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Патент USA US3059860

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Oct. 23, 1962
G. G. FAYARD
3,059,852
CONTROL UNIT FOR MACHINE TOOL
Filed D80. 5, 1957
6 Sheets-Sheet 1
Oct. 23, 1962
G. G. FAYARD
3,059,852
CONTROL UNIT FOR MACHINE TOOL
Filed Dec. 5, 1957
6 Sheets-Sheet 2
FIG. 7 2G
4"“
‘
i
‘__
_
FIG. 2b
m
.
____>.
Oct. 23, 1962
G, G. FAYARD
'
3,059,852
CONTROL UNIT FOR MACHINE TOOL
Filed Dec‘ 3, 1957
Y,‘ : 0.75 Acosq-OJ Ajcos 3x + 0,2OAsin4u
6 Sheets-Sheet 3
Oct. 23, 1962
e. G. FAYARD
3,059,852
CONTROL UNIT FOR MACHINE TOOL
Filed Dec. 3, 1957
6 Sheets-Sheet 4
?
4
mmRm
Q
Oct. 23, 1962
e. G. FAYARD
3,059,852
CONTROL UNIT FOR MACHINE TOOL
Filed Dec. 5, 1957
6 Sheets-Sheet 5
United States Patent O??ce
3,959,852
Patented Oct. 23, l 962
1
2
$359,852
Georges G. Fayard, Paris, France, assignor to Office Na
longer equal to the parameter, but is itself ‘a limited
Fourier series of the same. It results that machining
operations can no longer be performed by rotating the
workpiece support in terms of the parameter and by con
CONTROL UNIT FOR MACE-{WE TOQL
tional d’Etudes et de Recherches, Aeronautiques, Chan
tillon-sous-B-agncux, France, a French body corporate
Filed Dec. 3, 1957, Ser. No. 700,368
2 Claims. (Ci. 235-180)
trolling a radial tool in terms of the radius vector value.
Rather in accordance with the invention the machining
operation is controlled in terms of rectangular Cartesian
co-ordinates, no rotational movement being imparted to
The present invention relates to control units for auto—
the workpiece support.
matically controlled machines for the shaping of tur 10
I have disclosed, in my copending application Ser. No.
bine, compressor or propeller blades, wings and fuselages
545,397, now Patent No. 2,930,084, ?led November 7,
of airplane models and templates and the like.
1955 and assigned to the same assignee as the present
The invention provides a control unit for a machine
application, harmonic synthesizer means which, receiv
tool of this type which dispenses with memory devices
ing as input data the numerical values of the Fourier co
for the shapes of patterns such as cams to be followed 15 e?icients, supplies in the form of voltages the instanta
by a feeler, or magnetic or perforated tapes which re
cord a function of space for reproduction by the ma
chine.
neous values of the cartesian coordinates to servomech
anisrns adjusting the position of the cutter of a machine
tool with respect to the workpiece to be machined.
The object of the invention is to provide a control unit
I have further found that, due, and only due, to the
for a machine-tool requiring only that the pro?le to be 20 geometrical signi?cance of the chosen parameter, the
followed by the cutting tool of the machine be known by
geometrical data usually of dominant in?uence in the
the values of geometrical data of said pro?le.
design of turbine blades or aerodynamic pro?les or their
A further object of the invention is to provide means
square root are linear functions of the coe?icients of the
for producing machined pro?les or models in which a
sine and cosine terms in the developments of the co
certain number of geometrical data remain constant from 25 ordinates and consequently that said coe?icients are
sample to sample, whereas one or more other geometrical
given, from said data, by linear simultaneous algebraic
values vary from ‘sample to sample. This makes it pos
equations. This property will be explained later.
sible to determine experimentally the in?uence of such
The control unit of the invention comprises a comput
particular elements of data on the performance of the
ing machine transforming the geometrical data of the
?nished piece or model.
30 pro?le into coe?icients of the Fourier series representa
It is known that the pro?les of turbine blades, wings
tive of the coordinates and a harmonic synthesizer effect
and fuselages of airplane models are closed curves that
ing the summation of the series, said computing machine
can usually be de?ned in Cartesian or polar parametric
and synthesizer being suitably interconnected as to allow
coordinates which can be developed in the form of
the latter to contribute to the computation.
Fourier series of an angular parameter limited to a cer 35
The geometrical data which are particularly important
in the case of hydrodynamic and aerodynamic pro?les
pro?le is obtained by causing the angular parameter to
are for example, the sagitta of the median line of the
vary between zero and 211-. Prior attempts have been
pro?le and eventually the abscissa of the location of said
made to control machine tools by control units generat
sagitta, the ordinates and the radii of curvature of the
ing signals representative of the abscissa and the ordinate
leading and trailing edges and the maximum thickness
of the pro?le to be machined through Fourier analysis
of the pro?le and its location. Other data may be con
and synthesis. The parameter chosen has been, so far
sidered according to the general scope of the invention,
as I am aware, the polar angle of a point on the pro?le.
as for example the location of a point of in?ection, etc.
This has the advantage of making it possible to drive by
The invention will now be described in detail by refer
the same movement the pattern and workpiece supports 45 ence to the accompanying drawings in which:
and the analyzer and synthesizer of the control unit.
FIG. 1 is a diagram of a right section or pro?le of a
tain number of terms.
A complete description of the
But practice has shown that, for aerodynamic pro?les,
turbine blade, indicating the geometrical signi?cance of
the convergence of the Fourier series in terms of such
the angular parameter as a function of which the pro?le
a parameter was rather poor. I have found that, by a
coordinates are developed;
proper choice of the angular parameter in terms of which 50 FIGS. 2a and 2g represent well known aerodynamic
the Cartesian or polar coordinates of the pro?le are ex
pressed, it is possible, for a given limit of accuracy, to
obtain developments having good convergence and a
pro?les and indicate the corresponding parametric de
velopments. Under each pro?le, only the development in
Fourier series of the ordinate is written, the abscissa be
small number of terms. The geometrical signi?cance of
ing always taken as a simple sinusoidal function;
55
the parameter chosen according to the invention will be
FIG. 3 is a schematic representation of the succession
given hereinafter. Though I do not desire that the in
of operations involved in machining a pro?le from the
vention as set forth in the appended claims depend upon
geometric data values identi?ed in FIG. 1;
such an explanation, I am of mind that the reduction of
the terms of the Fourier series of the coordinate de
FIG. 4 is a diagram of the control unit of the inven
tion, showing the computing machine and the synthe—
velopments obtained with the parameter I choose is due 60 sizer cooperating therewith, together with the servomech
to the fact that two points respectively located on the
anisms for positioning the cutting tool of the machine,
extrados and the intrados of the pro?le at the same ab
scissa along the general extension of the same correspond
to simply interrleated values of the parameter. These are
the two values of the parameter relative to said points are 65
supplementary angles, while in the case where the param
eter is the polar angle of the running point of the pro?le,
there is not any simple relationship between these two
and
FIG. 5 is a particular view of the matrix of the ma»
chine.
FIG. 1 illustrates at reference character 1 the right
section or pro?le of a blade and at reference character
2 the curve traced out by the axis of a rotating cutter
3. The path followed by the axis of the cutter will here
values. With my choice of parameter, the abscissa is
inafter be referred to as “the parallel curve.” The an
then always a sine function of the parameter. Unfortu 70 gular parameter in terms of which are developed the
nately, the polar angle of a point of the pro?le is no
Cartesian coordinates of the pro?le or of the parallel
3,059,852
3
1-i
the leading edge and trailing edge of the same (in FIG.
The abscissa of said maximum thickness, to be called XT;
The sagitta of the median line, to be called Sp;
The abscissa of said sagitta, to be called XS.
‘Of course, certain of these quantities, such as Y1, Yt,
1, 4’—5' are tangent to the parallel curve 2) are traced
Rt, Sp, . . . may be made equal to zero.
out and their distance represents the length 2X0 of the
parallel curve or of the pro?le in their direction of major
extension.
These quantities may be written directly as functions
of a1! b1! a2’ 172! a3, b3: a4:
thus:
curve is de?ned in the following manner. Two tangents
4——5 (or 4’-—5’) parallel to each other and bordering
either the pro?le l itself or the parallel curve 2 nearest
(1°)—Ordinate of the Leading Edge Y1
The angle on taken as a parameter represents, in FIG.
1, the polar angle of a point m on a circle 6 tangent to 10
Y1=1/2[Y(a1)+Y(r—ai)l
the two parallel tangents 4—5 (or of a point m’ on a
where a1 is the value of the parameter corresponding to
circle 6’ tangent to the two parallel tangents 4'—5’) just
the leading edge which is approximately equal to 31r/ 2.
mentioned, the center 0 of this circle taken as the origin
of the coordinates being located inside the blade at a
Y1=—b1-'a2+bs+as
(1)
point the location of which is a matter of choice, but 15
(2° )-—Radias of Curvature of the Leading Edge R1
is preferably on the median line 7 of the blade. The
§
point in or m’ have the same abscissa as the point M’
( X11 + yrs ) 2
on the parallel curve and the point M on the pro?le.
Under these conditions, I have found that, the abscissa
of the points M (or M’) being taken equal to a sinusoidal
function of a, the ordinate may be developed in a Fourier
RPM
for
series of a, which, for the usual pro?les known in hydro
dynamics and aerodynamics, has a good convergence and
comprises four terms or less.
Theoretically, the machining of a model requires the
knowledge of the parametric equation of the parallel
curve. However, means are known from my abovemen
31r
.
a1=—2— (approximately)
where X’ and Y’ are the ?rst derivatives and X" and Y"
are the second derivatives of X and Y respectively with
respect to a. Calculation gives:
(2)
tioned copending application for automatically machin
ing models from the knowledge of the Fourier develop
ments of the pro?le itself. Consequently, there will be 30
considered only in the following the developments in
Fourier series of the pro?les and not those of the parallel
where at is the value of the parameter corresponding to
the trailing edge which is approximately equal to 1r/2.
curves.
FIGS. 2a to 2g represent well known aerodynamic pro
Yt=b1—a2'—b3+a4
(3)
(4° )——-Radius of Curvature of the Trailing Edge Rt
?les and the corresponding parametric developments. In
all of these pro?les, the coordinate X is taken equal
to X0 sin on. That of FIG. 2a is a pro?le by Joukowsky.
That of FIG. 2b is a pro?le of Legendre. FIG. 26 repre
R
_ (X/2+Y/2)a/2
sents a pro?le identi?ed as No. 64-1-212 of the National
Advisory Committee for Aeronautics (NACA). That of
FIG. 2d is a fuselage pro?le of the type of the Gloster
for
oa=g (approximately)
“Meteor,” whereas FIG. 2e is that of a super G. Constel~
lation. 'FIG. 2]‘ represents a pro?le of a fuselage show
ing in dashed lines wing junctions with recesses on the
fuselage according to the proposals of Whitcomb. This 45 Formulae 1 to 4 show that, due to the geometrical signi?
pro?le terminates in an ogive.
FIG. 2g represents a
wing pro?le, NACA No. 64-A—O~O6.
It will be seen that of the seven examples shown in
FIGS. 2a to 2g four, those of FIGS. 2a, 20, 2d and 2g
are pro?les obtained from developments which include
as regards the coordinate Y, at most one term in cos a,
one term in cos 20:, one term in sin 20c, and one term in
cos 304.
The other pro?les of FIGS. 2b, 2e and 2]‘ are
developed respectively in six, four and three terms.
cance of the chosen parameter which involves that the
parameter values of the leading and trailing edges are re—
spectively integral quarters of 21r, namely 31r/2 and 1r/2,
Y1, \/R1, Yt, \/R, are linear functions of the coet?cients
of the Fourier series development of Y considered as un
knowns and reversedly the unknowns a1—a4, b1—b.;= are
linear functions of Y1, \/R;, Y,, \/Rt, the said linear
functions having constant numerical coef?cients.
These pro?les and the developments by which they
may be reproduced underscore the utility of the inven
tion as hereinabove already described inasmuch as it
Tm=2(a1 cos am+b2 sin 2am+a3 cos Scam-H74 sin 4%,)
clearly appears that a very small number of coefficients
su?ices to reproduce any one of these known pro?les.
(5)
It will be assumed in the following that the ordinate may 60
where am and (qr-um) are the parameters of the points
be limited to the fourth order and written in the form:
of the pro?le between which extends the maximum thick
ness parallel to the axis OY. 0cm Must satisfy the condi
tion that the derivative of Tm with respect to am shall
65 be Zero, i.e.:
The geometrical data which de?ne the blade or more
—a1 sin am+2b2 cos ham-3113 sin 3um+4b4 cos 4am=0
generally the pro?le are shown in FIG. 1. They are:
The ordinate of the leading edge, to be designated by Y1;
The radius of curvature of the leading edge, to be called
R1;
The ordinate of the trailing edge to be designated by Y,;
The radius of curvature of the trailing edge, to be called
Rt;
The maximum thickness, to be called Tm;
(6)
The value of
.
X
am=S1IF1 Y:
results from Equation 6’ infra. In the case where XT is
not imposed, Equations 5 and 6 between which am is to
75 be eliminated are equivalent to one relation between the
‘3,059,852
6
coe?icients a—b. In the case where XT and consequently
am is imposed, these equations are equivalent to two rela
tions between the coefficients a-b.
b1 sin ap-l-az cos Zap-H23 sin 3ap+a4 cos 40£p=Sp
(15)
(6°)~—Abscissa 0f the Maximum Thickness XT
b1 cos ap—2a2 sin 2ap+3b3 cos Barf-4a‘; sin 4ap=0
(16)
XT=X0 sin am
whence
It may be noted that all these equations in which the
Fourier’s series coefficients a1, a2, a3, a4, b1, b2, b3, b4
are the unknowns. are of the general type:
10
0
(7°)—Sagitra of the Median Line Sp
1
.
SD=§[Y(ap)-|—Y(1r—a1,)]=b1 S111 ap+ag C08 201;.
where K is a constant which may be equal to zero, :11 de
+223 sin 3010+ (14 cos 4%
notes particular values of the angular parameter and e1
and q; are factors equal to unity or respectively to j or k
according to the equation concerned. When in the fac
tor multiplying the unknown aj (or bk), ej (or ck) is
equal to unity the said factor will be called in the ap
(7)
where up and (1r—¢xp) are the parameters of the points
at the intersection of the pro?le and of the straight line
parallel to OY passing through the point of upper ordi
nate of the median line. up Must satisfy the condition 20 pended claims “unweighted trigonometric function”; when
that the derivative of Sp with respect to up shall be zero,
Ej (or 6k) is equal to j (or k), the corresponding factor
1.e.:
will be called “weighted trigonometric function.”
All the ?rst members of the equations, Equations 9 to
b1 cos cap-M2 sin Zap-+3123 cos 3zxp—4a4 sin 4ap=O
12 included, are limited Fourier series of speci?c values
25 of the parameter. For example the ?rst member of
(8)
The value of
Equation 9 is equal to the ?rst member of Equation 15
with ap=37r/2; the ?rst member of Equation 11 is equal
is
to the ?rst member of Equation 15 with ap=1r/2; the
0
?rst member of Equation 10 is equal to the ?rst member
results from Equation 8' infra. In the case where X5 is 30 of Equation 14 with ozm=31r/2 and the ?rst member of
not imposed, Equations 7 and 8 between which up is to
Equation 12 is equal to the ?rst member of Equation 14
be eliminated are equivalent to one relation between the
With otm=7r/2.
coe?icients a——b. In the case where XS and consequently
The synthesizer comprised in the apparatus of the in
up is imposed, these equations are equivalent to two rela
vention has two modes of operations: (i) receiving as in
35 put data the coe?icients of the Fourier series develop
tions between the coe?icients a—b.
ment of the ordinate and a continuously varying param
(8°)—Abscissa of the Sagitta of the Median Line Xs
eter value, it produces a continuously varying output sig
XS=XO sin up
nal representing the said ordinate; (ii) receiving as input
whence
data approximative value of the coefficients of the Fourier
40
series development of the ordinate and a continuously
Xs
,
up = sin-1
varying parameter value, it is allowed to stop when its
X0
(8)
output signal is equal to a predetermined value, whereby
Formulae 5, 6, 6', 7, 8, 8' show that, due to the geometri
a corresponding particular value of the parameter is
cal signi?cance of the chosen parameter which involves
known and is used for deriving more precise values of
that the two points limiting the maximum thickness and 45 the coef?cients of the Fourier series.
the two points at which the sagitta of the median line
These relationships may be written in the matrical
cross the pro?le have supplementary parameter values,
form:
Yr
(R1X0)1/2
Y;
(R¢Xo)m
Tin/2
0
1
O
=
—1
0
1
—1
0
-—1
1
0
0
0
-—2
0
2
Cos am
0
0
sin 2am
XT
~S1n am
_ 0
0
Sp
X5
0
0
Sin an
005 up
Cos 211p
—2 Sm 2a,,
0
—3
0
—3
Cos 302m
2 Cos 262m —3 Sin 30am
0
0
0
0
1
0
—1
0
1
O
1
0
—4
a1
b1
8,2
b1
0
0
Sin 4am
at
0
0
4 Cos 4am
b3
0
0
84
b4
Sin 3a,,
Cos 4a,,
3 Cos 3a,, -4 Sin 40:;
0
4
0
(
17)
Tm, XT, Sp, XS are linear functions of the coe?icients
of the Fourier series developments of Y considered as
The question of the sign on the radical of Equations
unknowns and reversedly the unknowns a1—a4, 121-114
10 and 12 is unimportant. To change from 1+ to — is
are linear functions of Tm, XT, Sp, Xs the said linear
equivalent to changing from a to 1r——0c. The leading edge
functions having constant trigonometrical coe?icients.
and the trailing edge are thus interchanged.
It results from the preceding equations that the knowl 60 Computation of the unknowns (ll-b1 to ?it-b4 from
edge of the values of a certain nurnber of geometrical
the last eight equations may be performed. by means of
data of the pro?le, namely Y1, R1, Yt, Rt, Tm, XT, Sp, XS
an analog or digital machine adapted to solve systems
impose between the coe?icients a and b of the develop
of linear equations to the input of which are applied
ment of Y the following relationships
the geometrical data. Electrical voltages representative
65 of the values of said unknowns are ‘applied to the har
monic synthesizer of the control unit which produces
driving voltages for the cutter of the machine. It is
to ‘be stated that the computation of the trigonometric
coef?cients of Equations 13 to 16 is performed by the
70 synthesizer of the control unit.
a1 cos am+b2 sin 2am+a3 cos 3ocm+b4 sin 4am=Tm/2
Referring to FIG. 3 of the drawings, 8 represents the
plug board for the geometric data. These data are ap
(13)
plied by means of knobs 9--16 cooperating with dials
to the transducer or data translator 17 which transforms
(14) 75 them into analog electrical voltages. Of course the dials
3,059,852
8
assumes the angular displacement am (or up) thereby
solving Equation 6' or Equation 8' above. During the
cooperating with knobs 10 and 12 are graduated in square
root proportion of the corresponding radius of curva
ture and the dial cooperating with knob 13 is graduated
in half the maximum thickness. The translator 17 trans
mits the data in turn to the matrix 18 which develops
operation ‘an electromagnetic clutch 69 disconnects shaft
20 from shaft 77 and connects this latter shaft to the
shaft '78.
The synthesizer comprises in the embodiment disclosed
eight resolvers 441 to 444 and 451 to 454 whose rotors
are respectively energized by A.C. voltages available at
in the form of electrical voltages the coefficients al to (:4
respectively at terminals 51 to 54 and the coe?icients b1
to b4 respectively at terminals 55 to 58. Computers or
matrices for solving systems of 11 linear equations with
n unknowns are well known in the art and it is not nec
terminals 51—58 and proportional to al . . . £14, £11 . . .
10 b4.
Only one stator winding is necessary in each re
solver and the stator windings of resolvers 441-444 are
respectively perpendicular to the stator windings of re
essary to disclose them in full.
The values of the coe?icients are applied to a harmonic
solvers 451—454. The rotors of the resolvers are driven
by a tangent screw 79‘ through the shaft 77 driven itself
through clutches and bevel gears to a main shaft 77, a 15 either by shaft 20 or by shaft 78. Four worm wheels
481 to 4%.; drive directly the rotors and they have di
branching secondary shaft 773 and several other branch
ameters such that, when the rotor of resolvers 441 and
ing secondary shafts 771, 772, 78, 79 to‘ be disclosed
451 rotate through an angle 0:, those of resolvers 44, and
hereinafter in FIGS. 4 and 5. The rotation of these
synthesizer 19 driven by a motor 32 through a speed
reducer 46. The shaft 20 of this speed reducer is coupled
shafts represents the parameter a. This synthesizer gives
451 (z' integer from 1 to 4) rotate through ioc. The out
between the voltage representative of X(0L) and the
output voltage ‘from potentiometer 30 whose winding is
which comprise voltage multipliers, phase inverters and
slider is ?xed to the carriage 26.
of are well known in the art.
the ordinate Y(oc). The shaft 773 drives a resolver 21 20 put voltages of the stator windings of the ?rst set of
resolvers which represent the cosine terms of the Fourier
with one rotor and a single stationary winding which
series are individually available at terminals 61—64 and
gives the abscissa X(e). Resolver 21 may be considered
are applied together in parallel to resistor 39. In‘ the
‘as a second synthesizer in the case where the Fourier
same manner, the output voltages of the stator windings
series development of the coordinate to be obtained has
25 of the second set of resolvers which represent the sine
a single sine term.
terms of the series are individually available at terminals
The carriage 22 which supports the cutting tool is
65-68 and are also applied in parallel to resistor 3%.
subjected to two orthogonal motions with respect to the
From output 61-68, there are taken off the necessary
workpiece 23. The ?rst motion is derived from a motor
voltages to‘ produce by combination a voltage represen
24 which is coupled to a speed reducer 25 and then to
carriage 26 via lead screw 27. The motor 24 is energized 30 tative of the ?rst member of Equation 14 and similarly
a voltage representative of the ?rst member of Equation
via ampli?er 28, by an error voltage which appears
16. The combination is effected in devices 5% and 60
across resistor 29 and which is equal to the difference
adding means. Devices of this kind adapted to linearly
?xed to the frame of the machine-tool 31 and whose 35 combine a plurality of voltages and the multiples there
The output voltages of
devices 50 and 60 ‘are applied, through switch 59, to
the motor 32 which is stopped when the controlling
22 which supports the cutter itself. This motion is
voltage is zero.
developed by motor 34 which drives lead screw 37 through
If the motor 32 is controlled by the device 50, the
a speed reducer 35. The carriage 22 is, of course, 40
shaft Zil when the motor is stopped represents the angle
coupled to the lead screw by means of a nut.
am. If the motor 32 is controlled by device 60, the
Motor 34 is energized via ampli?er ‘38 from an error
shaft 20 when the motor is stopped represents the angle
voltage which appears across resistor 39 and which is
equal to the difference between the voltage representative
In order to enter into the matrix 18, the trigonometrical
of Y(oc) and the output voltage of potentiometer 40,
functions in am referred to in the ?fth and sixth lines
whose winding is ?xed to the main carriage 26 and whose
of the square matrix of Equation 17, there are provided
slider is ?xed to the secondary carriage 22 which supports
(FIG. 5) resolvers 711, 714 715 and 718 whose rotors
the cutting tool itself.
are driven by secondary shaft 771 separated from the
The coefficients of the matrix 18 are numerical coef
main shaft 77 by a clutch 70 and are energized by a
?cients as regards Equations 9 to 12 and trigonometrical
given voltage representative of the unit of length. There
coei?cients as regards Equations 13 to 16. Although
are also provided resolvers 721, 724, 725 and 728 whose
these trigonometrical coefficients can be obtained by com
rotors are driven by the same shaft 771 and are energized
putation, they could also be obtained by the control unit
by voltages respectively representative of one time, two
of the invention itself, whether the abscissa of the
times, three times and four times the length unit taken
maximum ‘thickness and of the median line sagitta be
respectively from sliders 81—84 of potentiometer 80.
imposed or not. Generally speaking, this computation
A second set of resolvers comprising resolvers 732,
is performed by the synthesizers 19 and 21 which re
733, 736, 737, 742, 743, 746, 747 is provided to enter the
ceives input data respectively constituted by the value
trigonometrical functions in up referred to in the seventh
of the coefficient X0 of the sine function representing
the abscissa, provisional values of the coel?cients (ll-a4, (if) ‘and eighth lines of the square matrix of Equation 17.
The second motion is applied directly to the carriage
b1—b4 of the Fourier series development representing the
ordinate, ‘and a continuously varying angular value rep
resenting the parameter and are stopped when their out
put signal is equal to a predetermined value.
When X119 (or X5) is known, Equation 6’__‘[‘or (8')] giv
They are driven by secondary shaft 772 separated from
the main shaft 77' by a clutch 75.
Their energization
voltage values results obviously from the last‘ line of
matrix 17 and the necessary voltages are picked up at
a.
423 D taps 81—84 of potentiometer ‘80 according to whether they
ing the corresponding value of the parameter is solved
represent one, two, three or four times the length unit.
for am (or up) with one resolver 33 or any other logo
meter device comprising an electro~mechanical servo
included in known manner in a feed-back loop. The
The operation of the apparatus is the following:
The geometrical data are ?rst entered into the plug
resolver 33 (FIG. 4) comprises essentially a ?rst stator
winding 41 energized by a voltage proportion to XTQ (or
XS) picked up at the output of analog translator 17
through switch 76, a second stator winding 42 energized
by a current source '33’ giving a voltage proportional to
board. If the geometrical data XT or XS, or both, are
imposed, the shaft 77 is disconnected by clutch 69 from
shaft 20 and connected to shaft 73. The stator winding
42 of the resolver being always energized by a voltage
representative of X0, the stator winding 41 is succes
sively energized by voltages representative of XT and
When XT is applied to
X0, and a rotor Winding 43 journaled on a shaft 78 which 75 X5 by means of switch 76.
3,059,852
1-0
stator winding 41, the clutch 70 is operative and the
stored therein, and means for deriving from said data and
clutch 75 unoperative. Conversely, when XS is applied
unweighted and weighted trigonometric functions the
to resistor 41, the clutch 75 is operative and the clutch
values of said constant coe?icients, and harmonic syn
'70‘ unoperative.
thesizer means for developing from said coei?cient values
11f the geometrical data XT or XS are not imposed, the
and said continuously varying angular parameter the value
shaft 77 remains connected to shaft 20‘ of speed reducer
of said ordinate continuously varying with said parameter.
46. The clutch 70 being engaged and the switch 59
2. Apparatus for producing a continuously varying
being on the position towards '50, the shaft ‘771 stops at
signal representative of the ordinate of a closed aerody
a position representative of 0am and the trigonometrical
namic pro?le, said ordinate being expressed in the form
functions of said angle are entered into the matrix 13. 10 of a limited Fourier series in terms of a parameter equal,
Then the clutch 75 being engaged and the switch 5? being
‘for a given point of the pro?le, to the polar angle of
on the position towards 60, the shaft 772 stops at a posi
a corresponding point on a circle circumscribing said
tion representative of up and the trigonometrical functions
pro?le and tangent to two parallel straight lines tangent
of said angle are entered into the matrix. Finally, both
to the pro?le near the leading and trailing edges of the
clutches 70* and 75 being disengaged and all the data 15 same, said corresponding point on said circle having the
being entered into the matrix, the machining operation
same abscissa as the point on said pro?le, said pro?le
may start.
being de?ned by geometrical data belonging to a group
comprising the ordinate and the square root of the radius
of curvature of the leading edge of said pro?le, the
While the invention has been described herein in
terms of a number of preferred embodiments, numerous
modi?cations and variations, particularly in the synthe
sizer structure (use of sine potentiometers instead of
resolvers) may be made therein without departing from
the scope of the invention itself which is set forth in the
appended claims.
What I claim is:
1. Apparatus for producing continuously varying sig
ordinate and the square root of the radius of curvature
of the trailing edge, the maximum thickness of the pro
?le, and the sagitta of the median line of the pro?le,
said data being related to the coe?icients of said limited
Fourier series by a set of simultaneous linear equations
25 in which said coef?cients are the unknowns, the ?rst
nals representative of the coordinates of a closed aero
dynamic pro?le in terms of a continuously varying angu
lar parameter equal, for a given point of the pro?le, to
members are in the form of limited Fourier series in
terms of particular values of the parameter and of the
multiples thereof, at least one of said particular values
being unknown, and the second members are quantities
the polar angle of a corresponding point on a circle 30 depending upon the data, said apparatus comprising
circumscribing said pro?le and tangent to two parallel
matrix means having as input data signals representative
straight lines tangent to the pro?le near the leading and
of said geometrical data and of supplementary data con
trailing edges of the same, said corresponding point on
stituted by at least the unknown particular value of the
said circle having the same abscissa as the point on said
parameter, said matrix means being adapted to derive
pro?le, said pro?le being de?ned by geometrical data 35 from said data-representative signals a plurality of co
belonging to a group comprising the ordinate and the
existing signals representative of the coe?icients of said
square root of the radius of curvature of the leading
limited Fourier series, means to generate a variable cycli
edge of said pro?le, the ordinate and the square root
cal signal representative of the parameter, main harmonic
of the ‘radius of curvature of the trailing edge, the maxi
synthesizer means connected to said matrix means hav
mum thickness of the pro?le and the abscissa of the 40 ing as input data said coexisting signals and said cyclical
maximum thickness, the sagitta of the median line of the
pro?le and the abscissa of said sagitta, whereby the
signal, said main synthesizer means being adapted to
derive from the input data thereto the value of the ordi
abscissa of a point on the pro?le is a sine function of said
nate, a secondary harmonic synthesizer means simulat
angular parameter and the ordinate is a limited Fourier
ing the particular linear equation containing the un
series of the parameter the coe?‘icients of which are re 45 known particular value of said parameter, said secondary
lated to said data by a set of simultaneous linear equa
synthesizer means being connected to said matrix means,
tions in which said coef?cients are the unknowns and
having as input data said coexisting signals and said
are each multiplied by non-weighted trigonometric func
cyclical signal and being adapted to derive from the input
tions of particular values of the parameter and multiples
data thereto the value of the ?rst member of said par
thereof and weighted trigonometric functions equal to 50 ticular equation varying with said cyclical signal, and
the products of said non-weighted functions of particular
means to stop the variable cyclical signal generating
values of the parameter and of the multiples thereof
means When said ?rst member varying value is equal
by a weight equal to said multiple, said apparatus com
to the second member of said equation depending upon
prising linear equation solving means having as input
the data, whereby the value of the cyclical signal when
data signals representative of said geometrical data and 55 the generating means is stopped constitutes the supple
including, ?rst sine potentiometer means having its output
mentary data.
connecting to a tool following the pro?le for storing
said unweighted trigonometric functions, second sine
References Cited in the ?le of this patent
potentiometer means having a slider ?xed to a support for
UNITED STATES PATENTS
the cutting tool for storing said weighted trigonometric 60
second potentiometer means by multiples of said reference
2,478,973‘
2,660,700
2,808,989
Younkin _____________ __ Oct. 8, 1957
voltage equal to the weight of the trigonometric functions
2,883,110
Spencer et a1. ________ __ Apr. 21, 1959
functions, means for energizing said ?rst potentiometer
means by a reference voltage, means for energizing said
Mahren ____________ __ Aug. 16, 1949
Gates ______________ _. Nov. 24, 1953
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