Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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Title: SELF-ADJUSTING SHOCK ABSORBER HAVING STAGED METERING
BACKGROUND OF T~ lNVENTION
The invention relates generally to the field of shock
absorbers or energy absorption or energy dissipation devices,
and particularly to fluid displacement-type shock absorbers.
Shock absorbers are normally designed to decelarate a load,
i.e., a moving mass, to rest without damage. Most loads have a
deceleration limit expressed in G's as a multiple of the effect
of gravity. Approaching or exceeding the G limit by stopping
too abruptly, risks substantial damage to the load itself. De-
celeration which is too abrupt can burst hydraulic shoc~ absorbers.
Moreover, since the shock absorber transmits force to the struc-
ture on which it is mounted, the mechanical strength of the struc-
ture must also be ta~en into account, particularly if a load may
have a positive velocity at the end of the stroke of the shock
absorber, and structural or mechanical stops are used to position
such load systems, wherein, the remaining energy of these systems
are absorbed elastically by the restraining structure.
There are many industrial appLications, for example~ rail-
roads or foundries, where very heavy loads are encountered re-
quiring very large stopping forces. In a foundry, for example,
where large metal castings are made, the sand molds into which
the molten metal is poured, referred to as the "cope" and "drag',
are conveyed to and from their respective stations on a "head
carriage". These carriages, weighing on the order of 50,000
pounds, are generally accelerated to velocities of 5 feet per
second by pneumatic cylinders which apply forces on the order of
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15,000 pounds. Typical hydraulic fluid displacement-type shock
absorbers used for this type of application have bore sizes rang-
ing from 3 to 4 inches, and piston strokes or displacements of
6 to 8 inches. It is conventional in this type of shock absorber
to provide some means of diminishing the orifice area used to
control the rate of fluid flow out of the cylinder, under the
action of the piston, into a reservoir of some kind. This can be
accomplished with a plurality of axially spaced holes through the
cylinder wall. As these holes are passed up by the piston head,
they are covered and no longer are available as exit ports for
the fluid. The size and spacing of the orifice holes used deter-
mines the deceleration characteristics that can be provided by
such devices. An example in the railway industry is referred
to in U. S. Patent No. 3,301,410 to Seay.
one of the problems in industrial applications such as
foundries is accommodating the wide variety of load systems en-
countered, whether due to variations of mass and/or velocity alone
or in combination with constant or varying propelling forces. In
very simple terms, a relatively stiff shock absorber i8 needed
for a heavy mass-high intensity load system~ and a relatively
soft shock absorber is needed ~or a light mass-low intensity load
system. Conventional shock absorbers are designed to handle con-
stant mass-constant intensity load systems.
The conventional way to accommodate a variety of constant
mass-constant intensity load systems is to use what has been
called an "adjustable" shock absorber having some means of mechan-
ically adjusting or presetting the relative size of the orifices
in a multi-port hydraulic shock absorber, as shown, for exampla,
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in U. S. Patent 4,071,122 to Schupner. While it is generally
understood that the most efficient way to arrest a constant mass-
constant intensity load system is to provide a constant level of
resistance over the entire stroke of the shock absorber, and there-
by, constant deceleration, the design efficiency of conventional
adjustable shock absorbers is seriously hampered by the inability
to reach an optimum preadjustment for the shock absorber. Such
preadjustment not only requires advance knowledge of the exact
mass, and intensity of the load system which will be encountered,
and the ability to pre-establish the optimum adjustment setting
required without use of expensive electronic instrumentation but
also that the intensity of the load system remain constant through-
out the deceleration excursion. once adjusted for a specific
constant mass-constant intensity load system, the conventional
shock absorber can only handle small deviations from the exact
mass, and intensity of this load system. For example, it cannot
efficiently stop a load system whose mass may be lower or higher
than that accounted for by the adjustment setting utilized, or
whose intensity tends to vary over the stroke due to increasing
propelling force. Moreover, conventional adjustable shock ab-
sorbers are only provided with one mode of adjustability, that
is, the size of their oriPices can be ad~usted but their locations
cannot be. The conventional adjustable shock absorber can there-
for do no more than adjust for constant mass~constant intensity
load systems, for example, by rotating a sleeve to eclipse the
orifices in a fixed spaced hole system as shown, for example, in
U. S. Patent No. 4,071,122. This type of sleeve structure also
introduces a temperature-dependent error factor due to leakage,
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as some of the h~draulic fluid leaving the orifices flows between
the outside of the pressure tube, containing the orifices, and
the inside of the adjustment sleeve, containing the adjustment
apertures, thereby bypassing the controlling apertures.
SUMMARY OF THE INVENTIO~
The general objective of the invention is to greatly in-
crease the operating range of a fluid displacement-type shock
absorber by designing a specific orifice structure that can
accommodate a large number of different load systems or mass
systems, wherein the intensities of these load sys-tems or mass
systems may remain constant or vary over a wide range, whereby,
the need for any adjustments of the controlling orifices is
eliminated, and furthermore, to provide predetermined decelera-
tion control for each mass system or load system considered with-
in the design range of the device, and to accomplish such deceler-
ation control most efficiently by utilizing the full stroke or
full displacement of the device for arresting each individual mass
system or load system considered.
These and other related o~jects of the invention are achieved
in a shock absorber with a fixed orifice structure inherently pro-
viding adaptive control of two or more mass system3, of constant,
or varying intensities. The orificed structure contains a pro-
gression of control regions, each distinctively different in ori-
fice area size, wherein the area size of each control region
diminishes progressively as a continuum, from the origin of the
progression (zero stroke position of piston displacement) to
stroke termination; wherein, each control region is responsive to
a corresponding mass system and its respective intensity; wherein,
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the equivalent mass of the mass system is used as a measure of
the intensity of the mass system; wherein, the progression re-
ferred to is based upon the ordering of all mass systems or equiva-
lent mass systems considered within the selected design range of
the device, and the deceleration rates imposed upon these mass
systems or equivalent mass systems is by design choice; wherein,
the rate at which the area size of each control region diminishes
with respect to displacement can be defined by the deceleration
rate imposed upon each respective mass system by design choice;
wherein, each control region is preferably designed to provide
a constant rate of deceleration for its respective mass system;
wherein, control regions designed for externally motivated or
externally propelled mass systems are preferably designed for
speed controlled mass systems to accommodate the highest intensity
levels of such mass systems during their deceleration modes; and
wherein, this invention device may also be referred to as a de-
celeration control device.
In that each control region of the device according to the
invention is designed to provide a specific deceleration rate for
its corresponding mass system, the ordering of these control
regions must comply with the ordering of the mass systems, the
ordering used by this invention being from the smallest mass
system of lowest intensity to the largest mas~ system of highest
intensity. In this design, for example, the first control region
that the piston traverses from its initiaL position, will provide
a constant rate of deceleration for the smallest mass system of
lowest intensity, whereas, the last control region will provide a
constant rate of deceleration for the largest mass system of
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highest intensity. If the available exit orifice area is plotted
against piston displacement for the entire stroke, the result is
a graph which depicts a continuous series of connected segments
of different exponential curves, starting at the beginning of the
stroke with the total area or all orifices used, and decaying to
zero at the end of the stroke.
If a series of axially spaced holes is used, the result is
a step function approximation of an exponential segment curve.
If a specifically contoured tapered metering pin orifice structure
or equivalent is employed, a smooth orifice curve can be obtained.
In one embodiment, the diameter of the holes in a given control
region is held constant and the exponential decay is provided
solely by axial spacing of the holes, wherein, the sizes of the
holes may or may not vary from region to region.
In accordance with the invention, an incoming mass system in
a sense "seeks out" its corresponding control region. If the mass
system is an intermediate mass system of intermediate intensity,
it will tend to reach its maximum allowed deceleration in its res-
pective intermediate control region.
~ he unique aspects of the invention include the ability o
a single device, without the need of adjustment mechanisms, to
provide predetermined deceleration control, and total arrestment
for two or more different mass systems, wherein, these mass systems
may be constant intensity mass systems or mass systems of varying
intensity, and to achieve such deceleration control most efficient-
ly by utilizing the full displacement stroke of the device for the
arrestment of each of the mass systems; wherein, the total dis-
placement stroke of the device is a function of (a) the total
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number of different mass systems being controlled~ (b) the velo-
cities of each of these mass systems at the zero stroke position
of piston displacement, and (c) the deceleration rates imposed
upon these mass systems by design choice.
DESCRIPTION OF THE DR~WINGS
Fig. 1 is an elevational view of a shock absorber according to
the invention having a portion of the outer sleeve broken away to
reveal the inner cylinder with a pattern of holes to be dimensioned
and spaced as described hereinafter according to the invention.
Fig. 2 is a view similar to that of Fig. 1~ except that the
inner cylinder is in section, illustrating an alternate embodiment
employing a tapered pin dimensioned and contoured as described
hereinafter according to the invention.
Fig. 3 is a composite containing Graphs I, II, III and IV de-
picting buffing force FB(x)~ velocity V(x)~ and orifice area A(x)
versus displacement, respectively, and related Equations 1 through 5
Fig. 4 is a composite containing Graphs V, VI and VII of
orifice area, deceleration and velocity versus displacement, res-
pectively, according to the invention.
Fig. 5 is a calibrated Graph VIII of orifice area versus dis-
placement for a pair of control regions corresponding to Example 1
in the following deseription~ aecording to the invention.
Fig. 6 is a Graph rX of orifice area versus displacement for
four different load systems, showing control regions corresponding
to Example 2 in the following deseription, according to the inven-
tion.
DESCRIPTION OF SPECIFIC EMBODIMENTS
The following disclosure is offered for public dissemination
in return for the grant of a patent. Although it is detailed to
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insure adequacy and aid understanding~ this is not intended to
prejudice that purpose of the patent which is to cover each new
inventive concept therein no matter how others may later disguise
it by variations in form or additions or further improvements.
The shock absorber of Fig. 1 co~prises a cylinder assembly
10 having an outer cylindrical body or casing 11 and a coaxial
inner cylinder 12. A piston assembly 13 has a piston 14 sealingly
slidable within the inner cylinder 12. A piston rod 15 is coaxi-
ally secured to the piston 14 and extends out through a coaxial
opening in the cylinder assembly 10 terminating in a shock re-
ceiving pressure member 17. The other ends of the cylinders 11
and 12 are closed. A coil compression spring 18 coaxially sur-
rounding the distal portion of the piston rod 15 bears against the
outer face of the cylinder assembly 10 and the annular shoulder
provided by the pressure member 17 thus urging the piston rod 15
out of the cylinder assembly 10 and causing the piston 14 to
assume an initial position J as indicated in Fig. 1. The annular
volume between cylinders 11 and 12 forms a reservoir 19 for hydrau-
lic fluid. A resilient cellular pad 20, such as nitrogen mole-
cules encapsulated in rubber, is located in reservoir 19. The
inner cylinder 12 is also filled with hydraulic 1uid and is in
fluid communication with the re~ervoir 19 via axially and circum-
ferentially spaced holes 21 and 21d formed through the wall of
the inner cylinder 12 in the stroke portion of the cylinder, i.e.,
between the initial and final positions, J and K, of the face of
the piston 14.
The cylinder 12 has one or more flow openings 22 which per-
mit filling the inner cylinder 12 with hydraulic fluid behind the
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piston 14 during the compression stroke of the piston 14. A chec]~
valve (not shown) is typically arranged in the piston 14 to seal
the piston 14 during the compression stroke. On the return stroke,
the check valve opens allowing hydraulic fluid to flow from the
portion of the cylinder 12 behind the piston 14 to the portion of
the cylinder 12 ahead of the piston via the piston 14. Openings
22a (shown in phantom) in the inner cylinder 12 at the end around
the piston rod 15 place the portion of the inner cylinder 12 be-
hind the piston 14 in continuous fluid communication with the
reservoir 19. Thus, in effect, the portion of the inner cylinder
12 behind the piston forms a part of the hydraulic fluid reservoir
19.
~ part from the orifice structure, the structure of the shock
absorber shown in Fig. 1 may be conventional. Further details of
the conventional structure, to the extent applicable or desirable,
can be found in the prior literature, for example, U. S. Patents
Nos. 3,301,410 and 4,071,122.
In use, the cylinder assembly 10 is typically mounted to a
fixed structure. If desired, however, the piston rod assembly 13
may be secured to a fixed structure and the opposite face o~ the
cylinder assembly 10 can be left ~ree to receive the shock force.
When an object or mass system strikes the pressure member
17, its momentum is transmitted to piston assembly 13, which in
turn transmits this momentum to the fluid contained in cylinder
12. As a result o~ this momentum exchange, piston assembly 13,
and the adjacent body o~ fluid it impinges upon are accelerated.
The resultant velocity of the object or mass system, the piston
assembly, and the adjacent body of fluid depends upon the rate at
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which the body of fluid can be displaced from orifices 21 and 21a
by the impending momentum of the object or mass system. As the
piston 14 moves away from its initial position in the cylinder 12,
fluid is forced out of the holes 2la and 21 into the reservoir
19. At the beginning of the compression or working stroke of the
piston 14, the amount of resistive force provided by holes 21 and
21a is determined by the total area of these holes or orifices.
For example, if there are n holes, each o~ diameter d, the total
area through which fluid can escape from the inner cylinder lZ
would be n~d2/4. As the piston 14 forces oil out through the
holes, it would eventually come to the point where it passes by
and closes off the hole which is closest to the face of the
approaching piston 14. Once this first hole had been passed,
relative to an n-hole system, the area available for discharging
fluid would be (n~ rd2/4, one hole having been eliminated from
the remaining orifice pattern or orifice structure. As the piston
continues its working stroke, the holes are successivel~ passed
and closed by the piston, thereby progressively diminishing the
number of holes discharging oil from the cylinder 12 into the
reservoir 19. As a result of the decreasing area available, rela-
tive to the impending momentum of the object or mass system, the
rate at which fluid can escape the c~linder is decreased, the
objective being to decelerate the moving ob~ect or mass system to
a rest position at a controlled rate before the piston 14 reached
the end of its stroke at K.
Axially spacing the holes 21 provides a way of making the
orifice area decline stepwise as a function of piston displacement.
The circumferential displacement of the holes has no effect on the
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operation of the orifices. It is their axial displacement and
diameter which determines the decay rate of the orifice area.
Arbitrarily, five circumferential displacements, each 15 apart,
are designated as A, B, C, D and E, as indicated in Fig. 1. There
are other known orifice structures for accomplishing this purpose,
some of which do it smoothly or continuously instead of stepwise.
one of these is shown schematically in Fig. 2. As in the embodi-
ment of Fig. 1, the shock absorber of Fig. 2 comprises a cylinder
assembly 10', including a similar outer cylinder 11 and a modified
coaxial inner cylinder 12', the annular volume between them again
forming a similar oil reservoir 19. Instead of holes 21, the
cylinder assembly 10' has a coaxial metering pin 23 tapered down
toward its distal end. The larger end of the metering pin 23 is
secured coaxially to the closed end of the cylinder 12' in close
proximity to the end position K of the full stroke. The pointed
end of pin 23 is received in apertured coaxial cylindrical bore 24
dimensioned to receive the entire working length of the metering
pin 23. As the piston assembly 13' moves through its worlcing
stroke, the bore 24 is in communication with the reservoir 19 via
holes 25 and 26 through the piston assembly 13 and the cylinder
12', respectively. As the piston assembly 13' moves away from its
initial pO9 ition, the metering pin cross-section intercepted by
the opening in the piston 14' increases continuously. The pin
23 can be contoured according to any given mathematical relation-
ship to displacement of the piston 14'. Examples of hydraulic
shock absorbers using metering pins to determine the orifice area
as a function of displacement are shown in U. S. Patents Nos.
3,729,101 to Brambilla et al, 3,774,895 to Willich et al, 3,568,856
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to Knippel~ 3,693,768 to Erdmann and 3,3~8,703 to Powell et al.
Except where otherwise indicated, in the following descrip-
tion and in the claims, ~he term orifice structure or orifice
means is meant to encompass axially displaced holes and tapered
metering pins. In addition, the term is intended to encompass
slots, grooves, projections and any other types of structural
features in a hydraulic shock absorber which has the effect of
progressively decreasing the rate at which fluid can escape from
the cylinder as a function of piston displacement. Any structure
or combination of structures which has this capacity can be em-
ployed to implement the invention described herein.
Fig. 3 shows four graphs which illustrate the underlying
principles of orifice area metering versus piston displacement
in fluid-displacement shock absorbers. Assume that an object to
be decelerated, having mass M, and propelling force Fp, strikes
the piston assembly of a hydraulic shock absorber with an initial
velocity V(o) = vO. The object has a design deceleration limit
a(x) ~: L which is no~ to be exceeded while the object is deceLer-
ated from VO to zero over a given distance or stroke XT.
The best way to keep peak deceleration low is to design the
system so that the deceleration is as constank as possible. From
Graphs I, II and Eq. t2), it is apparent that in order to maintain
a(x) constant, the ratio FB(x)/M (x) must remain constant. Graph
III and Eq. (4) illustrate pictorially and mathematically the
velocity versus displacement profile V(x) for constant decelera-
tion. Graph IV and Eq. (6) illustrate pictorially and mathematic-
ally the orifice area versus displacement profile A(x) required
to decelerate the equivalent mass system Me(x), depicted in Graph
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I, at a constant rate. Note that Eq. (6) is derived from Eq. (5)
for Me(o) = Me(x) = Me(xT) = constant, and that V(x) and A(x) de-
cay at the same exponential rate relative to displacement when
this is true. Manufacturers of conventional fixed orifice, and
adjustable orifice shock absorbers design their orifice structures
to accommodate such mass systems, and/or equivalent mass systems.
That is, mass systems wherein Fp(x) and thereby Me(x) remain con-
stant throughout the intended deceleration stroke xT.
For a spaced hole orifice structure defining a single con-
trol region wherein all orifice holes are of the same size, and
d = Diameter of orifice hole
N = Total number of orifice holes
n = n orifice hole
n = 1, 2, 3 ........ N
A(n) = Remaining orifice area as a function of the
nth hole location, then
A(n) = (N-n)~rd /~ Eq. (7)
From Eq. (S), Eq. (6) and Eq. (7), the spacing of orifice holes
can be expressed as follows:
X = XT ~1- (1- N) Me(O)} 2 Eq. (8)
2~
X = X ~ - (1- N) J ~ Eq. (9)
where the location of the axis of each orifice hole is determined
by subtracting hal~ its diameter d~ in Equations (8) and (9).
When metering by conventional methods, that is~ using a
single control region~ and assu~ing that the equivalent mass as
a function of displacement x remains constant, that is, Me(x) =
Me(O) = Me(XT) = constant, where X = O defines the beginning of
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the control region, and X = XT defines the end of the control
region or its total extent, it is apparent from Equation (8) that
the spacing of such orifice holes becomes solely a function of
the number and size of holes as given in Equation (9).
It is this principle that the manufacturers of conventional
adjustable shock absorbers use to design their orifice structures,
namely, by maintaining a fixed spaced hole system and simultane-
ously varying the area size of all orifice holes by equal amounts
to maintain the n/~ ratio given in Equation (~) constant. This
allows such manufacturers to adjust for different mass systems
with one mode of adjustability, and to provide a constant rate of
deceleration for such mass systems when their equivalent mass
remains constant throughout the deceleration excursion.
This is also the reason why conventional adjustable shock
absorbers cannot be adjusted to provide a constant rate of de-
celeration for mass systems wherein the propelling force varies
with displacement, such as depicted in Graph II, and why such
systems are inefficient.
To simplify the explanation of the principles of the present
invention, I shall refer to the intensity of mass systems as a
measure of the equivalent mass of these systems, wherein this
measure is given in Equation (1) of Fig. 3.
The present invention utilizes the principle of cascading
control regions as a continuum within the extent of a common
stroke control entity. Each control region is specifically de-
signed to provide a constant rate of deceleration for its respec-
tive or corresponding mass system in a specific sequential order.
The order referred to is from the lowest intens ity to the highest
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intensity for such mass systems or from the lightest mass to the
heaviest mass for non-propelled mass systems.
This method allows for the control of mass systems of con-
stant intensity as well as mass systems of increasing or varying
intensity within a given range of design.
Within the range of design, such mass systems eventually
reach their respective control regions as they progress into the
co~mon stroke control entity to their common location of total
arrestment, that is, stroke termination.
Fig. 4 (Graphs V-VII) illustrates the basic principle of
the present invention. Graph V shows orifice area in a fluid
displacement-type shock absorber as a function of piston displace-
ment from an initial position oE the piston at x=O corresponding
to the point of impact of an object to be decelerated. The
initial segment of the area curve 27 is a parabola of the same
form as in Graph IV. Taken together with the dashed extension 27a
of curve 27, it represents the decay rate of the orifice area Ao
over a stroke of length Sl. Instead of allowing the original
cur~e 27 to decay to zero at Sl through the extended portion of
the curve 27a, the progress of parabola 27 is halted at point S'
Truncation point S'l defines the beginning of a new parabola of
amplitude A'o. The decaying ori~ice area beginning at point S'l
follows the trajectory 28. At point S'l the curve of the orifice
area A is continuous but changes direction abruptly to a lower
rate of decay. The area decays alon~ curve 28 and if allowed to
proceed as in the Graph IV, it would traverse the dashed extended
curve 28a and decay to zero at point S2, that is, the stroke
length from the start of parabola 28 at point S'l. Instead of
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allowing the parabola 28 to complete its trajectory, the progress
along curve 28 is arrested at truncation point S'2 where a new
parabola with initial amplitude A~o is begun. If this is the
last of the cascading parabolas, the orifice area is allowed to
decay to zero over the full trajectory of the curve 29. The
orifice area finally declines to zero at point S3 measured from
the start of curve segment 29 at S'2.
The connected parabolic line segments 27, 28 and 29 in
Graph V define control regions 1, 2 and 3. By determinin~ the
initial orifice area Ao and the truncation points S', ~ach control
region can be designed for constant deceleration of a different
mass system. Region 1 with curve segment 27 is designed for con-
stant deceleration of the lowest intensity mass system. Regions
2 and 3 are designed for constant deceleration of an intermediate
intensity and the highest intensity mass systems, respectively.
In Graphs VI and VII of deceleration and velocity versus
displacement, respectively, three loads to be decelerated, referred
to as loads 1, 2 and 3, have di~ferent mass and the same impact
velocity VO. Each object also has the same design limit L for
maximum deceleration, and no propelling force. Examining the
curves in Graphs VI and VII together~ one will notice that the
order of the load intensities i8 reversed ~rom top to bottom. In
control region 1, the load with common velocity VO and the l~est
mass undergoes constant deceleration as indicated by curve 31 in
Graph VI and the corresponding curve 35 in Graph VII. Curve 35
is a true parabola along with its extension 35a to the virtual
stroke Sl. Following the corresponding deceleration curve 31 in
Graph VI, object 1, (lowest intensity load) undergoes constant
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deceleration throughout region 1 and decreasing deceleration in
regions 2 and 3. Similarly, for -the intermediate intensity load,
object 2, the deceleration curve 32 and velocity curve 36 indi-
cate that the load undergoes constant maximum deceleration L in
control region 2, and outside control region 2, deceleration is
less than L. I~hus in Graph VII, curve 36 between the truncation
points S' (i.e., control region 2) is a true parabola. Likewise,
for the highest intensity load, the deceleration curve 33 in
Graph VI and velocity curve 37 in Graph VII indicate that the
maximum design constant deceleration limit L is realized only in
the last control region, throughout which, that is, from point
S'2 to S3, the ve]ocity curve is parabolic.
With respect to the low mass system for which region 1 is
designed, the curve 27 does not continue along its projected path
27a; at x=S'l the rate of orifice closure "slows down" or "backs
off" at the start of curve segment 28, not unlike reducing the
pressure on a brake pedal. ThUS the deceleration rate falls as
shown in Graph VI.
The graphs in Fig. 4 are exaggerated for the sake of clarity.
The total energy expended by the shock absorber in bringing the
object to rest is directly proportional to it~ mass and mu~t
ultimately dissipate all of its kinetic energy (1/2 mv2) which
it had at impact. ~his is reflected in Graph VI since the product
of area under each of the curves and the respective mass is repre-
sentative of the total kinetic energy (l/2mv2) of each respective
mass system, that is
m ~ a(x)dx = 2 mV (Eq. (10)
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where the intensity of mass system m = me(x) constant, and a(x)
represents the deceleration rate of this mass system as a function
of displacement, and ST = Sl' + S2' + S3 or the total stroke
illustrated in Graph V.
It is also important to note that subsequent control regions
are designed with reference to the intensity of the load system at
the beginning of the control region. Thus, for the intermediate
mass load, the second control region is designed to give constant
deceleration to an object of intermediate intensity now traveling
at velocity VO' having already been decelerated through control
region 1. Similarly, the third control region is designed to
provide constant deceleration for a load with the highest mass or
highest intensity of the three, now traveling at a velocity VO'',
having been decelerated through the two preceding control regions.
The initial total orifice area Ao is chosen solely with res-
pect to the load system having the lightest mass and/or intensity.
The first truncation point S'l terminating the first control region
and starting the second region is determined as that displacement
of the piston at which the first intermediate mass (load system
of intermediate intensity) reaches its maximum allowable deceler-
ation L as shown in Graph VI. If the rate of orifice c los ure
continued to Eollow the projected curve 27a in Graph V, the inter-
medi.ate mass curve 32 would exceed the deceleration limit as shown
by projecting the curve 32a in Graph VI. Instead~ a new parabolic
decay of the orifice area is begun at point S'l to control the
deceleration of the intermediate mass. Similarly, the last trun-
cation point S'2 is determined as that displacement of the piston
at which the object with the highest mass (load system of highest
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intensity) first reaches its maximum deceleration Limit L. If
the orifice area were to continue to decay at the rate exhibited
by curve 28a in Graph V, the high mass load would exceed its de-
celeration limit as indicated by the projected curve 33a.
The system described above in connection with Fig. 4 can be
extended to any number of control regions as desired. In certain
industrial applications, load systems of constant and varying
intensities can be classified into predictable discrete categories.
For example, the object to be decelerated on a particular process
line may be 12,000 pounds or 30,000 pounds and it may be travel-
ing at either 2 feet per second or 8 feet per second, and be
motivated by a propelling force of 6,000 lbs. or 8,000 lbs.,
wherein the propelling force motivating the object may vary from
0 lbs. to either of the maximum values given or remain constant
at either of the two values given. The sixteen distinct combin-
ations of weight tmass), velocity, and propelling force can be
specifically accommodated in the orifice pattern according to the
invention. It can also be shown that the deceleration rate im-
posed upon any intermediate load system, that is, any load fiystem
not defined but whose intensity lies between the minimum and maximum
values designed for, by a device o~ this invention, sh~ll not ex-
ceed the maxirnum limitg of design~ when the imp~ct velocity of this
intermediate load system falls within the design range.
A shock absorber can also be designed, according to the in~
vention, having only two control regions. Since this is the least
complex system, a specific shock absorber with two control regions
will be described in detail.
~ .~.
--19--
1~551~6
Example l
In this example, the shock absorber orifice structure
according to the invention is designed to handle two load systems,
each having distinctively different intensities or equivalent
masses. To simplify matters, the weight of the impacting objects,
Nos. 1 and 2, will be arbitrarily chosen as 10,000 and 20,000
pounds, respectively. The masses of these objects, Ml = 310.56
lb.-sec. /ft and M2 = 621.12 lb.-sec. /ft, are obtained by
dividing their respective weights by 32.2 ft/sec.2. Let vl and
V2 be the changing velocities of objects 1 and 2 during the stroke.
At the point of impact, x=0, both objects are defined to have the
same impact velocity vl=v2=Vo=4 ft/sec. To further simplify matters,
consider the deceleration limit L to be 24 ft/sec.2, the same by
design for both objects and assume that they have no propelling
force.
Since there are no propelling forces involved, the intensi-
ties of these two load systems can be defined by their respective
rest masses lsee Eq. (1) in Fig. 3]. The controlling orifice
structure required to accommodate these two load systems will
therefore require two consecutive control region~ 1 and 2~ With
reference to Graph VIII of tiig~ 5, Sl is th~ total virtual stroke
length of region 1~ and Sl' is the actual stroke of region 1~
i.e.~ the truncation point for first orifice area decay curve.
S2 is the actual stroke length of the last region, region 2.
The virtual stroke length Sl associated with region 1 can
be obtained from the formula, Sl=Vo2/(2L). Eq. (11), where
Sl=1/3 ft. or 4 inches as shown in Fig. 5. Although region 1 is
designed for constant deceleration of object 1, the truncation
~. .
-20-
1~55146
point S'l~ defining the extent of or length of region 1, is de-
termined by finding the point at which object 2, separately im-
pacting the shock absorber, would reach the deceleration limit
L according to the following formula:
1- /2m2SlL~ 2 ( 1 21
S'l = Sl Ll -( ~2 1 ~ Eq. (12)
Substituting the numerical values, S'l is 1/4 ft. or 3 inches
as shown in Fig. 5.
Next, the stroke S2 of the second and last region must be
determined. However, this cannot be done in the same manner that
the virtual stroke Sl associated with region 1 was determined
since there is an unknown velocity to consider now~ ThusJ at
x=S'l~ the velocity of the second object after it has been de-
celerated through the first control region is determined accord-
ing to the following formula:
S ~ l ~ ml/ (2m2 )
( J Eq. (13)
Substituting the numerical values~ v2' at x=S'l (the b~ginning
of the second control region) is 2.828 ~t/sec. Since the de-
celeration limit is the same for the 6econd body, the stroke in
the second control region is: S2=(v2')2/~2L~. Eq. (14), where
S2= 1/6 ft. or 2 inches, i.e., 3.0 to 5.0 inches as shown in Fig.
5. The entire stroke length of course is s'l + S2 = ST or 5
inches.
Next, one must determine the values of Ao, the t~tal orifice
area available at the beginning of the stroke and Ao', the total
-2i-
1~55~'46
ori~ice area remaining at point x=S'1 The formula for the
orifice area as a function o displacement in the first control
region is
(1 - ,9 ) Eq. (15)
At x=0, Al=Ao, and kl is a constant based on the mass density of
fluid, the area of the piston and the orifice coefficient of dis-
charge. For a 2 inch bore shock absorber with hydraulic fluid
:~ ~
of mass density 1.677 lb.-sec. /ft.4 (slugs per cubic ft.),
kl = 1.777 x 10 5 lb.-ft.2-sec.2. Substituting the numericaL
values, Ao= 1.953 x 10 4 ft 2 or 0.02812 in.2 as indicated in
Fig 5
~. ,
The formula for the orifice area in the second region is:
: ` / k2 ~ / ~ X - S ' 1 ~ /
A2 = V2 m L 1 - Eq. (16)
2 2
where, v2' is the velocity of the second object at the start of
thc second control region and k2=kl. At x=S'1~
A2=A~o =9.764 x 10 5 ft 2 or 0.01406 inches2, as indicated in
Fig. 5.
Now that the orifice area profile versus displacement is
known for Examplc 1, i~ must be implemented. ~his can be done
directly with the metering pin embodiment of Fig. 2. To accom-
plish this, the orifice opening 24 in the piston 14' is sized in
conjunction with coaxial metering pin 23 to provide a cylindrical
orifice opening 24a whlch is equal to Ao at position J. From
position J, metering pin 23 must be tapered continuously to
stroke termination position K to provide the reduction of orifice
.
-22-
- : -, . .
, , , , . .~ -
,
- ~
.
1155~46
area required in accordance with the curve of ~ig. 5. For example,
at x = S'l~ the cylindrical orifice area remaining when the cross-
sectional area of the pin at this location is subtracted fr~m the
cross-sectional area of orifice opening 24 in the face of piston
14' should be equal to A~o~
Because of the increased structural re~uirements of the
metering pin embodiment, it is p~eferred, however, to use a suc-
cession of holes through the cylinder wall as shown in Fig. 1
to approximate the continuous orifice area curve. To use discrete
holes, the exact total number of holes and the precise diameter
of each or the average diameter must be established. For example,
in the system of Fig. 5, it is evident that half of the total
orifice area is allocated to each control region. Thus, holes of
the same diameter could be used and half of those holes allocated
to one region and half to the other. If many regions are involved,
the total orifice area at the beginning of each region will de-
termine the proportion of the number of holes which are allocated
to any given region. Given the orifice area for any region, the
number of holes and their diameter for that region can be manipu-
lated as desired. However, it is convenient to use the same
diameter holes throughout any given region, although the diameter
of the holes can vary from region to region.
The formula for the axial displacement, D, of each successive
hole of diameter d in a given control region can be derived from
Equation (9) as follows:
Let XT be represented by the total virtual stroke of each control
region, Sl~ S2....... etc. Let x be represented by D, the distance
from the beginning of each control region to the nth hole of that
-23-
,,
1~5~i14~;
control region. Let N be represented by Ao, the total orifice
area required at the beginning of each control region or the re-
maining orifice area required at the beginning of each control
region relative to a spaced hole orifice structure, wherein,
Ao--Ao, A'o~ A''o ... etc., relative to each respective control
region. Let n be represented by n~d /4, the area size of n
holes of diameter d, where ~l~dl/4, n2~r d22/4, .... etc., is
representative of a specific control region.
Then from Eq. (9) 2
Dl = Sl 1 (1 1~ 1 ) --~ 21 Eq. tl7)
where subscript notations 1 represent references to control
region 1 in Equation 17.
Arbitrarily using three holes of diameter 0.07721 inch with
a virtual stroke of 4 inches for the first region, the displace-
ment from x=0 for the first three holes can be determined from
the expression for D as 1.1836, 2.1836 and 2.9614, respectively.
The total orifice area for the second control region (i.e.,
Ao~) is 0.014046 inch. If a drill size of 0.06686 inch for the
diameter of four holes is arbitrarily chosen for region No. 2,
their dispLacements from the point x=S '1 (the start of the second
control region) are as follows: 0.8416, 1.4666, 1.8416, and
l.g666, respectively. This brings the axial separation between
the last two holes in control re~ion No. 2 to within 0.05814 inch.
If this or any of the other axial separations are too close, the
holes may be offset circumferentially.
1155146
EX~MPLE 2
In this example the shock absorber orifice structure accord-
ing to the invention wiLl be designed to handle four distinctive-
ly different load systems. To explain more clearly the signifi-
cance placed on the intensity of these load systems, each rest
mass selected will be motivated by one of the prope~ling forces
common to the other. To further simplify the subscript notations
used in identifying these mass systems by the respective inten-
sities, we will use the same impact velocity for all four load
systems, and impose the same limiting deceleration rate restric-
tions upon them.
The following subscripted equations will be used to define
and/or obtain the parameters of design required, that is, in-
tensities, orifice area sizes, truncation locations, deceleration
rates and velocities. Numerical values will not be obtained,
but rather the equations will be written in general to relate
to any number of different load systems that could have been
selected to identify a given design range.
In the Glossary of Terms provided, and throughout the follow-
ing equations, a notation is introduc~d which is meant to convey
the process most clearly. For example~ within the range of the
first control region~ oc x(i)C x(i,i')~ x(l,l'), i, and i' are
used as locations of design reference, namely~ the beginning or
origin of each control region, and the termination or truncation
location of each control region, respectively.
When x(i) is represented as x(l), x(l) is not necessarily
x(i) evaluated at one point i = L~ as in usual notation, bu-t
rather, x(i) is used to represent the displacement taken from an
"
-25-
1155146
i location of design reference. For example, for any displace-
ment in region x(l,l')~ x(i)C lX(l,l') + X(2,2')], x(i) may be
represented as x(2), wherein, with reference to the i = 1 loca-
tion, x(2) would be equal to the extent x(l,l') and with refer-
ence to the i = 2 location, x(2) may be equal to zero or the
extent x(2,2') or obtain any value in between, where the extents
of the control regions X(l,l') and X(2,2') may be represented as
X(l) and X(2) for brevity, respectively.
Since the equivalent mass or intensity of a load system may
vary from one location to another, Equation l given formerly will
be exparded as follows:
fF [Xli)~ ~
~ q[X(i)l ~a lXti)] + MmqlX(i)]J Eq. tl8)
The parameters of design in Equation 18 are expressed as functions
of displacement X(i), and subscripts m-n-q are used as identifiers
of mass, force, and velocity, respectively.
Since the deceleration rate amnq(i), imposed upon an Mmnq(i)
or ~ q(i) load system at the particular location i, is a function
of the resistive force FB(i) encountered by the load system at this
Location, and
mnq( ) E~. ~l9)
where the constant k(i) is some function of the mass density of
the fluid, the orifice discharge coefficient, and the piston area
of the shock absorber device, then at onset of impact or at the
origin of the first control region i = l, the equivalent mass or
..r
--26 ~
-
~ .
55~46
intensity of any load system at this location can be obtained by
the following equations:
mnq(i) = q F (i) Eq. (20
~ FB(i) J
or as
nt ) mn~ Eq. ~21)
k (i)V mnq(i)
where the resistive force FB(i) is proportional to the velocity
squared of the fluid being forced or metered through the control-
ing orifices, and thereby proportional to the velocity squared
of the mass system or load system providing the momentum.
Now if we introduce a relative order number "c~, wherein
this order number is used in conjunction with an i location of
design reference to identify the order of intensity of a particu-
lar Mmq(i) or Mmnq(i) load sys-tem, where the intensity of an
Mmq(i+C) or Mmnq(i+c)load system is greater than the intensity
of an Mmq(i) or Mmnq(i) load system at the i location of refer-
ence; wherein the order number "c" may take on integer values
from c=l to c=N-l~ where N repre~ent~ the total number of load
systems considered within a given design range, wherein, the
intensity of an Mmq(i+l) or M nq(i+l) load system is greater than
the intensity of an M q(i) or M nq(i) load system, and the inten-
sity of an Mmq(i+2) or M n~(i+2) load system is greater than the
intensity of an Mmq(i+l) or Mmnq(i+1) load system, then the equa-
tions for deceleration, and velocity of these load systems are
~, ~t -27-
1155146
defined as ~ollows:
mnq {~mq~i+c)-M IX(i)~ ~ B[X(i,i+c)][ 2 ~mna
ma(i~c)~Mmnq[X(i)l] [H[X(i)~ ) Eq. (22)
HIX(i)] = Ll S(i)] Eq. (~3)
B[X(i i+c)] = Mmnq~ ] Eq. (24)
M (i+c)
B'lX(i,i+c) = M ~X(i)]-Mm~(i+c) ~. (25)
Eq. (26)
where notations (i,i+c) are relative placement identi~iers used
to position a particular Mmq(i+C) or Mmnq~i+c) load system at an
i location o~ design reference and X(i,i+c) represents the relative
displacement of a particular Mmq(i+C) or Mmnq(i+C) load system
from an i location of design reference, and the parameters given
in Equation 22 are defined as follows:
FnlX(i~c)] A force o~ n-magnitude acting on an
Mmnq(i+c) load system, expressed as a
function of displacement of this load
system
Mmq(i+c) The intensity of an Mmq(i+c) load system
Mmnq[X~i)] The intensity of an Mmnq(i) load system
expressed as a function of displacement
X (i)
115~i~4~;
S(i) The virtual stroke of an i location
control region
Vmnq(i,i+c) The velocity of a particular Mm~i+c) or
Mmna(i+c) load system at an i location
of desian reference
amnq[X(i, i+c)l The deceleration rate of a particular
Mmq~i+c) or Mmn~(i+c) load system at
an i location of design reference,
- expressed as a function of its relative
displacement from this location
Accordingly,
2F [Xti~c)lS(i) ~ BlX(i,i~c)'
Vmnq~X(i i+c)~ ~ [V2mnq(i~i+C) + Mmq(i+c)-~mnqlx(i)~ Etx(i)~
2FnlX( +c)lS(it 1/2
_ _ mq(l+C)~MmnqlX(i)~ H 1 X ( i ) ] . Eq . ( 2 7 )
, .. ..
where truncation locations S', referred to in Example 1, represent
the shortest X[i,i+C] displacements. These displacements define
the locations at which the Mmq(i+C) or Mmnq(i+C) load systems
first reach their limiting deceleration rates Lmnq(i~C). This
relative displacement is measured from thc origin i of an Mmq(i)
or Mmnq(i) control region, and X[i,i-~c] as defined as follows:
B'~X(i,i+c)]
. F [X(i~c)]
, M [X(i]-M (i+c) ~ Lm"q(i+C)
Xli,i+cl=S(i) 1- mnq mq
Mmnq~X(i)]FnlX(i+C)~ Mmnq~x(i)lv~mnq(i~i+c)
Mma(i+c)Mmnq~X(i)~-M mq~i+c) 2Mmq(i+c)S(i)
Eq. (28)
--29_
1155146
From ~quation 2, FB(i) can be written as
FB(i) = Mmnq(i) amnq( Eq. (29)
Then from Equation (19) and Equation (2~)
_ _ 1/2
mnq k(i) mnq F,q. (30)
and expressing Amnq~i) as a function of displacement, Equation (30)
can be written as
~ 1/2
AmnqlX(i)] = Mmnq[X~i)lamnqlx(i)~ VmnqlX(i)] Eq. (31)
Then for constant deceleration, when amnq~i) = amnq[X(i~] = constant,
and k(i) = klX(i)] = constant, from F.quation (4) we get
1/2
Vmnq[X(i)] = Vmnq(i) [1 S(i)] Eq. (32)
Then from Equation (30) and Equation (31), AmnqlX(i)] can be
defined as
A q~X(i)] ~ Amnq(i) [1 ST~] ~ Eg. (33)
and when Mmn~(i) = Mmnq[X(i)l = constan~ throughout a given control
region, Equation 33 can be de~ined as an expansion of Equation 6,
where
_ _ 1/2
mnq[X(i)] = Amnq~i) _ _ Eq. (34)
.
-30-
1155146
To avoid numeric computations~ in Example 2, the Fn(i), FB(i)
and Mmq(i) parameters will be given the following proportional
magnitudes at the i = 1 location of design reference:
M21(1) = 2Mll( )
F2 (1) = 2Fl(l)
FB(l) = 2F2(1)
Furthermore, in this example, the Fn(i) forces motivating the
mass systems will remain constant with respect to displacement,
and each control region will be designed to maintain the deceler-
ation rate of its respective load system constant throughout its
extent, wherein,
amnq~i) = amnqtX(i)~ = LmnqlX(i)~ and
s(~ E~. (35)
Since Vmnq(l) and Amnq(l) is common for the four load systems
considered in this example, FB(l) will also be common~ and the
intensities of the Mmnq(l) load systems can be established and
defined at this i=l location o design reference~ with rcspect
to the proportional magnitudes of the Mmq(l) and Fn(l) mass
systems and motivating forces given, respectively.
From the Fn(l), FB(l) and Mmq~l) values given, and E~uation
(20) we can define the Mmnq(l) load systems and order them, that
is, from the lowest intensity first to the highest intensity last,
as follows:
-31-
.
, ~
115S146
( 111~ ) ~) 11 ( ~}
j 121~ ~ ~al21(1)
Mmn~ Fl(l) _ MATRIX 1
211( ~ ~a211tl) 21( )~
221(1) =~) M21~1)}
where, Mlll(l) C Ml21tl)~ M211( ) 221
Note that for the Mlll(l) load system given in Matrix 1,
the load system of lowest intensity, alll(l) is given as Llll(l).
This was done to indicate that control region 1, the extent of
which will be defined as X(l~l') or X(l) will be designed to
maintain the deceleration rate of this load system constant at
its limiting value Llll(l)~ where Llll(l) Llll[X( )]
fore, since Fl(l) = Fl[X(l)] = constant, and ~11(1) = Mll(2) =
constant~ that is Mmq(i) = Mmq(il)~ from Equation 18 we find that
Mlll(l) = Mlll[X(l)] = constant, and that, at the i' = 1' location
(truncation point of control region 1),
111(1 ) M111(2) 1~
, Mmnq(i) - Mmnq~i~) and from Equation ~35)
S(l) = V ~ ) E~. (36)
-32-
~15S146
From Matrix 1, relative to the "c" order number
( M121(1) M121 (1+1) where c = 1
Mmnq(l+c) ~ M211~1) = M2~ +2) where c = 2 MATRIX 2
~ 221(1) - M221(1+3) where c = 3
Then from Equation 28, we find that X[~ l]=X[1~2]cX[1,3]<X[1,4]
wherein the M121(1+1) load system reaches its limiting decelera-
tion rate L121(2) before load systems M2llll+2) and M221(1+3).
The X[1,2] displacement must therefore be used as the extent
of control region 1 to insure that the Ml2l[x(l)] load system
does not exceed the limiting deceleration rate Imposed upon it by
design choice.
Accordingly,
X[1,2] = X~l,l'] = X(l)
Since the extent of control region 1 defines the origin or
beginning of control region 2, that is, the i=2 location of de-
sign reference, we can establish the intensities of all subsequent
load systems at this location of design reference by use o.~ Equa-
tions 18, 22 and 27 and order them from tho lowest intensity to
the highest intensity as follows
! M121(2) = ~ + M11~2)}
M l2) ~ M ~2~ = { 1(2) + M (2 ~ ~ATRIX 3
221(2) ~a (2) ~ M21(2)~
-33-
~155146
Although the limiting deceleration rates Ll11(2) and L121(2)
are common for both load system 1 and load system 2, respectively,
that is, Llll(2) = L121(2), and rest mass system Mll(l) remains
constant, that is Mll(l) = Mll(2) MLl( ). ,
2 1( ) M111(2) Mlll(l), the intensity of load system
2, at the i = 2 location of design reference, must be greater
than the intensity of load system 1 at this location, that is,
M121(2)~ Mlll( )
If control region 2 is designed to maintain the deceleration
rate of the M121(2) load system constant at the limiting value
L121(2), through the X(2) extent of this control region, wherein
M121[X(2)] also remains constant throughout this extent, that is
M121(2 ) M121(3) = M121(2), then from Matrix 3, relative to
the "c" order number system adopted
~ M211(2) = M211(2+1) where c = 1
Mmnq(2+c) MATRIX 4
~ M221(2) = M221(2+2) where c = 2
Then from Matrix 3 and Matrix 4, for Mmnq(2) = Ml2l(2) =
M121[X(2)], Mmq(i+C) = M21(i+c) = M21(2+2) = M21(2) and
Fn[X(i+c)] = F2[X(i+c)] ~ F2[X~2+2)] = F2(2), and ~rom Equation
28~ after finding V mnq~i~i+c) = V 22L(i,i+c) = V 221(2,2+2) and
from Equation 27, wherein V221(2,2+2) is obtained as V221[X(1,1+3)]
evaluated at X(i) = X(l), that is, V22l(x(1,1+3)] - V211(2,2+2) =
V221(2) at X(l) = X(l), we find that
X[2,2+2] = X[2,4]~ X[2,3]
wherein the M221(2+2) load system reaches its limiting deceleration
-34-
~155146
rate L221(3) before load system M2ll(2+l). Therefore, the in-
tensity of the M21l(2+1) load system at this location, M211(3),
becomes superfluous. This being justified in that any expansion
of the existing orifice area from this location, having a decay
rate predicat~d upon a load system of higher intensity, will
contain the momentum of load system 3 below its limiting change
level. The X[2,4] displacement must therefore be used as the
extent of control region 2 to insure that load system M221[X(2)]
does not exceed its lImiting deceleration rate ~ 21(3). Accord-
ingly,
X~2,4] = X12,2'~ = X(2)
V 121(2)
and 2L1211X(2)1 Eq. ~37)
The V121~2) velocity of load system 2 can be ohtained by
~auation 27, where
V121(2) = V1211X~l,l+l)] evaluated at X~l) = X(l),
wherein Vmnq(i~i+C) = V121(1,1~1) = V121(1),
Fn[X(i+c)~= F~lX(l+l)] = F2(1), Mma(i+c) = Ml~ l) = Mll(l)
X~i)l = MllllX~l)l = Mlll(l)
Since the extent of control region 2 defines the origin
or beginning of control re~ion 3, that is, the i-~3 location of
design reference, and there are no subse~uent load systems of
higher intensity then the M221(3) load system at this location,
221(3) L221~3)' F2(3) = F2(2)~ and M21(3) - M2 (2),
control region 3 is designed for load system 4, that is, load
s~stem 4 is now defined as Mmnq(3), where
mna(3) ~ M221(3) =~ L (3) ~ M21(3)} .~ATRIX S
-35-
1155146
Therefore, the last control region, control region 3, is
designed to maintain the deceleration rate of the M221(3) load
system constant at the limiting value L221(3), throughout the
X(3) extent of this control region, wherein, X(3) = S(3). There-
fore,
M (~') = M221(4) = M221(3) = M22llXt3)]
V 221(3)
and S(3) = -2L221(3) E~. ~38)
r
The V221(3) velocity of load system 4 ~M221(3) , can be
obtained by Equation 27, where V221(3) V2211X( , )]
at X(2) = X(2~, wherein Vmnq(i~i+c) = V221(2, ) 221
Fn[X(i+c)] = F2[X(2 ~2)1 = F2(2), Mmq(i~C) = M21(2+2) = M21(2),
MmnqlX(i)] M1211X(2)] = M121(2)-
Now that we have established and defined these load systems,
and established that the intensities of the load systems will re-
main constant througlout their respective control regions, rela-
tive to the parameters of design selected in this example, we
can identify these load systems in relation to their respective
control regions and order of intensities as follows:
(M~ Xtl,l')] = ~ M lX(l)] ~
mnq~X(i~ M1211X(2,2')1 = ~ ~ MlllX(2)]3 MATRIX 6
I ~21X(3~
M221tXt3~3') ] - L221tX(3) ] 21tX(3) 1
-36-
11551~6
where X(i) = X(i,i'), and
ST = X~l~l') + X(2,~ (3,3~) Ea. (39)
or ST - X(l) + X(2) ~ ~(3) Eq. (40)
where Xt3) = S(3).
For Example 2, since Mmnq(i) Mmnq[ mnq
wherein Mmnq[X(i)] remains constant throu~hout the X(i) extent of
its respective cnntrol region, Eauation 33 can be evaluated as
follows:
For i = l,and O'X(i)~X(l,l') = X(l):
__
111 E111(1)L111(1 ~ Vlll(l~ [1 ~ S(ll Eq (41)
X(l) Alll~X(1)3
. . ..
~ where in Equation 41, X(l) = O
1 where in Equation 41, X(l) = 1
X(l) where in Equation 41, X(l) = X(l)
For i = 2, and X(l)~X~i)~tX(l,l')+X(2,2')]=tX(l~X(2)1:
~Ml 21 ( 2 ) L ~3 Vl 21 ( 2 )
[X(i)-X(l)] = X(2) Al?ltx(2)l
where in Equation 42, X(2) = O
1 where in Equation 42, X(2) = 1
X(2) where in Equation 42, X(2) = X(2
......
-37-
46
For i=3, and ~X(l)+X(2)~X(i)~X(l,l')+X(?,2')~X(3,3') =
!X(l)+X(2)~x~3) ~
~221(3)L221(33221(3) ~ ~ ~7~-J Eq. (43)
tX(.i)-X(l)-X(2)1=X(3)A2211X(3)]
O where in E~uation 43, X(3) = O
1 where in Equation 43, X(3) = 1
X(3) where in Equation 43, X(3) = X(3)
Now that all the pertinent data has been obtained, the orifice
area pattern can be representea graphically as illustrated in
Fig. 6.
Then if Equation 17 is expanded to represent the axial
displacement "D" as a function of two variables, location i, and
displacement X(i), relative to the equations given, the location of
orifice holes in a spaced hole ~evice of this invention can be
determined indepen~.~ntly for each control region as follows:
~ D[i,X(i)] = ~ 4~lx ( i) 3 ~ 2 ) E~ 4)
where A[X(i)] represents the total remaining orifice area expressed
as a function of displacement X(i) from a given i location of de-
sign reference, n(i) represents the nth orifice hole of the given
i location control region, wherein, n(i) = 1, 2, 3,....N(i),
where N(i) represents the total number of orifice holes used in
the given i location control region, where S(i) represents the
total virtual stroke of the given i location control region, and
-38-
l~SS14~;
d(i) represents the size of orifice holes used in the given i
location control region, wherein all N(i) orifice holes within
the given control region are of the same d(i) size.
For exa~le, with reference to Fig. 5 of Example 1, for i=l,
X(i)=X(l)=0, A[X(i)l=A[X(l)]-A[0]= .02812 in. , N(i) = N(l) = 3,
d(i) = d(l) = .07721 in., and S(i) = S(l) = 4.0 in., with respect
to control region 1, Eauation 44 becomes
D[l,X(l)] = S~ d4([)]n(1)~ q (45)
and for
n(l) D[l,X(l~]~,in.
1 1.1836
2 2.1~36
3 2.9614
Based on the foregoing disclosure, and the aspect of prac-
ticality and manufacturing economics, it has been established
that a device of this invention, having a total displacement
stroke of 6.0 inclles~ can be manufactured to control as few a.s
two distinctively different load systems and as many as 64 dis-
tinctively d:iffe.rent load flystems~ Further, a device of this
invention having a greater displacement can be economically
manufactured to control a greater number of distinctively differ-
ent load systems.
The shock absorber system described herein accomplishes
deceleration control over a wide range of distinctively differ-
ent load systems, wherein each load system is defined by its rest
mass, velocity, limiting deceleration rate, and propelling force,
-39-
.
l~SS~46
wherein when in effect, such propeLliny forces may vary or remain
constant. Without any adjustment mechanism, this type of shock
absorber provides individual deceleration control, and total
arrestment for all load systems considered within the scope of
its design range, wherein these load systems may be constant in-
tensity load systems or load systems of varying intensity, and
accomplishes this most efficiently by utilizing the full displace-
ment stroke of the device for the arrestment of each load system
Thus~ the self-adjusting shock absorber described hereln provides
proportional stopping forces: low stopping forces for low momen-
tum load systems and higher stopping forces for higher momentum
load systems. The self-adjusting shock absorber can also accommo-
date intermediate load systems, that is, load systems not specific-
ally accounted for but whose intensity lies between minimum and
maximum design values when the impact velocities of such inter-
mediate load systems fall within the design range.
Because the system does not require adjustment mechanisms
for varying the orifice area, the shock absorber's performance
stability relative to temperature is increased because there is
no inherent leakage. ~he installation time is reduced 9 ince
there is no need ~or trial runs and adjustments, so long as the
loads to be decelerated are known to be within the wide design
range. Since the shock absorber has already been designed to
handle a wide range of load intensities, the guesswork is taken
out of load system deceleration control.
-40-
-
146
GL06SARY OF TERMB
Rest Mass Body at rest or having no motion
Mass System or Load Body in motion with or without external
System force applied
Equivalent Mass A measure of force relative to motion,
or a measure of mass relative to motion,
or a measure of force and mass relative
to motion
Intensity A measure of the equivalent mass of a
load system reLative to its existing
state, wherein the measure may vary with
respect to time and place
Equivalent Mass System An equivalent mass, as deflned above, with
or Load System or without external forces applied
Potential The ability to do work
Potential Energy A state of energy that has the abiLity
to do work
Potential State A specific state of energy measured with
respect to location, displacement and
time
Total Energy State A specific state of one or more forms of
energy, such as potential energy, and
kinetic energy, measured with respect to
location, displacement and time
Kinetic Energy The energy of a body in motion
Limiting Deceleration The deceleration rate imposed upon an
Rate M~ or an ~ mass system or equivalent
m~a~s system,n~y design choice, which may
not be exceeded
Rest mass of m-magnitude measured in the
FT-LB~EC ~ystem
Mm Mass system or equivalent mass system of
q magnitude-m, having a finite velocity of
magnitude-q, wherein, the magnitude of
the mass or the eguivalent mass of this
system is measured in the FT-LB-SEC ~ystem
Mmn Ma9s system or equivalent mass system com-
q posed of a rest mass of m-magnitude, having
an applied force of n-magnitude; wherein,
the rest mass and applied force have a
common velocity of q-magnitude; wherein,
-41-
.. ~ .
- ..
. . .
llSS~46
~nnq (Cont.) the magnitude of the mass or the equiva-
lent mass of the combined system is
measured in the FT-LB-SEC system
(i) Rest mass of m-magnitude, wherein the
magnitude of the rest mass is measured
at the specific location (i) in the
FT-LB-SEC system
Mm[X(i)] Rest mass of m-magnitude expressed as a
function of displacement X(i), wherein,
the magnitude of the rest mass, measured
at the specific location (i)~ remains
constant with respect to displacement
X(i), wherein the magnitude of the rest
mass is measured in the FT~LBffEC system
M (i) Mass system or equivalent mass system,
mq where.in the magnitude of the mass of this
system is measured at the specific loca-
tion (i) in the FT-LB-SEC system
Mm ~X(i)] Mass system or equivalent mass system,
q expressed as a function of displacement
X(i), wherein, the magnitude of mass or
equivalent mass of this system, measured
at the specific location (i), may vary or
remain constant with respect to displace-
ment X(i), wherein the magnitude of the
mass or the equivalent mass o~ this system
is measured in the FT-LB-SEC system
mnq Mass system or equivalent mass system,
wherein the magnitude of the mass of this
system is measured at the specific loca-
tion (i) in the FT-LB-SEC system
Mmn [X(i)] Mass system or equivalent mass system
q expressed as a ~unction o~ displacement
X(i)~ wherein~ the magnitude of mass or
the equivalent mass of this system,
measured at the specific location (i), may
vary or remain constant with respect to
displacement X(i), wherein, the magnitude
of the mass or the equivalent mass of this
system is measured in the FT-LBffEC system
Vq A velocity of q-magnitude measured in the
FT-SEC system
V (i) A velocity of q-magnitude, wherein the
q magnitude of velocity is measured at the
specific location (i) in the FT-SEC system
-42-
~l~S~46
Vq~X(i)~ A velocity of q-magnitude expressed as
a function of displacement X(i), wherein,
the magnitude of velocity, measured at
the specific location (i), may vary or
remain constant with respect to displace-
ment X(i), wherein, the magnitude of
velocity is measured in the FT-SEC system
Vmnq~X(i)] The velocity of an Mmq or an Mmnq mass
system or equivalent mass system ex-
pressed as a function of dispLacement
X(i), wherein, the magnitude of velocity
of the Mmq or Mmn mass system or equiva-
lent mass system,qmeasured at the specific
location (i)~ may vary or remain constant
with respect to displacement X(i), where-
in, the magnitude o~ velocity is measured
in the FT-SEC system
amn (i) The deceleration rate oE an M~q or an
q Mmnq mass system or equivalent mass
system, wherein the magnitude of the de-
celeration rate of the Mmq or Mmnq mass
system or equivalent mass system lS
measured at the specific location (i) in
the FT-SEC sys tem
amnq[X(i)] The deceleration rate of an Mmq or an
Mmnq mass system or equivalent mass system
expressed as a function of displacement
X(i), wherein, the magnitude of the de-
celeration rate of the Mmq or Mmnq mass
system or equivalent mass system, measured
at the specific location (i), may vary or
remain constant with respect to displace-
ment X(i), wherein, the magnitude of the
deceleration rate is measured in the FT-SEC
system
mnq( ) The limiting deceleration rate imposed
upon an Ml~g or an Mmnq mass system or
equivalent mass system, wherein the
maynitude of the limiting deceleration
rate imposed is measured at the specific
location (i) in the FT-SEC sys~em
Lmnq[X(i)] The limiting deceleration rate imposed
upon an Mmq or an Mmnq mass system or
equivalent mass system, expressed as a
function of displacement X(i), wherein,
the magnitude of the limiting deceleration
rate imposed upon the Mmq or Mmnq mass
system or equivalent mass system, measured
at -the specific location (i), may vary or
remain constant with respect to displace-
ment X(i), wherein, the magnitude of the
limiting deceleration rate is measured
_ r~ in the FT~EC system
~43 ~
~55~46
Fn A force of magnitude-n, measured in the
LBS-force system
Fn(i) A force of n-magnitude, wherein the magni-
tude of force is measured at the specific
location (i) in the LBS-force system
Fn[X(i)~ A force of n-magnitude, expressed as a
function of displacement X(i), wherein,
the magnitude of force, measured at the
specific location (i), may vary or re-
main constant with respect to displace-
ment X(i), wherein, the magnitude of
force is measured in tne LBS-force system
(i) = i A location of design reference established
by a particular Mmq or Mmnq mass system
or equivalent mass system; wherein, this
Mmq or Mmnq mass system or equivalent
mass system has reached its limiting de-
celeration rate at this location; wherein,
upon reaching its limiting deceleration
rate, this mass system or equivalent mass
system can be defined at this location as
an Mmq(i) or Mmnq(i) design mass system
or equivalent design mass system; wherein,
the specific location or design reference
can be used to identify this design mass
system or evivalent design mass system;
wherein, this specific location of design
reference can also be considered a loca-
tion of common reference for all mass
systems or equivalent mass systems con-
sidered
X(i) A displacement from an i location of
design reference
X(i) The extent of an X(i) displacement,
measured from an i location of design
reference
(i) ~ a il ~ location of d~sign reference establish-
ed by a particular Mma(i~c) or Mmn(i~c)
mass system or equivaIent mass sys~em,
wherein, this mass system or equivalent
mass system has reached its limiting
deceleration rate at this location within
the shortest X(i) displacement; wherein,
the X(i) extent X(i,i') of this displace-
ment defines the respective (i,i') con-
trol region; wherein, this ~q(i+c) or
Mmnq(i+C) mass system or equlvalent mass
system can be redefined at this (i)'
location as an Mmq(i) or Mmnq(i) design
mass system or equivalent design mass
system
-44-
~lS5~6
(i,i') Locations of design reference used to
identify the control region established
for an Mmq(i) or Mmnqti) design mass
system or equivalent design mass system
Xli,i') The design extent of an X(i) displace-
ment, bounded by two locations of de-
sign reference, whi.ch is used to de~ine
the extent of an (i,i') control region,
wherein, a specific X(i,i') extent can
be used -to identify a specific Mmq(i) or
M~nnq(i) design mass system or equlvalent
deslgn mass system with reference to an
ordering matrix; wherein, the ordering
matrix is used to define all design mass
systems or equivalent design mass systems
in the ordering sequence established for
them
c ~ relative order number used in conjunc-
tion with an (i) location of design
reference to identify a particular mass
system or equivalent mass system with
respect to its ordered location from an
Mmq(i) or Mmnq(i) design mass system or
equivalent design mass system~ wherein,
the design mass system or equivalent
design mass system has been defined by
an ordering matrix; wherein, the ordering
matrix is established to define the rela-
tive order of all mass systems or equiva-
lent mass systems at a common location
of design reference (i); wherein, ths
ordering matrix is also established to
define the relative order of all design
mass systems or equivalent design mass
systems with respect to all (i) locations
of design reference, and wherein, this
relative order number "c" may take on
integer values rom c=l to c=N-l
(i+c) A random combination number u~ed to
identi~y a particular Mmq(l+c) or
Mmnq(i~C) mass system or equivalent mass
system with respect to its ordered loca-
tion from an Mmq(i) or Mmnq(i) design
mass system or equivalent design mass
system , wherein, the desiyn mass system
o.r equivalent design mass system has been
defined by an ordering matrix, wherein,
the Mmq(i+C) or Mmnq(i+C) mass system or
equivalent mass system is larger than an
Mmq(i) or M~nnq(i) design mass system or
equivalent design mass system, and larger
than or equal to an ~nq(i+l) or Mmnq(i+l)
mass system or equivalent mass system
-45-
1~55~6
Mmq(l+c) A particular mass system or equivalent
mass system identifiable with respect
to its ordered location from an Mmq( )
or Mmnq(i) design mass system or equiva-
lent design mass system~ wherein, the
design mass system or equivalent design
mass system has been defined by an order-
ing matrix
Mmnq(i+C) Same as for Mmq(i+C)
Mmq(i+l) A particular mass system or equivalent
mass system identifiable with respect to
its ordered location from an Mmq(i) or
Mmn~(i) design mass system or equivalent
deslgn mass system, wherein, the design
mass system or equivalent design mass
system has been defined by an ordering
matrix; wherein, the Mmq(i+l) or Mmnq(i+l)
mass system or equivalent mass system is
the closest larger mass system or equiva-
lent mass system to an Mmqti) or Mmnq(i)
design mass system or egulvalent deslgn
mass system, and wherein, an Mm~(i+2) or
Mmnq(i+2) mass system or equivaIent mass
system is the next closest larger mass
system or equivalent mass system .... etc.
X(i+c) A reference displacement, used in general
to represent the displacement of an
Mmq(i+c) or Mmnq(i+c) mass system or
equivalent mass system
(i,i+c) A relative location placement identifier,
used to position a particular Mmq(i+C) or
Mmnq(i+C) mass system or equivalent mass
system at an (i) location of design
reference
V nq(i,i+c) The velocity of a particular Mm~i+c) or
Mmnq(i+C) mass system or equiva ent ma~s
system at an (i) location o~ design
reference
X(i,i+c) The relative di.splacement of a particular
Ml~q(i+c) or Mmnq(i+c) mass system or
equivalent mass system from an (i) loca-
tion of design reference
vmnq[x(i~i+C)] The velocity of a particular Mm~(i+c) or
Mmnq(i+c) mass system or eguiva ent mass
system at an (i) location of design
reference, expressed as a function of
its relative displacement from this (i)
location of design reference
-46-
11SS146
S(i) The X(i) displacement progression re-
quired to generate a complete i location
control region, that is, the total
virtual stroke of the control region
H[X(i)] A dimensionless displacement ratio used
to define parametric variations
-47-
