(SANITIZED)UNCLASSIFIED SOVIET PAPERS ON HYDRAULIC SYSTEMS AS APPLIED TO THE AUTOMATIC CONTROL OF INDUSTRIAL EQUIPMENT(SANITIZED)

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80T00246A018700330001-8
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 113
• Document Creation Date: December 22, 2016
• Document Release Date: January 4, 2012
• Sequence Number: 1
• Publication Date: November 8, 1962
• Content Type: REPORT

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SEVERAL PROBLEMS OF THE DYNAMICS OF HYDRAULIC-
GEAR LATHES
by
This article examines the operating unit of a hydraulic gear lathe which
is a closed system. A generalized structural scheme of a hydraulic gear lathe
has been compiled which makes it possible to use frequency methods to study
the dynamics of a hydraulic gear.
In modeling the hydraulic gear of a broaching lathe, it is shown that it is
possible to sythesize the stabilizing devices in order to obtain the desired
transitional process of the operating unit of the lathe.
The advantages of using a hydraulic gear in automatic lathes and lines
which have brought about its extensive use, are well known. However, there
often occasions of instability of motion of the operating units, especially in lathes
with long hydraulic cylinders. Occasions of instability of motion are encountered
not only when there are low shifting velocities, where one of the causes of
instability is the "falling" characteristic of friction, but also when there are
relatively high travelling speeds where the force of friction in the controls
is slightly dependent upon the travelling speed.
Frequency methods of analyzing the synthesizing linear systems which
have been widely used in the technology of automatic controls, have been applied
only to solve the problems of instability in hydraulic tracking systems and, as
far as we know have not been used up to now in planning ordinary feed gear lathes.
This work attempts to present the dynamic system of a hydraulic gear
in a structural scheme which makes it possible to be analyzed by known fre-
quency methods using electronic modulating devices.
The hydraulic gear system can be represented as a closed system consisting
of two sections (Fig. 1): the mechanical section whose characteristics are
described by the transmission function Wm(s), and the hydraulic section with
the transmission function Wr(s). The input effect of the mechanical section is
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the change in the motive poweroj(s); the output coordinate is the change in
the velocity of the operating unit of the lathe P(s). There is a disturbance
in the operating unit of the lathe which corresponds to changes in the cutting
and friction forces which can be overcome by the operating unit. Depending
on the type of lathe, this disturbance can be either periodic, as in broaching
and cutting lathes, or single, as in planning and grooving lathes.
characterizes not only the construction of the mechanical part of the operating
unit of the lathe, but also the dynamic characteristics of the operating process,
i. e. , the relationship between velocity changes and the cutting and friction forces
produced by these changes. A number of works in the fields of cutting and friction
have been devoted to a determination of these characteristics e. g. [1] .
The task of a hydraulic gear, as for any other gear, is to obtain the
operating unit of the machine with the motive force converting the corresponding
form of energy into mechanical energy, and to make the motive force conform
to a given velocity. The dynamic characteristics of a hydraulic gear are
described by the transmission function
r C 5)
v` (sue _- m t1
where the input coordinate is the change in velocity//)?(s), and the output coordinate
is the change in the motive force Is).
In a general case, a regulating action can also be applied to the gear during
a programmed regulation of the velocity. In this work, the simplest case is
examined when the gear is constructed for a specific shifting velocity, the estab-
lished value of which is not regulated during the time interval under study.
Thus,we have aclosed system whose behavior is influenced by the character-
istics of both the mechanical and hydraulic parts. When the entire system is divided
into its mechanical and hydraulic parts, elements, which constructively, belong
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more to a hydraulic gear, may enter the mechanical system. For example,
when we study the operating unit of a lathe, which has been started by a
hydraulic cylinder, it is necessary to relate the mass of the piston and coupling
rod and their friction characteristics, when compressed, to the transmission
function of the mechanical section, although constructively they belong to
the hydraulic gear.
Since Wn(s) > 0, for, when the motive force increases, its velocity and
derivatives always increase; the necessary conditions for the stability of the
system is the negative value of the transmission function of the hydraulic gear,
since only under this condition is the system closed by the negative feedback.
The stability and quality of the transition processes of a system may be
made to conform to the operational requirements of the lathe by assigning the
corresponding characteristics of both the mechanical and hydraulic sections.
In this work, we assume that the transmission function of the mechanical
section is given, and that it is necessary to define the quality of the transition
processes with parameters and the scheme of the hydraulic gear. To do this,
let us make a structural scheme of the hydraulic gear in a general form, i. e.
a scheme which describes the occurence of the operating processes in the
hydraulic gear independent of the scheme used to do this.
The motive force of the hydraulic cylinder (Fig. 2) is determined by the
equation
where P is the motive force
p2 is the pressure in the pressure cavity of the cylinder
pI is the pressure in the counterpressure cavity
F23 FI are the areas of the corresponding cavities.
This equation can be written in relative increments as:
(R x - "~ X)
(1)
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4P
where ( _ is the relative change in the motive force;
0
_4 PP is the relative pressure change in the pressure cavity;
a is the relative counterpressure change
is ine ratio of pressures in the cavities of the cylinder at the
f~-
~"' ? established operational regime;
~~ fz is the relationship of the areas of the cylinder cavities.
Now, as well as later on, all the coordinate values with an established
movement will be written with the subscript "o", and all increases with the prefix A.
Since the operating fluid used in the hydraulic gears in compressible,
the process of pressure change in the cavities takes place with a certain delay
with respect to velocity change. If the wave processes are disregarded, the
equation of continuity of the cavities of the cylinder can be written for both
cavities in the following form:
for the pressure cavity:
67 VA
F v,
for the counterpressure cavity:
where v is the travelling velocity of the piston;
Ql, Q2 the second discharge of fluid from the cylinder;
Vl, V2 the volumes of the fluid in the corresponding cylinder cavities.
LEO cce
where E0 is the elastic modulus of the fluid.
This relationship holds true even for the pressure cavity. Therefore,
the equations of continuity in relative increments can be written as:
(2)
T. R. Note: "Second" here meaning unit of time.
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dY
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(3)
where / _ A v/v2 is the relative velocity change;
= AQ1/Q2 the relative change of discharge in the counterpressure cavity;
/.t = AQ2/Q20 is the relative change of discharge in the pressure cavity;
Tl - L1 p10/E0v0 the time constant of the compressibility of the fluid in the
counterpressure cavity;
T2 Z L2 p20/E0v0 the time constant of the compressibility of the fluid
in the pressure cavity;
Ll, L2 the lengths of the corresponding cylinder cavities.
Since the time constant of the compressibility of the fluid depends on the
position of the piston in the cylinder, then strictly speaking, they are variable
parameters. However, since we are studying the behavior of the system with
slight deviations, we can assume without any significant error that they are
constant during the transition process examined, but we shoud make a decision
as to the stability of the system when the piston is in different specific positions.
Since, in most cases, the volume of the fluid which is in the cylinder cavities
is considerably greater than the volume of fluid in the tubes, we can disregard the
latter although, if it is necessary, it can be easily calculated.
For the operation of the hydraulic gear, it is necessary to grease the
pressure cavity of the hydraulic cylinder and to take the grease from the counter-
pressure cavity. Depending on the scheme and designation of the gear, a different
hydraulic apparatus and pumps are used to do this. The main feature of this
apparatus is the dependence of the discharge on pressure. It is possible to
express the characteristics of the apparatus and pumps included in the corres-
ponding cavity of the hydraulic scheme of the pump, by the transmission functions.
(4)
(5)
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where WI(s) is the transmission function of the apparatus contained in the
counterpressure cavity;
W2(s) is the transmission function of the apparatus and pump contained
in the pressure cavity.
A simultaneous study of equations 1, 2, 3, 4, and 5 makes it possible to
make a generalized structural scheme of the hydraulic gear which is shown
in figure 3.
From the structural scheme of the hydraulic gear, it is clear that the
basic influence on the characteristics of the hydraulic gear is the time constant
of the compressibility of the fluid and the transmission functions of the hydraulic
apparatus contained in the corresponding cavity. Therefore, the transmission
function of the hydraulic gear can be written as:
I
5)
kI
W
.
(
VS) (6)
A. /C' I
rr;x
7s 7;..
In the examination of the general structural scheme of the system of the
operating unit -- gear, it was shown that for the system to be stable, the
necessary condition was the negative value of the transmission function of the
gear. From equation [ 6] , we see that this condition is always fulfilled when
W2(s) > 0 and W1(s) > 0. The structural scheme shows that if these conditions
are not fulfilled, the integrating sections of the compressibility of the fluid in
the cylinder cavities are the positive feedbacks.
Independent of the scheme of the hydraulic gear and of the characteristics
of the apparatus used in it, leakages in the hydraulic cylinder, which we did
not consider when making the structural scheme of the gear, can be very
important. Let us show what leakages can do. Since external leakages in
hydraulic cylinders areintolerable we shall study only those leakages which go
from one cylinder cavity into another. Leakages between cylinder cavities
are proportional to pressure drops in the cavities and are defined by the relation-
ship:
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where g is the second leakage discharge;
c is the coefficient of proportionality.
In relative coordinates, this equation has the form:
/, ~~ Y-- ~),
(7)
where = 0g/go is the relative leakage change.
The equations of continuity can be written in the following form when
leakages are taken into consideration:
ivy's 1- f y Z Y
where2 = g0/FIv2 is the relative leakage coefficient,
If we set d = 1, which corresponds to the equality of the areas of the
cylinder cavities, the structural scheme of the system will take the form
shown in figure 3b which shows that when the areas of both cylinder cavities
are the same, leakages form a negative feedback, which closes the entire
gear. If d>l, the leakages form negative feedbacks which separately close
each of the contours of the gear cavities. Moreover, the effect of the leakages
on each of these contours will be different, and this difference is determined
by the ratio of the areas. Leakages have more effect on a cavity with a smaller
area. However, the qualitative effect is preserved, i. e. , leakages between the
cavities favor conditions of system stability due to the introduction of a rigid
negative feedback with the coefficient of the feedback 'Z., . Therefore, when
a system is not required to be stable (independent of the load velocity), the
leakage can be artificially increased; and this is a very effective way of
stabilizing the system. Another limitation, besides rigidity, in the application
of such a stabilizing contour is the expenditure of the energy and correspondingly,
the heating of the grease in the system.
On the basis of the generalized structural scheme compiled, we studied
the dynamics of a vertically-broaching lathe for the purpose of decreasing
its vibrations while broaching. Figure 4 shows the main hydraulic scheme of
T. R. Note: "second" being a time interval.
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a broaching lathe. The system works in the following fashion: from a pump
of a variable capacity [ 1] , the grease enters under pressure into the pressure
cavity of the hydraulic cylinder [ 2]. The grease is forced out from the
opposite cavity back into the pump, but since the amount of grease being
forced out exceeds the amount being supplied by a magnitude which corresponds
to the area of the piston rod, this excess runs off through the counterpressure
valve [ 3] which is adjusted for a constant pressure.
Broaching lathes operate in a velocity range of 1-10 m/min. In this
velocity range, the dependence of the forces of cutting and friction on velocity
is very slight; therefore, the transmission function of the mechanical section
can be derived from the equation:
C( (
t
where M is the given mass of the operating carriage of the lathe, including the
moving parts.
The transmission function of the mechanical section has the following
(9)
where T 0 = Mv0/P0
In the hydraulic section, the transmission function of the apparatus of the
pressure cavity W2(s) is determined by the characteristics of the pump,
and the transmission function W1(s) is determined by the characteristics of
the counterpressure valve.
The operation of the pump is characterized by the dependence of discharge
on pressure. Generally speaking, this characteristic is non linear; but it can
be made linear without any serious errors, describing it by the following equation:
6f Q,y = C/ ii H
(10)
where QH is the second discharge of the pump under pressure of pH.
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PH is the pressure of the pump;
C1 is the angular coefficient.
If we disregard the counterpressures in the tube conductors, and the
leakages in the cylinder, then PH = P2 and QH = Q2'
The angular coefficient of the characteristic can be expressed by the volume
coefficient of the efficiency of the pump as:
f IPA
where /o is the volume coefficient of the efficiency of the pump:
The common solution of equations 10 and 11 gives
(12)
The pressure gate valve is used as the counterpressure valve in the lathe.
Its transmission function has the following form:
where 1 k is the relative discharge of the valve;
k11 is the amplification factor of the valve;
T, T0 are the time constants.
Considering that the time constant of the valve is several orders less
than the other time constants of the system, and that in practice they do not
effect the frequency characteristics of the system within the limits of the cutting
frequency, we get
"~' t1s), - /~~
(13)
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0624
4.G3 I r5
U.8
.9
isle.,
y
0.05 Z ,2 O '4
4,55
O -' ' 6
49S i
x?
09024
2
?~1,4l
s&! 2 ,
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The transmission function kI is determined from the experimental
statistical characteristics of the valve. Since the valve discharge corresponds
to the difference of the discharges of the cylinder,
Therefore, the transmission function of the apparatus of the counterpressure
cavity is determined as:
j el
(14)
The structural scheme of the system of the broaching lathe is shown
in figure 5.
The study of the system was carried out on an INT-5 electronic modulating
machine. The operation was carried out by engineer Iu. R. Chernova. Fig. 6
shows the scheme of the model. The study was made when the piston was in
different positions in the cylinder /LI, L2/ and when there were different specific
broaching velocities with a single disturbing effect and with the periodic external
effect of a right angle form with the frequency which corresponds to the broaching
operation of a given pitch with a given velocity. Table 1 shows the parameters
of the system for the middle position of the piston in the cylinder when three
speeds are given.
Figures 7a and 7b show the oscillograms and transition process of the
system which were derived on the model with an average broaching velocity
(8 cm/sec), with a single (a) and right angle periodic (b) effect. The top
curve corresponds to the velocity change the bottom curve -- to the
change in the motive force /,I/.
The oscillogram shows that although the system is stable, the transition
process is highly oscillating with a small attenuation decrement. The structure
of the amplitude and phase characteristics of the system show that the phase
margin in this system is about 10?. Oscillogram 76 shows that during broaching,
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the oscillations in the system do not attenuate between the two impulses from
the mouth of the broaching teeth. This can be confirmed by studying the machine
when there are strong vibrations during the broaching.
As was pointed out above, stabilization of the system by the artificial
increase of leakages is expedient in this case because the temperature of the
grease in the hydraulic gear is increased. Therefore, another stabilization
method was accepted which was developed on the basis of an analysis of the
structural scheme of the system. A study of the system on the model shows
that the effect on the stability of the system of the pressure cavity is consi-
derably greater than that of the counterpressure cavity, since R> a, T2 >> Tl
and WI >> W2. Therefore, it is expedient to introduce into the pressure
cavity an additional flexible feedback which encompasses the integrating section
- 1/T2S. Figure 8 shows the hydraulic scheme of the lathe with a device which
provides the required characteristics. The device consists of a hydraulic
holding capacity and a throttle. No explanation is required for the operation
of this device.
The transmission function of the stabilizing device can be introduced in the
following fashion.
The equation of continuity of the pressure cavity when the holding
capacity is included is
~4
(14)
where . e is the relative discharge of the holding capacity.
The throttle outlay is determined by the relationship:
A ,.-17 (?2-P)
where g is the throttle outlay ;
p3 is the pressure after choking;
A is the characteristic of the throttle.
(15)
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-s,--
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The equation of the holding capacity, when its mass, which is small,
is disregarded, has the form
(16)
where e is the spring rigidity of the holding capacity;
f is the piston area of the holding capacity.
The common solution of [ 15] and [ 16] gives
aq-
where Wc(s) is the transmission function of the stabilizing device
Te = f 2 P20/ e Q20 is the time constant of the holding capacity;
Tg = f2/Ae the damping time constant.
If we consider the equation of continuity [ 14] , when this device is included,
the transmission function of the pressure cavity may be defined as:
i.e., 4 a l$~:___ - Za f` K- c'))
zz---- r ~- Te-
7-4
The optimum values of the time c&nstants Te, Tg were derived directly
on the electronic model according to the form of the transition processes.
Figure 7c shows the transition process of the system when there is
the same regime as before, but with the included stabilizing contour /Te = 0. 02/
Tg = Tg : 4 x 10-8 sec. We can see that the transition process of the system
has improved considerably, and after two oscillations, the system returns to
a state of equilibrium.
The use of this apparatus on the lathe eliminated its vibrations and
considerably lowered its noise level.
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Thus, if we consider the hydraulic gear of the lathe as a closed system
consisting of a mechanical and hydraulic section, we can use the frequency
methods of investigation with the application of electronic modulating devices.
This method makes it convenient to synthesize the stabilizing devices which
provide the desired range of the transition processes of the operating unit
of the machine.
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1. Kudinov, V. A. "Osnovy dinamiki stankov" (Fundamentals of the dynamics
of lathes), Eksperimental'nyi nauchno-issledovatel'skii institut
metallorezhushchikh stankov, (Experimental Scientific Research
Institute of Metal-Cutting Lathes), 1957.
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Fig. 1. Closed system operating unit of the lathe - the hydraulic gear,
which is a closed system.
Fig. 2. Scheme of the hydraulic cylinder.
Fig. 3(a). Generalized structural scheme of the hydraulic gear.
Fig. 3(b). Structural scheme of the system when there are leakages in the
cylinder /d = T/.
Fig. 4. Hydraulic scheme of the operating behavior of the broaching lathe.
Fig. 5. Structural scheme of the gear of the broaching lathe.
Fig. 6. Principle scheme of the model.
Fig. 7(a). Transition process whenthere is a step impulse.
Fig. 7(b). Transition process when there is a periodic effect.
Fig. 7(c). The transition process when there is a step impulse with the
introduction of the stabilizing device.
Fig. 8. Scheme of the hydraulic gear with the stabilizing device.
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Declassified in Part - Sanitized Copy Approved for Release 2012/01/04: CIA-RDP80T00246AO18700330001-8
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