CN100347410C - Uniform strength blade moulding of radical flow type turbine radial element impeller and its method - Google Patents

Abstract

The present invention relates to an equal-strength vane modeling of a radial element impeller of a radical flow type turbine, and a method thereof. The modeling structure is characterized in that the modeling structure comprises a pneumatic modeling of an inclined meridian air outlet side radial element impeller and a modeling structure of an equal-strength radial element vane. The method comprises the following steps: (1) a middle cambered surface pneumatic modeling method of the inclined meridian air outlet side radial element impeller vane and (2) an equal-strength modeling method of the radial element impeller vane.

Description

Radial turbine is element impeller equal strength blade shape construction and method thereof radially

Technical field

The present invention relates to radial turbine impeller manufacturing technology field, particularly a kind of radial turbine is element impeller equal strength blade shape construction and method thereof radially.

Technical background

Radial turbine is widely used in the device of middle low power gas turbine and turbosupercharger and refrigeration and natural gas liquefaction.

The working speed of radial turbine that is applied to gas turbine and pressurized machine is very high usually, can reach that per minute 60,000 changes even higher.The turbine inlet fuel gas temperature is very high again, so just requires impeller blade will have enough intensity to bear very high centrifugal stress and thermal stress.In addition, for guaranteeing aeroperformance and reduce rotary inertia, vane thickness will be under the proof strength prerequisite, and is thin as much as possible.This has just proposed the notion of equal strength design, to reduce unnecessary material as far as possible.Thereby make the vane thickness of designing from the blade tip to the blade root, have one rationally to distribute, reach the purpose that requires to alleviate under the precondition impeller weight and rotary inertia in proof strength.

For reducing blade stress as far as possible, radial turbine, the impeller that particularly is applied to the higher specific speed design adopts radially element moulding usually.Being blade must pass through axis perpendicular to the profile center line of the arbitrary section of rotatingshaft, to guarantee that blade does not produce additional bending moment in high speed rotating.

At present, radial turbine (also comprising centrifugal compressor) impeller radially element blade shape construction be divided into for two steps.Cambered surface in the first step structure blade, it is made up of one group of radial alignment section.The aeroperformance of blade mainly is that the cambered surface moulding realizes in the blade by adjusting.Second step was to determine that the blade circumferential thickness distributes.

The cambered surface pneumatic modelling is to use circular arc in early days in the routine, develops into oval moulding afterwards.They all are with circular arc or the elliptical configuration intersection of element and this cylndrical surface radially with wheel rotation axle Z on the cylndrical surface of a certain radius that is axis.Intersection the θ in space coordinate promptly be by the blade of this point in the cambered surface circumferential angle of element radially.Use that there are two shortcomings in the cambered surface moulding in circular arc or the elliptical configuration blade: 1, the artificer be difficult to longshore current to blade loads adjust.2, can't guarantee that radially obtaining rational efflux angles at the impeller trailing edge distributes, be difficult to make that the leaving whirl velocity square radially all is zero.

Finishing in the blade behind the cambered surface pneumatic modelling, generally is to be provided along the blade circumferential thickness at impeller housing and wheel hub meridian molded lines blade root and blade tip place by the artificer to distribute.Then, cambered surface is set out and is added and subtracted the angular difference that vane thickness constitutes in the blade, just can at first determine the circumferential angular coordinates of the blade pressure surface and the suction surface at blade root and blade tip place.Use straight line that the coordinate points of blade root with blade tip place correspondence linked to each other, finish the configuration of blade pressure surface and suction surface.Next step is with finite element program the blade stress analysis to be checked.After finding that blade stress surpasses the situation of material allowable stress, need adjust vane thickness.This adjustment based on artificer's experience, often tries to gather to revise also to be difficult to make the thickness distribution of blade to satisfy requirement of strength through too much taking turns fully.

Summary of the invention

The object of the present invention is to provide a kind of radial turbine radially element impeller equal strength blade shape construction and method thereof.

The problem that exists at the design method of present use.The present invention proposes radially element impeller pneumatic modelling and equal strength two kinds of new design method of element blade shape construction radially of oblique meridian trailing edge.

A kind of radial turbine is element impeller equal strength blade shape construction structure radially,

(1) cambered surface has oblique meridian trailing edge in the impeller blade that is made of some radially elements; On the straight meridian trailing edge of the cambered surface basis, trailing edge and hub intersection point are constant in conventional impeller blade, and and the intersection point of wheel hub to extend to flowing out direction along the meridian molded lines of wheel hub, constitute oblique meridian trailing edge by two intersection points;

(2) gradient of this oblique meridian trailing edge and in each circumferential angle of straight edge line element of cambered surface can adjust as required to satisfy radial turbine impeller outlet blade profile angle along the high distribution requirement of leaf, guarantee minimum and guarantee that rational blade loading distributes in design point state turbine leaving loss;

(3) and the distributing to the blade circumferential thickness of root of each straight edge line element correspondence of middle cambered surface by point, to guarantee that vane thickness has one rationally to distribute from the blade tip to the blade root, reach in proof strength and require under the precondition, the purpose equal strength blade shape feature that alleviates impeller weight and rotary inertia is that blade is upright fir-tree type intersecting the section that obtains with the running shaft vertical plane, be that the blade circumferential thickness is increased to blade root gradually by blade tip, but this increase is not linear, begin to increase very slow, fast more near the increase of blade root blade circumferential thickness more.

Technological scheme

One, the oblique meridian trailing edge pneumatic modelling of element impeller radially

Pneumatic modelling will be designed cambered surface in the blade that is made of element radially according to the consideration of aerodynamic optimization.Usually moulding can divide two districts to carry out.

The I district is the impeller inlet district, adopts the radially plain circumferentially angle of each straight edge line of element definition.

θ(z)≡0，z＝z _O～z _A (1)

(this paper adopts the three-dimensional circulary cylindrical coordinates of z-θ-r, and z is an impeller rotating shaft, and r is a radius, and θ is circumferential angle) II district is impeller one an inducer transition zone, defines by carrying out integration at the plain circumferentially angle θ of each straight edge line of this subregion along the blade profile angle β distribution at impeller casing place,

$\mathrm{\θ}\left(z\right)=\mathrm{\θ}\left(z_A\right)+{\∫}_{z_A}^{z_B}\frac{\mathrm{tg}\left(\mathrm{\β}\right)}{r}\mathrm{ds}---\left(2\right)$

Wherein s is the meridian arc length; Blade profile angle β can be approximately in the formula:

tgβ＝W _θ/W _m (3)

W _θAnd W _mBe respectively blade conduit flow field circumferentially and the circumferential average mark speed of meridian direction.W _mCan calculate by one dimension; W _θThe circumferential speed square V relevant that can predesignate according to the artificer with adding the merit amount _θR calculates along the distribution of meridian direction.

Certainly, the artificer also can rule of thumb provide from the distribution of impeller inlet to outlet blade profile angle β along meridian direction.

For element impeller radially, blade profile angle β is O in the inducer value, and export value is β _ExitThis value is to be determined by the one dimension design load.

The distribution of β value in the middle of these 2, the artificer can adjust according to the criterion of aerodynamic optimization.After obtaining blade profile angle β distribution, can use formula (1) blade profile angle β integration to be obtained the II district and radially distribute at the circumferential angle of element along turbine case noon molded lines.

Then, can radially calculate along the blade profile angle of wheel hub and distribute in the circumferential angle of element according to I district and II district.Generally, the blade profile angle β of II district outlet port wheel hub can less than calculate according to 1 dimension give estimate the blade root efflux angles.If adopt conventional impeller trailing edge (promptly exporting limit meridian projection) perpendicular to impeller rotating shaft, then can cause impeller root efflux angles to reduce, the air-flow deficiency of turning back strengthens leaving loss.For this reason, different with the vertical meridian trailing edge of conventional impeller, increased the III district that adopts oblique meridian trailing edge structure.Make blade to continue to turn back, meet the value that the one dimension design obtains, reach the purpose that reduces leaving loss to guarantee the root efflux angles along root.Certainly, the artificer will be defined in the blade profile angle distribution of III district along wheel hub, along wheel hub meridian molded lines blade profile angle β integration is obtained the III district and radially distributes at the circumferential angle of element.

Tiltedly the trailing edge gradient is crossed conference and is strengthened the outlet area Radial Flow.Therefore, guaranteeing to reduce the gradient of trailing edge meridian projection under the prerequisite that distributes along the fairing of root blade profile angle as far as possible.Can check the different leaf eminence of trailing edge circumferential speed square V by three-dimensional computations _θR distributes.If circumferential speed square V _θSome point and null value differ bigger to r from root to point at the middle part, the projection of trailing edge meridian can be adjusted to curve, to satisfy the blade profile angle along the high distribution requirement of leaf.

Two, radially element vane thickness calculating of equal strength

Finish impeller blade radially in the element after the cambered surface shape-designing, according to the principle of equal strength calculate with the distributing to the blade circumferential thickness of root of each straight edge line element correspondence of middle cambered surface by point after, just can obtain the profile parameter of blade pressure surface and suction surface.

Generally, blade can be selected single ladder type cross section for use waiting on the Z sanction face, or the double trapezoid cross section.Like this, in case blade tip thickness is selected, after the ladder type cone angle was selected, Z cross sections such as blade just had been determined fully.After carrying out strength accounting, obtain blade from import to outlet (flows direction), the stress distribution of (open up to) from the blade tip to the blade root.If stress occurs, must strengthen the vane thickness (simultaneously, related increasing) that stress exceeds standard and locates from this vane thickness up to the blade root each point above after the situation of allowable stress level.Making amendment like this tends to bring chain reaction, acquires a certain degree of difficulty in the operation.Simultaneously, be difficult to also guarantee that blade stress is flowing to and opening up the roughly the same level that is on both direction, reduce blade consumption material to greatest extent, alleviate the weight and the rotary inertia of impeller to reach.

For element blade radially, can do following hypothesis:

1, only bears simple tensile stress, do not have flexural stress (because the centrifugal action line passes through running shaft).

2, this stretching direct stress is because the centrifugal force that the blade high speed rotating causes forms, the direct stress that acts on the high cross section of the plain arbitrary leaf of blade straight edge line can be obtained divided by this section area with the centrifugal force that top (up to blade tip) blade high speed rotating produces by this cross section.

σ＝F/(Δz×b) (4)

Wherein F is the centrifugal force that blade calculated stress cross section produces under high speed rotating with top.

Can obtain the Stress calculation formula through arrangement:

δ＝Sρgω ²R/b (5)

R is the radius that blade calculates the above partial blade barycenter in cross section, and g is a gravity accleration.

To be a part of blade cut area waiting to S on the Z cross section, and ρ is a blade material density.

According to above derivation, small vertically variable Δ z does not occur in the Stress calculation formula, and each of formation impeller radially can carry out respectively separately independently of each other by the Stress calculation and the Thickness Design of element blade profile.

Can define radially element blade circumferential thickness, b is the function of radius r.

Then, the centrifugal force that acts on a certain radius cross section can be by from blade tip r _TipThe integration of beginning obtains.Like this,, use the method for monobasic, can calculate the stress on any radius of a certain radially element of the blade cross section according to of the distribution of each blade circumferential thickness that radially element is known along radius.

$\mathrm{\δ}\left(r\right)=\frac{{\mathrm{\ω}}^2\mathrm{\ρg}}{b\left(r\right)}\underset{r_{\mathrm{Tip}}}{\overset{r}{\∫}}\mathrm{rb}\left(r\right)\mathrm{dr}---\left(6\right)$

We also can carry out the indirect problem design of vane thickness according to this direct problem formula.That is the thickness b (r of radially element blade tip given in advance, _Tip) and wish that the allowable stress obtain obtains the distribution of blade circumferential thickness along radius along the distribution σ (r) of radius.

In that program when calculating need (hub) be divided into enough thin some five equilibriums to blade tip (Tip) along radial direction from blade root with element blade radially.

Corresponding recursion formula is on the k cross section arbitrarily:

$F_k=F_{k-1}+{\mathrm{\ω}}^2\mathrm{\ρg}\×\frac{1}{2}(r_{k-1}+r_k)\×\frac{1}{2}(b_{k-1}+b_k)\×(r_{k-1}-r_k)---\left(7\right)$

${\mathrm{\σ}}_k=(F_{k-1}+\frac{1}{4}{\mathrm{\ω}}^2\mathrm{\ρg}(b_{k-1}+b_k)\×({r^2}_{k-1}-{r^2}_k)/b_k---\left(8\right)$

$b_k=(F_{k-1}+\frac{1}{4}{\mathrm{\ω}}^2\mathrm{\ρg}({r^2}_{k-1}-{r^2}_k)\×b_{k-1}/({\mathrm{\σ}}_k-\frac{1}{4}{\mathrm{\ω}}^2\mathrm{\ρg}({r^2}_{k-1}-{r^2}_k)\×b_{k-1})---\left(9\right)$

Use above formula draw program to calculate thickness distribution b (r) from the point to the root by given blade tip thickness and the phase of giving stress distribution from the blade tip to the blade root.

Generally speaking, wish to obtain the equal strength blade, then giving phase stress σ should be that certain value does not change with radius r.But at blade tip, for guaranteeing technologic requirement, b _TipGenerally can not be less than 0.8mm, the stress that calculates can be greater than giving phase stress.Usually need one section ladder type cross section in the blade tip zone, the cone angle in ladder type cross section is provided by the artificer, use the direct problem calculated stress in this zone, in case the stress that calculates greater than giving phase stress, then begins vane thickness from this cross section no longer is ladder type cross-sectional distribution and need to use above-mentioned inverse problem calculation step calculate definite.

Description of drawings

Fig. 1 is the projection drawing of radially element on R-Z and X-Y coordinate surface that constitutes cambered surface in the blade.

Fig. 2 is the meridian projection drawing of vertical meridian trailing edge and oblique meridian trailing edge impeller.

Fig. 3 is three zoning plans that contain oblique meridian trailing edge impeller.

Fig. 4 is the blade profile angle β distribution map in three subregions.

Fig. 5 root section has the equal strength design blade and the conventional trapezoid blade section comparison diagram of identical stress.

Fig. 6 is the radially pneumatic modelling flow chart of element impeller of oblique meridian trailing edge.

Fig. 7 be equal strength radially element blade strength-thickness just-the inverse problem calculation flow chart.

Fig. 8 is a 100KW micro fuel engine radial turbine impeller meridian molded lines.

Fig. 9 is along wheel hub and hub blade profile angle β distribution map.

Figure 10 is the blade profile angle distribution map along wheel hub.

The isopleth distribution map of cambered surface blade profile angle β coordinate on meridian plane in Figure 11 impeller.

Figure 12 calculates the isopleth distribution map of vane thickness on meridian plane.

Figure 13 is that three-dimensional finite element intensity is calculated the impeller stress distribution map that the program ANSYS accounting obtains.

Figure 14 is the radially blade stress distribution map that obtains of element vane thickness one dimension inverse problem calculation of equal strength.

Embodiment

One, the oblique meridian trailing edge pneumatic modelling method of element impeller radially, its step is as follows: as shown in Figure 6

Step S6-1, calculate to determine that according to one dimension impeller outlet blade tip (Fig. 3, Fig. 4 B point) and blade root locate the blade profile angle β of (Fig. 3, Fig. 4 D point) _BAnd β _D

Step S6-2, use BEZIER curve construction impeller along casing with along the meridian molded lines of wheel hub, trailing edge B point is fixing, and D point can be along the meridian molded lines slip of wheel hub with adjustment trailing edge gradient;

Step S6-3, I district are the impeller inlet district, and respectively radially the plain circumferentially angle perseverance of straight edge line is zero;

θ(z)≡0，z＝z _O～z _A

Step S6-4, II district are impeller one---the inducer transition zone, and radially the plain circumferentially angle of the straight edge line integration of order from the A point to B along the meridian molded lines of casing by blade profile angle β is definite for each;

$\mathrm{\θ}\left(z\right)=\mathrm{\θ}\left(z_A\right)+{\∫}_{z_A}^{z_B}\frac{\mathrm{tg}\left(\mathrm{\β}\right)}{r}\mathrm{ds}$

Blade profile angle β is that the artificer is selected according to the aerodynamic loading optimization principles along the distribution (Fig. 4 A is to the B point, and wherein the B point value is that step 1 is given in advance) of the meridian molded lines of casing;

Step S6-5, radially calculate distribute along the blade profile angle of wheel hub (Fig. 4 O is to the C point) in the circumferential angle of element according to I district and II district

$\mathrm{\β}\left(z\right)=r\frac{\mathrm{d\θ}}{\mathrm{ds}}$

Step S6-6, given III district C are to D point blade profile angle distribution (Fig. 4 C is to the D point, and wherein the D point value is that step 1 is given in advance).For guaranteeing that O-A-C-D blade profile angle distribute light is along adjusting the meridian molded lines axial position of D point along wheel hub;

Step S6-7, III district are the impeller outlet district, and radially the plain circumferentially angle of the straight edge line integration of order from the C point to D along the meridian molded lines of wheel hub by blade profile angle β is definite for each;

$\mathrm{\θ}\left(z\right)=\mathrm{\θ}\left(z_C\right)+{\∫}_{z_C}^{z_D}\frac{\mathrm{tg}\left(\mathrm{\β}\right)}{r}\mathrm{ds}$

Like this, each of cambered surface radially determined at the plain circumferentially angle of straight edge line fully in the formation blade shown in Figure 1, finished the generation work of cambered surface in the blade.

Two, the radially positive inverse problem calculation of element blade strength/thickness, moulding of radial turbine equal strength, its step is as follows: as shown in Figure 7

Step S7-1, given wheel speed, density of material and allowable stress value;

Step S7-2, to step S7-1, in each radially plain given its blade tip thickness of straight edge line and trapezoid cross section cone angle of cambered surface in the blade shown in Figure 1 determined, and this straight edge line element divided subdivisions such as enough thin from the blade tip to the blade root;

Step S7-3, direct problem is analyzed: begin to blade root direction unit computing unit bottom section upper stress value one by one from blade tip according to formula (6), stress value that calculates and allowable stress value compare, in case the stress value that calculates changes inverse problem calculation over to greater than the allowable stress value;

Step S7-4, inverse problem calculation: calculate the blade circumferential thickness in each unit bottom cross section according to inverse problem calculation formula (7)-(9) recursion successively, until the root of blade;

Step S7-5 gets back to step S7-2, finishes each step of S7-2-S7-4, in blade shown in Figure 1 cambered surface each radially the blade circumferential thickness of straight edge line element is all definite fully.

Fig. 1 is the projection drawing of radially element on R-Z and X-Y coordinate surface that constitutes cambered surface in the blade.The radial turbine impeller use often some radially element (its line stretcher necessarily passes through spin axis) constitute cambered surface in the blade, and " stick " vane thickness as skeleton and finish blade shape construction.This figure show a typical radial turbine impeller blade radially element in spatial distributions.

Fig. 2 is the meridian projection drawing of vertical meridian trailing edge and oblique meridian trailing edge impeller.Radial turbine impeller trailing edge can adopt perpendicular to axis and is not orthogonal to two kinds of forms of axis (tiltedly) in the projection of meridian plane.

Fig. 3 is three zoning plans that contain oblique meridian trailing edge impeller.For ease of narrating the radially pneumatic modelling of element impeller, impeller is divided into 3 districts.The I district is the impeller inlet district, and the plain circumferentially angle perseverance of the radially straight edge line in the I district is zero.The II district is impeller one an inducer transition zone, determines by carrying out integration along the blade profile angle β distribution at impeller casing place at the plain circumferentially angle θ of each straight edge line of this subregion.III contains in the district oblique meridian trailing edge, will stipulate in the III district to distribute along the blade profile angle of wheel hub, along wheel hub meridian molded lines blade profile angle β integration is obtained the III district and radially distributes at the circumferential angle of element.

Fig. 4 is the blade profile angle β distribution map in three subregions.Blade profile angle, I district β identically vanishing, blade profile angle, II district β is that the artificer is selected according to the aerodynamic loading optimization principles along the distribution (A is to the B point, and wherein the B point value calculates given in advance by one dimension) of the meridian molded lines of casing.Distribute along the blade profile angle of wheel hub (A is to the C point) calculate from element circumferential angle distribution radially.The III district is (wherein the D point value calculates given in advance by one dimension) that the artificer selectes along the blade profile angle distribution (C is to the D point) of wheel hub.

Fig. 5 is equal strength design blade and the comparison of conventional trapezoid blade section that root section has identical stress.Can obviously determine, use the equal strength design, compare with conventional method and can reduce the employed material of blade in a large number.(a) the conventional trapezoid blade section of equal strength design blade section (b)

Fig. 6 is the radially pneumatic modelling flow chart of element impeller of oblique meridian trailing edge.

Fig. 7 be equal strength radially element blade strength-thickness just-the inverse problem calculation flow chart.

Fig. 8 is the 100KW micro fuel engine radial turbine impeller meridian molded lines as example.For reducing impeller length, the gradient that tiltedly exports the limit is little.

Fig. 9 is that 100KW micro fuel engine radial turbine impeller as example is along wheel hub and hub blade profile angle β distribution map.Wherein, be that the artificer is selected according to the aerodynamic loading optimization principles along hub blade profile angle β.Distribute along the blade profile angle of wheel hub (A is to the C point) calculate from element circumferential angle distribution radially.The III district is (wherein the D point value calculates given in advance by one dimension) that the artificer selectes along the blade profile angle distribution (C is to the D point) of wheel hub.

Figure 10 is that the 100KW micro fuel engine radial turbine impeller as example is the blade profile angle distribution map along wheel hub.

Figure 11 is as the isopleth distribution map of cambered surface blade profile angle β coordinate on meridian plane in the 100KW micro fuel engine radial turbine impeller impeller of example.As can be seen along the variation of wheel hub blade profile angle β in the outlet port.

Figure 12 is the 100KW micro fuel engine radial turbine impeller as example, calculates the isopleth distribution map of vane thickness on meridian plane.The thickness distribution and the blades height at blade root place have direct relation.

Figure 13 is that the accounting of three-dimensional finite element intensity calculating program ANSYS obtains, as the 100KW micro fuel engine radial turbine impeller impeller stress distribution map of example.

Figure 14 is that radially element vane thickness one dimension inverse problem calculation obtains equal strength is 100KW micro fuel engine radial turbine impeller blade stress envelope as example.With Figure 13 result displayed relatively, although one dimension inverse problem calculation result and be that three-dimensional finite element intensity result of calculation is very approaching as can be seen.

Application example

List the problem of exploitation 100KW miniature gas turbine in country's high-tech development plan in.Radial turbine is one of them critical component.Its design parameter is: flow 1Kg/s; Inlet pressure 0.32Mpa; Outlet pressure 0.106Mpa; 900 ℃ of inlet temperatures; Rotating speed 61000rpm.The impeller of radial turbine adopts the precision casting process manufacturing.The homemade cast superalloy of material selection, its allowable stress is 7850Kg/m for 400Mpa density ³Use the radially at first radially cambered surface shape-designing in the element of impeller blade of pneumatic modelling method of element impeller of aforesaid oblique meridian trailing edge.Fig. 8 is designed radial turbine impeller meridian molded lines.For reducing impeller length, the gradient that tiltedly exports the limit is little.Fig. 9 is distributing along wheel hub and hub blade profile angle β of adopting in the design.Figure 10 distributes along wheel hub according to the blade profile angle that blade profile angle β distribution design obtains.Figure 11 shows that the isopleth of cambered surface blade profile angle β coordinate on meridian plane distributes in the designed impeller.

Obtain impeller blade radially in the element behind the cambered surface coordinate, use according to equal strength radially the program of element vane thickness formula establishment calculate vane thickness.(seeing Figure 12) can obviously be found out, maximum thickness is distributed in the root that blade the longest (radially) is located.In order to investigate the radially accuracy of element vane thickness one dimension indirect problem solution of equal strength, calculate program ANSYS with three-dimensional finite element intensity and adjusted the radially stress distribution of element impeller (Figure 13) of designed equal strength.With use equal strength radially the result (Figure 14) that obtains of element vane thickness one dimension indirect problem solution relatively, the result of one dimension indirect problem and three-dimensional finite element intensity are calculated very approaching, have confirmed the feasibility of this method.

Claims (3)

1, a kind of radial turbine element impeller equal strength blade shape construction structure radially is characterized in that,

(1) cambered surface has oblique meridian trailing edge in the impeller blade that is made of some radially elements; On the straight meridian trailing edge of the cambered surface basis, trailing edge and hub intersection point are constant in conventional impeller blade, and and the intersection point of wheel hub to extend to flowing out direction along the meridian molded lines of wheel hub, constitute oblique meridian trailing edge by two intersection points;

(2) gradient of this oblique meridian trailing edge and in each circumferential angle of straight edge line element of cambered surface can adjust as required to satisfy radial turbine impeller outlet blade profile angle along the high distribution requirement of leaf, guarantee minimum and guarantee that rational blade loading distributes in design point state turbine leaving loss;

(3) and the distributing to the blade circumferential thickness of root of each straight edge line element correspondence of middle cambered surface by point, to guarantee that vane thickness has one rationally to distribute from the blade tip to the blade root, reach in proof strength and require under the precondition, alleviate the purpose of impeller weight and rotary inertia, equal strength blade shape feature is that blade is upright fir shape intersecting the section that obtains with the running shaft vertical plane, be that the blade circumferential thickness is increased to blade root gradually by blade tip, but this increase is not linear, begin to increase very slow, fast more near the increase of blade root blade circumferential thickness more.

2, a kind of radial turbine element impeller equal strength blade shape construction method radially, its step is as follows:

Step S7-1, given wheel speed, density of material and allowable stress value;

Step S7-2, to step S7-1, in determine in the blade cambered surface each radially given its blade tip thickness of straight edge line element and trapezoid cross section cone angle, and this straight edge line element is divided subdivisions such as enough thin from the blade tip to the blade root;

Step S7-3, direct problem analysis: according to formula (6): $\mathrm{\δ}\left(r\right)=\frac{{\mathrm{\ω}}^2\mathrm{\ρg}}{b\left(r\right)}\underset{r_{\mathrm{Tip}}}{\overset{r}{\∫}}\mathrm{rb}\left(r\right)\mathrm{dr},$ Begin to blade root direction unit computing unit bottom section upper stress value one by one from blade tip, stress value that calculates and allowable stress value compare, in case the stress value that calculates changes inverse problem calculation over to greater than the allowable stress value, in the formula 6: stress δ, radius r, tip radlus r _Tip, vane thickness b, blade material density p, gravity acceleration g, vane angle speed omega;

Step S7-4, inverse problem calculation: according to inverse problem calculation formula (7)-(9),

$F_k=F_{k-1}+{\mathrm{\ω}}^2\mathrm{\ρg}\×\frac{1}{2}(r_{k-1}+r_k)\×\frac{1}{2}(b_{k-1}+b_k)\×(r_{k-1}-r_k)---\left(7\right)$

${\mathrm{\σ}}_k=(F_{k-1}+\frac{1}{4}{\mathrm{\ω}}^2\mathrm{\ρg}(b_{k-1}+b_k)\×({r^2}_{k-1}-{r^2}_k)/b_k---\left(8\right)$

$b_k=(F_{k-1}+\frac{1}{4}{\mathrm{\ω}}^2\mathrm{\ρg}({r^2}_{k-1}-{r^2}_k)\×b_{k-1}/({\mathrm{\σ}}_k-\frac{1}{4}{\mathrm{\ω}}^2\mathrm{\ρg}({r^2}_{k-1}-{r^2}_k)\×b_{k-1})---\left(9\right)$

Use above formula successively recursion calculate the blade circumferential thickness in each unit bottom cross section, until the root of blade; In formula (7), (8), (9), subscript k, k-1 are the blade profile numbering, b is the thickness distribution of blade, r is a radius, and ρ is a blade material density, and g is a gravity accleration, ω is a vane angle speed, b is the function of radius r, and σ is expection stress, and F is the centrifugal force that blade calculated stress cross section produces under high speed rotating with top;

Step S7-5 gets back to step S7-2, finishes each step of S7-2 to S7-4, in blade cambered surface each radially the blade circumferential thickness of straight edge line element is all definite fully.

3, a kind of oblique meridian trailing edge pneumatic modelling method of element impeller radially, described impeller moulding is divided into I, II, three districts of III carry out, and its step is as follows:

Step S6-1, calculate to determine the blade profile angle β at impeller outlet blade tip and blade root place according to one dimension _BAnd β _D

Step S6-2, use BEZIER curve construction impeller along casing with along the meridian molded lines of wheel hub, trailing edge B point is fixing, and blade profile angle distribution D point can be along the meridian molded lines slip of wheel hub with adjustment trailing edge gradient;

Step S6-3, I district are the impeller inlet district, and respectively radially the circumferential angle of straight edge line element perseverance is zero;

θ(z)≡0，z＝z _O～z _A

Step S6-4, II district are impeller-inducer transition zone, and radially the circumferential angle of the straight edge line element integration of order from blade profile angle distribution A point to trailing edge B along the meridian molded lines of casing by blade profile angle β is definite for each;

$\mathrm{\θ}\left(z\right)=\mathrm{\θ}\left(z_A\right)+{\∫}_{z_A}^{z_B}\frac{\mathrm{tg}\left(\mathrm{\β}\right)}{r}\mathrm{ds}$

Blade profile angle β is that the artificer is selected according to the aerodynamic loading optimization principles along the distribution of the meridian molded lines of casing;

Step S6-5, radially calculate along the blade profile angle of wheel hub and distribute in the circumferential angle of element according to I district and II district

$\mathrm{\β}\left(z\right)=r\frac{\mathrm{d\θ}}{\mathrm{ds}}$

Step S6-6, given III district blade profile angle distribution C point are to blade profile angle distribution D point, for guaranteeing that O-A-C-D blade profile angle distribute light is along adjusting the meridian molded lines axial position of blade profile angle distribution D point along wheel hub;

Step S6-7, III district are the impeller outlet district, and radially the circumferential angle of the straight edge line element integration of order from blade profile angle distribution C point to blade profile angle distribution D along the meridian molded lines of wheel hub by blade profile angle β is definite for each;

$\mathrm{\θ}\left(z\right)=\mathrm{\θ}\left(z_C\right)+{\∫}_{z_C}^{z_D}\frac{\mathrm{tg}\left(\mathrm{\β}\right)}{r}\mathrm{ds}$

Like this, in the blade cambered surface each radially the circumferential angle of straight edge line element determined fully, finished the generation work of cambered surface in the sheet.

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