Torsion Link

This invention relates to mechanical torsion link structures and in particular to torsion links which comprise a composite of elastomeric materials in combination with other materials such as metal.

In the past many structures have been devised which incorporate elastomeric materials in combination with various metal configurations to provide useful bearing or coupling structures for a wide variety of applications.

Of particular interest have been the structures proposed for use in helicopter rotor root designs due to the severe requirements of such use. In particular patents such as U.S. Pat. Nos. 4,142,833; 3,690,639; 3,750,249; 4,037,988 and 3,787,102. The patents disclosed and discussed therein provide an excellent review of some of the efforts to provide mechanical elements to function as bearings or linkages in helicopter applications. Further structures disclosed in this art include the use of laminated metal straps, plates, rubber or rubber and metal composite belts and the like as well as filaments and filament bundles embedded in a wide variety of elastomeric materials.

As described further in the hereinbefore identified patent literature and others, the initial experiences with elastomeric bearing designs have been somewhat disappointing. The thorough and well reasoned analysis of these early results and the extensive study of the applied forces and their resultant effect were applied almost exclusively to designs which employed metal reinforcing in the form of longitudinal or helically wound strips embedded in elastomer, or cylindrical structures in various configurations which seemed to address the problems encountered only from the point of view of reinforcement of the elastomer.

The prior devices utilizing as they did reinforced elastomeric materials encountered many drawbacks, some of which are detailed in the aforementioned patents. The prior reliance on the properties of the elastomer as modified by the incorporation of reinforcing materials is believed to be one of the principal reason for the results obtained.

It is therefore an objective of the present invention to provide a new mechanical element incorporating metal elements and elastomer which overcome some of the previously encountered problems.

It is a further object of the present invention to provide a new mechanical element which is suitable for a wide variety of design applications. Another object of this invention is to provide a mechanical or structural element that is resilient to twisting moments about one of three mutually perpendicular axes while being relatively resistant to deformations or displacements due to other forces or moments acting along or about other axes.

The prior problems have been eliminated by providing a plurality of differing cross-sectional sizes of open sections of metal nested or arrayed together in a manner which provides interstitial space between the sections. Elastomeric material is then incorporated into these spaces. When constructed according to this invention with retaining rings as further described hereinafter the novel mechanical element of this invention will, when properly mounted, meet all of the function requirements encountered by torsion links for an extremely wide variety of applications including helicopter rotor root assemblies.

The invention will now be described, by way of example, with reference to the accompanying drawings, in which:

FIG. 1 is a partially broken perspective view of one embodiment of the elastomeric torsion link of the present invention.

FIG. 2 is a side elevational view of the elastomeric torsion link of FIG. 1.

FIG. 3 is a cross-sectional view of the torsion link of FIG. 2 taken along the lines and arrows 3--3.

FIG. 4 is a cross-sectional view of the torsion link of FIG. 2 taken along the lines and arrows 4--4.

FIG. 5 is a pictoral perspective view graphically showing the forces and displacements that the torsion link of the present invention can encounter in use.

FIG. 6 is a pictorial perspective view of the distribution of distortion forces in a plane tangent to the surface of a circular open section.

FIG. 7 is a pictoral representation of the torsion link of the present invention utilized in a helicoptor rotor root design embodiment.

FIG. 8 is a pictorial representation of the torsion link of the present invention utilized in several motor car design embodiments, and

FIGS. 9 to 15 are graphs relating to characteristics of the torsion link.

In FIG. 1, the embodiment of the elastomeric torsion link 1 of the present invention is shown with cylindrical end caps 2 and 3 shown with fasteners 4, 5 and 6 in place. The concentric open sections 10, 11, 12, 13, 14, 15 and 16 are shown with the outermost sections broken so as to disclose the successive adjacent inner sections and the locations respectively of the openings or slits in open sections 10, 12, 14 and 16 designated as 10', 12', 14' and 16'. The darker shading in the spaces between concentric open sections is elastomer 20, which is shown filling the open space and the slits 10', 12, 14' and 16'. The respective relative locations of the slits on the open sections 11, 13 and 15 will be more clearly shown hereinafter. Likewise, it will be seen in the preferred embodiment shown, that the center of open section 16, designated as 18 is empty space. It can be filled with elastomer if necessary due to fabrication techniques or desirable for a particular application but is shown here as empty since it normally does not need to be filled. Further the elastomer 20 between the open sections need not be continuous as long as its function as described hereinafter is maintained in a given application.

FIG. 2 shows a side elevational view of the complete torsion link of FIG. 1. Here it can be seen that concentric tubular elements 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 and 40 are received on outermost open section 10 and spaced from each other so as to be independently displaced angularly during any twisting of the link where one end is fixed or otherwise angularly displaced in an opposite direction to the angular displacement imparted to the opposite end or to a lesser or greater angular displacement in the same direction. The size, position and relative spacing of the tubular elements can of course be varied depending on the particular design criteria, however, as will be more fully explained hereinafter the device shown in FIG. 2 demonstrates adherence to the principles applicable to this torsion link.

FIG. 3 is a cross-sectional view of the torsion link of FIG. 2 with the orientation of the slits 10', 12', 14', 16', 11', 13' and 15' shown where the even numbered slits are 180.degree. from the odd numbered slits. The open areas within outer tube 31 in FIG. 2 show where the elastomer 20 is located in this section. The outer tube 31 is also indicated. While again the elastomer torsion link of the present invention is shown in this embodiment with a specific slit orientation it is possible to pick almost any orientation as long as the function of the device is not impaired. For some applications with certain open section materials and wall thicknesses, when combined with specific elastomers, it can even be possible to have the slits of adjacent open sections aligned. Typically, it will be preferable to have some regular or random displacement of the slits of adjacent tubes so that they are not all aligned. The optimum locations will vary, however, the best locations can be obtained without undue experimentation for any given application.

FIG. 4 shows a cross-sectional view of another embodiment of the present invention where the space inside the innermost open section of the array contains a tube 60 similar to the tube 30 on the outside. As indicated previously there can be a multiplicity of these tubes spaced typically as shown or even smaller numbers than shown and even ultimately only one tube not fastened at either end to the end caps 2 or 3. It is preferred, also, to compliment the inside of the array at the end caps 2 and 3 with tubular members 61 and 62 for positive mechanical attachment of the fasteners 4, 5 and 6 and 7 for reasons more fully described hereinafter.

FIGS. 5 and 6 are graphical representations of the forces which ideally will act upon the torsion link of the present invention and will be related herein to the mathematical analysis required for understanding the suitability of a particular structure for the novel design applications it is capable of undertaking.

FIGS. 7 and 8 schematically represent applications where the torsion link of the present invention can be advantageously employed. For example, in the helicopter application shown in FIG. 7 the ability of the link to withstand substantial tension as well as transverse forces or two plane bending moments at the end affixed to a rotor blade makes this application particularly attractive and would greatly simplify existing structural designs for such equipment. Likewise, in the conceptual drawing of a motor car in FIG. 8 several torsion links are employed at various well known points to take advantage of the unique properties of this novel structural and mechanical element with the overall result that a simple, more reliable and extremely light structure could be provided.

The embodiments described for the new mechanical structure of the present invention show broadly how open section metal tubes i.e. having a longitudinal slit, can be assembled in a concentric array to achieve the objectives of the present invention as a flexible torsion link capable of flexure, to resist bending moments, tension, compression and transverse forces. These are properties normally not associated with open sections. Functionally this is achieved in a variety of ways depending on the particular application. For example, the elastomeric filling between the tubes helps resist the deformation normally associated with torsion and flexing an open section. Optionally further resistance to deformation can be provided with spaced sleeves encircling the torsion link which are mounted to be independant and unaffected by the twisting torques applied to the ends of the link. Further, in the embodiments shown, the mounts for the end of the link are designed to prevent lateral displacement of the tube ends which structure of necessity must cooperate with the elastomer and sleeves to achieve the novel effect of this element.

Many variables are present in the structure of the current device which must be considered when evaluating any particular design application. For example, the metal selected, the wall thickness of the open section, the width of the slit, the location of the slit for each adjacent concentric open section with respect to the location of the slit of the next adjacent open sections, the thickness of the space between concentric open sections to be completely or partially filled with elastomeric material, the properties of the elastomeric material itself in terms of manufacturing constraints, adhesion to the metal components, internal shear strength and the like must all be evaluated. Of course the overall outside dimensions of the link, the number of concentric open sections needed and the manner of mounting must also be considered.

The following theoretical analysis of the interaction of all these and other variables will give guidance to a designer in establishing how a specific structure must be made to satisfy specific criteria for any given application problem.

The following Table I of symbols and units will be applicable to the calculations shown.

Table II is a bibliography of the references whose theoretical analysis provide the foundations for the basic calculations required when approaching a given design problem utilizing the assumptions required herein.

In theory, if a thin walled open section is subjected to torsion, an induced tensile-compressive stress is generated. This stress can be calculated according to the following formula, where:

.sigma..sub.i is the induced axial stress (lb/in.sup.2); G is the shear modulus of slit tubes in (lb/in.sup.2); .theta. is the angular displacement (radians); t is the wall thickness (in); L is the length of the link or the distance between the innermost fasteners (in) and .nu. is Poisson's Ratio: ##EQU1##

This relationship shows that the induced axial stress is proportional to Saint Venant's shearing stress. Additionally even though the amplified shearing stresses are orthogonal to .sigma..sub.i both increase with increases in the wall thickness (t).

However, the second component of axial stresses, generated by external bending moments, decreases with wall thickness `t`, since in general, the flexural modulus is proportional to `t`.

For example, in the case of a thin-walled slit tube ##EQU2## From this, the principal stress whose components are .SIGMA..sigma. and .SIGMA..tau., will have minimum value when ##EQU3## By this condition an optimum wall thickness `t.sub.opt ` follows for which Rankine's theory of failure

is best satisfied.

The critical stress `.sigma..sub.crit ` of a thin-walled section is inversely proportional to the higher power of its aspect ratio (r/t).

However, the highest possible aspect ratios (r/t) are necessary to augment the flexural modulus. For example, the flexural modulus of a slit tube is proportional to the square of its aspect ratio: ##EQU4##

Since "total strain energy" and "shear strain energy" theories of failure are more restrictive than Rankine's, the optimum wall thickness expression is derived from a condition for minimum strain energy of a system subjected to simultaneous bending and torsion. ##EQU5##

Taking the fatigue limit or number of cycles till failure as a criterion, the second optimum thickness becomes: ##EQU6##

The optimum wall thickness may also be determined by the expression for principal stress: ##EQU7## in terms of the aspect ratio .sigma.p becomes: ##EQU8## If (r/t) and (.theta./L) are limited by elastic stability criteria and `N` selected, the thickness remains a primary variable.

By differentiating `.sigma..sub.p ` in respect to `t` and equating to zero: ##EQU9## Hence ##EQU10##

The best value of the wall thickness is interpolated between the ultimate principal and fatique optima.

Rotational displacement of one end through a given angular displacement requires a given twisting torque and together they define the torsional stiffness of the array by: ##EQU11##

Since an open section as defined herein is statically determinate, it has much lower torsional stiffness than a section with a continuous perimeter. Standard metals such as titanum, spring steel, aluminum alloys and the like can be employed in such an array of open sections, however, in using open sections alone, simply increasing wall thickness to prevent elastic instabilities is not feasible since the torsional stiffness is proportional to the third power of thickness. The onset of instabilities of an open section under stress can be expressed and solved by known differential equations. In the elastomeric torsion link of the present invention restraint against lateral deflections is also provided by the layers of elastomeric material between the tubes of the array. The layers will transmit compressive stress caused by radial amplitude advance at the initial stages of buckling, from one lamination to another until it reaches the outer and inner boundary segments. The boundary segments will balance this compressive stress by hoop tension, or, by the tensile stress due to radial precompression. Clearly then, the most preferred embodiments of the present invention would be provided with continuous elastomeric filler between the open sections of the link, in most applications. Some applications could use less than complete filling of the interstitial space between the open section. In addition, transverse deflections during bending, shearing, compressive or tensile loading can be completely suppressed by interactions between the layers and boundary segments. Also, bending moments applied to attachments are transmitted through the fasteners to the thin-walled tubes as shown in the drawings. While this design is capable of deconcentrating high local stress, the end boundary segments should typically be designed to have sufficient bearing area for adequate, gradual diffusion of externally applied bending moments to the tube sides relieving the stress at the fastener.

The torsional stiffness of the elastomeric torsion link of the present invention is proportional to the first power of its diameter. Conventional elastomeric bearings exhibit torsional stiffnesses proportional to higher powers of their outer diameters. Thus, relatively large angular displacements in conventional bearings are difficult to obtain, but can be obtained by the use of the torsion link of the present invention without hinderance from the normally low allowed shear strains of the materials currently available. This phenomenon suggests yet another embodiment of the present invention utilizing a yoke fixed to the restrained end of the present torsion link and extending around the link to a predetermined position along its length where a conventional elastomeric bearing engages the yoke and a sleeve around the torsion link of the present invention. Such a hybrid, while capable of exhibiting the greater angular displacement of the present invention could withstand a greater bending moment so the load carrying capacity utilizing the hybrid would be increased.

Further to the foregoing the elastomer filler while primarily acting as a transverse stabilizer for the open section array can also, by the judicious selection of its hardness with or without the addition of non-rubber-like-materials, be useful for dampening induced oscillations where desirable. This of course suggests that a wide variety of available materials can be employed with particular materials being selected depending on their performance in the array for the particular design application.

Likewise calculations for compression loading comparing an open section and the element of the present invention and test observations confirm that the elastomeric torsion link is more resistant to the onset of local instability under compressive load. Indeed the critical fatigue values for the onset of buckling or other failure modes under twisting torque; compression during shear; and tension during shear are all improved by the elastomeric torsion link of the present invention when compared with the same array of open section members without elastomeric bracing.

For an array it must be assumed that there are `n` slit tubes whose section constants are analyzed. The pitch `.delta.` and a uniform slit tube wall thickness `t.sub.opt ` are known quantities from prior calculations.

Since the outer radius rom is divided into `n` uniform pitches: ##EQU12##

Any slit tube mean radius `r` may be expressed in terms of the number of pitches from center so

where `X` is a whole number.

Raising both sides of this relation to the power of 3:

`r.sub.x.sup.3 ` for the expression for the total moment of inertia (second moment of AREA): ##EQU13## may be substituted by .delta..sup.3 x.sup.3 ##EQU14## i.e. the number of `X` values is exactly equal to `n` The sum: ##EQU15## can then be expressed as: ##EQU16## therefore ##EQU17## and with reference to the initial definitions `.delta..sup.3 ` and `n` are: ##EQU18## Substituting into the expression for `I` ##EQU19## and therefore, ##EQU20## and substituting ##EQU21## The second and third terms within parentheses are much smaller than the first.

If rom/.delta.=10, then the third term may be regarded as an infinitesimal of the second order and neglected during the design stress and stress analysis.

In case of the total cross-sectional area ##EQU22##

In the case of an array the torsional stiffness is given by: ##EQU23## and the sum of subsequent radii is ##EQU24## Total torsional stiffness, taking into account various secondary effects, by function: ##EQU25##

When various secondary effects are compared within the ".gamma." function it is obvious that the "torsion-flexion" interaction is greatest. This interaction was first investigated by Timoshenko and Wagner.

Its hyperbolic form can be reduced by Taylor's polinomial to read: ##EQU26##

It has been found experimentally that the torsional stiffness of the slit tube array without elastomeric interface will be increased by 15% or by the coefficient 1.15, when elastomeric material is injected:

Referring now to FIGS. 9 to 15 these are graphs showing various characteristics of the torsion link for varying thickness and aspect ratio (rom/t). These characteristics are as follows:

A thorough analysis of the shear strain in the elastomeric material for any given angular displacement of concentric open sections must be made to determine the optimum spacing and govern material selection.

The analysis must of course be undertaken for any given set of design requirements, for any application, however, it has straight forwardly been determined that the empirical results follow and exceed conventional open section evaluations to an extent that enables the use of the elastomeric torsion link of this invention in applications which hitherto would not have been considered acceptable for open sections alone.

Further analysis following accepted theory demonstrates that the induced by torsion tensile and compressive stresses, for example in the vicinity of the fasteners, are proportional to the shearing stress of a St. Venant's torsion.

The foregoing analysis does of course assume devices constructed with uniform wall thickness. It is contemplated that variations in wall thickness can be employed which will require further analysis to determine suitability of specific structures for specific design applications. Likewise the elastomeric material would vary in thickness in such a situation and this would have to be taken into consideration. For some applications it would even be possible to have discontinuous elastomer filling between the open sections using longitudinal beams or webs of elastomer or even spaced annular rings and it is even further possible to use foamed elastomer or filled elastomer. The selection of the particular elastomer composition or physical shape or form will be straightforwardly achieved by workers in that art given specific design criteria for a given application and the physical data for the elastomer.