Note: Descriptions are shown in the official language in which they were submitted.
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~ - Description
, . , . .. _ .. _ . _ . _
Temperature Compensated Gas Spring
Technical Field
. This invention relates to gas springs and more particularly to gas
springs which are automatieally compensating so as to operate uniformly over
a broad temperature range.
Backtrround Art
The springs used to support automobile trunk lids, hoods, and the like,
especially the hatch-back trunk lid, are often of the gas spring variety. A
gas spring i5 essentially a sealed cylinder containing a gas under high pressureand having a piston rod extending from one end of the cylinder. Typically,
nitrogen gas having a pressure of approximately 1000 psi is used in the
cylinder. The spring force results from the pressure of the gas acting on a
cross sectional area equal to that of the rod within the cylinder and urging
the rod outwardly. When the rod is pushed into the cylinder, as when the
hatch-back trunk lid is closed, the rod displaces a certain volume within the
cylinder which was previously occupied by the gas~ Since the totaI volume
within the cylinder is fixed, the remaining volume available to the gas
dccreases, resulting in an increase in the pressure of the gas. Thus, the force
2U acting to move the rod outward increases. In conventional gas springs, a
piston-like structure may be attached to the rod inside of the cylinder and
used for damping and limiting the extent of motion of the rod. Since the gas
pressure is normally equal on both sides of the piston, it produces little if any
force on the rod.
Ideally, the pressure of the gas should be sufficient to move the
piston rod outwardly from the cylinder and lift the trunk lid or the like which
is attached thereto. The gas pressure should also be low enough when the
rod is completely extended and the trunk lid or the like is raised to enable
a person to easily move the rod into the cylinder when the trunk lid is being
closed. A drawback arising from the use of a single gas in a gas spring is
that the pressure of any gas in a fixed volume is rclated to thc temperaturc
of the gas. For an ideal gas, which nitrogcn resembles, the pressure is
directly proportional to the absolute temperature of the gas. This
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dependence can cause considelable problems when such gas springs are used
in automobiles that are exposed to ambient temperatures ranging îrom below
0F to above 100F.
When the ambient temperature is low the pressure of the gas inside
5 the cylinder is low, resulting in insufficient force to urge the rod outwardlyto lift the weight of the trunk lid. When the ambient temperature is high
the pressure of the gas inside the cylinder is high, resulting in a large force
urging the rod out of the cylinder, a situation which may cause a trunk lid
connected to the rod to raise very quickly and strike a person opening the
hS/..
~? 10 trunk. Furthermore, when the ambient temperature is high, the gas pressure
inside the cylinder is large when the rod is completely extended, makinG it
difficult to move the rod into the cylinder when it is desired to clcse the
trunk lid.
Shock absorbers which automatically compensate for changes in
15 ambient temperature are known in the art. See, for example, U.S. Patent
No. 2,944,639 to Blake, U.S. Patent No. 3,107,752 to McCean, U.S. Patent
No. 3,301,410 'co Seay, U.S. Patent No. 3,971,551 to Kendall et al., and U.S.
Patent No. 3,~44,197 to Dachicourt. These devices generally provide an
extra chamber or the like within the shock absorber to accommodate the
20 changing volume of the primary damping fluid as the ambient temperature
changes. Such devices are not appropriate for providing temperature
compensation in a gas spring because they are concerned with keeping the
fluid volume constant, rather than wit~ keeping an outwardly directed
pressure constant.
It is an object of the present invention to provide a gas spring in
which the sensitivity of its spring force to temperature variation is reduced
to an acceptably low level.
Disclosure of the Invention
The invention is a temperature compensated gas spring which includes
a sealed casing, a slidable rod extending from the interior to the exterior of
the casing through one end thereof, and a piston mounted to the rod within
the casing. A primary pressure source is located within the casing and acts
against the piston to urge the rod out of the casing, and a secondary pressure
source is located within the casing and acts against the piston to urge the
35 rod into the casing. The primary pressure is greater than the secondary
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, ,,.~. .
pressure, and the percent change of the secondary pressure with temperature
,~, is ~rcater than the percent change of the primary pressure with temperature.
The primary pressure source is preferably a pressurized primary gas,
~-'' such as nitrogen gas, whose pressure varies essentially proportionally with
5 absolute temperature and which remains in the gas phase ove~ the
~; ~ temperature range to which the gas spring is exposed. A desirable
temperature range is-30C to 80C. I
The secondary pressure source is preferably the vapor pressure of a
~; two-phase system in which the liquid and vapor phases are in equilibrium over
10 the temperature range of -30C to 80C. Such vapor pressure varies
approximately exponentially with absolute temperature. Suitable two-phase
systcms include acetylene, ethane, ~REON-12, FREON-13, FREO~-114,
propane, propadiene, perfluoropropane, dimethyl ether, N-butane, ammonia,
hydrogen bromide, and hydro~en iodide. The secondary pressure source may
15 also be a two-phase system in which the liquid and vapor phases remain in
equilibrium over a substantial portion of the temperature range of -30C to
80C, such as sulfur hexafluoride.
In the preferred embodiment of the invention the sealed casing
includes a cylindrical tube with a closed end wall at one end and an end wall
20 having an opening to allow the rod to pass therethrough at the other end. An
inner tube is coaxially disposed within the casing, and one end of the inner
tube is attached to the closed end wall. The piston is disposed within the
inner tube and divides the inner tube into a first inner volume between the
piston and the closed end wall and a second inner volume in the remainder
25 of the inner tube. A baffle is located between the inner and outer tubes to
divide the casing volume, exterior of the inner tube, into a first outer volume
adjacent the closed end wall and a second outer volume adjacent the end wall
with the opening. A first conduit means permits fluid flow between the first
inner volume and first outer volume, and a second conduit means permits
30 fluid flow between the second inner volume and second outer volume. The
primary pressure source is located in the first inner volume and first outer
volume and the secondary pressure source is located in the second inner
volume and second outer volume.
The first conduit means is preferably one or more holes through the
35 inncr tube beyond the extcnt of travel of the piston toward the closed end
wall. In one embodiment the inner tube is shorter than the cylindrical tube,
1,
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....
and the inner tube is in fluid nOw communication with the second outer
volume to form the second conduit means. In a second embodiment, the
~- inner tube is the same length as the cylindrieal tube, and both ends are
attached to the end walls of the casing, and the second conduit means is one
5 or more holes through the inner tube beyond the extent of travel of the
- piston toward $he end wall with the opening.
~: The gas spring may also include a stop which limits the travel of the
piston. A fluid`seal is provided between the piston and the inner tube and
~: between the rod and the wall through which it passes.
. .
10 Brief Description of the Drawings
Fig. 1 is an axial, sectional view of a first embodiment of a gas
spring in accordance with the present invention;
Fig. 2 is a graph showing force as a function of temperature of the
gas spring shown in Fig. 1 wherein the primary pressure source is nitrogen gas
15 and the secondary pressure source is ammonia liquid and vapor in equilibrium;Fig. 3 is an axial, sectional view of a second embodiment of a gas
spring in accordance with the present invention;
Fig. 4 is a log-log graph showing the phase diagram for FREON-12;
Fig. 5 is a graph of net outward spring force versus temperature of
20 the gas spring shown in Fig. 3 wherein the primary pressure source is nitrogen
gas and the secondary pressure source is FREON-12;
Fig. 6 is a log-log graph showrng the phase diagram for sulfur
hexafluoride; and
Fig. ~ is a graph of net outward spring force versus ternperature of
25 the gas spring shown in Fig. 3 wherein the primary pressure source is nitrogen
gas and the secondary pressure source is sulfur hexafluoride.
Description of the Preferred Embodiments
. .
One embodiment of a temperature compensated gas spring in
accordance with the present invention is shown in Fig. 1. The gas spring 10
includes a sealed casing 12 made of an outer sleeve or tube 14 with a closed
end wall 16 mounted at one end and with a wall 18 mounted at the other end.
Wall 18 has an opening 20 therethrough. The gas spring 10 includes an inner
sleeve or tube 22 located inside of and coaxial with casing 12. One end of
inner tube 22 is attached to end wall 16, and the other end is axially spaced
. ~ '
5_
', from wall 18. A piston 24 is located within inner tube 22 and divides the
interior of inner tube 22 into a first inner volume 26 between closed end wall
16 and piston 24 and a second inner volume 28 on the side of the piston
~~ toward wall 18. An elongated rod 30 is attached to piston 24 and extends
' 5 out of casing 12 through opening 20 in wall 18.
~, A baffle 32 is attached to and extends between the outside of inner
tube 22 and the inside of outer tube 14 and divides the casing volume,
~.x~
exclllsive of the inner tube, into a first outer volume 34 adjacent wall 16 and
a second outer volume 36 adjacent the wall 18. The baffle is preferably an
i~- 10 annular plate. The baffle 32 also provides support to inner tube 22. One or
' more holes 38 are provided in inner tube 22 at a location beyond the extent
of travel of piston 24 therein in the direction toward end wall 16. Holes 38
form a first conduit means which permits fluid flow between first inner
volume ~6 and first outer volume 34. In the embodiment shown in Fig. 1,
inner tube 22 is open at the end closest to wall 18 and forms a second
conduit means which permits fluid flow between second inner volume 28 and
second outer volume 36.
The gas spring 10 may include a stop 40 at the free end of inner tube
22 which limits the travel of piston 24 toward the wall 18 and retains the
piston within inner tube 22. Stop 40 shown in Fig. 1 is a washer-like plate
attached to the end of inner tube 22 which surrounds, but does not contact,
rod 30 to leave an annular space 42 between rod 30 and stop 40 for fluid
flow. The gas spring 10 includes a first seal 44 between pis`ton 24 and the
inner surface of inner tube 22 to prevent fluid flow between the first and
second inner volumes 26, 28 and includes a second seal 46 between rod 30 and
wall 13 to prevent fluid flow between the interior and exterior of casing 12.
The gas spring 10 also includes a rod 48 attached to the exterior of
closed end 16 of casing 12 having an eye 50 at its end. Rod 30 has an eye
52 at its free end exterior of casing 12. Eyes 50 and 52 allow gas spring 10
to be mechanically connected between two points, such as between the body
and the trunk lid of an automobile. Preferably inner tube 22, outer tube 14
and piston 24 are cylindrical in shape.
A primary pressure source is located in first inner volume 26 and
first outer volume 34 and acts against piston 24 to urge rod 30 outwardly of
casing 12. A secondary pressure source is located in second inner volume 28
and second outer volume 36 and acts against piston 24 to urge the rod into
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the casing. The net force acting on piston 24 results from the difference
between the forces from the primary and secondary pressure sources. Since
gas spring 10 is to function as a spring with an outwardly directed spring
force, it is necessary that the primary pressu~e be greater than the secondary
5 pressure.
Preferably, the primary pressure source will be a pressurized primary
gas whose pressure varies proportionally with absolute temperature and which
will remain gaseous over the temperature range to which the gas spring is
~, exposed, A preferred primary gas is nitrogen gas which behaves essentially
y;, 10 according to the ideal gas law (PV = nRT) over the temperature range of30C to 8DC. It will be recognized in the art that no gas will perform
exactly in accordance with the theoretical ideal gas law. Other gases which
may be used include argon, helium, hydrogen, Icrypton, and neon.
The reduction of temperature sensitivity in gas spring 10 is
15 accomplished by providing a reverse force on piston 24 from the secondary
pressure source which tends to cancel out the extra force from the primary
pressure source due to increases in temperature. The secondary pressure is
chosen to behave quite differently from the essentially perfect gas behavior
of the primary gas. In one aspect of the invention, the secondary pressure
20 source is the vapor pressure of a two-phase system in which the liquid and
vapor phases are in equilibrium. The vapor pressure of such a two-phase
system varies approximately exponentially with absolute temperature rather
than directly proportionally. The mal~ requirement of any secondary
pressure source selected is that the percent change of secondary pressure
25 with temperature be greater than the percent change of the primary pressure
with temperature.
Th¢re are many organie and inorganic substances that can serve as a
secondary pressure source, including acetylene, ethane, FREON-12,
FREON-13, FREON-114, propane, propadiene, perfluoropropane, dimethyl
30 ether, N-butane, ammonia, hydrogen bromide, and hydrogen iodide. The
vapor pressure of these substances range from about 0 to 150 pounds per
square inch (psi) at a temperature of about -30C to about 100 psi to over
900 psi at 70C. In a two-phase system, for a given substance the pressure
exerted by its vapor will depend only on temperature. The best substance to
35 use in a given application is determined by design requirements for the
application, sucll as spring force, spring size, material cost, manufacturing
cost, seal lifetime, and degree of temperature compensation desired.
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,~t It is not absolutely necessary that the secondary pressure be
;~ generated by a two-phase system. As described in detail hereinaf7'er in
connection with Example 3, sulfur hexafluoride can be used as the secondary
pressure source. Above a critical temperature, sulfur hexafluoride cannot
5 exist as a two phase system, but exists solely as a vapor with no liquid phasec- - present. However, temperature compensation is achieved even above the
critical temperature because the percent change of the sulfur hexafluoride
~; vapor pressure (i.e., the secondary pressure) with temperature will still be
- greater than the percent chance of a perfect gas pressure with temperature.
Since a substance will remain in a two-phase system with its vapor
and liquid phases in equilibrium only for certain ranges of specific volume,
a requirement is placed on the volume available for the substance in the gas
spring. In general it is ~esired that both the liquid and vapor phases aIways
be present so that the vapor pressure will depend only on temperature. As
15 the spring is compressed, i.e., as the piston 24 is moved toward wall 16, thevolume available for the two-phase system is increased. If initially there is
an insufficient amount of the liquid phase of the suhstance, such an increase
of the total available volume could cause all of the liquid to convert to
vapor. The pressure of this vapor will in general vary with the temperature
20 in a fashion similar to other gases and thus provide little if any temperature
compensation. lowever, if too much of the substance is used, a problem
arises when the spring is allowed to expand, thus reducing the volume
available for the substance. This redueti=on in volume could cause all of the
vapor phase to condense, forcing the substance entirely into the liquid phase.
25 This would effectively prevent the piston from moving any further.
To avoid these possible problems with a two-phase system used as a
secondary pressure source, the following re~uirements must be met: (1) The
minimum amount of the substance necessary is that which is just sufficient
to provide a t~vo-phase system when the gas spring is fully compressed i.e.,
30 when the available volume is the greatest, at the highest temperature to
which the gas spring may be exposed, and (2) The volume available for the
substance should be sufficiently large so that the vapor does not entirely
condense into liquid when the gas spring is fully extended i.e., when the
available volume is t}7e smallest. The limiting environment for this second
35 requirement is also the highest temperature to which the gas spring may be
exposed.
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The concentric tube arrangement shown in Fig. 1 is particularly
advantageous in a gas spring. A sufficient additional volume exterior of
inner tube 22 is provided in first outer volume 34 for the primary gas so that
~: it is not excessively compressed when rod 3Q is completely retracted within
the gas spring. Otherwise, the resulting excessive pressures could cause
undesirable and excessive spring forces. Likewise, an additional volume
exterior of inner tube 22 is provided in second outer volume 36 for the
secondary pressure source so that it is not excessively compressed when rod
30 is completely extended.
;~ 10 All of the components of gas spring 10, with the exception of seals
k , 44 and 46 are made of a metal with sufficient strength to withstand the
pressures of the confined gases. The use of a cylindrical inner tube 22, outer
tube 14, and piston 24 is particularly advantageous.
EXAMPLE 1
The following is an example of a gas spring 10 in accordance with the
embodiment shown in Fig. 1 using nitrogen gas as the primary pressure source
and using ammonia as the two-phase system for the secondary pressure
source. The relationship between the various parame ters involved in gas
spring 10 can be described algebraically using the following variables:
Ag = area of the piston on which the nitrogen gas pressure acts (in.2)
Av = area of the piston on which the ammonia vapor pressure
acts (jn.2)
Dp = diameter of the piston (in~3 -
Dr = diameter of the rod (in.)
25 F = force of the gas spring (lb.)
Pg = pressure of the nitrogen gas (psi)
Pv = pressure of the ammonia vapor (psi)
Po = nitrogen gas pressure at 20C (psi)
T = ternperature (C)
The net outward spring force, F, is determined by subtracting the
force acting on the piston due to the ammonia vapor from the force acting
on the piston due to the nitrogen gas. The equation for calculating F,
ignoring the force of atmospheric pressure on the rod 30, is:
(1) F = Ag Pg - Av Pv
The pressure of the nitrogen gas is reasonably ~ell represented by:
1 ~26~54~?~
g
(2~ pg = ~T + 273) pO
For this example it is assumed that the desired spring force F is 1~0
lb. at the temperature extremes of -30C and 70C. The vapor pressure of
ammonia in a two-phase system can be determined from standard and well
known handbooks such as Chemical Engineers Handbook, edited by John H.
Perry (McGraw-Hill, 1950, 3d Edition). At -30C the vapor pressure of
~r' ammonia is 20 psi, and at 70C the vapor pressure is 475 psi. By inserting
these values, the desired F = lO0 lb., and equation 2 into equation 1, the
following equations are obtained:
(3) 100 = Ag (-30 + 273) Po _ 20 Av
4) 100 = Ag (70 273) P - 475 Av
Solving equations 3 and 4 simultaneously yields:
(5) Av = 0.0921 in.2
(6) Ag Po = 122.80 lb.
If the rod diameter, Dr, is chosen to be 5/161', a value typical for gas
springs, the area of the piston, Av, on which the ammonia vapor pressure
acts, is:
(7) Av = 7T /4 (Dg2 - Dr2) = 7T /4 (Dg2 - (5/16)2) = 0.0921 in.2
The solution of equation 7 results in Dg = 0.4636 in., from which it is
determined that Ag = 0.1688 in.2. Using equation 6 above, the necessary fill
pressure, Po, for the nitrogen gas at 20C is 727 psi.
By loading the first inner ~olume and first outer volumes with
nitrogen gas at 727 psi at 20C, selecting the rod diameter to be 5/16" and
the piston diameter to be 0.4636 in., and loading the second inner volume and
second outer volume with an amount of ammonia such that the liquid and
vapor phases will remain in equilibrium, the gas spring will have a nominal
outward force of 100 lb. at the temperature extremes of -30C and 70C.
The behavior of this gas spring at other temperatures can be determined by
calculating Pg at other temperatures using equation 2 above, determining the
values of Pv at various temperatures, and calculating the forces using
equation l above. Table I below lists this data over the desired temperature
range.
.
-10-
!~:~ - Table I
Pressure Spring Force
''Jii ~ Temp. Pg Pv PgAg PvAv F
[C~ [psi~ [psi] [lb~ [Ib~ [Ib]
~' -30 603.9 20 101.8 1.8 1~0.0
j,`_, ,
-20 627.8 30 106.0 2.8 103.2
-10 652.6 45 110.2 4.1 1q6.1
0 677.~ 65 114.4 6.0 108.4
- 702.2 90 118.6 8.3 110.3
10 2~ 727.0 12S 122.8 11.S 111.3
' 30 751.8 170 127.0 15.7 111.3
776.6 230 131.2 21.2 110.0
801.4 294 135.4 27.1 108.3
826.2 370 139.6 34.1 105.5
15 70 o51.1 d~75 143.7 43.7 100.0
The above results are shown graphically in Fig. 2 where curve "A'~
represents the outward force acting on the piston (PgAg), curve "B"
represents the inward force acting on the piston ~PvAv), and curve "C"
represents the net spring force of the gas spring of Example 1, all as a
function of temperature. 1`his gas spring has a maximum force of about
111.3 Ib. between 20 and 30C, and a minimum force of 100 lb. at the
temperature extremes. The temperature compensation of the gas spring of
Example 1 can be compared with the use of nitrogen gas alone by comparing
the maximum and minimum spring forces developed with the force at 20C
being the standard. The deviation is about 10,'o for the gas spring of Example
1 while the deviation is about 34a~0 for a gas spring using nitrogen gas alone.
It can be appreciated that the gas spring of the present invention
considerably reduccs the variation of spring force with temperature as
compared with thc use of nitrogen gas alone.
A second embodimcnt of a temperature compensated gas spring in
- accordance with the present invention is shown in Fig. 3. The gas spring 60
shown in Fig. 3 has many elements which arc identical with elements in the
gas spring 10 shown in Fig. 1 and discussed above. Accordingly, like elements
in both figures arc referred to by like refercnce numbers, and only the
diffcrences between the two embodiments will be discusscd.
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~h~,~ In the gas spring 60 shown in Fig. 3, the inner tube 62 extends
completcly between end walls 15 and 18 and is attached to both end walls.
The second inner volume 64 is located within inner tube 62 between piston
24 and wall 18, and second outer volume 66 is located exterior of the inner
tube between baffle 32 and wall 18. One or more holes 68 are located in
i~ inner tube 62 at a location beyond the extent of travel of piston 24 tow~rd
~- wall 18, as determined by stop 40. Holes 68 form a conduit means between
second inner volume 64 and second outer volume 66.
Other than the above mentioned structural differences, the embodi-
ment of the gas spring 60 shown in ~ig. 3 operates exactly the same as the
gas spring 10 shown in Fig. 1. A primary pressure source is located in the
first inner volume 26 and first outer volume 34, and a secondary pressure
source is located in second inner volume G4 and second outer volume 66, as
described above in connection with Fig. 1.
The relationship between the various parameters involved in gas
spring 60 can be described algebraically using the following variables:
Ag = area of the piston on which the primary gas pressure acts
(in.~)
Ar = area of the rod on which atmospheric pressure acts (in.2)
Av = area of the piston on which the secondary pressure acts (in.2)
Dp = diameter of the piston (in.)
Dr = diameter of the rod ~in.)
Dt = inner diameter of the outer~tube (in.)
F = net outward force of the gas spring (lb.)
L = length of the inner and outer tubes (in.)`
Ls = distance between stop 40 and the wall lS (in.)
Lt = length of gas spring between eye 50 and eye 52, which varies
with X (in.)
Lv = distance between baffle 32 and the wall 1~ (in.)
M = mass of the secondary pressure source material (lb.)
Pa = atmopsheric pressure (psi)
Pg = pressure of the primary gas (psi)
Po = pressure of the primary gas at 20C (psi)
Pv = pressure of the secondary pressurc source (psi)
S = stroke, or maximum design value for -the spring compression X
(in.)
~%1~5~
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-12-
T = temperature (C)
Vg = volume of the primary gas which varies with X (in.3)
;~ Yv = volume of the secondary pressure source material, also varying
i- with X (in.3)
; 5 Wc = thickness of the inner tube (in.)
Wp =thickness of the piston (in.)
Ws = thickness of the baffle (in.)
X = amount of spring compression, measured from the stop to the
piston (in.)
The characteristics of the preferred embodiment, shown in Figures 3,
can be described by selecting initial values for the following parameters: Dp,
Dr, Dt, L, Ls, Lv, Lt (maximum), Pa, Po, S, Wc, Wp, and Ws. It is also
necessary to l<now the dependence of both Pg and Pv on temperature. ~or
Pg it is usually sufficient to use the perfect gas law. For Pv, the dependence
of vapor pressure on temperature for the particular substance selected can
be obtained from well known handbooks.
The following equations relate to the remaining parameters to the
initial ones listed above.
20 (8) Ag = 4P
(g) Ar = 4
(10) Lt (minimum) = Lt tmaximum) ~ S
(11) Lt = Lt (maximum) - X
(12) Av = Ag - Ar
25 (13) Vg = ~ /4 (Dt2 - (Dp + 2 Wc)2) (L - Lv - Ws) +
Ag (L - Wp - Ls - X)
(14) Vv = ~ /4 (Dt2 - (Dp + 2Wc)2) Lv + Av (X + Ls)
The pressure of the primary gas is a function of X, through the
volume Vg, of the temperature T, and of the fill pressure Po. Under the
30 assumption that gas filling is done with the rod extended (i.e., X = O), and
that the gas essentially obeys the ideal gas law, its pressure is given by:
Po (T -~ 273) Vg (maximum)
(15) Pg = 293 Vg
The equation for the spring force as a function of compression and
35 temperature is given by:
~l
' --13--
~(16) F = Pg ~g- Pv Av- Pa Ar
iPl EXAMPLE 2
In this example, a gas spring in accordance with the second
embodiment using a two-phase secondary pressure source is chosen ~o have
5 an extended length of 50 inches and a strolce of 20 inches. At a temperature
of 20C it will have a net spring force F of 150 lb. when extended and 160
lb. when compressed. The primary gas is nitrogen and the secondary pressure
c,;source substance is FREON-12 which is maintained such that there is always
both the vapor and the liquid phases over the operating temperature range.
10 The temperature compensation is to extend from -30C to 8ûC.
The values of the initially seleeted parameters are:
Dp = 0.593 in.
Dr = 0.3125 in.
Dt = 2.25 in.
15 L = 26.0 in.
Ls - 3.214 in.
Lv = 0.179 in.
Lt (max) = 50.0 in.
M = 0.0400 lb.
20 Pa = 14.7 psi
Po = 604.4 psi
S = 20.0 in.
Wc = 0.0625 in.
Wp = 0.25 in.
~s = 0.0625 in.
Equations 8, 9, and 12 above, then yield the values: Ag = 0.277 in.2,
Ar - 0.077 in.2, and Av = 0.200 in.2.
The amount of FREON-12 to be inserted in gas spring 60 in this
example is 0.0400 lb. An amount less than about 0.029 lb. would cause all
30 of the liquid to convert to vapor when the spring is fully compressed if the
temperature was as high as 80C. An amount more than about 0.0500 lb.
would prevent the spring from extending fully if the temperature was as high
as 80C because all of the vapor would be cornpressed into the liquid state.
Fig. 4 is a phase diagram of FREON-12, where vapor pressure is plotted as
~5 a function of specific volume. There are twelve curves representing the
temperatures over which the spring is to be able to function. The dotted line
. .
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1 4--
~"
curve "D" shows the region inside of which the liquid and vapor are in
equilibrium together, and accordingly, where this example is supposed to
i` operate. Table II belows lists the quantities used to compute the specific
volume of the FREON-12 in the limiting cases where the gas spring is fully
S extended and fully compressed.
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Table II
Gas Spring Gas Spring
Pully Fully
Extended Compressed
Volume Vv [Eq. (14)] 1.28 eu. in. 5.28 cu. in.
Mass M of FREON-12 t~.0400 lb. 0.0400 lb.
Specific Volume = Vv/Mass 32.0 cu. in. per lb. 132 cu. in. per lb.
-, -.
The operating region corresponding to 0.0~00 lb. of FREON-12 is
shown by the dotted line curve "E" in Fig. 4. For the temperature range of
10 interest the FXEON-12 remains clearly within the liquid-vapor phaseO
Table III below presents the gas spring force over the full range of
spring compression and temperature for which it was designed. The force
values come from equation 16 above, together with equation 15, and the
FXEON-12 vapor pressure values are from the phase diagrarn of Fig. 4.
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Q,,_1 ~ ~ ~ ~ L" U~ :
c~ 1 ~7 ~ C~ ~r c~ c~
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I
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C~ C`~ C`~ ~:1
l ~ ~ ~ ~ ~ _I
.
.jj OOOOOO
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C~ C ~: ~ ~
o
-17-
Fig. 5 is a piot of the results of Table III for full compression andfull extension and compares the results with a gas spring that had no
temperature compensation. Curve "F" represents the spring force versus
temperature for the temperature compensated gas spring of Example 2 when
5 the spring is completely compressed. Curve 'IGt' shows the same data when
the spring is completely extended. Curves "~I" and 'lI" show the spring force
versus temperature for an uncompensated gas spring which is completely
compressed and completely extended, respectively.
Both Fig. S and Table III show that there is compensation for changes
10 in temperature. The degree of temperature compensation can be quantified
by computing the resulting percent variation of the spring force with
temperature using the data from Table III and comparing it with that
expected for an uncompensated design. Table IV gives the temperature-
compensated results. On a full swing basis, the deviation due to temperature
for gas spring 60 in Example 2 is under 12 percent.
-18- !~
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--19--
The corresponding variation for an uncompensated gas spring is much
larger, namely about 37.5%. It can be estimated by assuming that the gas
behaves like a perfect gas. Accordingly, for a given volume Vg, the pressure,
and thus the spring force, is proportional to the absolute temperature. For
5 comparison to the above example, a temperature swing of 30C to 80C
~243K to 353K) would cause the following variation:
F(80C) - F( 30C)
, . . F~20C) x,100 -
P(80C) -OP() 30C) x 100 =
p(353K) - P(243K) X 100 =
353K - 243K x 100 = 37.5%
E.gAMPLE 3
In this example, as in Example 2, the gas spring is to have an
extended length of 50 inches and a stroke of 20 inches. At a temperature
of 20C it will have a net spring force of 15û lb. in the extended position,
and 160 lb. in the compressed position. The primary gas is nitrogen, and the
secondary pressure source material is sulfur hexafluoride (SF6). The
temperature compensation range is -30C to 80C despite the fact that the
critical temperature for SF6 is 45.55C, above which it can only e~ist as a
gas.
The values of the initially selected parameters are: ~
Dp = 0.510 in. I
Dr ~ 0.3125 in.
Dt = 2.50 in.
L = 26.0 in.
Ls = 3.00 in.
Lv = 9.166 in.
Lt(~qax) = 50.0 in.
~ = 0.464 lb.
Pa - 14.7 psi
Po = 929.5 psi
S = 20.0 in.
Wc = 0.0625 in.
Wp = 0.25 in.
Ws = O.OG25 in.
~ ` ~
~? ` ~ 54~3
~20-
Equations 8, 9, and 12 above yield the following values: Ag = 0.204
in.2, Ar = 0.077 in.2, and Av = 0.128 in.2.
Fig. G is a phase diagram of sulfur hexanuoride, where vapor pressure
is plotted as a function of specific volume. There are twelve solid curves
5 representating the temperatures over which the gas spring is to function.
The dotted line curve "J" shows the region inside of which the liquid and
vapor are in equilibrium. For this example, 0.4644 lb. of sulfur hexafluoride
is to be inserted into the gas spring. Table V below lists the quantities used
to compute the specific volume of the sulfur hexafluoride in the two limiting
10 cases where the gas spring is fully extended and fully compressed.
. .
f
--21--
Table V
Gas Spring Gas Spring
Fully Extended Fully Compressed
Volume Vv ~Eq. (1~)] 4~.47 cu. in. 45.02 cu. in.
Mass ~l of SF6 0.4644 lb. 0.4644 lb.
- Specific Volume = Vv/Mass 91.45 cu. in. per lb. 96.95 cu. in. per lb~
- The operating region corresponding to 0.4644 lb. of sulfur hexa-
fluoride is shown by the dotted line curve "K" in Fig. 6. The range of
specific volume is quite narrow in this example. Furthermore, these specific
10 volumes extend to temperatures above the critical point where it is
impossible for the sulfur hexafluoride to exist in a liquid state. This example
is designed such as to limit the specific volume from changing substantially
from the extended to the compressed configuration. This limitation is
accomplished by locating the baffle 32 closer to end wall 16 than in Example
15 2. Note the difference in Lv in Examples 2 and 3. This feature has the
effect of making the pressure of the sulfur hexafluoride depend almost
entirely on the temperature and very little on the displacement parameter X.
It is important to note that even above 40C, where the operating region
leaves the liquid-vapor phase, the properties of sulfur hexafluoride are such
20 that the percent change of its pressure with temperature is greater than that of the primary gas, nitrogen.
Table Vl below presents the gas spring force over the full range of
spring compression and temperature for which the gas spring of Example 3
is designed. The force values come from equation 16 above, together with
25 equation 15 and the sulfur hexafluoride vapor pressure values from the phase
diagram of Fig. 6.
~ ? 12CI1$4~338
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-22-
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v ~ -I
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s~
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-23-
Fig. 7 is a piot of the results of Table VI for full compression and full
extension and compares the results with an uncornpensated gas spring. Curve
"Lt' represents the spring force versus temperature for the temperature
compensated gas spring of Example 3 wherein the spring is completely
5 compressed. Curve "Mtt shows the same data where the spring is completely
extended. Curves t'N" and I~O~t show the spring force versus temperature for
an uncompensated gas spring which is completely compressed and completely
extended, respectively.
Both Fig. 7 and Table VI show clearly that there is compensation for
10 changes in temperature, even when operating above the critical point of the
secondary pressure source substance for part of the time. As with the
FREON-12 example, the degree of temperature compensation for the sulfur
hexafluoride example can be quantified by computing the resulting percent
variation of the spring force with temperature using the data from Table VI
15 and comparing it with that expected for an uncompensated design. Table VII
gives the $emperature-compensated results. On a full swing basis, the
deviation due to temperature is under 6 percent, a value that is only half as
much as for the FREON-12 example and compares even more favorably with
the 37.5% deviation of the uncompensated gas spring as discussed above in
20 connection with Example 2.
054~
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Having described preferred embodiments of the invention, it is to be
understood that it may be otherwise embodied within the scope of the
appended clairns.
