曲轴连杆活塞机构及使用键合图法的万向联轴器的动力学仿真建模-外文翻译

1、modeling and simulation of the dynamics of crankshaft-connecting rod-piston-cylinder mechanism and a universaljoint using the bond graph approachabstractthis paper deals with modeling and simulation of the dynamics of two commonly used mechanisms, (1) the crankshaft - connecting rod - piston - cylin

2、der system,and (2)the universal joint system, using the bond graph approach. this alternative method of for mulation of system dynamics, using bond graphs, offers a rich set of features that include, pictorial representation of the dynamics of translation and rotation for each link of the mechanism

3、in the inertial frame, representation and handling of constraints at joints, depiction of causality,obtaining dynamic reaction forces and moments at various locations in the mechanism, algorithmic derivation of system equations in the first order state-space or cause and effect form, coding for simu

4、lation directly from the bond graph without deriving system equations,and so on.keywords: bond graph, modeling, simulation, mechanisms.1 modelingdynamics of two commonly used mechanisms, (1) the crankshaft - connecting rod - piston - cylinder system,and (2) the universal joint system, are modeled an

5、d simulated using the bond graph approach. this alternative method of formulation of system dynamics, using bond graphs, offers a rich set of features 1, 2. these include, pictorial representation of the dynamics of translation and rotation for each link of the mechanism in the inertial frame, depic

6、tion of cause and effect relationship,representation and handling of constraints at joints, obtaining the dynamic reaction forces and moments at various locations in the mechanism, derivation of system equations in the first order state-space or cause and effect form, coding for simulation directly

7、from the bond graph without deriving system equations.usually the links of mechanisms are modeled as rigid bodies.in this work, we develop and apply a multibond graph model representing both translation and rotation of a rigid body for each link. the links are then coupled at joints based on the nat

8、ure of constraint 3-5. both translational and rotational couplings for joints are developed and integrated with the dynamics of the connectinglinks. a problem of differential causality at link joints arises while modeling. this is rectified using additional stiffness and damping elements. it makes t

9、he model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits.multibond graph models for the crankshaft 一 connecting rod 一piston 一 cylinder system, and, the universal joint system 6, are developed using the bondgraph approach. reference frame

10、s are fixed on each rigid link of the mechanisms using the denavit-hartenberg convention |7j. the translational effect is concentrated at the center of mass for each rigid link.rotational effect is considered in the inertial frame itself,by considering the inertia tensor for each link about its resp

11、ective center of mass, and expressed in the inertial frame. the multibond graph is then causaled and codingin matlab, for simulation, is carried out directly from the bond graph a sketch of the crankshaft mechanism is shown in fig. 1, and its multibond graph model is shown in fig.2. a sketch of the

12、universal joint system is shown in fig.3, and its multibond graph model is shown in fig.4. results obtained from simulation of the dynamics of these mechanisms are then presented.! crankshaft connecting rod piston-cylinder mechanism left side of the bond graph shows the rotational part and right par

13、t shows the translational part. we restrict any motion between the origin of inertial frame o and point on the link 1 that is 01 by applying source of flow sf as zero. similarly we restrict any relative motion at point a, distinguished by al on link 1 and a2 on link 2, by applying source of flow sf

14、as zero. the piston which is link 3, is constrained to translate only along the xo direction. translation along yo and zo direction is constrained by applying source of flow sf as zero for these components- differential causality is eliminated by making the k(1 j) element of the stiffness matrix k b

15、etween link 2 and link 3 as zero.fig. 1 shows thecylinder system. ”sketch of the “ crankshaft - connectingrod 一 piston甘2fig. 1: crankshaft-connecting rod-piston-cylinder mechanism.the individual components are considered as rigid links,connected at joints. the first moving link is the crank,the seco

16、nd link is the connecting rod and the third link is the piston. a frame is fixed on each link. thus frame 1 is fixed on link 1, frame 2 on link 2, and frame 3 on link 3. a fixed inertial frame 0, whose origin coincides with frame 1, is chosen. however, it will neither rotate nor translate. cl, c2 an

17、d c3 are centres of mass of respective links. the frames are fixed on respective links using the denavit-hartenberg convention 4.dynamics of the system of fig. 1 is modeled in the multibond graph shown in fig. 2. the model depicts rotation as well as translation for each link in the system. theaddit

18、ional stiffness and damping elements used for eliminating differential causality make the model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits. these viscoelastic elements are represented in the bond graph by using c and r elements.we h

19、ave a source of effort se at link 3, which is the pressure force acting on the piston, although this force is also acting only in x direction.fig. 2: multibond graph model for the crankshaft - connecting rod - piston 一 cylinder system of fig. 1.1.2 universal joint mechanismthe fig. 3 shows the sketc

20、h of the " universal joint" mechanism.fig. 3: universal joint mechanism.it has three rigid links, two are yokes which are attached to rotating shafts and the middle one is the cross connecting the two yokes. the inertial frame is numbered o.and it is fixed. frame 1 is on link 1, frame 2 on

21、 the cross which is link 2, and frame 3 on the right yoke which is link 3- origin of the inertial frame coincides with that of frame 1 of link 1. the links 1 and 2 are connected with each other at two coincident end points points a - al on link 1 and a2 on link 2, and b - bl on link 1 and b2 on link

22、 2. similarly links 2 and 3 are connected at two points d d2 on link 2 and d3 on link 3, and e e2 on link 2 and e3 on link 3.link 1 rotates about z axis with respect to the inertial frame. the frame 2 is located at the centre of mass of the link 2. link 2 rotates with respect to the link 1 in direct

23、ion z2 as shown in fig. 3. frame 3 also coincides with frame 2 but it is located on the link 2. the frame 3 on link 3 rotates with respect to the link 2, about z3, as shown in fig. 3. the bond graph for this system is shown in fig. 4.fig. 4: multibond graph for the universal joint system of fig.the

24、issue of differential causality arises for this mechanism also. it is eliminated using additional stiffness and damping elements. as discussed earlier, this makes the model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits. the relative mo

25、tion between the links at joints, along certain directions, is restrained by applying the source of flow sf as zero. the constraint relaxation is tuned by changing the values of stiffness and damping at corresponding joints. here we restrict the motion of the link 3 in two directions y and z, and al

26、low motion in x direction by resolving the source of flow in three parts and by putting sf as zero in y and z directions only. for the simulation, an excitation torque is applied to link 1 about the z direction2 simulationthe results of computer simulation for the crankshaft mechanism of fig. 1 are

27、discussed first. the initial position of the crankshaft is at 1 。= 60o with the xo axis. it is then released under the effect of gravity. the force of gravity also acts on the connecting rod. no force due to gas pressure is considered for the simulation as it is not the main issue under focus for th

28、is pape匚 the upper row in fig. 5 shows the displacement of the centre of mass cl, as observed and expressed in frame 0. it moves in a circular arc about the z0 axis. the first figure in the lower row of fig. 5 shows the oscillation of the crankshaftabout the z0 axis through change in orientation of

29、the unit vectors of frame 1. the second figure in the second row shows the oscillation of the centre of mass cl with time. this could perhaps be ascribed to the nonlinearity imposed due to coupling with the connecting rod.simulation results for the universal joint system are presented in fig. 8. a c

30、onstant torque is applied to the driving shaft about its axis. the driven shaft makes an angle of 5° with the axis of the driving shaft. the first row shows the response of the driving shaft which is the first link. the component of angular momentum of the driving shaft about its axis increases

31、 linearly, which is as expected. the first two figures of the second row show the change in orientation of the cross, which is link 2. angular motion about all three axes is clearly visible. the driven shaft follows the motion of the driver shaft as is clear from the third row in fig. 8.fig 5 respon

32、se m oti on of the crankshaftfig 6 response motion of the connecting rodfig 7: response motion of the pi st on3 conclusionsthe bond graph approach is used to model dynamics of two commonly used mechanisms, (1) the crankshaft - connecting rod - piston - cylinder system, and (2) the universal joint sy

33、stem. pictorial representation of the dynamics of translation and rotation for each link of the mechanism in the inertial frame,representation and handling of constraints at joints, depiction of cause and effect relationships, coding for simulation directly from the bond graph without deriving syste

34、m equations, have been explained in this work. matlab based simulations have been presented and interpreted for both the systems.ifilg toe f8 simulation results for the universal joint system曲轴连杆活塞机构及使用键合图法的万向联轴器的动力学仿真建模摘要木文论述了与常用的两种机制的动力学仿真模型，(1)曲轴连杆活塞-缸系 统，及(2)万向接头系统，使用的键合图方法。这种替代方法的系统动力学仿 真，采用键合图

35、，提供了丰富的功能集，包括，对惯性系的机构的各个环节的平 移和旋转的动态图形表示，表示和约束节点处理，描述的因果关系，在不同的位 置获取动态反应的机理力和力矩，算法的系统方程的推导在第一阶状态空间或因 果形式编码进行了仿真，直接从键合图没有导出系统方程，等等。关键词：键合图，建模，仿真，机制。1建模常用的两种机制的动态，(1)曲轴连杆活塞 缸系统，及(2)万向 接头系统，进行了建模和模拟使用的键合图方法。这个系统的动力学方程的替代 方法，采用键合图，提供了丰富的功能集1, 2。这些措施包括，对惯性系的 机构的各个环节的平移和旋转的动态图形表示，因果关系，描述表示和约束缝隙 处理，在不同的位置获

36、取机制动态反应力和力矩，系统方程的推导在第一阶段状 态对空间或原因形式及影响编码进行了仿真，没有直接从键合图导出系统方程。 通常机制的链接被建模为刚性体。在这项工作中，我们开发和应用一个多元图模型的每一个环节都要翻译 和刚体的转动。环节进行耦合基于约束3-5 b然关节。平移和旋转接头的开发 和集成的动态连接。在建模的时候连接接头是一个问题。这能纠正使用附加的刚 度和阻尼元件。它使模型更逼真，使合规和耗散在关节的影响，定义在公差范围 内。多元图模型的曲轴连杆活塞缸系统，和万向接头系统6 ,采用键 合图方法。每一刚性连接的机制参考框架固定在采用denavi thartenberg公约 7 。翻译的

37、影响主要集中在质量屮心的每个刚性连接。旋转效应是惯性框架 本身考虑，通过考虑每个环节对各自质心惯性张量，并在惯性坐标系的表达。然 后使多元图的编码在matlab中，仿真，进行直接从键合图。种曲轴机构示意 图如图所示，其多元图模型如图2所示。一种万向接头系统示意图如图3所示, 其多元图模型如图4所示。从这些机制的动力学仿真得到的结果。1.1曲轴-连杆-活塞缸机构图1显示了 “曲轴连杆活塞 缸系统示意。”单个组件被视为刚性连接，连接的接头。第一个移动连接曲柄，第二连杆是 连杆、第三连杆是活塞。一架固定在每一个坏节。因此，框架1固定链接1,框架 2和框架3上连接2,连接3。一个固定的惯性坐标系0,其

38、起源与1帧被选择。然而， 它%不旋转也没有翻译。cl, c2和c3是各环节质量中心。该框架固定在各自的链 接采用denavi thartenberg公约4 。图1的系统动力学是在图2所示的多元图模型。该模型描述了旋转以及在系统 中的每个环节的翻译。键合图的左边显示的转动部分和右侧部分显示平移部分。 我们限制任何运动的惯性帧0点起源之间的链路上的流量是1, 01 sf应用源为零。 同样，我们限制在任何点的相对运动，由a1和a2链接1链接2,通过流量sf应用源 为零。活塞是链接3,是约束沿x0方向。这些组件沿y0和z0方向翻译是受流sf应 用源为零。微分因果关系是使k消除（1,1）的刚度矩阵kz间的联系2和链接3 元为零。附加的刚度和阻尼元件用于消除微分因果关系，使模型更逼真，使合规和耗 散在关节的影响，定义的公差范围内。这些粘弹性元件中的键合图用c和r元素。我们有一个硒在链接3源，这是作用在活塞的压力，尽管这力量也只有在x 方向。sf：o图2：为曲轴连杆活塞 缸液压系统图1多元图模型。1.2万向节机构图3显示了素描的“万向节”机制。它有三个刚性连接，两个线圈被连接到两个觇，旋转轴与中间一个是交叉连接。 惯