CN104075846B - A kind of based on the rotor unbalance degree recognition methods calculating reverse technology - Google Patents
A kind of based on the rotor unbalance degree recognition methods calculating reverse technology Download PDFInfo
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Abstract
The present invention relates to a kind of rotor unbalance degree recognition methods based on calculating reverse technology, including: according to carry out dynamically balanced rotor structure, determine out-of-balance force number to be identified；Instantaneous response analysis model adds out-of-balance force, finds response displacement and added force to have the response measuring point of dependency, and measured the dynamic response obtaining correspondence by experiment；Utilize the unit pulse power of rotor-support-foundation system structure and supposition, responded to the kernel function of response measuring point by the method assumed (specified) load application point of emulation, set up kernel matrix and be modified；Based on dynamic response obtained above and amended kernel matrix, obtain out-of-balance force by solving the mould of least residual in regularizing functionals, and then obtain amplitude and the phase place of amount of unbalance, and accordingly rotor-support-foundation system structure is carried out dynamic balance treatment；The present invention only needs once to test and the degree of unbalancedness of several measuring points just energy quick obtaining rotor, can not only obtain the dynamic loading that some traditional methods are difficult to determine accurately and effectively, and greatly reduce number of times and the cost of Physical Experiment.
Description
Technical field
The present invention relates to dynamic balancing technique field, particularly relate to a kind of based on the rotor unbalance degree knowledge calculating reverse technology
Other method.
Background technology
At present, during rotor dynamic balancing, conventional method generally requires and just can determine that correction mass by repeatedly test run, time-consuming
Laborious again, this is especially prominent to large rotor.In rotor-support-foundation system, degree of unbalancedness is divided into different etc. according to certain standard
Level, and provide concrete dynamic loading expression-form, but owing to the dynamic trait of structure itself is design variable or controls parameter
, there is the sensitivity to dynamic loading in nonlinear function.Therefore, the setting load modes in specification or standard and the reality suffered by structure
When the dynamic load on border has deviation, carry out the dynamic analysis of structure and optimize design it is possible to exist bigger with practical situation
Deviation.When failing the explicit value providing degree of unbalancedness, the dynamics Optimization Design of rotor and health monitoring and fault diagnosis etc.
The research of problem is with certain blindness.Therefore, accurately obtaining of degree of unbalancedness can provide definite for the research of these problems
Environmental condition, the safety and reliability of rotor structure is designed there is important practical significance.
Being limited by the condition such as technology and economic condition, degree of unbalancedness is difficult to directly measure.And rotor dynamics response (bag
Include the displacement of rotor, speed and acceleration etc.) measurement relatively easy and accurately, so utilizing the response of measurement to imbalance
Degree dynamic load carries out the research of reverse reconstruct and is very important.
Summary of the invention
In view of above-mentioned analysis, it is desirable to provide a kind of based on the rotor unbalance degree identification side calculating reverse technology
Method, the problem needing during in order to solve existing rotor dynamic balancing just to can determine that correction mass through repeatedly test run.
The purpose of the present invention is mainly achieved through the following technical solutions:
The invention provides a kind of rotor unbalance degree recognition methods based on calculating reverse technology, including:
According to carry out dynamically balanced rotor structure, determine out-of-balance force number to be identified；
Instantaneous response analysis model adds out-of-balance force, finds response displacement to have the response of dependency to survey with added force
Point, and the dynamic response obtaining correspondence is measured by experiment；
Utilize the unit pulse power of rotor-support-foundation system structure and supposition, calculate kernel matrix by the method for emulation and go forward side by side
Row is revised；
Based on dynamic response obtained above and amended kernel matrix, minimum by solving in regularizing functionals
The mould of residual error obtains out-of-balance force, and then obtains amplitude and the phase place of amount of unbalance, and moves rotor-support-foundation system structure accordingly
Balance Treatment.
Further, response displacement and added force is found to have the process responding measuring point of dependency to specifically include:
The Finite Element Method used by transfer matrix method or finite element emulation software sets up the instantaneous response analysis mould of rotor
Type, adds out-of-balance force and carries out instantaneous response analysis, finds response displacement and added force to have the response measuring point of dependency, and response
The number of measuring point can not be less than the number of out-of-balance force.
Further, the process of the dynamic response obtaining correspondence by experiment measurement specifically includes:
According to the response measuring point obtained, to carry out the sensor that dynamically balanced rotor arranges that test responds；
The dynamic response y at above-mentioned response measuring point is measured by the experiment of rotor transient responseδ。
Further, utilize the unit pulse power of rotor-support-foundation system structure and supposition, calculate core letter by the method for emulation
The process of matrix number specifically includes:
Use finite element emulation software to apply unit pulse power at out-of-balance force institute to be identified application point, solve rotor-support-foundation system
Structure under unit pulse power effect, the response of the response measuring point of arranged in front, and set up kernel matrix.
Wherein, the kernel matrix set up under single-point load effect is expressed as:
Yknow=G*Pknow
Wherein, PknowRepresentation unit impulsive force, YknowRepresent the dynamic response under the known load effect in emulation mode, G
Represent the kernel matrix set up under single-point load effect；
Kernel matrix form under multi-source load effect is expressed as:
In formula:
Y represents response corresponding in time domain, and G represents that kernel matrix, P represent load to be identified, and m represents load
The number of source point, n represents the number of response measuring point.
Further, also include:
Classical regularization method is used to select the regularizing operator f such as TiKhonov or truncated singular value decomposition (α, σ), profit
Determine suitable regularization parameter by Generalized Cross Validation criterion or L-curve method, the kernel matrix of morbid state is repaiied
Just.
Further, the process obtaining out-of-balance force by solving the mould of least residual in regularizing functionals specifically includes:
The mould of least residual in regularizing functionals is solved, i.e. according to being converted into load identification problem to solve
min||GαPα,δ-yδ| |, wherein, GαRepresent revised kernel matrix, yδRepresent the dynamic sound at response measuring point
Should, Pα,δRepresent out-of-balance force to be identified；
And use the LSQR method of conjugate gradient to be iterated solving, thus obtain out-of-balance force to be identified,
Good iterations can be determined by L-curve method.
Further, it is thus achieved that the amplitude of amount of unbalance and the process of phase place specifically include:
Relational expression according to the out-of-balance force identified with degree of unbalancedness, it is thus achieved that amplitude A of amount of unbalance and phase place
Above-mentioned relation formula is represented by:
A=me ω2
Wherein, feRepresenting out-of-balance force to be identified, A represents that amplitude, m represent that unbalance mass, e represent eccentric throw,Represent
Phase place, ω represents the angular velocity of rotor-support-foundation system, t express time.
The present invention has the beneficial effect that:
The present invention only needs once to test and the degree of unbalancedness of several measuring points just energy quick obtaining rotor, and the present invention is not only simultaneously
Can obtain the dynamic loading that some traditional methods are difficult to determine accurately and effectively, and greatly reduce the number of times of Physical Experiment and become
This, have preferable practical value.
Other features and advantages of the present invention will illustrate in the following description, and, becoming from description of part
Obtain it is clear that or understand by implementing the present invention.The purpose of the present invention and other advantages can be by the explanations write
Structure specifically noted in book, claims and accompanying drawing realizes and obtains.
Accompanying drawing explanation
Fig. 1 is the schematic flow sheet of the method for the invention；
Fig. 2 a is embodiment of the present invention rotor bearing experiment table；
Fig. 2 b is the phantom schematic diagram of embodiment of the present invention rotor bearing experiment table；
Fig. 3 a and 3b is to cross eddy current sensor in the embodiment of the present invention to record the dynamic respond schematic diagram of two measuring points；
Fig. 4 is the schematic diagram of L-curve in the embodiment of the present invention；
Fig. 5 a and 5b is the dynamic respond identification passing through test in the embodiment of the present invention by Dynamic Load Identification technology of the present invention
The out-of-balance force dynamic loading of rotor testbed；
Fig. 6 a and 6b is measuring point Oscillation Amplitude schematic diagram before and after dynamic balancing in the embodiment of the present invention.
Detailed description of the invention
The present invention discloses a kind of based on the rotor unbalance degree recognition methods calculating reverse.The method comprehensive utilization rotor
Dynamic test and corresponding finite element analysis model, combine direct regularization and Iteration Regularized method, use L-curve method
Determine suitable regularization parameter, degree of unbalancedness load identification problem is converted into and solves least residual in regularizing functionals
Mould.And be iterated solving by the LSQR method of conjugate gradient method, the most optimal iterations can be by criterions such as L-curve methods
Determine, thus identify the degree of unbalancedness of rotor.
Specifically describing the preferred embodiments of the present invention below in conjunction with the accompanying drawings, wherein, accompanying drawing constitutes the application part, and
Together with embodiments of the present invention for explaining the principle of the present invention.
As it is shown in figure 1, Fig. 1 is the schematic flow sheet of the method for the invention, specifically may include steps of:
Step 101: according to carry out dynamically balanced rotor structure, determine the number of out-of-balance force to be identified.
Step 102: the Finite Element Method used with conventional transfer matrix method or finite element emulation software sets up the wink of rotor
State response analysis model, adds out-of-balance force on instantaneous response analysis model, carries out instantaneous response analysis, find response displacement with
There is the response measuring point of certain dependency in added force, and the number of response measuring point can not be less than the number of out-of-balance force；According to
The response measuring point arrived, to carry out the sensor that dynamically balanced rotor arranges that test responds.
Step 103: measure the dynamic response y at above-mentioned response measuring point by the experiment of rotor transient responseδ, as the most anti-
Seek the factors such as the displacement (speed or acceleration) that out-of-balance force is to be had.
Step 104: extract the relevant parameter of rotor-support-foundation system structure itself, i.e. quality, rigidity and damping；
Specifically, the transient response of a structure includes three parts: the load (power) of input, structure itself (rigidity,
Damping, quality), output (response: displacement, speed, acceleration), the purpose of this step is done for setting up kernel matrix below exactly
Prepare；
Step 105: utilize the unit pulse power of rotor-support-foundation system structure and supposition, calculates kernel function by the method for emulation
Matrix；It is exactly to apply unit pulse by finite element emulation software above at out-of-balance force institute to be identified application point specifically
Power, solves rotor structure under unit pulse power effect, the response of the response measuring point of arranged in front, and sets up kernel matrix.
In time domain, the superposition principle of linear system time-invariant system understands, and any out-of-balance force p (t) is caused by system
Dynamic response y (t), can represent with the linear combination of the dynamic response of a series of unit pulse power, i.e. structural dynamic response
Convolution relation formula is:
Building dynamic response y (t) at response measuring point in above formula can be displacement, speed or acceleration etc..
Understand according to structural dynamic response convolution relation formula (1), the pass between predetermined load and dynamic response thereof
It is that formula is represented by:
Yknow=G*Pknow (2)
In formula:
PknowUnit pulse power
YknowThe dynamic response under known load effect in emulation mode
The kernel matrix set up under G single-point load effect
When rotor-support-foundation system structure is by multiple load effect, the structural response that the most single load causes still can lead to
Cross formula (2) to obtain, and the total response of system is the linear superposition of the response that each load is quoted, therefore can be by multi-source loading problem table
It is shown as following kernel matrix form.
In formula:
The response that Y is corresponding in time domain, such as YiRepresent the uneven transient response that i point obtains
G kernel matrix, such as Gij: represent at the arteries and veins that the unit pulse power of j point and the uneven transient response of i point obtain
Rush kernel function
The load that P is to be identified, such as PjRepresent the load that j point is to be identified
M represents the number of load source point,
N represents the number of response measuring point
Step 106: use classical regularization method to select the regularization such as TiKhonov or truncated singular value decomposition TSVD
Operator f (α, σ), utilizes existing Generalized Cross Validation (GCV) known method such as criterion or L-curve to determine that suitable regularization is joined
Number α, is modified the kernel matrix G of morbid state, and the kernel matrix that note is revised is G α, and here is omitted for detailed process.
Step 107: solve the mould of least residual in regularizing functionals according to being converted into load identification problem to solve,
I.e. min | | GαPα,δ-yδ| |, wherein, GαRepresent revised kernel matrix, yδRepresent response measuring point at dynamic
Response, Pα,δRepresent out-of-balance force to be identified；
Thus ensure to measure the degree of approximation between response and the response of numerical computations, and LSQR method is used to be iterated
Solving, thus obtain out-of-balance force to be identified, the most optimal iterations can be determined by L-curve method；Need exist for
Bright, different responses 2 can be produced owing to substituting into different out-of-balance forces, the most repeatedly find iteration, when response 2 and test
1 closely, namely error responds the out-of-balance force that the out-of-balance force of 2 correspondences seeks to look for time the least in response.
Step 108: according to the relational expression of the out-of-balance force identified with degree of unbalancedness, it is thus achieved that amplitude A of amount of unbalance and phase
Position
Above-mentioned relation formula is represented by:
A=me ω2
In formula: feOut-of-balance force P
A amplitude
M unbalance mass (counterweight)
E eccentric throw
Phase place
The angular velocity of ω rotor
The t time
Step 109: utilize amplitude A and the phase place of the amount of unbalance identifiedRotor is carried out dynamic balancing；The size of counterweight
Being determined by amplitude A of the amount of unbalance identified, phase angle is contrary, i.e. adds 180 ° on original phase angle or deducts
180°。
Step 110: solve the response point displacement (time-domain signal) after balance；
Step 111: before and after carrying out counterweight, response contrasts accuracy and the precision verifying degree of unbalancedness identification.
For the ease of understanding the present invention, will further illustrate with instantiation below.
As shown in Figure 2 a and 2 b, Fig. 2 a is embodiment of the present invention rotor bearing experiment table, and Fig. 2 b is that the present invention is real
Executing the phantom schematic diagram of example rotor bearing experiment table, the two ends of rotor are by sliding supported condition, 1 disk on axle
A diameter of 80mm, width be 15mm, D be the diameter of rotor, the disk distance away from left bearing is 149mm, away from the distance of right bearing
Being elastic modelling quantity for 341mm, E, G1 is the coefficient of rigidity, and ρ is density.Sliding bearing is cylindrical bearing.This phantom with
The rotor experiment table of research experiment is consistent.In computer sim-ulation, the amount of unbalance of calculating is added on disk.2 surveys chosen
The point distance and position from the left side of rotating shaft is shown in Table 1.
The axial location table (unit mm) of table 1 measuring point
| Measuring point 1 | Measuring point 2 | |
| Axial location | 73 | 334 |
Set up the FEM (finite element) model of rotor-support-foundation system, obtain the quality of rotor-support-foundation system, rigidity and damping by transfer matrix method
Matrix.Rotor-support-foundation system is divided into 13 shaft parts, 14 nodes.The X selecting measuring point response to be node 4 is to radial displacement and node 11
Y-direction radial displacement.In the case of rotating speed is 2000r/min, recorded the dynamic respond such as figure of two measuring points by eddy current sensor
Shown in 3a and Fig. 3 b.
The independent application time of load application point be a sampling period be 0.0001s, amplitude be the impulse load of 1N, logical
Cross the time history that finite element solving can obtain responding from the Green pulse kernel function of each point of load to each response measuring point, from
And set up the kernel matrix G of out-of-balance force load identification.Based on Generalized Cross Validation (GCV) criterion and truncated singular value decomposition
(TSVD) regularization method, L-curve such as Fig. 4, real by the dynamic respond identification rotor of test by above-mentioned Dynamic Load Identification technology
Test the out-of-balance force dynamic loading of platform as shown in figure 5a and 5b, by a cycle of the load identified be 0.03s understand with rotor turn
Speed is identical.It is 73.686um that the out-of-balance force identified can be obtained amount of unbalance by (2) formula, and phase place is 76.3965 °
In order to verify accuracy and the precision of amount of unbalance identification, carry out dynamic balancing with rotor experimental facility above, and
Rotor-support-foundation system after having added counterweight is emulated.The size of counterweight is determined by the amount of unbalance identified, and phase angle is contrary, i.e.
Original angle add 180 ° or deducts 180 °, solving the response of the vibration of rotor system after having added counterweight, and join
Response contrast before and after Chong.From Fig. 6 a and 6b it can be seen that measuring point Oscillation Amplitude before and after dynamic balancing has had the biggest decline, dynamic
The effectiveness comparison of balance is good.
The beneficial effect that technical solution of the present invention is brought
1) present invention is based on calculating reverse technology, by the mapping relations of degree of unbalancedness with rotor dynamics response, uneven
The identification of weighing apparatus degree is converted into the recognition methods of out-of-balance force dynamic load, can solve degree of unbalancedness on-the-spot test difficult problem,
Avoid common method needing just can determine that correction mass, the most laborious time-consuming shortcoming by repeatedly test run.
2) present invention obtains its degree of unbalancedness under rotor runs well, and scene carries out dynamic balancing, can directly eliminate because of dress
The imbalance that practical factor causes such as join.
The above, the only present invention preferably detailed description of the invention, but protection scope of the present invention is not limited thereto,
Any those familiar with the art in the technical scope that the invention discloses, the change that can readily occur in or replacement,
All should contain within protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims
Enclose and be as the criterion.
Claims (7)
1. a rotor unbalance degree recognition methods based on calculating reverse technology, it is characterised in that including:
According to carry out dynamically balanced rotor structure, determine out-of-balance force number to be identified；
Instantaneous response analysis model adds out-of-balance force, finds response displacement and added force to have the response measuring point of dependency,
And the dynamic response of correspondence is obtained by experiment measurement；
Utilize the unit pulse power of rotor-support-foundation system structure and supposition, calculate kernel matrix by the method for emulation and repair
Just；
Based on dynamic response obtained above and amended kernel matrix, by solving least residual in regularizing functionals
Mould obtain out-of-balance force, and then obtain amplitude and the phase place of amount of unbalance, and accordingly rotor-support-foundation system structure carried out dynamic balancing
Process；
The process obtaining out-of-balance force by solving the mould of least residual in regularizing functionals specifically includes:
The mould of least residual in regularizing functionals is solved, i.e. according to being converted into load identification problem to solve
min||GαPα,δ-yδ| |, wherein, GαRepresent revised kernel matrix, yδRepresent the dynamic response at response measuring point, Pα,δRepresent out-of-balance force to be identified；
And use the LSQR method of conjugate gradient to be iterated solving, thus obtain out-of-balance force to be identified, the most optimal
Iterations can be determined by L-curve method.
Method the most according to claim 1, it is characterised in that find response displacement and added force to have the response of dependency
The process of measuring point specifically includes:
The Finite Element Method used by transfer matrix method or finite element emulation software sets up the instantaneous response analysis model of rotor, adds
Out-of-balance force carries out instantaneous response analysis, finds response displacement and added force to have the response measuring point of dependency, and response measuring point
Number can not be less than the number of out-of-balance force.
Method the most according to claim 1, it is characterised in that measured the process of the dynamic response obtaining correspondence by experiment
Specifically include:
According to the response measuring point obtained, to carry out the sensor that dynamically balanced rotor arranges that test responds；
The dynamic response y at above-mentioned response measuring point is measured by the experiment of rotor transient responseδ。
Method the most according to claim 3, it is characterised in that utilize the unit pulse of rotor-support-foundation system structure and supposition
Power, the process being calculated kernel matrix by the method for emulation is specifically included:
Use finite element emulation software to apply unit pulse power at out-of-balance force institute to be identified application point, solve rotor-support-foundation system structure
Under unit pulse power effect, the response of the response measuring point of arranged in front, and set up kernel matrix.
Method the most according to claim 4, it is characterised in that
The kernel matrix set up under single-point load effect is expressed as:
Yknow=G*Pnow
Wherein, PnowRepresentation unit impulsive force, YnowRepresenting the dynamic response under the known load effect in emulation mode, G represents
The kernel matrix set up under single-point load effect；
Kernel matrix form under multi-source load effect is expressed as:
In formula:
Y represents response corresponding in time domain, and G represents that kernel matrix, P represent load to be identified, and m represents load source point
Number, n represent response measuring point number.
Method the most according to claim 1, it is characterised in that also include:
Use classical regularization method to select the regularizing operator f such as TiKhonov or truncated singular value decomposition (α, σ), utilize wide
Justice cross validation criterion or L-curve method determine suitable regularization parameter, are modified by the kernel matrix of morbid state.
Method the most according to claim 1, it is characterised in that the process of the amplitude and phase place that obtain amount of unbalance is specifically wrapped
Include:
Relational expression according to the out-of-balance force identified with degree of unbalancedness, it is thus achieved that amplitude A of amount of unbalance and phase place,
Above-mentioned relation formula is represented by:
A=me ω2
Wherein, feRepresenting out-of-balance force to be identified, A represents that amplitude, m represent that unbalance mass, e represent eccentric throw,Represent phase
Position, ω represents the angular velocity of rotor-support-foundation system, t express time.
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| CN105912504B (en) * | 2016-04-11 | 2018-05-15 | 西安交通大学 | A kind of compression sensing method of mechanical structure multi-source shock loading identification |
| CN105912854B (en) * | 2016-04-11 | 2018-05-15 | 西安交通大学 | A kind of sparse representation method of mechanical structure Dynamic Load Identification |
| CN105843780B (en) * | 2016-04-11 | 2018-06-26 | 西安交通大学 | A kind of sparse deconvolution method of mechanical structure shock loading identification |
| CN113642131B (en) * | 2021-08-30 | 2022-10-18 | 中国航发贵阳发动机设计研究所 | Engine stress simulation method |
| CN117824922B (en) * | 2024-03-01 | 2024-05-28 | 江苏枫景舜精密机械有限公司 | Dynamic balance performance test method and system for ultra-precise speed reducer |
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