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1、Modeling and Simulation of the Dynamics of Crankshaft-Connecting Rod-Piston-Cylinder Mechanism and a Universal Joint 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 Cylinder s
2、ystem,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 th
3、e 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 simulatio
4、n 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 and simulate
5、d 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 ca
6、use 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 B
7、ond 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 co
8、nstraint 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
9、 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 o
10、n 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 o
11、f 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 Universal joint
12、 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 MechanismFig. 1 shows the sketch of the “Crankshaft Connecting rod Piston Cylinder sys
13、tem.”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 fixe
14、d 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
15、 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 moti
16、on 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. D
