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Патент USA US2407469

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Sept. 10, 1946.
R. BIRMANN
2,407,469
ROTOR FOR ELASTIG FLUID MECHANISM
Original Filed MarchvZS? 1943
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8 sheets-sheet 1
Sept. 10, .11946.
R, BIRMÀNN
2,407,469
ROTOR FOR ELASTIC FLUID MECHANISM .
original Filed March 2è, 1945
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Sept. 10,1946.
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‘2,407,469’
R.B|RMANN
Orizgì‘nal Filed March 26, 1945 .
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Sept# 10, 1945.
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R.B1RMANN
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ROTOR FOR ELASTIC FLUID MEGHANISH
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2,407,469
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original Filed March 2e. V1943 _ s sheets-sheet 5
Sept. 10, 1946.
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2,407,459 -
R. BIRMANN
RpToR FOR ELASTI’C FLUID MEQHANISM
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original Filedvuarch 2e, 194s - a subis-sheet e
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Sept. 10, -1946.
R. BIRMANN
2,407,469
KOTOR FOR ELASTIC FLUID MECHANISM
y Original Filed March 26, 1943
8 Sheets-Sheet 8 I
PatenteclrSe’pt. 10, 1946
".
UNITED STATES lPATENT orrlce
ROTOR FOR ELASTIC FLUID MECIVPIANISM- l
“ Rudolph Birmann,
Newtown, Pa., assignor, by
mesne assignments, to Federal Reserve Bank of
, Philadelphia, a corporation of the United States
' of America
Original application YMarch 26, 1943,` Serial No.
480,633. Divided and this application April 8,
1,944, Serial No. 530,188
26 Claims.
(Cl. 230-134)
1
A further’ object of ther present invention is
This invention relates to improved rotors for
the provision of improved vanes> or blades for
impellers or turbine rotors by the adoption of a
' elastic fluid mechanisms and particularly to cen
trifugal impellers and turbine rotors. Speciñ
cally, the invention relates to the provision ofthe
novel method for thegeneration of elastic fluid
type of rotors for elastic iluid mechanism which 5 rotors of the type indicated.
are disclosed in my Patents 1,926,225, dated
A further object of the invention is the'pr'ovi
September 12, 1933, 1,959,703, dated May 22, 1934,
and 2,283,176, dated May 19, 1942. The‘present
sion of a centrifugal impeller wherein, without
violation of other requirements, there is secured'
application is in part a continuation of my applia >quite large angle about the axis of rotation
cation Serial No. 441,686, ñled May 4, 1942, now 10 between the inlet and the outlet portions of each
abandoned, and is a division'of application Serial
of its passages.l
No. 480,633, filed March 26, 1943.
'
'
These and other detailed objects of the inven
Inparticular, in my Patent 1,959,703, there is
tion willr become apparent from the following'
described an improved. type of impeller having
description, read in conjunction with the accom-`
very marked advantages over those theretofore in 15 Dani’ing drawings, ill Which?
use. As described in said patent, the impeller
blades or vanes may be considered as built up
upon surfaces containing two sets of straight line
elements contributing to effect substantially
`
Figure l is a plan view of one form >of machine'
.provided in accordance with the invention for the
generation of such rotors;
~
» Figure 2 is an elevation showin-g certain gear
straight line flow of elastic iiuid relative to the 20 change mechanism of the machine, in particu
impeller and great mechanical strength for high
lar looking at thei‘ìght hand end 0f the machine
speed operation` due to the fact that one set of
said straight. lines is radial.. The blading also has
asviewedv in Figure 1;
..
Figure 3 iS an eleVatìOn ' 0f the machine 0f
the advantage that inlet angles vary properly
with'the lradius so as» to'give 'smooth> entrance
Figure 1, partially in section, to illustrate certain
25 details;
throughout the vertical height of the leading edge>
`
y
o
„
Figure 4. is an elevation of. certain gear change
ci each blade. Variousv other advantages result
mechanism as viewed looking at the left hand
from this construction andare described in said
patent.
n
„
6nd 0f Figure 3;
,
Figure 5- is a diagram showing in plan the prin
For Very high speed 0peratí0n„ however, the 30 cipal èlenlents Of the machine (if Figure 1 and`
blading as disclosed in said patent, while far more
serving to make clear the nature of the surfaces
eilicient-than4 other types, has limitations in thatv
generated thereby;
the speciñc loading of thevanes is too great, or in
Figure 6 îS 2( Similar diagram of the same
other words, various >portions of the vane surfaces. ~
matter in elevation;
are required to do too much work in accelerating 35
the elastic;v uuid,
`
`
Figure 7 isa diagrammatic elevation indicat
' ing two radial sections through an impeller
It is the one object. of the present invention to
formed in accordance with. the invention illus
adapt the impeller construction of said patent for
trating ín particular hOW the impellel' passages
the provision oi' impellers having very high eiii`-are generated and the fashion in which the angle
ciency at high speeds of operation; This involves 40 between the inlet and outlet is. increased;
lowering the specific loading tosuch extent that
Figure 8 is an elevation of the type o-f cutter
smooth now takes place without. breaking away
used for the generation ofthe passages;
of the flow from the passage walls with the proFigure 9 is a View, generally similar to Figure 5,
duction of burbli'ng, or “stalling” As a result of
but provided in particular to illustrate the fashion
thematters of the present invention, impellers ofV Y45 in which a cutter generates both sides of an
very small dimensions and light weight may be
`
impeller passage simultaneously;
v
-
constructed to operate at .extremely> highzspeciñc.
Figure 10 is a side elevation of an alternative
speeds to >produce high outputs, speciñc speed
form of machine providedl in accordance with the
vbeing equall to
.
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invention;
*Wx/Ö
___,
Hg
50
‘ .
y
,
Figure >'11 is a plan vView of. the machine of
Figure 10'
,
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»12 1s
_,
,
Flgure
a fragmentary elevation
of thel
wherein Q is the. volume handled inv cubic feet
entrance side of` an impeller- ofthe improved
per minute, Il` is the total headA produced by the
design;
impeller infect, and n. is revolutions per minute. 55
~ A
i r
o
.
Figure l'13 isan axial section showing part of
2,407,469
3
an impeller of the improved type together with
a portion of its associated housing;
Figure le is a diagram showing in front eleva
along the trackway HJ. In addition, if desired,
the vertical axis 6 may be adjusted transversely
of the direction of the screw 28.
A carriage 42 supports the cutter and is ar
tain allied matters indicating the fashion in Ul ranged to slide in the direction of the axis of the
tion a pair of vane surfaces, together with cer
which such vanes are laid out;
screw 23 along the tracks 4I lprovided on the
Figure l5 is a plan view of part of the matter .
machine bed. A nut 44 carried by the carriage
of Figure 14 looking radially inwardly along the‘ `
leading edge of a vane;
V
42 embraces a screw 46, connected to a gear 43
,
Figure i6 is a diagrammatic sectional view
showing the vane and certain elements thereof
io
and associated matters in the form of a cir
cumferential projection about the axis of rota
tion into the plane of the paper; and
Figure 17 is a graph showing the relationship
between angles about the -axis of rotation and
(Figure 4) driven through change speed gearing
from the main shaft 3D. A shaft 5B, whose gear
48 is driven through change speed gearing from
the mainshaft 30, as indicated in Figure 4, has
' splinedV theretoy a bevel pinion 52 meshing with
a second bevel pinion 54 carried by a vertical
screw 56 mounted in the carriage, the bevel pin
ion 52 being so mounted as to move with the
axial distances for vanes constructed in ac
carriage lengthwise of the shaft 5B. The verti
cordance with the invention.
cal screw- 56 is embraced by a nut 58 carried by
The particular vane constructions involved will
the support 60 movable vertically relative to the
be best made clear by first considering certain 20 carriage 42 along the traokways 6l of the latter.
improved machines for generating the vanes.
The support 66 has mounted in bearings therein
There will first be described the physical as
the spindle iìïf'in which may be fitted the various
pects of the machine of Figures 1 to 4, the nature
milling cutters 64, the support also carrying the
of the operations performed thereby being there
driving motor 63 for this spindle. ‘
after described.
`
As a result of the construction indicated, it
The machine of these figures is essentially a
will be evident that the cutter is movable both
milling machine in which both the cutter and
in the direction of its axis of rotation, which is
the work are movable in predetermined deñnite
parallel to the tracks 4I, and also vertically by
relationship to secure the generation of skew
reason of the mounting of its support on the
surfaces. The machine comprises a bed 2' on
which there is mounted a work carrier 4 for
rotation about a vertical axis 6, the position of
30`
In Figures 5 and 6 there are illustrated di
agrammaticaly the fundamental elements of the
machine of Figures l to V4; In these Figures 5
which may, if desired, be made adjustable trans
versely of the machine. The work carrier »fl is
provided with an' arm 8 slotted as indicated at
lil to provide a trackway for the reception'of a
cross-head l2, which is pivoted, as indicated at
I4, to a block adjustable along a guideway iii
extending radially of an arm I8, which is se
cured at 2i! to a carriage 22 movable on tracks
23. The pivot IL!- is arranged to be fixed in ad
justed position radially of the arm i3, while the
arm I8 is adapted to be swung between two posi
tions defined by stop elements 24 and 24’ at op
posite sides of, and secured to, the carriage 22.
The provision for swinging the arm I8 to either
of these two positions is merely to make it easily
possible to generate right hand and left hand
rotors. As will become evident hereafter in dis
cussing the theory of operation, the fact that
the arm i8 extends at an acute angle with re
spect to the axis of the machine is not signifi
cant and, in fact, this arrangement is provided
solely to make possible certain clearances when
the carriage 22 reaches an extreme left hand po
sition. The adjustment of the pin I4 is solely for
the purposeV of adjusting it transversely of the
longitudinal axis of the machine, this adjustment
alone being of interest.
v
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The carriage 22 is provided with a nut Z'ä
which embraces the carriage-driving screw 28,
driven from the mainishaft 3i) of the machine
through change speed gearing comprising the
tracks El I.
35
and 6, the axis of rotation of the work is indi
cated at OT through which there extends the
horizontal line AOA’ parallel to the axis of the
screw 28 and to the tracks 23. Along this line
AOA’ there moves the foot M of a horizontal
perpendicular MIN, the length of which, though
subject to adjustment, is fixed during any par
ticular operation of the machine, the point N ,
corresponding to the pivot of the crosshead l2
arranged to slide along the line ON which may
be considered ñxed to the work support pivoted
about OT.
For the purpose of greater gener
ality of analysis, there are involved in Figures 5
and 6 adjustments in addition to those described
in connection with the physical machine. For
example, DE represents the axis (horizontal) of
the blank being cut which axis, however, is not
perpendicular to ON but to a line ON ’ making
with ON the angle qs. BC is perpendicular to
ON’ and parallel vto DE at a distance n >repre
senting the displacement of Vthe axis of the work
55 from the axis OT of rotation.
FQ is the axis of the cutter, extending horizon
tally at a distance e from the common horizontal
plane of AA', ON, DE, and BC, and for generality
assumed making van angle 0 with the direction
AA’ and displaced horizontally by> a distance p
from the axis OT.
It will be evident that Figures 5 and 6 repre
sent the essentials yof the machineV with some
end elements 32 and 34 and indicated in Figure
further generality introduced by the angles 0 and
2. The .work support 4 is provided with grooves 65 «p and the displacement p. While the physical’
as indicated at 36, along which there may be ad
form of the machine involves some vertical and
justed the table 38, which in turn carries tracks
40 so that the work W may be adjusted in the
direction of the tracks, i. e., in the direction of
the length of the trackway lll; It will _be evi
dent from the above that the work may be> ad- '
justed bothv in the directionA of the trackway lil
and transversely of that direction relative'to 'the
horizontal displacements of the physical equiv
alents of the diagrammed lines it will be evident
that what is accomplished by the machine is
identically what would> be accomplished by the
diagrammed mechanism.'r
First there will be considered the theoretical
surface which would be` generated by a cutter of
vertical axis 6 about which rotation maytake
zero diameter, i._e.'„by the cutter axis FQ. This
place by reason of the travel of the cross-head I2 75 involves seeking an equation for an arbitrary
2,407,416@
6
the surface (v1-constant) are not straight lines,r
point P :on FQ in terms of 'coordinates tied to the
curvature being introduced by the constant p;
work. Let PR be the perpendicular from the
Slight values «of the constant pmay be used,
arbitrary point P to the »plane AON, and RS the
however, without detrimental deviation from
perpendicular to line DE from R. As origin con
straight line Values of these sections. It is also
sider point 0' the foot ofthe perpendicular from 5 possible to use quite large Values of p provided
O to DE, the rotor axis, and let a: be measured
the other constants are properly chosen, partic
along the axis DE in the direction 'O’S, y per->
ularly to obtain for impellers quite large angles
pendicularto DE in a horizontal plane in the
direction SR, and e vertically in the direction
RP. For the purpose of the present analysis,
these rectangular coordinates will be most con
venient. 'For comparison with the aforemen
between the entrance and exit portions of the
fluid passages.
ent application is primarily directed. The equa
tioned patents, related cylindrical coordinates cc,
tions then become:
b, and r `may be noted, related to x, "J, and e as
follows:
`
'
If p is zero, there are obtained the surfaces to
which, and to the generation of which, the pres- y
15
ß
3’
.
i C[1_-178,11 a-n
v
c
y
1
z=fï1(an-.î.-K2>
y
20 From these the .parameter may be readily elim
inated giving the single equation for the surface:
by which relationships transformation from one
4,
set 4of coordinates to the other rmay be readily
effected.
i
'
K14-K2
:gli
:c
g
As will be evident from the machine, the point 25 As will be obvious >from the last equation, any
radial section, :I: constant, will be a straight line.
M moves along
towards the right as the cut
The straight line, however, will not be radial
ter axis FQ moves vertically in the direction of
unless n-K2IC=O. Since 'x varies from inlet to
increasing a at a definite ratio of speeds deter
outlet, it is possible to choose n and K2 so that at
mined by the change gearing. From this and
the 'geometry of Figures 5 and 6, the equations 30 the inlet 1L-K2œ is positive whereas at the outlet,
œ being then greater, ’ri-Kar is negative with both
of the surface generated are:
of these limiting deviations from Zero small. In
this fashion, advantageous results may be securedv
l.
n
as ‘pointed out below.
,
.
1
'
If n=0 and K2=0, the equation becomes:
35
z-K1<`tâ.'n '0D-_Ka
.
5.
Z
These are parametric equations for the surface
or, changing to cylindrical coordinates, :1::K1
in terms of the parameter a, the angle MON,
which cannot be eliminated from these .general 40 tan b, ther equation of the surface disclosed and
equations without giving rise to a very com
discussed in the aforementioned patents. As will
be pointed out hereafter, the surfaces generated
plicated single equation.
K1 in the above is the product of the length
in accordance'with the present invention may
conform very closely either to a single surface
0f MN by the ratio of the rate of movement of e
given by œ=Ktan b, or to a plurality of such sur
to that ofpoint M.
faces litted together, the advantage arising in the
If, theoretically, M reached 0,2 would then
latter case being that a single generation serves
have the value -K1K2; in other words, K2 'is `re
to provide a complete surface `which would other
lated to the initial relative settings of the cutter
wise require separate successive generating oper
axis and ,point M.
`
’
It will be noted yfrom the above equations that .
the angles 6 and ¢ are additive, i. e., the same
ations.
Y
The application of the above to the generation
of an impeller or turbine Wheel will be next de
effect of adjustment of both could be secured
by adjustment of one, or if they were of differ
scribed with reference to Figure 7, in which gen
eration will be assumed in accordance with Equa
ent signs they would tend to neutralize each
other. There is, therefore, no point in setting
the cutter axis FQ off parallelismwith the'axis
AA", the same effect being securable by turning
tions 3 or 4. In this figure, a indicates the axis
of the wheel being generated (=DE of Figure 5)
and az is the trace of the yz plane, the angle b
being measured positive in a clockwise direction
the blank on the table to change 4S. As a mat
and y being measured horizontally to the right.
terof fact, adjustment of ¿b is not -generally de
sirable (Causing the'vanes generated to depart (SO The entrance portion of an impeller passage is
illustrated at d and the exit portion of the same
from radial condition) and hence in the follow-,-Y
passage at e. The former will be regarded as .lo
ing 0 and qb will both be considered zero. Only
cated at x=:r:1, and the latter at x=x2, various
under special conditions may 6 and `5b be intro-`
'duced to advantage, forexam‘ple., to correct cur
illustrated elements being located in said planes.
It is >assumed that the constants K1, K2 and n
have been set by adjustment of the machine.
Preliminarily we will again consider generation
of 'surfaces by the axis of the cutter, passing later
to the effect of using a real cutter of particular
vatures otherwise introduced.
` If öfter-‘0, -the equations reduce to:
y_tan a sino:
,
'
1
.
The adjustment of p different from zero is also
a disturbing factor unless it is properly related
to the other constants. .As will be evident from
70
type.
'
At f1 and f2 there are indicated the radial lines
corresponding to the intersection of the planes
x=œ1 and rr=œ2 with the surface œ=K1 tan o,
i. e., the surface which would be generated by
making K2 and n zero ,in Equations 3 or 4.
75
the :form of these equations, radial sections of
2,407,469`
7
Assume' further that n. and K2 are so chosen as
above so that n-Kzœi is positive and u-Kzœz is
negative.
The element y1 of the general gen
erated surface then, in accordance with what was
proved above, lies to the left of f1, parallel to f1
and at a distance therefrom determined by
choicerof constants and the value of x1.
The element g2 of the same surface lies to
right of f2, parallel to ,fz and at a distance
termined by the choice of constants and
the
the
de
the
œ=K1 tan b having the same value of K1, it-will,
in view of the necessary thickness of a real vane,
conform to, and include, for a very considerable
axial extent, a surface m=K1 tan b where K1
differs from K1. Thus it follows that real vanes
of the improved type may be said to conform to
a series of surfaces r=K tan b (in most prac
tical cases to not more than three thereof) which
surfaces may be considered as smoothly merging.
The advantages of the present surfaces lie pri
marily in their ease of generation by single cut
ting operations to give a large angular spacing
for which u-K2rv=0, the element of the generated
between inlet and outlet.
surface will be truly radial and coincident with
The generation of real vanes of the type dis
the element f of œ=K1 tan b and the maximum 15 cussed based on the improved surfaces, results
deviations from radial condition will occur at g1
from the movement, during the generating mo
and gz. It will thus be seen that, for the indi
tions indicated, of cutters of improved types
cated relation of n and K2, the generated surface
along the cutter axis Vwhile it is moving in the
will pass from one side of œ=K1 tan b to the other
direction PR.
in the direction of increasing b with the result 20
The axis of a real cutter will follow a path
that between :r1 and x2 it will subtend a greater
intermediate adjacent theoretical surfaces. In
angle than the latter; in the diagram, for ex
Figure 7, for example, the cutter axis in moving
ample, the latter subtends about 37°, whereas the
inwardly follows a path intersecting plane œ=œ1
former subtends about 47°.
along a line Z1, identical with g1 but spaced there
This is very advantageous in reducing the load
from half the angular spacing of adjacent ele
ing on the blading as will be pointed out later. 25 ments g1. Likewise at plane x=œz, the cutter
Surfaces built upon the theoretical surface thus
axis traces a line Z2 midway between g2 and gzl.
generated have, however, a limitation in that the
The fluid passages therefore lie along the same
surface elements are not radial except at some
given by Equations 3 or 4 with the origin
intermediate position. Suppose, for example, 30 surfaces
plane :ce displaced by half the angular spacing
arcs y‘i and k1 define the inner and outer limits
of the vanes to ce1 (Fig. 7). Thus both the
of vanes at the entrance plane zv=œ1 and it is de
vanes and passages conform to surfaces given by
sired to construct a vane on the generated sur
the equation.
Y
face. If h1 is a radial line drawn from the inter
In
order
that
both
surfaces
of
each
passage
section of g1 with arc k1, it is obviously desirable 35
may be simultaneously generated, the cutter is
that the vane material should completely encom
given a tapered shape which may be conical but
pass such radial line, and similar radial lines in
which
is most desirably substantially hyper
all other radial sections. With g1 displaced only
boloidal
as illustratedin Figure 8 at 64 and di
to the extent shown from a radial direction, it is
obvious that this may be readily accomplished; 40 agrammatically at c in Figure 7. Referring ñrst
to the latter, sections (approximately elliptical)
however, if g1 were too far displaced off center,
of the cutter are shown in the two limiting planes
the vane to satisfy this requirement might have
:r1 and x2, to illustrate the mode of generation.
to be too thick at its base. As a matter of fact,
As the cutter axis moves in the direction of de
the requirement is not absolutely necessary, and
creasing
e, the cutter is uniformly moved in a
if a vane is of suflicient thickness, some under
retracting direction from the blank in the di
cutting of radial lines through it is permissible.
rection QF (Figs. 5 and 6). Thus a part of large
Under such conditions, the element g1 at the
diameter first cuts the outermost entrance por
entrance edge might well be carried further to the
tions of the passages, and as retraction takes
left to secure a still greater angular spread of
place, it proceeds to cut more inward parts of
each vane from inlet to outlet.
the entrance portions of the passages and por
At the discharge a similar condition arises, in
tions further towards the discharge. Successive
this case affecting the opposite face of a vane.
positions of the cutter axis are illustrated at q1,
A radial line h2 is Villustrated indicating the de
q2, and qa. The position qs corresponds to the
sirable limit of approach to an element gal of a
cutting of the trough of the passage.
vane adjacent that having elementsY g1 and g2.
The shape of the cutter is such that during
The radial outlet limits :i2 and k2 impose the
such action the space cut, which is the envelope
limitations, and, as illustrated, if the radial ex
of the successive positions of the cutter, will be
tent of the outlet is small compared to that of
such
as not to encroach (preferably) on the lim
the inlet, a correspondingly greater deviation of
the element g2 from radial condition is per 60 iting radial lines h1 and h2. If the cutter has
an approximately hyperboloidal shape as illus
trated, the result is to generate varies having the
As pointed out in my Patent, 1,959,703, the
desirable taper for securing sufficient strength
inlet angle of a surface x=K tan b varies pre
with production of fillets where the vanes join
cisely within the radius as required for smooth
the central portion of the disc. It will be evident
pick up of fluid being handled. It will be ap
that the shape ofthe cutter is subject to substan
parent without going into mathematical proof
tial variation and the hyperboloidal form may be
that the surfaces here considered, by reason of
approximated by VYthe rotation of circular arcs or
close approach to rv=K1 tan b will also be, `for
even successive straight lines about the cutter
practical purposes, completely satisfactory in this
axis. The actual shape depends in each instance
regard, particularly so when given radial entrance
upon the desired ,vane taper Yand whether or not
edges of airfoil characteristics since such edges
undercutting of radial lines fromV the vane tips
have fairly large‘tolerances for entrance angles
is permissible. The rate of retraction of the cut
consistent with maintenance of smooth flow.
ter is also dependent on these same factors and
However, it is also to be noted that while the
related to the cutter shape, as will be obvious.
improved surface is displaced from the surface 75
In Figure 9 there are diagrammed the factors
value of m2.
Obviously for some intermediate value of :C
missible.
'
`
'
.2,407,469
entering into the operation of the cutter c >in
generating more general surfaces for vanes in
accordance with Equations 2v involving adjust
ment p as well as n and K2.
10
-_desired trou'ghasja part‘of the surface of revo
' lution of the final cutter position.
Assuming that the `
V"cutter has a surface of revolution which, referred
to its axis and a movable point V on the cutter
axis as origin,- is given in cylindrical'coordinates
In such case
recourse. is had to the use ofseveral cuttersused
successively and of such 'corresponding shapes
that the proper vane shapes result from their
.successive operations. In each instance, how
ever, theV cutter is retracted as described for a
by 122:1’ (U) ,where U vis measured along the axis
lof the cutter from the forigin V, the cutter surface
;predetermined part of the cutter action.
The
>vane surfaces are then, except for the troughs,
will be given by the following equation in terms 10 made lup 'of 'a ser-ies of smoothly merging enve
lopes.
of' coordinates œ, y, z, referred to the same co
ordinate. -system used above in discussing the
generated surfaces:
.
6; , v (rc1l co's a-yl sin A«2r-n sin a-pV-l
In the ’above K1, K2, n, p, and u are the same as
previous1y'considered.„K3 and .K4 are constants
takinginto account the movement of the origin
.point of the cutter -surface along 'the cutter axis,
i.: e., the variationv of the coordinate u of the
yorigin point V. This, asevident from the de
scription of the machine, is proportional to the
movement of the point M' and also to the change
îo'f-z.`- K3 takes into account this speed ratio while
K4 takes into .account the 'starting position for
In Figures «10 and l1, there is shown a modified
form of machine adaptedparticularly for rapid
production -of rotors, therebeing, however, less
a-dj'ustability. This machine comprises a base 'B6
on which there is journalled about a horizontal
'axis Ii! a work `support 68 on which the blank
to be >cut is mounted as indicated in construction
lines in the two ñgures. Secured to the support
E8 'and arranged to rock the same is an arm 12
lprovided with a guideway 'M in which there slides
the cross-.head T5 pivoted at ‘i3 to a carriage 80
which is adapted to be moved along a horizontal
rackway 325 Vby a screw B2 driven through
change speed gearing St‘ from a shaft 83 connect'
ed by bevel gearing et to ‘the main `shaft 92 of
‘the machine.'
`
~
The main shaft k92 of the machine drives
through change speed gearing .§24 a transverse
hcrizontal screw S6 which engages a nut il!!! car
ried by' a carriage T98 whereby ythe carriage l:may
.be
moved transversely along the tracks 93. This
In Yaccordance with the. usual theory of enve
carriage in turn supports the spindle 'head ‘|82
lopes, lthe surface -given by v'lîlq'uatio-n »6 will gen
which .is guided'forilongitudinal movement along
erate, for variations of parameter a, a surface
given by eliminating the parameter a from it .35 the 'track IBS so as to provide movement of the
cutter l'ëâ mounted in the spindle 104 in the di
vand its partial derivative with respect to a. Tak
rection of its axisjthe cutter being driven from
ing the partial derivative of 6' with respect lto a
a motor llßß carried’by H32. To secure the axial
the movement.- Í
'
.
there is obtained:
` '
-
(x1 cos a-yl sin d-n sin a-K3
wherein f’ is the ñrst derivative of the :function 45 movement of the cutter, bevel gearing H0, hav
ing a splined connection with a shaft lll driven
f with respect to its argument.
,
by change speed gearing H3 from the main
The -solution of Equations 6 and '7 to eliminate
shaft B2, is provided to drive an upright shaft
.a is laborious, even though performedgraphical
H2 mounted in the carriage Q8 which in turn
ly, but the cross-section of a passage maybe thus
,drives through a ybevel gear lléa second bevel
accurately ascertained b-y plotting the ,values of
gear> HS ñxed against axial movement and in
r:131,- y1, and 21, for a series ofchosen'values of u.
ternally> threaded to engage a screw H3 secured
Graphical methods of descriptive geometry are
to »the head i532. By reason of the change speed
also. usable involving laying out the cross-'sec
gearing and connections described, it will be evi
tions >of the cutter in the various planes of œ con
stant and constructing the enveloping lines ,ew Ul _dent that the cutter may be given-predetermined '
axial and transverse horizontal movements while
thereof. It is to be noted that Equations k6 and
the cross-head 'i6 is moved horizontally in al di
7 give the generated surfaces only where they are
rection parallel to the cutter axis by the screw
yactually envelopes of the cutter surface given by
J‘LU): i. e., the troughs of the passages gener
v Comparison of the last described machine-With
ated by the ñnal position of thecutter are‘sur
that of Figure l .will reveal that the two Ina
faces of revolution of this cutter position.
chines are identical in operation, the last named
While 'the generation has been described for
y82.
the most general case, it will be obvious that it ‘is
equally applicable to the special >cases Vof having
either orboth of K2 or a equal zero. If both are
zero, the passages and vanes both conform strict
lyy to $=K1 tan b. In allcases hyperboloidal, or
substantially. hyperboloidal cutters _have been
found most advantageous to secure properly
shaped
varies.
Y
f
,
,
^
.
`ÍIn some instances, particularly where the ane
gie between inlet-and outlet'measured: about the
axis is _largehit will be found that a single gener
ation by a cutter 4having a pro-per :shape to'y form
the desired vane taper will not sufûce to give the 75
Y
‘
machine being . essentially the former turned
through 9o". It will be obvious, therefore, that
the theoretical considerations involved in Fig
ures `5, 6, and 9 fully apply to the machine of Fig
ures I9 andl l1.V It may be noted that, while in
this last described ‘,rnachine, the’length of the
>arm 'MN of -Figure 5 is unchangeable, neverthe
less, K1 is variable by changing the gear ratio,
for exampie atßt, it being pointed out above that
K1 is the product of the length of MN by the ra”
_tio ofthe rate of movement of z to that of point
M.
.
The machines lof the type ‘described may be
2,407,469
11
utilized for the generation of turbine rotors or
impellers. Turbine rotors generated thereby may
take the general forms described particularly
in my Patent 2,283,176.
'
In the case of impellers further important con
siderations are involved. So far, in connection
with the generating machines, there have been
considered only the vane surfaces
and the
troughs, produced by final cutter positions, with
the equation that this curve is a tangent curve
having a point of inflection at the origin E’ and,
if produced, being asymptotic to 17:90“ at in
ñnity.
From the standpoint of the present design, the
curve E’A’D’ represents approximately one ex
treme design providing, as Will be pointed out
later, substantially a minimum angular difference
between the inlet and outlet edges of Vthe theo
out reference to the circumferential and axial 10 retical vane surface, and a straight line element
boundaries of the impeller. These are of the
greatest importance and there will now be con
D’D’ of the surface defined by the curve E’A’D'
in Figure 17 is chosen as the innermost element
of the vane surface.
sidered these matters.
It may be noted, prelîminarily, that by the use
This straight line B'D’ is shown as such in Fig
of these machines, and particularly that of Fig 15 ure 14. In the axial projection vof that figure,
ure 1, which permits wide adjustment, a complete
it will appear as a straight line starting at a point
rotor of substantial axial length containing a
B at the entrance edge of the vane which, in that
number of impeller or turbine wheel stages, may '
ñgure, is indicated as the vertical line B'A'. This
be cut with no more than axial adjustment of
line, if continued, would have its closest approach
the blank along the support 4 in the direction 20 to the axis O’P’ at the point E', and as illustra
of the grooves 36. Such a combination rotor may
tive of the proper layout of this line, the angle
be provided by assembling a group of forgings
B’O’E’ is shown as approximately 15°. In the
into a single unit, as indicated, for example, in
circumferential projection of Figure 16, the
my application Serial No. 443,957, filed May 21,
straight line E'B’D’ will appear as one branch
1942.
25 of a hyperbola, the closest approach to the axis
Referring first to the diagrammatic Figures 14
of which will occur at E’ in advance of the en
to 17, inclusive, there is indicated therein a rotor
trance edge of the vane, a which point the hyper
|22 adapted to rotate about an axis O'S’ and
bola'is parallel with the axis O'P’.
having blading of the improved type of which one
If further skew straight line elements of the
vane is indicated at |26 and of which an associ 30 surface defined by the curve E’A’D' in Figure
ated adjacent vane is indicated at |26’. In these
17 are plotted, they would appear as the straight
diagrammatic figures, |26 and |26’ represent
lines G’ of Figure 14 projecting into the hyper
theoretical vane surfaces upon which the physical
bolas G’ of Figure 16. In accordance with the
vanes are constructed as described previously.
prior designs set forth in said patent, flow of the
The theoretical vane surfaces may be provided 35 air was caused to take place approximately along
in the form of portions of the doubly ruled sur
one of such straight lines G' constituting ap
faces described above or, alternatively, there may
proximately the center line of a vane between
be some departure from said ruled surfaces,
its inner and outer boundary edges. For ex
though, as pointed out, the departure, if any,
ample, with an entrance edge A’B' as indicated
should be relatively slight and, in fact, for ease 40 in Figure 1_6, the vane `would be designed to ex
of construction and machining, even such vane
tend approximately equal distances on opposite
surface as would depart substantially from a
sides of the inner line G’ indicated in Figures
single doubly ruled surface of the type indicated
14 and 16. In accordance with the present in
may be made up of a plurality of such surfaces.
vention, however, the flow path except along the
To simplify the discussion, however, there will
innermost portion of the vane Where it coincides
ñrst be described a vane4 surface built up from
fairly closely with the straight line element B’D’
a doubly ruled surface, the actual used portion
(subject to the trough formation of Figure 7)
n of the vane deviating substantially from the por
tion of the ruled surface used in accordance with
the specific disclosure of said prior Patent 1,959,- I
703.
As pointed out in said Patent 1,959,703, the dou
bly ruled surface involved conforms to an equa
tion .'L‘=K tan b, in which :i: is measured along
the axis of rotation, while b is measured about
said axis. It will be noted that this equation does
not involve the coordinate r, i. e., the radial dis
tance from the axis of rotation, consistent with
the actual fact that one of the sets of straight
lines making up the surface consists of radial
lines. The other set of straight lines, as pointed
out in said patent, are arranged in skew relation
ship to the axis of rotation in such fashion that
each, if rotated about the axis, would trace out a
hyperboloid of revolution.
Due to the absence of r from the equation, it
will be evident that any such surface may be
completely defined (as a mathematical surface of
infinite radial extent) by a single curve consist
ing of the angle b plotted against axial distance
:12, as indicated in Figure 17, the ordinates of
which are values of b and the abscissas of which
are values of x.
Such a curve is plotted at
E’A’D’, the origin of measurement of both b and
:n being at the point E’. It will be obvious from
departs quite substantially from the other skew
straight line elements of the surface, and the
vane is chosen from that part of the surface
œ=K tan b indicated at A’B'D’C’, Where A’B’ is
the inlet edge, C'D' is the outlet edge and B'D'
and A’C' are, respectively, the inner and outer
boundaries of the vane.
By reason of this se
lection of the vane surface, there is obtained for
a given axial and radial extent of the vane a very
substantial angular difference between the inlet
edge A’B' and the outlet edge C'D'. As will be
evident from Figure 17, in the example illus
trated the angular distance 'between B’ (or A’)
and D', is about 56.6°, and the angular distance
between the entrance edge A’B’ and the center
I’ of the outlet edge C’D’ is about 55°. It will be
evident that-to obtain such an angular differ
ence between the entrance and exit portions of
the vane, if the vane was caused to follow, for
example, the inner straight line clement G', the
diameter of the irn'peller would have to be very
much greater.
As a result of the improved design, the speciñc
loading of the vanes is kept down to such extent
that, during operation, the flow is gradually
deviated from its entrance direction without
production of burbling, and hence smooth flow at
î very high speeds of operation may be secured.
'2,407,469
A'13
As-a result of the fact that the improved vane
-fl26jis` a portion lof the vtheoretical doubly ruledy
surface, it consists throughout Íof radial straight
line elements 'F' giving a maximum strength
against vcentrifugal stresses arising at very high
speeds of rotation.
~
.
«
The anglesalong the inlet edge vary in proper
‘fashion with the radius, as >described in said
patent in such fashion thatl if n is the inlet angle
at a radius r,
‘
whereas in the axial projection of Figure 14 the
surface would appear as indicated at A’B’N’Q’,
i. e., extended considerably more than the sur
face A'B’D’C’ about the axis of rotation Within,
however, the Same radial and axial confines. For
the same capacity and speed of rotation, it is
evident that such a lsurface would be tangent to
the surface A’B’D’C’ 4along the entrance edge
7’
y
wher-eb’ is the constant value of b correspond
ing to the leading element. Thus the flow of gas
"into the impeller passages Yat the inlet edges of
the vanes takes place smoothly without shock
throughout its radial extent. While, in the case
illustrated, >the angle b' is shown as approxi
mately' 15°, this angle is subject to substantial
variation subject to the rgeneral limitations that
it should be small to obtain a maximum angle
between the inlet and outlet of the impeller but
not so small as to create machining diflìculties .
orygive'rise to an -entrance portion of each pas
sage which contributes little to the acceleration
Yof» the rfluid.
in this fashion would appear >identically the same
as the surface -A'B’D’C’ described previously,
A’B’, and as a result of such tangency, the same
ltan' ,n__K VSecvz b,
,
14
the circumferential projection, a surface formed
'
'
If sections are taken across the space between
Vadjacent vanes such as |26 and V126' perpen
variation of inlet angle with radius would be
secured as described previously, so .that shock
less entrance along the entire leading edge `would
take place. ’
~
A surface of such greater angular extent can
be satisfactorily provided'so long as it contains
radial straight line elements, even though it does
not contain throughout its extent, and, in fact,
Acannot contain, a single set of skew straight lines,
and such a surface may be cast or machined'bysuccessive cuts of a milling cutter as above de
scribed. or by the use of a radially arranged mill
ing cutter, as will be obvious to those skilled in
the art. Such an angularly extended surface,
however, may be desirably made'up of a series
of surfaces œ=K tan b having different constants
,K >and different origins for the measurement of
fr, and, for convenience of construction,
vvdicular ‘to the flow through such space, it will be 30 'bland
the rotor may be made in a plurality of parts se
Yevident thatV at the inlet the’section will have a
cured together :and each provided with partial
trapezoidal shape due to the radial divergence
vane surfaces conforming to the different vari
from eachîother of the inlet portions of the ad
ants of the equation. Forexample, as indicated
jacent vanes, Ywhile at the' outlet'the section will
in Figure 17, the entire surface A'N’ may be made
also be trapezoidal but with? a substantial >change
up of the parts A'L’, L’M' and M’N’, each of
"of proportions, the -trapezoid here being sub
which
may conform to the formula. A’L’, for
stantially reduced in an outward direction while
example, may be made in the form of such a
being of substantially greater extent circum
surface tangent to „A’D' at A' carried ¿to the
ferentially, approaching more nearly a paral
point
L’. (For the surface A'L’,fof course, the
lelogram. If a line be drawn through the centers
origin is no longer at E', and K will have a differ
of gravity of these sections, such line will appear
-ent value from that defining A’D’.) If such a
about as indicated at H’I', and it will be ap
surface was continued further, however, it would
'parent from the iîgures that this line, represent
tend
to turn in an axial direction, as viewed in
ing what might be called a mean path 'of flow,
Figure 1'?, as indicated by the continuation
involves only gradual curvature, having at no
marked Z’. It therefore becomes necessary at
`point thereof any small radius of curvature. As
L’ to provide a different surface L'M', which also
a result of such ñow patch, at no point thereof
will have »a different K and a different origin. As
-is »there any great curvature of the flow, mean
before, this surface may not reach the location
ing essentially that the loading of the passage
causing acceleration of the gas is relatively uni- «
form throughout to the end that all parts of -the
passage contribute to the acceleration without
N’ by reason of axial deviation, as indicated at
m', so .that Va third surface may be provided at
M’ extending through N'. It will be evident from
the nature of the equation for these doubly ruled
surfaces that tangency may be secured through
very nearly axially, as indicated by the 'Vector ’ ' out the entire radial extent o-f the surfaces at L’
and M’ so that a completely smooth composite
K', while at the exit point I’ (.whichis approxi
Asurface results. While the flow path, as viewed
mately, in the projection of Figure 5, both the
in an axial projection such as Figure 14, will, in
center of the exit edge C’D' 0f each vane and the
the case of such a surface, appear more curved
-center of gravity of the cross-section of 'the flow)
than the path ï-I'I’ previously described, it will
the ñow takes place in the direction indicated by
there being set up such forces as would result
in burbling. At the point H’ the entranceoccurs
the arrow J ' in Figures 14 and 16.
As indicated above, the design just described
approaches one extreme of desirable design for
high speed operation, and it is, in fact, desirabie
to secure an even greater change of the angle b
between the inlet and outlet edges. For example,
for the same capacity of the impeller and for the
same speed of rotation, it would be desirable to
secure a difference of angle between the entrance
and exit of 90° or more, and fcr'theis pur-pose
the surface, consisting of straightline radial ele
ments, might be as indicated at A'N" (or B’N'l `
iny Figure 17..
Such a surface, it will be noted.
’ would give a change of 90° between the entrance »
edge and the extreme limit 'of the exit edge'. In l
~ be evident that, as a matterof fact, the curvature
it imparts to the gas will be evenless, so that
the* speciñc loading of the vanes will be even
further reduced. in other words, it effects the
same `resulting acceleration of the gas, but the
Work done in accomplishing this is distribu" 'f
over a much more extended vane surface. While
there is an actual increase in the “wetted” vsur
faces of such vanes, the fact that an even more
gradual acceleration takes place results in less
tendency to produce any burleling condition re»
sulting from breaking of the flow away from
passage walls and the disadvantage of slightlj,1
increased friction los-ses is-paid for by a substan
tial net increase 4in efficiency.
,
2,407,469
15
The various relative dimensions involved in
accordance with the invention are not critical
within substantial ranges. For example, 'the
change of the angle b from the inlet edge of a vane
to the center of the outlet edge may vary from a
lower limit of about 35° through upwards of 100°.
Desirably, however, this angle should be at least
l
16
blade |26, that the line B’D’ should be astraight
line, projecting circumferentially into an hyper
bola. The boundary B’D’ is, in fact, in the case
of vane surface generation as described above,
merely an incident of the cutter shape and its
innermost position. Generally speaking, the
spacing'of these boundaries inwardly and out
45° and most desirably lies within a range of
wardly of the mean now path I-I’I’ is such that
about 55° to 85°. The most desirable portions of
for a smooth path H’I’, which is also to a de
the ranges indicated are dictated by the speeds 10 gree arbitrary, the cross-sections of the impeller
of operation, i. e., smaller angular changes are
_passages perpendicular to this ñow path have
consistent with lower speeds, while for higher
their centers of gravity lying approximately
speeds the angles should be within the upper
along the path H’I’. The areas of the cross-sec
portions of the ranges.
tions of the impeller passages perpendicular to
In the circumferential projection of Figure 5, 15 this iiow path gradually increase from the inlet
the angle made by the projection of the dis
to the outlet to secure a small equivalent cone
charge vector J ’ with the axis (i. e., the angle
angle (i, e., double the angle between the cone
J’I’S’) should lie within about the range 35°
axis and a straight line element), of the order,
to 60°. The backward angle made by this vector
for example, of 2° to 6° (and preferably about 4°)
with respect to the tangent to the circumferential 20 defining the equivalent cone (as is conventional
direction at I’ measured within a plane con~
in impeller design practice) as one of which a
taining both the tangent and the vector J' should
frustum, having the discharge area as its base
be between about 40° and 85°.
and the inlet area as its top, has as its height
The inlet angle at the outermost portion of the
the developed length of the flow path between
inlet edge, i. e., the angle n, should lie between 25 these areas. In the present case, this height is
the limits of about 20° and 45°, this angle in-~
very long for a given impeller diameter, so that
wardly thereof varying according to the expres
a small proper cone angle results in a large, de
sion above set forth.
sirable area ratio. As is well known from aero
The blade height at the inlet edge, i. e., A’B’,
dynamics, however, so long as flow paths do not
should be between about 0.5 and 0.7 of A'O','the 30 have sharp deviations or divergences when
eye radius.
viewed in the light of now velocities, it will be
The axial length of the mean flow path, i. e.,
evident that substantial latitude vin the design
O’R’ should be between about 0.7 and 1.2 of the
of the impeller passages is permissible even with
eye radius A’O’.
very high flow velocities and rotational speeds
The radius I’R’ (of the exit edge) should be 35 consistent with the avoidance of burbling.’ The
between about 1.0 and 1.5 of A’O’, the eye radius,
equivalent cone angle may, in fact, be slightly
and preferably between about 1.2 and 1.4 of
negative.
A’O’.
The number of vanes about the circumference
It Will be noted that the outlet edge C’D' is
of the impeller is subject to substantial variation,
not illustrated as perpendicular to the mean flow 40 though desirably this number should lie between
path, and generally speaking its circumferen
17 and 27, 21 to 23 vanes being the optimum
tial projection will make a small angle with re
number. The considerations determining the
spect to the axis of rotation about as illustrated,
proper number of vanes are those of proper
generally about 8° to 10°. It is found that such
guidance of the flow balanced against the in
an angle is desirable in order that the impeller
troduction of too great a total wall `area giving
will impart the same amount of energy to each
rise to excessive friction. If at least 17 vanes
particle of air irrespective of its flow path with
are used, good guidance of the flow results, i. e.,
in the radial limits of the passage. This results
there is no such great spacing between the vanes
in the same pressure at all points of the dis
as will permit any portions of the flow to depart
charge. If pressure differences are permitted to 50 substantially from parallelism in a, three-dimen
occur disturbances are set up with energy losses.
sional sense, with the vanes. With increase of
If a conical surface is constructed about the axis
the number of vanes up to 2l to 23, still better
of rotation perpendicular to the mean flow path,
guidance results and above this number the
in its circumferential projection, at I', which
guidance is not materially improved, so that if
conical surface is indicated at U'T’ in Figure 16, 55 the number of vanes rises above about 25, fric
the conical annulus U’V' may be considered as
tion losses begin to enter into the picture to lower
the virtual area through which the discharge
the efliciency.
takes place. This conical annulus is related to
The theoretical surfaces of the type described
the plane annulus about the center of rotation
may be considered as those upon which actual
and bounded by circle through A’ and B', re 60 vanes are constructed, i. e., such surfaces are
spectively, which annulus may be called the en
desirably the central surfaces of symmetry of the
trance annulus, in such fashion that the ratio
vanes. As a consequency, the passages between
of the area of the conical annulus to the area
the vanes may also be said to have substantially
of this entrance annulus is about 0.6 to 0.9, which
such surfaces as their boundaries, or these pas
is a result of the fact that the ratio of the 65 sages may be regarded as built up of imaginary
meridian velocities normal to these annuli should
laminae formed by such surfaces and extending
be approximately unity. The ratio of inlet vol
parallel to the flow through the passages. For
ume flow to the entrance annulus should be equal
mechanical strength, the actual vanes are desir
to the ratio of the discharge volume ñow to the
ably strictly radial, though some slight departure
area of the conical discharge annulus, and the 70 therefrom may be tolerated if necessitated by
design as just indicated gives this result.
special design'requirements as indicated above in
The outer boundary A'C’ and the inner bound
the discussion of Figure 7. Generally speaking,
ary B’D’ of each of the vanes may `be rather
the thickness of each vane along its entire outer
arbitrarily chosen within limits. It is not re
contour should be no more than one-half the
quired, as was assumed in the laying out of the 75 thickness at its base where it joins the impeller
31452714.69
hub, _the varies desirably tapering, as indicated
most clearly in Figure 12.
The vanes may be
formed by milling out a solid blanls of 'metah’as
indicated above, in which case.v it is vdesirable to
provide large fillets where the vane joins the hub
proper.
'
.
I
.
.
‘
~
The embodiment of the invention in an actual
impeller will be clearirom a consideration of
is
generated. by the mechanisms heretofore de
scribed with particular reference to Figures 5, 6,
7, and 9. As pointed out above, the theoretical
surfacesA on which the vanes may be regarded as
' constructed may be, despite their precise formu
lae indicated above, regarded as made up of a
series of simple surfaces in accordance with Fig
-ure 17, the other surfaces being close approxi
mations to a series of such surfaces.
Figures 12 and 13. Either for reasons of Vmachin
The various relative dimensional matters are
10
ing described above, i. e, to form a quite extended
tied up with performance to secure Various de
vane surface by milling separate doubly ruled
sirable features.
>
‘
e
surfaces, or for the damping of vibration as de
First is the matter of eilìciency which may be
scribed in my application Serial No. 407,408. íìled
deñned as the work required theoretically for
August 19, 1941, the impeller may bemade in> a
adiabatic compression divided by the actual Work
plurality of sections. In the instance illustrated. 15 required
to accomplish it. This involves the
in Figures 12 and 13, the impeller is> made up of
avoidance of inlet shock, the avoidance of break
two` sections |28 and |30, respectively, provided
age of the flow from the walls which would be
with aligned holes |32 in enlarged portions of
whichare located bushings |34- arranged to valign Y
attended with the production of turbulence and
accurately the sections withrespect to each other. 20v eddies, the avoidance of crowding of ñow in a
passageftoward some wall thereof, and the useThe holes accommodate alloy expansion rods con
of a proper number of Vanes to secure effective
trolling theV sliding of the impeller on its shaft to
guidanceof flow.~
n y v
maintain constant the clearances between the
A second criterion is the securing of the highest
impeller and its housing underall temperature
efficiencies for high pressure ratios cor
conditions. .The two impeller halves are heldV 25 possible
responding to highV tip speeds.
.
together by the pressure differences across the
' >The third criterion is' `that of, securing a useful
impellergsection |35 being _located by means of
broad operating range of lair flow handled by the
the heads of the expansible rods. As illustrated in
impeller at constant speed,~
Figure 13, there. is a slight undercut |36 of one
A fourth criterion is the securing of a maxi
hub section and the inner portions of its vanos 30 mum capacity for lthe size off-the Wheel, a small
where they abut the other hub section, so that
size meaning a minimum wetted surface and,
when the two sections are pressed together, the
therefore, less friction loss and also minimum
bulk and weight, the .latter being particularly im
vane
outermost
sections
portions.
engage This
each serves
other to
tightly
eifectatdamp
portant in aircraft applications.
ing of vibrations which may be set up during oper
¿A fifth criterion involves the securing `oi'- a '
ation. In order further to align the impeller sec
proper variation of capacity with the speed.
tions, and associate them' With other impellers in
These criteria are satisfied by the constructions
a. multiple stage arrangement, and to provide for
heretofore described. `Avoidance of inlet shock
bearing support, the bore. |24 in the hub is pro
is provided by a, 'proper variation of the inlet angle
vided with internal teeth |38 adapted to bel en
and proper values to suit the speed and volume
gaged with corresponding spline teeth on a tubum
handled. Breakage of flow from the walls of the
lar shaft, not shown. The taper of the vanes
will be apparent from considering the base por
tions |4û thereof and the outermost portions Itâ.
The entrance edges IM are desirably rounded to
provide airfoil action. If such airfoil edges are
provided, there is very little change inefficiency
from the standpoint of losses at the intake edges
of the vanes over a moderate variation in the
ratio of the volume of gas handled by theimpeller
to the speed of rotation despite the fact that this
ratio may deviate to such an extent that the en
trance angles along the inlet edges are no longer
strictly proper to secure shockless entrance. This
is due to the fact that an airioil edge will pro
impeller vanes is prevented by a large change of
the angle b from inlet to outlet and a` large ratio
of O’R' to A’O’, Axial crowding at the outlet
is prevented by a large ratio of O’R' to A’O’
and a small ratio of I’R’ to A’O’. Increase of the
number of vanos lessons the divergence angle
and therefore provides smooth flow. The proper
angle of the outlet C’D' also contributes to the
efliciency. High efliciency results from a large
change of the angle b between inlet and outlet,
a large ratio of O’R' to A’O’ and a small cross
section at the outlet corresponding to a cone
angle which may be smallv or which may even be
vide smooth ñow for substantial Changes-of angle.
negative. A small true discharge angle increases
the operating range. Small size involves a small
emcient operation >for variations of the ratioY of
ratio of I’R’ to A’O". The variation of capacity
the volume handled to speed between the limits
60 with speed is controlled by the inlet angle, and
a large inlet angle is desirable for high speeds.
of The
pulsation
exit edges
and maximum
of the vanos
capacity.
are also dosirably
`l'lV'hat I claim is:
’
'
tapered down to form good trailing airfoil edges. _
1. A rotor having passages therein for elastic
Conditions in this region, however, are not so im ' fluid, each passage conforming substantially to a
portant inasmuch as the impeller outlet veloc
surface having the parametric equations:
ities relative to the vanes are substantially smaller
Thus an impeller so constructed is adapted for
than the impeller entrance velocities relative to
the inlet edges of the vanes.
designed properly to receive' the gas at its high
speed of floW.
; „_.r_.'_ _. ._L.. __
'
Impellers designed in accordance with thefore
going are enclosed in suitable conventional hous
ings |46 and discharge into suitable diftusers |48 70
yvan (MM)
and
r
'
'
,
sin (MFM) ` `"
.
‘1
.
Y
. `~
It is to be noted that the dimensional matters
last described are applicable to the construction
of all impellers the vane surfaces of ‘which are
2.
rotor having passages therein for elastic
19
2,407,469
fluid, each passage conforming substantially to a
surface having the parametric equations:
and
20
radial lines extending inwardly from points there
of.
9. An impeller for a centrifugal compressor
having vanes deñning passages for elastic ñuid
and extending in skew relationship to the axis
of rotation, each of said vanes extending sub
stantially along radial lines, and having its exit
portion spaced from its inlet portion by an angle
3. A rotor having passages therein for elastic 10 about the axis of rotation substantially within
the range of 35° to 100°, each passage guiding the
fluid, each passage conforming substantially to a
now across the skew straight lines of at least one
surface having the parametric equations:
surface having the equation œ=K tan b and ap
proximating a radial median surface through
y
n
_tan a
the passage, :r in said equation being measured
15 along, and b about, the axis of rotation.
and
10. An impeller for a centrifugal compressor
l
having vanes defining passages for elastic fluid
and extending in skew relationship to the axis of
rotation, each of said -vanes extending substan
4. A rotor having passages therein for elastic
vfluid, each passage conforming substantially to a 20 tially along radial lines, having its inlet edge of
a radial extent measuring substantially between
surface having the parametric equations:
0.5 and 0.7‘times the maximum radius of the
“KIQ-Darm)
_
a:
tana
and
1
ZLKl(tan raz-K2)
5. An impeller having passages therein fol`
elastic fluid, each passage conforming substan
tially to a surface having the parametric equa
tions:
„L_ n
y“tan a
and
inlet edge, having a mean axial extent measur
ing substantially between 0.7 and 1.2 times the
25 maximum radius of the inlet edge, and having the
mean radius of its outlet edge measuring sub
stantially between 1.0 and 1.5 times the maxi
mum radius of the inlet edge, each passage guid
ing the flow across the skew straight lines of at
30 least one surface having the equation 1v=K tan
b and approximating a radial median surface
through the passage, :1: in said equation being
measured along, and b about, the axis of rotation.
11. An impeller for a centrifugal compressor
having vanes defining passages for elastic fluid
and extending in skew relationship to the axis of
rotation, each of said vanes extending substan
tially along radial lines, having its exit portion
n-Kzsc being positive at the inlet and ‘nf-Kar 40 spaced from its inlet portion by an angle about
the axis of rotation substantally Within the range
being negative at the outlet of said passages.
of 35° to 100°, having the tangent of the inlet
6. An impeller having passages therein for elas
tic fluid, each passage conforming substantially
to a surface having the parametric equations:
_
x
123.11 a
angle along its inlet edge varying substantially
in inverse proportion to the radial distance from
the axis of rotation, having the value of the in
45 let angle at the outermost portion of the inlet
edge substantally in the range 20° to 45°, having
its inlet edge of a radial extent measuring sub
stantially between 0.5 and 0.7 times the maxi
mum radius of the inlet edge, having a mean
7. An impeller having passages therein for elas 50 axial extent measuring substantially between
0.7 and 1.2 times the maximum radius of the in
tic fluid, each passage conforming substantially
let edge, and having the mean radius of its out
to a, surface having the parametric equations:
let edge measuring substantially between 1.0 and
1.5 times the maximum radius of the inlet edge,
tan a
55 said vanes numbering 17 to 27, each passage
guiding the flow across the skew straight lines
of at least one surface having the equation x=K
tan b and approximating a radial median sur
face through the passage, :z: in said equation be
n-Kzx being positive at the inlet and n-Kzx 60 ing measured along, and b about, the axis of
rotation.
` being negative at the outlet of said passages, said
passages being bounded by tapering vanes each
12. An impeller for a centrifugal compressor
having vanes defining passages for elastic fluid
of which encompasses substantially al1 radial lines
extending inwardly from points thereof.
and extending in skew relationship to the axis
8. A rotor having passages therein for elastic 65 of rotation, each of said vanes extending sub
fluid, each passage conforming substantially to a
stantially along radial lines, having its exit por
surface having the parametric equations:
tion spaced from its inlet portion by an angle
and
y
said passages being bounded by tapering vanes
each of which encompasses substantially all
about the axis of rotation substantially within
the range of 35°'to 100°, and having <the tangent
70 of the inlet angle along its'inlef, edge varying
substantally in inverse proportion to the radial
distance from the axis of rotation, each passage
guiding the ñow across the skew straight lines
of at least one surface having the equation œ=K
tan b and approximating a radial median sur
animes
-21
face through the passage, a: in said equation be
ing measured along, and b about, the >axis of
rotation.
.13. An .impeller for
having vanes defining
and extending in skew
rotation, each of said
'
a >centrifugal compressor
passages for elastic fluid
relationship to the axis of
vanes extending substan
tially along >radial lines, having its exit portion
spaced from its inlet portion by an angie about
stantially alongl radi-al lines, having its inlet edge
of a radial extent measuring substantially be
tween 0.5 and 0.7 times the maximum radius
of the inlet edge, 'having a mean axial extent
measuring substantially between 0.7 and 1.2 times
the maximum radius of the inlet edge, having
the mean radius of its outlet edge measuring sub
stantially between 1.0 and 1.5 times the maxi
mum radius of the inlet edge, and said vanes
the axis of rotation substantially within the 10 numbering 17 to 27, each passage guiding the
fiow across the skew straight lines of at least one
range of 35° to 100°, having the tangent of the
surfacey having the equation :1::K tan b and
inlet angle along its inlet edge varying substan
approximating a radial median surface through
tially in >inverse proportion to the radial distance
the passage, :1: in said equation being measured
from the axis of rotation, and having the value
of the inlet angle at the outermost portion of the 15 along, and b about, the axis o-f rotation.
1B; An impeller for a centrifugal compressor
inlet edge substantially in the range 20° to 45°,
having vanes defining passages for elastic fluid
each passage guiding the flow across the skew
and extending in skew relationship to the axis of
straight lines of at least one surface having the
rotation, each of said venes extending’ substan
equation xzK tan b and approximating a radial
tially along radial lines, having its inlet edge of a
median surface through the passage, x in said
equation being measured along, and o about, the
axis of rotation.
14. An impeller for a centrifugal compressor
having vanes defining passages for elastic ñuid
and extending in skew relationship to the axis 25
radial extent measuring substantially between
0.5 and 0.7 times the maximum radius of the
inlet edge, having a mean axial extent measuring
substantially between 0.7 and 1.2 times the maxi
mum radius of the inlet edge, having the mean
radius of its outlet edge measuring substantially
of rotation, each' of said >vanes extending sub
between 1.0 and 1.5 times the maximum radius
stantally along radial lines, .having its exit por
of the inlet edge, and the passages defined by said
tion spaced from its inlet portion 'by an angle
vanes having gradually increasing cross-sections
about the axis of rotation substantially within
the range of 35° to 100°, and having its inlet 30 normal to the pathsv of fiow therethrough, each
passage guiding the flow across the skew straight
edge of a radial extent measuring substantially
between 0.5 and 0.7 times the maximum radius
of theinlet edge, each passage guiding the flow
across’ the skew straight lines of at least one
surface having the equation œ=K tan b and ap
lines of at least one surface having the equation
:c=.K tan b and approximating a radial median
surface through the passage, m in said equation
being measured along, and b about, the axis of
proximating a radial median surface through
the passage, :c in said equation being measured
along, and b about, the axis of rotation.
rotation.
a radial extent measuring substantially between
0.5 and 0.7 times the maximum radius of the
inlet edge, and having the mean radius of its
edge measuring substantially between 1.0 and 1.5
times the maximum radius of the inlet edge, each
passage guiding the ñow across the skew straight
lines of at least one surface having the equation
œ=K tan b and approximating a radial median
surface through the passage, :c in said equation
being measured along, and b about, the axis of
radius of its outlet edge measuring substantially
between 1.0 and 1.5 times the maximum radius
of the inlet edge, and the annular area through
which discharge takes place from said passages
beingsubstantially 0.6 to 0.9 times the annular
19. An impeller for a centrifugal compressor
having vanes defining passages for elastic fluid
and extending in skew relationship to the axis of
15. An impeller for a centrifugal compressor
having vanes defining passages for elastic iiuid 40 rotation, each of said vanes extending substan
tially along radial lines, having its inlet edge of
and extending in skew relationship to the axis
a radial extent measuring substantially between
of rotation, each of said vanes extending sub
0.5 and 0.7 times the maximum radius of the
stantially along radial lines,y having its exit por
inlet
edge, having a- mean axial extent measuring
tion spaced from its inlet portion by an angle
substantially between 0.7 and 1.2 times the maxi.
about the axis of rotation substantially within
mum radius of the inlet edge, havin-g the mean
the range of 35° to 100°, having its inletedge of
rotation
.
Y
16. An impeller for a centrifugal compressor
having vanes defining passages for elastic fluid
and extending in skew relationship to the axis
of rotation, each of said vanes extending sub
area through which flow enters said passages,
each passage guiding the flow acrossthe skew
straight lines of at least one surface having the
equation :rzK tan b and approximating a radial
median surface through the passage, œ in said
equation being measured along, and b about, the
axis of rotation.
20. An impeller for a centrifugal compressor
having vanes defining passages for elastic fluid
and extending in skew relationship to the axis
of rotation, each of said vanes extending sub
stantially along radial lines, having its exit por
stantially along radial lines, having its inlet edge
tion spaced from its inlet portion by an angle
of a radial extent measuring substantially be
about the axis of rotation substantially within
the range of 35° to 100°, and said vanes number CB CA“ tween 0.5 and 0.7 times the maximum radius of
the inlet edge, having a mean axial extent measur
ing 17 to 27, each passage guiding the ñow across
ing substantially between 0.7 and 1.2 times the
the skew straight lines of at least one surface
maximum radius of the inlet edge, and having
having the equation .'L’=K tan bv and approxi
the vnean radius of its outlet edge measuring sub
mating a radial median surface through the pas
stantially between 1.0 and 1.5 times the maximum
sage, .r in said equation being measured along,
radius of the inlet edge, the angle between the
and 'b` about, the axis for rotation.
circumferential .projection of the direction of dis
17. An impeller for a centrifugal compressor»
charge from said passages and the axis of rotation
having vanes definingpassages for elastic fluid
being substantially 35° to 60°, each passage guid
and extending in skew relationship to the axis
of rotation, each of said vanes extending sub 75 ing the fiow across the skew straight lines of at
2,407,469
23
least one surface having the equation az=K tan b
and approximating a radial median surface
through the passage, :r in said equation being
measured along, and b about, the axis of rotation.
21. An impeller for a centrifugal compressor
having vanes deñning passages for elastic iluid
and extending in skew relationship to the axis of
rotation, each of said vanes extending substan~
tially along radial lines, having its exit portion
24
of rotation, each of said vanes extending sub-l
stantially along radial lines, having its exit por
tion spaced from its inlet portion by an angle
about the axis of rotation substantially within
the range of 35° to 100°, having an airfoil inlet
edge, and tapering outwardly so that its outer
most portions are no thicker than one-half the
thickness of its radially correspondingbase por
tions, each passage guiding the fiow across the
spaced from its inlet lportion by an angle about 10 skew straight lines of at least one surface hav
the axis of rotation substantially within the
ing the equation :czK tan b and approximating
range of 35° to 100°, the passages defined by
a radial median surface through the passage, a:
said vanes having .gradually increasing cross~
in said equation being measured along, and b
sections normal to the paths of flow thereÀ
about, the axis of rotation.
'
through, each passage guiding the iiow across 15
25. An impeller for a centrifugal compressor
the skew strai-ght lines of at least one surface
having vanes defining passages for elastic iluid
having the equation m=K tan b and approxi
and extending in skew relationship to the axis
mating a radial median surface through the
of rotation, each of said vanes extending sub
passage, :c in said equation being measured along,
stantially along radial lines, having its exit por
and b about, the axis of rotation.
20 tion spaced from its inlet portion by an angle
22. An impeller for a centrifugal compressor
about the axis of rotation substantially within
having vanes deñning passages for elastic fluid
the range of 35° to 100°, having the tangent of
and extending in skew relationship to the axis of
the inlet angle along its inlet edge varying sub
rotation, each of said vanes extending substan
stantially in inverse porportion to the radial dis
tially along radial lines, having its exit yportion 25 tance from the axis of rotation, having the Value
spaced from its inlet portion by an angle about
of the inlet angie at the outermost portion of the
the axis of rotation substantially within the range
inlet edge substantially in the range 20° to 45°,
of 35° to 100°, the annular area through which
having an airfoil inlet edge, and tapering out
discharge takes place from said passages being
wardly so that the outermost portions are no
substantially 0.6 to 0.9 times the annular area 30 thicker than one-half the thickness of its ra
through which iiow enters said passages, each
dially corresponding base portions, each passage
passage guiding the flow across the skew straight
guiding the flow across the skew straight lines
lines of at least one surface having the equation
of at least one surface having the equation
zzz=K tan b and approximating a radial median
5c=K tan b and approximating a, radial median
surface through the passage, œ in said equation 35 surface through the passage, :I: in said equation
being measured along, and b about, the axis of
being measured along, and b about, the axis of
rotation.
rotation.
26. An impeller for a centrifugal compressor
having vanes defining passages for elastic fluid
and extending in skew relationship'to the axis 40 and extending in skew relationship to the axis
of rotation, each of said vanes extending sub
of rotation, each of said vanes extending sub
stantially along radial lines, having its exit por
stantially along radial lines, having the mean
tion spaced from its inlet portion by an angle
radius of its outlet edge measuring substantially
about the axis of rotation substantially within
between 1.0 and 1.5 times the maximum radius of
the range of 35° to 100°, the angle between the o the inlet edge, the passage defined by said vanes
circumferential projection of the direction of
having gradually increasing cross-sections nor
discharge from said passages and the axis of ro
mal to the paths of flow therethrough, and the
tation being substantially 35° to 60°, each pas
annular area through which discharge takes
sage guiding the ñow across the skew straight
place from said passages being substantially 0.6
lines of at least one surface having the equation 50 t0 0.9 times the annular area through which flow
.1::K tan b and approximating a, radial median
enters said passages, each passage guiding the
surface through the passage, .r in said equation
flow across the skew straight lines of at least one
being measured along, and b about, the> axis of
surface having the equation œ=K tan b and ap
rotation.
proximating a radial median surface through the
24. An impeller for a centrifugal compressor
passage, a: in said equation being measured along,
having vanes defining passages for elastic iluid
and b» about, the axis of rotation.
and extending in skew relationship to the axis
RUDOLPH BIRMANN.
23. An impeller for a centrifugal compressor
having vanes defining passages for elastic iiuid
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