US 2669383 A
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Description (OCR text may contain errors)
Feb. 16, 1954 J. 'r. PURVIS ET AL ROTOR BLADE Filed Feb, 6, 1951 m m mmm Mmm n P? A c J m P Patented Feb. 16, 1954 Joseph Thompson Purvi York County,
s, North York "Township, Ontario, and Lloyd Calvin Secord, Toronto, Ontario, Canada,
assignors to A. V.
Roe Canada Limited, Malton, Ontario, 'Canada,
a corporation Application Eebruary 6, 1951, Serial No. 209,597
4 Claims. 1
This invention relates to the mounting of "blades in rotary power conversion machines and particularly to the mounting of blades in thehigh speed rotors of aero-engine compressors.
The principal forces to which a rotor blade is subjected are the reaction loading of the-working fluid and the centrifugal load due to rotation. In an axial flow compressor, such as is commonly used in aircraft gas turbine engines, the reaction loading or air load produces a bending moment at the blade root fillet, and any deflection of the blade due to this bending moment will provide an opposing moment due to the centrifugal forces. Thus to some extent the centrifugal load .can be said to balance the .air load and, if the blade is initially given some dihedral (displacement from a true radial situation),, it should be possible in theory .to arrange for the root. fillet to be substan. tially .free of bending stresses at some specific speed of rotation. In aero-engine practice, however, the air load, at a givenspeed of rotation, decreases with the altitude at which an engine operating so that it is impossible to construct a blade with a fixed dihedral which will result in a balance between the air load and centrifugal load in all conditionsoi operation. In some prior art constructions the blades are attached to the rotors by pin-joints or other types of pivots but, due to the very high rotational speeds to which such .rotors are subjected, the friction in the joints or pivots becomes so great under centriiugal loads that th mountings become efiectively rigid and cannot be relied upon to relieve the bendingstresses in the blades.
Themain object of this invention is to provide a means for mounting the blades ,in the rotors of rotary power conversion machines which will ,perm'it some automatic adjustment of the attitude or dihedral of the blades whereby the bending stresses in the blade root fillets maybe held within safe limits.
.Other objects and advantages will Ice-apparent during the course .of the following description,
In the accompanying drawings forming a part o1 this specification and in which like reference characters designate like parts throughout the same:
Figure 1 is a broken-away side elevation of a gas turbine engine showing a blade to which the invention is applied;
Figure 2 is aperspective of a section of a rotor .disc showing the mounting of two blades according tothe invention; and
Figure 3 is a diagrammatic representation of the forces acting upon a blade.
It will be noted from Figure 1 that the first few stages of an axial compressor l0 embody blading of relatively 'high aspect ratio and although the invention is described'herein as applied to the :firstrow of blades I! mounted on a rotor disc 12, it :may be applied advantageously to rotor blading in th second and third and even subsequent stages.
Figur 2 shows 'twoblades ll mounted in spaced relationship on the rotor disc 12. The effective portion of each blade consists of an element 13 of aerofoil section which, in accordance with normal practice, protrudes from a platform 44. The platform however is spaced from the blade root l5 by a web it extending longitudinally across the platform to conform substantially with the chord of the element I3 at its root fillet Ill that is at its juncture with the platform. The web It is of thin rectangular section and consequently it has no converging opposing surfaces to term sharp edges Where stress concentrations mayhe- :cur. It will be understood that the section of the Webmay be of any obtuse form, free :firom sudden discontinuities and sharp edges, and the :rectangular form of the preferred construction described herein is not to be taken as restrictive.
The structural properties of the web It are an important feature of the invention. The aeroioil element 13 is subjected to certain maximum and minimum air loads, which are known from the characteristics of the compressor, :and these air loads produce bending moments at the root fillet 3=-. The said element is also subjected to a maximum centrifugal load, which is also known from the characteristics of the compressor, and which produces a bending moment at the root fillet of a magnitudedependent upon thedihedral angle of the element, that is the angle by which the longitudinal axis of the element departs from a radial direction. The moment of the resisting couple exerted :by the iaerofoil element [-3 at its root fillet 13 :must equal the difference between the aforesaid bending moments du to air and centrifugal loading.
The dihedral angle of the aerofoil element, which may be considered stiff, is determined by the fiexibilityof the web, superimposed upon any angular offset to the radial-direction at which the longitudinal axis of the web may be initially set. The relationship between the moment of inertia of cross-section and the length of the web must therefore be such that when the web is deflected under the influence of the air and centrifugal loads acting :upon the aerofoil element and the reaction to the resisting couple exerted by the said element at its root fillet, the resulting di hedral angle of the aerofoi-l element is such as to produce, at the root fillet, a bending moment due to centrifugal load not less in absolute value than the difference between the bending moment due to the air load and the maximum bending moment permissible in the aerofoil element. It will be understood that, due to the initial offset aforementioned, the maXimum permissible bending moment has two values, one positive, that is in the same sense as the bending moment due to the air load, and one negative, that is in the same sense as the bending moment due to the centrifugal load; and that at the minimum air load the resultant bending moment in the aerofoil element is negative and attributable in the main to the centrifugal load.
The relationship between the moment of inertia and the length of the web may be defined more specifically in terms of the known features of the compressor. Referring to Fig. 3, it will be evident that the aerofoil element 43 is subject to an air load Fg acting at its centre of pressure P and to a centrifugal load Fe acting at its centre of gravity G, the radial distance between P and G being a. The centre of pressure P is at a distance b from the root fillet and the aerofoil element has a dihedral angle 9 due to the deflection of the Web It superimposed upon the angular offset 0. whereby the longitudinal axis of the web inherently departs from the radial direction. If
M is the moment of the resisting couple exerted by the aerofoil element at its root fillet, for equilibrium M=Fg.b-Fc. (b-a). tan 6 and W=Fg-Fc. tan 0 where W is the supporting force exerted by the web on the aerofoil element.
By resolving the aforementioned equations, or A The forces acting upon the web, which may be 4 regarded as an encastered beam supported in the rotor I! by the root I5, are also shown in Fig. 3 and comprise a load W (the reaction to the force W) and a couple (the reaction to the resisting couple exerted by the aerofoil element) having a moment M, equal and opposite to the moment M. Incidentally, the tensile forces in the web, including W. sin 0 and the forces due to the centrifugal effects upon the mass of the web itself, are not of immediate interest in these considerations.
The characteristics of the web must therefore be such that its slope or deviation from the radial direction at its juncture with the platform l4, under the inflence of a load tan If the web is of radial length Z, of uniform crosssection and mounted in the rotor at an initial angular offset a.
where E is Youngs modulus, or the modulus of elasticity. If 0 is small,
The maximum permissible values of M and the values of a and b are known from the characteristics of the aerofoil element. (Those skilled in the art will appreciate that the maximum permissible absolute value, M1, of M when Fg is large will usually be less than the minimum permissible absolute value, M2, of M when Fg is small.) The maximum and minimum values Pm and F92, of the air load Fg are known from the aerodynamic characteristics of the compressor and the corresponding value F01 of the centrifugal load F0 is also known from the mass of the aerofoil element and the design speed of rotation. Therefore if these limit values of air and centrifugal load are to occur simultaneously with the attainment of the limiting permissible bendin mo,- ments in the root fillet, the relationship of the moment of inertia I and the length I of the we is expressed by the equation (It will be remembered that M2 is a negative quantity.) This relationship means, in nonmathematical terms, that the relationship between the length and thickness of a web such as shown in the drawings will be such as to distribute the load uniformly throughout the length of the web and substantially eliminate stres concentration at the root fillet.
The value of the initial offset angle a can then be determined from the penultimate equation by considering, for example, the case when M is M1, Fg is For and Fe is F01. Thus the physical characteristics of the web I6 may be determined to ensure that at the extreme conditions of air and centrifugal loading the maximum bending moments permissible in the blade will not be exceeded.
The blade is attached to the rotor I! by th root 15 which is serrated and slid longitudinally into a similarly serrated slot in the periphery i! of the rotor disc. It will be understood that the form of this root is unimportant to the invention; any of the well-known forms, such as the fir tree or dovetail interlock, may be used.
It will be noted from the drawings that in this preferred construction the platforms (4 extend laterally on both sides of the blades and plugs 18, of rubber or some similarly resilient material, are provided between the webs l6 of adjacent blades to support plates [9 situated between adjacent platforms to form a flush surface exposed to the air stream flowing through the compressor. The arrangement of plates illustrated ensures a substantially smooth peripheral surface to the rotor assembly from which the aerofoil elements of the blades protrude, without material interference with the operation of the flexible webs It.
In operation the rotor rotates at high speed and -large centrifugal forces are imposed upon :the blades, so that .each blade tends to assume a radial attitude. However the .air load .on the blades produces deflection from the truly radial attitude, the extent of deflection being dependent upon the balance between the moment due to the air load, on the one hand, and the moment due to the centrifuged load and the resisting couple in the blade structure, on the other.
With variation of altitude of operation the air load on the blades will vary, though the speed of rotation, and therefore the centrifugal loading on the blade, may remain constant. At low altitudes where the air loading is relatively high the web allows the aerofoil element to assume a dihedral angle at which the centrifugal load will produce a bending moment tending to counteract the bending due to the air load. As the air load decreases with increasing altitude the aerofoil element will assume a more nearly radial position until the centrifugal load predominates and the resisting couple exerted by the aerofoil element is reversed. The principal strain in the blade occurs in the web which, having no aerodynamic function, can be designed to accommodate the strain without critical stress concentration, and since the physical characteristics of the web have been determined by the method hereinbefore described, taking into consideration the aerodynamic and physical properties of the aerofoil element inherent from the design of the compressor, the maximum bending moment permissible, in either sense, in the root fillet of the aerofoil section cannot be exceeded. The web in fact provides a flexible extension of the aerofoil element by means of which the aerofoil element can assume an attitude demanded by prevailing conditions; it is an extension which exercises substantial restraint on the element which it supports, but a restraint which, unlike the friction in a pin-joint, is independent of the tension due to the centrifugal influences.
The form of the invention herewith shown and described is to be regarded as a preferred example of the same and various changes to the shape, size and arrangement of the parts may be resorted to without departing from the spirit of the invention or the scope of the claims.
What we claim as our invention is:
1. In combination, a rotor and a plurality of blades each having an integral structure comprising an element of aerofoil section extending outwardlv from the periphery of the rotor with its longitudinal axis inclined in the plane of rotation at off-set angles to radii of the rotor, a resiliently defiectable web extending inwardly from the inner end of the said element, and a root rigidly fixed in the rotor inwardly of the web, the moment of inertia and the length of the web being related by the expression wherein:
I is the moment of inertia of the web;
I is the length of the web;
E is the modulus of elasticity of the web; and the parameters a, b, Fm, Figz, F01, M1 and M2 are known from the fluid-dynamic characteristics of the machine and the structural design of the aerofoil element, and more specifically a is the distance between the centre of gravity of the element and the centre .of fluiddynamic pressure thereon;
b is the distance between the said centre of fluid-dynamic pressure and the juncture of the aerofoil element and the web;
Far and F92 are respectively the maximum and minimum fluid loads on the aerofoil element;
F01 is the maximum centrifugal load on "the aerofoil element; and
M1 and M2 .are :bending moments respectively not greater than the maximum positive and the maximum negative bendi-ng moments permissible in the aerofoil element.
.2. The combination of claim 1, in which the web is of obtuse section free from sharp edges.
3. In combination, a rotor and a plurality of blades each having an integral structure comprising an element of aerofoil section extending outwardly from the periphery of the rotor with its longitudinal axis inclined in the plane of rotation at oiT-set angles to radii of the rotor, a resiliently deflectable web extending inwardly from the inner end of the said element, and a root rigidly fixed in the rotor inwardly of the web, the moment of inertia and the length 01' the web being related by the expression I is the moment of inertia of the web;
Z is the length of the web;
E is the modulus of elasticity of the web; and
the parameters a, 12, Pm, F01, M1 and a are known from the fluid-dynamic characteristics of the machine and the structural design of the aerofoil element, and more specifically:
a, is the distance between the centre of gravity of the element and the centre of fluiddynamic pressure thereon;
b is the distance between the said centre of fluid-dynamic pressure and the juncture of the aerofoil element and the web;
F91 and F01 are respectively the maximum fluid load and the maximum centrifugal load on the aerofoil element;
M1 is a bending moment not greater than the maximum positive bending moment permissible in the aerofoil element; and
a is the aforesaid offset angle of the blade.
4. The combination with a rotor of a plural ity of blades each having an integral structure comprising an element of aerofoil section, a root fillet at the inner end of the element and located at the periphery of rotor, a resiliently deflectable web extending inwardly from the root fillet, and a root rigidly in the rotor inwardly of the web, the aerofoil element being disposed 1 with its longitudinal axis inclined in the plane of rotation of the rotor at av predetermined (iihedral angle to the radius of the rotor at the root fillet, each of the webs being of regular obtuse section tc reduce critical concentration of stress, the aerofoil elements being subject in operation to and centrifugal loads causing deflection of the webs, the relationship between the length and thickness of each of the webs being such as to distribute the load uniformly throughout the length of the web and substantiaiiy eliminate stress concentration at the root fillet, such deflection of the Webs producing a change in the angle of inclination of the longi tudinal axes of the aeroioil elements and thereby producing a change in the magnitude of the bending moments produced by the centrifugal loads on the aerofoil elements such as to ensure that at extreme conditions of air and centrifugal loading predetermined maximum bending m0- ments in the blades will not be exceeded.
JOSEPH THOMPSON PURVIS. LLOYD CALVIN SECORD.
References Cited in the file of this patent UNITED STATES PATENTS Number Name Date Grun May 21, 1912 Number Name Date Davis Dec. 30, 1930 Allen Dec. 9, 1941 dAubarede Feb. 13, 1945 Benson Feb. 1'7, 1948 FOREIGN PATENTS Country Date Great Britain 1948 Great Britain 1948 France 1948