US2431604A - Method and machine for generating rotors for elastic fluid mechanism - Google Patents

Description

Nov. 25, 1947. R. BIRMANN 2,431,604

METHODVAND MACHINE FOR GENERATING ROTORS FOR ELASTIC FLUID MECHANISM Filed March 26, .1943 6 Sheets-Sheet 1 R. BIRMANN Nov. 25, .1947.

METHOD AND MACHINE FOR GENERATING ROTORS FOR ELASTIC FLUID MECHANISM Filed March 26, 1943 6 Sheets-Sheet 2 Nov. 25', 1947. R. BlRMAN N METHOD AND MACHINE FOR GENERATING ROTORS FOR "ELASTIC FLUID MECHANISM Filed March 26, 1943 6 Sheets-Sheet 5 IV/TA ESS: -WM

NOV. 25, 1947. R m N 2,431,604

7 METHOD AND MACHiNE FOR GENERATING ROTORS FOR ELASTIC FLUID MECHANISM Filed March 26, 1943 e Sheets-Sheet 4 mas/vim Y RM @Z 543772627272 NOV. 25, 1947. BlRMANN 2,431.30!-

METHOD AND MACHINE FOR GENERATING ROTORS FOR ELASTIC FLUID MECHANISM Filed March 26, 1945 6 Sheets-Sheet '5 I Awe/v70? W/m Ess:

Mfl- I fl w/hi gzkma'rzrz NOV. 25, 1947. v mM 'N 2,431,604

MET HOD AND MACHINE FOR GENERATING ROTORS FOR ELASTIC FLUID MECHANISM Filed March 26, 1943 6 Sheets-Sheet 6 Patented Nov. 25, 1947 Rudolph Birmann, Newtown, Pa., assignor, bymesne assignments; to, 1u rbo Engineering'Gor-Q poration, a-cornoration of Delaware P Appl ca i n March .6, Sexist 0,6 3.

14 Claims. (01. 910713.99

This invention relates to a method and machine for generating rotors, for example, centrifugal impellers and turbine rotors, forela'stic' fluid mechanism and to the improved rotors generated thereby. Specifically, theinvention relates to the provision of the type of rotors for elastic fluid mechanism which are disclosed in my Patents 1,926Q225, dated September 12, 1933, 1,959,703, dated May 22, 1 934, and 2,283,176, dated'May 'l- Q, 1942.. and my application Serial N 0. 441,686; filed May4,1942.'

As disclosed in said patents and application, there are highly desirableQfor the handling of elastic fluid, rotors having passages defined by vanes conforming to the disclosures thereof. In particular, such rotors are desirably formed by having the passages thereof milled out of soli'd blanks of metal so as to achieve' maximum strength at very high Speeds of operation; and in the case of turbine rotors, ample conduction of heat from the vanes to the central portions of the; rotor. to" avoid. overheating of the vanes which might result in their destruction. As pointedout" the disclosures aforementioned, the vanes'and passages, when made to conform closely to par ticular'. theoretical surfaces, have highly desirable aerodynamic, as well as mechanical, properties.v They are adapted to receive the elastic fluid and discharge it in the proper directions; and there are securable the proper curvature and diyergence of the elastic fluid assages to give rise to smooth flow despite extremely high speeds of. peration.

Qne broad object of the present invention is the. provision of a novel method for the gener-' ation of elastic fluid rotors of the type indicated. A further broad object of the invention is the provision of a machine for carrying out automatically the aforesaid method and capable of adjustment to secure desirable Variations in the surfaces generated. Various detailed objects of the invention which will become apparent hereafter have to do with details of both the methods and the machines whereby, in particular, the generation may be carried out in such fashion that both sides of a fluid passage may be simultaneously out.

A further object of the invention is the provision of a centrifugal impeller wherein, without Violation of other requirements, there is secured a quite large angle about "the axis of rotation between the inlet "and outlet portions of each or its pas ages." "A subsidiary object is'the cutting of such" an impeller T in one operation, Whereas heretoforeit has been generallynec'essary to take successive cuts to secure the 'd'esirecl result."

- "These and othendetailedjobjects of the invenlooking, at the, right hand. end "of. the machine as viewed. in Figure l;

Fi ure 3 is an el vation Q; the. machine office are. 1,: partial y. in; se tion; o" i ustrate e ta n details;

Fi ure. 4. is an elevatio ofrcertain ear chan e mec an sm a view d lookin at. th le t hand; nd of igures;

i ure i is a di ram. showi in El n th p incipal elements. of. the it i re and at he. c the urfaces "F 'fl s 11 i a Pl n Y sw 9 the machi of 6,5"

FigiirslZ and 13 show in diagrammatic elevation and" axial "section; "respectively; an impel ler of thetype'ge erated; "There willhrst be described the physical aspects of the machine of Figures 1 to l, the nature of the operations performed thereby being thereafter described.

The machine of these figures is essentially a milling machine in which both the cutter and the work are movable in predetermined definite relationship to secure the generation of skew surfaces. The machine comprises a bed 2 on which there is mounted a Work carrier ii for rtation about a vertical axis 6, the position of which may, if desired, be made adjustable transversely of the machine. The work carrier t is provided. with an arm 8 slotted as indicated at :8 to provide a trackway for the reception of a cross-head 12, which is pivoted, as indicated at M, to a block adjustable along a guide way it extending radially of an arm i8, which is ecured at 26 to a carriage 22 movable'on tracks 23. The pivot it is arranged to be fixed in adjusted position radially of the arm it, while the arm i8 is adapted to be swung between two positions defined by stop elements 25, and 2 at opposite sides of, and secured to, the carriage 22. The provision for swinging the arm it 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 discussing the theory of operation, the fact that the arm 58 extends at an acute angle with respect to the axis of the machine is not significant and, in fact, this arrangement is provided solely to make possible certain clearances when the carriage 22 reaches an extreme left hand position. The adjustment of the pin it is solely for the purpose of adjus ing it transversely of the longitudinal axis of the machine, this adjustment alone being of interest.

The carriage 22 is provided with a nut 26 which embraces the carriage-driving screw 28, driven from the main shaft 39 of the machine through change speed gearing comprising the end elements 32 and TA and indicated in Figure 2. The work support t is provided with grooves as indicated at 36, along which there may be adjusted the table 38, which in turn carries tracks 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 iii. It will be evident irom the above that the work may be adjusted both in the direction of the trackway ill and transversely of that direction relative to the vertical axis 6 about which rotation may take place by reason of the travel of the cross-head i2 along the trackway iii. In addition, if desired, the vertical axis 6 may be adjusted transversely of the direction of the screw 28,

A carriage &2 supports the cutter and is arranged to slide in the direction of the axis of the screw 28 along the tracks it provided on the machine bed. A nut ll carried by the carriage 32 embraces a screw Qt, connected to a gear 38 (Figure 4) driven through change speed gearing from the main shaft A shaft 5%, whose gear 38 is driven through change speed gearing from the main shaft Bil, as indicated in Figure 4, has splined thereto a bevel pinion 52 meshing with a second bevel pinion 54 carried by a vertical milling cutters M, the support also carrying the driving motor 63 for this spindle.

As a result of the construction indicated, it will be evident that the cutter is movable both in the direction of its axis of rotation, which is parallel to the tracks 4|, and also vertically by reason of the mounting of its support on the track 6|.

In Figures 5 and 6 there are illustrated diagrammatically the fundamental elements of the machine of Figures 1 to 4. In these Figures 5 and 6, the axis of rotation of the work is indi- (rated at OT through which there extends the horizontal line AOA parallel to the axis of the screw 28 and to the tracks 23. Along thie line AOA' there moves the foot M of a horizontal perpendicular MN, the length of which, though subject to adjustment, is fixed during any particular operation of the machine, the point N corresponding to the pivot of the crosshead [2 ar-- ranged to slide along the line ON which may be considered fixed to the work support pivoted about OT. For the purpose of greater generality 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 out which axis, however, is not perpendicular to ON but to a line ON making screw 56 mounted in the carriage, the bevel pinwith ON the angle BC is perpendicular to ON and parallel to DE at a distance n representing the displacement of the axis of the'work from the axis OT of rotation.

FQ is the axis of the cutter, extending horizontally at a distance 2 from the common horizontal plane of AA, ON, DE and BC, and for generality assumed making an 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 represent the essentials of the machine with some further generality introduced by the angles 0 and o and the displacement p. While the physical form of the machine involves some vertical and horizontal displacements of the physical equivalents 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.

First there will be considered the theoretical surface which would be generated by a cutter of zero diameter, i. e., by the cutter axis FQ.

This involves seeking an equation for an arbitrary point P on FQ in terms of coordinates tied to the work. Let PR. be the perpendicular from the arbitrary point P to the plane AON, and RS the perpendicular to line DE from R. As origin consider point 0 the foot of the perpendicular from O to DE, the rotor axis, and let at be measured along the axis DE in the direction 0'3, 3 perpendicular to DE in a horizontal plane in the direction SR, and 2 vertically in the direction RP. For the purpose of the present analysis, these rectangular coordinates will be most convenient. For comparison with the aforementioned patents and application, related cylindrical coordinates .r, b and 7" may be noted, related to m, y, and a as follows:

by which relationships transformation from one set. of, coordinates to the other may be readi y efiected...

As; will. be. evident, from: the; machine. the 1 1 1 lvLmovesalongAA! towards-the right as-the; cute teraxis FQ moves: vertically in the; direction. at increasing a at: a, definitev ratio, of. speeds deter.-v mined by the: change gearing. From; and the geometry of Figures. 5 and: 6, the, equations of the surf ace; generatedv are:

l (tan a) These are parametric equations for the surface in terms, of the parameter or, the, angle MON, which. cannot be. eliminated from these general equations without giving rise, to a very compliecatedlsingle equation.

K1, in the above is. the. product of the length ot- MNv by the, ratio of they rate of movement of a to. that. of point M,

If, theoretically, M. reached 0, 2 would then havethe value K1Kz;, in other words, K2; is. related, to. the initial. relative. settings. of the cutter axis and point M.

It will be. noted from the, above equationsthat the angles 0 and 1 are: additive, i. e., the same effect. of adjustment of both could be secured by adjustment of one, or if they were of difierent. signs they would tend to neutralize each other. There is, therefore, no point in setting the cutter axis FQ off parallelism with, the. axis. AA, the. same effect being secura-ble by turning the blank on the table to change As a matter of fact, adjustment of is not generally desirable (ca-us.- ing the vanes generated. to depart, from radial. condition) and hence in the, following 0 and will both be considered, zero. Only under specialconditions may 0 and o. be introduced to advantage, for example, to correct. curvatures otherwise introduced.

If 0+=0, the equations reducev to:

tan a sin 02 The adjustment of p difi'erent from zerois also a disturbing factor unless it is properly related to the other constants. As will be evident from. the form of these equations, radial sections of, the surface (a:=.constant) are, not straight lines, curvature being introduced by the constant p. Slight values of, the constant p may be used, however, without detrimental deviation from straight line values of these, sections. Itv is also possible to use. quite large values of p provided the other constants are properly chosen, particularly to obtain for impellers quite large angles between the entrance. and exit portions of the fluid passages.

If :0 is zero, there are obtained the surfaces towhich, and to the generation of which, the present application is primarily directed. The equations then become:

. 1 Z: K2) From these the parameter may be. readily eliminated giving the single equation for the surface:

As will be obvious from the last equation, any. radial section, :cconstant, will bea straight line. The straight line, however, will not be radial unless n--K2x;0. Since a: varies from inlet to Outlet, it is possible to choose n and K2 so that atthe inlet n-Kxc ispositive whereas at the out: let. :1: being then greater, n-K2:r is negative with both otthese limiting deviation-s from zero small. In this fashion, advantageous results may be secured as pointed out, below.

Ifn.;0, and K2,=.0, the equation becomes:

or, changing to cylindrical coordinates,

=K1 tan b the equation of the surface disclosed and discussed inthe aforementioned patents and application. As willbe pointed out hereafter, the surfaces generated in accordance with the present invention may conform very closely either to a single surface given by zr=K tan b, or a plurality of. such surfaces fitted together, the advantage arising in the latter case being that a single generation serves to provide a complete surface which would otherwise require separate successive generating operations.

The application of the above to the generation of an impeller or turbine wheel will be next described with reference to Figure '7, in which generation will be assumed in accordance with Equation 3 or 4. In this figure, a indicates the axis of; the wheel being generated (:DE of Figure 5) and; as is the trace of the are plane, the angle b. being measured positive in a clockwise direction and y being measured horizontally to the right. The entrance portion of an impeller passage is illustrated at d and the exit portion of the same passage at e. The former will be regarded as located at x=x1, and the latter at :c=r2, various 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, Prelirn-inarily 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 y At f1 and f2 there are indicated the radial lines corresponding to the intersection of the planes ar=xi and 23:2 with the surface ac=K1 tan b, i. e., the surface which would be generated by making K2 and n zero in Equation 3 or 4.

Assume further that n and K2 are so chosen as above so that nK2a':1 is positive and n-K2x2 is negative. The element 91 of the general generated 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 the choice of constants and the value of an.

The element oz of the same surface lies to the right of f2, parallel to f2 and at a distance determined by the choice of constants and the value of $2.

Obviously for some intermediate value of a: for which 1ZK2.B=0, the element of the generated surface will be truly radial and coincident with the element f of a:=K1 tan b and the maximum deviations from radial condition will occur at 91 and g2. It will thus be seen that, for the indicated relation of n and K2, the generated surface will pass from one side of x=K1 tan b to the other in the direction of increasing b with the result that between $1 and an it will subtend a greater angle than the latter; in the diagram, for example, the latter subtends about 37, whereas the former subtends about 47.

' As pointed out in my said application Serial Number 441,686, this is very advantageous in reducing the loading on the blading. Surfaces built upon the theoretical surface thus generated have, however, a limitation in that the surface elements are not radial except at some intermediate position. Suppose, for example, arcs 7'1 and k1 define the inner and outer limits of vanes at the entrance plane x==x1 and it is desired to construct a vane on the generated surface. If 7L1 is a radial line drawn from the intersection. of 91 with arc in, it is obviously desirable that the vane material should completely encompass such radial line, and similar lines in all other radial sections. With 91 displaced only to the extent shown from a radial direction, it is obvious that this may be readily accomplished; however, if 91 were too far displaced off center, the vane to satisfy this requirement might have to be too thick at its base. As a matter of fact, the requirement is not absolutely necessary, and if a vane is of sufficient thickness, some undercutting of radial lines through it is permissible. Under such conditions, the element 91 at the entrance edge might well be carried further to the left to secure a still greater angular spread of each vane from inlet to outlet.

At the discharge a similar condition arises, in this case affecting the opposite face of a vane. A radial line 722 is illustrated indicating the desirable limit of approach to an element 2 of a vane adjacent that having elements 91 and oz. The radial outlet limits 7'2 and k2 impose the limitations, and, as illustrated, if the radial extent of the outlet is small compared to that of the inlet, a correspondingly greater deviation of the element g2 from radial condition is permissible.

As pointed out in my Patent 1,959,703, the inlet angle of a surface II=K tan b varies precisely with the radius as required for smooth pick up of fluid being handled. It will be apparent without going into mathematical proof that the surfaces here considered, by reason of close approach to m=K1 tan b will also be, for practical purposes, completely satisfactory in this regard, particularly so when given radial entrance edges of airfoil characteristics since such edges have fairly large tolerances for entrance angles consistent with maintenance of smooth flow. However, it is also to be noted that while the improved surface is displaced from the surface x Ki tan I) 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 x K tan b where K differs from K1. Thus it follows that real vanes of the improved type may be said to conform to a series of surfaces x: tan b (in most practical cases to not more than three thereof) which surfaces may be considered as smoothly merging in accordance with the considerations in my application Serial No. 441,686. present surfaces lie primarily in their ease of generation by single cutting operations to give a large angular spacing between inlet and outlet.

The generation of real vanes of the type discussed based on the improved surfaces, results from the movement, during the generating motions indicated, of cutters of improved types along the cutter axis while it is moving in the direction PR.

The advantages of the The axis of a real cutter will follow a path intermediate adjacent theoretical surfaces; In Figure 7, fcr example, the cutter axis in movin inwardly follows a path intersecting plane x=x1 along a line Z1, identical with g1 but spaced therefrom half the angular spacing of adjacent elements g1. Likewise at plane :c:r2, the cutter axis traces a line 12 midway between 92 and 92. The fluid passages therefore lie along the same surfaces given by Equation 3 or 4 with the origin plane :02 displaced by half the angular spacing of the vanes to as (Figure '7). Thus both the vanes and passages conform to surfaces given by the equation.

In order that both surfaces of each passage may be simultaneously generated, the cutter is iven a tapered shape which may be conical but which is most desirably substantially hyperboloidal as illustrated in Figure 8 at 64 and diagrammatically at c in Figure 7. Referring first to the latter, sections (approximately elliptical) of the cutter are shown in the two limiting planes in and 0:2, to illustrate the mode of generation. As the cutter axis movesin the direction of decreasing a, the cutter is uniformly moved in a retracting direction from the blank in the direction QF (Figs. 5 and 6). Thus a part of large diameter first cuts the outermost entrance portions of the passages, and as retraction takes place, it proceeds to cut more inward parts of the entrance portions of the passages and portions further towards the discharge. Successive positions of the cutter axis are illustrated at (11, Q2 and (13. The position (13 corresponds to the cutting of the trough of the passage.

The shape of the cutter is such that during such action the space cut, which is the envelop of the successive positions of the cutter, will be such as not to encroach (preferably) on the limiting radial lines in and hz. If the cutter has an approximately hyperboloidal shape as illustrated, the result is to generate vanes having the desirable taper for securing sufficient strength with production of fillets where the vanes join the central portion of the disc. It will be evident that the shape of the cutter is subject to substantial variation and the hyperboloidal form may be approximated by the rotation of circular arcs or even successive straight lines about the cutter axis. The actual shape depends in each instance upon the desired vane taper and whether or not undercutting of radial lines from the vane tips is permissible. The rate of retraction of the cutter is also dependent on these same factors and related to the cutter shape, as will be obvious.

In Figure 9 there are diagrammed the factors entering into the operation of the cutter c in generating more general surfaces for vanes in accordance with Equation 2 involving adjustment 2 as well as n and K2. Assuming that the 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 by R (U), where U is measured along the axis of the cutter from the origin V, the cutter surface will be given by the following equation in terms of coordinates x, y, z, referred to the same coordinate system used above in discussing the generated surfaces:

6. (x cos ay sin an sin ap) In the above K1, im, m, p and :a are thegsame as previously considered. K3 and are constants taking into account the movement of the origin point of the cutter surface along the cutter axis, i. e., the variation-of the coordinate uo'f the origin point V. This, as evi'den't from the description of "the machine, is proportional to the movement of the point M and also to the change of 2. K3 takes into account this speed ratio while K4 takes into account the starting position for the movement.

In accordance with the-usual theory of envelopes, the surface given .by Equation 6 willgenerate, for variations of parameter, asur'face given by eliminating the parameter .a from it and its partial derivative with respect 170cc. Taking the partial derivative of (6) with respect 120.0: there is obtained:

(x cos (1- sin an'sin a-K est a) .f sin a+y cos a+n cos Q+ K tan or wherein f is the first-derivative of the function f with respect to its argument.

The solution of Equationso and 7 to eliminate a is laborious, even though performed graphically, but the cross-section of a ,passagemay be thus accurately ascertained Joy-plotting the values of $1,411, and 21 for aseriesof chosen values .of a. Graphical methods of descriptive geometry are also usable involving laying out the cross-sections of the cutter-in the various planes of ,w constant and constructing-the enveloping-lines thereof. It is to be noted -.that.Equations-.6 and 7 .give .the generated surfaces only where they are .actually envelopes oi the putter surface given by j (U) i.-e.,th'e-troughs-oi the passages generated by the finalpositionvofthe-cutter are-surfaces'of-revolution of this cutterposition.

While the: generation-has been-described for the most general :case,.-it1:wil1;b.e obvious that it is equally applicable to thespecial cases of having BithGT'QI'bOth .of K2 nr n-zequalzero. .If-both-are zero, the :passages :and =vanes .both conform strictl torrn=-Krtan-'b. lnzall easeshyperboloidal, or substantially *hyperboloidalacutters have been found most advantageous .to :"SGCuIfi properly shaped vanes.

In J-som'ednstances, iparticularlyiwhere the :angle bet-weeniinlet andoutlet measuredabout the axis is large, it -will beifourrd :that arsinglev generation by a cutter having ai'propemshapeltoform the desired vane tap'erwvilltnot'suifice .to give -'the :desiredLtrOughas-a part of-the surface :of revolution of -the finalcutter position. Izlnasuc'h caserecourse is had to t-he :use 10f :several cutters USEdISllGCES- sively and of suchic'orrespon'ding shapes that the proper :vane =Shapes :result from their ."successive operations. In each instance, however, theacutteris retractedas 'describedifor a predetermined part ofathercutterwaction. The :vane:surfaces are then, except for :th-e -troughs, made up 'of a'tseries of smoothly merging envelopes.

In 5 Figures T and -11, there is 'shown 'a modified "form of machine adapted particularly for rapid production of rotors, there :being, however, less adjustabi'lity. 'machine comprises a base 66 on'which thereiis joumalle'd about a horizontal axis 10 a work support 68 on which the blank to be out is mounted as indicated in constructlon'lines in the two figures. :Secured to the support 68 and arranged to rock the same is an arm 12 provided with a guideway 14 in which there slides the cross-head l6 pivoted at 18 to a carriage Bil which is adapted to :be moved along a horizontal trackway 84 by a screw 82 driven through change speedgearing BBfro-m a shaft 88 connected by'bevel gearing 90 to the main shaft '92 of the machine.

The main shaft "92 of the machine drives through change speed gearing 94 a transverse horizontal screw 93 which engages-a nut carried by a carriage 98 whereby the carriage may be moved transversely along the tracks 93. This carriage in turn supports the spindle head I02 which is guided for longitudinal movement along the track I03 so as to provide movement of the cutter I86 mounted in the spindle :IM in the direction of its axis, the cutter being driven from a motor I08 carried by Hi2. To secure the axial movement of the cutter, bevel gearing Ilfl, having a splined connection Witha shaft Ill driven by change speed gearing I I3 from the main shaft 92, is provided to drive an upright shaft H2 mounted in the carriage '98 which in turn drives through a bevel gear H4 a second bevel gear I I6 fixed against axial .movement and internally threaded to engage a screw I [8 secured to the head 102. By reasonof .the change speed gearin and connections described, it will be evi dent that the cutter may beg'iven predetermined axial and transverse horizontal movements while the cross-head 16 is moved horizontally .in a direction parallel to thecutter axis by thescrew 82.

Comparison of.the.1astdes0ribed machine with that of Figure 1 will reveal that the .two machines are identical in operation, the last named machine being essentially .the former turned through 90. It will "be obvious, therefore, that the theoretical considerations involved in Figures 5, 6 and 9 fully applyto-the machine of Figures 10 and 11. It may be noted that, while in this last described machine, the length-of the-arm MN of Figure 5 is unchangeable, nevertheless,

K1 .is variable by changing thegea-r ratio, foreaample at 8-6, it being pointed out above that K1 is the product of the length of MN by the ratio of the rate of movement of z to that of point M.

The machines of the-type described may be utilized for "the generation of turbine rotors or impellers. Turbine rotors generated therebymay take the general forms described particularly in my Patent 2,283,176. Impellers for which the machines are particularly adapted may take-the general forms described in my'application-Serial No. 441,686,;so faras axiaLradialand circumferential relative dimensions are involved. The shapes of the vanes, however, are provided inaccordance with What has been described above, each passage being generated by a single traverse of the cutter, tho-ugh slight modifications in shape may be introduced by additional cuts for the purpose of securing thinning of-vanes or other minor variations of characteristics.

.Figures 12 and 13 illustrate at I20 a characteristic type of impellerproduciblebyathesemechanisms.

It may be noted that by the use of these machines, and particularly'that of Figure 1, which permits wide adjustment, a complete rotor of substantial axial length containinga number of impeller or'turbine wheelstages, may be 'cut with no more than axial adjustment of the blank along the support 4 in the direction of the grooves 36.

Such a combination rotor may be provided by assembling a group of forgings into a single unit, as indicated, for example, in my application Serial No. 443,957, filed May 21, 1942.

What I claim and desire to protect by Letters Patent is:

l. Mechanism for the generation of elastic fluid passages in rotors comprising a rotary cutter movable in a plane with its axis constantly parallel to itself, means mounting a rotor for movement about an axis parallel to said plane of movement of said cutter axis, means for rotating said mounting about the last mentioned axis, and means relating said movements so that the axis of said cutter generates with respect to the axis of the rotor a surface having the parametric equations:

wherein m, and z are measured along mutually p mounting about the last mentioned axis, and

means relating said movements so that the axis of said cutter generates with respect to the axis of the rotor a surface having the parametric equations:

L P n y tana sina wherein a, y and z are measured along mutually perpendicular axes, in being measured along the rotor axis and y in a direction perpendicular to the rotor axis and to the axis of rotation of said mounting.

3. Mechanism for the generation of elastic fluid passages in rotors comprising a rotary cutter movable in a plane with its axis constantly parallel to itself, means mounting a rotor for movement about an axis parallel to said plane of movement of said cutter axis, means for rotating said mounting about the last mentioned axis, and means relating said movements so that the axis of said cutter generates with respect to the axis of the rotor a surface having the parametric equations:

wherein at, y and z are measured along mutually perpendicular axes, a: being measured along the rotor axis and y in' a direction perpendicular to the rotor axis and to the axis of rotation of said mounting.

4. Mechanism for the generation of elastic fluid passages in rotors comprising a rotary cutter movable in a plane with its axis constantly parallel 12 to itself, means mounting a rotor for movement about an axis parallel to said plane of movement of said cutter axis, means for rotating said mounting about the last mentioned axis, and means relating said movements so that the axis of said cutter generates with respect to the axis of the rotor a surface having the parametric equations:

1 \tan a wherein x, y and z are measured along mutually perpendicular axes, a: being measured along the rotor axis and y in a direction perpendicular to the rotor axis and to the axis of rotation of said mounting.

5. Mechanism for the generation of elastic fluid passages in rotors cpmprising a rotary cutter movable in a plane with its axis constantly parallel to itself, means mounting a rotor for movement about an axis parallel to said plane of movement of said cutter axis, means for rotating said mounting about the last mentioned axis, and means relating said movements so that the axis of said cutter generates with respect to the axis of the rotor a surface having the parametric equations:

tall a Z: IQ

tan or wherein 33, y and a are measured along mutually perpendicular axes, a: being measured along the rotor axis and y in a direction perpendicular to the rotor axis and to the axis of rotation of said mounting.

6. Mechanism for the generation of elastic fluid passages in rotors, said passages being separated by vanes decreasing in thickness outwardly from the rotor axis, comprising a rotary cutter movable in a plane with its axis constantly parallel to itself, means mounting a rotor for movement about an axis substantially parallel to said plane of movement of said cutter axis, means for rotating said mounting about the last mentioned axis, means for movingsaid cutter in the direction of its axis, and means relating said movements, said cutter having a tapered shape and arranged to cut simultaneously the major portions of the opposed vane surfaces bounding a passage.

'7. Mechanism for the generation of elastic fluid passages in rotors, said passages being separated by vanes decreasing in thickness outwardly from the rotor axis, comprising a rotary cutter movable with its axis constantly parallel to itself, means mounting a rotor for'movement about an axis transverse to the direction of said cutter axis, means for rotating said mounting about the last mentioned axis, means for moving said cutter in the direction of its axis, and means relating said movements, said cutter having a tapered shape and arranged to cut simultaneously the major portions of the opposed vane surfaces bounding a passage.

8. Mechanism for the generation of elastic fluid passages in rotors, said passages being separated by vanes decreasing in thickness outwardly from the rotor axis, comprising a rotary cutter movable in a plane with its axis constantly parallel to itself, means mounting a rotor for movement about an axis substantially parallel to said plane of movement of said cutter axis, means for rotating said mounting about the last mentioned axis,

13 means for moving said cutter in the direction of its axis, and means relating said movements, said cutter having a tapered, approximately hyperboloidal, shape and arranged to cut simultaneously the major portions of the opposed vane surfaces bounding a passage.

9. Mechanism for the generation of elastic fluid passages in rotors, said passages being separated by vanes decreasing in thickness outwardly from the rotor axis, comprising a rotary cutter movable with its axis constantly parallel to itself, means mounting a rotor for movement about an axis transverse to the direction of said cutter axis,

means for rotating said mounting about the last mentioned axis, means for moving said cutter in the direction of its axis, and means relating said movements, said cutter having a tapered, approximately hyperboloidal, shape and arranged to out simultaneously the major portions of the opposed vane surfaces bounding a passage.

10. The method of generating elastic fluid passages in rotors comprising moving a rotary cutter with its axis substantially constantly parallel to itself, and simultaneously rotating a rotor about an axis transverse both to the rotor axis and the direction of said cutter axis.

11. The method of generating elastic fluid passages in rotors comprising moving a rotary cutter having a tapered shape in a plane with its axis substantially constantly parallel to itself, and simultaneously rotating a rotor about an axis transverse to the rotor axis and substantially parallel to said plane of movement of said cutter axis, said cutter being moved in the direction of its axis and arranged to cut simultaneously the major portions of opposed vane surfaces bounding a passage.

12. The method of generating elastic fluid passages in rotors comprising moving a rotary cutter having a tapered shape with its axis substantially constantly parallel to itself, and simultaneously rotating a rotor about an axis transverse both to 14 the rotor axis and the direction of said cutter axis.

13. The method of generating elastic fluid passages in rotors comprising moving a rotary cutter having a tapered, approximately hyperboloidal, shape in a plane with its axis substantially constantly parallel to itself, and simultaneously rotating a rotor about an axis transverse to the rotor axis and substantially parallel to said plane of movement of said cutter axis, said cutter being moved in the direction of its axis and arranged to cut simultaneously the major portions of opposed vane surfaces bounding a passage.

14. The method of generating elastic fluid passages in rotors comprising moving a rotary cutter having a tapered, approximately hyperboloidal, shape with its axis substantially constantly parallel to itself, and simultaneously rotating a rotor about an axis transverse both to the rotor axis and the direction of said cutter axis.

RUDOLPH BIRMANN.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,006,280 Riddell Oct. 17, 1911 2,276,404 Lundquist Mar. 17, 1942 2,285,266 Fullemann June 2, 1942 2,092,142 Schuz Sept. 7, 1937, 1,959,703 Birmann May 22, 1934 1,555,530 Trbojevich Sept. 29, 1925) 630,325 Cheney Aug. 8, 1899 FOREIGN PATENTS Number Country Date 402,768 Great Britain Dec. 1, 1933 17,691 Great Britain Aug. 3, 1911 I 837,890 France Feb. 22, 1939

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