CN110532659A - A kind of finite element node modeling method considering contact surface pattern - Google Patents
A kind of finite element node modeling method considering contact surface pattern Download PDFInfo
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Abstract
The invention belongs to assemble with tightening technology field, provide it is a kind of consider contact surface pattern finite element node modeling method.It initially sets up threedimensional model and carries out the grid dividing of accurate control, need to add contact surface the pattern function of single scale or multiple dimensioned, random distribution or period profile further according to model, the height coordinate matrix for changing contact surface node, regenerates the model with pattern.The present invention focuses on the region division of grid while proposing modeling method, is realizing the number that grid node is also ensured while surface topography addition, it is ensured that calculating speed will not excessively slowly.
Description
Technical field
The invention belongs to assemble with tightening technology field, relate in particular to it is a kind of consider contact surface pattern finite element
Node modeling method.
Background technique
All kinds of machinery are assembled by various components, wherein the surface for the contact that cooperates is referred to as Machine Joint Surfaces.
Due to the randomness and randomness of machining surface, the contact performance of Machine Joint Surfaces will appear significantly in assembling process
Nonlinear characteristic.Therefore mechanism study is carried out to the touching act of Machine Joint Surfaces and simulation analysis is to study and optimize assembler
The essential part of skill.Research for faying face surface topography, carrying out contact analysis to it with finite element simulation is mesh
Preceding main stream approach, the method that the accuracy of model depends on grid precision and modeling.
Wherein, the surface appearance feature of Machine Joint Surfaces is broadly divided into 3 classes, i.e. roughness, percent ripple and geometry, and
The formation of every one kind shape characteristic is all influenced by a variety of processing factors.Want to probe into the surface topography of each scale to contact
The influence of characteristic, it is necessary to accurately reappear the parameters such as the shape characteristic of each scale such as wave height, the pitch of waves in finite element simulation
In model.
The mode of usual model addition surface appearance feature is by adding in the 3 d modeling software of profession to target face
Spline curve is added to be controlled, model imported into finite element software again by some simplification and carries out a series of pre-treatment work.
This method not only cannot accurately show due shape characteristic, and the grid of model is drawn in the interactive process of software
Divide difficulty to increase, and grid precision is very poor, more there is the possibility for losing data.
Summary of the invention
The present invention provides a kind of finite element node modeling method for considering contact surface pattern, may be implemented by this method
The single scale of surface topography and multiple dimensioned Accurate Model, and the present invention has general applicability.
Technical solution of the present invention:
A kind of finite element node modeling method considering contact surface pattern, steps are as follows:
A kind of finite element node modeling method considering contact surface pattern, steps are as follows:
Step 1, touching act approximation in surface is contacted with two plates and is characterized, three-dimensional is carried out to two plates to contact with each other and is built
Mould.
Step 2, it is two parts by the difference cutting of each plate, grid dividing is carried out to model, is divided into sparse layer and encryption
Layer, not excessive influence calculating speed while to guarantee accuracy；Wherein two plate contact areas are included in encryption layer, are enabled
The grid node of contact surface neatly corresponds to above and below contact position, and such as Fig. 2, all grids are hexahedral mesh；
Step 2.1, when the surface topography of addition is single scale,
The encryption layer of upper plate is as pattern layer, and the encryption layer of lower plate is as ideal plane；The sizing grid S of encryption layer presses formula
(1) it calculates:
Wherein, λnFor the distance between two adjacent peaks for the pattern of being added, n=1,2 ... ... represent each region
The serial number of interior pitch of waves value；
Step 2.2, span is big when the surface topography of addition is multiple scales and between each pattern scale,
The encryption layer of upper plate is as pattern layer, and the encryption layer of lower plate is as ideal plane；Encryption layer grid is carried out into one
Cutting is walked, three dimensional areas are divided into, subregion addition (such as Fig. 2) is carried out to pattern；Wherein large scale net region 1 includes one
Kind scale topography, that is, geometry, mesoscale net region 2 include two kinds of scale topography, that is, geometries and percent ripple, small scale
3 domain of grid regions includes three kinds of scale topography, that is, geometries, percent ripple and roughness, i.e., small scale net region realizes more rulers
The pattern of degree is superimposed；Each area grid size S is calculated by formula (2):
Wherein,For the distance between two adjacent peaks for the pattern of being added, i=1,2,3 be three dimensional areas
Code name, n=1,2 ... ... represent the serial number of pitch of waves value in each region；
Step 3, ready-portioned mesh point coordinate matrix is converted；
Step 3.1, assignment function is determined according to institute's shape characteristic to be added；
3.1.1, when the shape characteristic of addition is single scale probability distribution function,
As shown in figure 3, topographical height information is indicated with the random numbers of Gaussian distribution generated at random, it is random need to only to give it
Point number and variance yields produce, and probability density function is following formula:
Wherein, σ is variance yields, determines the amplitude size of addition pattern, μ is mean value, value 0；
3.3.2, when the shape characteristic of addition is single scale period profile function,
As shown in figure 4, the pattern of addition is the superposition of several different amplitudes generated at random, the sinusoidal wave function of frequency,
Topographical information is simplified, changes it in one direction, another direction topographical height is identical, then its height function is expressed
Are as follows:
H (x)=A1sin(ω1θ1)+B1sin(ω2θ2)+...... (3)
Wherein, AnFor the amplitude for adding pattern, ωnFor the frequency for adding pattern, the relationship with the pitch of waves isθnFor
The corresponding phase of grid node, x are node number, and the two is by x=fn(θ) functional relation is corresponding；
H (x) is topographical height function, and n=1,2 ... ... represent serial number；
3.3.3, when the shape characteristic of addition is that multi-scale period distribution function is superimposed,
As shown in figure 5, grid is divided into three regions when the pattern of addition is that multiple dimensioned and pitch of waves span is larger,
The assignment function in each region is different；Assignment function is replaced to simulate pattern, large scale grid in Fig. 2 with standard sine wave
A kind of corresponding assignment function in region 1, the corresponding two kinds of assignment functions in mesoscale net region 2, and small scale net region 3 corresponding three
Kind assignment function, height function expression are as follows:
Wherein, AnFor the amplitude for adding pattern, ωnFor the frequency for adding pattern, the relationship with the pitch of waves isθnFor
The corresponding phase of grid node, x are node number, and the two is by x=fn(θ) functional relation is corresponding；
hnIt (x) is topographical height function, n=1,2 ... ... represent serial number；
3.3.4, when the shape characteristic of addition is multiple dimensioned random distribution number,
It can be seen that small scale net region 3 contains the shape characteristic of three kinds of cardinal scales, it is folded to realize multiple dimensioned pattern
Add.On the contact surface by true actual measurement topographical information addition, it also needs to carry out interpolation processing to measured data, makes to survey surface shape
Looks data point number is equal with contact surface node number.
Step 3.2, assignment mode is determined according to institute's shape characteristic to be added；
3.2.1, when the shape characteristic of addition is single scale, assignment mode are as follows: extract contact surface node coordinate matrix, section
Point position coordinates are as with reference to the specified of assignment mode is carried out, and topographical height function directly adds and subtracts height of node coordinate, really
Determine finish node height coordinate, such as Fig. 6；If pattern waveform to be done to the simplification of one-dimensional square, changing assignment mode is along certain seat
Mark direction change；
3.2.2, when the shape characteristic of addition is multiple dimensioned, assignment mode are as follows: it is trizonal to extract contact surface respectively
Node coordinate matrix from small to large successively converts it according to mesh-density, node location coordinate be as with reference to come into
Row assignment mode is specified, and topographical height function directly adds and subtracts the height of node coordinate in region, finally by trizonal height
Coordinate carries out complex superposition, finish node height coordinate is determined, such as Fig. 7 mode.Wherein there is the part of common grid intersection to be assigned
The topographical height value of multiple scales is given, coordinate value is the superposition of multiple assignment function values, that is, realizes the folded of multiple dimensioned pattern
Add.
Step 4, grid file is regenerated, more new model carries out simulation analysis, that is, realizes and consider contact surface pattern
Finite element node modeling method.
Beneficial effects of the present invention:
(1) present invention can be realized the finite element node modeling of the macro Micro authenticity pattern of contact surface, can either individually add
Add the shape characteristic of a scale, and multiple scale topographies can be superimposed and carry out comprehensive analysis, is connect for assembly field
The research of touching surface mechanism provides simulation modeling basic technical means；
(2) present invention passes through change by modifying to the transformation of mesh point coordinate matrix to the details of model
The geometrical characteristic of node controls contact surface shape characteristic, and the precision of model, the accuracy of calculating be improved；
(3) present invention takes different assignment methods for different-shape feature, can accomplish that particular problem is specifically divided
Analysis, improves the Stringency of modeling, and can guide probing into for similar problems modeling method；
(4) present invention focuses on the region division of grid while proposing modeling method, is realizing surface topography addition
The number of grid cell and node is also ensured simultaneously, it is ensured that calculating speed will not excessively slowly.
Detailed description of the invention
Fig. 1 is the location map of each section in plate contact model of the present invention；
Fig. 2 is the net region distribution map of multiple dimensioned pattern model；
Fig. 3 is the illustraton of model of single scale probability distribution function shape characteristic；
Fig. 4 is the illustraton of model of the shape characteristic of single scale period profile function superposition；
Fig. 5 is the illustraton of model of multi-scale period distribution function shape characteristic；
Fig. 6 is the node offset schematic diagram for adding single scale pattern；
Fig. 7 is the node offset schematic diagram for adding multiple dimensioned pattern.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, below in conjunction with attached in the embodiment of the present invention
Figure, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is the present invention
A part of the embodiment, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art are not having
Every other embodiment obtained under the premise of creative work is made, shall fall within the protection scope of the present invention.
A kind of finite element modeling method considering contact surface pattern, comprising the following steps:
Step 1, most of mechanical surface touching act approximate can be contacted to characterize with two plates, and the present invention is i.e. with two
Plate is illustrated as example, establishes the two flatbed three-dimensional models to contact with each other.
Step 2, it is two parts by the difference cutting of each plate, grid dividing is carried out to model, is divided into sparse layer and encryption
Layer, not excessive influence calculating speed while to guarantee accuracy；Wherein two plate contact areas are included in encryption layer, are enabled
The grid node of contact surface neatly corresponds to above and below contact position, and such as Fig. 2, all grids are hexahedral mesh；
Step 2.1, when the surface topography of addition is single scale,
The encryption layer of upper plate is as pattern layer, and the encryption layer of lower plate is as ideal plane；The sizing grid S of encryption layer presses formula
(1) it calculates:
Wherein, λnFor the distance between two adjacent peaks for the pattern of being added, n=1,2 ... ... represent each region
The serial number of interior pitch of waves value；
Step 2.2, span is big when the surface topography of addition is multiple scales and between each pattern scale,
The encryption layer of upper plate is as pattern layer, and the encryption layer of lower plate is as ideal plane；Encryption layer grid is carried out into one
Cutting is walked, three dimensional areas are divided into, subregion addition (such as Fig. 2) is carried out to pattern；Wherein large scale net region 1 includes one
Kind scale topography, that is, geometry, mesoscale net region 2 include two kinds of scale topography, that is, geometries and percent ripple, small scale
3 domain of grid regions includes three kinds of scale topography, that is, geometries, percent ripple and roughness, i.e., small scale net region realizes more rulers
The pattern of degree is superimposed；Each area grid size S is calculated by formula (2):
Wherein,For the distance between two adjacent peaks for the pattern of being added, i=1,2,3 be three dimensional areas
Code name, n=1,2 ... ... represent the serial number of pitch of waves value in each region；
Step 3, ready-portioned mesh point coordinate matrix is converted；
Step 3.1, assignment function is determined according to institute's shape characteristic to be added；
3.1.1, when the shape characteristic of addition is single scale probability distribution function,
As shown in figure 3, topographical height information is indicated with the random numbers of Gaussian distribution generated at random, it is random need to only to give it
Point number and variance yields produce, and probability density function is following formula:
Wherein, σ is variance yields, determines the amplitude size of addition pattern, μ is mean value, value 0；
3.3.2, when the shape characteristic of addition is single scale period profile function,
As shown in figure 4, the pattern of addition is the superposition of several different amplitudes generated at random, the sinusoidal wave function of frequency,
Topographical information is simplified, changes it in one direction, another direction topographical height is identical, then its height function is expressed
Are as follows:
H (x)=A1sin(ω1θ1)+B1sin(ω2θ2)+...... (3)
Wherein, AnFor the amplitude for adding pattern, ωnFor the frequency for adding pattern, the relationship with the pitch of waves isθnFor
The corresponding phase of grid node, x are node number, and the two is by x=fn(θ) functional relation is corresponding；
H (x) is topographical height function, and n=1,2 ... ... represent serial number；
3.3.3, when the shape characteristic of addition is that multi-scale period distribution function is superimposed,
As shown in figure 5, grid is divided into three regions when the pattern of addition is that multiple dimensioned and pitch of waves span is larger,
The assignment function in each region is different；Assignment function is replaced to simulate pattern, large scale grid in Fig. 2 with standard sine wave
A kind of corresponding assignment function in region 1, the corresponding two kinds of assignment functions in mesoscale net region 2, and small scale net region 3 corresponding three
Kind assignment function, height function expression are as follows:
Wherein, AnFor the amplitude for adding pattern, ωnFor the frequency for adding pattern, the relationship with the pitch of waves isθnFor
The corresponding phase of grid node, x are node number, and the two is by x=fn(θ) functional relation is corresponding；
hnIt (x) is topographical height function, n=1,2 ... ... represent serial number；
3.3.4, when the shape characteristic of addition is multiple dimensioned random distribution number,
It can be seen that small scale net region 3 contains the shape characteristic of three kinds of cardinal scales, it is folded to realize multiple dimensioned pattern
Add.On the contact surface by true actual measurement topographical information addition, it also needs to carry out interpolation processing to measured data, makes to survey surface shape
Looks data point number is equal with contact surface node number.
Step 3.2, assignment mode is determined according to institute's shape characteristic to be added；
3.2.1, when the shape characteristic of addition is single scale, assignment mode are as follows: extract contact surface node coordinate matrix, section
Point position coordinates are as with reference to the specified of assignment mode is carried out, and topographical height function directly adds and subtracts height of node coordinate, really
Determine finish node height coordinate, such as Fig. 6；If pattern waveform to be done to the simplification of one-dimensional square, changing assignment mode is along certain seat
Mark direction change；
3.2.2, when the shape characteristic of addition is multiple dimensioned, assignment mode are as follows: it is trizonal to extract contact surface respectively
Node coordinate matrix from small to large successively converts it according to mesh-density, node location coordinate be as with reference to come into
Row assignment mode is specified, and topographical height function directly adds and subtracts the height of node coordinate in region, finally by trizonal height
Coordinate carries out complex superposition, finish node height coordinate is determined, such as Fig. 7 mode.Wherein there is the part of common grid intersection to be assigned
The topographical height value of multiple scales is given, coordinate value is the superposition of multiple assignment function values, that is, realizes the folded of multiple dimensioned pattern
Add.
Step 4, grid file is regenerated, more new model carries out simulation analysis, that is, realizes and consider contact surface pattern
Finite element node modeling method.
Claims (1)
1. a kind of finite element node modeling method for considering contact surface pattern, which is characterized in that steps are as follows:
Step 1, touching act approximation in surface is contacted with two plates and is characterized, three-dimensional modeling is carried out to two plates to contact with each other；
Step 2, each plate is first distinguished cutting is two parts: sparse layer and encryption layer；Grid dividing is carried out to model again；Its
In two plate contact areas be included in encryption layer, enabling contact position, the grid node of contact surface neatly corresponds to up and down, all nets
Lattice are hexahedral mesh；
Step 2.1, addition surface topography is single scale:
The encryption layer of upper flat plate is as pattern layer, and the encryption layer of lower plate is as ideal plane；The sizing grid S of encryption layer presses formula
(1) it calculates:
Wherein, λnFor the distance between two adjacent peaks for the pattern of being added, n=1,2 ... ... represent wave in each region
Serial number away from value；
Step 2.2, span is big when the surface topography of addition is multiple scales and between each pattern scale:
The encryption layer of upper flat plate is as pattern layer, and the encryption layer of lower plate is as ideal plane；Encryption layer grid is carried out into one
Cutting is walked, three dimensional areas are divided into；Wherein large scale net region 1 includes a kind of scale topography, that is, geometry, mesoscale
Net region 2 includes two kinds of scale topography, that is, geometries and percent ripple, and small scale net region 3 includes that three kinds of scale topographies are
Geometry, percent ripple and roughness, i.e., small scale net region realize multiple dimensioned pattern superposition；Size of mesh opening size S
It is calculated by formula (2):
Wherein,For the distance between two adjacent peaks for the pattern of being added, i=1,2,3 be the generation of three dimensional areas
Number, n=1,2 ... ... represent the serial number of pitch of waves value in each region；
Step 3, ready-portioned mesh point coordinate matrix is converted；
Step 3.1, assignment function is determined according to institute's shape characteristic to be added；
3.1.1, when the shape characteristic of addition is single scale probability distribution function,
Topographical height information is indicated with the random numbers of Gaussian distribution generated at random, need to only give its random point number and variance yields
It produces, probability density function is following formula:
Wherein, σ is variance yields, determines the amplitude size of addition pattern, μ is mean value, value 0；
3.3.2, when the shape characteristic of addition is single scale period profile function,
The pattern of addition is the superposition of several different amplitudes generated at random, the sinusoidal wave function of frequency, and topographical information is carried out
Simplify, change it in one direction, another direction topographical height is identical, then its height function is expressed are as follows:
H (x)=A1sin(ω1θ1)+B1sin(ω2θ2)+......(4)
Wherein, AnFor the amplitude for adding pattern, ωnFor the frequency for adding pattern, ωnRelationship with the pitch of waves isθnFor net
The corresponding phase of lattice node, x are node number, and the two is by x=fn(θ) functional relation is corresponding；
H (x) is topographical height function, and n=1,2 ... ... represent serial number；
3.3.3, when the shape characteristic of addition is that multi-scale period distribution function is superimposed,
When the pattern of addition is that multiple dimensioned and pitch of waves span is larger, grid is divided into three regions, each area's valuation of a field
Function is different；Assignment function is replaced to simulate pattern, a kind of corresponding assignment letter in large scale net region 1 with standard sine wave
Number, the corresponding two kinds of assignment functions in mesoscale net region 2, the corresponding three kinds of assignment functions in small scale net region 3, height function
Expression are as follows:
Wherein, AnFor the amplitude for adding pattern, ωnFor the frequency for adding pattern, ωnRelationship with the pitch of waves isθnFor net
The corresponding phase of lattice node, x are node number, and the two is by x=fn(θ) functional relation is corresponding；
hnIt (x) is topographical height function, n=1,2 ... ... represent serial number；
3.3.4, when the shape characteristic of addition is multiple dimensioned random distribution number,
On the contact surface by true actual measurement topographical information addition, it also needs to carry out interpolation processing to measured data, makes to survey surface
Topographic data point number is equal with contact surface node number；
Step 3.2, assignment mode is determined according to institute's shape characteristic to be added；
3.2.1, when the shape characteristic of addition is single scale, assignment mode are as follows: extract contact surface node coordinate matrix, node position
Setting coordinate is as with reference to the specified of assignment mode is carried out, and topographical height function directly add and subtract height of node coordinate, determination is most
Terminal note height coordinate；If pattern waveform to be done to the simplification of one-dimensional square, changing assignment mode is to change along certain coordinate direction；
3.2.2, when the shape characteristic of addition is multiple dimensioned, assignment mode are as follows: extract the trizonal node of contact surface respectively
Coordinates matrix from small to large successively converts it according to mesh-density, and node location coordinate is as with reference to being assigned
Value mode is specified, and topographical height function directly adds and subtracts the height of node coordinate in region, finally by trizonal height coordinate
Complex superposition is carried out, determines finish node height coordinate；Wherein there is the part of common grid intersection to be endowed the shape of multiple scales
Looks height value, coordinate value are the superposition of multiple assignment function values, that is, realize the superposition of multiple dimensioned pattern；
Step 4, grid file is regenerated, more new model carries out simulation analysis, that is, realizes and consider having for contact surface pattern
Limit first node modeling method.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113127998A (en) * | 2021-04-30 | 2021-07-16 | 大连理工大学 | Finite element modeling method considering bolt stress field change in actual assembly process |
| CN113435085A (en) * | 2021-06-23 | 2021-09-24 | 西安交通大学 | Complex-morphology magnetic head steady-state flight modeling method considering viscous effect |
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| CN108168492A (en) * | 2017-12-17 | 2018-06-15 | 北京工业大学 | A kind of Contact method based on three-dimensional microcosmic surface topography |
| CN109408887A (en) * | 2018-09-21 | 2019-03-01 | 大连理工大学 | A kind of finite element method for calculating rotor assembly axis deviation considering contact resilient deformation |
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| JPH10208079A (en) * | 1997-01-23 | 1998-08-07 | Hitachi Ltd | Method and device for generating analytical mesh |
| CN108168492A (en) * | 2017-12-17 | 2018-06-15 | 北京工业大学 | A kind of Contact method based on three-dimensional microcosmic surface topography |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113127998A (en) * | 2021-04-30 | 2021-07-16 | 大连理工大学 | Finite element modeling method considering bolt stress field change in actual assembly process |
| CN113435085A (en) * | 2021-06-23 | 2021-09-24 | 西安交通大学 | Complex-morphology magnetic head steady-state flight modeling method considering viscous effect |
| CN113435085B (en) * | 2021-06-23 | 2023-01-03 | 西安交通大学 | Complex-morphology magnetic head steady-state flight modeling method considering viscous effect |
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