CN108052756A - A kind of method that faying face exposure parameter is determined based on FFT - Google Patents

A kind of method that faying face exposure parameter is determined based on FFT Download PDF

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CN108052756A
CN108052756A CN201711404086.4A CN201711404086A CN108052756A CN 108052756 A CN108052756 A CN 108052756A CN 201711404086 A CN201711404086 A CN 201711404086A CN 108052756 A CN108052756 A CN 108052756A
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张学良
赵越
王余松
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Taiyuan University of Science and Technology
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Abstract

A kind of method that faying face exposure parameter is determined based on FFT, belong to Surface-micromachining process field, it is characterized in the frequency domain transfer characteristic with reference to Fourier transformation, it proposes a kind of for the total contact stiffness of calculating machine faying face and the model of actual total contact area, according to the contact situation at each mechanical bond position of the method research, including the parameters such as contact damping and thermal resistance.Three kinds of deformation stages according to residing for micro-bulge come the total contact stiffness in calculations incorporated face and actual total contact area on the basis of multiple dimensioned contact model, mainly comprise the following steps：1. sampling length is set to obtain profile elevations h；2. pair surface profile carries out Fourier transformation, the parameters such as nominal contact area are obtained；3. actual total contact area and the total contact stiffness of the deformation state gauging surface according to residing for micro-bulge.Advantage is that the present invention can be directly used in actual surface, and result of calculation is more accurate.

Description

A kind of method that faying face exposure parameter is determined based on FFT
Technical field
The invention belongs to Surface-micromachining process fields, and in particular to a kind of side that faying face exposure parameter is determined based on FFT Method,
Background technology
There are substantial amounts of faying face in machine tool structure, the contact situation between faying face is that research lathe its static and dynamic performance must An indispensable link.Faying face is being macroscopically a smooth surface, but from microcosmic angle, machinery adds Work surface is coarse, and with the increase of amplification factor, the details that surface is showed is pole out-of-flatness, this is illustrated Mechanical surface pattern has multiple dimensioned and self-similarity characteristics in distribution.Machining surface is commonly considered as by a series of differences What the micro-bulge of size was formed, the area that actual participation contacts between two surfaces is much smaller than the area observed by macroscopic view, Ke Yixian The contact situation of single micro-bulge is studied, then these micro-bulges are entire to study in a manner that certain mode combines The contact situation on surface, surface micro-bulge mechanics contact on be usually generate perfect elasticity deformation, elastic-plastic deformation with completely Three phases are plastically deformed, elastic deformation stage is more using the Hertzian contact theory proposed by hertz in 1882；Bullet Plastic period generally using the elastoplastic mechanical performance for the technique study micro-bulge that finite element is combined by L.Kogut etc., carries The empirical equation of the micro-bulge elastic-plastic deformation gone out, i.e. KE models；Perfect plasticity deformation stage it is more using Abbott and The Truncation for being used to calculate micro-bulge and being in asperity contact area after perfect plasticity deformation that Firestone is drawn.
Archard establishes the multiple dimensioned model of Studies On Contacts of Rough Surfaces in nineteen fifty-five earliest, and it is micro- that he has studied coarse hemisphere The Elastic Contact of the multiple dimensioned surface of convex body and rigid smooth interplanar finds relation between contact area and contact load close to line Property, although this relation can be very good to explain Amoton law of friction, the assumed condition mistake of the contact model of Archard In idealization, actual surface is very difficult to apply in.
The content of the invention
It, can be efficiently against existing the present invention seeks to propose a kind of method that faying face exposure parameter is determined based on FFT The shortcomings that with the presence of technology, what the object of the invention was realized in, it is characterized in that implementation steps are as follows：
(1) sampling length is set to obtain surface profile height：
Simulate surface profile：Pass through MB functionsEmulation obtains surface profile pattern, z (x) surface profile height is represented；D is Surface Fractal Dimension；G is to divide shape roughness；Spatial frequencyN refers to for frequency Number, nlCorresponding is the Minimum sample rate index of profile, fiFor sample frequency, γ is the real number more than 1, takes γ=1.5；
(2) Fourier transformation is carried out to surface profile：
Fourier transformation is done to rough surface, surface is decomposed into the superposition of different frequency grade cosine micro-bulge, with i tables Show the frequency series residing for micro-bulge, in this model, i-stage micro-bulge is located on (i-1)-th grade of micro-bulge, therefore i-stage owns The nominal contact area of micro-bulge is equivalent to the real contact area of (i-1)-th grade of all micro-bulge, the number of i-stage micro-bulge by The surface density that its apparent area is multiplied by i-stage micro-bulge obtains,
Each frequency level micro-bulge surface densityRadius of curvature value
The contact area of first frequency grade micro-bulge, that is, nominal contact area A=L2；Each frequency level micro-bulge participation connects Tactile number isThe actual gross contact area of micro-bulge is
The contact load of each frequency level
In above formula, L is sampling length；βiFor the amplitude of i-stage micro-bulge；Represent the contact of i grades of single micro-bulges Area；Represent the contact load of i grades of single micro-bulges；AiRepresent the contact area of all micro-bulges of i-stage；
(3) actual total contact area of the deformation state gauging surface according to residing for micro-bulge and total contact stiffness：
(1) contact area of each frequency level micro-bulgeWith normal direction contact loadIt is according to the deformation residing for micro-bulge The calculation formula in corresponding deformation stage solves in stage；
(2) when normal direction contact load be less than elastic deformation critical value, i.e.,When, micro-bulge is in perfect elasticity change Shape or elastic-plastic deformation state,
The contact area of single micro-bulge is calculated under elastic stage by Hertz theoryWith contact stiffnessSingle micro-bulge Contact radiusContact area byIt calculates, R is the radius of curvature of single dimpling in formula, and F is application Normal load, E is elastic model.Micro-bulge deflection：Contact stiffness by It calculates；
When normal direction contact load is less than elastic plastic strain critical value and more than elastic deformation critical value, i.e., When, micro-bulge is in the elastic-plastic deformation stage, using KE models, single micro-bulge contacted with rigid plane after contact area with Contact stiffness is calculated by following equation：
A. the relation of contact load-displacement
B. the relation of contact area-displacement
In formula,R represents critical displacement amount when single micro-bulge is plastically deformed；H is micro-bulge material Expect hardness, expression formula H=2.8Sy, SyFor the yield strength of material；K=0.454+0.41 υ represent material hardness coefficient, and υ is Micro-bulge material Poisson's ratio；For elastic elastoplasticity critical contact load；Ac=π R ωcFace for elastic elastoplasticity Boundary's contact area；
(3) elasticity and the total contact area A of elastic-plastic deformation stage micro-bulges at different levels are calculatediWith single-stage contact stiffness ki:Total contact stiffnessIf residing frequency level reaches maximum at this time Frequency series, then iteration ends, export as a result, otherwise repeating the iteration of front；
(4) plastic period, the expression formula of contact area is Ap=2 π R ω, contact load Fp=ApH=2 π R ω H, into plastic stage, iteration ends, the contact area obtained at this time is actual total contact surface product value.
Advantages of the present invention and good effect
Machining surface contact performance influence the friction of component contact position, abrasion, lubrication, sealing, vibration, fatigue and The quality of thermal conductivity, therefore the exposure parameter for accurately obtaining machining surface is extremely important.In mechanical processing table In the calculating of face exposure parameter, traditional statistics contact model can be influenced be subject to surface profiler resolution ratio, the present invention It is based on fractal property possessed by machining surface and multiple dimensioned characteristic, the scale of multiple dimensioned model and fractal model is independent Property combines so that model will not be influenced be subject to measuring instrument resolution ratio.And it overcomes Archard contact models to be difficult to The shortcomings that being applied in actual surface.The inventive method step is succinct, and thinking is simple, using the related matlab programs write, Only some initial parameters need to be specified and inputted in program, by the iteration of program can obtain total contact stiffness of faying face with Actual total contact area.
Description of the drawings
Fig. 1 is the fitting schematic diagram of discrete Fourier transform Rough Surface Profile,
Fig. 2 is the arrangement mode schematic diagram of each frequency level micro-bulge, and 20 rank cosine waves are superimposed before a is represented in figure；B tables in figure Show simulation Rough Surface Profile.
Fig. 3 is to solve contact area and the iterative process figure of contact stiffness
Fig. 4 is the Rough Surface Profile that the fractal dimension of MB functions emulation is 1.597
Fig. 5 is the graph on the actual total contact surface of present invention iterative calculation rough surface
Fig. 6 is the graph of the actual total contact stiffness of present invention iterative calculation rough surface
Fig. 7 is the graph of present invention iterative calculation rough surface mean exposure stress
Specific embodiment
The iterative process of entire calculating process, i.e. implementing procedure of the invention are as shown in Figure 1.
By the superposition of different frequency series cosine wave, the profile of mechanical surface is fitted, preceding 20 grades of frequency contents Superposition have been able to capture the substantially pattern of original surface profile, as shown in a in Fig. 2.
Implementation steps are：
(1) generation simulation profile
Based on MB functions(1 ＜ D ＜ 2, γ ＞ 1), setting fractal dimension D are 1.597 sampling interval fiFor 2.4114 μm, sampling length L is 500 μm, divides shape roughness G=2.86 × 10-10(m), imitated Very, Rough Surface Profile as shown in Figure 3 is obtained.
(2) Fourier transformation (FFT) is carried out to simulation profile and is iterated calculating
1) Fourier transformation is carried out to profile in Fig. 3, converted it on frequency domain, set each parameter to be：Faying face material Complex elastic-modulus E=200GPa, yield limit Sy=0.2GPa, material Poisson's ratio ν=0.28, material hardness H=2.8Sy。
2) byWithAcquire micro-bulge surface densities and radius of curvature at different levels, apparent area An= L2；
3) full payload contact load F=5N is substituted into, obtains the single micro-bulge load of each frequency level：With it is every One frequency level micro-bulge participates in the number of contact：
4) by each frequency level micro-bulge institute F loadediWith elasticity-elastic-plastic deformation critical value Fcei, elastoplasticity-plasticity Deform critical value FcpiIt makes comparisons, ifThen in elastic deformation stage, carried out calculating its actual contact by Hertz theory Contact area area byCalculate, contact stiffness byIt calculates；If Contact load is then by the relation of contact load-displacement in KE modelsIt calculates, connects Contacting surface product by contact area-displacement relationIt calculates.Iterative cycles iteration, Until reaching maximum iteration.What is be calculated at this time is the related parameter values of single micro-bulge, between micro-bulges at different levels Arrangement mode as shown in figure 4, to be connected in parallel between same frequency grade micro-bulge, the micro-bulge between different frequency grade is arranged for series connection It arranges, then total contact stiffnessTotal contact area
If 5)Then illustrate that micro-bulge enters plastic period, the contact stiffness of the micro-bulge is 0, and iteration is whole Only, the stage contact area is by expression formula Ap=2 π R ω are calculated, and contact load is by Fp=ApH=2 π R ω H are calculated, and are obtained at this time Contact area be actual total contact surface product value.
Contact area, contact stiffness, mean exposure stress are by Fig. 5, Fig. 6, Fig. 7 in the entire iterative process being calculated Shown, iterations N is 96, and not up to peak frequency series just terminates, and illustrates that micro-bulge has been enter into plastic deformation rank at this time Section, total contact area A=8.929 × 10-2μm2, contact stiffness K=2.349 × 106N/m, mean exposure stress P= 539MPa。

Claims (1)

  1. A kind of 1. method that faying face exposure parameter is determined based on FFT, it is characterised in that：Implementation steps are as follows：
    (1) sampling length is set to obtain surface profile height：
    Simulate surface profile：Pass through MB functionsEmulation obtains surface profile pattern, z (x) tables Presentation surface profile elevations h；D is Surface Fractal Dimension；G is to divide shape roughness；Spatial frequencyN is frequency index, nl Corresponding is the Minimum sample rate index of profile, fiFor sample frequency, γ is the real number more than 1, takes γ=1.5；
    (2) Fourier transformation is carried out to surface profile：
    Fourier transformation is done to rough surface, surface is decomposed into the superposition of different frequency grade cosine micro-bulge, dimpling is represented with i Frequency series residing for body, in this model, i-stage micro-bulge is located on (i-1)-th grade of micro-bulge, therefore all micro-bulges of i-stage Nominal contact area be equivalent to the real contact area of (i-1)-th grade of all micro-bulge, the number of i-stage micro-bulge is by its name The surface density that area is multiplied by i-stage micro-bulge obtains,
    Each frequency level micro-bulge surface density ηi=2fi 2, radius of curvature value
    The contact area of first frequency grade micro-bulge, that is, nominal contact area A=L2；Each frequency level micro-bulge participates in of contact Number isThe actual gross contact area of micro-bulge is
    The contact load of each frequency level
    In above formula, L is sampling length；βiFor the amplitude of i-stage micro-bulge；Represent the contact area of i grades of single micro-bulges；Represent the contact load of i grades of single micro-bulges；AiRepresent the contact area of all micro-bulges of i-stage；
    (3) actual total contact area of the deformation state gauging surface according to residing for micro-bulge and total contact stiffness：
    (1) contact area of each frequency level micro-bulgeWith normal direction contact loadIt is according to the deformation stage residing for micro-bulge The calculation formula in interior corresponding deformation stage solves；
    (2) when normal direction contact load be less than elastic deformation critical value, i.e.,When, micro-bulge be in perfect elasticity deformation or Elastic-plastic deformation state,
    The contact area of single micro-bulge is calculated under elastic stage by Hertz theoryWith contact stiffnessSingle asperity contact RadiusContact area byIt calculates, R is the radius of curvature of single dimpling in formula, and F is the method applied To load, E is elastic model.Micro-bulge deflection：Contact stiffness by It calculates；
    When normal direction contact load is less than elastic plastic strain critical value and more than elastic deformation critical value, i.e.,When, it is micro- Convex body is in the elastic-plastic deformation stage, using KE models, single micro-bulge contacted with rigid plane after contact area with contacting Rigidity is calculated by following equation：
    A. the relation of contact load-displacement
    B. the relation of contact area-displacement
    In formula,Represent critical displacement amount when single micro-bulge is plastically deformed；H is micro-bulge material Hardness, expression formula H=2.8Sy, SyFor the yield strength of material；K=0.454+0.41 υ represent material hardness coefficient, and υ is micro- Convex body material Poisson's ratio；For elastic elastoplasticity critical contact load；Ac=π R ωcIt is critical for elastic elastoplasticity Contact area；
    (3) elasticity and the total contact area A of elastic-plastic deformation stage micro-bulges at different levels are calculatediWith single-stage contact stiffness ki:Total contact stiffnessIf residing frequency level reaches maximum at this time Frequency series, then iteration ends, export as a result, otherwise repeating the iteration of front；
    (4) plastic period, the expression formula of contact area is Ap=2 π R ω, contact load Fp=ApH=2 π R ω H enter Plastic stage, iteration ends, the contact area obtained at this time are actual total contact surface product value.
CN201711404086.4A 2017-12-22 2017-12-22 Method for determining joint surface contact parameters based on FFT Active CN108052756B (en)

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Publication number Priority date Publication date Assignee Title
CN110940587A (en) * 2019-12-17 2020-03-31 北京工业大学 Lathe bed-foundation joint surface contact rigidity calculation method based on multi-scale theory
CN111781134A (en) * 2020-07-09 2020-10-16 中国人民解放军国防科技大学 Measuring method and measuring system for normal contact parameter of joint surface
CN115171093A (en) * 2022-06-20 2022-10-11 中国人民解放军96963部队 Mechanical joint surface parameter calculation method and device

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CN111781134A (en) * 2020-07-09 2020-10-16 中国人民解放军国防科技大学 Measuring method and measuring system for normal contact parameter of joint surface
CN115171093A (en) * 2022-06-20 2022-10-11 中国人民解放军96963部队 Mechanical joint surface parameter calculation method and device

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