Shaped spring element for a non-contact seal device

1. A non-contact seal assembly, comprising:

a plurality of seal shoes arranged about an axis in an annular array;

a seal base circumscribing the annular array of the seal shoes; and

a plurality of spring elements, a first of the spring elements radially between a first of the seal shoes and the seal base, and the first of the spring elements including:

a first mount connected to the first of the seal shoes;

a second mount connected to the seal base; and

a spring beam extending a length longitudinally along a centerline from the first mount to the second mount, and the spring beam including opposing first and second surfaces;

wherein the first surface is disposed a first distance from the centerline, and the second surface is disposed a second distance from the centerline;

wherein the first distance and the second distance change as the spring beam extends longitudinally along the centerline to provide at least a portion of the spring beam with a tapered geometry; and

wherein the portion of the spring beam has a longitudinal length that is at least about five percent of the length of the spring beam.

2. The assembly of claim 1 , wherein the portion of the spring beam has a longitudinal length that is between about five percent and about ten percent of the length of the spring beam.

3. The assembly of claim 1 , wherein the portion of the spring beam has a longitudinal length that is between about ten percent and about twenty-five percent of the length of the spring beam.

4. The assembly of claim 1 , wherein the portion of the spring beam has a longitudinal length that is greater than about twenty-five percent of the length of the spring beam.

5. The assembly of claim 1 , further comprising a fillet longitudinally between the portion of the spring beam and a respective one of the first and the second mounts.

6. The assembly of claim 1 , wherein at least one of:

the first surface is convex at least along a part of the portion of the spring beam; or

the second surface is convex at least along a part of the portion of the spring beam.

7. The assembly of claim 1 , wherein the first distance and the second distance change, along at least a part of the portion of the spring beam, as a function of a square root of a longitudinal distance from a longitudinal mid-point of the spring beam.

8. The assembly of claim 1 , wherein:

the portion of the spring beam is a first portion of the spring beam disposed longitudinally next to the first mount;

the first distance and the second distance further change as the spring beam extends longitudinally along the centerline to provide a second portion of the spring beam, disposed longitudinally next to the second mount, with a tapered geometry; and

wherein the second portion of the spring beam has a longitudinal length that is at least about five percent of the length of the spring beam.

9. The assembly of claim 8 , wherein the longitudinal length of the first portion of the spring beam is substantially equal to the longitudinal length of the second portion of the spring beam.

10. The assembly of claim 8 , wherein:

an intermediate portion of the spring beam extends longitudinally between the first portion and the second portion of the spring beam; and

at least one of the first distance or the second distance is substantially constant along the intermediate portion.

11. The assembly of claim 10 , wherein the intermediate portion of the spring beam has a longitudinal length that is between about five percent and about ten percent of the length of the spring beam.

12. The assembly of claim 10 , wherein the intermediate portion of the spring beam has a longitudinal length that is between about ten percent and about twenty-five percent of the length of the spring beam.

13. The assembly of claim 10 , wherein the intermediate portion of the spring beam has a longitudinal length that is between about twenty-five percent and about fifty percent of the length of the spring beam.

14. The assembly of claim 1 , wherein the spring beam extends radially relative to the axis between the first and the second surface, and the tapered geometry comprises a radial tapered geometry.

15. The assembly of claim 1 , wherein the spring beam extends axially relative to the axis between the first and the second surfaces, and the tapered geometry comprises an axial tapered geometry.

16. The assembly of claim 1 , wherein:

the first of the spring elements further includes a second spring beam extending a length longitudinally along a second centerline from the first mount to the second mount;

the second spring beam includes opposing third and fourth surfaces;

the third surface is disposed a third distance from the second centerline, and the fourth surface is disposed a fourth distance from the second centerline;

the third and the fourth distances change as the second spring beam extends longitudinally along the second centerline to provide at least a portion of the second spring beam with a tapered geometry; and

the portion of the second spring beam has a longitudinal length that is at least about five percent of the length of the second spring beam.

17. The assembly of claim 1 , further comprising:

a ring structure axially engaged with the seal base; and

a secondary seal device mounted with the ring structure and configured to substantially seal an annular gap between the ring structure and the annular array of the seal shoes.

18. A non-contact seal assembly, comprising:

a plurality of seal shoes arranged about an axis in an annular array;

a seal base circumscribing the annular array of the seal shoes; and

a plurality of spring elements, a first of the spring elements radially between a first of the seal shoes and the seal base, and the first of the spring elements including:

a first mount connected to the first of the seal shoes;

a second mount connected to the seal base; and

a spring beam extending a length longitudinally along a centerline from the first mount to the second mount, and the spring beam including first and second surfaces;

wherein the first surface is disposed a first distance from the centerline, and the second surface is disposed a second distance from the centerline and opposite the first surface;

wherein the first distance and the second distance change as the spring beam extends longitudinally along the centerline to provide at least a portion of the spring beam with a tapered geometry; and

wherein the first surface and the second surface are convex at least along a part of the portion of the spring beam.

19. The assembly of claim 1 , wherein the portion of the spring beam has a longitudinal length that is at least about five percent of the length of the spring beam.

20. A non-contact seal assembly, comprising:

a plurality of seal shoes arranged about an axis in an annular array;

a seal base circumscribing the annular array of the seal shoes; and

a plurality of spring elements, a first of the spring elements radially between a first of the seal shoes and the seal base, and the first of the spring elements including:

a first mount connected to the first of the seal shoes;

a second mount connected to the seal base; and

a spring beam having a length and a centerline, the length of the spring beam extending longitudinally along the centerline from the first mount to the second mount, and the spring beam including opposing first and second surfaces;

wherein, in a first portion of the spring beam, the first surface and the second surface substantially symmetrically converge towards the centerline as the first portion of the spring beam extends longitudinally along the centerline; and

wherein the first portion of the spring beam has a longitudinal length that is equal to or greater than about fifteen percent of the length of the spring beam.