CN103116689A - Turbine blade ordering method relating to turbine thickened blades - Google Patents

Abstract

The invention provides a turbine blade ordering method relating to turbine thickened blades and relates to a location and sort algorithm of turbine blades. At present, thickened blades in turbine blades are fixed randomly through manual work in an entire circle of blades, no accurate location and ordering method exists, over-concentrated problem or over-dispersive problem exists in assembling, and the problem that grinding of an assembling clearance in assembling is incapable is prone to occur, however, the turbine blade ordering method relating to the turbine thickened blades solves the above problems. The ordering method comprises the main steps: S1, confirming the number of the thickened blades of the products participating in ordering according to product design requirements, S2, arranging the thickened blades through an equally distributed principle and confirming the sequence numbers of the thickened blades, S3, confirming the installation site sequence numbers of numbers of the thickened blades and processing random numbers, S4, weighing the thickened blades, S5, ordering the thickened blades, S6, weighing ordinary blades, and S7, ordering the ordinary blades. The invention relates to turbine blade ordering of the thickened blades.

Description

A kind of turbine blade sort method that relates to the steam turbine bulged blading

Technical field

The present invention relates to a kind of turbine blade location and sort algorithm, be specifically related to a kind of turbine blade sort method that relates to the steam turbine bulged blading.

Background technology

The steam turbine bulged blading refers to the blade radial size and exceeds the special vane of 0.20mm～0.30mm thickness than common blade, is used for when assembling, reconditioning being carried out in the fit-up gap.By artificial random fixing, does not locate and sort method accurately the position of steam turbine bulged blading in whole circle blade at present, has the problem of too concentrating or disperseing in assembling, easily causes can't carrying out reconditioning to the fit-up gap when assembling.

Summary of the invention

The objective of the invention is for solving the position of bulged blading in whole circle blade in present turbine blade by artificial random fixing, do not locate accurately and sort method, there is the problem of too concentrating or disperseing in assembling, easily cause to carry out the problem of reconditioning to the fit-up gap when assembling, and then a kind of turbine blade sort method that relates to the steam turbine bulged blading is provided.

The present invention addresses the above problem the technical scheme of taking to be: a kind of turbine blade sort method that relates to the steam turbine bulged blading of the present invention carries out according to following steps,

Step 1, according to the product design requirement, determine that bulged blading number and total leaf number purpose ratio that this kind product participates in sequence are A, wherein, this kind product total leaf number order is T, special vane (first and last blade, locking-blade) number is a; The number of common blade is b, b=T-n-a;

Step 2, according to the designing requirement of product, bulged blading adopts equally distributed principle arrange and determine sequence number:

Wherein, the bulged blading number is n, is obtained bulged blading number n=T * A by step 1;

, the installation site sequence number of n bulged blading on wheel disc is respectively: X1, X2, X3, X4 ... Xn,

X1＝a+1；

X2＝X1+〔(T-a)/n〕；

X3＝X2+〔(T-a)/n〕＝X1+〔2(T-a)/n〕；

Xn＝X1+〔(T-1)×(T-a)/n〕；

Draw X1, X2, X3, X4 corresponding on wheel disc ... on the Xn position, bulged blading should be installed;

Step 3, n bulged blading of above-mentioned definite installation site sequence number carried out random number;

Step 4, all bulged bladings of random number are weighed, determine when weighing that the bulged blading of random number need to be weighed by number, guarantee that namely the sequence number of weighing is consistent with fixed random number;

Weighing bulged blading: bevel gear lifter 7 and the bracing frame 11 of described turbine blade weighing device are slided along guide rail 3, make bevel gear lifter 7 corresponding with the position that the steam turbine leaf pushes up, bracing frame 11 is corresponding with the position of steam turbine blade root, and the employing grating scale records the distance L between steam turbine blade root and postive stop baffle 12 ₁And the distance L between steam turbine leaf top and postive stop baffle 12 ₂, read blade root weight N by pressure transducer ₁With leaf top weight N ₂

Step 5, bulged blading sequence

Step 5-1, try to achieve the ideal torque in the turbine rotor center of circle:

The center of gravity of trying to achieve the steam turbine bulged blading according to mechanics principle is to the distance L of postive stop baffle 12:

L＝(N ₁·L ₁+N ₂·L)/(N ₁+N ₂) (1)

The steam turbine bulged blading is big or small with respect to the ideal torque in the impeller center of circle:

M＝(N ₁+N ₂)·(L+R)＝m·r (2)

N wherein ₁Be blade root weight; N ₂Be leaf top weight; L can be tried to achieve by formula (1); R is the turbine rotor radius;

Step 5-2, when considering blade root to centre distance and bulged blading setting angle, try to achieve the steam turbine bulged blading with respect to the actual moment in the impeller center of circle:

$\stackrel{\→}{M_i}=m_i{r}_i{e}^{{\mathrm{i\θ}}_i}---\left(3\right)$

M wherein _iBe steam turbine bulged blading quality, m _i＞0, i=1,2 ..., n;

Step 5-3, find the solution steam turbine bulged blading sortord optimum solution:

When the remaining amount of unbalance of impeller hour, steam turbine bulged blading sortord is optimum solution, namely

$\min \left\{{\left|\right|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2\right\}---\left(4\right)$

Wherein n represents steam turbine bulged blading quantity;

Wherein

${\left|\right|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2=\underset{i,j=1}{\overset{n}{\mathrm{\Σ}}}(\stackrel{\→}{M_i},{\stackrel{\→}{M}}_j)=M^T\mathrm{\ΔM}---\left(5\right)$

Wherein

The expression inner product, M=(m ₁r ₁, m ₂r ₂..., m _nr _n) ^T, Δ=(Δ _{I, j}) _{N * n}=(cos (θ _i-θ _j)) _{N * n}

Because the angle between adjacent two blades of steam turbine is fixed, can obtain formula (6) and formula (7):

${\mathrm{\θ}}_i-{\mathrm{\θ}}_j=\frac{2\mathrm{\π}|i-j|}{n}---\left(6\right)$

Wherein: j=i+1

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{e}^{{\mathrm{i\θ}}_i}=0---\left(7\right)$

Therefore, solution formula (4) is converted into solution formula (8):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T\mathrm{\ΔM}\right\}---\left(8\right)$

Wherein ∑ is for allowing collection;

By Δ _{I, j}=(cos (θ _i-θ _j)) _{N * n}And formula (6) as can be known Δ be symmetrical Semidefinite Matrices, but have inverse matrix C, namely

Δ＝C ^TC (9)

So solution formula (8) is converted into solution formula (10):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T{C}^T\mathrm{CM}\right\}=\underset{M\∈\mathrm{\Σ}}{\min }{\left|\right|\mathrm{CM}\left|\right|}_2^2---\left(10\right)$

Wherein C is a definite matrix, only needs to determine the component m of M _ir _iBuilt-up sequence get final product;

Step 5-4, employing ant group algorithm carry out the blade optimization sequence:

The component m of step 5-4-1, initialization M _ir _iEvery paths on telergone concentration, as shown in the formula:

${\mathrm{\τ}}_{i,j}\left(0\right)=\frac{1}{\left|C\right|}---\left(11\right)$

Step 5-4-2, the component m of initialization M _ir _iBe placed on randomly on circumference n point, the circumferential point of having accessed is write taboo list;

If step 5-4-3 k (k=1,2 ... m) the component m of individual M _ir _iAlso have the not circumferential point of access, this k (k=1,2 ... m) the component m of individual M _ir _iLoca i current according to this component and probability function P _{I, j}Select the next circumferential point j that also there is no access in the value of current time, obtain formula (12):

$P_{i,j}=\left\{\begin{array}{cc}\frac{{\mathrm{\τ}}_{i,j}\left(t\right)}{\underset{l\∈T}{\mathrm{\Σ}}{\mathrm{\τ}}_{i,j}\left(t\right)},& j\∈T\\ 0,& j\∉T\end{array}\right.---\left(12\right)$

Wherein

And

The component m of L (s) expression M _ir _iThe set of point, τ _{I, j}(t) be illustrated in t constantly, the information concentration on limit (i, j) in t+1 information concentration constantly is:

Wherein W is current optimum solution, the component m of each M _ir _iFirst element assignment of W be first point; ρ _tFor the volatilization factor, get ρ herein _t=e ^-t

Successively the point of selecting is write taboo list, until all points have all been accessed;

Step 5-4-4, with C _{I, j}As path, calculating k (k=1,2 ... m) path of paths is selected the optimal path of every paths according to every paths, upgrade optimum solution according to optimal path;

Step 5-4-5, upgrade telergone concentration on each paths according to the access situation of every paths, empty taboo list;

Step 5-4-6, judge whether to satisfy termination condition, satisfy condition and finish; Do not forward step 4-2 to and again access if do not satisfy termination condition, until all access satisfactory sufficient termination condition;

Step 6, weighing common blade: bevel gear lifter 7 and the bracing frame 11 of described turbine blade weighing device are slided along guide rail 3, make bevel gear lifter 7 corresponding with the position that the steam turbine leaf pushes up, bracing frame 11 is corresponding with the position of steam turbine blade root, and the employing grating scale records the distance L between steam turbine blade root and postive stop baffle 12 ₃And the distance L between steam turbine leaf top and postive stop baffle 12 ₄, read blade root weight N by pressure transducer ₃With leaf top weight N ₄

Step 7, common blade sequence

Step 7-1, try to achieve the ideal torque in the turbine rotor center of circle:

The center of gravity of trying to achieve the steam turbine common blade according to mechanics principle to postive stop baffle 12 apart from S:

S＝(N ₃·L ₃+N ₄·S)/(N ₃+N ₄) (14)

The steam turbine common blade is big or small with respect to the ideal torque in the impeller center of circle:

M＝(N ₃+N ₄)·(S+R)＝m·r (15)

N wherein ₃Be blade root weight; N ₄Be leaf top weight; S can be tried to achieve by formula (14); R is the turbine rotor radius;

Step 7-2, when considering blade root to centre distance and common blade setting angle, try to achieve the steam turbine common blade with respect to the actual moment in the impeller center of circle:

$\stackrel{\→}{M_i}=m_i{r}_i{e}^{{\mathrm{i\θ}}_i}---\left(16\right)$

M wherein _iBe steam turbine common blade quality, m _i＞0, i=1,2,3 ... b;

Step 7-3, find the solution steam turbine common blade sortord optimum solution:

When the remaining amount of unbalance of impeller hour, steam turbine common blade sortord is optimum solution, namely

$\min \left\{{\left|\right|\underset{i=1}{\overset{b}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2\right\}---\left(17\right)$

Wherein b represents steam turbine common blade quantity;

Wherein

${\left|\right|\underset{i=1}{\overset{b}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2=\underset{i,j=1}{\overset{b}{\mathrm{\Σ}}}(\stackrel{\→}{M_i},{\stackrel{\→}{M}}_j)=M^T\mathrm{\ΔM}---\left(18\right)$

Wherein

The expression inner product, M=(m ₁r ₁, m ₂r ₂... m _br _b) ^T,

Δ＝(Δ _i，j) _b×b＝(cos(θ _i-θ _j)) _b×b；

Because the angle between adjacent two blades of steam turbine is fixed, can obtain formula (19) and formula (20):

${\mathrm{\θ}}_i-{\mathrm{\θ}}_j=\frac{2\mathrm{\π}|i-j|}{b}---\left(19\right)$

J=i+1 wherein

$\underset{i=1}{\overset{b}{\mathrm{\Σ}}}{e}^{{\mathrm{i\θ}}_i}=0---\left(20\right)$

Therefore solution formula (17) is converted into solution formula (21):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T\mathrm{\ΔM}\right\}---\left(21\right)$

Wherein ∑ is for allowing collection;

By Δ=(cos (θ _i-θ _j)) _{B * b}And formula (19) as can be known Δ be symmetrical Semidefinite Matrices, but have inverse matrix C, namely

Δ＝C ^TC (22)

So solution formula (21) is converted into solution formula (23):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T{C}^T\mathrm{CM}\right\}=\underset{M\∈\mathrm{\Σ}}{\min }{\left|\right|\mathrm{CM}\left|\right|}_2^2---\left(23\right)$

Wherein C is a definite matrix, only needs to determine the component m of M _ir _iBuilt-up sequence get final product;

Step 7-4, employing ant group algorithm carry out the blade optimization sequence:

The component m of step 7-4-1, initialization M _ir _iEvery paths on telergone concentration, as shown in the formula:

${\mathrm{\τ}}_{i,j}\left(0\right)=\frac{1}{\left|C\right|}---\left(24\right)$

Step 7-4-2, the component m of initialization M _ir _iBe placed on randomly on circumference n point, the circumferential point of having accessed is write taboo list;

If step 7-4-3 k (k=1,2 ... m) the component m of individual M _ir _iAlso have the not circumferential point of access, this k (k=1,2 ... m) the component m of individual M _ir _iLoca i current according to this component and probability function P _{I, j}Select the next circumferential point j that also there is no access in the value of current time, obtain formula (25):

$P_{i,j}=\left\{\begin{array}{cc}\frac{{\mathrm{\τ}}_{i,j}\left(t\right)}{\underset{l\∈T}{\mathrm{\Σ}}{\mathrm{\τ}}_{i,j}\left(t\right)},& j\∈T\\ 0,& j\∉T\end{array}\right.---\left(25\right)$

Wherein And

The component m of L (s) expression M _ir _iThe set of point, τ _{I, j}(t) be illustrated in t constantly, the information concentration on limit (i, j) in t+1 information concentration constantly is:

Wherein W is current optimum solution, the component m of each M _ir _iFirst element assignment of W be first point; ρ _tFor the volatilization factor, get ρ herein _t=e ^-t

Successively the point of selecting is write taboo list, until all points have all been accessed;

Step 7-4-4, with C _{I, j}As path, calculating k (k=1,2 ... m) path of paths is selected the optimal path of every paths according to every paths, upgrade optimum solution according to optimal path;

Step 7-4-5, upgrade telergone concentration on each paths according to the access situation of every paths, empty taboo list;

Step 7-4-6, judge whether to satisfy termination condition, satisfy condition and finish; Do not forward step 7-4-2 to and again access if do not satisfy termination condition, until all access satisfactory sufficient termination condition.

The invention has the beneficial effects as follows: the present invention has facilitated the blade fit-up gap reconditioning in follow-up assembling by the application to steam turbine bulged blading sequence software.Avoided due to certain regional bulged blading position too concentrate cause can't reconditioning.The present invention uses in many units, for example 300,000 kilowatts, 600,000 kilowatts overcritical, air-cooled steam turbines, and combination circulation steam turbines etc. when satisfying the unit balance, have satisfied the assembling needs of unit, and effect is good.The present invention has solved the position of bulged blading in whole circle blade in present turbine blade effectively by artificial random fixing, do not locate accurately and sort method, there is the problem of too concentrating or disperseing in assembling, easily causes the problem that to carry out reconditioning to the fit-up gap when assembling.

Description of drawings

Fig. 1 is that the turbine blade weighing device master of combination of the present invention looks cut-open view, and Fig. 2 is the vertical view of Fig. 1, and Fig. 3 is that cut-open view is looked on the left side of Fig. 1, and Fig. 4 is steam turbine bulged blading moment principle figure, and Fig. 5 is steam turbine common blade moment principle figure.

Embodiment

Embodiment one: in conjunction with Fig. 1-Fig. 5, present embodiment is described, a kind of turbine blade sort method that relates to the steam turbine bulged blading of present embodiment carries out according to following steps,

Step 1, according to the product design requirement, determine that bulged blading number and total leaf number purpose ratio that this kind product participates in sequence are A, wherein, this kind product total leaf number order is T, special vane (first and last blade, locking-blade) number is a; The number of common blade is b, b=T-n-a;

Step 2, according to the designing requirement of product, bulged blading adopts equally distributed principle arrange and determine sequence number:

Wherein, the bulged blading number is n, is obtained bulged blading number n=T * A by step 1;

, the installation site sequence number of n bulged blading on wheel disc is respectively: X1, X2, X3, X4 ... Xn,

X1＝a+1；

X2＝X1+〔(T-a)/n〕；

X3＝X2+〔(T-a)/n〕＝X1+〔2(T-a)/n〕；

Xn＝X1+〔(T-1)×(T-a)/n〕；

Draw X1, X2, X3, X4 corresponding on wheel disc ... on the Xn position, bulged blading should be installed;

Step 3, n bulged blading of above-mentioned definite installation site sequence number carried out random number;

Step 4, all bulged bladings of random number are weighed, determine when weighing that the bulged blading of random number need to be weighed by number, guarantee that namely the sequence number of weighing is consistent with fixed random number;

Weighing bulged blading: bevel gear lifter 7 and the bracing frame 11 of described turbine blade weighing device are slided along guide rail 3, make bevel gear lifter 7 corresponding with the position that the steam turbine leaf pushes up, bracing frame 11 is corresponding with the position of steam turbine blade root, and the employing grating scale records the distance L between steam turbine blade root and postive stop baffle 12 ₁And the distance L between steam turbine leaf top and postive stop baffle 12 ₂, read blade root weight N by pressure transducer ₁With leaf top weight N ₂

Step 5, bulged blading sequence

Step 5-1, try to achieve the ideal torque in the turbine rotor center of circle:

The center of gravity of trying to achieve the steam turbine bulged blading according to mechanics principle is to the distance L of postive stop baffle 12:

L＝(N ₁·L ₁+N ₂·L)/(N ₁+N ₂) (1)

The steam turbine bulged blading is big or small with respect to the ideal torque in the impeller center of circle:

M＝(N ₁+N ₂)·(L+R)＝m·r (2)

Wherein N1 is blade root weight; N ₂Be leaf top weight; L can be tried to achieve by formula (1); R is the turbine rotor radius;

Step 5-2, when considering blade root to centre distance and bulged blading setting angle, try to achieve the steam turbine bulged blading with respect to the actual moment in the impeller center of circle:

$\stackrel{\→}{M_i}=m_i{r}_i{e}^{{\mathrm{i\θ}}_i}---\left(3\right)$

M wherein _iBe steam turbine bulged blading quality, m _i＞0, i=1,2 ..., n;

Step 5-3, find the solution steam turbine bulged blading sortord optimum solution:

When the remaining amount of unbalance of impeller hour, steam turbine bulged blading sortord is optimum solution, namely

$\min \left\{{\left|\right|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2\right\}---\left(4\right)$

Wherein n represents steam turbine bulged blading quantity;

Wherein

${\left|\right|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2=\underset{i,j=1}{\overset{n}{\mathrm{\Σ}}}(\stackrel{\→}{M_i},{\stackrel{\→}{M}}_j)=M^T\mathrm{\ΔM}---\left(5\right)$

Wherein

The expression inner product, M=(m ₁r ₁, m ₂r ₂..., m _nr _n) ^T, Δ=(Δ _{I, j}) _{N * n}=(cos (θ _i-θ _j)) _{N * n}

Because the angle between adjacent two blades of steam turbine is fixed, can obtain formula (6) and formula (7):

${\mathrm{\θ}}_i-{\mathrm{\θ}}_j=\frac{2\mathrm{\π}|i-j|}{n}---\left(6\right)$

Wherein: j=i+1

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{e}^{{\mathrm{i\θ}}_i}=0---\left(7\right)$

Therefore, solution formula (4) is converted into solution formula (8):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T\mathrm{\ΔM}\right\}---\left(8\right)$

Wherein ∑ is for allowing collection;

By Δ _{I, j}=(cos (θ _i-θ _j)) _{N * n}And formula (6) as can be known Δ be symmetrical Semidefinite Matrices, but have inverse matrix C, namely

Δ＝C ^TC (9)

So solution formula (8) is converted into solution formula (10):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T{C}^T\mathrm{CM}\right\}=\underset{M\∈\mathrm{\Σ}}{\min }{\left|\right|\mathrm{CM}\left|\right|}_2^2---\left(10\right)$

Wherein C is a definite matrix, only needs to determine the component m of M _ir _iBuilt-up sequence get final product;

Step 5-4, employing ant group algorithm carry out the blade optimization sequence:

The component m of step 5-4-1, initialization M _ir _iEvery paths on telergone concentration, as shown in the formula:

${\mathrm{\τ}}_{i,j}\left(0\right)=\frac{1}{\left|C\right|}---\left(11\right)$

Step 5-4-2, the component m of initialization M _ir _iBe placed on randomly on circumference n point, the circumferential point of having accessed is write taboo list;

If step 5-4-3 k (k=1,2 ... m) the component m of individual M _ir _iAlso have the not circumferential point of access, this k (k=1,2 ... m) the component m of individual M _ir _iLoca i current according to this component and probability function P _{I, j}Select the next circumferential point j that also there is no access in the value of current time, obtain formula (12):

$P_{i,j}=\left\{\begin{array}{cc}\frac{{\mathrm{\τ}}_{i,j}\left(t\right)}{\underset{l\∈T}{\mathrm{\Σ}}{\mathrm{\τ}}_{i,j}\left(t\right)},& j\∈T\\ 0,& j\∉T\end{array}\right.---\left(12\right)$

Wherein

And

The component m of L (s) expression M _ir _iThe set of point, τ _{I, j}(t) be illustrated in t constantly, the information concentration on limit (i, j) in t+1 information concentration constantly is:

Wherein W is current optimum solution, the component m of each M _ir _iFirst element assignment of W be first point; ρ _tFor the volatilization factor, get ρ herein _t=e ^-t

Successively the point of selecting is write taboo list, until all points have all been accessed;

Step 5-4-4, with C _{I, j}As path, calculating k (k=1,2 ... m) path of paths is selected the optimal path of every paths according to every paths, upgrade optimum solution according to optimal path;

Step 5-4-5, upgrade telergone concentration on each paths according to the access situation of every paths, empty taboo list;

Step 5-4-6, judge whether to satisfy termination condition, satisfy condition and finish; Do not forward step 4-2 to and again access if do not satisfy termination condition, until all access satisfactory sufficient termination condition;

Step 6, weighing common blade: bevel gear lifter 7 and the bracing frame 11 of described turbine blade weighing device are slided along guide rail 3, make bevel gear lifter 7 corresponding with the position that the steam turbine leaf pushes up, bracing frame 11 is corresponding with the position of steam turbine blade root, and the employing grating scale records the distance L between steam turbine blade root and postive stop baffle 12 ₃And the distance L between steam turbine leaf top and postive stop baffle 12 ₄, read blade root weight N by pressure transducer ₃With leaf top weight N ₄

Step 7, common blade sequence

Step 7-1, try to achieve the ideal torque in the turbine rotor center of circle:

The center of gravity of trying to achieve the steam turbine common blade according to mechanics principle to postive stop baffle 12 apart from S:

S＝(N ₃·L ₃+N ₄·S)/(N ₃+N ₄) (14)

The steam turbine common blade is big or small with respect to the ideal torque in the impeller center of circle:

M＝(N ₃+N ₄)·(S+R)＝m·r (15)

N wherein ₃Be blade root weight; N ₄Be leaf top weight; S can be tried to achieve by formula (14); R is the turbine rotor radius;

Step 7-2, when considering blade root to centre distance and common blade setting angle, try to achieve the steam turbine common blade with respect to the actual moment in the impeller center of circle:

$\stackrel{\→}{M_i}=m_i{r}_i{e}^{{\mathrm{i\θ}}_i}---\left(16\right)$

M wherein _iBe steam turbine common blade quality, m _i＞0, i=1,2,3 ... b;

Step 7-3, find the solution steam turbine common blade sortord optimum solution:

When the remaining amount of unbalance of impeller hour, steam turbine common blade sortord is optimum solution, namely

$\min \left\{{\left|\right|\underset{i=1}{\overset{b}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2\right\}---\left(17\right)$

Wherein b represents steam turbine common blade quantity;

Wherein

${\left|\right|\underset{i=1}{\overset{b}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2=\underset{i,j=1}{\overset{b}{\mathrm{\Σ}}}(\stackrel{\→}{M_i},{\stackrel{\→}{M}}_j)=M^T\mathrm{\ΔM}---\left(18\right)$

Wherein

The expression inner product, M=(m ₁r ₁, m ₂r ₂... m _br _b) ^T,

Δ＝(Δ _i，j) _b×b＝(cos(θ _i-θ _j)) _b×b；

Because the angle between adjacent two blades of steam turbine is fixed, can obtain formula (19) and formula (20):

${\mathrm{\θ}}_i-{\mathrm{\θ}}_j=\frac{2\mathrm{\π}|i-j|}{b}---\left(19\right)$

J=i+1 wherein

$\underset{i=1}{\overset{b}{\mathrm{\Σ}}}{e}^{{\mathrm{i\θ}}_i}=0---\left(20\right)$

Therefore solution formula (17) is converted into solution formula (21):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T\mathrm{\ΔM}\right\}---\left(21\right)$

Wherein ∑ is for allowing collection;

By Δ=(cos (θ _i-θ _j)) _{B * b}And formula (19) as can be known Δ be symmetrical Semidefinite Matrices, but have inverse matrix C, namely

Δ＝C ^TC (22)

So solution formula (21) is converted into solution formula (23):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T{C}^T\mathrm{CM}\right\}=\underset{M\∈\mathrm{\Σ}}{\min }{\left|\right|\mathrm{CM}\left|\right|}_2^2---\left(23\right)$

Wherein C is a definite matrix, only needs to determine the component m of M _ir _iBuilt-up sequence get final product;

Step 7-4, employing ant group algorithm carry out the blade optimization sequence:

The component m of step 7-4-1, initialization M _ir _iEvery paths on telergone concentration, as shown in the formula:

${\mathrm{\τ}}_{i,j}\left(0\right)=\frac{1}{\left|C\right|}---\left(24\right)$

Step 7-4-2, the component m of initialization M _ir _iBe placed on randomly on circumference n point, the circumferential point of having accessed is write taboo list;

If step 7-4-3 k (k=1,2 ... m) the component m of individual M _ir _iAlso have the not circumferential point of access, this k (k=1,2 ... m) the component m of individual M _ir _iLoca i current according to this component and probability function P _{I, j}Select the next circumferential point j that also there is no access in the value of current time, obtain formula (25):

$P_{i,j}=\left\{\begin{array}{cc}\frac{{\mathrm{\τ}}_{i,j}\left(t\right)}{\underset{l\∈T}{\mathrm{\Σ}}{\mathrm{\τ}}_{i,j}\left(t\right)},& j\∈T\\ 0,& j\∉T\end{array}\right.---\left(25\right)$

Wherein

And

The component m of L (s) expression M _ir _iThe set of point, τ _{I, j}(t) be illustrated in t constantly, the information concentration on limit (i, j) in t+1 information concentration constantly is:

Wherein W is current optimum solution, the component m of each M _ir _iFirst element assignment of W be first point; ρ _tFor the volatilization factor, get ρ herein _t=e ^-t

Successively the point of selecting is write taboo list, until all points have all been accessed;

Step 7-4-4, with C _{I, j}As path, calculating k (k=1,2 ... m) path of paths is selected the optimal path of every paths according to every paths, upgrade optimum solution according to optimal path;

Step 7-4-5, upgrade telergone concentration on each paths according to the access situation of every paths, empty taboo list;

Step 7-4-6, judge whether to satisfy termination condition, satisfy condition and finish; Do not forward step 7-4-2 to and again access if do not satisfy termination condition, until all access satisfactory sufficient termination condition.

For fear of being absorbed in locally optimal solution, if optimum solution has continued repeatedly not upgraded, carry out a M component miri seek the footpath, find the current optimum solution of rear renewal and pheromones, then begin the circulation of a new round; When the number of times of circulation when reaching regulation or the component m of all M _ir _iWhen all having selected same path mode or the component m of special M _ir _iThe number of times of rollback arrives when requiring or the component m of special M _ir _iWhen the path of finding equaled current optimum solution, whole program stopped.

the weighing device of present embodiment institute combination comprises worktable 1, pallet 8, tray rack 9, bracing frame 11, postive stop baffle 12, platen 14, bevel gear lifter 7, the first steel plate 23, the second steel plate 25, two guide rails 3, two bridge type weighing sensors 10, two position-adjustable tightening handles 21, two limited blocks 22 and a plurality of slide block 24, described platen 14 is arranged on the upper surface of worktable 1, described two guide rails 3 are set in parallel on the upper surface of platen 14 along the length direction of worktable 1, the lower surface of described the first steel plate 23 is arranged on two guide rails 3 by slide block 24, the middle part of described the first steel plate 23 upper surfaces is provided with boss 23-1, a sensor in two bridge type weighing sensors 10 is horizontally disposed with and an end is packed on boss 23-1, described bevel gear lifter 7 is packed on the upper surface of the described sensor other end, described tray rack 9 is packed on the upper surface of bevel gear lifter 7, described pallet 8 is positioned on the upper surface of tray rack 9, the lower surface of described the second steel plate 25 is arranged on two guide rails 3 by slide block 24, by the remainder in two bridge type weighing sensors 10 one of support frame as described above 11 is packed on the upper surface of the second steel plate 25, described postive stop baffle 12 is packed on the upper surface of platen 14 1 ends, described postive stop baffle 12 is positioned on the same end of platen 14 with bracing frame 11, be fixed with a limited block 22 on the lower surface of every block plate 23, a position-adjustable tightening handle 21 is installed on each limited block 22, each limited block 22 is locked on guide rail 3 by the position-adjustable tightening handle 21 of correspondence, length direction along worktable on described worktable 1 has groove 1-1.

described bevel gear lifter 7 comprises interior sinuate handwheel 16, bearing 19, bearing seat 20, turbine 25, worm screw 26, transmission shaft 27, conical gear 28 and housing 29 consist of, described bearing seat 20 is packed on housing 29, described bearing is arranged on bearing seat 20, described turbine 25 and conical gear 28 all are positioned at housing 29, described turbine 25 is arranged on the upper surface at housing 29 bottom centre places, the upper end of described worm screw 26 is passed the bottom face of housing 29 from the bottom to top successively, the upper surface of turbine 25 and housing 29 and tray rack 9 are affixed, described transmission shaft 27 is arranged on housing 29 by bearing 19, sidewall and conical gear 28 that one end of described transmission shaft 27 passes housing 29 fix as one, described conical gear 28 is meshed with turbine 25, described interior sinuate handwheel 16 is arranged on the other end of transmission shaft 27, groove 1-1 is passed in the lower end of described worm screw 26.

Described bevel gear lifter 7 also comprises bearing cap 18, and described bearing cap is packed on bearing seat 20.

Described weighing device also comprises fixing and locking handle 30, and described fixing and locking handle 30 is arranged on tray rack 9.

In actual moving process at the scene, when a lot of impeller is arranged, when installing according to being designed with of impeller may needs fixed part blade at the assigned address of turbine rotor.

The resolution of two bridge type weighing sensors 10 of present embodiment is 0.6g, through repeating the requirement of satisfied≤4g/60kg fully of weighing measuring accuracy;

The distance measuring sensor resolution of grating scale is 0.05mm, through the requirement of satisfied≤1mm/2200mm fully of duplicate measurements measuring accuracy;

Bracing frame 11 is adjustable with bevel gear lifter 7 centre distance, and namely steam turbine root locating device and steam turbine top locating device centre distance can realize minimum spacing 50mm, guarantees that short blade can measure;

Root locating device and top locating device all can and can lock along the guide rail transverse shifting.

Can draw through experimental result, in long-time actual measurement process at the scene, for the various actual conditions at scene, ant group algorithm all can find the sortord of an optimization, and the remaining amount of unbalance of the impeller that finally draws is far below original typical set value; The advantages such as the fast convergence rate of ant group algorithm, operation result are stable have all obtained embodiment.And due to the characteristics such as distributed controlled, self-organization of ant group algorithm, can also satisfy fixed blade in rig-site utilization, replace the specific (special) requirements such as blade.

Claims (1)

1. turbine blade sort method that relates to the steam turbine bulged blading, it is characterized in that: described sort method carries out according to following steps:

Step 1, according to the product design requirement, determine that bulged blading number and total leaf number purpose ratio that this kind product participates in sequence are A, wherein, this kind product total leaf number order is T, special vane (first and last blade, locking-blade) number is a; The number of common blade is b, b=T-n-a;

Step 2, according to the designing requirement of product, bulged blading adopts equally distributed principle arrange and determine sequence number:

Wherein, the bulged blading number is n, is obtained bulged blading number n=T * A by step 1;

, the installation site sequence number of n bulged blading on wheel disc is respectively: X1, X2, X3, X4 ... Xn,

X1＝a+1；

X2＝X1+〔(T-a)/n〕；

X3＝X2+〔(T-a)/n〕＝X1+〔2(T-a)/n〕；

Xn＝X1+〔(T-1)×(T-a)/n〕；

Draw X1, X2, X3, X4 corresponding on wheel disc ... on the Xn position, bulged blading should be installed;

Step 3, n bulged blading of above-mentioned definite installation site sequence number carried out random number;

Step 4, all bulged bladings of random number are weighed, determine when weighing that the bulged blading of random number need to be weighed by number, guarantee that namely the sequence number of weighing is consistent with fixed random number;

Weighing bulged blading: bevel gear lifter (7) and the bracing frame (11) of described turbine blade weighing device are slided along guide rail (3), make bevel gear lifter (7) corresponding with the position that the steam turbine leaf pushes up, bracing frame (11) is corresponding with the position of steam turbine blade root, and the employing grating scale records the distance (L between steam turbine blade root and postive stop baffle (12) ₁) and steam turbine leaf top and postive stop baffle (12) between distance (L ₂), read blade root weight (N by pressure transducer ₁) and leaf top weight (N ₂);

Step 5, bulged blading sequence

Step 5-1, try to achieve the ideal torque in the turbine rotor center of circle:

The center of gravity of trying to achieve the steam turbine bulged blading according to mechanics principle is to the distance (L) of postive stop baffle (12):

L＝(N ₁·L ₁+N ₂·L)/(N ₁+N ₂) (1)

The steam turbine bulged blading is big or small with respect to the ideal torque in the impeller center of circle:

M＝(N ₁+N ₂)·(L+R)＝m·r (2)

N wherein ₁Be blade root weight; N ₂Be leaf top weight; L can be tried to achieve by formula (1); R is the turbine rotor radius;

Step 5-2, when considering blade root to centre distance and bulged blading setting angle, try to achieve the steam turbine bulged blading with respect to the actual moment in the impeller center of circle:

$\stackrel{\→}{M_i}=m_i{r}_i{e}^{{\mathrm{i\θ}}_i}---\left(3\right)$

M wherein _iBe steam turbine bulged blading quality, m _i＞0, i=1,2 ..., n;

Step 5-3, find the solution steam turbine bulged blading sortord optimum solution:

When the remaining amount of unbalance of impeller hour, steam turbine bulged blading sortord is optimum solution, namely

$\min \left\{{\left|\right|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2\right\}---\left(4\right)$

Wherein n represents steam turbine bulged blading quantity;

Wherein

${\left|\right|\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2=\underset{i,j=1}{\overset{n}{\mathrm{\Σ}}}(\stackrel{\→}{M_i},{\stackrel{\→}{M}}_j)=M^T\mathrm{\ΔM}---\left(5\right)$

Wherein The expression inner product, M=(m ₁r ₁, m ₂r ₂..., m _nr _n) ^T, Δ=(Δ _{I, j}) _{N * n}=(cos (θ _i-θ _j)) _{N * n}

Because the angle between adjacent two blades of steam turbine is fixed, can obtain formula (6) and formula (7):

${\mathrm{\θ}}_i-{\mathrm{\θ}}_j=\frac{2\mathrm{\π}|i-j|}{n}---\left(6\right)$

Wherein: j=i+1

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{e}^{{\mathrm{i\θ}}_i}=0---\left(7\right)$

Therefore, solution formula (4) is converted into solution formula (8):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T\mathrm{\ΔM}\right\}---\left(8\right)$

Wherein ∑ is for allowing collection;

By Δ _{I, j}=(cos (θ _i-θ _j)) _{N * n}And formula (6) as can be known Δ be symmetrical Semidefinite Matrices, but have inverse matrix C, namely

Δ＝C ^TC (9)

So solution formula (8) is converted into solution formula (10):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T{C}^T\mathrm{CM}\right\}=\underset{M\∈\mathrm{\Σ}}{\min }{\left|\right|\mathrm{CM}\left|\right|}_2^2---\left(10\right)$

Wherein C is a definite matrix, only needs to determine the component m of M _ir _iBuilt-up sequence get final product;

Step 5-4, employing ant group algorithm carry out the blade optimization sequence:

The component m of step 5-4-1, initialization M _ir _iEvery paths on telergone concentration, as shown in the formula:

${\mathrm{\τ}}_{i,j}\left(0\right)=\frac{1}{\left|C\right|}---\left(11\right)$

Step 5-4-2, the component m of initialization M _ir _iBe placed on randomly on circumference n point, the circumferential point of having accessed is write taboo list;

If step 5-4-3 k (k=1,2 ... m) the component m of individual M _ir _iAlso have the not circumferential point of access, this k (k=1,2 ... m) the component m of individual M _ir _iLoca i current according to this component and probability function P _{I, j}Select the next circumferential point j that also there is no access in the value of current time, obtain formula (12):

$P_{i,j}=\left\{\begin{array}{cc}\frac{{\mathrm{\τ}}_{i,j}\left(t\right)}{\underset{l\∈T}{\mathrm{\Σ}}{\mathrm{\τ}}_{i,j}\left(t\right)},& j\∈T\\ 0,& j\∉T\end{array}\right.---\left(12\right)$

Wherein And The component m of L (s) expression M _ir _iThe set of point, τ _{I, j}(t) be illustrated in t constantly, the information concentration on limit (i, j) in t+1 information concentration constantly is:

Wherein W is current optimum solution, the component m of each M _ir _iFirst element assignment of W be first point; ρ _tFor the volatilization factor, get ρ herein _t=e ^-t

Successively the point of selecting is write taboo list, until all points have all been accessed;

Step 5-4-4, with C _{I, j}As path, calculating k (k=1,2 ... m) path of paths is selected the optimal path of every paths according to every paths, upgrade optimum solution according to optimal path;

Step 5-4-5, upgrade telergone concentration on each paths according to the access situation of every paths, empty taboo list;

Step 5-4-6, judge whether to satisfy termination condition, satisfy condition and finish; Do not forward step 4-2 to and again access if do not satisfy termination condition, until all access satisfactory sufficient termination condition;

Step 6, weighing common blade: bevel gear lifter (7) and the bracing frame (11) of described turbine blade weighing device are slided along guide rail (3), make bevel gear lifter (7) corresponding with the position that the steam turbine leaf pushes up, bracing frame (11) is corresponding with the position of steam turbine blade root, and the employing grating scale records the distance (L between steam turbine blade root and postive stop baffle (12) ₃) and steam turbine leaf top and postive stop baffle (12) between distance (L ₄), read blade root weight (N by pressure transducer ₃) and leaf top weight (N ₄);

Step 7, common blade sequence

Step 7-1, try to achieve the ideal torque in the turbine rotor center of circle:

The center of gravity of trying to achieve the steam turbine common blade according to mechanics principle is to the distance (S) of postive stop baffle (12):

S＝(N ₃·L ₃+N ₄·S)/(N ₃+N ₄) (14)

The steam turbine common blade is big or small with respect to the ideal torque in the impeller center of circle:

M＝(N ₃+N ₄)·(S+R)＝m·r (15)

N wherein ₃Be blade root weight; N ₄Be leaf top weight; S can be tried to achieve by formula (14); R is the turbine rotor radius;

Step 7-2, when considering blade root to centre distance and common blade setting angle, try to achieve the steam turbine common blade with respect to the actual moment in the impeller center of circle:

$\stackrel{\→}{M_i}=m_i{r}_i{e}^{{\mathrm{i\θ}}_i}---\left(16\right)$

M wherein _iBe steam turbine common blade quality, m _i＞0, i=1,2,3 ... b;

Step 7-3, find the solution steam turbine common blade sortord optimum solution:

When the remaining amount of unbalance of impeller hour, steam turbine common blade sortord is optimum solution, namely

$\min \left\{{\left|\right|\underset{i=1}{\overset{b}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2\right\}---\left(17\right)$

Wherein b represents steam turbine common blade quantity;

Wherein

${\left|\right|\underset{i=1}{\overset{b}{\mathrm{\Σ}}}\stackrel{\→}{M_i}\left|\right|}^2=\underset{i,j=1}{\overset{b}{\mathrm{\Σ}}}(\stackrel{\→}{M_i},{\stackrel{\→}{M}}_j)=M^T\mathrm{\ΔM}---\left(18\right)$

Wherein

The expression inner product, M=(m ₁r ₁, m ₂r ₂... m _br _b) ^T,

Δ＝(Δ _i，j) _b×b＝(cos(θ _i-θ _j)) _b×b；

Because the angle between adjacent two blades of steam turbine is fixed, can obtain formula (19) and formula (20):

${\mathrm{\θ}}_i-{\mathrm{\θ}}_j=\frac{2\mathrm{\π}|i-j|}{b}---\left(19\right)$

J=i+1 wherein

$\underset{i=1}{\overset{b}{\mathrm{\Σ}}}{e}^{{\mathrm{i\θ}}_i}=0---\left(20\right)$

Therefore solution formula (17) is converted into solution formula (21):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T\mathrm{\ΔM}\right\}---\left(21\right)$

Wherein ∑ is for allowing collection;

By Δ=(cos (θ _i-θ _j)) _{B * b}And formula (19) as can be known Δ be symmetrical Semidefinite Matrices, but have inverse matrix C, namely

Δ＝C ^TC (22)

So solution formula (21) is converted into solution formula (23):

$\underset{M\∈\mathrm{\Σ}}{\min }\left\{M^T{C}^T\mathrm{CM}\right\}=\underset{M\∈\mathrm{\Σ}}{\min }{\left|\right|\mathrm{CM}\left|\right|}_2^2---\left(23\right)$

Wherein C is a definite matrix, only needs to determine the component m of M _ir _iBuilt-up sequence get final product;

Step 7-4, employing ant group algorithm carry out the blade optimization sequence:

The component m of step 7-4-1, initialization M _ir _iEvery paths on telergone concentration, as shown in the formula:

${\mathrm{\τ}}_{i,j}\left(0\right)=\frac{1}{\left|C\right|}---\left(24\right)$

Step 7-4-2, the component m of initialization M _ir _iBe placed on randomly on circumference n point, the circumferential point of having accessed is write taboo list;

If step 7-4-3 k (k=1,2 ... m) the component m of individual M _ir _iAlso have the not circumferential point of access, this k (k=1,2 ... m) the component m of individual M _ir _iLoca i current according to this component and probability function P _{I, j}Select the next circumferential point j that also there is no access in the value of current time, obtain formula (25):

$P_{i,j}=\left\{\begin{array}{cc}\frac{{\mathrm{\τ}}_{i,j}\left(t\right)}{\underset{l\∈T}{\mathrm{\Σ}}{\mathrm{\τ}}_{i,j}\left(t\right)},& j\∈T\\ 0,& j\∉T\end{array}\right.---\left(25\right)$

Wherein And

The component m of L (s) expression M _ir _iThe set of point, τ _{I, j}(t) be illustrated in t constantly, the information concentration on limit (i, j) in t+1 information concentration constantly is:

Wherein W is current optimum solution, the component m of each M _ir _iFirst element assignment of W be first point; ρ _tFor the volatilization factor, get ρ herein _t=e ^-t

Successively the point of selecting is write taboo list, until all points have all been accessed;

Step 7-4-4, with C _{I, j}As path, calculating k (k=1,2 ... m) path of paths is selected the optimal path of every paths according to every paths, upgrade optimum solution according to optimal path;

Step 7-4-5, upgrade telergone concentration on each paths according to the access situation of every paths, empty taboo list;

Step 7-4-6, judge whether to satisfy termination condition, satisfy condition and finish; Do not forward step 7-4-2 to and again access if do not satisfy termination condition, until all access satisfactory sufficient termination condition.

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