Schematically, the process of modeling a multicomponent mechanical system (MMS) in EULER can be divided into the stages shown in Figure 1. Let's consider these steps in more detail.

Fig. 1. The basic stages of modeling MMS with EULER.

1.Initial system.

The object of the analysis carried out with the help of EULER is a technical or other structure that can be represented in the form of MMS. Such a multicomponent mechanical system must exist either in real form, in the form of a project, or in the imagination of the user.

2.Formation of the initial data and the concept of the model

The success of analysis primarily depends on the representation of the original mechanical system, that is, the concept of an idealized model. This stage of the process is performed before working with EULER. However, the researcher who creates the concept of an idealized model must imagine the possibilities of the software package. From the experience of the researcher and understanding of the degree of influence of various factors on the behavior of the initial mechanical system, the correct choice between the accuracy of the model being created and the complexity of its description depends.

First of all, the user must decide from which links the model of the initial mechanical system will consist and with which joints these links are connected. Links are the bodies from which a mechanical system is formed. The joint, or kinematic assembly, is a mobile connection of several links.

In the EULER, the MMS bodies can be either rigid or deformable bodies. If during research it is necessary to take into account the possibility of deformation of some integral structure, for example, the wing of an airplane or a car frame, then this can be done in one of two ways:

  1. Divide the elastic structure into a series of rigid links connected by joints and power elements simulating the elastic properties of the structure.
  2. Set the elastic structure with a deformable link based on the elastic body model created by the finite element method.

The masses of the source system must be spread over the bodies of its model.

The types of joints in the model must be chosen so that they provide all the necessary body movements in the original system. At the same time, it is necessary to avoid the addition of unnecessary joints for the study and to minimize the number of links as much as possible. The EULER software complex supports a wide range of possible types of joints. Their rational choice facilitates the solution of this problem. Fulfillment of these requirements allows to reduce the total calculation time.

Further, to form an idealized model, it is necessary to pick out all the active forces that affect the movement of the original system. These include the elasticity of springs, the damping forces of shock absorbers, the driving forces and forces of resistance to movement, the forces of action on the links of the external environment. All active forces should be described in the model in the form of force elements. And for them it is necessary to prepare the corresponding initial data.

When modeling some mechanical systems, it is sometimes necessary to organize control over them in the process of motion. Sensors and software movements must be created in EULER to model the control channels. Sensors are used to generate and convert control signals. Programmatic movements create controlling force effects in the model of a mechanical system. They, for example, can determine the change of one sensor depending on another in accordance with the specified function - the motion program.

When modeling relatively simple mechanical systems, the first and second stages can actually be combined with the third and fourth stages - the formation of geometric and dynamic models. In this case, the user simply describes the source system in terms of EULER.

3. Forming a geometric model

At this stage, work begins directly in the EULER software. The geometric model is the basis for constructing the dynamic model of the MMS. The geometric model allows visualizing a mechanical system. According to it, mass-inertial characteristics of parts of the system are calculated in the EULER. Geometric objects are used when specifying kinematic constraints, force effects and other objects of the dynamic model of the system. To create a geometric model, the following types of objects are used: point, vector, node, plane, line, surface, road, solid. It should be noted that the image of parts (links) of a mechanical system in the form of a set of points, lines or bodies is not mandatory. However, it is very convenient for the formation of the model, and especially for research, because it allows you to observe the process of motion of the system on the screen.

4. Formation of a dynamic model

The ability to create a dynamic model of the MMS differs in principle from EULER from computer-aided design systems intended for geometric modeling. The dynamic model is described in clear engineering terms. For this, the following types of objects are used: a body, a joint, a force element, a sensor, a motion, a change of mechanism, an event, a condition condition of the mechanism (condition ), gravitational attraction (gravity) and other types of objects.

The separation of steps 3 and 4 is conditional. In fact, the creation of geometric objects can alternate with the generation of MMC dynamic representation objects.

5. Automatic generation of a mathematical model

The formation of a mathematical model is performed automatically in EULER, without the direct involvement of the user.

The mathematical model is a system of algebraic and differential equations. It is formed in a nonlinear formulation with the assumption of large displacements of links. For all characteristics describing behavior, control and force effects in a mathematical model, their non-linear nature is taken into account.

6.System Research

The study of MMS is understood as carrying out the calculations necessary for the user. During the research, the user can observe the behavior of the mechanical system in special interface windows. In these windows, a wireframe or real (with clipping of invisible lines and halftone coloring of surfaces) is displayed graphical representation of the system. Simultaneously with the graphical representation in the windows, you can display graphs and numerical values ??of various parameters of the motion of the mechanical system. To save the results of the study, special files of the EULER software package are used, as well as files of various formats of the Windows system. In addition, images of the appearance of MMS and graphics can be printed on the printer.

When researching complex mechanical systems, it is necessary to check the accuracy of the generated model. This is especially true for those types of systems that the user did not previously have to model. The most reliable estimate of the accuracy of the model can be obtained by comparing the behavior of a real system with the results of mathematical modeling. The unsatisfactory accuracy of the model means that when designing an idealized model, the user has neglected the factors important for describing the behavior of the original system, or has simplified the model too much. In this case, it is necessary to modernize the idealized model. An important advantage of the software complex EULER, manifested in this situation, is the possibility to expand the model under study. Thanks to which the researcher can quickly complement the existing model taking into account new factors.


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