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US 8,025,297 B2Granted
Bellows with alternating layers of high and low compliance material for dynamic applications
AssigneeThe Penn State Research Foundation
InventorRobert W.M. Smith
Life of this patent
Estimating the term…
Abstract
A bellows has a generally tubular elongated bellows body. The bellows body is defined by a wall generally enclosing a volume. The wall has a generally cylindrical inner surface and a generally cylindrical outer surface. The bellows body is formed by alternating layers of low compliance material and high compliance material. The cross sectional shape and dimension of the bellows body are generally constant between the first and second ends.
Claims18
A bellows for use in a dynamic device, comprising:
- a generally tubular elongated bellows body having a first end and a second end with a midportion extending therebetween, the body having a cross sectional shape and a cross sectional dimension, a longitudinal bellows axis being defined from the first end to the second end;
- the bellows body defined by a wall generally enclosing a volume, the wall having a generally cylindrical inner surface and a generally cylindrical outer surface;
- the bellows body comprising a stack of generally hoop shaped elements alternating between generally hoop shaped elements formed of a high compliance material and generally hoop shaped elements formed of a low compliance material, the generally hoop shaped elements formed of the high compliance material having an inner radius defining a portion of the inner surface of the wall and an outer radius defining a portion of the outer surface of the wall, the inner radius spaced from the outer radius by a thickness, t, and the generally hoop shaped element having a height, h;
- and
- the cross sectional shape and dimension are generally constant between the first and second ends;
- wherein the thickness, t, and the height, h, for each of the layers of high compliance material are chosen such that;
- the total strain energy, Ustrain—total, in each of the high compliance layers, as given by the formula:
- U
- strain
-
- _
-
- total
- =
- 1
- 2
-
- G
-
-
- ɛ
- 2
-
- (
- 4
-
- (
- t
- ·
- h
- )
- +
- t
- 3
- h
- )
- +
- (
- Δ
-
-
- P
- 2
- 2
-
- G
- )
-
- h
- 3
- 12
-
- t
- .
- is within 20% of a minimum obtainable total strain energy for any values of t and h;
- or;
- the maximum shear strain, γxy—max, in each of the high compliance layers, as given by the formula:
- γ
- xy
-
- _
-
- max
- =
- (
- Δ
-
-
- P
- G
- )
-
- h
- 2
-
-
- t
- +
- 3
-
- ɛ
-
-
- t
- h
- is within 20% of a minimum obtainable maximum shear strain for any values of t and h;
- wherein G is a predetermined shear modulus of the high compliance material;
- ε is a predetermined axial strain of the high compliance material along the longitudinal axis of the bellows;
- and
- ΔP is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.
87 more elements
A dynamic device comprising:
- a base;
- a moving element spaced from the base,
- a bellows comprising:
- a generally tubular elongated bellows body having a first end sealed to the moving element and a second end connected to the base, the bellows body having a longitudinal axis extending from the first end to the second end, the body having a cross sectional shape and a cross sectional dimension;
- the bellows body defined by a wall generally enclosing a volume, the wall having an inner surface and an outer surface;
- the bellows body comprising alternating layers of low compliance material and high compliance material, each of the layers of high compliance material of the bellows body being a generally hoop shaped element formed of the high compliance material, the hoop shaped element having an inner radius defining a portion of the inner surface of the wall and an outer radius defining a portion of the outer surface of the wall, the inner radius spaced from the outer radius by a thickness, t, and the generally hoop shaped element having a height, h:
- the cross sectional shape and dimension of the bellows body being generally constant between the first and second ends;
- wherein the moving element oscillates relative to the base along the longitudinal axis so as to expand and compress the volume enclosed by the bellows;
- and
- wherein the thickness, t, and the height, h, for each of the layers of high compliance material are chosen such that the total strain energy, Ustrain—total, in each of the high compliance layers, as given by the formula:
- U
- strain
-
- _
-
- total
- =
- 1
- 2
-
- G
-
-
- ɛ
- 2
-
- (
- 4
-
- (
- t
- ·
- h
- )
- +
- t
- 3
- h
- )
- +
- (
- Δ
-
-
- P
- 2
- 2
-
- G
- )
-
- h
- 3
- 12
-
- t
- .
- is within 20% of a minimum obtainable total strain energy for any values of t and h;
- wherein G is a predetermined shear modulus of the high compliance material;
- ε is a predetermined axial strain of the high compliance material along the longitudinal axis of the bellows;
- and
- ΔP is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.
59 more elements
A dynamic device comprising:
- a base;
- a moving element spaced from the base,
- a bellows comprising:
- a generally tubular elongated bellows body having a first end sealed to the moving element and a second end connected to the base, the bellows body having a longitudinal axis extending from the first end to the second end, the body having a cross sectional shape and a cross sectional dimension;
- the bellows body defined by a wall generally enclosing a volume, the wall having an inner surface and an outer surface;
- the bellows body comprising alternating layers of low compliance material and high compliance material, each of the layers of high compliance material of the bellows body being a generally hoop shaped element formed of the high compliance material, the hoop shaped element having an inner radius defining a portion of the inner surface of the wall and an outer radius defining a portion of the outer surface of the wall, the inner radius spaced from the outer radius by a thickness, t, and the generally hoop shaped element having a height, h;
- the cross sectional shape and dimension of the bellows body being generally constant between the first and second ends;
- wherein the moving element oscillates relative to the base along the longitudinal axis so as to expand and compress the volume enclosed by the bellows;
- and
- wherein the thickness, t, and the height, h, for each of the layers of high compliance material are chosen such that the maximum shear strain, γxy—max, in each of the high compliance layers, as given by the formula:
- γ
- xy
-
- _
-
- max
- =
- (
- Δ
-
-
- P
- G
- )
-
- h
- 2
-
- t
- +
- 3
-
- ɛ
-
-
- t
- h
- is within 20% of a minimum obtainable maximum shear strain for any values of t and h;
- wherein G is a predetermined shear modulus of the high compliance material;
- ε is a predetermined axial strain of the high compliance material along the longitudinal axis of the bellows;
- and
- ΔP is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.
39 more elements
Dependencies are inferred from the claim text.