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Патент USA US3049199

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Aug. 14, 1962
H. E. RIORDAN
3,049,189
MECHANICAL FILTER
Filed Feb. 9, 1956
2 Sheets-Sheet 1
AERODYNAMIC FORCES
3236336
34 353337
38
F/6.4.
HUGH E. R/ORDAN
INVENTOR
BY 16%
@4366
m’
ATTORNEYS
United States
atent 6 1
1:
3,049,159
MECHANICAL FILTER
Hugh E. Riordan, Silver Spring, Md, assignor to the
United States of America as represented by the Secre
tary of the Navy
Filed Feb. 9, 1956, Ser. No. 564,597
6 Claims. (Cl. 181-.5)
3,049,189
Patented Aug. 14, 1962
2
output of the lead network is ampli?ed by the torque
ampli?er 13 and applied to the vanes 14.
De?ection
of the vanes, which are located in the jet stream, gives
rise to reactionary forces which act upon the missile air
frame 15. These forces cause a displacement of the
missile in such a direction as to reduce the deviation of
the missile from a predetermined course.
It will be understood that the description above is typi
The present invention relates to a mechanical ?lter.
cal of many self-regulating devices. An analysis prop
In more detail, it relates to a mechanical ?lter for elimi 10 erly applied to such a system would disclose the likeli
nating undesired sinusoidal oscillations in a mechanical
hood of inherent instability due to time lags in the ele
control system.
The mechanical ?lter of the present invention is anal
ogous to electrical circuits devised for a similar pur
pose. When undesired oscillatory currents are present
in an electrical system, a ?lter comprising circuit elements
such as capacitors, inductances and resistors is connected
into the system to eliminate the undesired oscillations.
Closed loop mechanical servo systems are used as
ments forming the system. Compensation for these time
lags can be made ‘by the proper adjustment of the param
eters of the lead network 12, with the result that stable
operation might reasonably be expected. In practice,
however, performance has been otherwise. The missile
airframe cannot properly be considered as a rigid body.
The missile, when subjected to aerodynamic forces, de—
forms elastically and gives rise to vibrations in its natural
positioning devices to actuate the wings, jet vanes, or 20 mode. These vibrational displacements have the prop
other aerodynamic surfaces used for controlling a mis
sile in ?ight. A typical system of this kind includes a
gyroscope which provides a signal indicating the position
er phase relationship with vane forces to form a regen
erative system, and thus uncontrolled oscillations arise
which render the steering system useless. The notch ?lter
11 in the forward loop of the system provides effective
of the missile with respect to one of its axes, a torque
ampli?er which provides the necessary energy to actuate 25 correction to eliminate regeneration as described above.
the control surfaces, and a feedback path. In general,
The transfer characteristic of a notch ?lter is given
these elements are su?icient to form a self-regulating de
in the expression
vice. However, such a device might fail to function as
a result of oscillations in the loop.
It is therefore an object of the present invention to
provide a ?lter for attenuating mechanical oscillations
occurring within a particular band of frequencies.
Another object of the present invention is to provide
a ?lter capable of completely absorbing mechanical os
cillations of a predetermined frequency and transmitting
with little or no attenuation oscillations of other fre
quencies. ‘
It is a further object of the present invention to pro
vide a mechanical ?lter that may be inserted in a closed
loop mechanical servo system to eliminate oscillations of
the system at unwanted frequencies.
Still another and more speci?c object of this invention
is to provide a mechanical ?lter which may be connected
into a mechanical guided missile control system to elimi
nate undesired oscillations so that the system will follow
the signal from the gyroscope and properly position the
vane surfaces which steer the missile.
where
9o=output angle
0i=input angle
S=ditferential operator d/dt
§=damping factor and §l<§2
w=frequency.
The amplitude response to a sinusoidal input for a
network characterized by Equation 1 is very nearly unity
when the frequency of the input function is either well
above or well below the natural frequency w of the ?lter.
As the frequency of the input approaches the frequency
of the ?lter, the amplitude of the output decreases, reach
ing a minimum when the input frequency is equal to the
frequency of the ?lter. The ?lter is therefore said to be
a notch ?lter. The width of the notch, or the frequencies
Other objects and many of the attendant advantages
at which the ratio of the output amplitude to the input
of the present invention will be readily appreciated as
amplitude begins to change substantially from unity, is
50
the same becomes better understood by reference to the
controlled by the choice of the damping factors {1 and §2.
following detailed description when considered in con
A diagram of a notch ?lter appears in FIG. 2. Input
nection with the accompanying drawings, wherein:
deflections 61 are applied to the input shaft 16 of a
FIG. 1 is a block diagram of a control system incorpo
viscous damper 17 which may conveniently comprise a
rating a mechanical ?lter;
rotor disc of light conducting material and a permanent
FIG. 2 is a diagrammatic illustration of a mechanical
magnet stator assembly. The output of the damper 17
notch ?lter according to the present invention;
FIG. 3 is a similar illustration of a modi?cation of
appears at shaft 18. A ?ywheel 19 having a moment of
inertia I, is formed integrally with shaft 18 and is re
strained from free rotation by a torsion spring 21 having
FIG. 4 is a diagrammatic illustration of a second
modi?cation of the mechanical ?lter providing a notch 60 a spring constant K, one end “21s” of said spring being.
secured to a ?xed support S, and the opposite end “21)‘”
having theoretically in?nite depth;
of said spring being secured to said ?ywheel ‘19. Oscil-'
FIG. 5 is a diagrammatic illustration of a third modi—
lations of the shaft 18 are applied to a gear box 22 and
?cation of the ?lter having a di?erent attenuation char
appear
at shaft 23 which is one input to a differential 24.
acteristic from the ?lter of FIG. 4; and
The differential 24 is arranged to provide the difference
FIG. 6 is a plot of the amplitude response obtainable
between input de?ections applied to shaft 23 and a sec
with the ?lter shown in FIG. 4.
ond
input shaft 24). The ratio of the de?ection of shaft
The mechanical steering system utilizing the notch ?l
23 to the de?ection of shaft 18 is the gear box ratio N.
ter is illustrated in FIG. 1. The precessional forces of
Input de?ections 0i are applied through shaft 25 to the
the gyroscope 10, which arise by a displacement of the
other input 20 of differential 24. The difference between
70
missile from a predetermined course, are linked through
the de?ection of shaft 23 and the de?ection of shaft 20
a mechanical notch ?lter 11 to a lead network 12. The
appears at shaft 26 and is the output 00 of the ?lter.
the ?lter;
3,011.9 7 1st
3
4
It can be shown that the transfer characteristic of such
preserving the output-input characteristics desired. The
an arrangement is
t?xed damper shaft is, of course, the heavy magnet assem
bly of the damper, while the movable shaft is the
0.,__J1S2+(l—N)CS—l-K
(2)
light rotor assembly.
A ?lter theoretically having zero output at its natural
frequency is shown in FIG. 4. This ?lter has the ad
Where
vantage of the elimination of the additional differential
J_—'_-moment of inertia of ?ywheel
2'7 appearing in FIG. 3, at the expense, however, of being
K=spring constant
liable
to saturation with large input amplitudes.
C=constant associated with viscous damper.
input de?ections 01 are coupled to shaft 32 of differen
10
A comparison of Equation 2 with Equation 1 yields
tial 33. A mass 34, having moment of inertia I1, is cou
the following facts: First, the transmission characteristics
pled to the second input shaft 3.; of a differential 33. A
of the arrangement shown in FIG. 2 are those of a notch
torsion spring 3-6, having a spring constant K1, is ?xed at
?lter. Second, the frequency at which the notch occurs
one end 36s to a ?xed support 5’, and has its opposite end
is a function of the spring constant K and the moment
of inertia J. Third, the width of the notch is a function
of the spring constant K, the moment of inertia I, the
viscous damper constant C, and the gear ratio N.
Again referring to FIG. 2, it is well to note the oper
ation of two of the elements, that is, the viscous damper
17, and the differential 24. The important property of
the viscous damper is that forces transmitted through
it are proportional to the difference in velocity of its
rotor and stator shafts. The important property of the
3am attached to mass 34. The combination of mass 34
and spring
forms a torsion pendulum having a resonant
The output shaft 3'7 of differential 33 is coupled by
gears 35} having a ratio N to the rotor 39 of an eddy cur
two angular displacements.
Thus, at low input frequencies, the difference in veloci
rent damper 4i} similer to damper 17. The stator 4-1 of
damper 44} is ?xed.
The output 00 of the ?lter appears at shaft 37, and
formed integral with shaft 37 is a mass 42, having a
moment of inertia I2. Mass 42 is restrained by a torsion
ties appearing across the damper 17 is small, as a con
spring 43, having a spring constant K2.
sequence little force is transmitted through the damper
to the ?ywheel 19, and since the ?ywheel is restrained
by spring 21, it is de?ected very little. The output ap
pearing at shaft 26 of the di?erential 24- is the difference
of spring 43 is attached to mass 42 and its opposite end
435 is attached to a ?xed support S”. The combination
of mass 42 and spring 43 comprises a second torsion
pendulum having a resonant frequency
differential is its ability to measure the difference between
between the input transmitted through the parallel path
25 and the de?ection of the shaft 23. It has been shown
(1)2:
that the de?ection of the ?ywheel shaft 18, and hence
shaft 23, at low frequencies will be negligible, hence the
output is equal to the input.
At high input frequencies the force transmitted through
One end 43m
1K2
I
The operation of the filter illustrated in FIG. 4 in
volves the cooperation of two mechanically resonant sys
tems, i.e., the two torsion pendulums. The ?rst torsion
the damper 17 is considerable. However, in this case
pendulum provides a means for absorbing the input de
the ?ywheel is incapable of responding to the transmitted 40 ?ections at the natural frequency of the pendulum. The
forces because of its inertial properties. Again, as in
second torsion pendulum provides a means of preventing
the case of low frequencies, the output is equal to the
extreme magni?cation of input de?ections which would
input.
otherwise appear at the output when the input frequencies
At intermediate frequencies ?ywheel 19 and spring 21
are higher than the natural frequency of the ?lter. As
will be recognized by those familiar with the equations
behave as a torsional pendulum, the amplitude of the
de?ections of the shaft 23 increasing as the input fre
stated hereinafter, torsion pendulums having different
quencies approach the resonant frequency of the ?ywheel
spring combination. Correspondingly, variations in the
resonant frequencies may be employed, thereby present
ing an opportunity for controlling the shape of the ?lter
phase of the de?ections of shaft 23 occur until ?nally at
characteristic curve. A more complete understanding of
the operation of the ?lter can be gained by a consideration
of the equations of motion associated with the ?lter.
resonance the de?ections of the two shafts 23 and 25
are matched and occur substantially simultaneously,
whereby the de?ections of said shafts are in phase, and
the difference of the de?ections of shaft 23 and shaft 25
is at a minimum. Thus input frequencies which excite
?ywheel resonance de?ne the location of the notch in the
amplitude response of the ?lter shown in H6. 2. It
should be noted that this arrangement requires both the
Torques T1, T2, and T3 acting upon shafts 32, 35 and
37, respectively, of differential 33 are related to each
other in the following manner:
and
T2=T3
damper rotor and stator to be rotatable relative to a ?xed
reference. Usually, the damper rotor possesses a high
moment of inertia and an upper limitation is thereby im
posed upon the notch frequency of the ?lter.
FIG. ,3 illustrates an improved con?guration of the
?lter in FIG. 2 which overcomes the foregoing limitation
by the addition of ‘a second differential 27. The differ
ential 27 now occupies a position similar to the location
of damper 17 in FIG. 2. Input de?ections 01 are applied.
to shaft 28 of differential 27.
The rotor shaft in of
damper 17 is coupled through gears 29 to the other input
(4)
The angular displacements 1%, 01 and 6'0 of shafts 32,
35 and 37, respectively, are related in the following
manner:
The motion of ?ywheel 34 is described by the equation
d2
in?eld-K101: _ T2
(6)
where 11 is the moment of inertia of ?ywheel 3d and K1 is
the spring constant of spring 36.
The motion of ?ywheel
is described by the equation.
shaft 31 of differential 27. The difference shaft of dif
ferential 27 is coupled directly to shaft K8. With the 70
i"
<7)
exception of the relocation of the damper, as just de
(it
scribed, the ?lter is otherwise similar to the ?lter shown
where I2 is the moment of inertia of ?ywhecl 42, N is the
in FIG. 2. However, the present arrangement possesses
ratio of the gears 33, K2 is the spring constant of spring
a distinct advantage over the preceding arrangement in
a3 and C is a constant associated with damper
that one shaft of the damper 17 may be ?xed while still
3,649,189
5
6
By substituting in and rearranging Equations 3 through
7 and writing S for the differential operator
put shafts, said ?rst input shaft receiving the mechanical
oscillations to be ?ltered, a torsion pendulum rigidly
secured to said second input shaft and resiliently secured
to said ?rst input shaft so that said pendulum oscillates
relative to said ?rst input shaft, a ?ywheel secured to
said output shaft, and means connected with said ?ywheel
for damping the motion of said ?ywheel and said output
shaft.
2. A ?lter as claimed in claim 1, with additionally
tion of the individual properties J2 and K2, of the ?ywheel 10 means connected with said torsion pendulum for damp
ing the motion thereof.
42 and spring 43 cornlbination alone, but inciudes the
It is evident, from the right hand side of Equation 8,
that the frequency of the output of the ?lter is not a func
3. A mechanical oscillation notch ?lter comprising, a
differential
including a ?rst shaft for transmitting angu
order for the assembly shown in FIG. 4 to comprise a
lar displacements and torques, a second shaft for trans
symmetrical notch ?lter as described by Equation 1, the
15 mitting angular displacements and torques and a third
condition
shaft, operatively associated with said ?rst and said second
properties, J1 and K1, of ?ywheel 34 and spring 36. In
K1+K2_§ 2
J1+ J2 _ J.“
shafts, for transmitting angular displacements constituting
(9)
must prevail.
the difference between the displacements of said ?rst and
second shafts, said ?rst shaft receiving the mechanical
oscillations to be ?ltered, a first torsion pendulum mounted
The arrangement of FIG. 4 provides a ?lter in which
on and receiving torque from said second shaft, a second
the entire input at the resonant frequency is absorbed.
torsion pendulum mounted on and receiving torque from
The transfer characteristic plotted logarithmically, as in
said third shaft, means operatively connected with said
FIG. 6, therefore exhibits a notch of in?nite depth.
third shaft for damping the motion of said second torsion
A third modi?cation of the basic ?lter of FIG. 2
provides a transfer characteristic conforming with the 25 pendulum, said ?rst and second pendulums having res
onant frequencies of such magnitude that the entire input
transfer characteristic de?ned by Equation 1. The third
to the ?lter of mechanical oscillations having a frequency
modi?cation is illustrated in FIG. 5.
equal to the resonant frequency of said ?lter will be ab
Input de?ections 6, are applied to an input shaft 51
sorbed thereby.
of a differential 52. The second input shaft 53 of differ
30
4. A mechanical oscillation ?-lter comprising, a differ
ential 52 is secured to a ?ywheel 54, having a moment
ential including a ?rst input shaft, a second input shaft,
of inertia J1. Flywheel '54 is coupled to input shaft 51
and an output shaft operatively associated with each of
by a torsion spring 55, one end 55s of said spring being
said input shafts, one of said input shafts receiving me
attached to said shaft 51, and the other end 55]‘ thereof
chanical oscillations to be ?ltered, a torsion pendulum
being attached to said ?ywheel. Gears 56, having a ratio
N, couple the oscillations of ?ywheel 54 to the rotor 35 operatively connected to the other of said input shafts for
establishing the oscillation frequencies to be ?ltered out
39 of a damper 40 having a constant C1. The stator
by said ?lter, said pendulum including a mass and a re
assembly 41 of damper 40 is ?xed.
silient means, said mass being coupled to said other input
A second ?ywheel 57 is secured to the output shaft
58 so as to rotate therewith.
The rotor 59 of a second
shaft and said resilient means being secured at one end
damper 61 having a constant C2 is coupled to ?ywheel 57 40 thereof to said mass and at the other end thereof to a
point removed from said mass, said mass being rotatable
through gears 62 having a ratio N2. The stator 63 of
with respect to said point, said differential acting to
damper 61 is ?xed.
compare the motion of said pendulum with the motion
The transfer function of the ?lter of FIG. 5 can be
of said shaft receiving the mechanical oscillations and
shown to be
45 to transmit the resultant difference between said motions
to said output shaft, and damping means operatively con
nected with one of said shafts.
5. A ?lter as claimed in claim 4, including additionally
If I1 is made equal to J2, Equation 10 becomes identical
a second torsion pendulum operatively connected to said
to Equation 1, the frequency being
50 output shaft, said second pendulum including a mass and
a resilient means, said mass of said second pendulum
being secured to said output shaft and said resilient means
of said second pendulum being secured at one end thereof
and the damping factors Ibeing
to said mass of said second pendulum and at the other
: N 1201
55 end thereof to a point removed from said mass of said
second pendulum, said mass of said second pendulum
IKJI
being rotatable with respect to said point, said second
2
pendulum acting to prevent extreme magni?cation of me
and
(10)
chanical oscillations transferred to said output shaft by
60 said differential ‘when the frequencies of such oscillations
are higher than said aforementioned frequencies to be
?ltered out.
The arrangement of FIG. 5 therefore provides a ?lter
6. A ?lter as claimed in claim 4, wherein said damping
in which a choice is presented as to the depth of the
means is operatively connected to said output shaft, and
transfer characteristic notch, as opposed to the ?lter of 65 including additionally a second damping means operatively
FIG. 4 in which the notch is of in?nite depth.
connected with said mass of said pendulum for damping
Obviously many modi?cations and variations of the
the motion thereof.
present invention are possible in the light of the above
References Cited in the ?le of this patent
teachings. It is therefore to be understood that within
the scope of the appended claims the invention may be 70
UNITED STATES PATENTS
practiced otherwise than as speci?cally described.
1,681,554
Norton _____________ __ Aug. 21,
What is claimed is:
2,126,855
Wunsch et al. ________ __ Aug. 16,
1. A mechanical ?llter comprising, a differential in
2,283,753
Harcum _____________ __ May 19,
cluding a ?rst input shaft, a second input shaft and an
2,333,122
Prescott _____________ __ Nov. 2,
output shaft operatively associated with each of said in 75 2,473,335
Hardy ______________ __ June 14,
1928
1938
1942
1943
1949
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