GB2055169A - Compression spring particularly for use in vertical seismometers - Google Patents

Abstract

A compression spring, particularly for use in a vertical seismometer, which comprises two end members 6, 7 between which extend two arms each in the form of a respective leaf spring 4, 5. Each leaf spring includes two rigid sections 8, and is prestressed to take up, in its unstressed condition, the shape shown in Figure 3A. In the invention, the spring is constrained to take up the "lazy tongs" configuration shown in Figure 3B, in which condition the spring exhibits a negative rate, in that pressure P applied to the upper end member 7 results, as the spring is compressed, in a decreasing spring thrust. <IMAGE>

Description

SPECIFICATION Compression spring particularly for use in vertical seismometers This invention relates to compression springs particularly, but not exclusively, for use in vertical seismometers, and to a vertical seismometer incor porating such a spring.

Seismometers are instruments designed for the detection of small movements of the ground, the basic principle being that a mass is supported on a system of elastic members which distort when the mounting frame responds to the earth movement.

Output is derived from a transducer which senses the relative velocity or displacement betwen the mass and the frame.

A property common to all such instruments is that the mass will execute free oscillations if momentarily displaced from its equilibrium position when the frame is at rest. The natural period of these oscillations depends on the ratio of the spring stiffness to the suspended mass. The relative displacement between the mass and frame which results from earth motion of any given amplitude is reduced if the period of the earth motion is longer than the period of free osciliation of the mass. It is therefore important to ensure that the free period of the suspended mass is not too short in relation to the longest period of ground oscillation which is of interest.

If the suspension is designed to allow horizontal relative motion between mass and frame, the lower limit to the stiffness is set largely by the requirement to provide adequately robust construction. If vertical movement is envisaged, there is a further requirement to provide enough "lift" to supportthe mass against the force of gravity, and suitable periods of oscillation tend to conflict with the need to accommodate the extended lifting spring within a reasonably small housing.

There have been a number of historical solutions to this problem, of which a famous example due to La Coste utilises a "zero-length spring" combined with the variable geometry of a hinged boom to produce almost perfect neutral equilibrium. This, however, suffers from the disadvantage that the over-wound coil spring which is an inherant part of the design introduces undesirable cross-coupling between short-period transverse vibrations of the ground, and the desired long-period vertical motion.

An invention of the present applicant described in British Patent No. 968,299 overcame the problem of cross-coupling in a system which approximated to the La Coste performance, and two other inventions (British patents numbered 980,496 and 1,442,297 have been applied together in a more recent generation of seismometers. These, however, involve complexities in construction or introduce constraints on the minimum size of practicable embodiments which it now seems possible and desirable to circumvent.

During the last few years, the requirement for a very compact, inexpensive and high-performance system has been strengthened by the realisation that much better recording conditions can be found in boreholes than those which exist anywhere on the surface of the earth. As small holes are much less expensive to drill than larger ones of the same depth, seismometers of the smallest possible diameter bring considerable economic advantages. The seismometer of the present application may be readily adapted to meet this requirement, as an instrument having a total diameter of 50 mm. or less would be practicable.

In accordance with the invention there is provided a compression spring comprising two end members respectively defining the ends of the spring, and two arms each being pivotally attached at one end to one of said end members and at the other end to the other of said end members, each arm comprising a pair of substantially rigid levers pivotally connected together by means of a respective pre-stressed spring hinge, the arrangement being such that the spring thrust as exerted between said end members decreases as the spring is compressed by bringing together said end members.

If the spring of this invention is used to support the mass element of a vertical seismometer, the "negative rate" of the spring will have the effect of exerting, on the mass element, an upward force which decreases as the mass moves downwards, thereby offsetting the normal positive stiffness of the suspension.

In a practical form of the invention, each of said arms takes the form of a sheet of resilient material in the form of a leaf spring attached at one end to one of said end members and at the other end to the other of said end members. Each of said levers is constituted by a respective section of each of said leaf springs which has been rendered relatively rigid.

In a preferred embodiment, each rigid section comprises a length of said spring whose edges are turned up to form a channel cross section so as to provide axial rigidity.

The theory of the invention together with an embodiment thereof will now be described by way of example only and with reference to the accompanying drawings in which: Figures 1A and IB are diagrammatic views of a pin jointed framework for explaining the operation of the spring of this invention; Figure 2 is a plot of bending moment against the angular position of the framework of Figure 1; Figures 3A and 3B are views equivalent to Figures 1A and 1 B respectively, showing a practical embodiment of the spring; Figure 4shows, in enlarged detail, part of the spring of Figure 3; Figure 5 is a plan view of one of the leaf springs making up the spring of Figure 3; and Figure 6 is a side elevation of one embodiment of a seismometer according to the invention.

Reference is firstly made to Figures 1 and 2 in order to explain the approximate theory of the invention. Consider a pin-jointed frame work (Figure 1A) of four levers 1 in which each of the six pin joints incorporates a spring (not shown), whose moment about the pin is proportional to its angular deflection 6, relative to a fixed axis from an initially unstressed condition in which 6 = - 6o. Now assume thatthe linkage is put into its operating condition by pushing the working arms past the condition 6 = 0 into the working condition 6 = 61, shown in Figure 1 B, in which the application of a thrust P on a horizontal platform 3 tends to increase 6. The interaction of forces and bending moments is illustrated in Figure 2, in which the line A-B represents the linear increase in bending moment as the levers 1 are deflected, and the sinusoidal segments OP, OP2, OP3 represent the moments about any one of the pin joints 2 of constant forces P1, P2 or P3 for various values of 6. If the force P1 is sufficiently small, the positive segment of the sine wave will lie entirely below the line AB, and the springs will force the levers 1 through the position 6 = 0 into an equilibrium position represented by point C.With the somewhat greater thrust P2 which makes the sine wave tangential to the line AB, the point of contact D will represent a metastable position of zero rate. With still larger thrust P3, the point E will represent a condition of unstable equilibrium, in which the axial thrust arising from spring moment will increase as the angle 6 decreases and the framework extends. The resulting "negative rate" of the spring framework can be adjusted so as to cancel the positive stiffness of other elastic elements which may be used to constrain a mass attached to the platform 3, so that the desired combination of a robust framework with low resistance to axial displacement can be achieved.

In practice, pin-jointed hinges are unsuited as elements which can respond to the minute forces which exist in seismometry, and elasticflexure pivots provide an acceptable alternative. One could reproduce the linkage of the four levers by using short flat springs at the corners, but this would have the disadvantage of requiring the necessary elastic energy to be stored in a rather small part of the total volume of the system. A preferred arrangement is to make the system from two flat sheets of flexible material cut to a shape such as to distribute the working stress through a much largervolume, subject to some stiffening (which turns out to be a stability requirement) between sections of opposite curvature.

Asuitable design forthe spring is shown in Figures 3A and 3B. The spring comprises two leaf springs 4, 5 attached at their respective bottom ends to a base member 6 and at their top ends to a platform 7. The stiffening referred to above is constituted by relatively rigid sections 8 positioned between spring sections of opposite curvature. The leaf springs 4,5 are mutually displaced in a direction at right angles to the drawing in order to allow the springs to be crossed over; as shown in Figure 3B.

A plan view of one of the leaf springs 4 or 5 is shown in Figure 5. The dotted lines show the necessary outline shape of the leaf, as dictated by theory (see later). The rigid sections 8 take the form of wider sections whose axially-extending edges 20 are bent up to form a trough-like cross-section.

Uniform stress distribution can be developed in a leaf spring if the deformation from the unstressed to a working position can be represented by deformation of the leaf from one circular form to another.

Given, then, that the working sections of the final spring configuration should be made up entirely of circular arcs, we need to devise a form for the leaves which enables this working condition to be derived from an unstressed condition (as shown in Figure 3A) in which the working sections are also circular arcs. We can see the condition more clearly in the geometry of Figure 4, which represents the form of one quarter of one of the two leaf springs 4 or 5. In Figure 4, it should be noted that the theory to be described applies strictly to the leaf spring in the unstable form, without the stiffening sections 8, in other words as represented by the dotted line 9.

Referring to Figure 4, the axial force P/2 applied to each spring produces no bending moment at the point of inflection A. At any other point B, the bending moment is Pr Pr P12.r(1 -cos62- 1 2 (coski-cos61) where r is the radius of curvature. As the length x measured along the leaf from the clamped end is r, we can obtain the desired distribution of bending moment by making the width of each leaf spring proportional to (cos x/r - 6), as shown by the curved parts of the outline, and their dotted extensions, in Figure 5. Slight perturbations in the relation between the initial and final forms of the elastica can either be tolerated in the final form, or compensated by adjustments to the initial form.It now requires the insertion only of the proper scale dimensions in the initial flat spring, and in the form which will produce the stress-free profile of Figure 3 by appropriate heat treatment, to produce a spring which, when set up in the form of Figure 3B will fit required design parameters for the force P, and the rate dP/dz.

Figure 6 shows the use of the above-described spring in a complete seismometer. The seismometer comprises a cylindrical mounting tube 10 which may be of small diameter, for example 50 mm, in order to enable its use in narrow boreholes. The tube 10 is closed at the top by a tubular frame 11 and at the bottom by a base plate 12. On the base plate 12 is mounted a negative rate spring comprising two leaf springs of the type shown in Figure 5 arranged as described above in relation to Figure 3. Since Figure 6 is a sectional view, only one of the leaf springs (referenced 5) is visible.

The upper ends of the two leaf springs are mounted on a fixing plate 19 which is itself attached to a mass element 13. The mass element 13 is mainly situated within the frame 11, but its upper end is provided with a hollow former 14 carrying a coil of wire. A magnet 15 carried by an end cap 16 extends into the hollow interior of former 14 so that, when electric current is passed through the coil, a lifting force to counteract the effect of the mass element 13, is provided. The end cap 16 is itself attached to a top plate 17 which closes the top of the frame 11.

The mass element 13 is suspended within the frame 11 by means of suspension spokes 18 and suspension clamps 21 in such a way as to leave a small air gap 22 between itself and the lower face of the top plate 17. This air gap is used to form a capacitance transducer so that the axial position of the mass element within the framework 11 can be detected.

Claims (10)

1. A compression spring comprising two end members respectively defining the ends of the spring, and two arms each being pivotally attached at one end to one of said end members and at the other end to the other of said end members, each arm comprising a pair of substantially rigid levers pivotally connected together by means of a respective pre-stressed spring hinge, the arrangement being such that the spring thrust as exerted between said end members decreases as the spring is compressed by bringing together said end members.

2. A compression spring as claimed in claim 1 wherein said spring hinges are pre-stressed in such a manner that, in its stress-free state, the spring takes up a shape in which the two arms bow outwards away from one another, but wherein the spring is constrained to take up a shape in which the arms cross over one another in the manner of a lazy tongs.

3. A compression spring as claimed in either one of claims 1 or 2 wherein each of said arms takes the form of a sheet of resilient material in the form of a leaf spring attached at one end to one of said end members and at the other end to the other of said end members, and wherein each of said levers is constituted by a respective section of each of said leaf springs which has been rendered relatively rigid.

4. A compression spring as claimed in claim 3 wherein each rigid section comprises a length of said spring whose edges are turned up to form a channel cross section so as to provide axial rigidity.

5. A compression spring as claimed in either one of claims 3 or 4 wherein the shape of the outside contour of each of said leaf springs is such that, over the non-rigid sections, the width of the leaf is proportional to: x cos-- cos o where x = the length measured along the leaf spring from one of the end members; r = the radius of curvature of the spring; and 6 = the angle between respective levers of each arm.

6. A compression spring as claimed in any one of claims 3, 4 or 5 wherein the rigid sections of each leaf spring constitute approximately half the total length of each spring.

7. A compression spring substantially as hereinbefore described with reference to the accompanying drawings.

8. Avertical seismometercomprising a hollow body, a mass element suspended under the force of gravity within said body, a transducer for providing a signal representative of the movement of said mass element within the body and a compression spring as claimed in any one of the preceding claims positioned within said body to support said mass eiement.

9. A vertical seismometer as claimed in claim 8 wherein said body is generally cylindrical in shape.

10. A vertical seismometer substantially as hereinbefore described with reference to Figure 6 of the accompanying drawings.