BELLOWS WITH ALTERNATING LAYERS OF HIGH AND LOW COMPLIANCE MATERIAL FOR DYNAMIC APPLICATIONS

• US 20080060442A1
• Filed: 11/06/2007
• Published: 03/13/2008
• Est. Priority Date: 04/10/2002
• Status: Active Grant

• Current Assignee: Penn State Research Foundation
• Original Assignee: Penn State Research Foundation
• Inventors: Smith, Robert
• Granted Patent: US 8,025,297 B2
• Time in Patent Office: Days
• US Class Current: 73/729.1
• CPC Class Codes: F16L 27/11 the sleeve having the form of a bellows with multiple corrugations
• CPC Class Codes: G01L 7/061 construction or mounting of bellows

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.

Claims

1. A bellows 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 alternating layers of low compliance material and high compliance material; and

the cross sectional shape and dimension are generally constant between the first and second ends.

2. The bellows of claim 1, wherein each of the layers of high compliance material is 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.

3. The bellows of claim 2, wherein each of the layers of low compliance material is a generally hoop shaped element formed of the low 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 the thickness, t, the inner radius of the generally hoop shaped element formed of the high compliance material being the same as the inner radius of the generally hoop shaped element formed of the low compliance material.

4. The bellows of claim 2, 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, U_strain—

_total, in each of the high compliance layers, as given by the formula;

$U_{\mathrm{strain\_total}}=\frac{1}{2}<br><br>G<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varepsilon <br><br>}}^2\left(4<br><br>\left(t·<br><br>h\right)+\frac{t^3}{h}\right)+\left(\frac{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>P^2}{2<br><br>G}\right)<br><br>\frac{h^3}{12<br><br>t}.$

is within 20% of the 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

Δ

P is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.

5. The bellows of claim 2, 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, γ

<sub>xy—

max</sub>, in each of the high compliance layers, as given by the formula;

${\mathrm{\gamma <br><br>}}_{\mathrm{xy\_max}}=\left(\frac{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>P}{G}\right)<br><br>\frac{h}{2<br><br>t}+3<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{\varepsilon <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}{h}$

is within 20% of the 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

Δ

P is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.

6. The bellows of claim 2, wherein the each of the layers of low compliance material is a generally hoop shaped element formed of the low compliance material, the hoop shaped element formed of the low compliance material having an inner radius and an outer radius spaced apart by distance less than the thickness between the inner radius and the outer radius of the generally hoop shaped elements formed of the high compliance material.

7. The bellows of claim 1, wherein the high compliance material is a strain crystallizing elastomer.

8. The bellows of claim 7, wherein the strain crystallizing elastomer is natural rubber.

9. The bellows of claim 1, further comprising a coating covering the inner and/or outer surface of the wall defining the bellows body.

10. 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, U<sub>strain—

total</sub>, in each of the high compliance layers, as given by the formula;

$U_{\mathrm{strain\_total}}=\frac{1}{2}<br><br>G<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varepsilon <br><br>}}^2\left(4<br><br>\left(t·<br><br>h\right)+\frac{t^3}{h}\right)+\left(\frac{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>P^2}{2<br><br>G}\right)<br><br>\frac{h^3}{12<br><br>t}.$

is within 20% of the minimum obtainable total strain energy for any values of t and h;

or;

the maximum shear strain, γ

<sub>xy—

max</sub>, in each of the high compliance layers, as given by the formula;

${\mathrm{\gamma <br><br>}}_{\mathrm{xy\_max}}=\left(\frac{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>P}{G}\right)<br><br>\frac{h}{2<br><br>t}+3<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{\varepsilon <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}{h}$

is within 20% of the 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

Δ

P is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.

11. The bellows of claim 10, wherein each of the generally hoop shaped element formed of the low compliance material, the hoop shaped element has 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 the thickness, t, the inner radius of the generally hoop shaped element formed of the high compliance material being the same as the inner radius of the generally hoop shaped element formed of the low compliance material.

12. The bellows of claim 10, wherein the high compliance material is strain crystallizing elastomer.

13. The bellows of claim 12, wherein the strain crystallizing elastomer is natural rubber.

14. The bellows of claim 107 further comprising a coating covering the inner and/or outer surface of the wall defining the bellows body.

15. 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;

the cross sectional shape and dimension are generally constant between the first and second ends; and

wherein the moving element oscillates relative to the base alone the longitudinal axis so as to expand and compress the volume enclosed by the bellows.

16. The dynamic device according to claim 15, wherein the dynamic device is a thermoacoustic device;

and wherein;

the base is a housing with a thermal core disposed in the housing, the thermal core including at least a first and a second heat exchanger; and

the moving element is a piston spaced from the thermal core, the piston being operable to oscillate with respect to the thermal core;

17. The dynamic device of claim 15, wherein each of the layers of high compliance material of the bellows body is 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.

18. The dynamic device of claim 17, wherein each of the layers of low compliance material of the bellows body is a generally hoop shaped element formed of the low 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 the thickness, t, the inner radius of the generally hoop shaped element formed of the high compliance material being the same as the inner radius of the generally hoop shaped element formed of the low compliance material.

19. The dynamic device of claim 17, 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, U_strain—

_total, in each of the high compliance layers, as given by the formula;

$U_{\mathrm{strain\_total}}=\frac{1}{2}<br><br>G<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varepsilon <br><br>}}^2<br><br>\left(4<br><br>\left(t·<br><br>h\right)+\frac{t^3}{h}\right)+\left(\frac{\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>P^2}{2<br><br>\text{\hspace{1em}<br><br>}<br><br>G}\right)<br><br>\frac{h^3}{12<br><br>\text{\hspace{1em}<br><br>}<br><br>t}.$

is within 20% of the 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

Δ

P is a predetermined peal dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.

20. The dynamic device of claim 17, 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, γ

<sub>xy—

max</sub>, in each of the high compliance layers, as given by the formula;

${\mathrm{\gamma <br><br>}}_{\mathrm{xy\_max}}=\left(\frac{\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>P}{G}\right)<br><br>\frac{h}{2<br><br>\text{\hspace{1em}<br><br>}<br><br>t}+3<br><br>\frac{\mathrm{\varepsilon <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}{h}$

is within 20% of the 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

Δ

P is a predetermined peak dynamic pressure difference between a pressure in the volume enclosed by the bellows and a pressure exterior to the bellows.

21. The dynamic device of claim 17, wherein the each of the layers of low compliance material of the bellows body is a generally hoop shaped element formed of the low compliance material, the hoop shaped element formed of the low compliance material having an inner radius and an outer radius spaced apart by distance less than the thickness between the inner radius and the outer radius of the generally hoop shaped elements formed of the high compliance material.

22. The dynamic device of claim 15, wherein the high compliance material is strain crystallizing elastomer.

23. The dynamic device of claim 15, further comprising a coating covering the inner and/or outer surface of the wall defining the bellows body.