CN109033680A - A method of mistuned bladed disk is repaired using coating - Google Patents
A method of mistuned bladed disk is repaired using coating Download PDFInfo
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Abstract
The present invention provides a kind of method for repairing mistuned bladed disk using coating.This method by carrying out geometric dimension measurement to mistuned bladed disk, mould measurement, detuning identification calculate, the rigidity compensation amount that obtains different-thickness coating, the design of coating recovery scenario, the detuning identification of recovery scenario finite element model, determined by numerical simulation whether recovery scenario up to standard, mistuned bladed disk carries out actual coating reparation, determine actual repair after leaf dish whether deposit it is up to standard, repair after leaf dish reprocessing, determine whether leaf dish deposits up to standard after reprocessing, if up to standard complete to repair.Principles of the invention are more in line with blade dynamics requirement, and rehabilitation cost is low.In addition, the coat type that the present invention is applicable in is wide.As long as being suitble to the coating material of leaf dish operating condition applicable.
Description
Technical field
The present invention relates to mistuned bladed disk recovery technique field, in particular to a kind of side that mistuned bladed disk is repaired using coating
Method.
Background technique
Important core component one of of the leaf dish as aero-engine, quality good or not directly determines aero-engine
Performance and service life.Usual leaf dish has joggle leaf dish and integral blade disk two types.Theoretically, leaf dish should be cyclic-symmetry structure,
But due to material characteristic is uneven, the random abrasion in manufacture mismachining tolerance, rigging error, use process and artificially design etc. because
Inevitably there is a small amount of difference between each sector in element, reality, these a small amount of difference are referred to as detuning, these are detuning
So that each sector generates difference on kinetic characteristics.Especially blade, it is very high for detuning sensibility, even a small amount of
It is detuning, also the vibration of individual blades can be made to aggravate at double, generate high cycles fatigue and destroy.Therefore, scientifically determine detuning journey
Degree and reasonable design recovery scenario, have great importance for the raising of mistuned bladed disk performance.
Currently, having devised some restorative procedures for mistuned bladed disk, but still there are some problems.Patent
The table of CN200610057921.7, patent CN201710371309.5, patent CN201510289304.9 primarily directed to leaf dish
Planar defect and matrix damaged part carry out bladed-disk assemblies reconstruction using technologies such as welding material, laser melting coating, laser 3D printings,
Secondary correction of the flank shape processing is carried out again, reaches reparation purpose.And for aero-engine leaf dish often using titanium alloy material, this
The hardness of kind material is higher, and leaf dish requirement on machining accuracy is harsh in addition, greatly improves mechanical processing difficulty, while also to processing
The machine of equipment adds ability to propose higher requirement.Meanwhile the equipment for being also required to profession of the techniques such as laser melting coating, these are all big
The cost of leaf dish reparation is improved greatly.At the same time, the above reparation means only realize mistuned bladed disk in geometric dimension level
On it is consistent, but it is consistent on kinetic characteristics that each sector can not be completely secured.Above method also lacks repairing effect
Differentiation link, there are repairing effect hidden danger not up to standard.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of method for repairing mistuned bladed disk using coating.This hair
Bright technical solution are as follows:
A method of mistuned bladed disk is repaired using coating, comprising the following steps:
Step 1: detuning identification is carried out to mistuned bladed disk, obtain each blade quality is detuning and detuning of stiffness data；
Step 1.1: the greasy dirt on mistuned bladed disk surface, corrosion being cleared up, required with meeting coating coating；
Step 1.2: the outer dimension of each blade of mistuned bladed disk being measured, the volume of each blade is obtainedAccording to
Following formula calculates the quality mismatching angle of each blade
In formula (1), j is mistuned bladed disk blade serial number,For j-th of leaf quality mismatching angle of mistuned bladed disk, b is as subscript
Indicate practical mistuned bladed disk, VypFor theoretical coordination blade volume, yp coordinates the blade of leaf dish as subscript representation theory；
Step 1.3: mould measurement being carried out to mistuned bladed disk, obtains the natural frequency ω of mistuned bladed diskbWith vibration shape X；
Step 1.4: detuning of stiffness identification being carried out to mistuned bladed disk in conjunction with the quality detuning identification result of step 1.2, is obtained
The detuning of stiffness amount of each bladeSpecific step is as follows:
Step 1.4.1: the leaf dish finite element model coordinated is established according to the Theoretical Design size of mistuned bladed disk, and carries out mould
State analysis obtains the natural frequency ω of mistuned bladed diskiWith canonical vibration shape matrix Φ, and each leaf is extracted from modal analysis result
Piece vibration shape matrix Φj；
Step 1.4.2: mistuned bladed disk canoncial coordinates vector P is obtained by following formula respectivelybWith the canonical for coordinating leaf dish
Stiffness matrix Λ；
Pb=Φ-1X (2)
In formula, i is rank number of mode, and n is the leaf dish finite element model number of degrees of freedom, coordinated；
Step 1.4.3: establishing ideal cantilever blade finite element model, to extract the stiffness matrix K of ideal cantilever bladeCBWith
Mass matrix MCB, CB carries out model analysis as subscript representation theory cantilever blade, obtains inherent circular frequency diagonal matrix ωCB
And vibration shape matrix ΦCB；The modal participation factors of detuning of stiffness are calculated separately by following formula againThe detuning mode with quality
Participate in the factorWherein K, M respectively indicate rigidity and quality as subscript:
In formula, ΛCBFor the diagonal matrix of theoretical cantilever blade inherent circular frequency square；
Step 1.4.4: the detuning of stiffness amount of each blade of mistuned bladed disk is calculated according to the following formula
In formula, I is unit matrix, and N is blade amt, and T is the transposition in matrix operation；
Step 2: the mistuned bladed disk detuning of stiffness amount obtained according to the detuning of stiffness compensation rate and step 1 of unit thickness coating
Detuning recovery scenario design is carried out, and numerical simulation judgement and improvement are carried out to the repairing effect of scheme；
Step 2.1: obtaining the detuning compensation rate of unit thickness coating by finite element simulation, increased in the leaf dish of coordination
The coating for adding different-thickness, the mismatching angle generated to coating recognize, and obtained identification result is exactly different-thickness coating
Detuning compensation rate, then, the further compensation rate of unit of account thickness coatings, the specific steps are as follows:
Step 2.1.1: the coating for formulating coating leaf dish simulation model applies scheme: according to the design feature of leaf dish and selected
The characteristic of coating material determines the application pattern of coating, the coating unit thickness of simulation model is concurrently set, then, it is determined that respectively
The thickness of a blade coatings, and coating layer thickness is the integral multiple thickness of the unit coating layer thickness of setting on each blade；
Step 2.1.2: the volume of coating on each blade is calculated according to the coating layer thickness of the obtained each blade of step 2.1.1The quality mismatching angle of coating leaf dish simulation model is obtained according to following calculation formula
In formula (7), ρtcFor the density of coating material, tc indicates the coating of finite element model as subscript；ρypFor blade base
The density of body material；
Step 2.1.3: with the Theoretical Design of mistuned bladed disk having a size of matrix, scheme is applied according to the coating of step 2.1.1
The finite element model of the coating leaf dish is established, and carries out the natural frequency ω that model analysis obtains the coating leaf dishbcAnd the vibration shape
Xbc, coating leaf dish of the bc as subscript expression finite element model；
Step 2.1.4: the canoncial coordinates vector P of coating leaf dish finite element model is calculated according to following calculation formulabc；
Pbc=Φ-1Xbc (8)
Step 2.1.5: the detuning of stiffness amount of each blade of coating leaf dish finite element model is obtained according to following calculation formulaObtain the corresponding detuning of stiffness amount of different-thickness coating, that is, the corresponding rigidity compensation amount of different-thickness coating；
Step 2.1.6: according to the calculated result of step 2.1.5, the detuning of stiffness for further calculating unit thickness coating is mended
The amount of repaying；
Step 2.2: the unit thickness coating that the mistuned bladed disk detuning of stiffness amount and step 2.1 obtained according to step 1 obtains
Detuning of stiffness compensation rate carry out coating recovery scenario Preliminary design；Specific design process is as follows:
Step 2.2.1: the mistuned bladed disk detuning of stiffness amount obtained by step 1 determines standard of compensation, and according to compensation base
Standard compensates other blades, so that each blade stiffness mismatching angle is equal, so that entire leaf dish reaches a new association
Tune state；
Step 2.2.2: the mistuned bladed disk detuning of stiffness amount obtained according to step 1, the unit thickness coating that step 2.1 obtains
Detuning of stiffness compensation rate and the standard of compensation that determines of step 2.2.1 carry out the design of preliminary coating recovery scenario；
Step 2.3: repairing effect judgement and improvement, specific steps are carried out by numerical simulation to the preliminary recovery scenario of coating
It is as follows:
Step 2.3.1: the volume of coating on each blade is calculated according to coating coating schemeAccording to following calculation formula
The quality mismatching angle of mistuned bladed disk after obtaining coat coatingWherein SX indicates that the coating of finite element model loses as subscript
Humorous leaf dish):
Step 2.3.2: the painting that the mistuned bladed disk quality and detuning of stiffness amount and step 2.2 obtained according to step 1 obtains
Layer recovery scenario establishes the mistuned bladed disk finite element model after coat coating, and carries out model analysis, and coat coating is established in acquisition
The natural frequency ω of mistuned bladed disk afterwardssxWith vibration shape Xsx；
Step 2.3.3: the canoncial coordinates vector of the mistuned bladed disk model after calculating coat coating according to following calculation formula
Psx；
Psx=Φ-1Xsx (11)
Step 2.3.4: the detuning of stiffness amount of each blade of mistuned bladed disk after obtaining coat coating according to following calculation formula
Step 2.3.5: determined according to the repairing effect that the calculated result of step 2.3.4 determines, if up to standard, completed
The design of coating recovery scenario；If repairing effect is not up to standard, coating schemes are modified, and repeat to determine again and scheme again
The process of modification, until recovery scenario, which meets, repairs requirement；
Step 3: the coating recovery scenario determined according to step 2 carries out coating Repair gene to actual mistuned bladed disk, and
Repairing effect is determined, determines to need to carry out improvement and secondary reparation again when result is not up to standard, detailed process is as follows:
Step 3.1: the coating recovery scenario determined according to step 2, using coated technique pair corresponding with coating material
Actual mistuned bladed disk is repaired, coating leaf dish after being repaired；
Step 3.2: detuning identification being carried out to coating leaf dish after reparation, determines whether to reach reparation mark according to identification result
It is quasi-: to determine that result up to standard, is completed to repair；If it is determined that result is not up to standard, then repair process again is carried out；Detailed process is as follows:
Step 3.2.1: each blade profile size of coating leaf dish after coating reparation is measured to obtain coating blade
VolumeThe coating blade for the coating leaf dish that wherein tcyp indicates to repair practical mistuned bladed disk as subscript,
And quality mismatching angle is calculated according to following formulaWherein xf is repaired to obtain as subscript expression to practical mistuned bladed disk
Coating leaf dish；
Step 3.2.2: coating leaf dish carries out mould measurement after repairing to coating, obtains natural frequency ωxfWith vibration shape Xxf；
Step 2.3.3: the canoncial coordinates vector P of the coating leaf dish after coating is repaired is calculated according to following formulaxf；
Pxf=Φ-1Xxf (14)
Step 2.3.4: the detuning of stiffness amount of each blade of coating leaf dish after coating is repaired is obtained according to following formula
Step 3.2.5: determining repairing effect according to the identification result of step 3.2.4, if up to standard, completion is repaired
It is multiple；If it does not meet the standards, then reason judgement is carried out, corresponding modification is formulated and working process again is carried out to coating leaf dish, and
The process for determining again with improving processing again is repeated, until repairing requirement until reaching.
Further, the principle of standard of compensation is determined in the step 2.2.1 is: if the mismatching angle of blade has and positive also has
It is negative or entirely positive, using maximum positive mismatching angle as standard of compensation；If the mismatching angle of blade is entirely to bear, with absolute
Being worth the smallest negative mismatching angle is standard of compensation.
Beneficial effects of the present invention:
The present invention is based on the detuning identifications to leaf dish, and the mismatching angle of leaf dish is compensated by the way of coating reparation, is reached
The detuning purpose of leaf dish is repaired, this method has following technical advantage:
(1) Principles are more in line with blade dynamics requirement.Previous repair mode is only based on holding leaf dish mostly
The consistency of each sector geometric dimension, and this method to the mismatching angle judgement of leaf dish is obtained detuning from aerodynamic point
The quality and detuning of stiffness amount of each sector of leaf dish, obtained mismatching angle are related to the kinetic characteristics that leaf dish operates.This method base
Mistuned bladed disk reparation is carried out in these dynamics mismatching angles to be better able to meet the demanding kinetics of leaf dish.
(2) rehabilitation cost is low.This method relative to previous repair mode, in addition to necessary blade surface cleaning treatment it
Outside, almost without the workload of other machinings, the accuracy guarantee difficulty of leaf dish processing and the problem of equipment valuableness are avoided.
(3) the applicable coat type of this method is wide.As long as being suitble to the coating material of leaf dish operating condition applicable.
Detailed description of the invention:
Fig. 1 is the structural schematic diagram of the mistuned bladed disk of the specific embodiment of the invention, and wherein 1-18 is blade number.
Fig. 2 is the specific flow chart for repairing the method for mistuned bladed disk in the specific embodiment of the invention using coating.
Specific embodiment:
The present invention is described in further details with specific embodiment with reference to the accompanying drawing, described is to solution of the invention
It releases rather than limits.
In present embodiment, one mistuned bladed disk (its structure is as shown in Figure 1, blade quantity is 18) is carried out using coating
Operation is repaired, blade geometry is 45 steel having a size of 80mm × 22mm × 5mm (length × width x thickness), material, and elasticity modulus is
209GPa, Poisson's ratio 0.265, density 7890kg/m3.It repairs the coating used and selects ZN-1 type viscoelastic material, elasticity
Modulus is 30MPa, Poisson's ratio 0.49, density 789.5kg/m3。
The specific implementation process of this method is as shown in Figure 2, comprising the following steps:
Step 1: detuning identification is carried out to mistuned bladed disk, obtain each blade quality is detuning and detuning of stiffness data.
Step 1.1: greasy dirt, the corrosion etc. on mistuned bladed disk surface being cleared up, required with meeting coating coating.
Step 1.2: the outer dimension of each blade of mistuned bladed disk being measured, the volume of each blade is obtainedAccording to
Formula (1) calculates the quality mismatching angle of each blade
Step 1.3: mould measurement being carried out to mistuned bladed disk, obtains the natural frequency ω of mistuned bladed diskbWith vibration shape X.
Step 1.4: in conjunction with the quality mismatching angle of step 1.2As a result detuning of stiffness identification is carried out to mistuned bladed disk, calculated
The detuning of stiffness amount of each blade of mistuned bladed diskSpecific step is as follows:
Step 1.4.1: the leaf dish finite element model coordinated is established according to the Theoretical Design size of mistuned bladed disk, and carries out mould
State analysis obtains the natural frequency ω of mistuned bladed diskiWith canonical vibration shape matrix Φ, and each leaf is extracted from modal analysis result
Piece vibration shape matrix Φj。
Step 1.4.2: mistuned bladed disk canoncial coordinates vector P is obtained by formula (2) and (3) respectivelybWith coordination leaf dish
Canonical stiffness matrix Λ.
Step 1.4.3: establishing ideal cantilever blade finite element model, to extract the stiffness matrix K of ideal cantilever bladeCBWith
Mass matrix MCB, and model analysis is carried out, obtain inherent circular frequency diagonal matrix ωCBAnd vibration shape matrix ΦCB；Pass through formula (4) again
(5) modal participation factors of detuning of stiffness are calculated separatelyThe detuning modal participation factors with quality
Step 1.4.4: the detuning of stiffness amount of each blade of mistuned bladed disk is calculated according to formula (6)Calculated result is shown in Table 1.
The detuning of stiffness amount of 1 mistuned bladed disk of table
Step 2: the mistuned bladed disk detuning of stiffness amount obtained according to the detuning of stiffness compensation rate and step 1 of unit thickness coating
Detuning recovery scenario design is carried out, and numerical simulation judgement and improvement are carried out to the repairing effect of scheme.
Step 2.1: the detuning compensation rate of unit thickness coating is obtained by finite element simulation, the specific steps are as follows:
Step 2.1.1: the coating for formulating coating leaf dish simulation model applies scheme.The coating used in this embodiment
Application pattern is to carry out coating coating to the unilateral whole surface of blade, and the coating material of different-thickness is applied on each blade
Material, with a thickness of 0.0001mm, various coating layer thicknesses are really set the coating unit of setting according to the multiple of unit coating layer thickness,
The thickness of each blade coatings is shown in Table 2.
Step 2.1.2: the volume of coating on each blade is calculated according to the coating layer thickness of the obtained each blade of step 2.1.1The quality mismatching angle of coating leaf dish simulation model is obtained according to calculation formula (7)
Step 2.1.3: with the Theoretical Design of mistuned bladed disk having a size of matrix (i.e. correlated state), according to step 2.1.1's
Coating schemes establish the finite element model of the coating leaf dish, and carry out model analysis and obtain natural frequency ωbcWith vibration shape Xbc。
Step 2.1.4: the canoncial coordinates vector P of coating leaf dish finite element model is calculated according to calculation formula (8)bc。
Step 2.1.5: each blade stiffness mismatching angle of coating leaf dish finite element model is obtained according to calculation formula (9)?
See to the corresponding detuning of stiffness amount of different-thickness coating, that is, the corresponding rigidity compensation amount of different-thickness coating, calculated result
Table 2.
The detuning of stiffness compensation rate that the coating layer thickness of 2 coating leaf dish finite element model of table and identification obtain
Step 2.1.6: according to the calculated result (being shown in Table 2) of step 2.1.5, further unit of account thickness
The detuning of stiffness compensation rate of (0.0001m) coating is 382307.7.
Step 2.2: the unit that the mistuned bladed disk detuning of stiffness amount (being shown in Table 1) and step 2.1 obtained according to step 1 obtains is thick
The detuning of stiffness compensation rate (being shown in Table 2) for spending coating carries out coating recovery scenario Preliminary design.
Step 2.2.1: the standard of compensation that the mistuned bladed disk detuning of stiffness amount (being shown in Table 1) that is obtained by step 1 determines is
1638719.23 corresponding No. 12 blades.Other blades are compensated with the standard of compensation, reach the detuning of stiffness of No. 12 blades
Level, so that the entire each blade of leaf dish reaches a kind of new correlated state.
Step 2.2.2: the mistuned bladed disk detuning of stiffness amount (being shown in Table 1) obtained according to step 1, the unit that step 2.1 obtains
The standard of compensation that the detuning of stiffness compensation rate and step 2.2.1 of thickness coatings determine carries out preliminary coating recovery scenario design,
It is shown in Table 3.
3 mistuned bladed disk coating of table repairs preliminary project
Step 2.3: the preliminary recovery scenario of coating is changed by progress repairing effect judgement and scheme in numerical simulation level
Into, the specific steps are as follows:
Step 2.3.1: the coating coating scheme obtained according to step 2 calculates the volume of coating on each bladeAnd root
The quality mismatching angle of mistuned bladed disk after obtaining coat coating according to calculation formula (10)It is shown in Table 4.
Step 2.3.2: the painting that the mistuned bladed disk quality and detuning of stiffness amount and step 2.2 obtained according to step 1 obtains
Layer recovery scenario establishes the mistuned bladed disk finite element model after coat coating, and carries out model analysis, and coat coating is established in acquisition
The natural frequency ω of mistuned bladed disk afterwardssxWith vibration shape Xsx。
Step 2.3.3: the mistuned bladed disk canoncial coordinates vector P after calculating coat coating according to calculation formula (11)sx。
Step 2.3.4: the detuning of stiffness amount of each blade of mistuned bladed disk after obtaining coat coating according to calculation formula (12)Calculated result is shown in Table 4.
The quality mismatching angle and detuning of stiffness amount of mistuned bladed disk finite element model after 4 coat coating of table
Step 2.3.5: determining repairing effect according to the calculated result of step 2.3.4, it can be seen from Table 4 that respectively
The mismatching angle of blade is substantially all the level for having reached No. 12 blades, determines that repairing effect is up to standard, completes recovery scenario design.
Step 3: the coating recovery scenario determined according to step 2 carries out coating Repair gene to actual mistuned bladed disk, and
Repairing effect is determined, improved again when necessary with secondary reparation, detailed process is as follows；
Step 3.1: the coating recovery scenario determined according to step 2, using coated technique pair corresponding with coating material
Actual mistuned bladed disk is repaired, coating leaf dish after being repaired.
Step 3.2: mistuned bladed disk carries out detuning identification after repairing to coating, determines whether to reach reparation according to identification result
Standard, and necessary repair process again is carried out, detailed process is as follows:
Step 3.2.1: each blade (including coating) outer dimension of mistuned bladed disk measures to obtain after repairing to coating
The volume of coating bladeAnd quality mismatching angle is calculated according to formula (13), calculated result is shown in Table 5.
Step 3.2.2: mistuned bladed disk step carries out mould measurement after repairing to coating, obtains natural frequency ωxfAnd the vibration shape
Xxf。
Step 2.3.3: the canoncial coordinates vector P of mistuned bladed disk after repairing is calculated according to calculation formula (14)xf。
Step 2.3.4: the detuning of stiffness amount of each blade of mistuned bladed disk after being repaired according to calculation formula (15)Meter
Calculation the results are shown in Table 5.
The quality mismatching angle and detuning of stiffness amount of mistuned bladed disk after the reparation of 5 coating of table
Step 3.2.5: determining repairing effect according to the calculated result of step 3.2.4, it can be seen from Table 5 that respectively
The mismatching angle of blade is substantially all the level for having reached No. 12 blades, determines that repairing effect is up to standard, and the reparation of mistuned bladed disk is completed.
Mistuned bladed disk is repaired in the specific embodiment of the invention, the mismatching angle judgement to leaf dish is from dynamics angle
Degree sets out, and obtains the quality and detuning of stiffness amount of each sector of mistuned bladed disk, the dynamics spy of obtained mismatching angle and leaf dish operating
Property it is related.Therefore repair process is better able to meet the demanding kinetics of leaf dish.In addition, this method is in addition to necessary blade surface
Except cleaning treatment, almost without the workload of other machinings, rehabilitation cost is low.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art within the scope of the invention can be to above-mentioned
Embodiment is changed, modifies, replacement and variant.
Claims (2)
1. a kind of method for repairing mistuned bladed disk using coating, which comprises the following steps:
Step 1: detuning identification is carried out to mistuned bladed disk, obtain each blade quality is detuning and detuning of stiffness data；
Step 1.1: the greasy dirt on mistuned bladed disk surface, corrosion being cleared up, required with meeting coating coating；
Step 1.2: the outer dimension of each blade of mistuned bladed disk being measured, the volume of each blade is obtainedAccording to as follows
Formula calculates the quality mismatching angle of each blade
In formula (1), j is mistuned bladed disk blade serial number,For j-th of leaf quality mismatching angle of mistuned bladed disk, b is indicated as subscript
Practical mistuned bladed disk, VypFor theoretical coordination blade volume, yp coordinates the blade of leaf dish as subscript representation theory；
Step 1.3: mould measurement being carried out to mistuned bladed disk, obtains the natural frequency ω of mistuned bladed diskbWith vibration shape X；
Step 1.4: detuning of stiffness identification being carried out to mistuned bladed disk in conjunction with the quality detuning identification result of step 1.2, obtains each leaf
The detuning of stiffness amount of pieceSpecific step is as follows:
Step 1.4.1: establishing the leaf dish finite element model coordinated according to the Theoretical Design size of mistuned bladed disk, and carries out mode point
Analysis obtains the natural frequency ω of mistuned bladed diskiWith canonical vibration shape matrix Φ, and each blade vibration is extracted from modal analysis result
Type matrix Φj；
Step 1.4.2: mistuned bladed disk canoncial coordinates vector P is obtained by following formula respectivelybWith the canonical rigidity square for coordinating leaf dish
Battle array Λ；
Pb=Φ-1X (2)
In formula, i is rank number of mode, and n is the leaf dish finite element model number of degrees of freedom, coordinated；
Step 1.4.3: establishing ideal cantilever blade finite element model, to extract the stiffness matrix K of ideal cantilever bladeCBAnd quality
Matrix MCB, CB carries out model analysis as subscript representation theory cantilever blade, obtains inherent circular frequency diagonal matrix ωCBAnd vibration
Type matrix ΦCB；The modal participation factors of detuning of stiffness are calculated separately by following formula againIt is participated in the detuning mode of quality
The factorWherein K, M respectively indicate rigidity and quality as subscript:
In formula, ΛCBFor the diagonal matrix of theoretical cantilever blade inherent circular frequency square；
Step 1.4.4: the detuning of stiffness amount of each blade of mistuned bladed disk is calculated according to the following formula
In formula, I is unit matrix, and N is blade amt, and T is the transposition in matrix operation；
Step 2: being carried out according to the mistuned bladed disk detuning of stiffness amount that the detuning of stiffness compensation rate and step 1 of unit thickness coating obtain
Detuning recovery scenario design, and numerical simulation judgement and improvement are carried out to the repairing effect of scheme；
Step 2.1: obtaining the detuning compensation rate of unit thickness coating by finite element simulation, increased not in the leaf dish of coordination
The coating of stack pile, the mismatching angle generated to coating recognize, and obtained identification result is exactly the detuning of different-thickness coating
Compensation rate, then, the further compensation rate of unit of account thickness coatings, the specific steps are as follows:
Step 2.1.1: the coating for formulating coating leaf dish simulation model applies scheme: according to the design feature of leaf dish and selected coating
The characteristic of material determines the application pattern of coating, the coating unit thickness of simulation model is concurrently set, then, it is determined that each leaf
The thickness of piece coating, and coating layer thickness is the integral multiple thickness of the unit coating layer thickness of setting on each blade；
Step 2.1.2: the volume of coating on each blade is calculated according to the coating layer thickness of the obtained each blade of step 2.1.1
The quality mismatching angle of coating leaf dish simulation model is obtained according to following calculation formula
In formula (7), ρtcFor the density of coating material, tc indicates the coating of finite element model as subscript；ρypFor blade base material
The density of material；
Step 2.1.3: with the Theoretical Design of mistuned bladed disk having a size of matrix, scheme is applied according to the coating of step 2.1.1 and is established
The finite element model of the coating leaf dish, and carry out the natural frequency ω that model analysis obtains the coating leaf dishbcWith vibration shape Xbc, bc
The coating leaf dish of finite element model is indicated as subscript；
Step 2.1.4: the canoncial coordinates vector P of coating leaf dish finite element model is calculated according to following calculation formulabc；
Pbc=Φ-1Xbc (8)
Step 2.1.5: the detuning of stiffness amount of each blade of coating leaf dish finite element model is obtained according to following calculation formulaIt obtains
The corresponding detuning of stiffness amount of different-thickness coating, that is, the corresponding rigidity compensation amount of different-thickness coating；
Step 2.1.6: according to the calculated result of step 2.1.5, the detuning of stiffness compensation rate of unit thickness coating is further calculated；
Step 2.2: according to step 1 obtain mistuned bladed disk detuning of stiffness amount and step 2.1 obtain unit thickness coating it is rigid
It spends detuning compensation rate and carries out coating recovery scenario Preliminary design；Specific design process is as follows:
Step 2.2.1: the mistuned bladed disk detuning of stiffness amount obtained by step 1 determines standard of compensation, and according to standard of compensation pair
Other blades compensate, so that each blade stiffness mismatching angle is equal, so that entire leaf dish reaches a new coordination shape
State；
Step 2.2.2: according to step 1 obtain mistuned bladed disk detuning of stiffness amount, step 2.1 obtain unit thickness coating it is rigid
The standard of compensation for spending detuning compensation rate and step 2.2.1 determination carries out preliminary coating recovery scenario design；
Step 2.3: repairing effect judgement and improvement being carried out by numerical simulation to the preliminary recovery scenario of coating, specific steps are such as
Under:
Step 2.3.1: the volume of coating on each blade is calculated according to coating coating schemeIt is obtained according to following calculation formula
The quality mismatching angle of mistuned bladed disk after coat coatingWherein SX indicates the detuning leaf of coating of finite element model as subscript
Disk):
Step 2.3.2: the coating that the mistuned bladed disk quality and detuning of stiffness amount and step 2.2 obtained according to step 1 obtains is repaired
Compound case establishes the mistuned bladed disk finite element model after coat coating, and carries out model analysis, after coat coating is established in acquisition
The natural frequency ω of mistuned bladed disksxWith vibration shape Xsx；
Step 2.3.3: the canoncial coordinates vector P of the mistuned bladed disk model after calculating coat coating according to following calculation formulasx；
Psx=Φ-1Xsx (11)
Step 2.3.4: the detuning of stiffness amount of each blade of mistuned bladed disk after obtaining coat coating according to following calculation formula
Step 2.3.5: determined according to the repairing effect that the calculated result of step 2.3.4 determines, if up to standard, complete coating
Recovery scenario design；If repairing effect is not up to standard, coating schemes are modified, and repeat to determine again and scheme modifying again
Process, until recovery scenario meet repair require until；
Step 3: coating Repair gene being carried out to actual mistuned bladed disk according to the coating recovery scenario that step 2 determines, and to repairing
Multiple effect is determined, determines to need to carry out improvement and secondary reparation again when result is not up to standard, detailed process is as follows:
Step 3.1: the coating recovery scenario determined according to step 2, using coated technique corresponding with coating material to reality
Mistuned bladed disk repaired, coating leaf dish after being repaired；
Step 3.2: detuning identification being carried out to coating leaf dish after reparation, is determined whether to reach repairing standard according to identification result: be sentenced
Result is determined up to standard, completes to repair；If it is determined that result is not up to standard, then repair process again is carried out；Detailed process is as follows:
Step 3.2.1: each blade profile size of coating leaf dish after coating reparation is measured to obtain the volume of coating bladeThe coating blade for the coating leaf dish that wherein tcyp indicates to repair practical mistuned bladed disk as subscript, and root
Quality mismatching angle is calculated according to following formulaWherein xf indicates the painting repaired to practical mistuned bladed disk as subscript
Layer leaf dish；
Step 3.2.2: coating leaf dish carries out mould measurement after repairing to coating, obtains natural frequency ωxfWith vibration shape Xxf；
Step 2.3.3: the canoncial coordinates vector P of the coating leaf dish after coating is repaired is calculated according to following formulaxf；
Pxf=Φ-1Xxf (14)
Step 2.3.4: the detuning of stiffness amount of each blade of coating leaf dish after coating is repaired is obtained according to following formula
Step 3.2.5: determining repairing effect according to the identification result of step 3.2.4, if up to standard, completes to repair；If
It is not up to standard, then reason judgement is carried out, corresponding modification is formulated and working process again is carried out to coating leaf dish, and repeat again
Secondary judgement and the process for improving processing again, until repairing requirement until reaching.
2. a kind of method for repairing mistuned bladed disk using coating according to claim 1, which is characterized in that the step
2.2.1 the principle of standard of compensation is determined in is: if the mismatching angle of blade have it is positive also have it is negative or entirely positive, with maximum
Positive mismatching angle is standard of compensation；It is compensation base with the smallest negative mismatching angle of absolute value if the mismatching angle of blade is entirely negative
It is quasi-.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109992856A (en) * | 2019-03-19 | 2019-07-09 | 东北大学 | A kind of hard conating leaf dish finite element modeling method suitable for different coating thickness |
| CN111898290A (en) * | 2020-06-29 | 2020-11-06 | 西安交通大学 | Method for improving dynamic and static performances of assembly body based on interface hardness degree design |
| CN112241600A (en) * | 2020-08-31 | 2021-01-19 | 北京化工大学 | Blade disc frequency modulation testing and calculating method using blade tip timing and digital twin model |
| CN114036664A (en) * | 2021-11-03 | 2022-02-11 | 南京航空航天大学 | Blisk finite element modeling and detuning identification method based on optical detection |
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| CN102564750A (en) * | 2011-12-27 | 2012-07-11 | 中国科学院工程热物理研究所 | Method for correcting blade modal testing result of horizontal axis wind turbine |
| CN103984813A (en) * | 2014-05-09 | 2014-08-13 | 西安交通大学 | Vibration modeling and analyzing method of crack impeller structure of centrifugal compressor |
| CN106528933A (en) * | 2016-10-09 | 2017-03-22 | 西安交通大学 | Mistuned parameter simulation method for entire circle of free blades |
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| CN102564750A (en) * | 2011-12-27 | 2012-07-11 | 中国科学院工程热物理研究所 | Method for correcting blade modal testing result of horizontal axis wind turbine |
| CN103984813A (en) * | 2014-05-09 | 2014-08-13 | 西安交通大学 | Vibration modeling and analyzing method of crack impeller structure of centrifugal compressor |
| CN106528933A (en) * | 2016-10-09 | 2017-03-22 | 西安交通大学 | Mistuned parameter simulation method for entire circle of free blades |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109992856A (en) * | 2019-03-19 | 2019-07-09 | 东北大学 | A kind of hard conating leaf dish finite element modeling method suitable for different coating thickness |
| CN109992856B (en) * | 2019-03-19 | 2023-04-18 | 东北大学 | Finite element modeling method for hard coating leaf disc suitable for different coating thicknesses |
| CN111898290A (en) * | 2020-06-29 | 2020-11-06 | 西安交通大学 | Method for improving dynamic and static performances of assembly body based on interface hardness degree design |
| CN111898290B (en) * | 2020-06-29 | 2024-04-12 | 西安交通大学 | Assembly body dynamic and static performance improving method based on interface softness degree design |
| CN112241600A (en) * | 2020-08-31 | 2021-01-19 | 北京化工大学 | Blade disc frequency modulation testing and calculating method using blade tip timing and digital twin model |
| CN112241600B (en) * | 2020-08-31 | 2023-12-15 | 北京化工大学 | Blade disc frequency modulation testing and calculating method using blade tip timing and digital twin model |
| CN114036664A (en) * | 2021-11-03 | 2022-02-11 | 南京航空航天大学 | Blisk finite element modeling and detuning identification method based on optical detection |
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