# Патент USA US2407469

код для вставкиSept. 10, 1946. R. BIRMANN 2,407,469 ROTOR FOR ELASTIG FLUID MECHANISM Original Filed MarchvZS? 1943 f¿3%„L Mrk-ss. 8 sheets-sheet 1 Sept. 10, .11946. R, BIRMÀNN 2,407,469 ROTOR FOR ELASTIC FLUID MECHANISM . original Filed March 2è, 1945 _ 8 sheets-sheet s ¿W M u * ¿rra N575. i Sept. 10,1946. » l ‘2,407,469’ R.B|RMANN Orizgì‘nal Filed March 26, 1945 . , 8 Sheets Sheet 4 n a 'frm/2157s . Sept# 10, 1945. ' ' R.B1RMANN l y ROTOR FOR ELASTIC FLUID MEGHANISH ' 2,407,469 - original Filed March 2e. V1943 _ s sheets-sheet 5 Sept. 10, 1946. .Y ' 2,407,459 - R. BIRMANN RpToR FOR ELASTI’C FLUID MEQHANISM . original Filedvuarch 2e, 194s - a subis-sheet e N 00 n//r/vfsss.-` A ' - y I ' Rua/o 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 . ‘ « Y . invention; *Wx/Ö ___, Hg 50 ‘ . y , Figure >'11 is a plan vView of. the machine of Figure 10' , ~ _ o »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 ' 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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