EULER’s simulation technology

Main steps of simulation

The process of simulation in EULER system can be represented as a sequence of steps as shown in next figure:

Initial system

Input data and model concepts

Forming geometric model

Forming dynamic model

Automated creation of mathematical model

System analysis

Initial system

EULER system performs analysis of technical or any other system which can be represented as MMS. This multi-component mechanical system should be real or designed or at least it should exist in user’s mind.

Input data and model concepts

The success of system analysis depends mostly on the presentation of the initial mechanical system, i.e. on the concepts of ideal model. This step is performed before the work with EULER started. However, the analyst creating the conception of ideal model must estimate the capabilities of EULER software system. A proper alternative of model accuracy and descriptive complexity depends on analyst’s experience and his or her understanding of different factors that affect the behavior of MMS.

Above all, the user must decide which bodies form the initial MMS and which joints connect them. Bodies are parts included into mechanical system. A joint or a kinematical node is a movable connection for several bodies.

In this version of EULER system the bodies may not be other than solids. If a possible deformation of some integral structure (e.g., a plane wing or a motor-car fender) is to be considered during analysis, this structure must be divided into bodies. In most general case, the bodies might be combined via joints or force elements.

The mass of initial system must be also distributed among the bodies of its model. We must remember that maximum detailed mass distribution (in case when each body has a nonzero mass) improves the accuracy of simulation. However, in this case the model grows more complicated and the calculation time increases.

Joint types for a model must be selected in such way that the joints are capable of providing all needed motions for solids in this system. At the same time the user must avoid adding superfluous joints; the user must make the number of bodies as small as possible. EULER system maintains a wide range of possible joint types. Selecting joint types rationally the user facilitates an easier solution for a task. If all these requirements are fulfilled the calculation time is reduced.

Next move to ideal model creation is determination of the active forces that influence initial system motion. These are force of elasticity, damping forces of shock-absorbers, moving forces and forces of tractive resistance, forces of medium that influence the bodies. All the active forces must be described as force elements in the system. The corresponding input data must be prepared for all these forces.

Sometimes mechanical systems must be controlled during their motion simulation. EULER provides a possibility of simulating control channels via sensors, actuators and motions. Sensors are used for forming and conversing controlling signals. Actuators create controlling forces in MMS model. Motions are used for making system model motion description. For example, they can determine the change of a sensor depending on another sensor in accordance with given function which simulate the motion program.

Due to mighty facilities of EULER software system the 1st and the 2nd steps can be easily joined with the 3rd and the 4th ones that include geometric and dynamic models forming. In this case the user can just describe the initial system in EULER terms.

Forming geometric model

This step starts real work with EULER software. The geometric model serves as a basis for dynamic model creation. The geometric model provides a visual image of the mechanical system. EULER uses it for the calculation of mass-inertial properties of the system elements. Geometric objects are used for determination of kinematical connections, force effects and other parts of MMS dynamic model. The following types of objects are used for the creation of geometric model: points, vectors, nodes, planes, lines, surfaces, solids. We must note that representing the MMS elements (bodies) as a set of points, lines and solids is not obligatory. However, it is useful for forming the model; especially it is convenient while performing analysis because the analyst is able to observe all the motions on the display.

Forming dynamic model

The ability to create a dynamic model of MMS is the main advantage of EULER software in comparison with automated design systems that perform geometric simulation. The dynamic model is described in clear technical terms. The following object types are used: bodies, joints, force elements, actuators, sensors, motions, events, conditions, mechanism reform, gravity and others.

The 3rd and the 4th steps are divided synthetically. In fact, geometric objects creation can take turns with creation of dynamic model elements.

Automated creation of mathematical model

Mathematical model is formed by EULER system automatically.

Initially, the topological analysis of MMS structure is performed for this step. During analysis the closed kinematical sequences are discovered and operative kinematical sequences are formed. After that equations sets are generated. Kinematical sequences are determined according to the results of analytical model optimization. This approach substantially decreases the volume of calculations.

Then, EULER system generates sets of equations that describe the motion of MMS being analyzed. These are equations:

• of bodies motion;
• of kinematical connections of the MMS (for closed kinematical sequences);
• of holonomic and non-holonomic connections in joints;
• of motions (control channels).

Mathematical model is a set of algebraic and differential equations. It is formed in nonlinear statement of problem considering bodies coarse transfers. When describing behavior, control and forces, the mathematical model pays attention to nonlinear origin of all the system properties.

System analysis

MMS analysis is interpreted as a complex of user required calculations. While the analysis is being performed the user can observe the system behavior through specially designed interface windows. These windows show skeleton or real (invisible lines are cut; surfaces are painted in halftones) graphic image of MMS. Along with the image the plots and the values of different parameters can be displayed in these windows. The analysis results are saved in EULER specific files and MS Windows files of different formats. Besides, the MMS graphic representation and the plots can be printed.

During analysis of a complicated system the accuracy of created model must be tested. It has particular importance for system types the user has to analyze for the first time. The most reliable estimate of model accuracy is made by comparison of real system behavior to the results of mathematical simulation. The fact that the model is unreliable means that important aspects of initial system behavior description were dropped when forming the ideal model; or that the model was built too simple. In this case the model must be updated. EULER has an important advantage which works in such situation; the ideal model in EULER can be extended. Due to this fact the analyst can efficiently complete existing model considering new conditions.

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