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1、畢業(yè)設(shè)計(jì)(論文)報(bào)告紙共 頁 第 1 頁┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ 裝 ┊ ┊ ┊ ┊ ┊ 訂 ┊ ┊ ┊ ┊ ┊ 線 ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊Multi-Domain Simulation:Mechanics and Hydraulics of an Excavator AbstractIt is demonstrated how to model and simulat

2、e 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

3、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. IntroductionThe design of a new product requires

4、 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

5、 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 dif

6、ficult 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

7、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 especia

8、lly 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,

9、 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 r

10、equired 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

11、 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 wel

12、l 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

13、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

14、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 comp

15、onents. 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

16、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.

17、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 ne

18、xt version of HyLib. 3. Construction of ExcavatorsIn 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 manoeu

19、vre 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, th

20、e 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 cylind

21、ers.畢業(yè)設(shè)計(jì)(論文)報(bào)告紙共 頁 第 3 頁┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ 裝 ┊ ┊ ┊ ┊ ┊ 訂 ┊ ┊ ┊ ┊ ┊ 線 ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊orientation of the attachment points of the “l(fā)eft” and “right” revolute joints of the jointRRR component are kn

22、own. 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 analyt

23、ically 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 p

24、erformed 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 spri

25、ngs 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 t

26、he 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 tu

27、rn 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 adaptation

28、s) 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 c

29、olor) 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 visual

30、ly, 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

31、 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

32、 data could be utilized for the animation, but this was not available for the examination of this excavator. 6. The Hydraulics Library HyLibThe (commercial) Modelica library HyLib (Beater 2000, HyLib 2003) is used to m

33、odel 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 o

34、f 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 co

35、mponents 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 consi

36、dered 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

37、 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

38、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 hierarch

39、ically. 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 resi

40、stance 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 th

41、e 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 CircuitThe comp

42、osition 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

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