U.S. patent number RE30,262 [Application Number 06/000,553] was granted by the patent office on 1980-04-29 for compressive load carrying bearings.
This patent grant is currently assigned to Lord Corporation. Invention is credited to Warren E. Schmidt.
United States Patent |
RE30,262 |
Schmidt |
April 29, 1980 |
**Please see images for:
( Certificate of Correction ) ** |
Compressive load carrying bearings
Abstract
A compressive load carrying laminated bearing comprising
alternating bonded layers of a resilient material and a
non-extensible material generally concentrically disposed about a
common center with successive layers being disposed at successively
increasing radii. The fatigue life thereof, when subjected to cylic
rotational or torsional motion about the common center, is
substantially enhanced by progressively increasing the thickness of
the layers of resilient material with increasing radii while
simultaneously progressively decreasing the modulus of elasticity
of the layers of resilient material with increasing radii.
.Iadd.
Inventors: |
Schmidt; Warren E. (Erie,
PA) |
Assignee: |
Lord Corporation (Erie,
PA)
|
Family
ID: |
26667806 |
Appl.
No.: |
06/000,553 |
Filed: |
December 26, 1978 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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893886 |
Apr 6, 1978 |
|
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Reissue of: |
147488 |
May 27, 1971 |
03679197 |
Jul 25, 1972 |
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Current U.S.
Class: |
267/152;
384/221 |
Current CPC
Class: |
B60G
5/053 (20130101); B60G 11/02 (20130101); F16F
1/403 (20130101); B60G 2200/318 (20130101); B60G
2202/112 (20130101) |
Current International
Class: |
B60G
11/02 (20060101); B60G 5/00 (20060101); B60G
5/053 (20060101); F16F 1/36 (20060101); F16F
1/40 (20060101); B60G 011/22 () |
Field of
Search: |
;308/26,2
;267/21R,21A,152,63R,63A,140,141 ;287/85 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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680988 |
|
Aug 1939 |
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DE2 |
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934336 |
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May 1948 |
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FR |
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465394 |
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May 1937 |
|
GB |
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828065 |
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Feb 1960 |
|
GB |
|
Other References
Lord Manufacturing-Technical Proposal 7L69-6, 5/23/69. .
USAAVLABS Technical Report 71-16, Flight Evaluation of Elastomeric
Bearings in an AH-1 Helicopter Main Rotor, C. H. Fagan, Mar. 1971.
.
Dynafacts, Lord Manufacturing Company, vol. 3, No. 4, 1960. .
"Dynafacts", Lord Manufacturing Company, vol. 7, No. 3, 1964. .
"Innovation in Vibration/Shock/Noise Control", Bulletin No. 910,
1966. .
Dynafacts, Lord Manufacturing Company, vol. 11, No. 3, 1968. .
Lord Library of Vibration/Shock/Noise Control, No. 49,
1968..
|
Primary Examiner: Lazarus; Ronald H.
Attorney, Agent or Firm: Howson and Howson
Parent Case Text
This Application is a Reissue of Ser. No. 147,488 filed 5/27/71 now
patent 3,679,197. This Application is also a continuation of
Reissue Application 893,886 filed 4/6/78 now abandoned. .Iaddend.
Claims
What is claimed is:
1. A compressive load carrying laminated bearing comprising
alternating bonded layers of a resilient material and a
non-extensible material generally concentrically disposed about a
common center with successive layers being disposed at successively
increasing radii with the thickness of said layers of resilient
material progressively increasing with radii while the modules of
elasticity of said layers of resilient material simultaneously
decreases with radii.
2. A compressive load carrying laminated bearing comprising an
inner support member having an outwardly facing convex surface, an
outer support member having an inwardly facing concave surface
radially spaced from the convex surface of said inner member, said
convex and concave surfaces being concentrically disposed about a
common center, alternating bonded layers of a resilient material
and a non-extensible material disposed between and fixedly secured
to the convex and concave surfaces of said inner and outer members,
respectively, said layers of non-extensible material being
concentrically disposed about said common center, successive layers
of said resilient material and non-extensible material being
disposed at successively increasing radii with the thickness of
said layers of resilient material progressively increasing with
radii while the modulus of elasticity of said layers of resilient
material simultaneously decreases with radii. .Iadd. 3. A
compressive load carrying laminated bearing comprising alternating
bonded layers of
a resilient material and
a non-extensible material
generally concentrically disposed about a common center with
successive layers being disposed at successively increasing
radii
with the thickness of said layers of resilient material
progressively increasing with radii while the modulus of elasticity
of said layers of resilient material simultaneously decreases with
radii;
said compressive load carrying laminated bearing having a
configuration comprising a generally conical, cylindrical or
spherical shape or a segmented form thereof; and
said compressive load carrying laminated bearing being
characterized by extended fatigue life resulting from a concurrent
increase in resilient layer thickness and decrease in modulus of
resilient layer elasticity moving generally radially outward from
said common center. .Iaddend. .Iadd. 4. A compressive load carrying
laminated bearing comprising an inner support member having
an outwardly facing convex surface, an outer support member
having
an inwardly facing concave surface radially spaced from the convex
surface of said inner member,
said convex and concave surfaces being concentrically disposed
about a common center, alternating bonded layers of a resilient
material and a non-extensible material disposed between and fixedly
secured to the convex and concave surfaces of said inner and outer
members respectively, said layers of non-extensible material being
concentrically disposed about said common center, successive layers
of said resilient material and non-extensible material being
disposed at successively increasing radii
with the thickness of said layers of resilient material
progressively increasing with radii while the modulus of elasticity
of said layers of resilient material simultaneously decreases with
radii,
said compressive load carrying laminated bearing having a
configuration comprising a generally conical, cylindrical or
spherical shape or a segmented form thereof; and said compressive
load carrying laminated bearing being characterized by extended
fatigue life resulting from a concurrent increase in resilient
layer thickness and decrease in modulus of resilient layer
elasticity, moving generally radially outward from said common
center. .Iaddend.
Description
This invention relates to compressive load carrying bearings and
more particularily to laminated bearings comprising alternating
bonded layers of a resilient material such as an elastomer and
non-extensible material such as metal.
It has been shown that the compressive load carrying ability or
capacity of a layer of resilient material in a direction
perpendicular thereto may be increased many times through the
inclusion of spaced parallel laminate of non-extensible material
while the yielding capacity in that direction is correspondingly
reduced. That is, a given thickness of rubber for instance loses
its compressive resilience increasingly with the increased number
of layers it is divided by parallel laminae of non-extensible
material. At the same time its compressive load carrying capacity
in that direction increases proportionately. However, the ability
of the resilient material to yield in shear or torsion in a
direction along the layers is almost completely unaffected by the
laminations and is essentially the same whether the rubber is in
one layer or a plurality of layers separated by layers of
non-extensible material. For a more detailed understanding of such
laminated bearings and basic factors to be considered in their
design, reference is made to Wildhaber, U.S. Pat. No. 2,752,766 and
Hinks, U.S. Pat. No. 2,900,182.
The above briefly described bearing concept has begun to find wide
commercial acceptance in bearings characterized in their ability to
carry relatively large compressive loads generally perpendicular to
the layers while simultaneously being relatively soft in shear
and/or torsion along the layers so as to readily accommodate
relative movement in designated directions.
While the concept may be employed in bearings of a variety of
configurations, depending on the compressive loads to be carried
and the motions to be accommodated, many are constructed such that
the alternating bonded layers of resilient material and
non-extensible material are generally concentrically disposed about
a common center with successive layers being disposed at
successively increasing radii. Such configurations include
cylindrical, conical, spherical, sectors of cylinders, cones and
spheres, etc. Due to the configuration and use of these bearings to
carrying large compressive loads while accommodating cyclic
torsional motion about the common center, greater compressive
stresses and shear stresses and strains are established in the
resilient layers closest to the common center as compared to
resilient layers more remote from the common center. In the normal
case, these bearings are constructed with the layers of resilient
material having the same modulus of elasticity, thickness and
length. The prolonged use of such a bearing in accommmodating
cyclic torsional motion results in failure from fatigue
preferentially at the innermost resilient layer. Accordingly, the
fatigue life of such a bearing is typically determined by the
stresses and strains established during use in the innermost
resilient layer.
It is an object of the present invention to improve the fatigue
life of a laminated bearing comprising alternating bonded layers of
resilient material and non-extensible material generally
concentrically disposed about a common center with successive
layers being disposed at successively increasing radii.
Briefly, the object of the present invention is accomplished by
progressively increasing the thickness of the layers of resilient
material with increasing radii while simultaneously progressively
decreasing the modulus of elasticity of the layers of resilient
material with increasing radii.
One of the objects of the invention having been stated, other
objects wll appear as the description proceeds, when taken in
connection with the accompanying drawings, in which:
FIG. 1 is a schematic plan view of a prior art laminated
bearing;
FIG. 2 is a schematic plan view of a laminated bearing similar to
that of FIG. 1 incorporating the present invention;
FIG. 3 graphically illustrates the effect of shape factor on
allowable compressive stress; and
FIG. 4 diagramatically illustrates shear strain distribution in a
laminated bearing.
With reference to FIG. 1, there is shown a conventional prior art
laminated bearing 10 comprising an inner member 11 having an
outwardly facing convex surface and an outer member 12 radially
spaced from the inner member 11 and having an inwardly facing
concave surface. Between and bonded to the members 11 and 12 are
alternating bonded layers 13 and 14 of a resilient material such as
an elastomer and a non-extensible material such as metal,
respectively. The convex and concave surfaces and each of the
layers 13 and 14 are concentrically disposed about a common center.
Bearing 10 is in the form of a sector of a cylinder with each of
layers 13 or resilient material having a generally uniform length.
The layers 13 of resilient material are of uniform thickness and
the resilient material of each layer 13 has the same modulus of
elasticity. It will be apparent that the mean circumferential area
of each layer 13 of resilient material increases with radii. Thus,
the shape factor or ratio between effective load carrying area for
a compressive load C centrally applied and bulge free area
progressively increases with radii. Accordingly, for a given
compressive load C, the compressive stress and strain are much
greater on the innermost layer 13. Likewise for a torque T, the
greatest shear stress and strain are on the innermost layer 13. The
result is preferential fatigue at the innermost layer 11.
The problems in these prior art laminated bearings have been
recognized to some extent as evidenced by Orain, U.S. Pat. No.
2,995,907 and Boggs, U.S. Pat. No. 3,377,110. Both of these
references teach altering the shape of the bearing, namely length,
to adjust the mean circumferential area of the outer resilient
layers 13 and thus, provide a more uniform shear stress and strain
distribution in the resilient layers 13 when subjected to a cyclic
torsional motion to prolong the life of the innermost resilient
layer 13. When graded length is employed to uniformly distribute
shear stresses and strain, compressive stresses in the outermost
layers is substantially increased. Thus, failure from excessive
compressive stresses becomes important. Furthermore, stability of
the bearing under high compressive loads is unfavorable. In
addition, such bearings are often inadequate from a compression
load capacity or are impractical to manufacture.
By the present invention the shape of the convention laminated
bearing can be retained while substantially enhancing the fatigue
characteristics of the bearing without substantial sacrifice in
compression deflection or compression load capacity. With reference
to FIG. 2, there is shown a bearing 20 of the present invention in
the form of a sector of a cylinder. As illustrated, bearing 20
comprises an inner member 21 having an outwardly facing convex
surface and an outer member 22 radially spaced from the inner
member 21 and having an inwardly facing concave surface. Between
and bonded to the members 11 and 12 are alternating bonded layers
23 and 24 of a resilient material such as an elastomer and a
non-extensible material such as metal, respectively. Inner and
outer members 21 and 22 are identical to members 11 and 12 of
bearing 10. As with bearing 10, the convex and concave surfaces and
each of the layers 23 and 24 are concentrically disposed about a
common center and each layer 23 of resilient material has a
generally uniform length. However, rather than layers 23 of a
resilient material having uniform thickness and uniform modulus of
elasticity, the thickness of the layers 23 progressively increases
from the common center while the modulus of elasticity
progressively decreases from the common center. This simultaneous
grading of thickness and modulus in the resilient layers 23 has
been found to substantially enhance the fatigue life of a bearing
subject to cyclic torsional motion.
To understand the benefits obtained by the present invention, let
us first look at the effect of a compressive load C on a bearing.
Each layer of resilient material in series must carry this
compressive load C. For prior art bearing 10, FIG. 1, having
uniform resilient layer 13 thickness, the effective load carrying
area of each layer increases with increasing radii. Accordingly,
the compressive stresses in the layers 13 decreases with increasing
radii. With reference to FIG. 3 there is shown the typical relation
between allowable compressive stress and shape factor for a given
compressive load and modulus of elasticity of the resilient
material. In the bearing 10, let us suppose the shape factor for
the innermost layer is S, with a compressive stress C.sub.1 and
that the shape factor for the outermost layer is S.sub.2. Since the
compressive stress C.sub.2 in the outer most layer is less than
C.sub.1, the shape factor at the outermost layer may be reduced to
S.sub.3, a value substantially less than that provided by bearing
10. One approach, as previously mentioned, is to grade the
circumferential area. However, by the present invention, it has
been found most desirable to grade the thickness of the resilient
layers proportionally with radii. If the bearing 20 is to have the
same overall dimensions of bearing 10, it is seen that by grading
the thickness of resilient layers 23 additional resilient material
can be used and less non-extensible material. While this approach
also reduces to some extent the resistance to compression
deflection of bearing 20, the advantages obtained are more than
offsetting. By the inclusion of more resilient material radially of
the bearing within the available space, the rotational stiffness of
the bearing is decreased to require less work of the resilient
layers in torsion for a given torsional motion reducing to some
extent the shear stresses and strains on the innermost resilient
layers.
Having considered the compressive stress distribution and the
effect of grading the thickness of the resilient layers on shear
stresses and strains, let us look in more detail at the bearing in
torsion. It can be shown that the torsional or rotational spring
rate K.sub.R of a spring is governed by the equation
K.sub.S =spring rate in shear translation, and
R=distance from fixed pivot to center line of spring K.sub.S.
Thus, for a laminated bearing wherein the layers are concentric
about a common center, all other things being equal, the
contribution of the outermost resilient layers to the rotational
stiffness is considerably greater than the innermost resilient
layers. Since the inner resilient layers are much softer in
rotation than the outer resilient layers, the major portion of the
deflection (strain) in torsion will occur at the inner layers, the
innermost layer in particular.
The torsional strain in layers of resilient material in a laminated
bearing 30 at different radial distances from the common center are
shown in FIG. 4 where 31 designates an inner layer of thickness
t.sub.1 and mean radius R.sub.1 and 32 designates an outer layer of
thickness t.sub.n and mean radius R.sub.n, each subject to a torque
T. Under this torque, the inner layer 31 deflects in shear a
distance d.sub.1 or through an angle .theta..sub.1 and the outer
layer 32 deflects in shear a distance d.sub.n or through an angle
.theta..sub.2. The equations giving these strains are as
follows:
1. K.sub.r.sbsb.1 =rotational spring rate of layer
31=(T/.theta..sub.1);
2. K.sub.r.sbsb.n =rotational spring rate of layer
32=(T/.theta..sub.2);
3. .theta..sub.1 =(d.sub.1 /R.sub.1) where d.sub.1 is the
tangential deflection of layer 31;
4. .theta..sub.2 =(d.sub.n /R.sub.n) where d.sub.n is the
tangential deflection of layer 32;
5. e.sub.1 =strain of layer 31=(d.sub.1 /t.sub.1); and
6. e.sub.n =strain of layer 32=(d.sub.n /t.sub.n).
Substituting Equations 3 and 5 in Equation 1 gives:
7. K.sub.r.sbsb.1 =(TR.sub.1 /d.sub.1)=(TR.sub.1 /e.sub.1
t.sub.1).
Substituting Equations 4 and 6 in Equation 2 gives:
8. K.sub.r.sbsb.n =(TR.sub.n /d.sub.n)=(TR.sub.n /e.sub.n
t.sub.n).
The ratio of Equations 7 and 8 gives: ##EQU1## Substituting the
values of K.sub.R =K.sub.S R.sub.1.sup.2 and K.sub.R.sbsb.n
=K.sub.S.sbsb.n R.sub.n.sup.2, Equation 9 becomes ##EQU2##
Substituting in Equation 10 the values of K.sub.S.sbsb.1 =(A.sub.1
G.sub.1 /t.sub.1) and K.sub.S.sbsb.n =(A.sub.n G.sub.n
/t.sub.n)
where: A.sub.1 and A.sub.n =Surface area of the respective layers
31 and 32; and
G.sub.1 and G.sub.n =Shear modulus of the respective layers 31 and
32, Equation (10) becomes: ##EQU3## 12. (A.sub.1 G.sub.1 R.sub.1
/A.sub.n G.sub.n R.sub.n)=e.sub.n /e.sub.1.
In a given design then Equation 12 means that the strain is a
direct function of area, modulus, and radius. In fatigue
applications, then the desirable thing to have would be a condition
where the strain e.sub.n across the outer layer 32 is equal to or
approaching the strain e.sub.1 across the inner layer 31.
Applying the Equation 12 to the layers a and n for a cylindrical or
tube form laminated bearing having length 1,
13. (e.sub.n /e.sub.n)=A.sub.n G.sub.n R.sub.n /A.sub.n G.sub.n
R.sub.n)=2.pi.R.sub.a G.sub.a R.sub.a /2.pi.R.sub.n G.sub.n
R.sub.n)=(G.sub.a R.sub.a 2/G.sub.n R.sub.n.sup.2) or
14. (G.sub.n /G.sub.n)=R.sub.n.sup.2 e.sub.n /R.sub.a.sup.2
e.sub.a).
From Equation 14 it appears that the strain in layers n and a are
equal if the modulus of elasticity varies inversely as the square
of the mean radius of the respective resilient layers or (G.sub.a
/G.sub.A',)=(R.sub.n.sup.2 /R.sub.a.sup.2).
It also appears that if the modulus of the layer a is equal to the
modulus of the layer n, the strain will vary inversely as the
square of the radius. For example, when G.sub.n =G.sub.a and
R.sub.n =2 and R.sub.a =1, e.sub.a =e.sub.n (R.sub.n.sup.2
/R.sub.a.sup.2)=4.sub.e.sbsb.n.
Applying equation 12 to the layers x and n of a spherical laminated
bearing:
15. (e.sub.n /e.sub.x)=(A.sub.x G.sub.x R.sub.x /A.sub.n G.sub.n
R.sub.n)=(2.pi.R.sub.x.sup.2 G.sub.x R.sub.x /2.pi.R.sub.n.sup.2
G.sub.n R.sub.n)=(G.sub.x R.sub.x.sup.3 /G.sub.n
R.sub.n.sup.3).
From Equation 14 it appears that the strains in layers n and x are
equal if the modulus of elasticity varies inversely as the cube of
the mean radius of the respective resilient layers of (G.sub.x
/G.sub.AH)=(R.sub.n.sup.3 /R.sub.x.sup.3).
It also appears that if the modulus of the layers x is equal to the
modulus of the layer n, the strain will vary inversely as the cubes
of the radius. For example, when G.sub.n =G.sub.x, R.sub.n =2 and
R.sub.x =1, e.sub.x =(e.sub.n R.sub.n.sup.3
/R.sub.x.sup.3)=8e.sub.n.
For the cylindrical laminated bearing, the strain in each resilient
layer is uniform throughout the length. For the spherical laminated
bearing, the strain varies along the length of each layer. This
suggests that for spherical shapes the spring should occupy less
than a hemisphere if permitted by other design requirements.
In practical designs, the variation in strain may be subject to
correction factors due to variation in the geometry of the springs
from the simple cylindrical and spherical shapes discussed. These
correction factors in many instances may be empirically derived
from test experiences. However, in general, it may be stated that
for laminated bearings of the present invention, the fatigue life
will be improved if the modulus of each layer varies inversely as
an exponential of its radius as given by the following equation:
##EQU4## where M is a number less than or equal to 1. More
generally, it may be stated that improvement in fatigue life will
be obtained if there is a progressive decrease in modulus of
elasticity of the resilient material with increase in radii.
The above presentation clearly illustrates that in a laminated
bearing comprising alternating bonded layers of a reslient material
and a non-extensible material generally concentrically disposed
about a common center with successive layers being disposed at
successively increasing radii, it is advantageous to progressively
increase the thickness of the layers of resilient material with
increasing radii and to progressively decrease the modulus of
elasticity of the layers of resilient material with increasing
radii. By progressively increasing the thickness of the layers of
resilient material with increasing radii more resilient material
may be radially disposed within the same space with the compressive
stresses in the resilient layers maintained within allowable
limits. The increased amount of resilient material favorably
redistributes the shear stresses and strains in torsion to enhance
the fatigue life thereof. In addition the number of non-extensible
laminae are decreased to reduce the overall weight and cost of
manufacture. However, the graded thickness of the resilient layers
approach cannot be utilized to optimize the shear-strain
distribution. To complete optimization in design, it is necessary
to grade the modulus of elasticity of the layers of resilient
material such that it decreases with increasing radii. These two
concepts cooperate to provide an optimum design in a laminated
bearing adapted to accommodate relatively large cyclic torsional
motions while carrying a high compressive load.
By way of illustration, a laminated bearing of the cylindrical or
tube form was designed to carrying a compressive load of 70,000
pounds and to accommodate a cyclic torsional motion of 7.degree..
The overall length of the bearing was 6 inches. The inside and
outside radii were 1.620 and 2.750 inches, respectively. In a prior
art design, having uniform thickness and modulus of elasticity in
the resilient layer, a calculated fatigue life of 530 hours
resulted. Where the thickness and modulus of elasticity were
simultaneously graded in accordance with the present invention with
the innermost resilient layer having the same thickness and modulus
of elasticity as that of the innermost layer of the prior art
bearing, a calculated fatigue life of approximately 6,200 hours
resulted. Needless to say, the advantage obtained in fatigue life
by the present invention is quite substantial.
In the drawings and specification, there has been set forth a
preferred embodiment of the invention and, although specific terms
are employed, they are used in a generic and descriptive sense only
and not for purposes of limitation.
* * * * *