Coupling apparatus

1. A single piece unitary metal coupling comprising:

a first end;

a second end; and

a plurality of convolutions between the first and second ends, adjacent convolutions separated by a land, each convolution of the plurality of convolutions including:

a cylindrically-shaped tip end having substantially uniform material thickness disposed at an external plateau of the convolution, relative to an axis of the coupling;

a convolution arm extending from the cylindrically-shaped tip end toward the land and having an outer wall and an inner radial wall, the inner radial wall being substantially perpendicular to a longitudinal axis of the coupling;

a continuously decreasing material thickness of the convolution as a radial distance from the axis of the coupling increases; and

a root portion disposed between the land and the convolution arm, the root portion including a curvilinear outer root surface and a chamfered inner root surface, the chamfered inner root surface intersecting the inner radial wall of the convolution arm radially outwardly of a radial extent of the land, and intersecting a radially innermost surface of the land axially beyond an axial extent of the cylindrically-shaped tip end;

a convolution distance between adjacent convolutions of the plurality of convolutions being substantially equal, and less than an end distance between the first end or second end and a nearest convolution of the plurality of convolutions;

each convolution of the plurality of convolutions having a substantially identical convolution cross-sectional profile, the convolution cross-sectional profile differing from substantially identical end profiles of the first end and the second end;

a convolution thickness substantially consistent in a rounded portion of the convolution between the convolution arm and the cylindrically-shaped tip end;

the first end and the second end having an end outer diameter less than a tip end outer diameter;

the first end and the second end having a sharp corner at an intersection of an axial end surface and an inner diametrical end surface of the first end and the second end; and

the first end and the second end having an outer surface including a substantially curvilinear end portion disposed at the land between the first end and the nearest convolution of the plurality of convolutions and the second end and the nearest convolution of the plurality of convolutions, the curvilinear end portion being larger axially and radially than the curvilinear root surface of each convolution of the plurality of convolutions.

2. The single piece unitary metal coupling of claim 1 wherein the coupling is cylindrical at an inside dimension thereof.

3. The single piece unitary coupling of claim 1 wherein the first and second ends include a connection arrangement.

4. The single piece unitary metal coupling of claim 3 wherein the connection arrangement is a flange.

5. The single piece unitary metal coupling of claim 1 wherein the coupling is made from a material selected from one of titanium, corrosion resistant steels, high strength steels, nickel materials, carbon steel and maraging steel, and combinations including at least one of the foregoing.

6. The single piece unitary metal coupling of claim 1 further including nitriding for enhanced fatigue properties and wear resistance.