CN106991219A - A kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal - Google Patents
A kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal Download PDFInfo
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Abstract
The present invention relates to a kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal, step is：Description two-dimensional fractal curvilinear function is improved to simulate to the correction function of three-dimensional fractal pattern, the crest that this function is described is expressed as juxtaposition metamorphose amount with trough difference in magnitude；Contact between two coarse micro-bulges is equivalent to the contact between a rigid plane and an equivalent micro-bulge, then the real contact area between equivalent micro-bulge and rigid plane；Elastic deformation stage, the deflection in elastic-plastic deformation stage are calculated respectively；Area distributions function is calculated with real contact area；Single micro-bulge rigidity and total interface rigidity are calculated；Elastic stage rigidity kn1With elastic-plastic phase rigidity kn2With the calculating of total interface rigidity.The present invention provides a kind of Forecasting Methodology simple to operation for the acquisition of rigidity between precision optical machinery interface, consider micro-bulge elastic-plastic deformation, contact between friction factor and three-dimensional fractal distribution influence, obtained result can for predict, control interface dynamic characteristic Technical Reference be provided.
Description
Technical field
The present invention relates to a kind mechanical interface mechanical technology, specifically a kind of normal direction interface for considering three-dimensional fractal
Stiffness Prediction method.
Background technology
Piece surface after machine tooling, macroscopically sees very smooth, but then shows from microcosmic a large amount of coarse
Body, i.e. part have coarse surface topography.Rough surface morphology is to the friction on interface, and fatigue and vibration noise etc. to be had
Material impact.By the observation to metal surface pattern, scholars have found that the surface topography under different measurement scales has statistics
On self affine and self-similarity nature, therefore fractal theory is introduced into and is widely used in the description and contact to rough surface morphology
Analysis.Accurate modeling is carried out to the characterisitic parameter (predominantly contact stiffness and contact damping) on Rough Contact interface, to analyze
With prediction complete machine static and dynamic performance, this by be common mechanical research and development and analysis during key technology.
Current China has been carried out that " the high-grade precise numerical control machine in the strategy of made in China 2025 ", strategy is described as a state
The symbol of the high-end equipment manufacturing of family, it has a substantial amounts of interface as typical complicated electromechanical equipment, these interfaces it is quiet, dynamic
Characteristic is largely fixed the static and dynamic characteristics of whole lathe, namely decide operating efficiency during machine tooling, it is steady
Qualitative and machining accuracy.The theoretically touching act on careful research interface, and it is high to set up related important dynamic characteristic
Accuracy prediction model is not only that trueness error compensation provides foundation, and technology ginseng can be also provided for prediction, control interface dynamic characteristic
Examine, with extensive engineering significance.
The Strategic Context of intelligence manufacture requires just to can be good at the dynamic spy that anticipation is entirely equipped in Machine Design early stage
Property, and the stiffness characteristics that this characteristic is largely depended on interface.Conventional people's obtaining for mechanical interface rigidity
Must have and there is limitations, be primarily present these problems：First, people often handle interracial contact problem with finite element software,
But this complex difficulty of method grid division, and computational efficiency is low；Secondly, the analytic method based on fractal theory is again
The characteristic of friction factor and micro-bulge three-dimensional surface fractal cloth is have ignored, these are assumed and limitation obviously cannot be directly used to height
Seem not enough in accurate mechanical interface analysis (such as accurate micro-nano device, precision machinery person joint's decelerator etc.), accuracy.
The content of the invention
There is the deficiencies such as inefficiency, poor accuracy for the acquisition of mechanical interface rigidity in the prior art, the present invention will
The problem of solution be to provide a kind of interface rigidity for making to be difficult to detect become to be readily available, improve accuracy of forecast consideration it is three-dimensional
Divide the normal direction interface rigidity Forecasting Methodology of shape.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal of the present invention, includes following steps：
1) 3 d surface topography is simulated：Description two-dimensional fractal curvilinear function is improved to simulate to the amendment of three-dimensional fractal pattern
Function, the crest that this function is described is expressed as juxtaposition metamorphose amount δ=2G with trough difference in magnitudeD-2(lnγ)0.5(2r′)3-D, its
In, D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is frequency density parameter, r '
For micro-bulge truncation radius；
2) asperity contact equivalent process：Contact between two coarse micro-bulges is equivalent to a rigid plane and one equivalent micro-
Contact between convex body, then real contact area a=π R δ between equivalent micro-bulge and rigid plane；Wherein, δ connecing for micro-bulge
Deflection is touched, R is the radius of curvature of micro-bulge；
3) micro-bulge deformation includes three phases, i.e. elastic deformation stage, elastic-plastic deformation stage and plastic deformation rank
Section；Elastic deformation stage, the deflection in elastic-plastic deformation stage are calculated respectively；
4) area distributions function is calculated with real contact area：Entirely the area distributions function on contact interface isEntirely the real contact area of contact interface isWherein, D
For 3 d surface topography fractal dimension, 2<D<3, alRepresent contact area maximum in all asperity contacts；A contacts to be actual
Area；
5) single micro-bulge rigidity and total interface rigidity are calculated：Single micro-bulge rigidity includes its elastic deformation and elastoplasticity
Deform two stages, i.e. elastic stage rigidity kn1With elastic-plastic phase rigidity kn2,
Always interface rigidity is：
Wherein, LeFor the load of single micro-bulge elastic stage, aeFor the critical elasticity deformation area of single micro-bulge, al
Contact area maximum in all asperity contacts is represented, δ is the juxtaposition metamorphose amount of micro-bulge, and D is 3 d surface topography point shape
Dimension, 2<D<3, LepFor the load of single micro-bulge elastic-plastic phase, G is point shape roughness of surface topography, apFor critical modeling
Property deformation area, σyThe softer yield strength in material that contacts with each other is represented, λ is the coefficient of definition, and a is real contact area, n
For material hardness index.
The elastic critical deflection of the Deformation calculation of elastic deformation stage including stand under load micro-bulge, single micro-bulge face
The load of boundary's elastic deformation area, single micro-bulge elastic stage, wherein,
The elastic critical deflection of stand under load micro-bulge is：
Wherein kμFor friction correction factor, φ is the characteristic coefficient of material, and R is the radius of curvature of micro-bulge；
The critical elasticity deformation area of single micro-bulge is：
Wherein, D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is that frequency is close
Spend parameter, kμFor friction correction factor；
The load of single micro-bulge elastic stage is：
Wherein, E is the equivalent elastic modulus of interface two-phase contact material, is expressed asE1、E2
The respectively modulus of elasticity of two-phase contact material, v1、v2Respectively the Poisson's ratio of two-phase contact material, represents two contact materials
Stock attribute.
The Deformation calculation in elastic-plastic deformation stage include stand under load micro-bulge elastic-plastic phase critical amount of plastic deformation,
The load of the critical plastic deformation area of stand under load micro-bulge and single micro-bulge elastic-plastic phase, wherein：
Stand under load micro-bulge is in the critical amount of plastic deformation of elastic-plastic phase：
Wherein, D is 3 d surface topography fractal dimension, 2<D<3, kμFor friction correction factor, φ is the feature system of material
Number, γ is frequency density parameter, and G divides shape roughness for surface topography.
Stand under load micro-bulge is in the critical plastic deformation area of elastic-plastic phase：
Wherein, D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is that frequency is close
Spend parameter, kμFor friction correction factor, φ is the characteristic coefficient of material.
The load of single micro-bulge elastic-plastic phase is：
Wherein, σyThe softer yield strength in material that contacts with each other is represented, λ is definition
Coefficient, λ=H/ σy, H two contacts with each other the hardness of softer material in material, and n is material hardness index, is expressed asaeFor the critical elasticity deformation area of single micro-bulge.
The invention has the advantages that and advantage：
1. the present invention provides a kind of Forecasting Methodology simple to operation for the acquisition of rigidity between precision optical machinery interface, make difficulty
Become to be readily available with the interface rigidity of detection, overcome the defect of conventional method, it is contemplated that the elastic-plastic deformation of micro-bulge, connect
The influence of friction factor and three-dimensional fractal distribution between touching, obtained result can provide technology for prediction, control interface dynamic characteristic
With reference to.
Brief description of the drawings
Fig. 1 is Forecasting Methodology flow chart of the present invention；
The 3 d surface topography simulation graftal that Fig. 2 the inventive method is related to；
The contact isoboles of what Fig. 3 the inventive method was related to contact with each other micro-bulge；
The interface equivalent process figure that Fig. 4 the inventive method is related to；
The vibration-testing proof diagram that Fig. 5 the inventive method is related to.
Embodiment
With reference to Figure of description, the present invention is further elaborated.
As shown in figure 1, a kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal of the present invention comprises the following steps：
1) 3 d surface topography is simulated：Description two-dimensional fractal curvilinear function is improved to simulate to the amendment of three-dimensional fractal pattern
Function, the crest that this function is described is expressed as juxtaposition metamorphose amount δ=2G with trough difference in magnitudeD-2(lnγ)0.5(2r′)3-D, its
In, D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is frequency density parameter, r '
For micro-bulge truncation radius；
2) asperity contact equivalent process：Contact between two coarse micro-bulges is equivalent to a rigid plane and one equivalent micro-
Contact between convex body, then real contact area a=π R δ between equivalent micro-bulge and rigid plane；Wherein, δ is asperity contact
Deflection, R is the equivalent radius of curvature of micro-bulge；
3) micro-bulge deformation stage is divided into three phases, i.e. elastic deformation stage, elastic-plastic deformation stage and plasticity and become
The shape stage；Elastic deformation stage, the deflection in elastic-plastic deformation stage are calculated respectively；
4) area distributions function is calculated with real contact area：Entirely the area distributions function on contact interface isEntirely the real contact area of contact interface isWherein, al
Represent contact area maximum in all asperity contacts；
5) single micro-bulge rigidity and total interface rigidity are calculated：Single micro-bulge rigidity includes its elastic deformation and elastoplasticity
Deform two stages, i.e. elastic stage rigidity kn1With elastic-plastic phase rigidity kn2,
Always interface rigidity is：
In step 1) in, the inventive method will describe the Weierstrass-Mandelbrot of two-dimensional fractal curve first
(W-M) function, is improved to simulate the amendment W-M functions of three-dimensional fractal pattern, such as Fig. 2 institutes, is three be related in the inventive method
Tie up surface topography simulation graftal.In the present embodiment, given analog parameter is：3 d surface topography fractal dimension D=2.45,
Point shape roughness G=5.42 × 10 of surface topography-8M, frequency density parameter γ=1.5.
In step 2) in, by classical Hertz theory, the contact between two coarse micro-bulges is equivalent to a rigidity after stand under load
Contact between plane and an equivalent micro-bulge, as shown in Figure 3.Equivalent plane cut equivalent micro-bulge can be formed nominal contact area and
Real contact area, therefore analyzed with this and obtain real contact area a=π R δ between equivalent micro-bulge and rigid plane, wherein,
R is the equivalent radius of curvature of micro-bulge；
In step 3) in, three phases, i.e. elastic deformation, elastic-plastic deformation and modeling are divided into by the deformation of micro-bulge is careful
Property deformation three phases, the wherein Deformation calculation of elastic deformation stage includes elastic critical deflection, the list of stand under load micro-bulge
The load of the critical elasticity deformation area of individual micro-bulge, single micro-bulge elastic stage, wherein,
The elastic critical deflection of stand under load micro-bulge is：
Wherein kμFor friction correction factor, φ is the characteristic coefficient of material, and R is the radius of curvature of micro-bulge；
The critical elasticity deformation area of single micro-bulge is：
Wherein, D is 3 d surface topography fractal dimension, and G is point shape roughness of surface topography, and γ is frequency density ginseng
Number, kμFor friction correction factor；
The load of single micro-bulge elastic stage is：
Wherein, E is the equivalent elastic modulus of interface two-phase contact material, is expressed asE1、E2、
v1、v2It is the stock attribute of two contact materials, E1、E2The respectively modulus of elasticity of two-phase contact material, v1、v2Respectively
The Poisson's ratio of two-phase contact material.
In step 3) in, the Deformation calculation in elastic-plastic deformation stage includes stand under load micro-bulge in the critical of elastic-plastic phase
The load of the critical plastic deformation area of amount of plastic deformation, stand under load micro-bulge and single micro-bulge elastic-plastic phase, wherein：
Stand under load micro-bulge is in the critical amount of plastic deformation of elastic-plastic phase：
Stand under load micro-bulge is in the critical plastic deformation area of elastic-plastic phase：
The load of single micro-bulge elastic-plastic phase is：
Wherein, σyThe softer yield strength in material that contacts with each other is represented, λ is the coefficient of definition, λ=H/ σy, H is two-phase
The hardness of softer material in mutual contact material, n is material hardness index, is expressed asaeTo be single
The critical elasticity deformation area of micro-bulge.
It is now that two piece of 45 steel plate comes with two pieces of reproducible simple test specimens to verify the prediction accuracy of the inventive method
Carry out Vibration Modal Test.Steel plate long 400mm, wide 50mm, thick 6mm, are formed, interface is added by milling with 16 M6 bolt connection
Work is formed.Correlation engineering parameter is shown in Table 1.
Table 1 tests steel plate parameter
According to document " Li X, Liang Y, Zhao G, et al.Dynamic characteristics of joint
surface considering friction and vibration factors based on fractal theory
[J].Journal of Vibroengineering,2013,15(2):872-883. ", interface is carried out as shown in Figure 4 etc.
Effect processing, tries to achieve the modulus of elasticity of equivalent layer, modulus of shearing and Poisson's ratio can just be embedded into normal direction interface rigidity respectively,
So as to which Modal frequency must be calculated, the vibration test modal frequency of this result and Fig. 5 is done into comparative analysis as shown in table 2.
Table 2 gives the calculated results when ignoring three-dimensional fractal simultaneously, it is known that the error for ignoring three-dimensional fractal is more three-dimensional than considering
Fractal surface pattern error is big.
Table 2 is calculated and comparison of test results
Specific implementation described above for the present invention, but the scope of the present invention is not limited thereto, it is any easily to change
Dynamic and conversion, is belonged within the scope of the present invention.
Claims (3)
1. a kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal, it is characterised in that comprise the following steps：
1) 3 d surface topography is simulated：Description two-dimensional fractal curvilinear function is improved to simulate to the amendment letter of three-dimensional fractal pattern
Number, the crest that this function is described is expressed as juxtaposition metamorphose amount δ=2G with trough difference in magnitudeD-2(lnγ)0.5(2r′)3-D, wherein,
D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is frequency density parameter, and r ' is micro-
Convex body truncation radius；
2) asperity contact equivalent process：Contact between two coarse micro-bulges is equivalent to a rigid plane and an equivalent micro-bulge
Between contact, then real contact area a=π R δ between equivalent micro-bulge and rigid plane；Wherein, δ becomes for the contact of micro-bulge
Shape amount, R is the radius of curvature of micro-bulge；
3) micro-bulge deformation includes three phases, i.e. elastic deformation stage, elastic-plastic deformation stage and plastic period；Point
Ji Suan not elastic deformation stage, the deflection in elastic-plastic deformation stage；
4) area distributions function is calculated with real contact area：Entirely the area distributions function on contact interface isEntirely the real contact area of contact interface isWherein, D
For 3 d surface topography fractal dimension, 2<D<3, alRepresent contact area maximum in all asperity contacts；A contacts to be actual
Area；
5) single micro-bulge rigidity and total interface rigidity are calculated：Single micro-bulge rigidity includes its elastic deformation and elastic-plastic deformation
Two stages, i.e. elastic stage rigidity kn1With elastic-plastic phase rigidity kn2,
Always interface rigidity is：
Wherein, LeFor the load of single micro-bulge elastic stage, aeFor the critical elasticity deformation area of single micro-bulge, alRepresent
Maximum contact area in all asperity contacts, δ is the juxtaposition metamorphose amount of micro-bulge, and D is 3 d surface topography fractal dimension,
2<D<3, LepFor the load of single micro-bulge elastic-plastic phase, G is point shape roughness of surface topography, apFor critical plastic deformation
Area, σyThe softer yield strength in material that contacts with each other is represented, λ is the coefficient of definition, and a is real contact area, and n is material
Stiffness.
2. the normal direction interface rigidity Forecasting Methodology of the consideration three-dimensional fractal as described in claim 1, it is characterised in that：Elastic deformation
The elastic critical deflection of the Deformation calculation in stage including stand under load micro-bulge, the critical elasticity deformation area of single micro-bulge,
The load of single micro-bulge elastic stage, wherein,
The elastic critical deflection of stand under load micro-bulge is：
Wherein, kμFor friction correction factor, φ is the characteristic coefficient of material, and R is the radius of curvature of micro-bulge；
The critical elasticity deformation area of single micro-bulge is：
Wherein, D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is that frequency density is joined
Number, kμFor friction correction factor；
The load of single micro-bulge elastic stage is：
Wherein, E is the equivalent elastic modulus of interface two-phase contact material, is expressed asE1、E2Respectively
For the modulus of elasticity of two-phase contact material, v1、v2Respectively the Poisson's ratio of two-phase contact material, represents the basic of two contact materials
Material properties.
3. the normal direction interface rigidity Forecasting Methodology of the consideration three-dimensional fractal as described in claim 1, it is characterised in that：Elastoplasticity becomes
The Deformation calculation in shape stage includes critical amount of plastic deformation of the stand under load micro-bulge in elastic-plastic phase, the critical modeling of stand under load micro-bulge
The load of property deformation area and single micro-bulge elastic-plastic phase, wherein：
Stand under load micro-bulge is in the critical amount of plastic deformation of elastic-plastic phase：
Wherein, D is 3 d surface topography fractal dimension, 2<D<3, kμFor friction correction factor, φ is the characteristic coefficient of material, γ
For frequency density parameter, G divides shape roughness for surface topography,
Stand under load micro-bulge is in the critical plastic deformation area of elastic-plastic phase：
Wherein, D is 3 d surface topography fractal dimension, 2<D<3, G divide shape roughness for surface topography, and γ is that frequency density is joined
Number, kμFor friction correction factor, φ is the characteristic coefficient of material；
The load of single micro-bulge elastic-plastic phase is：
Wherein, σyThe softer yield strength in material that contacts with each other is represented, λ is for definition
Number, λ=H/ σy, H is two hardness for contacting with each other softer material in material, and n is material hardness index, is expressed asaeFor the critical elasticity deformation area of single micro-bulge.
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| CN112395754A (en) * | 2020-11-12 | 2021-02-23 | 清华大学 | Dynamic weakening prediction method for rigidity of mechanical connection structure joint surface |
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Application publication date: 20170728 |