Omarov Kazbek Altynsarovich, Dr. of engineering  sciences., professor, Kungurov Aslan Rahmetullayevich, Candidate of engineering sciences., docent (PhD doctor)

(Astana  city, Eurasian National University named by Gumilyov L.N ),

(Almaty city, KazNTU named by Satpayev K. I.)

 

DETERMINATION THE OPTIMAL MODEL OF BRAKE MECHANISMS

         

 

As is known, the task of optimal designing in the traditional formulation reduces to the generalized task of nonlinear programming:

it’s necessary to determine the optimal parameters =, which extremalize the function of object

extn F=F                                                                           (1)

where closed area  define as follows:

               :                                                                                                            

Here – description of model behavior in the form of equations; - functional constraints on a model behavior;  - constants; - boundaries of parameter variations.

Numerous works are devoted to the decision of the given task. The result of the decision depends as on the task area    and, in particular, restrictions [1], and from the search method .

It should be noted that at the stage of outline design of brake mechanisms such a statement of the problem in most cases is unacceptable: no information on the reasoned purpose of constants ;

The area of the task parameters is often significantly more than area of defining models;

due to the lack of data on the possibilities of projected demand model , applicable to the projected model, are contradictory; no clear idea of ​​what should be considered functional limitations, and what is the quality criteria, etc..

Lack of information on projected model of brake mechanism and the impossibility of complete formalization of requirements essentially led to the fact that in most cases, the projector refuses to solving the problem of mathematical programming [1]÷ [3].

Let's consider a new approach [1,4] to determine the optimal model of brake mechanism, based on the analysis of the parameter space and making decisions based on the results of this analysis.

Requirements for the projected model of brake mechanism, defined as  of functional limitations. Last should be divided into two groups:of functional limitations, which constants  assign "tough" and their variation is unacceptable;   functional limitations, which constants  can be in some field of admittance (as by constructive reasons, and by standard data ). This admittance field sets in some cases, and in other cases is determined only by solving the task.

It should be noted that in the first and second cases, the choice of the constants is not a priori realized, to solve the task.

Consider the way to solve formalized task determining the optimal model of brake mechanism.

1.    functional limitations transmitted to quality criteria:

                                                                                                (5)

2.  – dimensional space  by functional limitations  it is probed by uniformly distributed sequence of points  as the projector on the stage of outline designing does not give preference to any part of the space [4].

3. In each point  identifying all object functions , where , and selected  models , satisfying functional limitations.

4. Based on the analysis  models of quality criteria are transmitted into the category of restrictions that should be called criterial constraints:

                                                                                            (6)                                                  

  or

 

               ,                                                                                    (7)

 

where  - boundaries of permissible values of quality criteria, defined by projector on the analysis basis  models of brake mechanisms.

5. Analyzed the multitude, consist of  brake mechanisms models, simultaneously satisfy all criterial constraints. From a given set by integral estimates determines the optimal model of brake mechanism.

For the analysis of a set consisting of  brake mechanism models, introduced two types of complementary comparative evaluations denoted respectively  and . Estimations   characterize the models in terms of their proximity to the best result for each criteria (assume that all criteria should be minimized). For calculation  used ratio

                                                                          (8)

where  - the smallest value,  - from all obtained from the calculations; it belongs to one of the  models, for . It should be noted that the same model is generally not the best on all counts ; therefore, in order to find a compromise variant  must be set admittance for deviation  îò (or  îò 1) , hereinafter referred to as criterial admittance and designated . We believe that  brake mechanism models simultaneously satisfy all conditions (7)

                                                          (9)

Complex criterion  is used as an integrated estimation  for brake mechanism models by all quality criteria

                                                                       (10)

where  – Moisture coefficient

In the case, when =1

   

where .

          The set   always has a lower limit ; the brake mechanism model should have such estimation, in which all the criteria are minimal. Consequently, because of the antagonism of the criteria .

The optimal model of  brake mechanism  on the set  models is as follows:

                                                                                                      (11)

If there is information about the moisture coefficients  of optimal model of a brake mechanism corresponds an estimation

                                                                                            (12)

Constructive formation depending  finally depends on concrete requirements, required to projected brake mechanism models and its related to operations research sphere [3].

In case, if any of brake mechanism models doesn't meet requirements, it makes decision on increase number of tests, changes in formulation of the task or on transition to other block scheme of a brake mechanism.

Conclusions.

         Statement of optimal projecting task of  brake mechanism on the stage of outline projecting in most cases is unacceptable. The proposed approach to the determination of the optimal model of the brake mechanism is based on the transition from a one-criterion nonlinear programming task to the multicriteria task. The algorithm of the decision includes research of space parameters, introduction criterial restrictions and an estimation of models by complex (integrated) criteria.

 

 

Literature

1.         I. I. Artobolevsky, M.D Genkin, G.V. Kreinin and etc. Search of compromise decision in choosing the machine parameters.- DAN , USSR, 1984, t.218, ¹ 1, p. 78-82.

2.         A. I. Birger. Strength analysis.- M: Mechanical Engineering, 1986, 340 p.

3.         Y.B. Germeyer.  Introduction to operations research theory. - M., Science, 1981, 287 p.

4.         I. M. Sobol, R. B. Statnikov LP- search and optimal design / / Coll. "Problems of random search - Riga: Knowledge, ¹ 1, 1992, 28-33 p.