要的是關(guān)于系統(tǒng)工作的信息，例如活塞的速度，泵軸所需的輸入動力。從而判定這個設計是否符合此任務的原則要求。因此，這種模型必須是方便的，也就是，對特殊元件沒有詳細了解 時能在短時間內(nèi)建立起來。 學者們打算建立第二類的一個模型，并運行它，但在最少的時間內(nèi)得到第一類的結(jié)論，為了達到此目的，使用了建摸 Modelica， Modelica模擬環(huán)境 Dymola，用于三維機械系統(tǒng)的新 Modelica聯(lián)合體程序庫，和液壓組件的 Modelica程序庫 Hylib，模型包含挖掘機的三維機械結(jié)構(gòu)，動力液壓學的詳細描述和通用的負載傳感控制器。它在 Hylib的下一個版本中可應用為一種樣本。 3 挖掘機的結(jié)構(gòu) 圖一給出了正在考慮中的特殊挖掘機的簡圖。它包含履帶和液壓推動裝置，液壓推動裝置用 畢業(yè)設計（論文）報告紙 共 頁 第 7 頁 裝 訂 線 于操縱機械，但通 常不在一個工作循環(huán)的時候。它的上面是供操作者坐的車廂，廂體能相對于履帶繞垂直軸旋轉(zhuǎn)，柴油發(fā)動機液壓泵和控制系統(tǒng)卻在里面，另外轉(zhuǎn)臂，動臂。在末端是鏟斗，鏟斗經(jīng)由一平面運動回路連接到動臂上。特定的液壓缸使轉(zhuǎn)臂，動臂，鏟斗旋轉(zhuǎn)。 圖二表示出油缸所需的壓力是根據(jù)位置確定的，當在伸展開來的情況下，動臂油缸中的壓力比收縮的情況高 60%。不僅位置，而且運動也必須考慮。圖三表示動臂下降的情況，如果車廂沒有旋轉(zhuǎn)，油缸則需要一個拉力，當旋轉(zhuǎn)時，挖掘機旋轉(zhuǎn)通常能達到每分鐘 12轉(zhuǎn)，則動臂油缸中的受力改變方向，此時需要一個推力。這個 改變是非常重要的，因為此時活躍的油缸內(nèi)箱轉(zhuǎn)變，這必須由控制系統(tǒng)加以考慮。兩幅圖都表明一個仿真模型考慮挖掘機四個自由度相互之間的聯(lián)結(jié)，每個油缸和回轉(zhuǎn)驅(qū)動使用連續(xù)載荷的簡單模型將導致錯誤結(jié)果。 4 負載傳感器 挖掘機通常具有一臺柴油發(fā)動機，兩臺液壓馬達和三臺油缸，為這些消耗機器提供所需的液壓油源的液壓線路上不同的。一種特殊的設計是負載傳感線路，它能有效控制能量，使用方便。這種想法是使泵有一個流體速率控制系統(tǒng)，因而能準確傳遞所需的流體速率。在傳感器中，使用經(jīng)過節(jié)孔而產(chǎn)生壓降的方法，孔的阻力是參考值。圖四給出了簡圖，關(guān) 于這個話題的更好的介紹已經(jīng)給出。 泵控制閥，使得泵出口的壓力通常比負載傳感器中的壓力高 15MPA，如果方向閥關(guān)閉，則泵因此有 15 MPA的壓力。如果方向閥打開，泵輸出一流體速度導致通過方向閥時產(chǎn)生 15 MPA的壓降。注意：方向閥不是用做泵流體，而是作為一個流體儀表（反饋的壓降）和作為一個參考（阻力）。此線路對能量是有效率的，因為泵只輸出所需的流體速率，相對其他線路，油管的損失很小。 看圖五，如果不只一個油缸使用這種線路，則變得復雜。如果轉(zhuǎn)臂需要 300 MPA的壓力，鏟斗需要 300MPA的壓力，則泵輸出的壓力 高于 300MPA，這會使轉(zhuǎn)臂油缸產(chǎn)生一個不要的運動。因此，使用補償器來約束油流體，因此達到通過特殊定向伐時產(chǎn)生 15MPA的壓降，這些補償器可以安裝在定向閥的前面或后面。如果達到最大泵流體速度或泵最大壓力，則附加的閥減少容許壓力差。 5 機械部分的模型 圖六為機械部分的一個 Modelica簡圖，履帶不是模擬的，也就是，假設履帶為不動的，組件“ rev1 rev4”是使得相互聯(lián)系的部分運動的旋轉(zhuǎn)關(guān)節(jié)，長黑色線的圖象是實質(zhì)是的閂，用于標明機械部分上的特別的關(guān)節(jié)。特別是液壓油缸的固定關(guān)節(jié)，淡藍球是有質(zhì)量和慣量張量的球體 ，是用于模擬挖掘機的相應部分，“ cy11f.cy12f和 cy13f”三個部分是線性力部件，描述兩個連接之間沿著線的力相互作用，這些部件中的小綠方格表示 Modelica機械翻譯程序庫中的一維翻譯連接器，他們用于表示兩連接關(guān)節(jié)之間的一維力法規(guī)。這里，將在下一部分中介紹餓液壓油缸是直接連接的?！?cy11f.cy12f和 cy13f”部件圖象上的兩個小球表示有選擇的考慮兩點的質(zhì)量，在沿連接線上的連接點之間的已定距離上，這方便于模擬，只有少計算液壓油缸的質(zhì)量部分（質(zhì)量和 畢業(yè)設計（論文）報告紙 共 頁 第 8 頁 裝 訂 線 作用中心） 關(guān)節(jié) RRR組件（圖六右邊）是包含三個旋 轉(zhuǎn)關(guān)節(jié)的裝配元件，其中旋轉(zhuǎn)關(guān)節(jié)在連接動臂時一起形成一片面回路。圖七為挖掘機這方面的一張圖片，在相應的 Modelica簡圖的一張電子放大圖象和動畫制作圖。當移動旋轉(zhuǎn)關(guān)節(jié)“ rev4”（圖七下面部分中的大紅油缸，表示關(guān)節(jié) RRR裝配部件中三個旋轉(zhuǎn)關(guān)節(jié)的小紅缸），關(guān)節(jié) RRR部件中左右旋轉(zhuǎn)關(guān)節(jié)的連接點的位置和定位是已知的，關(guān)節(jié)RRR部件中有非線性代數(shù)回路用以計算連接點運動時產(chǎn)生的 3個旋轉(zhuǎn)關(guān)節(jié)的角度。這非線性方程系統(tǒng)在關(guān)節(jié) RRR中分解解決，如，一種快速有效的方法。 第一步，在沒有液壓系統(tǒng)獨立測試時，模擬挖掘機的機械部分， 通過連接轉(zhuǎn)換彈簧和代替液壓油缸的合適彈簧慣量來完成。當動力制作看起來不錯，節(jié)點上的力和扭矩達到要求時，彈簧以下將介紹的液壓系統(tǒng)代替。 新的聯(lián)合體程序庫的所有組件有內(nèi)部的默認定義，也就是，默認部分都是通過聯(lián)合體系統(tǒng)中的已知定義讀用推導的，例如連接兩旋轉(zhuǎn)關(guān)節(jié)的閂被錯誤的理解為油缸，油缸的直徑 d相對油缸的長度很小（ d=L/40）。長度反過來是由兩旋轉(zhuǎn)關(guān)節(jié)之間的距離