CN102778335A - Anisotropic rotor holographic dynamic balancing method based on equivalent initial phase vector - Google Patents

Abstract

The invention discloses an anisotropic rotor holographic dynamic balancing method based on equivalent initial phase vector. According to the method, the holographic spectrum principle is taken as the basis, vibration data in two directions are taken into account and are subjected to data fusion, so the anisotropic characteristic can be completely formulated, and the balance fault diagnosis is facilitated; furthermore, the rule of angular momentum conservation is utilized, a holographic spectrum ellipse is converted into an equivalent rotating frequency circle, the equivalent initial phase vector is taken as the characteristic for unbalanced vibration, and the requirement on fine balance is met. Through the equivalent initial phase vector, the defects of traditional initial phase vector on describing the amplitude of unbalance and phase position caused by anisotropy can be eliminated, the unbalance characteristic can be accurately characterized, and the spatial dynamic property of a rotor can be truly indicated. Therefore, the anisotropic rotor holographic dynamic balancing method based on the equivalent initial phase vector, provided by the invention, facilitates improving the accuracy and efficiency of on-site dynamic balance, so that the operating precision and service life of a rotary machine can be effectively improved and prolonged.

Description

A kind of anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase

Technical field

The invention belongs to rotary machinery fault diagnosis and control technology field, relate to a kind of anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase.

Background technology

Common single vibration of employing of tradition dynamic balance method or displacement transducer obtain the vibration information of rotor, and carry out balance identification based on the signal of this sensor.For isotropic rotor-bearing arrangement, its vibration signal along the circumferential direction is consistent, and single-sensor can reflect the rotor oscillation state well.Therefore, traditional dynamic balance method based on single-sensor often just can be obtained gratifying effect.

Yet rotor-bearing arrangement is after operation after a while, and the rigidity of its bearing and damping generally all are anisotropy.Also possibly there is structural anisotropy or the like in rotor itself because the main moments of inertia does not in a circumferential direction wait in addition.Obviously, for this type support stiffness had certain anisotropic rotor, the folk prescription in rotor measurement cross section can not accurately be described the rotor oscillation state to vibration.In fact, receive that support stiffness is anisotropic to be influenced, the commentaries on classics of rotor orbit of shaft center frequently be an ellipse, must consider the orbit of shaft center of rotor precession when rotor is carried out the high precision transient equilibrium.Therefore, industry spot often adopts the vertically arranged mode of dual sensor to realize the comprehensive monitoring to each rotor measurement cross section vibration information.

Holographic spectral technology is through the vibration information at the integrated both direction of frequency domain; Utilize the spectrogram or the orbit of shaft center that form to describe the rotor oscillation state; Because holographic spectrum is at data Layer information to be merged, thus to integrated signal and the process of data fusion strict requirement is arranged.Holographic spectrum has taken into full account the influence of the anisotropy of support stiffness to orbit of shaft center, can be used for rotor fault diagnosis in early stage and judge.The holographic dynamic balance technology is based on the on-line dynamic balancing technology of holographic spectrum, and it vows to be the balance target with the first phase in the holographic spectral technology, can be oval through monitoring first phase point and power frequency, judge whether the rotor unbalance state changes, and calculate unbalance vector.

Characterize unbalance response though holographic dynamic balance method is vowed with first phase, still find the solution amount of unbalance in essence based on the vector feedback principle.And utilize the vector feedback principle need satisfy certain condition precedent; Be the balance target want and amount of unbalance between satisfy linear relationship; The size and the relation of being in proportion of amount of unbalance that this first phase that just requires to characterize unbalance response is vowed, the phase place of first phase arrow and the phase differential between the unbalance phase place remain unchanged.Yet first phase only vows when rotor shows as isotropy, and the linear relationship between it and the amount of unbalance is just set up, and when the rotor anisotropy, this relation can not satisfy, and therefore, traditional first phase vows that there is certain defective in the description to unbalance response.

Summary of the invention

The problem that the present invention solves is to provide a kind of anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase; Vow as unbalance vibration sign amount with equivalent first phase; The equivalence first phase vow with the rotor imbalance amount between have strict and clear and definite linear relationship, can avoid utilizing in the traditional holography spectrum transient equilibrium theory changeing frequently oval first phase and vowing defective as unbalance vibration sign amount existence.

The present invention realizes through following technical scheme:

A kind of anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase is vowed EIPV as unbalance vibration sign amount with equivalent first phase, and is following for the equilibrium step of anisotropic rotor under the imbalance state:

1) after the selection vibration signal is measured face and phase discrimination signal measurement face, starts rotor, gather the two-way original vibration signal on the mutual vertical direction in measurement cross section under the rotor balancing rotating speed;

2) utilize the phase demodulation sign as phase reference, extract the power frequency composition of two-way vibration signal, carry out spectrum analysis and extract power frequency vibration, change oval frequently based on holographic spectral technology structure;

3) ellipse is composed in holography and converted into equivalence commentaries on classics circle frequently,, calculate the equivalent radius of a circle r frequently that changes according to oval major semi-axis a and the minor semi-axis b of holography spectrum ₀, and as with original uneven U ₀The pairing initial equivalent first phase of state is vowed EIPV ₀Amplitude;

4) change radius of circle adjustment frequently according to equivalence and change elliptic equation frequently, obtain the phase place ∠ EIPV that equivalent first phase is vowed ₀, in conjunction with r ₀, obtain initial equivalent first phase and vow:

EIPV ₀=r ₀∠EIPV ₀；

5) the counterweight face is set on rotor, confirms to add on the counterweight face size and the direction of test mass to add test mass W according to the rotor oscillation situation _TAfterwards once more according to step 1)～3) operation, obtain rotor and add test mass unbalance response afterwards, and frequency radius of circle r is changeed in equivalence after calculating the interpolation test mass ₁

6) the frequently oval first phase of the commentaries on classics of the rotor before and after the test mass is vowed IPV ₀, IPV ₁Being converted into equivalence according to conservation of angular momentum principle respectively changes on the frequency circle, and calculates equivalence based on this and change the amount of unbalance angle changes delta γ on the frequency circle;

7) change radius of circle r frequently according to equivalence after adding test mass ₁Obtain adding behind the test mass equivalent first phase with amount of unbalance angle changes delta γ and vow EIPV ₁, its amplitude is r ₁, phase place is ∠ EIPV ₀+ Δ γ;

8), calculate the original unbalance U of rotor according to the principle of vector feedback equalization ₀, unloading test mass W _T, add counterweight W _C=-U ₀

9) test adds the rotor oscillation data after the counterweight, if the balance requirement is satisfied in rotor oscillation, then the rotor balancing operation is accomplished; Require to judge further then whether imbalance is the leading factor that causes vibration if do not satisfy balance, if repeating step 1 then)～8), carry out fine equilibrium and satisfy the balance requirement until rotor oscillation.

Described initial equivalent first phase is vowed EIPV ₀Be calculated as:

1) changes oval frequently according to holography spectrum dynamic balancing technique structure; Utilize elliptic motion to convert the identical uniform circular motion of vibrational energy into; Thereby ellipse is composed in holography converted into equivalence commentaries on classics circle frequently,, calculate the equivalent radius of a circle r frequently that changes according to oval major semi-axis a and the minor semi-axis b of holography spectrum ₀, and the amplitude of vowing as initial equivalent first phase:

$r_0=\sqrt{\mathrm{ab}}=\sqrt{c_x{s}_y-s_x{c}_y}$

Obtaining equivalence commentaries on classics radius of a circle r frequently ₀After, be the center of circle with the true origin, draw out equivalence and change circle frequently;

2) radius of circle r is frequently changeed in equivalence ₀Be set to change the constant term of expression amplitude in the elliptical configuration function frequently, and be benchmark, set up equivalence and change circle parametric equation frequently with the phase information of a certain direction sensor:

$\left\{\begin{array}{c}{x}_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β}+\mathrm{\π}/2)\\ y_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β})\end{array}\right.$

3) find the solution equivalence change equation of a circle frequently just, the cosine term coefficient:

$s_{\mathrm{ex}}=-\sqrt{\mathrm{ab}}\sin \mathrm{\β},$ $c_{\mathrm{ex}}=\sqrt{\mathrm{ab}}\cos \mathrm{\β}$

$s_{\mathrm{ey}}=\sqrt{\mathrm{ab}}\cos \mathrm{\β},$ $c_{\mathrm{ey}}=\sqrt{\mathrm{ab}}\sin \mathrm{\β}$

4) basis is just, the cosine term coefficient obtains equivalence changes the matrix of coefficients EH and the first phase point EIPP of circle frequently:

$\left\{\begin{array}{c}\mathrm{EH}=\left[\begin{array}{cccc}{s}_{\mathrm{ex}}& c_{\mathrm{ex}}& s_{\mathrm{ey}}& c_{\mathrm{ey}}\end{array}\right]\\ \mathrm{EIPP}=(c_{\mathrm{ex}},c_{\mathrm{ey}})\end{array}\right.$

With the true origin is the equivalent commentaries on classics center of circle of circle frequently, and according to matrix number EH and first phase point EIPP, equivalence commentaries on classics frequency circle and equivalent first phase point are confirmed by unique, thereby confirmed equivalent first phase arrow EIPV ₀

Described imbalance is measured being calculated as of changes delta γ:

1) change oval frequently according to holographic spectral technology structure, the frequently oval first phase of commentaries on classics that obtains the test mass front and back is vowed IPV ₀, IPV ₁, and both are plotted in IPV ₀On the pairing commentaries on classics frequency ellipse, obtain both angle Δ δ=δ ₂-δ ₁

2) based on changeing oval frequently, find the solution from first phase and vow IPV ₀Beginning is until IPV ₁Inswept area S1;

3) with r ₀Be radius, draw equivalence and change circle frequently, keep IPV ₀Phase invariant, it is transplanted to equivalence changes frequently on the circle, obtain IPV ₀';

4), draw IPV on the circle frequently in the equivalence commentaries on classics according to conservation of angular momentum principle ₁', make from IPV ₀' begin until IPV ₁' inswept area S2=S1;

5) find the solution IPV ₀' and IPV ₁' between angle Δ γ:

$\mathrm{\Δ\γ}=\arctan \left(\frac{a}{b}\tan {\mathrm{\δ}}_2\right)-\arctan \left(\frac{a}{b}\tan {\mathrm{\δ}}_1\right).$

Describedly change frequently according to holographic spectral technology structure that ellipse is:

If rotor has n carrying plane, the commentaries on classics on i bearing cross section is oval frequently by sine term coefficient [sx _i, sy _i] and cosine term coefficient [cx _i, cy _i] decision:

$\left\{\begin{array}{c}{x}_i=A_{\mathrm{xi}}\sin (\mathrm{\Ωt}+{\mathrm{\α}}_i)=s_{\mathrm{xi}}\sin \left(\mathrm{\Ωt}\right)+c_{\mathrm{xi}}\cos \left(\mathrm{\Ωt}\right)\\ y_i=A_{\mathrm{yi}}\sin (\mathrm{\Ωt}+{\mathrm{\β}}_i)=s_{\mathrm{yi}}\sin \left(\mathrm{\Ωt}\right)+c_{\mathrm{yi}}\cos \left(\mathrm{\Ωt}\right)\end{array}\right.$

Then long axis of ellipse a and minor axis b are respectively:

$\left\{\begin{array}{c}a=\frac{1}{2}\·(\sqrt{p+q}+\sqrt{p-q})\\ b=\frac{1}{2}\·(\sqrt{p+q}-\sqrt{p-q})\end{array}\right.$

Wherein, $p=s_x^2+c_x^2+s_y^2+c_y^2,$ Q=2c _xs _y-2s _xc _y

Compared with prior art, the present invention has following beneficial technical effects:

1. the rotor dynamic balancing method of vowing based on equivalent first phase is the basis with holographic spectral theory, has considered the vibration data of both direction, and it is carried out data fusion, and ability complete expression anisotropic character is beneficial to the balancing fault diagnosis;

2. the rotor dynamic balancing method of vowing based on equivalent first phase is utilized the principle of the conservation of angular momentum, has eliminated anisotropy traditional first phase is vowed in the defective of describing amount of unbalance amplitude and phase place, can accurately characterize unbalance characteristic, has satisfied the demand of fine equilibrium.

3. the definition of vowing according to equivalent first phase can be known; The equivalence first phase vows it is a vibration vector based on data fusion; It can compensate the negative effect that anisotropy causes; Accurately describe rotor space Mode Shape curve, truly reflect the rotor space dynamic perfromance, and support for the balance method of other types provides data.

On the whole, a kind of anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase provided by the invention helps the judgement of rotor balancing fault, the identification of rotor unbalance value and the formulation of counterweight scheme.

Description of drawings

Fig. 1 is a rotor data acquisition system (DAS) synoptic diagram;

Fig. 2 is that holographic spectrum is changeed the frequency ellipse and the first phase arrow makes up synoptic diagram;

Fig. 3 is that radius of circle synoptic diagram is frequently changeed in equivalence;

Fig. 4 is the balance method flow process of vowing based on equivalent first phase

Fig. 5 first phase is vowed the equivalence conversion of inswept area, and Fig. 5 (a) is an elliptical orbit; Fig. 5 (b) is a circular trace.

Embodiment

A kind of anisotropic rotor holographic dynamic balance method of vowing provided by the invention based on equivalent first phase; Be the basis with holographic spectral theory; Ellipse is composed in holography converted into equivalence commentaries on classics circle frequently; Vow as unbalance vibration sign amount with equivalent first phase, utilize the principle of the conservation of angular momentum, to satisfy the demand of fine equilibrium.Below respectively the data acquisition system (DAS) that relates in the inventive method, equivalent first phase arrow, vector are fed back uneven recognition principle and be described in detail; Said is to explanation of the present invention rather than qualification.

1, data acquisition system (DAS) is built

Holographic spectral technology essence is a kind of method of carrying out information fusion at data Layer; Can analyze through signal mutual vertical reference; And extract two direction power frequency component x, y and synthesize and obtain; Power frequency component biosynthesis locus on the both direction is generally an ellipse, is referred to as to change oval frequently.

As shown in Figure 1, balancing run carries out on rotor platform, and axle is provided with vibration-testing face and balance correction face, is being provided with the phase demodulation mark near motor-driven end place.Mounting frame for sensor is installed on vibration measuring face, can guarantees that the vibration transducer gauge head can keep vertically installing in twos.

In above-mentioned vibration signals collecting and test mass, the counterweight process, need to select one or more vibration signals to measure face, one or more counterweight face, a phase discrimination signal measurement face at rotor.On each vibration signal measurement cross section, 2 displacements or vibration transducer are installed, the mutual angle of two sensors is 90 °; Be provided with balancing disk at the counterweight face and can be used to add the weight mass piece; Phase demodulation sign on phase discrimination signal measurement face is used to change the phase demodulation sensor signal.The measuring-signal that said displacement or vibration transducer are gathered exports a high-speed data acquisition card to after amplifying through the conditioning of fore-lying device, finally through the Xpress bus with data transmission to computing machine.

As shown in Figure 1; The vibration transducer data export NI multi-channel high-speed data capture card to after being amplified by the conditioning of advance signal conditioning module, and the analog signal conversion that representative is vibrated is a data-signal; And through the Express data bus; Vibration data and phase demodulation information transmission to computing machine, are carried out pre-treatments operations such as sensing data demarcation, gross error processing, data filtering, reduce because the error that Design of Test System, hardware performance and environmental disturbances are introduced.

2, the structure of equivalent first phase arrow

Referring to Fig. 2; The equivalent commentaries on classics structure of circle frequently is on the basis of changeing the frequency ellipse, to carry out; Corresponding equivalent first phase vows that EIPV vows that according to traditional first phase the IPV equivalence obtains; The anisotropic rotor holographic dynamic balance method of therefore, vowing EIPV based on equivalent first phase is identical with traditional holographic dynamic balance method to the requirement of the installation of sensor and vibration signal sampling.

If rotor has n carrying plane, the commentaries on classics on i bearing cross section is oval frequently by sine term coefficient [sx _i, sy _i] and cosine term coefficient [cx _i, cy _i] decision:

$\left\{\begin{array}{c}{x}_i=A_{\mathrm{xi}}\sin (\mathrm{\Ωt}+{\mathrm{\α}}_i)=s_{\mathrm{xi}}\sin \left(\mathrm{\Ωt}\right)+c_{\mathrm{xi}}\cos \left(\mathrm{\Ωt}\right)\\ y_i=A_{\mathrm{yi}}\sin (\mathrm{\Ωt}+{\mathrm{\β}}_i)=s_{\mathrm{yi}}\sin \left(\mathrm{\Ωt}\right)+c_{\mathrm{yi}}\cos \left(\mathrm{\Ωt}\right)\end{array}\right.---\left(1\right)$

In the moment of t=0, when promptly rotor rotated to its key phase groove alignment keys phase device, the corresponding point of changeing on the frequency ellipse were defined as first phase point IPP:

IPP=(cx,cy) (2)

Correspondingly be defined as first phase arrow IPV changeing the vector of frequency elliptical center to first phase point:

$\mathrm{IPV}=\sqrt{{\left(A\sin \mathrm{\α}\right)}^2+{\left(B\sin \mathrm{\β}\right)}^2}\∠\arctan \frac{B\sin \mathrm{\β}}{A\sin \mathrm{\α}}---\left(3\right)$

According to formula (1), change frequency long axis of ellipse a and minor axis b and be respectively:

$\left\{\begin{array}{c}a=\frac{1}{2}\·(\sqrt{p+q}+\sqrt{p-q})\\ b=\frac{1}{2}\·(\sqrt{p+q}-\sqrt{p-q})\end{array}\right.---\left(4\right)$

Wherein, $p=s_x^2+c_x^2+s_y^2+c_y^2,$ Q=2c _xs _y-2s _xc _y

As shown in Figure 3, equivalence changes frequently that circle is to convert elliptic motion into vibrational energy identical uniform circular motion gained, equivalence change the frequency radius of a circle should for:

$r=\sqrt{\mathrm{ab}}=\sqrt{c_x{s}_y-s_x{c}_y}---\left(5\right)$

After trying to achieve equivalence commentaries on classics frequency radius of circle, be the center of circle, just can draw out equivalence and change round frequently with the true origin.Yet this circle can only characterize the size of vibrational energy, promptly can only obtain the amplitude r that equivalent first phase is vowed EIPV, but not have the phase identification ability, can not be used for transient equilibrium, so must change the phase place of the equivalent first phase arrow of definition EIPV on the round basis of frequency in equivalence.

The method that traditional first phase vows is similar with finding the solution, and equivalent first phase vows that EIPV can change frequently in equivalence and extract in the circle parametric equation, according to formula (1) and formula (5) but the constructing variable equation:

$\left\{\begin{array}{c}{x}_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\α})\\ y_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β})\end{array}\right.---\left(6\right)$

Yet if x, y direction mechanical hysteresis angle is different; Alpha-beta ≠ pi/2 then, the orbit of shaft center of being drawn according to formula (6) so still are not circular, and this can introduce error to subsequent calculations; Therefore; Can only utilize the phase information of a certain direction sensor, avoid rotor mechanical characteristic or the inhomogeneous phase identification error that causes of angular velocity owing to X, Y both direction, the parametric equation after the improvement can be written as:

$\left\{\begin{array}{c}{x}_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β}+\mathrm{\π}/2)\\ y_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β})\end{array}\right.---\left(7\right)$

Parametric equation is launched, can find the solution improve after just, the cosine term coefficient is following:

$s_{\mathrm{ex}}=-\sqrt{\mathrm{ab}}\sin \mathrm{\β},$ $c_{\mathrm{ex}}=\sqrt{\mathrm{ab}}\cos \mathrm{\β}$

$s_{\mathrm{ey}}=\sqrt{\mathrm{ab}}\cos \mathrm{\β},$ $c_{\mathrm{ey}}=\sqrt{\mathrm{ab}}\sin \mathrm{\β}---\left(8\right)$

According to following formula, equivalence is changeed round frequently matrix of coefficients EH and first phase point EIPP and can be expressed as:

$\left\{\begin{array}{c}\mathrm{EH}=\left[\begin{array}{cccc}{s}_{\mathrm{ex}}& c_{\mathrm{ex}}& s_{\mathrm{ey}}& c_{\mathrm{ey}}\end{array}\right]\\ \mathrm{EIPP}=(c_{\mathrm{ex}},c_{\mathrm{ey}})\end{array}\right.---\left(9\right)$

With the true origin is the center of circle that the frequency circle is changeed in equivalence, and according to formula (9), equivalence is changeed round frequently and equivalent first phase point can be confirmed by unique, thereby can confirm the phase place ∠ EIPV that equivalent first phase is vowed, promptly unique definite equivalent first phase is vowed EIPV.

3, vector feeds back uneven recognition principle

For a rotating object, when its rotation center does not overlap with barycenter, can produce energy imbalance, and cause the centrifugal force that deviates from rotation center relevant thereupon with rotating speed.Set up plane coordinate system perpendicular to rotation; Can know through mechanical analysis; The vibration signal of this rotating object and the actual distribution of barycenter are related, and its amplitude depends on the distance of barycenter and rotation center, and its phase place depends on that barycenter is in orientation that planimetric coordinates is fastened.Obviously, according to this characteristic, if on this rotating object, add a new unbalance amount, its vibration signal also can produce corresponding variation thereupon.

If the original vibration in certain cross section of this rotating object under certain specific rotation speeds is a vector V ₀, add new unbalance amount W _TAfterwards, the vibration at same position place is a vector V under the same rotating speed ₁, so only by W _TThe variation of the vibration signal that causes can be expressed as V ₁-V ₀Thus, the caused vibration of unit mass can be expressed as:

$G=\frac{V_1-V_0}{W_T}---\left(10\right)$

In the formula, G is an influence coefficient.

For suppressing original unbalance U ₀Vibration V ₀, establish and to apply counterweight W _C=-U ₀, serve as zero to guarantee residual oscillation δ, that is:

δ=V ₀+GW _C=0 (11)

Then according to formula (11), W _CCan be expressed as:

$W_C=-\frac{V_0}{G}=-\frac{V_0}{V_1-V_0}{W}_T---\left(12\right)$

Formula (11) is the simplest rotating object equilibrium strategy based on the vector feedback principle, and the equilibrium problem of common rotor is wanted the many of complicacy in the industry, need guarantee under many rotating speeds also in the reality that the vibration of multi-section is suppressed in certain limit.Thus, can formula (11) be expanded to the many planes of multi-measuring point by single measuring point monoplane.

The anisotropic rotor holographic dynamic balance method of 4, vowing based on equivalent first phase

Referring to Fig. 4, based on the anisotropic rotor holographic dynamic balance method that equivalent first phase is vowed, vow EIPV as unbalance vibration sign amount with equivalent first phase, following for the equilibrium step of anisotropic rotor under the imbalance state:

1) after the selection vibration signal is measured face and phase discrimination signal measurement face, starts rotor, gather the two-way original vibration signal on the mutual vertical direction in measurement cross section under the rotor balancing rotating speed;

2) utilize the phase demodulation sign as phase reference, extract the power frequency composition of two-way vibration signal, carry out spectrum analysis and extract power frequency vibration, change oval frequently based on holographic spectral technology structure;

3) ellipse is composed in holography and converted into equivalence and change circle frequently, according to oval major semi-axis a and the minor semi-axis b of holography spectrum, calculating equivalence changes radius of a circle r frequently, and as the amplitude r of equivalent first phase arrow ₀:

After obtaining equivalence commentaries on classics frequency radius of a circle r, be the center of circle with the true origin, draw out equivalence and change round frequently;

4) change radius of circle adjustment frequently according to equivalence and change elliptic equation frequently, obtain the phase place ∠ EIPV that equivalent first phase is vowed ₀, in conjunction with r ₀, obtain original uneven U ₀The equivalent first phase that state is corresponding is vowed:

EIPV ₀=r ₀∠EIPV ₀；

5) the counterweight face is set on rotor, confirms to add on the counterweight face size and the direction of test mass to add test mass W according to the rotor oscillation situation _TAfterwards once more according to step 1)～3) operation, obtain rotor and add test mass unbalance response afterwards, and frequency radius of circle r is changeed in equivalence after calculating the interpolation test mass ₁

6) the frequently oval first phase of the commentaries on classics of the rotor before and after the test mass is vowed IPV ₀, IPV ₁Being converted into equivalence according to conservation of angular momentum principle respectively changes on the frequency circle, and calculates equivalence based on this and change the amount of unbalance angle changes delta γ on the frequency circle;

7) change radius of circle r frequently according to equivalence after adding test mass ₁Obtain adding behind the test mass equivalent first phase with amount of unbalance angle changes delta γ and vow EIPV ₁, its amplitude is r ₁, phase place is ∠ EIPV ₀+ Δ γ;

8), calculate the original unbalance U of rotor according to the principle of vector feedback equalization ₀, unloading test mass W _T, add counterweight W _C=-U ₀

9) test adds the rotor oscillation data after the counterweight, if the balance requirement is satisfied in rotor oscillation, then the rotor balancing operation is accomplished; Require to judge further then whether imbalance is the leading factor that causes vibration if do not satisfy balance, if repeating step 1 then)～8), carry out fine equilibrium and satisfy the balance requirement until rotor oscillation.

Referring to Fig. 5, described imbalance is measured being calculated as of changes delta γ:

1) change oval frequently according to holographic spectral technology structure, the frequently oval first phase of commentaries on classics that obtains the test mass front and back is vowed IPV ₀, IPV ₁, and both are plotted in IPV ₀On the pairing commentaries on classics frequency ellipse, obtain both angle Δ δ=δ ₂-δ ₁

2) based on changeing oval frequently, find the solution from first phase and vow IPV ₀Beginning is until IPV ₁Inswept area S1;

3) with r ₀Be radius, draw equivalence and change circle frequently, keep IPV ₀Phase invariant, it is transplanted to equivalence changes frequently on the circle, obtain IPV ₀';

4), draw IPV on the circle frequently in the equivalence commentaries on classics according to conservation of angular momentum principle ₁', make from IPV ₀' begin until IPV ₁' inswept area S2=S1;

5) find the solution IPV ₀' and IPV ₁' between angle Δ γ:

$\mathrm{\Δ\γ}=\arctan \left(\frac{a}{b}\tan {\mathrm{\δ}}_2\right)-\arctan \left(\frac{a}{b}\tan {\mathrm{\δ}}_1\right).$

Claims (4)

1. an anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase is characterized in that, vows EIPV as unbalance vibration sign amount with equivalent first phase, and is following for the equilibrium step of anisotropic rotor under the imbalance state:

1) after the selection vibration signal is measured face and phase discrimination signal measurement face, starts rotor, gather the two-way original vibration signal on the mutual vertical direction in measurement cross section under the rotor balancing rotating speed;

2) utilize the phase demodulation sign as phase reference, extract the power frequency composition of two-way vibration signal, carry out spectrum analysis and extract power frequency vibration, change oval frequently based on holographic spectral technology structure;

3) ellipse is composed in holography and converted into equivalence commentaries on classics circle frequently,, calculate the equivalent radius of a circle r frequently that changes according to oval major semi-axis a and the minor semi-axis b of holography spectrum ₀, and as with original uneven U ₀The pairing initial equivalent first phase of state is vowed EIPV ₀Amplitude;

4) change radius of circle adjustment frequently according to equivalence and change elliptic equation frequently, obtain the phase place ∠ EIPV that equivalent first phase is vowed ₀, in conjunction with, r ₀Obtaining initial equivalent first phase vows:

EIPV ₀=r ₀∠EIPV ₀；

5) the counterweight face is set on rotor, confirms to add on the counterweight face size and the direction of test mass to add test mass W according to the rotor oscillation situation _TAfterwards once more according to step 1)～3) operation, obtain rotor and add test mass unbalance response afterwards, and frequency radius of circle r is changeed in equivalence after calculating the interpolation test mass ₁

6) the frequently oval first phase of the commentaries on classics of the rotor before and after the test mass is vowed IPV ₀, IPV ₁Being converted into equivalence according to conservation of angular momentum principle respectively changes on the frequency circle, and calculates equivalence based on this and change the amount of unbalance angle changes delta γ on the frequency circle;

7) change radius of circle r frequently according to equivalence after adding test mass ₁Obtain adding behind the test mass equivalent first phase with amount of unbalance angle changes delta γ and vow EIPV ₁, its amplitude is r ₁, phase place is ∠ EIPV ₀+ Δ γ;

8), calculate the original unbalance U of rotor according to the principle of vector feedback equalization ₀, unloading test mass W _T, add counterweight W _C=-U ₀

9) test adds the rotor oscillation data after the counterweight, if the balance requirement is satisfied in rotor oscillation, then the rotor balancing operation is accomplished; Require to judge further then whether imbalance is the leading factor that causes vibration if do not satisfy balance, if repeating step 1 then)～8), carry out fine equilibrium and satisfy the balance requirement until rotor oscillation.

2. anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase as claimed in claim 1 is characterized in that, described initial equivalent first phase is vowed EIPV ₀Be calculated as:

1) changes oval frequently according to holography spectrum dynamic balancing technique structure; Utilize elliptic motion to convert the identical uniform circular motion of vibrational energy into; Thereby ellipse is composed in holography converted into equivalence commentaries on classics circle frequently,, calculate the equivalent radius of a circle r frequently that changes according to oval major semi-axis a and the minor semi-axis b of holography spectrum ₀, and the amplitude of vowing as initial equivalent first phase:

$r_0=\sqrt{\mathrm{ab}}=\sqrt{c_x{s}_y-s_x{c}_y}$

Obtaining equivalence commentaries on classics radius of a circle r frequently ₀After, be the center of circle with the true origin, draw out equivalence and change circle frequently;

2) radius of circle r is frequently changeed in equivalence ₀Be set to change the constant term of expression amplitude in the elliptical configuration function frequently, and be benchmark, set up equivalence and change circle parametric equation frequently with the phase information of a certain direction sensor:

$\left\{\begin{array}{c}{x}_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β}+\mathrm{\π}/2)\\ y_e=\sqrt{\mathrm{ab}}\sin (\mathrm{\Ωt}+\mathrm{\β})\end{array}\right.$

3) find the solution equivalence change equation of a circle frequently just, the cosine term coefficient:

$s_{\mathrm{ex}}=-\sqrt{\mathrm{ab}}\sin \mathrm{\β},$ $c_{\mathrm{ex}}=\sqrt{\mathrm{ab}}\cos \mathrm{\β}$

$s_{\mathrm{ey}}=\sqrt{\mathrm{ab}}\cos \mathrm{\β},$ $c_{\mathrm{ey}}=\sqrt{\mathrm{ab}}\sin \mathrm{\β}$

4) basis is just, the cosine term coefficient obtains equivalence changes the matrix of coefficients EH and the first phase point EIPP of circle frequently:

$\left\{\begin{array}{c}\mathrm{EH}=\left[\begin{array}{cccc}{s}_{\mathrm{ex}}& c_{\mathrm{ex}}& s_{\mathrm{ey}}& c_{\mathrm{ey}}\end{array}\right]\\ \mathrm{EIPP}=(c_{\mathrm{ex}},c_{\mathrm{ey}})\end{array}\right.$

With the true origin is the equivalent commentaries on classics center of circle of circle frequently, and according to matrix number EH and first phase point EIPP, equivalence commentaries on classics frequency circle and equivalent first phase point are confirmed by unique, thereby confirmed equivalent first phase arrow EIPV ₀

3. anisotropic rotor holographic dynamic balance method of vowing based on equivalent first phase as claimed in claim 1 is characterized in that described imbalance is measured being calculated as of changes delta γ:

1) change oval frequently according to holographic spectral technology structure, the frequently oval first phase of commentaries on classics that obtains the test mass front and back is vowed IPV ₀, IPV ₁, and both are plotted in IPV ₀On the pairing commentaries on classics frequency ellipse, obtain both angle Δ δ=δ ₂-δ ₁

2) based on changeing oval frequently, find the solution from first phase and vow IPV ₀Beginning is until IPV ₁Inswept area S1;

3) with r ₀Be radius, draw equivalence and change circle frequently, keep IPV ₀Phase invariant, it is transplanted to equivalence changes frequently on the circle, obtain IPV ₀';

4), draw IPV on the circle frequently in the equivalence commentaries on classics according to conservation of angular momentum principle ₁', make from IPV ₀' begin until IPV ₁' inswept area S2=S1;

5) find the solution IPV ₀' and IPV ₁' between angle Δ γ:

$\mathrm{\Δ\γ}=\arctan \left(\frac{a}{b}\tan {\mathrm{\δ}}_2\right)-\arctan \left(\frac{a}{b}\tan {\mathrm{\δ}}_1\right).$

4. any one describedly introduces method that equivalent first phase is vowed in holography spectrum dynamic balance method like claim 1～3, it is characterized in that, describedly changes frequently based on holographic spectral technology structure that ellipse is:

If rotor has n carrying plane, the commentaries on classics on i bearing cross section is oval frequently by sine term coefficient [sx _i, sy _i] and cosine term coefficient [cx _i, cy _i] decision:

$\left\{\begin{array}{c}{x}_i=A_{\mathrm{xi}}\sin (\mathrm{\Ωt}+{\mathrm{\α}}_i)=s_{\mathrm{xi}}\sin \left(\mathrm{\Ωt}\right)+c_{\mathrm{xi}}\cos \left(\mathrm{\Ωt}\right)\\ y_i=A_{\mathrm{yi}}\sin (\mathrm{\Ωt}+{\mathrm{\β}}_i)=s_{\mathrm{yi}}\sin \left(\mathrm{\Ωt}\right)+c_{\mathrm{yi}}\cos \left(\mathrm{\Ωt}\right)\end{array}\right.$

Then long axis of ellipse a and minor axis b are respectively:

$\left\{\begin{array}{c}a=\frac{1}{2}\·(\sqrt{p+q}+\sqrt{p-q})\\ b=\frac{1}{2}\·(\sqrt{p+q}-\sqrt{p-q})\end{array}\right.$

Wherein, $p=s_x^2+c_x^2+s_y^2+c_y^2,$ Q=2c _xs _y-2s _xc _y

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