Study of Stresses in Plane Models of Pressure-Gauge Spring Sections by the Photoelastic Method

G. I. Tyzhnov, N. A. Shumskaya

(Presented by the scientific seminar of the Department of Strength of Materials)

1. The principal part of a technical pressure gauge is the tubular spring, which determines the main metrological characteristics of the instrument. In turn, such important characteristics of the spring as creep, the proportional limit, and sensitivity depend on the magnitude of the stresses. As far as we know, not a single experiment has yet been carried out to determine the stresses in pressure-gauge springs, and therefore theoretical studies [1], [2] have still not been verified.

The only explanation for this circumstance is the very small size of tubular springs.

Previous experiments on the study of stresses on strain-gauge models (see the article in the present collection) showed that the predominant stresses are \(\sigma_2\), whose direction is perpendicular to the axis of the tube. The stresses \(\sigma_1\), parallel to the axis of the spring, are passive, and their magnitude may be taken as approximately equal to \(\mu \sigma_2\).

However, it was not possible to study the stress state completely on strain-gauge models because of the presence of small-radius curves, where strain gauges could not be bonded.

As a supplement to these studies, it was decided to employ the optical method as well. The stress state of the spring material is three-dimensional, but experimental study on three-dimensional models is a rather complicated problem, and therefore in investigations one most often confines oneself to considering a plane model of the part. Such a study, of course, will not be exact; however, for a comparative assessment of the stresses in plane sections of springs of various shapes, this method gives sufficiently reliable results with a minimal expenditure of time.

1. The investigations were carried out on the instructional polarization apparatus PU-1 of TPI, designed by the authors. In this apparatus, an epidiascope with a mercury lamp was used as the illuminator. Between the condenser and the Polaroid there is a light-and-heat filter, which is a rectangular glass vessel filled with a saturated solution of nickel nitrate.

Polaroids 50 mm in diameter serve as the polarizer and analyzer. The polarizer is located at the focus of the condenser, and the analyzer is placed in front of the camera lens; both can be rotated in mounts with degree graduations marked on them. The “quarter-wave” plates, measuring \(50 \times 50\) mm, are made of mica. Their thickness is 0.028 mm. To increase the illumination, a lens is installed in front of the model.

The photographing part consists of a \(13 \times 18\) camera with a long-focus lens. When the ground glass is removed, the image of the model can be projected onto a screen with fivefold magnification.

A disadvantage of such an arrangement is that the bundle of rays passing through the model is not parallel, but conical. The cone angle is determined by the size of the model and the distance to the lens. However, illumination of the model by either a parallel or a converging beam of light does not affect the quality of the fringe image. In practice, nonparallelism of the rays up to \(3^\circ\) has no effect on the accuracy of measurement and only in two cases can lead to an error of up to 2%: when investigating a plane stress state of the hydrostatic type (the zero order of fringes has a large sum of principal stresses) and when investigating zones of high stress gradients [3].

In accordance with the above, when it is necessary to obtain greater accuracy, the model is moved so that the point under investigation is located on the axis of the optical system.

The installation described is very simple and can be made without great expense in any educational institution.

1. Models of the sections of pressure-gauge springs were made of ED6-M epoxy resin. The scale adopted for the manufacture of the models was \(10 : 1\), with the model thickness equal to 5.6 mm. The fringe value was determined by compressing a disk and was found to be \(9.2\ \text{kg}/\text{cm}^2\).

To bring the loading conditions of the plane model closer to the conditions under which pressure-gauge springs operate, a special loading device was designed (Fig. 1), in which the pressure is transmitted through branch pipe 6 to the inner contour of model 3 by means of rubber tube 2. The model is placed with a small clearance between two plates 4 of organic glass, which are fastened to metal strip 1 by screws 5.

Fig. 1.

1. From models of two forms of spring sections used in pressure gauges, isochromatic patterns were recorded at the same pressure (Figs. 2 and 3). To determine the magnitude of stress concentration

Fig. 2.

Fig. 3.

the places with the densest arrangement of fringes were photographed with magnification.

From the data of the fringe patterns, diagrams of the stress distribution along the outer and inner contours of the models were constructed, and the relative magnitude of the stresses was calculated for the most highly stressed points of both sections (Fig. 4). The signs of the stresses were not taken into account.

The coefficients obtained were determined as the ratio of the stress at a given point to the magnitude of the stress at point \(K\), conventionally taken to be equal to unity.

Fig. 4.

1. On the basis of the investigations carried out, the following conclusions may be drawn.

In a comparative study of the stressed state of pressure-gauge springs, it is advisable to use the optical method, which gives a clear visual picture. This method may prove especially useful in selecting the most advantageous shape of the spring section. As is known, the magnitude of the uncoiling of a tubular spring depends on the deformation of its section. Therefore, by transmitting polarized light through the models and measuring the deformation of the minor axis (the amount of “bulging”), one can obtain a comparative assessment of the sections under investigation with respect to stresses and deformations.

Studies of two section shapes showed that the stresses in a spring of segment-shaped section are distributed more nonuniformly than in a spring of flat-oval section (Fig. 4). If in the first case the conditional coefficient of nonuniformity is equal to \(3.66 : 0.48 = 7.6\), then in the second it is equal to \(2.06 : 0.95 = 2.16\). The greatest increase in stresses is observed at the ends of the major axes.

Pressure-gauge springs with a segment-shaped cross section should not be manufactured; a better form is the flat-oval one.

The cross section of the spring is usually obtained by flattening a tube. As the minor axis is reduced, the displacement of the end of the spring increases, but at the same time the magnitude of the stresses also increases. The problem of finding the most optimal amount of flattening is most easily solved likewise by means of the optical method.

REFERENCES

1. V. I. Feodos'ev. Elastic Elements of Precision Instrument Engineering. Oborongiz, 1949.

2. Prospects for the Development of Elastic Sensitive Elements. Collection, TsINTI, Moscow, 1961.

3. K. Fink and H. Rohrbach. Measurement of Stresses and Deformations. Mashgiz, 1961.