活塞连杆机构的外文及翻译.doc

Modeling and Simulation of the Dynamics of Crankshaft-
Connecting Rod-Piston-Cylinder Mechanism and a Universal Joint Using The Bond Graph Approach
Abstract
This paper deals with modeling and simulation of the dynamics of two commonly used mechanisms, (1) the Crankshaft – Connecting rod – Piston – Cylinder 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 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 simulation directly from the Bond Graph without deriving system equations,and so on.
Keywords: Bond Graph, Modeling, Simulation, Mechanisms.
1 Modeling
Dynamics of two commonly used mechanisms, (1) the Crankshaft – Connecting rod – Piston – Cylinder system,and (2) the Universal Joint system, are modeled and 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, depiction 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 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 nature of constraint [3-5]. Both translational and rotational couplings for joints are developed and integrated with the dynamics of the connecting links. A problem of differential causality at link joints arises while modeling. This is rectified using additional stiffness and damping elements. It makes the model more realistic, bringing in effects of compliance and dissipation at joints, within definable tolerance limits.Multibond Graph models for the Crankshaft – Connecting rod – Piston – Cylinder system, and, the Universal Joint system [6], are developed using the BondGraph Approach. Reference frames are fixed on each rigid link of the mechanisms using the Denavit-Hartenberg convention [7]. 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 respective center of mass, and expressed in the inertial frame. The multibond graph is then causaled and coding
in 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 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.

1.1 Crankshaft - Connecting Rod - Piston-Cylinder Mechanism
Fig. 1 shows the sketch of the “Crankshaft – Connecting rod – Piston – Cylinder system.”

Fig. 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 second 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. C1, C2 and 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. The left side of the bond graph shows the rotational part and right part shows the translational part. We restrict any motion between the origin of inertial frame O and point on the link 1 that is O1 by applying source of flow Sf as zero. Similarly we restrict any relative motion at point A, distinguished by A1 on link 1 and A2 on link 2, by applying source of flow Sf as zero. The piston which is link 3, is constrained to translate only along the X0 direction. Translation along Y0 and Z0 direction is constrained by applying source of flow Sf as zero for these components. Differential causality is eliminated by making the K(1,1) element of the stiffness matrix [K] between link 2 and link 3 as zero.
Additional 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 have 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 – Cylinder system of Fig. 1.
1.2 Universal Joint Mechanism
The Fig. 3 shows the sketch 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 0,and it is fixed. Frame 1 is on link 1, frame 2 on 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 - A1 on link 1 and A2 on link 2, and B - B1 on link 1 and B2 on link 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 direction 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 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 motion 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 allow 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 direction

2 Simulation
The results of computer simulation for the crankshaft mechanism of Fig. 1 are discussed first. The initial position of the crankshaft is at 1 θ = 60o with the X0 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 this paper. The upper row in Fig. 5 shows the displacement of the centre of mass C1, 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 crankshaft
about the Z0 axis through change in orientation of the unit vectors of Frame 1. The second figure in the second row shows the oscillation of the centre of mass C1 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 constant 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 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.

3 Conclusions
The 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 system. 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 system equations, have been explained in this work. MATLAB based simulations have been presented and interpreted for both the systems.

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
本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，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与旋转的动态图形表示，表示与约束节点处理，描述的因果关系，在不同的位置获取动态反应的机理力与力矩，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，进行了建模与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与旋转的动态图形表示，因果关系，描述表示与约束缝隙处理，在不同的位置获取机制动态反应力与力矩，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，我们开发与应用一个多元图模型的每一个环节都要翻译与刚体的转动。环节进行耦合基于约束[3-5]自然关节。平移与旋转接头的开发与集成的动态连接。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与阻尼元件。它使模型更逼真，使合规与耗散在关节的影响，定义在公差范围内。多元图模型的曲轴连杆活塞–––缸系统，与万向接头系统[ 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Denavit-Hartenberg公约[ 7 ]。翻译的影响主要集中在质量中心的每个刚性连接。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。一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。一架固定在每一个环节。因此，框架1固定链接1，框架2与框架3上连接2，连接3。一个固定的惯性坐标系0，其起源与1帧被选择。然而，它既不旋转也没有翻译。C1，C2与C3是各环节质量中心。该框架固定在各自的链接采用Denavit-Hartenberg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与右侧部分显示平移部分。我们限制任何运动的惯性帧O点起源之间的链路上的流量是1，O1 SF应用源为零。同样，我们限制在任何点的相对运动，由A1与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与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[k]之间的联系2与链接3元为零。
附加的刚度与阻尼元件用于消除微分因果关系，使模型更逼真，使合规与耗散在关节的影响，定义的公差范围内。这些粘弹性元件中的键合图用C与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。

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轭，旋转轴与中间一个是交叉连接。惯性帧编号为0，它是固定的。1帧是1帧2连接，在十字架上，连接2与3帧，右边的轭是链接3。惯性坐标系的原点重合的链接1 1机架。链接1与2在两个重合点相互连接的链接1与A2链接2 - A1点，与B - B1与B2链接1链接2。同样的联系2与3连接在两个点D - D2与D3链接2链接3，与E - E2与E3链接2链接3。
链接1绕Z轴相对于惯性帧。框架2位于2链路质量中心。链接2相对于方向Z2，如图3所示的链接1转动。3帧也恰逢框架2但它位于链接2。框架3连杆3相对于链接2，关于Z3转动，如图3所示。这个系统的键合图如图4所示。。

图4：为万向节多元图系统图
该机构还有微分因果关系出现的问题。它是使用额外的刚度与阻尼元件消除。如前面所讨论的，这使模型更逼真，使合规与耗散在关节的影响，定义在公差范围内。在节点的链接之间的相对运动，沿着一定的方向，运用流SF源为零的约束。约束松弛是通过改变刚度值与相应的关节阻尼调整。在这里，我们限制的链接3在两个方向上运动的Y与Z，并允许通过解决三个部分流源在x方向的运动，将SF为零，Y与Z方向。对于仿真，励磁转矩施加链接1关于Z方向
2模拟
首先对图1的曲轴机构的计算机仿真结果进行了讨论。曲轴的初始位置是在1θ= 60o与X0轴。然后，在重力的作用下释放。重力也作用于连杆。由于气体压力没有力考虑为仿真不是主要问题，本文的焦点。观察图5中的上行显示的质量中心位移C1在0帧的表达。它移动到Z0轴圆弧。在图5的下行的第一个图显示了曲轴的振动通过对1帧的单位矢量方向变化。在第二排第二个数字表明C1中心随时间振荡。这也许可以归因于非线性造成的耦合与连杆。
为万向接头系统的仿真结果如表8所示。恒转矩被施加到驱动轴的轴。使驱动轴与驱动轴的轴线成 5° 角度。第一行显示驱动轴的第一环节的响应。角动量的驱动轴的轴线呈线性增加的成分，这是预料之中的。第二行的前两个数字显示的横方向的变化，这是链接2。所有三个轴的角运动是清晰可见的。驱动轴的驱动轴的运动：从图8中的第三行是明确的。

3结论
键合图的方法是使用两个常用机构动力学模型，（1）曲轴连杆活塞–––缸系统，及（2）万向接头系统。对惯性系的机构各环节的平移与旋转的动态图形表示，表示与约束节点处理，因果关系的描述编码进行了仿真，直接从键合图没有导出系统方程，一直在这工作了。基于MATLAB的仿真结果进行介绍与解释的系统。

出处：
http://www.nacomm09.ammindia.org/NaCoMM-2009/nacomm09_final_pap/DVAM/DVAMAV3 .pdf