CN109145512A - Any orbit of shaft center eddy current sensor of Hydropower Unit stable state places angle analysis method - Google Patents
Any orbit of shaft center eddy current sensor of Hydropower Unit stable state places angle analysis method Download PDFInfo
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Abstract
The present invention relates to Hydropower Unit operation throw sensor placement optimization technical fields more particularly to a kind of any orbit of shaft center eddy current sensor of Hydropower Unit stable state to place angle analysis method.The present invention establishes geometrical relationship model to the arbitrarily large axis orbit of shaft center of some given, the derivation of equation is carried out to the geometrical relationship model, obtain the throw vector expression of the given arbitrarily large axis orbit of shaft center, and the maximum long and maximum long corresponding orientation of throw mould of throw mould, throw vector expression is converted to the throw vector expression of polar form, and seek throw e to the derivative of angle, θ by the throw vector expression to polar form, and then obtain maximum throw value and the corresponding angle of maximum throw value, it is used to instruct the best placement angle of throw sensor in engineering practice with this, to improving Hydropower Unit vibration throw on-line monitoring system, improving Hydropower Unit status monitoring and fault diagnosis level has weight engineering application value.
Description
Technical field
The present invention relates to Hydropower Unit operation throw measurement eddy current sensors under steady state condition to place optimisation technique field, especially
It is related to a kind of any orbit of shaft center eddy current sensor placement angle analysis method of Hydropower Unit stable state.
Background technique
There is point of operation throw and jiggering throw in the throw signal of unit, what China Electric Power Publishing House published for 2003
The throw computation model provided in " hydrogenerator machinery overhaul " book " is accurately held primarily directed to jiggering throw, document
The connotation of Hydropower Unit " throw " " in specify jiggering throw and run throw point.
Jiggering throw is exactly that the throw of unit axis is checked with the rotating part of the interim slow rotating machine sets of external force,
During jiggering, spiral case is in anhydrous state, and water guide shoe, lower guide shoe unclamp, and the big axis of unit is in free state, big axis
The out-of-balance force being subject to can be ignored, and big axis is stress balance.
Operation throw is exactly the vibration that unit rotating part in actual motion and big axis are generated by out-of-balance force, practical
It is entirely different when unit rotating part and big axis stress are with jiggering in operation, it will receive various power and lead to stress
Imbalance, uneven centrifugal force, runner bucket manufacture deviation and the placement angle generated as rotatable parts quality is uneven are inclined
Waterpower out-of-balance force, motor poor and generate install the air gap unevenly and the uneven radial magnetic pull, rotor magnetic of generation
Pole center mounts the axial magnetic pull out-of-balance force of depth displacement generation, bearing guide shoe restraining force etc., even if stable operation of unit feelings
Under condition, these power will lead to relative rotation center, and there is a phenomenon where magnitude sizes and direction continuously alternately to change, i.e.,
Generate shaft vibration, namely operation throw.
In engineering practice, excessive operation throw causes that unit vibration is bigger than normal, carbon in excitation unit in unit running process
Brush wear aggravates, and causes unit bearing bush temperature to increase under serious conditions, possibly even generates tile kilning phenomenon, thereby it is ensured that engineering
The accuracy that throw measurement is run in practice acquires vibration throw on-line monitoring system in authenticity, the assay machine of data
Group axis operation posture all has significance.Currently in the detection process of operation throw, need to use eddy current sensor
Maximum throw value is measured, but when eddy current sensor riding position difference, will cause the difference of measurement coordinate system and cause to survey
Error in amount, i.e., the coordinate value obtained to same throw vector measurement are also different, will lead to measurement obtain most put on
Angle value inaccuracy, then to operation throw detection when will there is a situation where for throw value false alarm, fail to report it is alert, even
Cause Hydropower Unit that catastrophe failure occurs.
Often measurement ± X, ± Y-direction throw value in engineering practice, however in unit actual motion by various out-of-balance forces,
The influence of the factors such as eddy current sensor mounting bracket and the pedestal stiffness difference of sensor installation, orbit of shaft center shape, measurement ±
X, ± Y-direction throw value may fail to include maximum operation throw value.Actually standard " ISO 7919-1Mechanical
vibration of non-reciprocating machines-Measurements on rotating shafts and
Evaluation criteria-Parat1:General guidelines " the B.3.2.3 definition in trifle to operation throw
In also proposed the problem.Analysis shows under round orbit of shaft center, even if the eddy current sensor of ± X, ± Y-direction rotate through centainly
After angle, the throw signal amplitude of measurement is still remained unchanged, but the orbit of shaft center eddy current sensor of other patterns is rotated
It crosses throw measured waveform shape and amplitude after certain angle to change, the orbit of shaft center pattern in actual motion is more multiple
It is miscellaneous, more irregular.
It is current to lack to instructing grinding for the estimation of throw maximum value in engineering practice and the placement of throw measurement sensor
Study carefully, places throw under influence and different orbit of shaft center of the angle to operation throw measured value therefore, it is necessary to study sensor and pass
The best placement angle of sensor.
Summary of the invention
(1) technical problems to be solved
In order to solve the above problem of the prior art, the present invention provides a kind of best placement that can instruct throw sensor
Any orbit of shaft center eddy current sensor of the Hydropower Unit stable state of angle places angle analysis method.
(2) technical solution
In order to achieve the above object, the main technical schemes that the present invention uses include:
The present invention provides eddy current sensor under a kind of any orbit of shaft center of Hydropower Unit stable state and places angle analysis method, packet
Include following steps:
Step S1: geometrical relationship model is established to the arbitrarily large axis orbit of shaft center of some given；
Step S2: the geometrical relationship model described in step S1 carries out the derivation of equation, obtains the given arbitrarily large axis
The throw vector expression of orbit of shaft center；
Step S3: throw vector expression described in step S2 is converted to the throw vector expression of polar form；
Step S4: it carries out seeking throw e by the throw vector expression of the polar form described in step S3 diagonal
The derivative of θ is spent, and then obtains maximum throw value emaxAnd maximum throw value emaxCorresponding angle is used to instruct engineering real with this
Trample the placement angle of middle throw sensor.
According to the present invention as described above, the geometrical relationship model in step S1, which includes one, has vertical coordinate axle OX and OY
Coordinate system, the first model circle, the second model circle and represents practical axis geometric center O greatly1Any closed curve of track；
First model circle represents ideally i.e. big axis geometric center and is overlapped with rotation center, and with rotation center O point
For the big shaft section geometry of the circle model in the center of circle；
Second model circle, which is represented i.e. big axis geometric center under virtual condition and enclosed with arbitrary trajectory, to be rotated about the center of rotation, and with
O2Point is the big shaft section geometry of the circle model in the center of circle；
O2Point, which is located at, represents practical big axis geometric center O1On any closed curve of track；
First model circle is identical as the second model radius of circle.
According to the present invention, the derivation process of the throw vector expression under the arbitrary orientation in step S2 is as follows:
According to the geometrical relationship model of step S1, any closed curve can be expressed as formula (1) on two-dimensional surface:
F (x, y)=0 (1)
In formula, x indicates any point X axis coordinate on closed curve, and y indicates any point Y axis coordinate on closed curve；
If O2The coordinate representation of point is (PX, PY), this when inscribe OO2With+X to angle be θ, then point O2Specific coordinate value can
To be expressed as formula (2):
In formula, e indicates that the offset distance of big axis geometric center/centroid relative rotation center, θ indicate OO2With the folder of+X-axis
Angle；
Main shaft runout vector can simplify as following formula (6):
In formula,Indicate main shaft runout vector, exIndicate +X direction throw value, eyIndicate +Y direction throw value；
Assuming that the position that the eddy current sensor of current research is placed is OXY coordinate system, then OXY coordinate system is rotated counterclockwise
α angle obtains a new coordinate system OST, introduces transformation matrix of coordinates T and is expressed as formula (7), then the throw at new coordinate system OST
VectorIt is expressed as formula (8):
In formula,For the throw vector under OST coordinate system, T is transformation matrix of coordinates,For main shaft runout vector, α is
OXY coordinate system rotates counterclockwise obtains the angle of OST coordinate system；
Enable f (θ)=PX, g (θ)=PY, convolution (6) and formula (7), substitute into formula (8) sensor arrangement at an arbitrary position under
Throw waveform is expressed as formula (9):
According to the present invention, the throw vector expression of the polar form in step S3 is expressed as following formula (10):
In formula, e (θ) is the equation that the distance of point to rotation center on orbit of shaft center curve changes with angle, θ, and α is coordinate
It is the angle of rotation.
According to the present invention, (11) acquire the extreme value of e (θ) according to the following formula in step S4:
By formula (11), when finding out the maximum of e (θ), angle, θ corresponding to e (θ) maximum is that sensor is most preferably pacified
Angle is put, maximum throw value can be obtained in the best placement angle lower sensor.
According to the present invention, when big axis orbit of shaft center shows as toed-out shape, the throw waveform of big axis is expressed as:
Composite type (11) and (12) can derive following formula (13):
Solving to formula (13) can obtain, and the throw value measured when θ=0, pi/2, π, 3 pi/2s, 2 π is maximum value or minimum value；
E can be obtained to the second dervative such as following formula (14) of θ by further solving to formula (13):
Solving to formula (14) can obtain, and the throw value measured as θ=0, π, 2 π is maximum, the OO when θ=pi/2,3 pi/22
The throw value of measurement is minimum.
According to the present invention, when big axis orbit of shaft center shows as heart-shaped, the throw of big axis is expressed as following formula (15):
Composite type (11) and (15) can derive following formula (16):
Solving to formula (16) can obtain, and the throw value measured as θ=0, π, 2 π is maximum value or minimum value；
According to formula (16), further derivation obtains e to the second dervative such as following formula (17) of θ:
Solving to formula (17) can obtain, and the throw value measured when θ=0,2 π is maximum.
(3) beneficial effect
The beneficial effects of the present invention are:
1, the present invention proposes any orbit of shaft center eddy current sensor of Hydropower Unit stable state by theory analysis and places angle
Analysis method, further investigation eddy current sensor difference place influence of the angle to throw measurement result, are used to instruct engineering with this
The best placement angle of throw sensor in practice provides theory for throw measurement maximum in engineering practice and sensor placement
Foundation and technological guidance improve Hydropower Unit status monitoring and failure to Hydropower Unit vibration throw on-line monitoring system is improved
Diagnostic level has important engineering application value.
2, for the present invention by establishing throw computational geometry model under arbitrary curve, proposing orbit of shaft center is arbitrary curve
Lower throw, which calculates general theory and furthers investigate eddy current sensor difference, places influence of the angle to throw measurement result, fills up
The blank of correlative study theory.
Detailed description of the invention
Fig. 1 is throw computational geometry illustraton of model under any orbit of shaft center of the invention；
Fig. 2 is toed-out shape Chart of axes track；
Fig. 3 is throw measured waveform figure under different direction under toed-out shape orbit of shaft center；
Fig. 4 is heart-shaped Chart of axes track；
Fig. 5 is throw measured waveform figure under different direction under heart-shaped orbit of shaft center.
Specific embodiment
In order to preferably explain the present invention, in order to understand, with reference to the accompanying drawing, by specific embodiment, to this hair
It is bright to be described in detail.
Overall plan
Before being derived, the hypothesis that the present invention studies is provided first.
Assuming that 1: assuming that the big shaft section of the hydraulic turbine is absolute circle.Engineering requires throw to sense in measurement process in practice
Device installation site should be close to finishing axial plane position, while the circularity of big shaft section circle should meet standard requirements, therefore, Ke Yi
Big axis shape is assumed in theory deduction.
Assuming that 2: assuming that turbine-generator units orbit of shaft center is arbitrary curve under steady-state operation, and heavy under different rotation periods
It closes.Actual eddy current sensor installation site is influenced by sensor stand and pedestal rigidity in engineering, as unit is fixed
The phenomenon that part vibrates together, and the orbit of shaft center of unit is not overlapped there is also the period under orbit of shaft center.In the big axis rotation of unit
It is influenced by radial support watt, the rotation center of big axis further aggravates orbit of shaft center there is deviating, rotating
Poor repeatability.For simplifying demand, the present invention ignores that sensor stand and pedestal rigidity is uneven, rotation center pivot offset
Etc. factors influence, it is assumed that the orbit of shaft center of arbitrary curve can be overlapped under different cycles.
Assuming that 3: assuming that selected big shaft section Mass Distribution is uniform, the mass center in section is overlapped with geometric center.With adding
The quality of the big axis of raising of work precision is generally distributed more uniformly.Ignore Mass Distribution in derivation process of the invention for the time being to pendulum
Spend the influence calculated.
Assuming that 4: assuming that eddy current sensor detecting head surface is complete vertical with big axis contact surface.The sensor of actual installation according to
Lai Yu experience abundant, it is ensured that eddy current sensor detecting head surface is vertical with big axial section, in derivation process of the invention temporarily
When do not consider the influence of the factor, ignore that big axis is static and movement in eddy current sensor detecting head surface and big axis surface inclination conditions
Generation.
Assuming that 5: assuming that the rigidity indifference of the mounting bracket rigidity of eddy current sensor and base support.It is put in engineering practice
The measurement of degree and the installation of eddy current sensor are closely related, and eddy current sensor is often mounted on the angle steel branch of custom-made in practice
On frame, and angle bar frame is pasted on oil tray cover board or pedestal by specific glue, in practice due to firm pasting degree is different,
Oil tray cover board, which exists, divides the factors such as valve, and the rigidity and Oscillation Amplitude of pedestal are also different, derive for convenience, derivation of the invention
Temporarily ignore the influence of mounting bracket rigidity Yu base support stiffness difference in journey.
Assuming that 6: assuming that eddy current sensor different rotation angle is apart from rotation center radius having the same.In practice due to
Installation influences, and sensor rotation is reinstalled after crossing certain angle, and the distance of the big axis rotation center of potential range changes.It is real
On border different rotary angle lower sensor installation deviation can be reduced as far as possible by controlling sensor mounting process, it is of the invention
Ignore the influence of the factor in derivation process.
Assuming that 7: assuming that the orbit of shaft center that the throw sensor of rotation front and back reconstructs is identical.Under given orbit of shaft center, peace
Throw waveform mounted in the vortex sensor measuring of different direction is different, the axle center gone out according to two pairs of different throw Waveform Reconstructings
Geometric locus may be also different, the axle center that the throw sensor in derivation process of the invention for the time being based on rotation front and back reconstructs
This identical hypothesis of track is studied.
Calculation method of the invention generally divides following steps:
Step S1: geometrical relationship model is established to the arbitrarily large axis orbit of shaft center of some given；
Step S2: the geometrical relationship model described in step S1 carries out the derivation of equation, obtains the given arbitrarily large axis
The throw vector expression of orbit of shaft center；
Step S3: throw vector expression described in step S2 is converted to the throw vector expression of polar form；
Step S4: it carries out seeking throw e by the throw vector expression of the polar form described in step S3 diagonal
The derivative of θ is spent, and then obtains maximum throw value emaxAnd maximum throw value emaxCorresponding angle is used to instruct engineering real with this
Trample the placement angle of middle throw sensor.
Geometrical relationship model in step S1 is as shown in Fig. 1, the coordinate including one with vertical coordinate axle OX and OY
System, the first model circle, the second model is round and represents practical big axis geometric center O1Any closed curve of track.
Specifically, the first model circle represents ideally i.e. big axis geometric center and is overlapped with rotation center, and with rotation
Center O is the big shaft section geometry of the circle model in the center of circle, and the second model circle represents under virtual condition i.e. big axis geometric center with any
Track, which is enclosed, to be rotated about the center of rotation, and with O2Point is the big shaft section geometry of the circle model in the center of circle, O2Point is several positioned at practical big axis is represented
What center O1On any closed curve of track, the first model circle is identical as the second model radius of circle
Step S2 is derived by the throw vector expression of the given arbitrarily large axis orbit of shaft center, and detailed process is as follows:
It takes a certain section of big axis to be analyzed, geometrical relationship mould is established to the arbitrarily large axis orbit of shaft center of some given
Type, ideally when main-shaft axis is overlapped with rotation center, big axis geometric center O1It is overlapped with rotation center O, in big axis
In rotary course, when difference goes to the position that amesdial or eddy current sensor are placed in cross-sectional periphery, amesdial or whirlpool
The reading of flow sensor is constant, and each point reading draws a straight line.
However big axis geometric center is not overlapped with rotation center in actual motion, big axis geometric center O1In different situations
The lower closed curve that can rotate and ultimately form according to hypothesis 2 arbitrary shape around rotation center O along arbitrary curve, and big axis
Section is a two-dimensional surface, can be expressed as formula (1) for the closed curve of arbitrary shape on two-dimensional surface:
F (x, y)=0 (1)
In formula, x indicates any point X axis coordinate on closed curve, and y indicates any point Y axis coordinate on closed curve.
Step S2: O is set2The coordinate representation of point is (PX, PY), this when inscribe OO2With+X to angle be θ, then point O2It is specific
Coordinate value can be expressed as formula (2):
In formula, e indicates that the offset distance of big axis geometric center/centroid relative rotation center, θ indicate OO2With the folder of+X-axis
Angle.
Geometrical model in step S1, in conjunction with attached drawing 1 it is found that big axis deviates the distance OO of rotation center in figure2Length
For e, although being all to have a common feature i.e. shape all since track shaft big in reality is irregular and shape has very much
It is the curve of closure and is at every moment moved along closed curve, therefore the track diagram computation model in attached drawing 1 can represents
Situation under arbitrary trajectory, big axis geometric center is not overlapped with rotation center in actual motion in actual conditions, the track in Fig. 1
Model is the arbitrary trajectory represented on two-dimensional surface, and the calculation expression of throw all meets following formula under a certain moment in office:
In formula, exIndicate +X direction throw value, eyIndicate +Y direction throw value.
And it obviously can be derived that following geometrical relationship from attached drawing 1:
Therefore following formula (5) can be derived in conjunction with the above geometrical relationship formula (4) and formula (3):
In formula, R indicates the radius of big axis.
Because the radius R of big axis is usually 10 of big eccentric shaft away from e in engineering practice4Times, therefore, enable the half of relatively large axis
Diameter R is that the big eccentric shaft of dimensionless is cast out away from e, then main shaft runout vector can simplify as following formula (6):
In formula,Indicate main shaft runout vector, exIndicate +X direction throw value, eyIndicate +Y direction throw value.
For research eddy current sensor to the influence of throw under different riding positions, it is assumed that Current eddy current sensor was placed
Position is OXY coordinate system, then OXY coordinate system rotation alpha angle counterclockwise is obtained a new coordinate system OST, transformation matrix of coordinates T
Be expressed as formula (7), then at new coordinate system OST, throw vectorIt is expressed as formula (8):
In formula,For the throw vector under OST coordinate system, T is transformation matrix of coordinates,For main shaft runout vector, α is
OXY coordinate system rotates counterclockwise obtains the angle of OST coordinate system, α ∈ (0,360 °).
As shown in Figure 1, existing further to coordinate transform for example, such as the O in figure2Point, the coordinate in OXY coordinate system
Vector isThen its coordinate vector under OST coordinate system isRelationship meeting formula (8) between the two.
When due to actual measurement, eddy current sensor is mutually perpendicular to place, so being mutually perpendicular to the currents sensing placed
Device, which is equivalent to, constitutes a rectangular coordinate system, it is assumed that and it in some position is coordinate system OXY, then the whirlpool of OX axis direction placement
The throw shift value that flow sensor measurement obtains is X-direction throw value, what the vortex sensor measuring of OY axis direction placement obtained
Throw shift value is Y-direction throw value, the throw waveform diagram of X-direction and Y-direction is then drawn out respectively, finally according to X-direction
Synthesize orbit of shaft center with the throw waveform diagram of Y-direction.
When due to measuring every time, the measurement position of eddy current sensor is not fixed, therefore when the measurement for changing eddy current sensor
When position, it is equivalent to that coordinate system OXY is rotated to obtain a new coordinate system, although finally synthesizing under the new coordinate system
Orbit of shaft center can have deviation in practical situations, but general shape be it is constant, herein according to assuming that 4,5 and 6 ignore
Eddy current sensor during the installation process caused by deviation, and according to assuming 7, the orbit of shaft center measured under different direction is
Same throw vector that is identical, therefore measuring at this time, coordinate is at former coordinate system OXY and in new coordinate system
It is different under OST, to know the throw coordinate value under different measurement orientation, it is necessary to which introducing coordinate transform can obtain
The throw measured value that eddy current sensor obtains under arbitrarily measurement orientation, while probing into the shadow under different measurement orientation to throw value
It rings.
Simultaneously, it is assumed that rotation angle is α, then can not necessarily obtain maximum throw value under the angle [alpha], be vortexed in practice
Sensor be it is fixed, big axis is rotating always is with 360 ° to get to what is measured in the direction (such as OX axis direction)
Period does not stop the throw waveform diagram of wheel measuring in periodically variable throw waveform diagram to axis big under the α angle, according to
α and θ determines the corresponding orientation of maximum throw value jointly, if in conjunction with the position that key mutually marks, it can more accurately
It determines the corresponding orientation of maximum throw value, to be used to instruct the best riding position of eddy current sensor, prevents because most putting on
False alarm caused by angle value measurement inaccuracy fails to report police, even results in what vortex sensor measuring when catastrophe failure occurs obtained
Maximum throw value has perfect operation throw operation throw on-line monitoring and early warning system also in the situation in safe range
Great realistic meaning, the generation preferably prevented accident.
Enable f (θ)=PX, g (θ)=PY, convolution (6) and formula (7) substitute into formula (8) up to sensor arrangement at an arbitrary position
Lower throw waveform table is shown as formula (9).
Step S3: according to the formula (9) in step S2, formula (9) is converted into polar form and is expressed as following formula (10):
Step S4: by seek throw e to the derivative of angle, θ to the formula (10) in step S3, and then maximum is obtained
Throw value emaxAnd maximum throw value emaxCorresponding angle is used to instruct the laying angle of throw sensor in engineering practice with this
Degree.
Formula (10) shows when any value of α, two orthogonal direction vortex sensor measuring values depend on both sides because
Element: (1) point O on orbit of shaft center2The distance e (θ) apart from rotation center O；(2) angle, θ-α.Due to point on orbit of shaft center curve
Distance to rotation center is variation, so, the throw value that eddy current sensor turns over different angle measurement is different, while root
It can be in the hope of in the extreme value of e (θ) according to formula (10):
In the case of formula (11) is set up, there are maximum value or minimum values by e (θ), this is exactly to adjust throw value in engineering practice to exist
It is concerned about the most when in prescribed limit value, therefore, throw in engineering practice can be instructed to pass according to formula (10) and formula (11)
The placement angle of sensor.
When acquiring maximum, show the maximum value e under the angle, θ there are throwmax, then worked as according to this solving result
E is deflected under the position that preceding eddy current sensor is placedmaxCorresponding angle, θ instructs the throw sensor can to measure throw with this
The estimation of throw maximum value in riding position and engineering practice at maximum value.
Embodiment 1
When big axis orbit of shaft center shows as toed-out shape, the throw of big axis is indicated are as follows:
Known to composite type (11) and (12):
Therefore, the OO when θ=0, pi/2, π, 3 pi/2s, 2 π2The throw value of measurement is maximum value or minimum value.
E can be obtained to the second dervative such as following formula (14) of θ according to above formula (13):
Solving to formula (14) can obtain, the OO when θ=0, π2The throw value of measurement is maximum, the OO when θ=pi/2,3 pi/22
The throw value of measurement is minimum.Can be seen from figure 3 corresponded to when θ=0, π α angle+X-axis and+Y-axis throw value synthesis
Throw vector field homoemorphism value out is maximum, corresponded to when θ=pi/2,3 pi/2 α angle+X-axis and+Y-axis throw value synthesize
The throw vector field homoemorphism value come is minimum, and the conclusion obtained with formula (14) is consistent.
If a=10 μm, b=20 μm, and α is set as the corresponding toed-out shape orbit of shaft center of 0, π, pi/2,3 pi/2s and sees Fig. 2,
The throw waveform that corresponding X-axis, Y-axis vortex sensor measuring obtain is shown in that Fig. 3, Fig. 3 show under toed-out shape orbit of shaft center
Measure influence of the orientation to the amplitude and phase of throw waveform, i.e., with initial installation position be 0 ° i.e. α=0 ° when it is corresponding measure+
Corresponding+X-axis and+Y-axis throw waveform after X-axis and+Y-axis throw waveform diagram, and 180 ° of installation position of rotation i.e. α=180 °
Figure, hence it is evident that find out that the amplitude of α=180 ° shaft displacement waveform corresponding with α=0 ° is constant, corresponding angle, θ becomes at amplitude maximum
Change, but be all to refer to the same place in fact, is i.e. the best riding position of eddy current sensor can measure pendulum when being α=0 °
Spend waveforms amplitude maximum value, i.e., α=0 ° and on the basis of α=0 ° rotate angle, θ=180 ° when can obtain maximum throw value；
The best riding position of eddy current sensor can measure throw waveforms amplitude maximum value, i.e. α=180 ° when being α=180 ° when, revolve
Maximum throw value can be obtained when gyration θ=0 °.
Embodiment 2
When big axis orbit of shaft center shows as heart-shaped, the throw of big axis is expressed as following formula (15):
Composite type (11) and (15) can derive following formula (16):
Solving to formula (16) can obtain, the OO as θ=0, π, 2 π2The throw value of measurement is maximum value or minimum value.
E is further acquired to the second dervative such as following formula (17) of θ according to above formula (16):
Solving to formula (17) can obtain, the OO when θ=0,2 π2The throw value of measurement be maximum, from Fig. 5 it can also be seen that
Be consistent with above-mentioned calculated result, corresponded to when θ=0,2 π α angle+the throw vector that is synthesized of X-axis and+Y-axis throw value
Modulus value be maximum, wherein same α=360 ° in α=0 ° in Fig. 5, i.e., α=0 °+X-axis and+Y-axis throw waveform diagram and α=360 °
+ X-axis is identical with+Y-axis throw waveform diagram.
If a=50 μm and α is set as 0, π/6, the corresponding heart-shaped orbit of shaft center in π/4 is shown in Fig. 4, corresponding X-axis, Y-axis
See that Fig. 5, Fig. 5 show to measure orientation under heart-shaped orbit of shaft center to the amplitude of throw waveform and phase to throw measured waveform
Influence, i.e., be 0 ° i.e. α=0 ° with initial installation position, then rotate 180 ° i.e. after α=180 °, hence it is evident that find out α=180 ° and α=
The amplitude of 0 ° of corresponding shaft displacement waveform is constant, and corresponding angle, θ changes at amplitude maximum, but is all to refer to together in fact
One place.
That is the best riding position of eddy current sensor can measure throw waveforms amplitude maximum value, i.e. α=0 ° when being α=0 °
When, rotation angle, θ=180 ° when can obtain maximum throw value；The best riding position of eddy current sensor can be with when being α=180 °
Maximum throw value can be obtained when measuring throw waveforms amplitude maximum value, i.e. α=180 °, when rotation angle, θ=0 °.
The present invention proposes a kind of any orbit of shaft center eddy current sensor laying angle of Hydropower Unit stable state by theory analysis
Analysis method is spent, eddy current sensor difference is had extensively studied and places influence of the angle to throw measurement result, filled up correlation and ground
Study carefully theoretical blank, be used to instruct the best placement angle of throw sensor in engineering practice with this, is maximum in engineering practice
Throw measurement and sensor placement provide theoretical foundation and technological guidance, are to Hydropower Unit operation throw on-line monitoring is improved
System, improving Hydropower Unit status monitoring and fault diagnosis level has weight engineering application value.
It is to be appreciated that describing the skill simply to illustrate that of the invention to what specific embodiments of the present invention carried out above
Art route and feature, its object is to allow those skilled in the art to can understand the content of the present invention and implement it accordingly, but
The present invention is not limited to above-mentioned particular implementations.All various changes made within the scope of the claims are repaired
Decorations, should be covered by the scope of protection of the present invention.
Claims (7)
1. a kind of any orbit of shaft center eddy current sensor of Hydropower Unit stable state places angle analysis method, which is characterized in that the party
Method the following steps are included:
Step S1: geometrical relationship model is established to the arbitrarily large axis orbit of shaft center of some given；
Step S2: the geometrical relationship model described in step S1 carries out the derivation of equation, obtains the given arbitrarily large axis axle center
The throw vector expression of track；
Step S3: throw vector expression described in step S2 is converted to the throw vector expression of polar form；
Step S4: seek throw e to angle, θ by the throw vector expression of the polar form described in step S3
Derivative, and then obtain maximum throw value emaxAnd maximum throw value emaxCorresponding angle is used to instruct in engineering practice with this
The placement angle of throw sensor.
2. any orbit of shaft center eddy current sensor of a kind of Hydropower Unit stable state according to claim 1 places angle analysis side
Method, it is characterised in that:
Geometrical relationship model described in step S1 include one with vertical coordinate axle OX and OY coordinate system, the first model circle,
Second model is round and represents practical big axis geometric center O1Any closed curve of track；
The first model circle represents ideally i.e. big axis geometric center and is overlapped with rotation center, and using O point as the center of circle
Big shaft section geometry of the circle model；
Second model circle, which is represented i.e. big axis geometric center under virtual condition and enclosed with arbitrary trajectory, to be rotated about the center of rotation, and with
O2Point is the big shaft section geometry of the circle model in the center of circle；
O2Point, which is located at, represents practical big axis geometric center O1On any closed curve of track；
First model circle is identical as the second model radius of circle.
3. any orbit of shaft center eddy current sensor of a kind of Hydropower Unit stable state according to claim 2 places angle analysis side
Method, it is characterised in that:
The derivation process of throw vector expression under arbitrary orientation described in step S2 is as follows:
According to geometrical relationship model described in step S1, any closed curve can be expressed as formula (1) on two-dimensional surface:
F (x, y)=0 (1)
In formula, x indicates any point X axis coordinate on closed curve, and y indicates any point Y axis coordinate on closed curve；
If O2The coordinate representation of point is (PX, PY), this when inscribe OO2With+X to angle be θ, then point O2Specific coordinate value can be with table
It is shown as formula (2):
In formula, e indicates the offset distance of big axis geometric center/centroid relative rotation center；
Main shaft runout vector can simplify as following formula (6):
In formula,Indicate that main shaft runout vector, ex indicate +X direction throw value, ey indicates +Y direction throw value；
Assuming that the position that the eddy current sensor of current research is placed is OXY coordinate system, then by OXY coordinate system rotation alpha angle counterclockwise
Degree obtains a new coordinate system OST, introduces transformation matrix of coordinates T and is expressed as formula (7), then the throw at new coordinate system OST to
AmountIt is expressed as formula (8):
In formula,For the throw vector under OST coordinate system, T is transformation matrix of coordinates,For main shaft runout vector, α is OXY seat
Rotation obtains the angle of OST coordinate system counterclockwise for mark system；
Enable f (θ)=PX, g (θ)=PY, convolution (6) and formula (7), substitution formula (8) obtain sensor arrangement and descend throw at an arbitrary position
Waveform is expressed as formula (9):
4. any orbit of shaft center eddy current sensor of a kind of Hydropower Unit stable state according to claim 3 places angle analysis side
Method, it is characterised in that:
The throw vector expression of polar form described in step S3 is expressed as following formula (10):
In formula, e (θ) is the equation that the distance of point to rotation center on orbit of shaft center curve changes with angle, θ, and α is coordinate system rotation
The angle turned.
5. any orbit of shaft center eddy current sensor of a kind of Hydropower Unit stable state according to claim 4 places angle analysis side
Method, it is characterised in that:
(11) acquire the extreme value of e (θ) according to the following formula in the step S4:
By formula (11), when finding out the maximum of e (θ), angle, θ corresponding to e (θ) maximum is the best laying angle of sensor
Degree, can obtain maximum throw value in the best placement angle lower sensor.
6. any orbit of shaft center eddy current sensor of a kind of Hydropower Unit stable state according to claim 5 places angle analysis side
Method, it is characterised in that:
When big axis orbit of shaft center shows as toed-out shape, the throw waveform of big axis is expressed as:
Composite type (11) and (12) can derive following formula (13):
Solving to formula (13) can obtain, and the throw waveform values that measurement obtains when θ=0, pi/2, π, 3 pi/2s, 2 π are maximum or minimum
Value；
E can be obtained to the second dervative such as following formula (14) of θ by further solving to formula (13):
Solving to formula (14) can obtain, and the throw waveform values that measurement obtains as θ=0, π, 2 π are maximum, when θ=pi/2,3 pi/2s
When OO2Measuring obtained throw waveform values is minimum.
7. any orbit of shaft center eddy current sensor of a kind of Hydropower Unit stable state according to claim 5 places angle analysis side
Method, it is characterised in that:
When big axis orbit of shaft center shows as heart-shaped, the throw of big axis is expressed as following formula (15):
Composite type (11) and (15) can derive following formula (16):
Solving to formula (16) can obtain, and the throw value measured as θ=0, π, 2 π is maximum value or minimum value；
According to formula (16), further derivation obtains e to the second dervative such as following formula (17) of θ:
Solving to formula (17) can obtain, and the throw value measured when θ=0,2 π is maximum.
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|---|---|---|---|---|
| JPH06113462A (en) * | 1992-09-28 | 1994-04-22 | Chubu Electric Power Co Inc | Control system for stabilization of line |
| WO1996027231A2 (en) * | 1995-02-25 | 1996-09-06 | Nanjing Automation Research Institute | Qualitative analysis and policy decision method and control system for power system stability |
| CN107450473A (en) * | 2017-08-03 | 2017-12-08 | 南京航空航天大学 | A kind of calculating of CFXYZA types five-axle number control machine tool rotary shaft geometric error, compensation and its verification method |
| CN107885699A (en) * | 2017-09-26 | 2018-04-06 | 昆明理工大学 | A kind of method for the shafting vibration throw analytical expression for establishing vertical water pump shaft system of unit track |
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2018
- 2018-09-27 CN CN201811137985.7A patent/CN109145512B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH06113462A (en) * | 1992-09-28 | 1994-04-22 | Chubu Electric Power Co Inc | Control system for stabilization of line |
| WO1996027231A2 (en) * | 1995-02-25 | 1996-09-06 | Nanjing Automation Research Institute | Qualitative analysis and policy decision method and control system for power system stability |
| CN107450473A (en) * | 2017-08-03 | 2017-12-08 | 南京航空航天大学 | A kind of calculating of CFXYZA types five-axle number control machine tool rotary shaft geometric error, compensation and its verification method |
| CN107885699A (en) * | 2017-09-26 | 2018-04-06 | 昆明理工大学 | A kind of method for the shafting vibration throw analytical expression for establishing vertical water pump shaft system of unit track |
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