CN107229772A - A kind of flexible casing of improved rotating vane touches Mo Li and determines method - Google Patents
A kind of flexible casing of improved rotating vane touches Mo Li and determines method Download PDFInfo
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- CN107229772A CN107229772A CN201710268588.2A CN201710268588A CN107229772A CN 107229772 A CN107229772 A CN 107229772A CN 201710268588 A CN201710268588 A CN 201710268588A CN 107229772 A CN107229772 A CN 107229772A
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Abstract
Mo Li is touched the present invention relates to a kind of flexible casing of improved rotating vane and determines method, is belonged to blade stator System and is touched Dynamic Modeling field of rubbing.The softening effect that rubs is touched it is characterized in that considering caused by the centrifugation rigidifying of blade, Spin softening, Coriolis stress effect and being touched with casing are rubbed, meanwhile, casing is simulated using spring-supported flexible ring is carried, and can consider the entirety because touching the generation that rubs and local deformation.Touch rub new in addition, the present invention has also set up blade casing and touch power characterization model of rubbing.The present invention can reflect that the parameters such as casing radius, thickness touch the influence for power of rubbing to blade casing, and more can truly portray real blade casing touches the mechanism of rubbing.Compared with using traditional finite element analysis, the invention has higher computational efficiency and precision.In addition, the invention can also greatly reduce experimentation cost, and the design for blade casing system architecture provides reference, with the performance and security of lifting system.
Description
Technical field
The invention belongs to mechanical kinetics technical field, and in particular to a kind of improved rotating vane-flexibility casing is touched and rubbed
Power determines method, and the Mo Li that touches for especially relating to contain casing flexibility determines method.
Background technology
In aero-engine, the touching of blade-casing, which is rubbed, can cause the complete machine oscillation of complexity, reduce the performance of system, contracting
The working life of short blade and casing.The power research that rubs is touched for blade and casing, should than more typical linear spring model
Model assumption normal direction is touched Mo Li and is directly proportional to depth of invasion；Consider the centrifugation rigidifying influence that blade rotation is produced, casing is assumed
For rigid body, the power model that rubs is touched accordingly so as to derive；Mo Li and depth of invasion are touched using Hertz Elastic Contact scale-model investigations
Relation.But being assumed to be rigid body casing in impact-rub malfunction research at this stage more.The touching of blade-casing is related to leaf during rubbing
Centrifugation rigidifying, Spin softening and Coriolis stress effect caused by piece rotation, and touch rub caused by touch the softening effect that rubs, in addition, touching
Overall deformation and the local deformation of casing are also resulted in during rubbing.Therefore, set up accurate blade-casing and touch the power model that rubs,
Designed for blade construction and raising aero-engine overall performance is significant.
The content of the invention
In view of the shortcomings of the prior art, the present invention proposes that a kind of improved rotating vane-flexibility casing touches Mo Li determination sides
Method, to consider the centrifugation rigidifying of blade, Spin softening and coriolis force influence, touch rub caused by touch rub softening effect and casing
Flexibility, so as to accurately determine that rotating vane-casing touches power of rubbing.
A kind of improved rotating vane-flexibility casing touches Mo Li and determines method, comprises the following steps：
Step 1, the plastic deformation of rotating vane is determined；
Blade is reduced to Timoshenko beam models, calculate centrifugal force suffered by blade, aerodynamic force, normal direction contact force with
And frictional force.
Step 1-1, calculate micro unit centrifugal force be：Df=ρ A ω2(Rd+x)dx (1)
In formula：ρ is density of material；A is area of blade section；ω is blade angular velocity of rotation；RdFor leaf disk radius；
X is horizontal range of the arbitrfary point away from blade cantilever end on blade.
Step 1-2, by normal direction contact force, frictional force and centrifugal force are decomposed into：
In formula：FnFor normal direction contact force；L is length of blade；FtFor frictional force；θLFor blade tip to circle disk center line segment with
The angle of horizontal direction；θxA little to arrive the line segment of circle disk center and the angle of horizontal direction on blade.
Step 1-3, dynamic balance and equalising torque relation on blade simultaneously omit high-order and derive scratching for blade in a small amount and write music
Line is：
Wherein
In formula：μ is coefficient of friction；E is Young's modulus；I is cross sectional moment of inertia；FeFor the aerodynamic force suffered by blade.
Step 2, casing is modeled using flexible ring, and the deformation of flexible casing is derived by energy method；
Step 2-1, calculate flexible ring elastic potential energy be：
In formula：EcFor the Young's modulus of flexible ring；IcFor flexible ring cross sectional moment of inertia；RcFor casing radius；usRadial compliance
Displacement.
Step 2-2, according to Reciprocal work theorem, external force acting is：
Step 2-3, calculating case structure rigidity is：
Step 3, quasistatic touches the power model inference that rubs；
Step 3-1, blade radial displacement can be expressed as：
In formula：uLFor the radial displacement of blade；Y (x) is the sag curve of blade.
Step 3-2, by elastic accommodation consistency condition, the depth of invasion δ (F that blade-casing is touched during rubbingn) can express
For：
In formula：ucnTranslation displacements of the palm-rubbing technique to casing are touched for edge；usnElastic displacement of the palm-rubbing technique to casing is touched for edge.
Step 3-3, brings case structure rigidity and blade radial displacement expression formula into blade-casing and touches the depth of invasion rubbed
Expression formula, and it is a small amount of to omit high-order, obtain normal direction and touch power expression formula of rubbing be：
Wherein
Beneficial effects of the present invention are：
The present invention touches Mo Li for a kind of improved rotating vane-flexibility casing and determines method, and this touches the power model that rubs and considered
Centrifugation rigidifying effect, Spin softening effect, Coriolis stress effect with established angle blade, touch rub softening effect and aerodynamic force and machine
The flexible influence of casket, the model is applied to non-yielding prop and elastic bearing casing.In the contrast with experiment expansion, of the invention
To the power model that rubs that touches touch touching and rub produced by rubbing touching power of rubbing and be numerically more nearly true aero-engine and actually occur
Power size.
Brief description of the drawings
Fig. 1 touches Mo Li for a kind of improved rotating vane-flexibility casing of the embodiment of the present invention and determines method flow diagram；
Fig. 2 is the vane stress schematic diagram of the embodiment of the present invention；
Fig. 3 is the blade moment decomposing schematic representation of the embodiment of the present invention；
Fig. 4 is the bending displacement schematic diagram of the blade of the embodiment of the present invention；
Fig. 5 is the flexible casing model schematic of the embodiment of the present invention；
Fig. 6 deforms schematic diagram for the casing displacement comparison of the embodiment of the present invention；
Fig. 7 touches the schematic diagram that rubs for blade-flexibility casing of the embodiment of the present invention；
Fig. 8 touches power model contrast schematic diagram of rubbing for the difference of the embodiment of the present invention.
Fig. 9 touches power contrast schematic diagram of rubbing for the embodiment of the present invention.
Embodiment
The present invention will be further described with specific embodiment below in conjunction with the accompanying drawings.
A kind of improved rotating vane-flexibility casing touches Mo Li and determines method in the embodiment of the present invention, and method flow diagram is such as
Shown in Fig. 1, comprise the following steps：
Step 1, the plastic deformation of rotating vane is determined；
Blade is reduced to Timoshenko beam models, it is considered to the centrifugal force suffered by blade, aerodynamic force, normal direction contact force with
And frictional force.
Step 1-1, calculate micro unit centrifugal force be：
Df=ρ A ω2(Rd+x)dx (1)
In formula：ρ is density of material；A is area of blade section；ω is blade angular velocity of rotation；RdFor leaf disk radius；
X is horizontal range of the arbitrfary point away from blade cantilever end on blade.
Step 1-2, derives the elastic equation of beam；
There is detrusion in Timoshenko beams, if detrusion is 0, the tangent line of center line is by the normal in section
Overlap, the amount of deflection of line centered on y,For the slope caused by bending,Lost for slope, equal to the angle of shear, Q
For the shearing in section, the elastic equation of beam is：
In formula：κ is shearing factor, and G is modulus of shearing, M moments of flexure.
Normal direction contact force, frictional force and centrifugal force, are decomposed into by step 1-3 according to Fig. 2：
In formula：FnFor normal direction contact force；L is length of blade；FtFor frictional force；θLFor blade tip to circle disk center line segment with
The angle of horizontal direction；θxA little to arrive the line segment of circle disk center and the angle of horizontal direction on blade.
Step 1-4, can obtain blade bending displacement equation according to dynamic balances of the Fig. 3 on blade and equalising torque relation is：
Step 1-5, omits high-order and derives the sag curve of blade in a small amount and be：
Wherein
In formula：μ is coefficient of friction；E is Young's modulus；I is cross sectional moment of inertia；FeFor the aerodynamic force suffered by blade.
Direct reference mechanics of materials formula can obtain blade bending displacement and be：
Step 1-6, above-mentioned two computation model and Ma models are deployed to contrast with finite element result
Consider blade centrifugation rigidifying, Spin softening and touch the influence for the softening that rubs, be 5000r/min by speed setting,
Power of rubbing is touched in Fig. 4 (a) for 2000N, now softening effect is greater than centrifugation rigidifying effect, actual flexion shift value is greater than three
All irrespective result.Fig. 4 (b) touches power of rubbing and is set as 200N, and now softening effect is less than centrifugation rigidifying effect, actual flexion
Shift value is again smaller than mechanics of materials result.Fig. 4 (a) Literatures result is then very close to differing larger herein in Fig. 4 (b),
By contrast as can be seen that document has taken into full account centrifugation rigidifying effect, and do not consider excessively for touching the softening that rubs.
Step 2, casing is modeled using flexible ring, and the deformation of flexible casing is derived by energy method；
Such as Fig. 5, the width of blade is b, and established angle is β, then touch rub width of the casing axially with blade is Lc=b ×
Cos β, fetch bit is in touching this section of casing rubbed in width as research object, and its equivalent support stiffness can pass through beam function method meter
Calculate or experiment is measured, plastic deformation is then simulated using flexible ring, the final mean annual increment movement of its arbitrfary point is casing overall displacements and soft
The vector sum of property displacement, altogether including horizontal direction displacement components uc, vertical direction displacement vc, radial compliance displacement components us, centripetal is just, to cut
To flexible displacement ws, along angle augment direction for just.
Step 2-1, calculate flexible ring elastic potential energy be：
In formula：EcFor the Young's modulus of flexible ring；IcFor the cross sectional moment of inertia of flexible ring；RcFor casing radius；usFor radially
Flexible displacement.
Step 2-2, according to Reciprocal work theorem, external force acting is：
The plastic deformation of flexible ring is generally expressed using pitch diameter vibration mode, and mould is used as using all pitch diameters vibration of n >=2
The state vibration shape, its tangential displacement and radial displacement can be expanded into：
In formula, n represents pitch diameter number, also referred to as circumferential wave number.
Formula (5) is deployed according to pitch diameter displacement, can be obtained：
Step 2-3, the elastic potential energy of flexible ring is done work equal to external force, is so as to obtain case structure rigidity：
In order to verify that the overall displacements of arbitrfary point are translation displacements and the vector sum of flexible displacement, casing is expanded to herein
4 ranks, certain casing radius is 224mm, and thickness is 3mm, touches the length 50mm that rubs, and applies constant radial excitation F=1N, with horizontal direction
Angle is 60 °, in kcx=kcy=∞ and kcx=kcy=20000N/m asks for the maximum displacement in casing circumference and imitative with finite element
True expansion contrast, as shown in table 1.Fig. 6 depicts casing shape under two kinds of operating modes, and all displacements amplify 1000 times.
The casing displacement comparison result of table 1
Step 3, quasistatic touches the power model inference that rubs；
Step 3-1, blade radial displacement can be expressed as：
In formula：uLFor the radial displacement of blade；Y (x) is the sag curve of blade.
Step 3-2, such as Fig. 7 are by elastic accommodation consistency condition, the depth of invasion δ (F that blade-casing is touched during rubbingn) can
It is expressed as：
In formula：ucnTranslation displacements of the palm-rubbing technique to casing are touched for edge；usnFor elastic displacement.
Step 3-3, brings case structure rigidity and blade radial displacement expression formula into blade-casing and touches the depth of invasion rubbed
Expression formula, and it is a small amount of to omit high-order, obtain normal direction and touch power expression formula of rubbing be：
Wherein
Model is verified and Numerical Simulation Analysis
In order to verify the accuracy of above-mentioned model, rotor-blade-casing rub experiment platform has been built.The experimental bench is by moving
Force system, rotor-support-foundation system, feed system and test system composition.The testing stand detail parameters and support stiffness are shown in Ma etc. in A
revised model for rubbing between rotating blade and elastic casing[J]
.Journal of Sound and Vibra-tion,2015,337：244-262. described in.Due to limited conditions, this experiment
The plastic deformation of casing can not be realized, the influence of blade and supporting casing rigidity can only be considered, therefore by KsIt is set to infinitely great.
Experiment deploys under tri- kinds of rotating speeds of 1000r/min, 1500r/min and 2000r/min.Casing uses steel and aluminum
Two kinds of materials, the support stiffness of aluminum casing is 2 × 107N/m, and the support stiffness of steel casing is 3.5 × 107N/m.Blade
It is 3mm slim vane and 5mm two kinds of thick blade to be divided into thickness, contrasts as shown in Figure 8 with model of literature expansion herein.Each operating mode
Lower this paper precision is slightly above model of literature.Comparison diagram 8 (a) and 8 (b) understand that increase vane thickness will improve bending rigidity, invade
Enter amount it is identical when, touching power of rubbing can be significantly increased.From Fig. 8 (c) and 8 (d) and Fig. 8 (e) and 8 (f) contrast, intrusion volume phase
Simultaneously as support stiffness is big, the normal direction of steel casing touches power of rubbing and is greater than aluminum casing, comparison diagram 8 (c) and 8 (e) and figure
8 (a), 8 (d) and 8 (f) are as can be seen that with the raising of rotating speed, centrifugation rigidifying effect can increase the bending rigidity of blade, keep
Intrusion volume is constant, and touching power of rubbing will increase a little.
Document, which is modeled and measured by force snesor to aero-engine complete machine, touches power of rubbing.For further checking casing
Plastic deformation and the influence of relevant parameter, it is special with the blade vibration load under rub-impact state such as Li Yong and vibration herein
Property test analysis [J] aviation power journals, 2008,23 (11)：Experiment in 1988-1992. its made further contrast.
Fixed rotating speed and support stiffness are constant, are gradually aggravated with the degree of rubbing is touched, and touching power of rubbing gradually increases, experimental result such as Fig. 9 (a) institutes
Show.It is respectively herein h in casing thicknessc=3mm, hc=4mm and hcCalculated under tri- kinds of operating modes of=5mm and touch Mo Li and depth of invasion
Relation, shown in such as Fig. 9 (b), it can be seen that because casing is relatively thin, its rigidity of structure is much smaller than support stiffness, and normal direction touches power of rubbing
The relation of linear change is showed with depth of invasion.When casing thickness hcDuring for 4mm, normal direction touches the calculating for power of rubbing in this paper models
As a result it is closest with experimental result.
Claims (1)
1. a kind of improved rotating vane-flexibility casing touches Mo Li and determines method, it is characterised in that comprise the following steps：
Step 1, the plastic deformation of rotating vane is determined；
Blade is reduced to Timoshenko beam models, the centrifugal force suffered by blade, aerodynamic force, normal direction contact force is calculated and rubs
Wipe power；
Step 1-1, calculate micro unit centrifugal force be：
Df (x)=ρ A ω2(Rd+x)dx (1)
In formula, ρ is density of material；A is area of blade section；ω is blade angular velocity of rotation；RdFor leaf disk radius；X is leaf
Horizontal range of the arbitrfary point away from blade cantilever end on piece；
Step 1-2, by normal direction contact force, frictional force and centrifugal force are decomposed into：
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In formula, FnFor normal direction contact force；L is length of blade；FtFor frictional force；θLFor the line segment and level of blade tip to circle disk center
The angle in direction；θxA little to arrive the line segment of circle disk center and the angle of horizontal direction on blade；
Step 1-3, according to the dynamic balance on blade and equalising torque relation, and removes the sag curve that high-order derives blade in a small amount
For：
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</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein
In formula, μ is coefficient of friction；E is Young's modulus；I is cross sectional moment of inertia；FeFor the aerodynamic force suffered by blade；
Step 2, the deformation of flexible casing is derived according to energy method, described casing is modeled using flexible ring；
Step 2-1, calculate flexible ring elastic potential energy be：
In formula, EcFor the Young's modulus of flexible ring；IcFor flexible ring cross sectional moment of inertia；RcFor casing radius；usRadial compliance displacement；
Step 2-2, according to Reciprocal work theorem, external force acting is：
Step 2-3, calculating case structure rigidity is：
Step 3, derive quasistatic and touch the power model that rubs；
Step 3-1, calculating blade radial displacement is：
<mrow>
<msub>
<mi>u</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mi>L</mi>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>x</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, uLFor the radial displacement of blade；Y (x) is the sag curve of blade；
Step 3-2, according to elastic accommodation consistency condition, the depth of invasion δ (F that blade-casing is touched during rubbingn) be：
<mrow>
<mi>&delta;</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>c</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>s</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>u</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<msub>
<mi>K</mi>
<mi>c</mi>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<msub>
<mi>K</mi>
<mi>s</mi>
</msub>
</mfrac>
<mo>+</mo>
<msub>
<mi>u</mi>
<mi>L</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, ucnTranslation displacements of the palm-rubbing technique to casing are touched for edge；usnElastic displacement of the palm-rubbing technique to casing is touched for edge；
Step 3-3, brings case structure rigidity and blade radial displacement into blade-casing and touches the depth of invasion expression formula rubbed, and
Remove high-order a small amount of, obtain normal direction and touch power expression formula of rubbing be：
<mrow>
<msub>
<mi>F</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>F</mi>
<mi>e</mi>
</msub>
<msup>
<mi>L</mi>
<mn>3</mn>
</msup>
<mi>&mu;</mi>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&beta;</mi>
<mo>+</mo>
<mi>&Gamma;</mi>
<mi>L</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>9</mn>
<mi>&Gamma;</mi>
</mrow>
<mi>K</mi>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mfrac>
<mi>&delta;</mi>
<mi>L</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msqrt>
<mrow>
<msup>
<msub>
<mi>F</mi>
<mi>e</mi>
</msub>
<mn>2</mn>
</msup>
<msup>
<mi>L</mi>
<mn>6</mn>
</msup>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mi>&beta;</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>9</mn>
<msup>
<mi>&Gamma;</mi>
<mn>2</mn>
</msup>
<mi>L</mi>
</mrow>
<mi>K</mi>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>9</mn>
<msup>
<mi>&Gamma;</mi>
<mn>2</mn>
</msup>
<mi>L</mi>
</mrow>
<mi>K</mi>
</mfrac>
<mo>+</mo>
<mn>12</mn>
<mi>&Gamma;</mi>
<mi>&delta;</mi>
<mo>+</mo>
<mn>4</mn>
<msup>
<mi>L</mi>
<mn>2</mn>
</msup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&beta;&mu;</mi>
<mn>2</mn>
</msup>
<mi>&delta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mrow>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mfrac>
<mi>&delta;</mi>
<mi>L</mi>
</mfrac>
<mo>-</mo>
<msup>
<mi>L</mi>
<mn>2</mn>
</msup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<msup>
<mi>&beta;&mu;</mi>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108956068A (en) * | 2018-05-25 | 2018-12-07 | 东北大学 | A kind of rubbing test device turning stator |
| CN109100068A (en) * | 2018-08-24 | 2018-12-28 | 北京航空航天大学 | Blade-casing touching under complicated contact condition is rubbed power testing experiment device |
| CN110532732A (en) * | 2019-09-17 | 2019-12-03 | 东北大学 | A kind of blade-casing touches the determination method for the relationship of rubbing |
| CN110610049A (en) * | 2019-09-18 | 2019-12-24 | 东北大学 | Method for analyzing mechanical characteristics of blade and casing system under rub-impact fault |
| CN113486460A (en) * | 2021-06-22 | 2021-10-08 | 湖南科技大学 | Rotor multi-blade and case fixed-point rub-impact simulation method considering deformation of case |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108956068A (en) * | 2018-05-25 | 2018-12-07 | 东北大学 | A kind of rubbing test device turning stator |
| CN109100068A (en) * | 2018-08-24 | 2018-12-28 | 北京航空航天大学 | Blade-casing touching under complicated contact condition is rubbed power testing experiment device |
| CN109100068B (en) * | 2018-08-24 | 2019-10-29 | 北京航空航天大学 | Blade-casing touching under complicated contact condition is rubbed power testing experiment device |
| CN110532732A (en) * | 2019-09-17 | 2019-12-03 | 东北大学 | A kind of blade-casing touches the determination method for the relationship of rubbing |
| CN110532732B (en) * | 2019-09-17 | 2023-03-24 | 东北大学 | Method for determining rubbing relationship between blade and casing |
| CN110610049A (en) * | 2019-09-18 | 2019-12-24 | 东北大学 | Method for analyzing mechanical characteristics of blade and casing system under rub-impact fault |
| CN110610049B (en) * | 2019-09-18 | 2022-12-02 | 东北大学 | Method for analyzing mechanical characteristics of blade and casing system under rub-impact fault |
| CN113486460A (en) * | 2021-06-22 | 2021-10-08 | 湖南科技大学 | Rotor multi-blade and case fixed-point rub-impact simulation method considering deformation of case |
| CN113486460B (en) * | 2021-06-22 | 2022-11-22 | 佛山科学技术学院 | Rotor multi-blade and case fixed-point rub-impact simulation method considering deformation of case |
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