多畴模拟：挖掘机的机械学和液压学

1、多畴模拟：挖掘机的机械学和液压学概要：通过使用用于多体和液压系统的Modelica程序库，示范Modelica和Dymola如何模拟和仿真挖掘机。液压系统由“负载传感”控制器控制。一般来说模型包含了难以模拟的三维机械和液压组件。对于挖掘机将演示Modelica是如何有效适地用于这种系统的仿真。1.绪论一种新产品的设计在开始阶段需要一系列决定，这些决定对最终产品是否成功产生很大的影响。因此，今天在初始阶段使用数字模拟来检验不同的想法。这篇论文的目的是设计一台新的挖掘机并评估几个备选的液压系统。模拟包含三维机械和液压组件的系统是很难的，如挖掘机，两个不同的模拟环境必须连结在一起，这很不方便，导致不

2、必要的数字问题和边界相互干涉问题。在这篇文章中，将对挖掘机模型的开始进行演示以证明Modelica是适合这些系统的。挖掘机的三维组件由新开发的，丰富的Modelica，联合体程序库来模拟，这使得可以使用铲斗运动规律的分析结论，并直接考虑液压缸（也就是动力元件）的质量。液压元件被模拟，从一个用于Modelica的液压程序库中使用泵，阀和缸。在控制部分使用一个普通的负载传感器，由一简单方程组模拟。这种方法得到要求的结果，并使得分析问题所需的时间限制在合理的要求内。2.模型选择模拟一个系统有几种方法。根据任务的需要建立一个很精确的模型，包含系统的每一个细节，需要许多的信息，比如模型参数。建立这种模型

3、很麻烦。但另一方面，如果一个定义系统的参数需要修正，建立这种模型是很有效的。挖掘机上平衡阀参数的优化就是一个特殊的例子。对一个系统的初步研究需要另外一个模型，在这种情况下，泵，阀和负载的容量是具体的，需要的是关于系统工作的信息，例如活塞的速度，泵轴所需的输入动力。从而判定这个设计是否符合此任务的原则要求。因此，这种模型必须是方便的，也就是在没有详细了解特殊元件的情况下，能在短时间内建立起来。学者们打算建立一个第二类的模型，运行它，并在最少的时间内得到初步结论，为了达到此目的，使用了建摸Modelica(Modelica 2002)，Modelica模拟环境Dymola (Dymola 2003

4、),用于三维机械系统的新Modelica联合体程序库和液压组件的Modelica程序库Hylib，模型包含挖掘机的三维机械结构，动力液压学的详细描述和通用的负载传感控制器。3.挖掘机的结构图一给出了正在考虑中的特殊挖掘机的简图。它包含履带和液压驱动装置，液压驱动装置用于操纵机械。它的上面是供操作者坐的驾驶室，驾驶室能相对于履带绕垂直轴旋转。它还拥有柴油机，液压泵和液压控制系统。另外有一个动臂、斗杆以及和斗杆相连的铲斗。专门的液压油缸使斗杆，动臂，铲斗旋转。图二表示出油缸所需的压力是根据位置确定的，当在伸展开来的情况下，动臂油缸中的压力比收缩的情况高60%。不仅位置，而且运动也必须考虑。图三表示

5、动臂下降的情况，如果驾驶室没有旋转，油缸则需要一个拉力，当旋转时，挖掘机旋转通常能达到每分钟12转，则动臂油缸中的受力改变方向，此时需要一个推力。这个改变是非常重要的。两幅图都表明一个仿真模型考虑挖掘机四个自由度相互之间的联结，每个油缸和回转驱动使用连续载荷的简单模型将导致错误结果。4.负载传感器挖掘机通常具有一台柴油发动机，两个液压马达和三个油缸，存在不同的液压回路，以提供机器消耗所需的液压油源。一种特殊的设计是负载传感油路，它能有效控制能量，使用方便。这种想法是使泵有一个流体速率控制系统，因而能准确传递所需的流体速率。在传感器中，使用经过节孔而产生压降的方法，孔的阻力是参考值。图四给出了简

6、图，关于这个话题的更好的介绍已经给出(anon. 1992)。泵控制阀，使得泵出口的压力通常比负载传感器中的压力高15bar，如果方向阀关闭，则泵因此有15 bar的压力。如果方向阀打开，泵输出一流体速度导致通过方向阀时产生15 bar的压降。注意：方向阀不是用做泵流体，而是作为一个流体仪表（反馈的压降）和作为一个参考（阻力）。此油路对能量是有效率的，因为泵只输出所需的流速，相对其他油路，油管的损失很小。看图五,如果不只一个油缸使用这种油路，则变得复杂。如果斗杆需要300 bar的压力，铲斗需要300bar的压力，则泵输出的压力高于300 bar，这会使斗杆油缸产生一个不必要的运动。5.液压程

7、序库Hylib商业Modelica程序库Hylib用于模拟泵调节孔，负载补偿器，液压回路缸，所有这些元件是液压回路的标准元件，能从许多制造商获得。Hylib中包括所有这些元件的模型。这些数学模型包含教科书上的标准模型，也包含对真实元件的运行进行考虑的最先进的，如果输入口压力下降到底于大气压，输出的液体就会减小，这样的普通泵模型就上例子。选择一种 模型时，还有许多因素要考虑，值得一提的一点是所有模型能被原代码水平看待，并且可以由从易得文献得来的大约100个参数来证明。打开程序库后，展示了主要窗口（图十），双击泵图象打开所有元件的选项。开始或结束油流体所需要元件。为了现在的问题，使用带有内泄口和外

8、部限定流速的液压流体源。同样，选择关于阀，缸和其他元件的所需模型。所有组件都是分级模拟的，从连接器的确定开始（连接器是油进入或流出元件的通口），带有两个口的元件模版如图。这能继承下来到理想的模型。如一薄层阻力阀或释压阀。当为这些基本模型使用文字上的输入是有道理的。许多程序库主要模型以图形编制。由使用图形使用者界面的基本程序库模型组成。图12给出了图形编制的一个例子。所有提及的元件从程序库中选出来并分明的连接起来。6.液压回路中的程序库元件图12中的结构图是挖掘机模型图形组成的液压部分，以下的模型是从专属的程序库中选出，连接并输入参数。注意到从Hylib来的缸和马达能简单连接为所示的多功能程序库

9、的组件。输入信号如，挖掘机发动机的相关信号由图框给出。如控制流体速度的参考阀。对于挖掘机的机械部分，只要图12中所示的元件直接与液压元件相连接。如液压缸接触的直线压力元件。7.负载传感控制器模型在这个学习中，选择下面的方法：模拟挖掘机的机械器件，并一定程度上详细的模拟泵和测量阀。因为只有元件的参数将改变，一般结构是固定的。这意味着缸筒的直径可能改变，但确切的只有个一缸那样工作（如图1所示）这个液压系统其余部分是不同的，在这篇文章中使用一泵的负载传感系统如图所示。但在开始设计阶段还有其他的想法必须评估。例如在回转运动中使用两泵或单泵。根据实际元件设计的全面的模型会大得多。通常在初始设计阶段的开始

10、不适用。它能由液压程序库中的元件建立起来，但需要相当多的时间，这在工程的开始是行不通的。在表格1和2中所示的是LS控制器执行的方程式。一般，联合体模型选择使用图形模型分解或通过方程式定义模型。但不是在一样的模型标准上混合两种描述形式。 对于LS系统这是不同的。因为它有7个输入信号和5个输出信号，建立带有17个输入和5个输出的块。并把它们连接到液压回路。但是，在这种情况下，如上面液压回路，在一样的标准上直接提供方程式并直接输入输入信号和输出信号，看起来更加可以理解。例如，格中“”是测量孔metoril的通口的度量压力。LS控制器的计算值。例如，泵流体速率“pump.inport.signal1=

11、” 是在泵元件的蓝色矩形中的信号。图12。Modelica的重点是三维机械程序库和非标准的无缝连接。并且，因此在没程序库可用时，控制系统的模型很容易的处理。程序库元件在目标图表中能连接起来，根据模型的本文能得到所需的各种变化。8.仿真结果使用Modelica模型和仿真环境Dymola建立完全模型，并转换，编译和模拟5秒钟，仿真时间17秒，使用一个1.8Ghz笔记本上相对误差10-6级的DASSI综合器（比真实时间满3.4倍），Dymola的仿真特点使用可能在几乎真实的情况下观察运动，即使相对于非专家。这也有助于解释结果。看图9。图13给出了三个缸和摇摆的相关信号，泵流体速率和压力从t=1.1秒

12、到t=1.7秒和t=3.6秒到t=4.05秒。泵以最高流速工作。从t=3.1秒到t=3.6秒达到最高允许压力。图14给出了斗杆缸和铲斗缸的位置和摇动角度。能看出在另一个运动开始或结束时，活塞的运动没有重大的改变。控制系统减少油缸之间的耦合，这种耦合在单路控制中特别严重。图15给出铲斗缸的操作。上面数据显示参考轨道，也就是方向阀的开启中间数据，表示补偿器的传导系数。两钉道是例外，从t = 0秒开到t = 1 s 秒，这表示在这段间隔的时间里，泵压力由铲斗缸控制。它从t=0秒后，斗杆缸需要一个相对高的压力，铲斗补偿器因此增加阻力。下面数据表明流体速率控制工作良好。即使存在一个严重的扰乱。带有小误差

13、的要求的流体速率有铲斗缸供足。9. 结论建立一个挖掘机的动力模型以评估不同的液压回路。它包括厢体三维机构的完整模型。包括动臂，斗杆，铲斗和像泵和缸等标准液压元件。控制系统不是在组件基础上的模拟，而是通过一系列非线性方程描述。使用Modelica的联合体程序库，液压程序库Hylib和一系列具体应用方程，模拟了系统。通过工具Dymola，系统得以建成并且短时间内测试。使得能计算所需的油路来评估控制系统。Dymola仿真特性，使得有可能在几乎真实的情况下观看运动。即使对非转泵，这也有助于解释结果。Multi-Domain Simulation:Mechanics and Hydraulics of

14、an ExcavatorAbstractIt 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 “load sensing” controller. Usually, models containing 3-dimensional mechanical and hydr

15、aulic 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. IntroductionThe design of a new product requires a number of decisions in the initial phase that severely affect the success of the finished machine.

16、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 comp

17、onents 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 i

18、s 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 “forc

19、e 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 “load sensing” control system is used, modeled by a set of simple equations. This approach gives the

20、 required results and keeps the time needed for analyzing the problem on a reasonable level. 2. Modeling ChoicesThere 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 i

21、nformation, 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

22、 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 de

23、sign 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 min

24、imum 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 HyL

25、ib (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 “load sensing” controller. 3. Construction of ExcavatorsIn Figure 1 a schematic drawing of a typical excavator under consideration

26、 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 Diese

27、l 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.Figure 2 shows that the required pressures in the cylinders depend

28、 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

29、 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. Both figures demonstrate that a simulation model must take in

30、to 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 SystemExcavators have typically one Diesel engine, two hydraulic motors and three cylinders. Th

31、ere 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. A

32、s 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 hi

33、gher 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

34、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

35、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 thu

36、s 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.

37、Nikolaus 1994). 5. The Hydraulics Library HyLibThe (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 obtaine

38、d 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

39、 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

40、 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 t

41、he 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 oi

42、l 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 programme

43、d 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 connected6. Library Components in Hydraulics CircuitThe composition diagram in Fi

44、gure 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.

45、 The input signals, i.e., the reference signals of the driver of the excavator, are given by tables, i.e. the reference value for the flow rate. From the mechanical part of the excavator only the components are shown in Figure 12 that are directly coupled with hydraulic elements, such as line force

46、elements to which the hydraulic cylinders are attached. 7. Model of LS ControlFor 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 chan

47、ged, 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

48、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 beha

49、vior 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

50、 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 t

51、o 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 th

52、is 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

53、 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

54、 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.8. Some Simulation ResultsThe complete model was built using the Modelica m

55、odeling 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 po

56、ssible 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