CN103500287B - The defining method of rotary blade-box rub-impact force - Google Patents

Abstract

The defining method of rotary blade-box rub-impact force, belongs to mechanical kinetics technical field.The present invention includes following steps: according to the law of conservation of mechanical energy, set up blade and the casing functional equation in certain moment: U _e+ U _c=W; Set up the dynamic balance relation of blade and casing, obtain the radial force F at blade tip place _nexpression formula: ; According to the flexural deformation of blade, by blade tip radial force F _naccording to blade tip normal direction and tangentially decompose :-F _l=-F _ncos [v ' (L, t)] ,-F _t=-F _nsin [v ' (L, t)]; Finally the stressed of blade tip place is synthesized: , <maths num=" 0001 " >

Description

The defining method of rotary blade-box rub-impact force

Technical field

The invention belongs to mechanical kinetics technical field, relate to a kind of defining method of rotary blade-box rub-impact force, particularly relate to a kind of defining method of rotary blade-box rub-impact force of the rotation effect, buckling effect and the casing rigidity that contain blade self.

Background technology

At present, the defining method that existing blade-casing touches the power of rubbing mainly contains following several:

1. touch based on collision energy conservation the power model that rubs

Blade is assumed to be semi-girder, relation between the normal direction contact force of blade of having derived and radial deformation, analyze the nonlinear dynamic characteristic of system under single blade and multiple-blade two kinds touch the situation of rubbing, consider that single blade touches blade when rubbing-casing normal direction and touches the power of rubbing and be:

$F_n=\frac{{\mathrm{\&pi;}}^2}{4}\frac{\mathrm{EI}}{L^2}\frac{\frac{\mathrm{\&pi;}}{2}\sqrt{\frac{\mathrm{\&delta;}}{L}}}{\mathrm{\&mu;}+\frac{\mathrm{\&pi;}}{2}\sqrt{\frac{\mathrm{\&delta;}}{L}}}$

In formula: EI is the bendind rigidity of blade; L is length of blade; δ is the radial intrusion volume of blade tip; μ is friction factor.

On the basis of above-mentioned formula, by considering the impact of leaf dish and blade rotary centrifugal force, be deduced blade-casing normal direction and touch the power of rubbing, obtaining its expression formula is:

$F_n=\frac{{\mathrm{\&pi;}}^2}{4}\frac{\mathrm{EI}}{L^2}\frac{\frac{\mathrm{\&pi;}}{2}\sqrt{\frac{\mathrm{\&delta;}}{L}}}{\mathrm{\&mu;}+\frac{\mathrm{\&pi;}}{2}\sqrt{\frac{\mathrm{\&delta;}}{L}}}+\frac{11}{56}\mathrm{\&rho;}{\mathrm{AL\&Omega;}}^2(\frac{5}{22}L+\frac{35}{22}R)\frac{\frac{\mathrm{\&pi;}}{2}\sqrt{\frac{\mathrm{\&delta;}}{L}}}{\mathrm{\&mu;}+\frac{\mathrm{\&pi;}}{2}\sqrt{\frac{\mathrm{\&delta;}}{L}}}---\left(1\right)$

In formula: EI is the bendind rigidity of blade; L is length of blade; δ is the radial intrusion volume of blade tip; μ is friction factor; ρ is density of material; A is area of blade section; Ω is angular velocity of rotation; R is leaf dish radius.

2. fusing adhesion rubbing model strikes off rubbing model with wearing away

Fusing adhesion model: when casing touches and rubs assuming that metal blade and metal are obturaged, blade tip will melt, and when blade to rub by touching, have adhesive coating at the metal surface area cooled.Because blade moves with speed u in resisting medium, therefore tangential force can be produced at blade tips.In addition, because blade tip and interlayer of obturaging also exist diametrically speed, therefore also normal force can be produced.When supposing that blade tip width is far longer than its thickness (b>>a), the normal force F of fusing adhesion model _nwith tangential force F _texpression formula is as follows:

$\left\{\begin{array}{cc}{F}_n=\mathrm{cvb}{\left(\frac{a}{h}\right)}^3& F_n\&le;F_s\\ F_n=k(r-C)& F_n>F_s\end{array}\right.$

$F_t=\frac{\mathrm{cuab}}{h}$

In formula: c is the viscosity of deposite metal; V is that the normal direction of blade tip invades speed; U is the tangential velocity of blade tip; A is blade tip thickness; B is blade tip width; H is deposite metal thickness; F _sfor the supporting power of seal structure; K is casing radial rigidity; R is the radial displacement of blade tip; C is the radial play of blade tip and sealing.

When blade melts and sticks on cooling seal structure, engine performance can reduce because of the reduction of blade wear pressure ratio very soon, and recover its efficiency and then must change blade, this will shorten overhaul time, thus increases maintenance cost.In order to reduce the wearing and tearing of blade tip, adopt at present mostly the easily low intensive layer of obturaging of mill, when metal blade and these materials touch rub time, each blade by time all to ream some granules, remove the energy U needed for unit volume material according to each blade, the expression formula obtaining its tangential force is:

F _t=(r-C)Ub

Its normal force is:

F _n=k(r-C)。

3. continuous elastic touches the power model that rubs

Normally used normal force model is linear rigidity model, and expression formula is as follows:

F _n=k _nδ(2)

In formula: k _nfor contact stiffness; δ is the radial intrusion volume of blade tip.Due to k _nvalue more difficultly to determine, therefore concerning blade-casing rubbing model, its numerical value generally adopts the radial rigidity of blade.

Except linear model, nonlinear rigidity model is also often used, wherein modal is based on Hertz contact theory, the collision of blade tip and casing is approximated to the contact between elastic cylinder and elastic half-space, then determines normal force according to the local deformation between elastic body.Its normal force expression formula is as follows:

$F_n={\left(\frac{\mathrm{\&delta;}}{a}\right)}^{\frac{3}{2}}---\left(3\right)$

In formula: δ is the radial intrusion volume of blade tip; A is contact radius, r ₁, R ₂be the radius-of-curvature of two contacts, R here ₁and R ₂be respectively thickness radius h/2 and the casing radius R of blade _c; E ₁, υ ₁, E ₂, υ ₂be respectively elastic modulus and the Poisson ratio of two contacts.

4. surging force model

Impulse model is a kind of simplified model of normal force model, and it mainly simplifies calculating by linearization, raises the efficiency.Impulse model can be represented by many kinds of function form:

The pulse of (a) sine function

$F_n=\left\{\begin{array}{cc}{F}_{\max }\sin \left(\frac{\mathrm{\&pi;}}{t_c}t\right)& 0\&le;t\&le;t_c\\ 0& t_c\&le;t\&le;t_p\end{array}\right.$

The pulse of (b) cosine function

$F_n=\left\{\begin{array}{cc}-\frac{F_{\max }}{2}+\frac{F_{\max }}{2}\cos \left(\frac{\mathrm{\&pi;}}{t_c}t\right)& 0\&le;t\&le;t\\ 0& t_c\&le;t\&le;t_p\end{array}\right.$

The pulse of (c) rectangular function

$F_n=\left\{\begin{array}{cc}{F}_{\max }& 0\&le;t\&le;t_c\\ 0& t_c\&le;t\&le;t_p\end{array}\right.$

In formula: F _maxfor maximum normal force; t _cfor duration of contact; t _pfor cycle length; T is the time.Duration of contact t _cdetermine (as shown in Figure 1) by blade tip running orbit, expression formula is as follows:

$t_c=\frac{{2\cos }^{-1}\left(\frac{R_c^2+{(\mathrm{\&Delta;}+{\mathrm{\&delta;}}_{\max })}^2-r_g^2}{{2R}_c(\mathrm{\&Delta;}+{\mathrm{\&delta;}}_{\max })}\right)}{\mathrm{\&Omega;}}$

In formula: o ₁, o ₂be respectively blade track centers and casing center; R _cfor casing radius; r _gfor tip radlus; Δ be casing concentric with blade track time mean gap, Δ=R _c-r _g; δ _maxfor maximum blade tip-casing intrusion volume; Ω is angular velocity of rotation.

The applicable elements of above-mentioned each defining method is as follows:

1. touch based on collision energy conservation the power model that rubs: assuming that casing is rigidity, considers the elastic deformation of collision process Leaf, although based on conservation of mechanical energy, do not consider energy dissipation.Therefore it is mainly applicable to based on elastic collision, and the rotating machinery that casing rigidity is very large, as gas turbine etc.

2. fusing adhesion rubbing model strikes off rubbing model with wearing away:

Fusing adhesion rubbing model: for spinner blade with touch the situation of rubbing without coating metal seal structure.When this happens, one deck deposite metal may be produced between blade and basic unit of obturaging (as metal honeycomb structure) or seal structure (as comb tooth of obturaging).

Can wear away and strike off rubbing model: be mainly theoretical based on energy loss, touching that the stator casing described with the blade of abradable material and coating (as pottery is obturaged material) occurs rubs.

3. continuous elastic touches the power model that rubs:

(1) spring-damper model, is mainly applicable to turn stator elastic collision, and as touching between rotor seal part is rubbed, what be not too applicable to that blade has a moderate finite deformation touches the situation of rubbing; (2) Hertz contact model, both being applicable to elastic collision is that main touching rubs, situation (contact relative speed is less than 0.5m/s) is slowly contacted as turned stator, by introducing hysteresis contact force, (lambda limiting process is to maximum intrusion volume again, provide set deformation volume), consider the impact of plastic yield.

4. surging force model: surging force partial rub power model: by will the form that the process simplification that rubs is surging force be touched, avoid complicated contact judgement and the solution procedure of nonlinear iteration, greatly reduce calculated amount, thus can the partial rub of the comparatively complicated real blade-casing of simple analog.But this model needs emulated by Contact Dynamics or test the duration of contact accurately determining blade-casing.

By above-mentioned introduce known: all there is significant limitation in use in the defining method that existing blade-casing touches the power model that rubs, this will cause the feature of blade-casing collision not reflected completely, and differ comparatively large with actual conditions, and the impact of each factor in blade-casing collision process can not be considered.

The research of present stage focuses mostly on the research of between rotor and stator impact-rub malfunction, and also less for the research of blade and casing.Compare and turn stator and touch and rub, it is more outstanding that blade-casing touches the nonlinear characteristic of rubbing.Due to much smaller the bending stiffness of blade compares casing rigidity, and because be High Rotation Speed in the course of the work, so blade can bend when collision friction, thus can forced vibration be there is, whole system is had an impact.In order to better understand the impact-rub malfunction feature of blade-casing, avoid the generation of accident, the proposition of reasonably touching the power model defining method that rubs just seems particularly important.

Summary of the invention

For prior art Problems existing, the invention provides a kind of defining method of rotary blade-box rub-impact force.Different from traditional the touching power defining method that rubs, the method, for the feature of blade-casing collision friction, considers various factors, by setting up suitable model, can describe the collision friction phenomenon of blade-casing more accurately.

To achieve these goals, the present invention adopts following technical scheme, and a kind of defining method of rotary blade-box rub-impact force, comprises the steps:

Step one: the physical dimension of blade and casing and service condition are measured, comprising length L, the width b of blade, the thickness h of blade, the radius R of leaf disk of blade _d, casing radius R _c, minor increment c between blade tip and casing inwall _minand rotating speed Ω;

Step 2: according to the law of conservation of mechanical energy, set up blade and the casing functional equation in certain moment:

U _e+U _c=W

In formula, U _efor the flexural deformation energy of blade, U _cfor centrifugal potential energy, W is blade tip radial force and transverse force work;

Step 3: the dynamic balance relation setting up blade and casing, obtains the radial force F at blade tip place _nexpression formula:

$F_n=\frac{5}{3}{\mathrm{L\&Gamma;k}}_{\mathrm{ca}\sin g}\frac{\frac{\mathrm{\&delta;}}{L}+\frac{5\mathrm{\&Gamma;}}{6}-\frac{\sqrt{15}}{6}\sqrt{\frac{15}{9}{\mathrm{\&Gamma;}}^2+4({\mathrm{\&mu;}}^2-\mathrm{\&Gamma;})\frac{\mathrm{\&delta;}}{L}}}{\frac{10\mathrm{\&Gamma;}}{3}-\frac{5}{3}{\mathrm{\&mu;}}^2+\frac{\mathrm{\&delta;}}{L}}$

In formula, Γ is stiffness term coefficient, k _casingfor casing rigidity; E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade, and ρ is the density of blade, and A is the area of section of blade, and L is the length of blade, R _dfor the radius of leaf disk, μ is the friction factor of surface of contact, and δ is intrusion volume, and Ω is the angular velocity of rotation of blade;

Step 4: according to the flexural deformation of blade, by blade tip radial force F _naccording to blade tip normal direction and tangentially decompose:

-F _L=-F _ncos[v′(L,t)]

-F _T=-F _nsin[v′(L,t)]

In formula, F _lfor radial force F _ndecompose the power in blade tip normal direction, F _tfor radial force F _ndecompose blade tip tangential on power, the bending displacement angle that v ' (L, t) is blade tip, L is the length of blade, and t is the time;

Step 5: finally the stressed of blade tip place is synthesized:

${\stackrel{\&OverBar;}{F}}_n=-F_L=-F_n\cos \left[v^{\&prime;}(L,t)\right]$

${\stackrel{\&OverBar;}{F}}_t=-\mathrm{\&mu;}{\stackrel{\&OverBar;}{F}}_n-F_T=-\mathrm{\&mu;}{\stackrel{\&OverBar;}{F}}_n-F_n\sin \left[v^{\&prime;}(L,t)\right]$

In formula, for the normal force after the synthesis of blade tip place, for the tangential force after the synthesis of blade tip place, F _lfor radial force F _ndecompose the power in blade tip normal direction, F _tfor radial force F _ndecompose blade tip tangential on power, the bending displacement angle that v ' (L, t) is blade tip, L is the length of blade, and t is the time, and μ is the friction factor of surface of contact.

The mathematical model adopted for the intrusion volume δ described in determining step three is:

δ=u _L(t)-c _rub(t)

In formula, c _rubt () for the gap of t blade-casing, its expression formula is:

In formula, R _cfor casing radius; r _gfor blade tip orbital radius, r _g=L+R _d, L is the length of blade, R _dfor the radius of leaf disk; Δ be casing concentric with blade track time mean gap, Δ=R _c-r _g; c _minfor the minor increment between blade tip and casing inwall, wherein, c _min>0 represents initial minimum clearance, c _min<0 represents initial maximum invasion depth; for phasing degree; n _pfor pitch diameter number; T is the time; Ω is the angular velocity of rotation of blade.

Beneficial effect of the present invention:

Defining method of the present invention is for the feature of blade-casing collision friction, consider various factors, by setting up suitable model, the collision friction phenomenon of blade-casing can be described more exactly, different operating mode lower blade-casing fault is simulated, and its accuracy also can improve greatly; Meanwhile, the fault signature of blade-casing collision friction local can be reacted more really; The adjustment that the method not only can be blade-casing gap provides theoretical foundation, and the early diagnosis that also can be blade impact-rub malfunction provides technical support, also has important directive significance to raising overall performance.

Accompanying drawing explanation

Fig. 1 is blade tip running orbit schematic diagram;

Fig. 2 is the dynamic balance schematic diagram in blade-casing collision process;

Fig. 3 be single blade-elasticity casing touch the schematic diagram that rubs;

Fig. 4 is blade-stator System schematic diagram;

Fig. 5 is that the blade-casing adopted in the present invention touches in the example that rubs the motion schematic diagram determining rotating vane under rotating speed;

Fig. 6 is the change curve (μ=0.3) of the normal force after the synthesis of blade tip place with intrusion volume;

Fig. 6 (a) is for the normal force after blade tip place synthesis when casing is rigidity is with the change curve (μ=0.3) of intrusion volume;

Fig. 6 (b) is for work as k _casingbe 5 × 10 ⁸n/m, c _casing=1 × 10 ³during Ns/m, the normal force after the blade tip place synthesis under different rotating speeds is with the change curve (μ=0.3) of intrusion volume;

Fig. 7 is the change curve (k of the normal force after the synthesis of blade tip place with rotating speed _casing=5 × 10 ⁸n/m, c _casing=1 × 10 ³ns/m, δ=20 μm, μ=0.3);

Fig. 8 is the change curve of the normal force after the synthesis of blade tip place with stiffness term coefficient;

Fig. 9 is the change curve (k of the normal force after the synthesis of blade tip place with friction factor _casing=5 × 10 ⁸n/m, c _casing=1 × 10 ³ns/m, δ=20 μm, Ω=5000r/min);

Figure 10 is the change curve (δ=20 μm, μ=0.3) of casing radial deflection distance with casing rigidity;

In figure, 1-blade, 2-casing.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail:

A defining method for rotary blade-box rub-impact force, comprises the steps:

Step one: the physical dimension of blade and casing and service condition are measured, comprising length L, the width b of blade, the thickness h of blade, the radius R of leaf disk of blade _d, casing radius R _c, minor increment c between blade tip and casing inwall _minand rotating speed Ω;

Step 2: according to the law of conservation of mechanical energy, set up blade and the casing functional equation in certain moment:

Suppose that blade meets conservation of mechanical energy within certain time that blade contacts with casing:

U _e+U _c=W(4)

Wherein:

U _efor the flexural deformation energy of blade, its expression formula is:

$U_e=\frac{1}{2}{\&Integral;}_0^L\mathrm{EI}{\left(\frac{{\&PartialD;}^{2}v}{{\&PartialD;x}^2}\right)}^2\mathrm{dx}---\left(5.1\right)$

In formula, E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade, and L is the length of blade, and v is the bending displacement of blade;

U _cfor centrifugal potential energy, its expression formula is:

$U_c=\frac{1}{2}{\&Integral;}_0^L\frac{1}{2}{\mathrm{\&rho;A\&Omega;}}^2(L^2+{2R}_{d}L-2R_{d}x-x^2){\left(\frac{\&PartialD;v}{\&PartialD;x}\right)}^2\mathrm{dx}---\left(5.2\right)$

In formula, L is the length of blade, and v is the bending displacement of blade, and ρ is the density of blade, and A is the area of section of blade, R _dfor the radius of leaf disk, Ω is the angular velocity of rotation of blade;

W is blade tip radial force F _nwith transverse force F _twork, blade tip transverse force F _tfor the friction force produced during blade-casing contact, friction force adopts Coulomb friction model here, i.e. F _t=μ F _n, then the expression formula of merit is:

$W=\frac{1}{2}{F}_n{u}_L+\frac{1}{2}{\mathrm{\&mu;F}}_n{v}_L---\left(5.3\right)$

Wherein: v _lfor the bending displacement at blade tip place, μ is the friction factor of surface of contact, u _lfor the radial displacement at blade tip place, its expression formula is:

$u_L=\frac{1}{2}{\&Integral;}_0^L{\left(\frac{\&PartialD;v}{\&PartialD;x}\right)}^2\mathrm{dx}---\left(6\right)$

In formula, L is the length of blade, and v is the bending displacement of blade;

Step 3: the dynamic balance relation setting up blade and casing, obtains the radial force F at blade tip place _nexpression formula:

The dynamic balance relation of radial impact can be obtained by Fig. 2, and the radial displacement u at intrusion volume δ shown in Fig. 3 and casing radial deflection distance d and blade tip place _lrelation:

F _n=k _casingd(7)

δ=u _L+d(8)

In formula, k _casingfor casing rigidity;

In Fig. 3, o ₁for disc centre, c _casingfor casing damping;

Obtaining blade semi-girder line of deflection formula by integral method is:

$v=\frac{F_t{x}^2}{6\mathrm{EI}}(3L-x)---\left(9\right)$

In formula, E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade, and L is the length of blade, F _tfor blade tip transverse force, v is the bending displacement of blade;

According to blade semi-girder line of deflection formula, by the bending displacement v of the bending displacement v of rotating vane with blade tip place _lrepresent:

$v=v_L\frac{1}{2}(\frac{{3x}^2}{L^2}-\frac{x^3}{L^3})---\left(10\right)$

In formula, L is the length of blade, v _lfor the bending displacement at blade tip place;

The bending displacement v expression formula (10) of rotating vane is substituted into formula (5.1) and formula (5.2), and convolution (5.3), the bending displacement v at blade tip place is obtained eventually through conservation of mechanical energy equation (4) _lfor:

$v_L=\frac{{\mathrm{\&mu;F}}_n}{\frac{3\mathrm{EI}}{L^3}-\frac{{3F}_n}{5L}+3{\mathrm{\&rho;A\&Omega;}}^2(\frac{27}{280}L+\frac{1}{8}{R}_d)}---\left(11\right)$

In formula, L is the length of blade, and ρ is the density of blade, and A is the area of section of blade, R _dfor the radius of leaf disk, Ω is the angular velocity of rotation of blade, and μ is the friction factor of surface of contact, F _nfor blade tip radial force, E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade;

Obtain v _lafter, through type (6) and formula (10) u can be tried to achieve _l, then by u _lwith the expression formula of d be updated in formula (8):

$\mathrm{\&delta;}=\frac{5L{\mathrm{\&mu;}}^2{F_n}^2}{3{[F_n-5L(\frac{\mathrm{EI}}{L^3}+{\mathrm{\&rho;A\&Omega;}}^2(\frac{27}{280}L+\frac{1}{8}{R}_d))]}^2}+\frac{F_n}{k_{\mathrm{ca}\sin g}}---\left(12\right)$

In formula, L is the length of blade, and ρ is the density of blade, and A is the area of section of blade, R _dfor the radius of leaf disk, Ω is the angular velocity of rotation of blade, and μ is the friction factor of surface of contact, F _nfor blade tip radial force, E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade, k _casingfor casing rigidity, δ is intrusion volume;

Omit high-order term, finally arrange and obtain F _nanalytical expression;

$F_n=\frac{5}{3}\mathrm{L\&Gamma;}{k}_{\mathrm{ca}\sin g}\frac{\frac{\mathrm{\&delta;}}{L}+\frac{5\mathrm{\&Gamma;}}{6}-\frac{\sqrt{15}}{6}\sqrt{\frac{15}{9}{\mathrm{\&Gamma;}}^2+4({\mathrm{\&mu;}}^2-\mathrm{\&Gamma;})\frac{\mathrm{\&delta;}}{L}}}{\frac{10\mathrm{\&Gamma;}}{3}-\frac{5}{3}{\mathrm{\&mu;}}^2+\frac{\mathrm{\&delta;}}{L}}---\left(13\right)$

In formula, Γ is stiffness term coefficient, k _casingfor casing rigidity, E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade, and ρ is the density of blade, and A is the area of section of blade, and L is the length of blade, R _dfor the radius of leaf disk, μ is the friction factor of surface of contact, and δ is intrusion volume, and Ω is the angular velocity of rotation of blade, F _nfor blade tip radial force;

Step 4: according to the flexural deformation of blade, by blade tip radial force F _naccording to blade tip normal direction and tangentially decompose:

Because rotating vane may produce the larger situation of flexural deformation touching in the process of rubbing, therefore the radial force of blade should be revised along the bending direction of blade.When radial invasion depth is larger, this revision just becomes necessary.Blade tip radial force F _nthe normal direction of blade tip is decomposed with tangential with the form at bending displacement angle v ' (L, t) of blade tip:

-F _L=-F _ncos[v′(L,t)]

-F _T=-F _nsin[v′(L,t)]

In formula, F _lfor blade tip radial force F _ndecompose the power in blade tip normal direction, F _tfor blade tip radial force F _ndecompose blade tip tangential on power, the bending displacement angle that v ' (L, t) is blade tip, L is the length of blade, and t is the time;

Step 5: finally to the normal force at blade tip place and tangential force synthesize:

${\stackrel{\&OverBar;}{F}}_n=-F_L=-F_n\cos \left[v^{\&prime;}(L,t)\right]$

${\stackrel{\&OverBar;}{F}}_t=-\mathrm{\&mu;}{\stackrel{\&OverBar;}{F}}_n-F_T=-\mathrm{\&mu;}{\stackrel{\&OverBar;}{F}}_n-F_n\sin \left[v^{\&prime;}(L,t)\right]$

In formula, for the normal force after the synthesis of blade tip place, for the tangential force after the synthesis of blade tip place, F _lfor blade tip radial force F _ndecompose the power in blade tip normal direction, F _tfor blade tip radial force F _ndecompose blade tip tangential on power, the bending displacement angle that v ' (L, t) is blade tip, L is the length of blade, and t is the time, and μ is the friction factor of surface of contact.

The defining method of the intrusion volume δ described in step 3 is as follows:

Blade-stator System as shown in Figure 4, in figure, o, o ₁be respectively casing center and disc centre; R _cfor casing radius; r _gfor blade tip orbital radius, r _g=L+R _d, L is the length of blade, R _dfor the radius of leaf disk; Δ be casing concentric with blade track time mean gap, Δ=R _c-r _g; c _minfor the minor increment between blade tip and casing inwall, if c _min>0, c _minrepresent initial minimum clearance, if c _min<0, c _minrepresent initial maximum invasion depth; Ω is the angular velocity of rotation of blade; c _rubt () is the gap of t blade-casing;

Geometric relationship according in figure:

AB ²+oB ²=oA ²

Above formula is launched:

In formula, R _cfor casing radius; for phasing degree; c _rubt () is the gap of t blade-casing; r _gfor blade tip orbital radius, r _g=L+R _d, L is the length of blade, R _dfor the radius of leaf disk; Δ be casing concentric with blade track time mean gap, Δ=R _c-r _g; c _minfor the minor increment between blade tip and casing inwall, if c _min>0, c _minrepresent initial minimum clearance, if c _min<0, c _minrepresent initial maximum invasion depth; Ω is the angular velocity of rotation of blade; T is the time;

By solving the expression formula in the gap that can obtain blade-casing to the expansion of above formula, if consider the impact of casing pitch diameter, then obtain following expression:

In formula, R _cfor casing radius; for phasing degree; c _rubt () is the gap of t blade-casing; r _gfor blade tip orbital radius, r _g=L+R _d, L is the length of blade, R _dfor the radius of leaf disk; Δ be casing concentric with blade track time mean gap, Δ=R _c-r _g; c _minfor the minor increment between blade tip and casing inwall, if c _min>0, c _minrepresent initial minimum clearance, if c _min<0, c _minrepresent initial maximum invasion depth; n _pfor pitch diameter number; Ω is the angular velocity of rotation of blade; T is the time;

Intrusion volume between actual rotating vane and casing inwall is:

δ=u _L(t)-c _rub(t)

In formula, u _lt () is the radial displacement of t blade tip, c _rubt () is the gap of t blade-casing, its expression formula is such as formula shown in (14).

As δ >0, touch the generation that rubs; When δ≤0, then do not touch and rub.As can be seen from the above equation, δ is a variations per hour, the u that each moment gap width all will be obtained by a upper moment _l(t) and c _rubt () is recalculated.

The present invention will be further described to touch below in conjunction with a blade-casing example that rubs.

It is as shown in table 1 that the geometric parameter of blade and blade tip touch the simulation parameter that rubs, and as shown in Figure 5, in Fig. 5, u is the radial displacement of blade to leaf model, and v is the bending displacement of blade, and w is the swing displacement of blade, and x is integration amount.

Geometric parameter and the blade tip of table 1 blade touch the simulation parameter that rubs

As seen from Figure 6, the normal force after the synthesis of blade tip place and intrusion volume are nonlinear relationship, and along with the increase of intrusion volume, the amplitude of variation of the normal force after the synthesis of blade tip place reduces, in weak characteristic.In Fig. 6 (a), under the prerequisite being all rigidity casing, the curve that the present invention obtains and formula (1) curve substantially identical.Fig. 6 (b) is, at k _casing=5 × 10 ⁸during N/m, the normal force after the blade tip place synthesis under different rotating speeds is with the change curve of intrusion volume.Can see from Fig. 6 (b), the normal force after rotating speed increase can make blade tip place synthesize increases.

As seen from Figure 7, normal force after the synthesis of blade tip place is nonlinearities change with rotating speed: the normal force after the synthesis of incipient stage blade tip place is larger with the amplitude of rotation speed change, but the normal force after the synthesis of blade tip place is not along with rotating speed increases always, but slow down ascendant trend gradually and be finally tending towards a constant value.

As seen from Figure 8, the normal force after the synthesis of blade tip place is nonlinearities change with stiffness term coefficient, and after quick ascent stage, the normal force after the synthesis of blade tip place slows down gradually along with the speed of stiffness term index variation, is finally tending towards k _casingδ.The increase of stiffness term coefficient is larger, illustrates that the resistant to bending ability of blade is stronger, and finally when blade no longer bends, the normal force after the synthesis of blade tip place also no longer increases along with the increase of stiffness term coefficient.This also can explain the reason of the normal force after the synthesis of blade tip place with rotation speed change: the rising of rotating speed adds the bending stiffness of blade, also just adds relative rigidity.Contact due to blade and casing is the friction process of a Non-smooth surface, so the formula that the present invention derives, considers and to touch in the process of rubbing rubbing characteristics to the impact of the normal force after the synthesis of blade tip place.

Contemplated by the invention the impact of friction force on the normal force after the synthesis of blade tip place, as seen from Figure 9, along with the increase of friction factor, the normal force after the synthesis of blade tip place has in non-linear trend of successively decreasing.When friction factor is less, the speed that the normal force after the synthesis of blade tip place reduces is very fast, and the speed reduced afterwards slows down gradually.Fig. 9 also illustrate that: the existence of friction force also serves certain inhibiting effect to the radial force after the synthesis of blade tip place.

As seen from Figure 10, when casing rigidity is less, intrusion volume is exactly mainly the offset distance of casing radial direction; After casing rigidity increases, the offset distance of casing radial direction reduces to some extent, shows thus: due to the increase of casing rigidity, makes blade also start raw shape occurs; And when casing rigidity is larger, the offset distance of casing radial direction is almost 0, show that casing is now equivalent to be completely fixed, be then all converted into the elastic potential energy of blade by blade institute work.Further, under same casing rigidity, high-revolving translational movement is greater than slow-revving.

The Changing Pattern of the normal force after the Changing Pattern of tangential force after the synthesis of blade tip place synthesizes with above-mentioned blade tip place is identical, at this no longer Ao Shu.

Claims (2)

1. a defining method for rotary blade-box rub-impact force, is characterized in that, comprises the steps:

Step one: the physical dimension of blade and casing and service condition are measured, comprising length L, the width b of blade, the thickness h of blade, the radius R of leaf disk of blade _d, casing radius R _c, minor increment c between blade tip and casing inwall _minand the angular velocity of rotation Ω of blade;

Step 2: according to the law of conservation of mechanical energy, set up blade and the casing functional equation in certain moment:

U _e+U _c＝W

In formula, U _efor the flexural deformation energy of blade, U _cfor centrifugal potential energy, W is blade tip radial force and transverse force work;

Step 3: the dynamic balance relation setting up blade and casing, obtains the radial force F at blade tip place _nexpression formula:

$F_n=\frac{5}{3}{\mathrm{L\&Gamma;k}}_{ca\sin g}\frac{\frac{\mathrm{\&delta;}}{L}+\frac{5\mathrm{\&Gamma;}}{6}-\frac{\sqrt{15}}{6}\sqrt{\frac{15}{9}{\mathrm{\&Gamma;}}^2+4({\mathrm{\&mu;}}^2-\mathrm{\&Gamma;})\frac{\mathrm{\&delta;}}{L}}}{\frac{10\mathrm{\&Gamma;}}{3}-\frac{5}{3}{\mathrm{\&mu;}}^2+\frac{\mathrm{\&delta;}}{L}}$

In formula, Γ is stiffness term coefficient, k _casingfor casing rigidity; E is the elastic modulus of blade, and I is the cross sectional moment of inertia of blade, and ρ is the density of blade, and A is the area of section of blade, and L is the length of blade, R _dfor the radius of leaf disk, μ is the friction factor of surface of contact, and δ is intrusion volume, and Ω is the angular velocity of rotation of blade;

Step 4: according to the flexural deformation of blade, by blade tip radial force F _naccording to blade tip normal direction and tangentially decompose:

-F _L＝-F _ncos[v′(L,t)]

-F _T＝-F _nsin[v′(L,t)]

In formula, F _lfor radial force F _ndecompose the power in blade tip normal direction, F _tfor radial force F _ndecompose blade tip tangential on power, the bending displacement angle that v ' (L, t) is blade tip, L is the length of blade, and t is the time;

Step 5: finally the stressed of blade tip place is synthesized:

${\stackrel{\&OverBar;}{F}}_n=-F_L=-F_{n}cos\&lsqb;v^{\&prime;}(L,t)\&rsqb;$

${\stackrel{\&OverBar;}{F}}_t=-\mathrm{\&mu;}{\stackrel{\&OverBar;}{F}}_n-F_T=-\mathrm{\&mu;}{\stackrel{\&OverBar;}{F}}_n-F_{n}sin\&lsqb;v^{\&prime;}(L,t)\&rsqb;$

In formula, for the normal force after the synthesis of blade tip place, for the tangential force after the synthesis of blade tip place, F _lfor radial force F _ndecompose the power in blade tip normal direction, F _tfor radial force F _ndecompose blade tip tangential on power, the bending displacement angle that v ' (L, t) is blade tip, L is the length of blade, and t is the time, and μ is the friction factor of surface of contact.

2. the defining method of rotary blade-box rub-impact force according to claim 1, is characterized in that the mathematical model adopted for the intrusion volume δ described in determining step three is:

δ＝u _L(t)-c _rub(t)

In formula, u _lt () is the radial displacement of t blade tip, c _rubt () for the gap of t blade-casing, its expression formula is:

In formula, R _cfor casing radius; r _gfor blade tip orbital radius, r _g=L+R _d, L is the length of blade, R _dfor the radius of leaf disk; Δ be casing concentric with blade track time mean gap, Δ=R _c-r _g; c _minfor the minor increment between blade tip and casing inwall, wherein, c _min>0 represents initial minimum clearance, c _min<0 represents initial maximum invasion depth; for phasing degree; n _pfor pitch diameter number; T is the time; Ω is the angular velocity of rotation of blade.