Optimal design of nonferrous corrugated diaphragms.

Negoescu, Florin ; Iosub, Adrian ; Axinte, Eugen 等

1. INTRODUCTION

Regarding the construction of the measure appliances, we affirm, that because the property of corrugated diaphragms to measure the value of inflection at relative small efforts, as elastic elements, those are used in top technological areas, such as aero-spatial industry, military industry, control and automation for industrials process. Applicable areas for that type of diaphragm are large, so that the modest enumeration for contrivances in which construction are used, may contain some tenthly appliances and are include example part of the most variety technical fields, beginning with the regulators of temperature used at hatcheries and end with measure indicators of high and speed of airplanes. It is important to remark the fact that, the diaphragms may also be used as separating tool between two medias and for elastic tightens, allowed the transmission of movement from medias with pressure or vacuum.

2. EXPERIMENTAL SETUP AND RESEARCHES

2.1 Targets and the problem statement

The main objectives and targets of this theoretic and experimental research are:

1. Establishing the influence of geometrical parameters on the value of the arrow of deformation's diaphragms under the action of pressure

2. Determination of the influence of diaphragm geometrical parameters on the linear characteristics and establishing the effects of the facts and the interactions of those

3. The experimental validation of theoretic data.

2.2 The actually stage of researches

The advantage of those diaphragms, are (Negoescu et al., 2002): characteristics closer to linear, sow a shorter variation for effective surface; give possibilities for designer to adopt easy the characteristics of some given dates; bigger sensitivity give possibilities to keep constant effective surface of the diaphragm when centre of the diaphragm are moving along to plan in which are the diaphragm situated; biggest arrows without appearance of permanent deformations, the characteristic by simply modifying the height H of the undulations.

(in Fig.1 is shown an example of a corrugated diaphragm)

[FIGURE 1 OMITTED]

In the design of corrugated diaphragms, designer it is interested not only by the size of deformation, but also by the linearity of relation between deformations--pressure. Although that linearity of the relation is useful on all area, that thing it is right only for certain portion of that. Pursuant to SAMA Standard (Scientific Apparatus Makers Association), who is affiliated at Instrument Society of America, usually it is measured at an non-linearity and experimented as linearity; represent the maximum deviation between the obtained curve and a straight line. Principal problem clung of studying the corrugated diaphragm it is the determination of the principal characteristics, witch mean to determine a relation between the arrow or deformation "W" and the force or pressure "P" witch product her, in the case of given form of corrugate.

W = f(P) (1)

Is one of the most important base parameters of the analytical and elastic diaphragms the characteristic of elastic diaphragms can be express, according the action load, by a relation as (1), and the graphic representation of characteristic can be linear, call constant or non-linear. Some of those elastic diaphragms presenter a linear characteristic only on a certain part linear areas, specific to the corrugate metallic diaphragms depending on geometrical parameters whence characterized it is necessary the following resources.

In choosing the materials destination to execute the elastic diaphragms have to be taken in consider all the facts which characterize operating system (request of the material, work medium, the behavior of the material and eventually change in time of some of those characteristics), the possibilities of supply, the character of production.

2.3 About the design of our experiment

For this paper, the planning and drive the experiments he accomplished taking count of a series of appearances considerate accepted on world plans. To the matrix construction used the experiment with notation Yates (-1, accordingly the inferior level of a respective factor + 1, of superior level of a factor) her originality consist in the fact as the permits the procurement directly the general formula ale of average effects, carry is calculated totalized the all answers of the experiences, preciously of the signs of the factors from each experience and divide the total in number attempts effectuate (Pillet, 1992; Alexis, 1999 & Vigier, 1993).

For the qualitative of a determination sizes on experimental path he accomplished a number finite of experimentations with a sufficient accuracy, maintaining same conditions of menstruation. The gathering of the date and the statistical their remaking he achieved taking count of the general valid methods and using specific programs of computer (Negoescu et all, 2002)

To accomplish the porpoise objectives was betake to realize the tests pursuant to the requests of factorial orthogonal complete experiment at two levels, such [2.sup.n] ([2.sup.4] = 16 tests).

The experiments had place for each combination of those two level, for those four independent variables take in consideration (the active diameter of diaphragm D, the thickness of material h, the amplitude of corrugated H and the number of those n), as the table 1.

For the quantification of the admeasurements on the experimental path, are shall accomplished a number finite of measurements with a sufficient accuracy maintaining same conditions of measuring (Kenett, & Shelemayu ,1998). Established most probable value of moderate size, carry estimates the true value is shall utilized the law of natural repartition, and the accuracy of measuring shall be evaluate of the average quadratic his error the standard error.

When the linearity is big (or non-linearity is low) the relation signal out--signal in can be consider a straight line, and so the sensibility can be consider constant. On the other hand, when the linearity is low, (or the non-linearity is big) the sensibility depend by the in--signal. Prosecution of the experiments take place pursuant to the matrix of experiments which was presented in table 2.

2.4 The new mathematic model

The results obtained are expressed in figure 2

[FIGURE 2 OMITTED]

By analyzing the graph from figure 2 is certain a very good preachment between the values determinate experimental (measured) and the theoretical ones so, in consequently, the values are low, fact which evidence the low influence of interactions on answer.

3. RESULTS, DISCUSSIONS AND NEXT STEPS

The target for the experiment is to find a optimal configuration for a set of facts taking analyze, configuration which are lead to maximize the elastic deformation it is recommends for independent facts that type of matrix D = [1 0], H = [1 0], h = [1 0]. It can be told that the rigidity of the diaphragm grow if the diameter and the thickness of the materials have small values, and the amplitude of corrugates grow, in time to sensibility of diaphragm for same value at the mentioned parameters go low. So is confirmed the fact that sensibility became low in the same time with growing the rigidity.

The optimization of metallic corrugated diaphragms, is adverted to touch the maximum technical performances, only that satisfy the concomitance the all criteria enforced is difficult, sometimes just impossible, because one factors can be antagonistic his subjective. With all these an optimum design is admissible and she assure to obtain the maximum performances, in certain conditions.

4. ACKNOWLEDGEMENTS to the Romanian Ministry of Education, Research and Youth & CNCSIS .This paper is financed by Research Grant type AT code 28.

5. REFERENCES

Alexis, J. (1999) Metoda Taguchi in practica industrials, (Taguchi Method in Industrial Practice) Editura Tehnica, ISBN 9975-63-176-x Bucuresti; Romania

Kenett,R & Shelemayu,Z (1998) Modern Industrial Statistics ,Brooks & Cole, ISBN 0-534-35370-3,Pacific Grove CA-USA,

Negoescu, F., Braha V.& Nagit, Gh. (2002), Membrane metalice ondulate--Elemente de proiectare si tehnologii de fabricare.( Metallic Corugated Diaphragms-Design and manufacturing) Editura Tehnica-Info, ISBN 9975-63-1762, Chisinau;

Pillet, M. (1992), Introduction aux plans d'experiences par la methode Taguchi. Les Editions d'Organizations, ISBN 9975-63-176-2, Paris,;

Vigier, M. (1993), Pratique des plans d'experiences. Methodologie Taguchi. Les Editions D'Organizations, ISBN 9975-63-176-2 Paris.

Table 1. The factors and levels of test

 The The factor Level 1 Level 2 Unit of
symbol of test gauge
 -1 +1

 D The diameter's 60 43 mm
 diaphragm

 h The thickness 0,06 0,12 mm
 of material

 H The amplitude's 0,52 0,87 mm
 corrugated

 n The number's 6 4 --
 corrugated

Table 2. The experimental matrix

 The Factors Elastic
 Pressure Deformation
 D H h n [bar] [mm]

1 -1 -1 -1 -1 0,12 1,98
2 -1 -1 -1 +1 0,12 0,98
3 -1 -1 +1 -1 0,12 1,84
4 -1 -1 +1 +1 0,12 0,78
5 -1 +1 -1 -1 0,12 1,84
6 -1 +1 -1 +1 0,12 0,87
7 -1 +1 +1 -1 0,12 1,68
8 -1 +1 +1 +1 0,12 0,6
9 +1 -1 -1 -1 0,12 0,83
10 +1 -1 -1 +1 0,12 0,32
11 +1 -1 +1 -1 0,12 0,41
12 +1 -1 +1 +1 0,12 0,16
13 +1 +1 -1 -1 0,12 0,88
14 +1 +1 -1 +1 0,12 0,33
15 +1 +1 +1 -1 0,12 0,45
16 +1 +1 +1 +1 0,12 0,17