CN107229772B - A kind of improved rotating vane-flexibility casing touches power of rubbing and determines method - Google Patents
A kind of improved rotating vane-flexibility casing touches power of rubbing and determines method Download PDFInfo
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- CN107229772B CN107229772B CN201710268588.2A CN201710268588A CN107229772B CN 107229772 B CN107229772 B CN 107229772B CN 201710268588 A CN201710268588 A CN 201710268588A CN 107229772 B CN107229772 B CN 107229772B
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- G06F2119/06—Power analysis or power optimisation
Abstract
Power of rubbing is touched the present invention relates to a kind of improved rotating vane-flexibility casing 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 touching with casing are rubbed, meanwhile, casing is simulated using spring-supported flexible ring is had, and can consider the entirety and local deformation because touching the generation that rubs.It touches rub new in addition, the present invention has also set up blade-casing and touches power characterization model of rubbing.The present invention is able to reflect the influence that the parameters such as casing radius, thickness touch power of rubbing to blade-casing, more can really portray real blade-casing and touch the mechanism of rubbing.Compared with using traditional finite element analysis, invention computational efficiency with higher and precision.In addition, the invention can also greatly reduce experimentation cost, and reference is provided for the design of blade-stator System structure, with the performance and safety of lifting system.
Description
Technical field
The invention belongs to mechanical kinetics technical fields, and in particular to a kind of improved rotating vane-flexibility casing is touched and rubbed
Power determines method, especially relates to contain casing power of rubbing flexible of touching and determines method.
Background technique
In aero-engine, blade-casing, which touches to rub, will lead to complicated complete machine oscillation, reduces the performance of system, contracts
The working life of short blade and casing.The power research that rubs is touched for blade and casing, it, should than more typical linear spring model
It is directly proportional to depth of invasion that model assumption normal direction touches Mo Li；The centrifugation rigidifying for considering that blade rotation generates influences, and casing is assumed
For rigid body, the power model that rubs is touched accordingly to derive；Mo Li and depth of invasion are touched using the research of Hertz Elastic Contact model
Relationship.But casing is assumed to be rigid body more in impact-rub malfunction research at this stage.Blade-casing touches to rub is related to leaf in the process
Be centrifuged 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, it establishes accurate blade-casing and touches the power model that rubs,
Aero-engine overall performance is designed and improved for blade construction to be of great significance.
Summary of the invention
In view of the deficiencies of the prior art, the present invention proposes that a kind of improved rotating vane-flexibility casing touches the power determination side that rubs
Method, with consider the centrifugation rigidifying of blade, Spin softening and coriolis force influence, touch rub caused by touch rub softening effect and casing
Flexibility, to accurately determine that rotating vane-casing touches power of rubbing.
A kind of improved rotating vane-flexibility casing touches power of rubbing and determines method, comprising the following steps:
Step 1, the plastic deformation of rotating vane is determined；
Blade is reduced to Timoshenko beam model, calculate centrifugal force suffered by blade, aerodynamic force, normal direction contact force with
And frictional force.
Step 1-1 calculates the centrifugal force of micro unit are as follows: 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 distance of the arbitrary point away from blade cantilever end on blade.
Step 1-2, by normal direction contact force, frictional force and centrifugal force are decomposed are as follows:
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 by the dynamic balance and equalising torque relationship on blade and omits high-order and derives scratching for blade in a small amount and write music
Line are as follows:
Wherein
In formula: μ is coefficient of friction；E is Young's modulus；I is cross sectional moment of inertia；FeFor 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 calculates the elastic potential energy of flexible ring are as follows:
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 are as follows:
Step 2-3 calculates case structure rigidity are as follows:
Step 3, quasi-static to touch 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, blade-casing touches the depth of invasion δ (F during rubbingn) can express
Are as follows:
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.
Case structure rigidity and blade radial displacement expression formula are brought into blade-casing and touch the depth of invasion rubbed by step 3-3
Expression formula, and it is a small amount of to omit high-order, obtains normal direction and touches power expression formula of rubbing are as follows:
Wherein
The invention has the benefit that
The present invention touches power of rubbing for a kind of improved rotating vane-flexibility casing and determines method, this touches the power model that rubs and considers
Centrifugation rigidifying effect, Spin softening effect with established angle blade, touch rub softening effect and aerodynamic force and machine at Coriolis stress effect
Casket influence flexible, the model are suitable for non-yielding prop and elastic bearing casing.In the comparison with experiment expansion, the present invention is obtained
To touch rub power model touch power of rubbing numerically be more nearly true aero-engine actually occur touch rub caused by touch and rub
Power size.
Detailed description of the invention
Fig. 1 touches power of rubbing 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 decomposition diagram 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 is that the casing displacement comparison of the embodiment of the present invention deforms schematic diagram；
Fig. 7 is that blade-flexibility casing of the embodiment of the present invention touches the schematic diagram that rubs；
Fig. 8 is that the difference of the embodiment of the present invention touches power model contrast schematic diagram of rubbing.
Fig. 9 touches power contrast schematic diagram of rubbing for the embodiment of the present invention.
Specific embodiment
The present invention will be further described in the following with reference to the drawings and specific embodiments.
A kind of improved rotating vane-flexibility casing touches power of rubbing and determines method in the embodiment of the present invention, and method flow diagram is such as
Shown in Fig. 1, comprising the following steps:
Step 1, the plastic deformation of rotating vane is determined；
Blade is reduced to Timoshenko beam model, considers centrifugal force suffered by blade, aerodynamic force, normal direction contact force with
And frictional force.
Step 1-1 calculates the centrifugal force of micro unit are as follows:
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 distance of the arbitrary point away from blade cantilever end on blade.
Step 1-2 derives the elastic equation of beam；
Timoshenko beam is there are shear-deformable, if shear-deformable is 0, the tangent line of center line will be in the normal in section
It being overlapped, y is the amount of deflection of center line,For due to bending caused by slope,For slope loss, it is equal to the angle of shear,
Q is the shearing in section, the elastic equation of beam are as follows:
In formula: κ is shearing factor, and G is modulus of shearing, M moment of flexure.
Step 1-3 according to fig. 2 decomposes normal direction contact force, frictional force and centrifugal force are as follows:
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, according to Fig. 3 by blade dynamic balance and equalising torque relationship can obtain blade bending displacement equation are as follows:
Step 1-5 omits the sag curve that high-order derives blade in a small amount are as follows:
Wherein
In formula: μ is coefficient of friction；E is Young's modulus；I is cross sectional moment of inertia；FeFor aerodynamic force suffered by blade.
Directly reference mechanics of materials formula can obtain blade bending displacement are as follows:
Step 1-6 compares above-mentioned two computation model and the expansion of Ma model and finite element result
Comprehensively consider blade centrifugation rigidifying, Spin softening and the influence for touching the softening that rubs, revolving speed be set as 5000r/min,
It is 2000N that power of rubbing is touched in Fig. 4 (a), and softening effect is greater than centrifugation rigidifying effect at this time, and actual flexion shift value is greater than three
All irrespective result.Fig. 4 (b) touches power of rubbing and is set as 200N, and softening effect is less than centrifugation rigidifying effect, actual flexion at this time
Shift value is again smaller than mechanics of materials result.Fig. 4 (a) Literature result with differ larger herein, and be then very close in Fig. 4 (b),
By comparison as can be seen that document has fully considered centrifugation rigidifying effect, and does not consider excessively for touching to rub to soften.
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, established angle β, then casing is axially L with the width that rubs that touches of bladec=b ×
Cos β, in touching this section of casing to rub in width as research object, equivalent support stiffness can pass through beam function method meter for fetch bit
It calculates or experiment measures, plastic deformation then uses flexible ring to simulate, and the final mean annual increment movement of arbitrary point is casing overall displacements and soft
Property displacement vector sum, altogether include horizontal direction displacement components uc, vertical direction displacement vc, radial compliance displacement components us, it is centripetal to be positive, it cuts
W is displaced to flexibilitys, it is positive along angle augment direction.
Step 2-1 calculates the elastic potential energy of flexible ring are as follows:
In formula: EcFor the Young's modulus of flexible ring；IcFor the cross sectional moment of inertia of flexible ring；RcFor casing radius；usFor radial direction
Flexibility displacement.
Step 2-2, according to Reciprocal work theorem, external force acting are as follows:
The plastic deformation of flexible ring generallys use pitch diameter vibration mode to express, using all pitch diameters vibration of n >=2 as mould
The state vibration shape, tangential displacement and radial displacement can be unfolded are as follows:
In formula, n represents pitch diameter number, also referred to as circumferential wave number.
Formula (5) is displaced according to pitch diameter and is unfolded, can be obtained:
The elastic potential energy of step 2-3, flexible ring are done work equal to external force, so as to obtain case structure rigidity are as follows:
In order to verify the vector sum that the overall displacements of arbitrary point are translation displacements and flexible displacement, casing is expanded to herein
4 ranks, certain casing radius is 224mm, with a thickness of 3mm, touches the length 50mm that rubs, and applies constant radial and motivates F=1N, with horizontal direction
Angle is 60 °, in kcx=kcy=∞ and kcx=kcy=20000N/m seeks the maximum displacement in casing circumference and imitates with finite element
True expansion comparison, as shown in table 1.Fig. 6 depicts casing shape under two kinds of operating conditions, and all displacements amplify 1000 times.
1 casing displacement comparison result of table
Step 3, quasi-static to touch 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, if Fig. 7 is by elastic accommodation consistency condition, blade-casing touches the depth of invasion δ (F during rubbingn) can
Expression are as follows:
In formula: ucnTranslation displacements of the palm-rubbing technique to casing are touched for edge；usnFor elastic displacement.
Case structure rigidity and blade radial displacement expression formula are brought into blade-casing and touch the depth of invasion rubbed by step 3-3
Expression formula, and it is a small amount of to omit high-order, obtains normal direction and touches power expression formula of rubbing are as follows:
Wherein
Model verifying 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 macro 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, described in 2015,337:244-262..Due to limited conditions, this experiment
It can not achieve the plastic deformation of casing, can only consider the influence of blade and supporting casing rigidity, therefore by KsIt is set as infinitely great.
Experiment is unfolded under tri- kinds of revolving 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 divided into the slim vane with a thickness of 3mm and two kinds of thick blade of 5mm, it is as shown in Figure 8 with model of literature expansion comparison herein.Each operating condition
The precision of lower this paper is slightly above model of literature.Comparison diagram 8 (a) and 8 (b) will improve bending stiffness it is found that increasing vane thickness, invade
Enter amount it is identical when, touching power of rubbing will increase dramatically.By the comparison of Fig. 8 (c) and 8 (d) and Fig. 8 (e) and 8 (f) it is found that 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) can be seen that the raising with revolving speed, and centrifugation rigidifying effect will increase the bending stiffness of blade, keep
Intrusion volume is constant, and touching power of rubbing will increase a little.
Document model and measure by force snesor to aero-engine complete machine touching power of rubbing.Further to verify casing
The influence of plastic deformation and 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 journal, 2008,23 (11): experiment in 1988-1992. its made further comparison.
Fixed rotating speed and support stiffness are constant, gradually aggravate with the degree of rubbing is touched, and touch power of rubbing and gradually increase, experimental result such as Fig. 9 (a) institute
Show.It is respectively herein h in casing thicknessc=3mm, hc=4mm and hcIt is calculated under tri- kinds of operating conditions of=5mm and touches Mo Li and depth of invasion
Relationship, as shown in Fig. 9 (b), it can be seen that since casing is relatively thin, the rigidity of structure is much smaller than support stiffness, and normal direction touches power of rubbing
The relationship of linear change is showed with depth of invasion.When casing thickness hcWhen for 4mm, normal direction touches the calculating for power of rubbing in this paper model
As a result closest with experimental result.
Claims (1)
1. a kind of improved rotating vane-flexibility casing touches power of rubbing and determines method, which comprises the following steps:
Step 1, the plastic deformation of rotating vane is determined；
Blade is reduced to Timoshenko beam model, calculate centrifugal force suffered by blade, aerodynamic force, normal direction contact force and is rubbed
Wipe power；
Step 1-1 calculates the centrifugal force of micro unit are as follows:
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 distance of the on piece arbitrary point away from blade cantilever end；
Step 1-2, by normal direction contact force, frictional force and centrifugal force are decomposed are as follows:
In formula, FnPower of rubbing is touched for normal direction；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 and equalising torque relationship on blade, and removes the sag curve that high-order derives blade in a small amount
Are as follows:
Wherein
In formula, μ is coefficient of friction；E is Young's modulus；I is cross sectional moment of inertia；FeFor aerodynamic force suffered by blade；
Step 2, the deformation of flexible casing is derived according to energy method, the casing is modeled using flexible ring；
Step 2-1 calculates the elastic potential energy of flexible ring are as follows:
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 are as follows:
Step 2-3 calculates case structure stiffness KsAre as follows:
Step 3, derivation is quasi-static touches the power model that rubs；
Step 3-1 calculates blade radial displacement are as follows:
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, blade-casing touches the depth of invasion δ (F during rubbingn) are as follows:
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；
Case structure rigidity and blade radial displacement are brought into blade-casing and touch the depth of invasion expression formula rubbed by step 3-3, and
It is a small amount of to remove high-order, obtains normal direction and touches power expression formula of rubbing are as follows:
Wherein,
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Families Citing this family (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 |
| 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 |
| CN110532732B (en) * | 2019-09-17 | 2023-03-24 | 东北大学 | Method for determining rubbing relationship between blade and casing |
| 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 |
| 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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