CN105930669B - A kind of non-gravity is dominant cracked rotor rigidity breathing function calculation method - Google Patents
A kind of non-gravity is dominant cracked rotor rigidity breathing function calculation method Download PDFInfo
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Abstract
The present invention provides a kind of non-gravity and is dominant cracked rotor rigidity breathing function calculation method, solving precision is high, strong applicability, it includes the following steps, firstly, turning at the declinate of whirlpool a certain, by assuming that initial restoring force direction, the stress tension and compression distribution for determining cracks rotor cross-section under the state, obtains crackle section enclosed region；Wherein, cracks rotor cross-section is crackle section；Crackle section enclosed region is closed section；Then, using flexure theory, the rotor rigidity under the state is calculated；Using rotor rigidity is acquired, the restoring force under the state is corrected, successively iteration is until rigidity restrains；Traversal turns all discrete values in the declinate domain of whirlpool, obtains its corresponding discrete rigidity value；Finally, using data fitting method, the rigidity of discrete state is fitted to obtained about the Based on Triangle Basis continuous expression formula for turning whirlpool declinate non-gravity be dominant cracked rotor be in respiratory state variation rigidity.
Description
Technical field
The present invention relates to mechanical kinetics field, specially a kind of non-gravity be dominant cracked rotor rigidity breathing function calculate
Method.
Background technique
The large rotating machineries such as steam turbine, compressor are the most key in State Grid and chemical industry and using the most
Extensive one kind mechanical equipment.Since structure is complicated for this kind of large scale equipment, operating condition changes greatly, it is easy to cause the tired of equipment and materials
Labor crackle.In the actual moving process of equipment, rotor crack is one of most important failure.To realize rotor crack monitoring,
Avoid the catastrophic failure of fatal crass, it is necessary in depth study the kinetic characteristics of cracked rotor system.Crackle turns
The accurate calculating of son breathing rigidity, is the premise for studying its kinetic characteristics.
Currently, there are two types of transversal crack rigidity models: standard-sized sheet crack model and witching crack model.Witching crack model is
Refer to during rotor operation, open when crackle, when and be closed, when and half-open semi-closure, because it has comprehensively considered crackle section
Three kinds of states, can more reflect the operating condition of actual rotor.The existing witching crack rigidity parsing based on neutral axis theory
Solution has ignored neutrality axle offset caused by the asymmetry of crackle section, it will again be assumed that neutral although the cell breath of crackle can be reacted
Axis passes through the crackle section center of circle, therefore the model has the situation of determining crack opening region inaccuracy.
The improved witching crack Rigidity Calculation in neutral axis theory is in the hypothesis item for not considering that crack tip stress is concentrated
Under part, when crackle is in standard-sized sheet or half-open half closed state, consider crack opening region to the shadow of crackle cross-sectional neutral axis position
It rings, obtains the neutral axis for deviateing intact cross-section centroid certain distance, the partial crack face above neutral axis is in compression
Area is in closed state, and the partial crack face below neutral axis is in Tension Stress Zone, is in open configuration.But it is this
It improves the direction for thinking that the direction of elastic-restoring force is displaced with rotor axis to be consistent, then, due to the presence of crackle, cause
The direction of restoring force is not consistent with axle center direction of displacement to rigidity etc. for rotor each, and this method, which still cannot be calculated accurately, to be split
The rigidity of line rotor.
Summary of the invention
Aiming at the problems existing in the prior art, the present invention provides a kind of non-gravity and is dominant cracked rotor rigidity breathing function
Calculation method, solving precision is high, and strong applicability can accurately solve different cross section shape, the rotor with breath crack any
Rigidity under rotation status.
The present invention is to be achieved through the following technical solutions:
A kind of non-gravity is dominant cracked rotor rigidity breathing function calculation method, firstly, turning to pass through at the declinate of whirlpool a certain
Assuming that initial restoring force direction, determines the stress tension and compression distribution of cracks rotor cross-section under the state, obtains crackle section and close
Close region；Wherein, cracks rotor cross-section is crackle section；Crackle section enclosed region is closed section；Then, sharp
With flexure theory, the rotor rigidity under the state is calculated；Using rotor rigidity is acquired, the restoring force under the state is corrected,
Successively iteration is until rigidity restrains；Traversal turns all discrete values in the declinate domain of whirlpool, obtains its corresponding discrete rigidity value；Most
Afterwards, using data fitting method, the rigidity of discrete state is fitted to about the Based on Triangle Basis continuous expression formula for turning whirlpool declinate,
Obtain non-gravity be dominant cracked rotor be in respiratory state variation rigidity.
Preferably, specifically includes the following steps:
1) domain for turning whirlpool declinate ψ [0,2 π] is separated into N equal part, it is single that crackle section is divided into multiple discrete faces
Member；
2) some in selection turns under the declinate of whirlpool, it is assumed that restoring force direction and rotor axis direction of displacement are reversed, calculate
Closed section is calculated by neutral shelf theory in the stress of each face unit；
3) principal axis of inertia position for calculating current closed section, repeats step 2, recalculates the stress of its face unit,
Until obtaining convergent closed section；
4) rotor rigidity of the state is calculated using flexure theory by convergent closed section；
5) turn the rotor rigidity under the declinate of whirlpool using acquiring this, rotor restoring force calculated by following formula:
Wherein, FxAnd FyFor the component of restoring force x and x-axis along fixed coordinate system o-xy, kx, kyAnd kxyIt is opposite for rotor
In the three-dimensional curved rigidity of fixed coordinate system, xo'And yo'Axle center for rotor relative to fixed coordinate system is displaced；
6) step 2)~5 are repeated), until the restoring force convergence under the state, obtains this and turns the rotor rigidity under the declinate of whirlpool；
7) choose again it is any it is not calculated turn whirlpool declinate, repeat step 2)~6), until having traversed in domain N number of turn
Whirlpool declinate；It obtains each turning corresponding rotor rigidity under the declinate of whirlpool；
8) data fitting method is utilized, is fitted to Based on Triangle Basis in the discrete rotor rigidity for turning whirlpool declinate state for N number of
Continuous expression formula, as rigidity breathe function, to obtain the rigidity value of respiratory variations.
Further, described to utilize data fitting method, it is poor about whirlpool is turned that N number of rotor rigidity in discrete state is fitted to
The Based on Triangle Basis continuous expression formula at angle, comprising the following steps:
For axial symmetry distribution horizontal and vertical two to rigidity, the step of it is cos (ψ) basic function form is enabled, wherein
kx=a (1) cos (ψ)+a (2) cos (ψ)2+a(3)cos(ψ)3+a(4)cos(ψ)6+a(5)cos(ψ)7+a(6)cos
(ψ)8+a(7)cos(ψ)9+a(8)cos(ψ)10+a(9)cos(ψ)15+a(10)cos(ψ)19+a(11)
For the intersection rigidity of central symmetry distribution, the step of it is Fourier space form is enabled, wherein
In upper 3 formula, a (i) is undetermined coefficient, turns whirlpool declinate ψ ∈ [0,2 π]；
It is obtained according to least square data fitting principle using the N number of discrete rigidity value turned under the declinate of whirlpool acquired
Coefficient a (i) determines the continuous expression formula of rigidity breathing function.
Further, centroid and the centroid principal axis of inertia position of current closed section are calculated by following formula,
In formula, AiFor the area of closed section inner face unit, n is closed section inner face element number；WithRotation is sat
Centroid coordinate under mark system o'-x'y',WithClosed section is to centroid axis x*And y*The moment of inertia and the product of inertia,θ is shape
The heart principal axis of inertia and centroid axis x*Angle.
Compared with prior art, the invention has the following beneficial technical effects:
The present invention is by the way that in section stress solution procedure, the discrete face forming unit in crackle section is appointed due to that can calculate
The rotor rigidity of meaning cross sectional shape, and existing method is only limitted to the calculating of circular section rotor rigidity；It is adopted during Rigidity Calculation
With the modified iterative step of restoring force, the restoring force direction for arbitrarily turning whirlpool declinate state lower rotor part may thereby determine that.And show
In the model for having the hypothesis that is dominant based on gravity, it can only assume that restoring force direction is the reversed of gravity.Therefore, this method breaches weight
Power is dominant the constraint of hypothesis, is dominant the solution of cracked rotor breathing rigidity suitable for non-gravity.Obtained cracked rotor breathing is rigid
Computation model is spent, provides support to study the vibration characteristics of cracked rotor, to realize the monitoring of Diagnosing System for Oil Pump rotor crack
Provide theoretical basis.
Further, rigidity fitting is carried out by Based on Triangle Basis, convenient for Crack Rotational Dynamic Modeling and solves, improves
Computational accuracy and efficiency.
Detailed description of the invention
Fig. 1 is that rigidity described in present example breathes function calculation method flow chart.
Fig. 2 is crackle schematic cross-section described in present example.
Fig. 3 is iterative process coordinate system and principal axis of inertia schematic diagram described in present example.
Closed section schematic diagram when Fig. 4 a is present example transfer whirlpool declinate ψ=0.
Closed section schematic diagram when Fig. 4 b is present example transfer whirlpool declinate ψ=π/8.
Closed section schematic diagram when Fig. 4 c is present example transfer whirlpool declinate ψ=π/4.
Closed section schematic diagram when Fig. 4 d is the present example transfer whirlpool π/8 of declinate ψ=3.
The solution schematic diagram of the opposite breathing rigidity of three-dimensional when Fig. 5 is crackle relative depth μ=0.2 in present example.
Fig. 6 be in present example x to relative rigidity fitting function and discrete data comparison diagram.
Fig. 7 be in present example y to relative rigidity fitting function and discrete data comparison diagram.
Fig. 8 is to intersect relative rigidity fitting function and discrete data comparison diagram in present example.
Specific embodiment
Below with reference to specific embodiment, the present invention is described in further detail, it is described be explanation of the invention and
It is not to limit.
The tension and compression stress equilibrium in crackle section in the case where arbitrarily turning whirlpool declinate is former according to cracked rotor for method of the present invention
Reason, determines the closed section in the crackle section under the state.According to closed section, in conjunction with flexure theory, the state is calculated
Under cracked rotor rigidity.Using rigidity under the state acquired, corresponding restoring force is solved, for correcting the tension and compression of the state
Stress area corrects the restoring force direction under the state.By iterative calculation, obtain under the state that corresponding to turn whirlpool declinate convergent
Rotor rigidity.Using same method, obtain all turning convergent rotor rigidity under the declinate of whirlpool；Finally, utilizing data fitting side
Rotor rigidity at discrete state is fitted to the continuous expression formula of Based on Triangle Basis by method, is obtained rigidity breathing function, is obtained non-
Gravity is dominant the dynamic rate of cracked rotor.This method solving precision is high, strong applicability, can accurately solve different cross section shape,
Rigidity of the rotor with breath crack under any rotation status, grinds convenient for cracked rotor Dynamic Modeling with response characteristic
Study carefully.
Wherein, using alternative manner, the restoring force direction under the current rotation status of rotor and size is corrected, restoring force is passed through
The stress tension and compression distribution for determining crackle section under the state, obtains closed section, using flexure theory, the state is calculated and turns
Sub- rigidity.Using rigidity is acquired, restoring force is corrected, successively iteration is until convergence.
Using data fitting method, the rigidity at discrete state is fitted to the continuous expression formula of Based on Triangle Basis.
Basic procedure when method of the present invention is implemented successively solves inertia master as shown in Figure 1, by iteration three times
Shaft position and restoring force direction, and traversal is all turns whirlpool declinate, is arbitrarily turned the three-way rigidity discrete value of whirlpool declinate, it is specific
Steps are as follows.
First as shown in Fig. 2, cracked zone is closed in crackle section by 1. flawless area, 2. and 3. Crack area three parts form, V
For the normal direction of crackle, d is crack depth, and o-xy is fixed coordinate system, and o'-x'y' is rotating coordinate system, and θ is corner,For whirling motion
Angle, ψ are to turn whirlpool declinate, and F is restoring force.Crackle section is divided into multiple discrete rectangular surfaces units.Turn whirlpool declinate ψ a certain
In the case of, it is assumed that elastic-restoring force F is along x' opposite direction.Such as Fig. 3, o in figureIFor the centroid of closed section (1.+2. region), x*With
y*For the centroid axis for being parallel to x' and y', xIAnd yIThe moment of inertia of centroidal principal axes,For xIWith x*Angle.Assuming that principal axis of inertia xI,yIWith
X'y' overlapping of axles by tension and compression stress equilibrium, obtain closed section in this state, i.e. 1.+2. region in Fig. 2.
Pass through following formula again
The centroid and centroid inertia shaft position for calculating the closed section, such as x in Fig. 3I,yIIt is shown.Process changes as shown in Figure 1
In generation, calculates, until the position of the principal axis of inertia is restrained.After obtaining the convergent centroid axes of inertia, it is calculated at coordinate system o'-x'y'
Along each axial rigidityWith
It is converted by following formula
It is obtained in the next each axial rigidity k of fixed coordinate systemx,kyAnd kxy.Wherein,It is rotor in fixed coordinate system
Whirling motion angle under o-xy, as shown in Figure 3.
By the rigidity under the rotor condition, restoring force is corrected:Iteration is until restoring force
Convergence.So far, it has obtained this and has turned the rotor rigidity under the declinate of whirlpool.Calculating others are any to turn whirlpool declinate, repeats the above process, obtains
To each discrete cracked rotor rigidity turned at the declinate of whirlpool.
In data fit procedure, first according to the symmetry of data, the expression formula of its three-way rigidity is enabled to be respectively
kx=a (1) cos (ψ)+a (2) cos (ψ)2+a(3)cos(ψ)3+a(4)cos(ψ)6+a(5)cos(ψ)7+a(6)cos
(ψ)8+a(7)cos(ψ)9+a(8)cos(ψ)10+a(9)cos(ψ)15+a(10)cos(ψ)19+a(11)
Then least square data fitting method is utilized, solution obtains fitting coefficient a (i), and as rigidity breathes function, from
And obtain the rigidity value of respiratory variations.
This preferred embodiment, by taking crackle section shown in Fig. 2 as an example, wherein crackle relative depth is μ=d/D=0.2, and d is
Crack depth, D are diameter of section.It will turn whirlpool declinate and be divided into 128 parts in domain [0,2 π], crackle section is separated into side
The face unit of a length of diameter 1/100.Crackle is calculated and cuts by writing MATLAB program according to basic procedure shown in FIG. 1
Face it is variant turn whirlpool declinate when closed section, Fig. 4 gives 4 therein and turns whirlpool declinate ψ=0, the He of ψ=π/8, ψ=π/4
Closed section calculated result at π/8 ψ=3.Fig. 5 be 3 to rigidity in the different checkout results for turning the discrete value at the declinate of whirlpool,
I.e. the rigidity of cracked rotor breathes function, and rigidity value is respiratory variations.After being fitted by data, it is obtained with triangular basis letter
The continuous breathing function expression of number description are as follows:
In order to illustrate the accuracy of data fitting, Fig. 6~Fig. 8 compared 3 to the original dispersion number of rigidity using relative rigidity
According to the data difference after fitting, wherein KmaxIndicate the bending stiffness of normal rotor.It can be seen from the figure that fitting function
Curve is almost overlapped with discrete rigidity point, illustrates the error of the fitting function within the allowable range.
Claims (3)
1. a kind of non-gravity is dominant, cracked rotor rigidity breathes function calculation method, which is characterized in that firstly, to turn whirlpool poor a certain
At angle, by assuming that initial restoring force direction, determines the stress tension and compression distribution of cracks rotor cross-section, obtains crackle section and close
Close region；Wherein, cracks rotor cross-section is crackle section；Crackle section enclosed region is closed section；Then, sharp
With flexure theory, the rotor rigidity under a certain turn at the declinate of whirlpool is calculated；Using rotor rigidity is acquired, correct that a certain to turn whirlpool poor
Restoring force under at angle, successively iteration is until rigidity restrains；Traversal turns all discrete values in the declinate domain of whirlpool, obtains its correspondence
Discrete rigidity value；Finally, the rigidity of discrete state is fitted to about the triangular basis for turning whirlpool declinate using data fitting method
Continuous expression formula, obtain non-gravity be dominant cracked rotor be in respiratory state variation rigidity；
Specifically includes the following steps:
1) domain for turning whirlpool declinate ψ [0,2 π] is separated into N equal part, crackle section is divided into multiple discrete face units；
2) some in selection turns under the declinate of whirlpool, it is assumed that restoring force direction and rotor axis direction of displacement are reversed, calculate each
Closed section is calculated by neutral shelf theory in the stress of a face unit；
3) principal axis of inertia position for calculating current closed section, repeats step 2, recalculates the stress of its face unit, until
Obtain convergent closed section；
4) a certain rotor rigidity turned at the declinate of whirlpool is calculated using flexure theory by convergent closed section；
5) turn the rotor rigidity under the declinate of whirlpool using acquiring this, rotor restoring force calculated by following formula:
Wherein, FxAnd FyFor the component of restoring force x and y axis along fixed coordinate system o-xy, kx, kyAnd kxyIt is rotor relative to solid
The three-dimensional curved rigidity of position fixing system, xo'And yo'Axle center for rotor relative to fixed coordinate system is displaced；
6) step 2)~5 are repeated), up to the restoring force convergence under a certain turn at the declinate of whirlpool, obtains this and turn the rotor under the declinate of whirlpool
Rigidity；
7) choose again it is any it is not calculated turn whirlpool declinate, repeat step 2)~6), until having traversed, N number of in domain to turn whirlpool poor
Angle；It obtains each turning corresponding rotor rigidity under the declinate of whirlpool；
8) data fitting method is utilized, by N number of company for being fitted to Based on Triangle Basis in the discrete rotor rigidity for turning whirlpool declinate state
Continuous expression formula, as rigidity breathe function, to obtain the rigidity value of respiratory variations.
2. a kind of non-gravity according to claim 1 is dominant, cracked rotor rigidity breathes function calculation method, and feature exists
In, it is described to utilize data fitting method, N number of rotor rigidity in discrete state is fitted to about the triangular basis letter for turning whirlpool declinate
Number continuous expression formula, comprising the following steps:
For axial symmetry distribution horizontal and vertical two to rigidity, the step of it is cos (ψ) basic function form is enabled, wherein
kx=a (1) cos (ψ)+a (2) cos (ψ)2+a(3)cos(ψ)3+a(4)cos(ψ)6+a(5)cos(ψ)7+a(6)cos(ψ)8+
a(7)cos(ψ)9+a(8)cos(ψ)10+a(9)cos(ψ)15+a(10)cos(ψ)19+a(11)
For the intersection rigidity of central symmetry distribution, the step of it is Fourier space form is enabled, wherein
In upper 3 formula, a (i) is undetermined coefficient, turns whirlpool declinate ψ ∈ [0,2 π]；
Its coefficient is obtained according to least square data fitting principle using the N number of discrete rigidity value turned under the declinate of whirlpool acquired
A (i) determines the continuous expression formula of rigidity breathing function.
3. a kind of non-gravity according to claim 1 is dominant, cracked rotor rigidity breathes function calculation method, and feature exists
In, centroid and the centroid principal axis of inertia position of current closed section are calculated by following formula,
In formula, AiFor the area of closed section inner face unit, n is closed section inner face element number；WithRotating coordinate system
Centroid coordinate under o'-x'y',WithClosed section is to centroid axis x*And y*The moment of inertia and the product of inertia, θ is used for centroid
Property main shaft and centroid axis x*Angle.
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