Научная статья на тему 'Application of finite elements within the nodal myltlbody dynamic simulation software complex PA7'

Application of finite elements within the nodal myltlbody dynamic simulation software complex PA7 Текст научной статьи по специальности «Компьютерные и информационные науки»

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Аннотация научной статьи по компьютерным и информационным наукам, автор научной работы — Mezentsev A. A.

The attitude with Finite Elements approach utilization for elaboration of mathematical models (MM) of 3D bodies, undergoing large displacements, for PA7 node method multibody dynamic simulation software is described. The results of SLIMFEA model creation, depicting the properties of massive rigid/deformable slider with various number of mountaining points, are presented.

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Текст научной работы на тему «Application of finite elements within the nodal myltlbody dynamic simulation software complex PA7»

Полученные соотношения позволяют оценить значение пе следующим образом. При просмотре карты поверхности на экране дисплея можно указать некоторое среднее значение стороны квадрата просмотра, при котором обеспечивается необходимый уровень разрешения. Эта величина определяется реальными размерами объектов на карте и не зависит от числа образующих их примитивов. Например, как показал экспериментальный анализ, просмотр планшетов масштаба 1:500 реализуется квадратом со стороной 10 см, что составляет 50 м на земной поверхности.

Пусть имеется общая карта с числом примитивов Р0. Рассмотрим применительно к ней соотношение (1). Можно получить, что минимум рассматриваемого выражения имеет место при

Пусть исходная карта охватывает площадь поверхности 5. Разделив ее на N частей в соответствии с (3), получим размер квадрата элемента карты

и полагая (1=(1(1ор , в соответствии с приведенными выше соотношениями из модели определяем пе.

Может оказаться, что неравенство (2) не имеет решений в действительных числах при заданной величине Р В этом случае необходимо решить следующую задачу имеется карта , содержащая Р примитивов , необходимо представить ее в виде совокупности М подкарт с числом примитивов р1 , 1е[1,М] , для каждого из которых неравенство (2) имеет решение в действительных числах Решение этой задачи приводит к построению поискового дерева , с помощью которого пользователь ГИС будет выбирать требуемую подкарту Здесь следует учитывать смысловое содержание карты : подкарта может представлять один или несколько слоев коммуникаций , район административного деления , область однородного ландшафта, экологическую зону и т.д.

В целом , таким образом , представление сложной карты в ГИС выполняется на двух логических уровнях верхний связан со смысловой структурой карты , нижний - с механизмом ее хранения в сервере локальной сети ЭВМ Полученные соотношения позволяют с единых позиций проводить декомпозицию карты , обеспечивая эффективное сочетание навигационного поиска и физического доступа к информации.

YflK 658.512

Andrei A. Mezentsev Application of FINITE ELEMENTS within the nodal myltibody dynamic simulation software complex PA7.

ABSTRACT: The attitude with Finite Elements approach utilization for elaboration of mathematical models (MM) of 3D bodies, undergoing large displacements, for PA7 node method multibody dynamic simulation software is described. The results of

(3)

Считая, что

L=M = jp = jN,

Ш

SLIMFEA model creation, depicting the properties of massive rigid/deformable slider with various number of mountaining points, are presented.

It is known, that application of mitibody dynamic simulation in the design of machinery improves productivity of the design process and leads directly to the creation of concurrent engineering environment, which is considered to be the major way of CAD/CAE/CAM development [1] .-The application of software prototyping is especially important for spheres of machinebuilding, where physical prototyping is impossible due to its cost or hazard [1,3]. The creation and testing of the physical prototypes for unique mylticrank sheet cutting presses is extremely expensive and" timely consuming; that is why Voronez Heavy Presses plant (Central Russia) for years is successfully applying software complexes PAS and PA7 [4], using the popular node attitude for automatic generation of MM of multibody objects, mainly of mechanical nature. The solution of dynamic and inverse dynamic tasks for the systems with positive degrees of freedom, represented in form of ordinary differential equations (ODE) systems, is carried out by application of numeric methods (Runge-Kutta, Adams, etc.) and finally reported in form of graphics and animations [3,4].

Special library of MM for presses' parts and units was elaborated in Moscow State Technical University [4], thus permitting application of PA7 at the Voronez plant by rank-and-file engineers. During that work some major attitudes for elaboration of MM for presses' elements were formulated, including rather interesting solution for application of Finite/Super Elements Analysis technic for creation complicated models such as 3D sliders of four crank presses.

Many programs of multibody dynamics can solve the tasks of liner elastic bodies, subjected to large displacements, either by direct including some finite elements, beams as a rule, or by interface with FEA software complexes [1,5]. The problem with PA7 modeling software is, that it uses specific, but efficient attitude for converting equations of motion to explicit second order ODE systems (and not mixed differential -algebraic equations as in popular DADS program [5]) on base of introducing constraints on the structure of component equations. Studying the applied methods, ref.[3] expressed concern about efficiency of direct application of FEA methods within the programs, using the similar node attitudes.

Let us discuss, how we modeled solid deformable slider for two-crank press. The described model SLIMFEA2 is the realization of direct finite element attitude. The model is based as per [2] on calculation of node forces and coefficients of conductivity with concluding the conductivity matrix, containing the following coefficients:

Vector of node coordinates as a result of slider's force interaction in the system of

(1)

The scheme of the model is presented at Fig. 1. The following main vectors are considered:

U,

press: TJ =

;(2)

Full vector of node coordinates as a result of slider's force interaction in the system of

u,

press, received by integration of node velocities: 5st =

;(3)

where g =

Si

g6.

Ц.

gl

g6

- vector of generalized slider coordinates as a body

SLIMFEA »

Fig. 1.

The model's algorithm is as following:

1) The full node velocities vector V(l) is integrated with final obtaining vector of node displacements формула 5lt(3) within the integration step limits;

2) New current meanings for the node coordinates are:

3=5 +3;t;(4)

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where 5 is the initial values of node coordinates or the values on the previous step;

3) Increment of node coordinates of the slider as a result of it's movement, hereinafter

refereed to as a, can be presented as a =[-<4]g;(5) where g as per (3) and [A] is

kinematic matrix of the slider, which can be as follows: [A] =

A s

Ль в

;(6)

and each matrixes element Ay is the displacement of slider at the direction of i-coordinate (i==l,18) upon the displacement for the j generalized coordinates (j==l,6). The matrix (6) depends on dimension parameters of the modeled slider.

4) Full increment of node coordinates within the integration step limits as a result of sliders displacement as a body under the effect of g and its force interaction in the system

of press 5 =

'ie_

= {U + a);(7) Thus, S can be obtained.

5) Calculation of the full accumulated node coordinates vector 5^(8), understood as sum of displacement on current step and displacement on the previous successful step Sq ;

“51

+ 3W8)

:is ;I9

lAf

where vector S consists of node coordinates U and generalized coordinates g vectors as in (8). So g vector can be calculated from Sat.

6) Definition of forces vector in kinematic nodes as result of S deformation:

Fs=[R]S,and Fs =

A8,

;(9) where R • slider's stiffness matrix;

7) Calculation of forces projections on generalized coordinates g: Fg =

Conductivities are as stipulated in (1).

Definition of conductivity matrix of the slider which is appearing as:

1819

24

18

19

R im

5T '’V'l; ft: " T ;* im tf-:

-[APP1

where R is the same as in (9).

The described algorithm was realized in the SLIMFEA2 and SLIMFEA4 MM for PA7 node dynamic simulation software, which showed suitable applicability for simulation of multicrank presses' accuracy.

Special four-crank sheet cutting press KA4037 for production of large dimension panels is depicted at fig. 2, the results of it's mathematical simulation using the PA7 complex and described model of slider SLIMFEA4. The problems of that press were low accuracy, so it was important to use the MM of it's slider, which could depict the properties of 3D body very accurately.

PA7 simulation results for press' parameters during it's working cycle without loading, giving the forces in connecting rods (FNI-4), angles of slider rotation during movement (yox- yov) differences in vertical displacements of points on slider (DD14,DD12) down surface. The mechanism of press has initial errors in the details of slider-crank group and the influence of such errors on output accuracy was studied. This example shows the possibilities of described MM SLIMFEA4 together with others forming the MM of press with 137 degrees of freedom.

Due to solving of the problem as above, formulated in [4,7] opinion on impossibility of real application of major FEA attitudes to models within the PA7 software because of overcomplicated resulted models and slow solving of obtained set of ODE, becomes rather controversial. So, FEA attitude can probably be recommended for other matrix-topological node method based dynamic modeling software complexes as well.

MAIN CONCLUSIONS.

The described FEA attitude shows desirable efficiency,the algorithm can simply be implemented for various dynamic modeling software on base of node methods and can be recommended for creation of 3D MM of various machinery units.

References.

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1. Concurrent Engineering: tools and technologies for mechanical systems design/Proc. of NATO advanced study institution on concurrent engineering tools and technologies for Mechanical system design. May 25 - June 5 1992, Iowa/Ed. by Haug E.J., -Berlin et all: Springer, 1993. -998 p.:ill.

2. Galager R. Finite elements method. Foundations. -1977: Sringer-Verlag 1977. -428p.

3. CAD/CAE systems. In 9 books./Ed. 1. P. Norenkov. - Moscow: Highest School publishers, 1986. -633p. (in Russian).

4. E. Scladchicov, An. Vlasov, An. Mezentsev. ADVANCED ATTITUDE TO THE DYNAMIC SIMULATION AS A STAGE IN CAD OF FORGING EQUIPMENT//ADVANCES IN COMPUTER SCIENCE APPLICATION TO THE MACHINERY. -Beijing:IAP, 1991. AP.293-300.

5. DADS User's Manual Rev. 7.5 Computer Aided Design Software inc., Corp. Headquarters, 2651 Crosspark Road, 1993.

УДК 51.001.57

С.В.Астанин Автоматные модели поведения стратегического управления

Решение многих интеллектуальных эадач является не одномоментным актом, а процессом. При этом достижение цели осуществляется посредством последовательной реализации множества подцелей, связанных между собой временем, последовательностью либо приоритетом выполнения. К таким задачам, в частности, относятся задачи управления организационными системами, задачи реализации проекта, задачи управления разработками НИР, задачи управления военными операциями и т.д. Особенностью моделирования подобных задач

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