Abstract:
A torsional joint assembly and method of making same having members of formed of dissimilar materials bonded together at calculated angles to result in essentially singularity-free joints.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    This is a continuation-in-part of pending U.S. patent application Ser. No. 08/895,653 filed on Jul. 17, 1997. 
     
    
     
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
         [0002]    Not applicable.  
         BACKGROUND OF THE INVENTION  
         [0003]    The present invention relates to torsional joint assemblies and methods of making same and more particularly to a joint assembly having a singularity-free joint.  
           [0004]    Various techniques are known in the art to form torsional bonded joint assemblies using dissimilar materials. Unfortunately, typically even in good designs there are some small zones along the joint where the stresses are very high. These zones are typically located where the bonding surface reaches the outer or the inner surface of the assembly, and also where the adjacent surfaces create the angles. When the linear elasticity theory is used for mathematical modeling of the assembly, these zones manifest themselves by presence of so called singularity points where the stresses become infinitely large. In reality, if the applied load is high, the material fails at the vicinity of the singularity points and the fracture surface may then propagate through the assembly resulting in the complete structure failure. For moderate loads, the stresses near the singularity points may reach the plasticity limit and the material experiences plactic deformation, leading to crack initiation and growth.  
           [0005]    Therefore, it would be advantageous to have a torsional joint assembly which is free of such singularity points.  
         BRIEF SUMMARY OF THE INVENTION  
         [0006]    The present invention relates to a joint assembly and method of making same that includes securing surfaces that are specially configured to essentially eliminate singularity points along the securing joints thereby facilitating an extremely strong bond with a relatively short joint length.  
           [0007]    The invention also includes a general purpose joint assembly for co-axially connecting cylindrical members which are formed of different materials having different shear modulai, the assembly essentially eliminating stress singularities along the joint. In one embodiment, the assembly includes a first tubular member formed of a first material having a first shear modulai. The first member is formed around an axis and has a proximal edge at a proximal end and has internal and external surfaces, the internal and external surfaces each being first surfaces. One of the first surfaces forms a first proximal surface at the proximal end, at least a portion of the first proximal surface sloped radially to the proximal edge so as to define a first angle with respect to the axis.  
           [0008]    A second tubular member is formed of a second material having a second shear modulai. The second member has a proximate edge at a proximate end and has inner and outer surfaces, the inner and outer surfaces each being second surfaces. One of the second surfaces forms a proximate surface at the proximate end and the other of the second surfaces forming an incline surface.  
           [0009]    The proximate surface includes second proximal and second distal surfaces, the second proximal surface separating the second member from the second distal surface. The second distal surface slopes radially to the proximate edge such that the second distal surface conforms to the first proximal surface. At least a portion of the incline surface slopes radially to the proximate edge so as to define a second angle with respect to the axis. The second proximal surface is parallel to the incline surface. The first proximal and second distal surfaces are secured together by an adhesive layer wherein, the first and second angles are a function of the shear modulus. Preferably, in applications providing a thermal barrier, the first material is a glass-epoxy composite and the second material is a metal.  
           [0010]    In one embodiment the external surface forms the second distal surface, the inner surface forms the first proximal surface and the outer surface forms the incline surface.  
           [0011]    Thus, another object of the invention is to provide a general, all purpose joint configuration for joining two cylindrical member at their ends in a manner which essentially eliminates singularity points along the length of the joint. This is accomplished by choosing bonding angles as a function of various material characteristics as described in detail below.  
           [0012]    It is yet another object of the present invention to provide a joint assembly where members of dissimilar material can be bonded in numerous manners including the use of adhesive, as well as brazing, soldering and other bonding techniques, such as in the case of bonding dissimilar metals together.  
           [0013]    These and other objects, advantages and aspects of the invention will become apparent from the following description. In the description, reference is made to the accompanying drawings which form a part hereof, and in which there is shown a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention and reference is made therefor, to the claims herein for interpreting the scope of the invention. 
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0014]    [0014]FIG. 1 is a partial cross-sectional view of a prior art superconducting motor system;  
         [0015]    [0015]FIG. 2 is a cross-sectional view of a singularity-free joint according to the present invention;  
         [0016]    [0016]FIG. 3 is a two-dimensional schematic of a section of the joint of FIG. 2 illustrating specific joint tapered angles;  
         [0017]    [0017]FIG. 4 is a partial cross-sectional view of a superconducting motor, including torque tubes according to the present invention;  
         [0018]    [0018]FIG. 5 is an enlarged cross-sectional view of the rotor assembly of FIG. 4;  
         [0019]    [0019]FIG. 6 is a perspective view of a torque tube according to the present invention;  
         [0020]    [0020]FIG. 7 is a cross-sectional view taken along the line  7 - 7  of FIG. 5; and  
         [0021]    [0021]FIG. 8 is similar to FIG. 2, albeit being a second embodiment of a joint according to the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0022]    A. Theory  
         [0023]    In the description that follows, like reference numerals throughout the figures and the specification are used to identify the same components, assemblies, systems, directions, angles, etc. In addition, subscripts “c” and “s” are often used to identify parameters related to a composite material and to a metal (e.g. steel) material, respectively. However, in the broadest sense, it should be understood that such designations may also simply refer to one material versus a second material where any two dissimilar materials may be employed in a joint assembly according to the present invention. Where the later description uses an embodiment of composite to metal bonding with adhesive, it should be understood that one can apply the same equations and techniques with other dissimilar materials and bonding materials.  
         [0024]    Referring to FIG. 2, the present invention allows two tubular members  10 ,  12  which are formed of materials characterized by disparate shear moduli, where the modulus associated with the member  12  is larger than the modulus associated with member  10 , via an adhesive layer  15 , or other bonding material in the case of bonding by brazing or soldering, end to end along securing external and inner surfaces  18 ,  20  to form a singularity-free securing joint  14  having a length L 2 . “Singularity-free” means that when torque causes member  12  to rotate about a central axis  16 . through member  12 , the resulting stresses provided by the solution of the theory of elasticity problem are finite over the whole joint assembly structure, including all locations where one may typically expect infinitely large stresses, such as angular points and the ends of the joint. Therefore the likelihood of joint failure is substantially reduced.  
         [0025]    To eliminate singularity points along length L 2 , angles formed by external and inner surfaces  18 ,  20  and an incline angle formed by an outer incline surface  22  with respect to surface  20  are precisely chosen. In addition, an inner proximal surface  22   a  is parallel to surface  22 .  
         [0026]    It should be appreciated that in practice some stress concentrations will be introduced into a joint. The physical application of a mathematical model will never be exact without some degree of error or round-off. Accordingly, the teachings of the present invention eliminate singularity points in theory, and provide an essentially singularity-free joint in practice. To develop equations which essentially eliminate singularity points, it is helpful to begin with a simple model from which several general conclusions about a singularity-free joint can be derived. To this end, for large tube diameters a specific portion of a joint can be modeled as a two dimensional asymmetrical problem. In order to find singularity point parameters in a closed form, it is also helpful to first consider isotropic materials. Isotropic means that a material exhibits properties with identical values when the values are measured along axis in all directions.  
         [0027]    Referring also to FIG. 3, a two-dimensional section of joint  14 , without bonding layer  15 , is illustrated. For the purposes of this explanation, it will be assumed that member  10  is formed of an isotropic composite material  0  (e.g. glass-epoxy composite) while member  12  is formed of an isotropic metal  0  (e.g. steel). Composite  0  is characterized by a shear modulus G c  while metal  0  is characterized by a shear modulus G s  where G c  is substantially less than G s . Both Polar (è, ñ, z) and first (x,y,z) and second (x′ ,y′ ,z) Cartesian coordinate systems have been superimposed on FIG. 3 with securing joint  14  (i.e., OB) aligned with radial coordinate ñ, the y axis vertical and parallel to the length of member  10  (i.e. CO), the z axis (not illustrated) extending perpendicular to the x and y axes, and the y′ axis parallel to external surface  22  (i.e. OA).  
         [0028]    The points of interest along securing joint OB are generally adjacent first and second joint ends  24 ,  26 , respectively. It is at these joint ends  24 ,  26  that singularity points typically first occur. First joint end  24  will be analyzed, then joint end  26  will be separately analyzed and then the results of both analyses will be combined to provide singularity free equations.  
         [0029]    At first end  24 , external surface  18  forms an angle á (i.e. &lt;COB) with the vertical y-axis. A “composite tapered” angle ö is equal to ö−á. Inner surface  20  conforms to surface  18  (i.e. to angle ö) and outer surface  22  forms a “metal tapered” angle â with surface  20 . Similarly, at second end  26 , member  10  forms an angle á′ (=ö−á) with the y-axis while member  12  forms an inner angle â′. Equations for singularity point parameters at both ends  24  and  26  can be derived.  
         [0030]    With respect to first end  24 , the way to determine singularity parameters is as follows. Consider angle AOB and extend lines OA and OB to infinity, so that member  12  becomes a cone with vertex O and angle â. Similarly, consider angle COB and extend line OC and OB to infinity SO that member Ù c  also becomes a cone with vertex 0 and angle á. After this artificial extension of actual areas Ω s  and Ω c , consider the following homogeneous, two-dimensional, asymmetrical problem:  
           u   z   =u (ρ,θ)  Eq. 1  
         [0031]    [0031]                 γ     ρ                 z       =       ∂   u       ∂   ρ         ;       γ     θ                 z       =       1   ρ                       ∂   u       ∂   θ                   Eq   .              2                   σ     ρ                 z       =     G                   γ     ρ                 z           ;       σ     θ                 z       =     G                   γ     θ                 z           ;     G   =     {             G   c                   in                   Ω   c                   G   s                   in                   Ω   s                         Eq   .              3                                 
         [0032]    where σ represents stress,  
                               ∂   2        u       ∂     ρ   2         +       1   ρ            ∂   u       ∂   ρ         +       1     ρ   2                ∂   2        u       ∂     θ   2             =   0     ;     0   &lt;   ρ   &lt;   ∞       ,       -   β     ≤   θ   ≤   α     ,                     ∂   u       ∂   θ       =   0     ,     θ   =   α     ,     θ   =     -   β                     Eq   .              4                               
 
                     G   s          1   ρ            ∂     u   s         ∂   θ         =       G   c          1   ρ            ∂     u   c         ∂   θ           ;       u   s     =     u   c         ,     θ   =   0             Eq   .              5                               
 
         [0033]    Here and below the solutions in members  12  and  10  are distinguished by upper case indexes S and C, respectively. Next, we must derive solutions to Equations 1 through 5 having the form:  
           u=ρ   λ   U (θ)  Eq. 6  
         [0034]    Substituting Equation 6 into Equations 1 through 5 and simplifying, Equations 1 through 5 reduce to a boundary value problem for an ordinary differential equation as:  
                       λ   2        U     +            2        U            θ   2           =   0     ;            U          θ       =   0       ,     θ   =   α     ,     θ   =     -   β               Eq   .              7                               
 
                   G   s                 U   s            θ         =       G   c                 U   c            θ           ,       U   s     =     U   c       ,     θ   =   0             Eq   .              8                               
 
         [0035]    Solutions satisfying the boundary conditions at θ=α, θ=−β, are as follows:  
           U   s   =A   s  cos(λ(θ+β));  U   c   =A   c  cos(λ(θ+β))  Eq. 9  
         [0036]    Continuity conditions in Equations 7 and 8 can be used to provide an equation for λ such that:  
                            cos        (     λ                 β     )             cos        (     λ                 α     )                   G   s          sin        (     λ                 β     )                 -     G   c            sin        (     λ                 α     )                    =       0   ⇒       κ                   tan        (     λ                 α     )         +     tan        (     λ                 β     )           =   0       ,     κ   ≡       G   c       G   s                 Eq   .              10                               
 
         [0037]    The original problem will not have a singularity point at point O if, between 0&lt;λ≦1 the only solution to Equation 10 is λ=1. Therefore, angle β to eliminate singularities at point O should be:  
         β=arctan(−κ tan(α)); or β=arctan(κ tan(φ)); φ≡π−α  Eq. 11  
         [0038]    To show that there are no other solutions of Equation 10 in the interval 0&lt;λ&lt;1, make the left-hand side of Equation 10 a function of λ such that:  
         f(λ)=κ tan(λα)+tan(λβ)  Eq. 12  
         [0039]    Assuming that angle β is given by Equation 11, we get f(λ)=0 for λ=1. Function f(λ) monotonically decreases when λ decreases, and hence it does not have any roots at least in the interval α/(π/2)&lt;λ&lt;1. For λ=α/(π/2) function f(λ)=−∞, and for 0&lt;λ&lt;α/(π/2), function f(λ) is positive. Thus, function f(λ) does not have any roots within the interval 0&lt;λ&lt;1. It is clear that if angle α is exactly equal to π, value λ=1 satisfies Equation 10 only when angle β=π, which is not of interest in our application.  
         [0040]    Thus, a first conclusion is that without tapering the securing surfaces of composite. material Ω c  and steel Ω s , singularity points cannot be eliminated.  
         [0041]    Modulus ratio κ (see Eq. 10) is relatively small as composite modulus G c  is much smaller than steel modulus G s . Angle β is also small while α is close to, but smaller than π to ensure that Equation 11 does not provide a negative β value. Equation 11 can be represented asymptotically as:  
         β=κφ  Eq. 13  
         [0042]    Thus, we arrive at a second conclusion which is that for a small modulus ratio, the ratio of the metal tapered angle β to the composite tapered angle Φ is inversely related to the modulus ratio κ (see FIG. 1).  
         [0043]    A third conclusion regards stress concentration in metal member  12  corresponding to the case where λ=1. It follows from Equations 1 through 6 that stresses within member  12  do not depend on radial coordinate ρ. Therefore:  
         σ ρz   =GU (θ); σ θz   =GU ′(θ)  Eq. 14  
         [0044]    Only radial components σ ρz  is discontinuous along joint OB, and this component is of extreme importance. Since both angles φ and β are small, in the vicinity of joint OB component σ ρz  is very close to a Cartesian stress component σ yz  which mainly carries the torque. It follows from Equation 14 that stress in the composite are smaller than in the metal and the ratio of composite to metal stresses can be expressed as:  
                 σ     ρ                 z     c       σ     ρ                 z     B       =   κ           Eq   .              15                               
 
         [0045]    Thus, the third conclusion is that the metal stress component σ ρz   s  is larger than the composite stress component σ ρz   c  by the ratio 1/κ.  
         [0046]    Referring still to FIG. 3, with respect to second end  26 , angle α′ is small while angle β′ is large. Here, β′ and α′ can be substituted into Equation 10 where λ=1 to express β′ in terms of α′ as:  
         β′=π−arctan(κα′)  Eq. 16  
         [0047]    The asymptotic formula for small values of angle α is:  
         β′=π−κα′  Eq. 17  
         [0048]    The reasoning above can be used to prove that Equation 16 is the only solution to Equation 10 in the interval 0&lt;λ&lt;1. In particular, where angle α′ is equal to φ=π−α, then:  
         β′=π−β  Eq. 18  
         [0049]    This particular case is of special interest because there is an elementary analytical solution of an asymmetrical two dimensional elasticity problem for the entire joint OB which theoretically has no singularity point. The solution can be obtained for anisotropic material properties for both members  10  and  12 , with the restriction that both materials should be orthotropic and coordinate z-axis should be one of the axis of orthotropy.  
         [0050]    Referring still to FIG. 3, for simplicity, it is assumed that in the composite material the x and y-axis are the axis of orthotropy and that in metal material Ω s , the x′ and y′-axis are the axis of orthotropy. Joint OB will be referred to herein as a singularity-free shear joint. It will be assumed that angles β and φ satisfy Equation 11. In this case, as developed above:  
                 tan        (   β   )       =     κ                   tan        (   φ   )           ;       where                 κ     =       G   yz   c     /     G       y   ′        z     s         ;           Eq   .              19                               
 
         [0051]    In addition:  
                    AP   CR          =       sin                 β       sin                 φ               Eq   .              20                               
 
         [0052]    and:  
         σ α =σ c  sinφ  Eq. 21  
         [0053]    where σ α  is an adhesion or bonding stress and σ c =σ yz   c    
         [0054]    Equations describing the asymmetric plane elasticity in member  10  are as follows:  
           u   z   =u   z ( x,y )  Eq. 22  
         [0055]    [0055]                 γ   yz     =       ∂     u   z         ∂   y         ;       γ   xz     =       ∂     u   z         ∂   x                 Eq   .              23                 (           σ   xz               σ   yz           )     =       (           G   xz   c         0           0         G   yz   c           )          (           γ   xz               γ   yz           )               Eq   .              24                     ∂     σ   xz         ∂   x       +       ∂     σ   yz         ∂   y         =   0           Eq   .              25                                 
         σ xz =0 on  OC, BR   Eq. 26  
         σ yz =σ c  on  CR   Eq. 27  
         [0056]    where σ c  is a constant. Equations describing the asymmetric plane elasticity in member  12  are as follows:  
           u   z   =u   z ( x′,y ′)  Eq. 28  
         [0057]    [0057]                 γ       y   ′        z       =       ∂     u   z         ∂     y   ′           ;       γ       x   ′        z       =       ∂     u   z         ∂     x   ′                   Eq   .              29                 (           σ       x   ′        z                 σ       y   ′        z             )     =       (           G       x   ′        z     S         0           0         G       y   ′        z     S           )          (           γ       x   ′        z                 γ       y   ′        z             )               Eq   .              30                     ∂     σ       x   ′        z           ∂     x   ′         +       ∂     σ       y   ′        z           ∂     y   ′           =   0           Eq   .              31                                 
         σ x′z =0 on  OA, PB   Eq. 32  
         σ y′z =σ S  on  PA   Eq. 33  
         [0058]    where σ s  is a constant. It follows from equilibrium conditions that:  
         σ s =ζσ c   Eq. 34  
         [0059]    where:  
             ζ   ≡       sin                 φ       sin                 β       ≈     κ     -   1               Eq   .              35                               
 
         [0060]    Parameter ζ is referred to hereinafter as a stress concentration factor. For small tapering angles factor ζ is essentially equal to the ratio of metal shear modulus G s  to composite shear modulus G c . Note that Equation 34 is similar to Equation 15.  
         [0061]    To check the solutions of Equations 34 and 35, with σ x′z =0, σ y′z =σ s , σ xz =0 and σ yz =σ c :  
                 u   z          (       x   ′     ,     y   ′       )       =         y   ′     ·       σ   s       G       y   ′        z     s                       in                   Ω   s               Eq   .              36                               
 
         [0062]    and  
                   u   z          (     x   ,   y     )       =       y   ·       σ   s       G   yz   c                       in                   Ω   c         ;           Eq   .              37                               
 
         [0063]    Equations 36 and 37 satisfy equations 22 through 33. To check continuity along joint OB, σ a  (the adhesion stress) is assumed to be the shear stress on joint OB. Stress continuity along joint OB exists if:  
         σ a =σ s  sin β=σ c  sinφ  Eq. 38  
         [0064]    Assuming l is the direction B 0  (see FIG. 3) then:  
             l   =       (           sin                 β               cos                 β           )                   in                 the                   x   ′          y   ′                   system                 and             Eq   .              39               l   =       (           sin                 φ               cos                 φ           )                   in                 the                 xy                   system   .               Eq   .              40                               
 
         [0065]    Displacement continuity conditions can be expressed as:  
                 ∂     u   z   c         ∂   l       =           ∂     u   z   s         ∂   l       ⇔         σ   s       G       x   ′        z     s          cos                 β       =         σ   c       G   xz   c          cos                 φ               Eq   .              41                               
 
         [0066]    Equation 41 is satisfied because of the relationships expressed in Equations 11, 34 and 35.  
         [0067]    Thus, to design a singularity free shear joint, the following steps should be taken:  
         [0068]    (1) First, with a known adhesion stress (i.e. σ a ) and known composite stress value σ c , the composite taper angle φ is determined from Equation 38. Equation 38 is repeated here as Equation 42:  
               sin                 φ     =       σ   a       σ   c               Eq   .              42                               
 
         [0069]    (2) Second, knowing the composite and metal shear moduli G yz   c  and G y′z   s , respectively, Equation 19 is used to find metal tapering angle β. Equation 19 is repeated here as Equation 43.  
                 tan                 β     =     κ                 tan                 φ       ,     κ   ≡       G   yz   c       G       y   ′        z     s                 Eq   .              43                               
 
         [0070]    (3) Third, Equations 34 and 35 (repeated as Eqs. 44 and 45) are used to determine shear stresses in metal member  12 :  
         σ s =ζσ c    Eq. 44  
         [0071]    [0071]             ζ   ≡       sin                 φ       sin                 β               Eq   .              45                                 
         [0072]    The solution derived above can be extended to a joint with a bonding layer between members  10  and  12 , and to the case of general orthotropy of material properties for all regions. Stress and strains in each member  10  are constant, while displacement u z  is a linear function of coordinates. Consider vector {right arrow over (σ)}, whose components are stresses σ xz , σ yz . Also consider vector {right arrow over (∇)}, which is equal to the gradient of displacement u z . If material is isotropic, vectors {right arrow over (σ)} and {right arrow over (∇)} are parallel. Vectors {right arrow over (σ)} and {right arrow over (∇)} are also parallel, if material is orthotropic with vector {right arrow over (σ)} parallel to one of the axis of orthotropy (e.g. like the above case, where vector {right arrow over (σ)} in material Ω c  is parallel to the y-axis where the y-axis is the axis of orthotropy). Since vectors {right arrow over (σ)} and {right arrow over (∇)} are related to each other through elasticity law, vector {right arrow over (σ)} may be chosen arbitrarily, and vector {right arrow over (∇)} will be determined from elasticity law. Assuming each member  10 ,  12  has two edges parallel to vector {right arrow over (σ)}, there are no stresses at the parallel edges.  
         [0073]    Vectors {right arrow over (σ)} 1  and {right arrow over (∇)} 1  are chosen in member  10  where member  10  has edges parallel to vector {right arrow over (σ)} 1 . Now member  10  is cut along the line comprising some angle φ to the parallel edges. Angle φ is arbitrary and referred to as the composite tapered angle. The resulting third edge of member  10  will be sheared by a third edge of member  12 . From continuity conditions, component σ n  of vector {right arrow over (σ)} 1 , which is normal to the third edge, is continuous. In addition, a component ∇ τ , tangent to vector {right arrow over (∇)} 1  is continuous. Then, from elasticity law, in member  12 , vectors {right arrow over (σ)} 2  and {right arrow over (∇)} 2  may be found. The direction of vector {right arrow over (σ)} 2  defines the direction of the stress free edges of wall  12 . This process may be continued to add more regions to this chain. Once material properties of the next region are decided upon, the only parameter which is an arbitrary one is the tapered angle.  
         [0074]    Referring again to FIGS. 2 and 3, bonding layer  15  of constant thickness is placed between members  10  and  12 . Since adhesive  15  contact lines with adherends  10  and  12  are parallel, components σ n  and ∇ τ  on both securing surfaces  18  and  20  are the same. Thus, metal tapering angle β is the same as before. Thus, a fourth conclusion related specifically to the case where a bonding layer is provided between two securing surfaces  18  and  20  is that design steps 1 through 3 are not influenced by the adhesive thickness or its elastic properties.  
         [0075]    FE analysis showed that for a steel ±45° glass-epoxy composite tube joint, even with tube radius of as small as 1 inch for a thickness of 0.25 inches, stresses along a securing joint  14  differed less than 10% from ideal uniform distribution when the inventive joint was employed.  
         [0076]    Thus, it should be appreciated that the relatively complex mathematics above yield a relatively simple set of three equations which can be used to determine characteristics of a joint between two tubular members having disparate shear modulus wherein the resulting joint is essentially singularity-free and has practically uniform bonding stress distribution. In addition to providing an extremely strong bond between two tubular members, the inventive joint is also advantageous in that it is relatively short and is simple and inexpensive to construct.  
         [0077]    In the superconducting motor environment, the inventive bond is particularly advantageous in that joint length, strength and cost are all important design criteria. In addition, the inventive joint allows a thermally insulating material (i.e., the composite) to be adhesively bonded to metal without singularity points along the joint. In an example application, the inventive joint can be used to form composite-metallic torque tubes which can withstand massive torque levels associated with large motor shafts.  
         [0078]    B. Torque Tube Configuration  
         [0079]    Referring now to FIG. 4, the present invention will be described in the context of a superconducting motor system  30 . System  30  includes a stator assembly  32 , a rotor assembly  34 , a cryogenic refrigeration system  36 , an agent transfer coupling  38 , an inverter  40 , a connection box  42 , a synchronous DC exciter  44  and various other components which will be described in more detail below.  
         [0080]    Stator assembly  32  includes a cylindrical motor frame  46  which forms a motor chamber  48  about a rotation axis  16 , frame  46  forming first and second shaft openings  52 ,  54  at opposite ends which are centered along axis  16 .  
         [0081]    A plurality of stator windings collectively referred to by numeral  56  are mounted on an internal surface  58  of frame  46 , windings  56  forming a stator cavity  60  therebetween. Two ball bearings  62 ,  64  are provided, one at each opening  52 ,  54 , respectively. Supply lines  66  (only one is shown) connect windings  56  through box  42  to inverter  44  for supplying voltages to windings  56  as well known in the art. A laminated flux shield  68  is provided between frame  46  and windings  56 .  
         [0082]    Referring also to FIG. 5, rotor assembly  34  includes first and second shaft ends  70 ,  72 , respectively, first and second torque tubes  74 ,  76  respectively, a coil support  78 , rotor coils collectively referred to by numeral  80 , an AC flux shield  82  and an outer vacuum jacket  84 .  
         [0083]    Support  78  includes a generally cylindrical member  86  having an internal surface  88  and an external surface  90 . External surface  90  forms a plurality of recesses collectively referred to by numeral  92  for receiving windings  80 . First and second annular flanges  94 ,  96 , respectively, extend radially inwardly from surface  88  at opposite ends of member  86 . Each flange  94 ,  96  forms a plurality of bolt receiving apertures collectively referred to by numeral  98  which are parallel to axis  50  and are equispaced about an associated flange  94  or  96 .  
         [0084]    Windings  80  are wound about member  86  within recesses  92  as well known in the art. Shield  82  is provided outside windings  80  and is spaced apart therefrom.  
         [0085]    Tubes  74  and  76  are essentially identical and therefore, only tube  74  will be explained in detail here.  
         [0086]    Referring to FIGS. 5 through 8, tube  74  consists of three separate components including a thermally insulating composite cylinder  10  and first and second stainless steel couplers  11  and  12  adhesively secured to opposite proximal and distal ends  10   a  and  10   b  of cylinder  10 . Adhesive is identified be reference numeral  15  in FIG. 2. Couplers  11  and  12  are identical, construction of ends  10   a  and  10   b  is identical and characteristics of the bonds between couplers  11 ,  12  and cylinder  10  are identical and therefore only coupler  12 , end  10   a  and the bond therebetween will be explained her in detail.  
         [0087]    Cylinder  10  has a midsection  10   m  between ends  10   a  and  10   b . Along midsection  10   m , cylinder  10  is completely cylindrical, defined by uniform internal and external diameters. However, at each end  10   a  and  10   b , cylinder  10  forms a frusto-conical tapered external surface  18  which slopes radially inwardly from the midsection  10   m  to an adjacent end of the cylinder  110  (see FIG. 3).  
         [0088]    Coupler  12  includes a circular end plate  114  and an integrally connected flange  115 . Plate  114  forms a large central aperture  116  and a plurality of circumferentially equispaced bolt apertures around aperture  116 , the bolt apertures collectively referred to by numeral  120 . Apertures  120  are arranged such that they are alignable with apertures  98 .  
         [0089]    Flange  115  extends from the circumferential edge of plate  114 . Referring specifically to FIG. 2, flange  115  is defined by inner and outer surfaces  20 , and  22 , respectively, inner proximal surface  22   a  has a frusto-conical shape which slopes radially outwardly and axially away from plate  114 . Inner surface  20 , also has a frusto-conical shape which slope radially outwardly and axially away from plate  114 . However, surface  20  slopes outwardly to a greater degree than surface  22   a . Outer surface  22 , also referred to as an inclined surface, also has a frusto-conical shape which slopes radially outwardly and axially away from plate  114  and is parallel to surface  22   a  such that surfaces  20  and  22  intersect at a distal end  128  of flange  115 . In addition, surface  20  slopes outwardly to the same degree that surface  18  slopes inwardly such that surface  20  is parallel to surface  18  at all points. Referring to FIG. 3, surface  22   a  is BP, surface  22  is OA, and surfaces  18  and  20  are OB as marked.  
         [0090]    When secured together, surface  20  is adhered to surface  18  (see FIG. 2). The spacial relationship between plate  114  and internal surface  20  is such that, when surface  20  is parallel to surface  18 , plate  114  is perpendicular to midsection  10   m.    
         [0091]    Referring to the mathematics described above and to FIGS. 2 and 3, tapered angles ö and â are illustrated. The three step process described above is used to determine both the composite tapered angle ö and the metal tapered angle â. Once angles ö and â have been determined, cylinder  10  and flanges  115  can be formed.  
         [0092]    Referring to FIGS. 2 through 7, after surfaces  18 ,  20 ,  22   a  and  22  which define angles ö and â have been formed, tube  74  can be assembled. To assembly tube  74 , an adhesive  15  is evenly applied to surface  18 . Preferred adhesives are HYSO EA-9330, HYSOL EA 9628 and AF-563. Then, coupler  12  is positioned adjacent cylinder  10  such that end  10   a  is received inside flange  115  with surface  20  parallel to surface  18  and in contact with adherend  15 . Adherend  15  is allowed to cure forming a strong bond between coupler  12  and cylinder  10 . Coupler  11  is secured to cylinder  10  in a similar fashion.  
         [0093]    Referring again to FIGS. 2, 4 and  5 , first shaft end  70  is cylindrical and hollow and forms a radially outwardly projecting extension  110 . Extension  110  forms a plurality bolt apertures  112  which are parallel to axis  16 , equispaced around extension  110  and should be arranged so as to align with apertures  120 .  
         [0094]    Second shaft end  72  is similar shaft end  70  except that it is not hollow. Although not illustrated, end  72  is configured so as to be securely attachable to a load (i.e. end  72  is a drive shaft).  
         [0095]    Vacuum jacket  84  includes a generally cylindrical lateral wall  152  and first and second end walls  154 ,  156  on opposite ends of wall  152 . Walls  154  and  156  each form a central aperture  158 ,  160 , apertures  158  and  160  alignable along rotation axis  16 . Jacket  84  should be formed of stainless steel. A seal  106 ,  108  is provided along the edge of each aperture  158 ,  160 , respectively.  
         [0096]    To assemble assembly  34 , tube  74  is positioned so that extension  114  is adjacent extension  110  with apertures  120  aligned with apertures  98 . Nuts and bolts are used to secure tube  74  to supporter  78 . Similarly, tube  76  is attached to flange  96 . When so attached, tubes  74  and  76  should only contact support  78  via flanges  94  and  96 .  
         [0097]    With windings  80  arranged inside recesses  92  and shield  82  secured adjacent windings,  80 , shaft end  70  and wall  154  are attached to end plate  11  via bolts and nuts. Similarly, shaft end  72  and wall  156  are attached to the distal end of tube  76  (see FIG. 5). A cryogenic delivery tube  97 , including supply and return sections  97   a  and  97   b , respectively, extends through end  70  and tube  74  into supporter  78  as well known in the art. Tube  97  provides cryogenic coolant to supporter  78 .  
         [0098]    When assembly  34  is configured in the manner described above and as illustrated in FIGS. 2 through 7, tubes  74  and  76  and supporter  78  are coaxial around axis  16 .  
         [0099]    Referring again to FIG. 4, refrigeration system  36 , transfer coupling  38 , exciter  44 , connection box  42 , delivery tube  97  and inverter  40  are all well known in the art and therefore will not be explained here in detail.  
         [0100]    Referring still to FIG. 4, assembly  34  is mounted inside cavity  60  so that a gap exists between the external surface of jacket  84  and stator windings  56 . Shaft ends  70 ,  72  extend axially outwardly along axis  16  and are supported by bearings  62 ,  64  within openings  158 ,  160 . First end  70  is connected to transfer coupling  38 . Tube  97  extends through coupling  36  to system  16  for receiving cooling agent for delivery to support  78 . The agent cools windings  80  through supporter  78 .  
         [0101]    It should be understood that the methods and apparatuses described above are only exemplary and do not. limit the scope of the invention, and that various modifications could be made by those skilled in the art that would fall under the scope of the invention. For example, while the invention is described as including a torque tube formed from a composite conduit and two steel end ring couplers, clearly, the couplers. could be formed as integral pieces of the shaft and the internal surface of the support, the shaft and internal surface forming the securing inner and outer surfaces at the angles described above. In addition, while the invention is described as one wherein a composite external surface forms the composite securing surface, an inner surface of the coupler forms the metal securing surface and an outer surface of the coupler forms the incline surface, the invention could also be practiced where a composite internal surface forms the composite securing surface, an outer surface of the coupler forms the metal securing surface and an inner surface of the coupler forms the incline surface. FIG. 8 illustrates a single two-dimensional section of a joint configured in accordance with this second embodiment. In FIG. 8, components, angles and surfaces which are similar to components, angles and surfaces in FIGS. 2 through 7 are identified by the same numbers, albeit further distinguished by a “′”. Thus,  10 ′ is a composite member,  12 ′ a metal member,  14 ′ a joint,  15 ′ an adhesive layer and so on. In FIG. 8, internal surface  18 ′ of member  10 ′ is the composite securing surface, surface  20 ′ is the metal securing surface, distal outer surface  22 ′ is the incline or inner surface and  22   a ′ is a metal proximal surface or proximate outer surface. Angles â and ö are as illustrated. The three step procedure described above is used to find angles ö and â thus producing an essentially singularity-free joint  14 ′.  
         [0102]    Furthermore, while it is preferred that the first and second angles be determined according to the equations above, clearly, other similar angles could be used although the likelihood of a singularity point may be increased. In this respect, in a broad sense, the invention is meant to cover any composite/metal torque tube wherein joints between composite and metal are secured via an adhesive. Moreover, the invention is also meant to generally cover bonding of two cylindrical members end to end wherein the materials have disparate shear modulus. While the bonding of some materials may utilize a bonding material of adhesive, other bonding, such brazing or soldering will be best suited for the bonding process of depending on the materials used and desired application. To this end, the Equations above should be used to identify precise first and second angles.  
         [0103]    To apprise the public of the scope of this invention, we make the following claims.