CN108846154A - Consider the faying face thermal contact resistance three-dimensional fractal prediction technique of micro-bulge matrix deformation - Google Patents
Consider the faying face thermal contact resistance three-dimensional fractal prediction technique of micro-bulge matrix deformation Download PDFInfo
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Abstract
The present invention provides a kind of faying face thermal contact resistance three-dimensional fractal prediction technique of consideration micro-bulge matrix deformation, is related to Machine Joint Surfaces technical field.This method first with more can the faying face surface topography three-dimensional fractal function of closing to reality situation substitute two-dimensional fractal function, and the juxtaposition metamorphose amount of micro-bulge is indicated with the difference in magnitude of this three-dimensional function wave crest and trough；Then the elastic critical deflection of micro-bulge elastic deformation stage and the deflection of critical contact area and micro-bulge matrix are calculated；Finally, establishing the relationship between the relationship between the total normal load of faying face and contact area and the total normal load of faying face and the total thermal contact resistance of faying face.The faying face thermal contact resistance three-dimensional fractal prediction technique provided by the invention for considering the deformation of micro-bulge matrix, it is more accurate to obtain faying face thermal contact resistance, closer to actual conditions, can provide theoretical foundation for the thermal contact resistance of faying face in machinery Thermal analysis.
Description
Technical field
The present invention relates to Machine Joint Surfaces technical fields more particularly to a kind of faying face for considering the deformation of micro-bulge matrix to connect
Touch thermal resistance three-dimensional fractal prediction technique.
Background technique
In the manufacture and assembly of lathe or all kinds of mechanical equipments, mechanical structure is not generally one continuous whole,
Comprising a large amount of components, the contact surface assembled between components is known as faying face.Mechanical equipment during the work time, each component,
Each component and entire mechanical equipment all can just will form certain temperature under the action of various heat sources in component internal in this way
, to make Machine Joint Surfaces inevitably generate thermal deformation, to influence the overall performance of mechanical structure.Therefore from theory
The touching act of upper research faying face, the thermal characteristics of faying face can be predicted in the design phase, for improving machining equipment
Stability and machining accuracy be particularly important.
Research for faying face thermal contact resistance, a part of scholar on the basis of classical Hertzian contact theory (Hertz),
Assuming that the height of faying face micro-bulge is distributed approximate Gaussian distribution and from statistical angle, Machine Joint Surfaces are established
Thermal contact resistance microcomputer statistical contact model；Another part scholar is based on fractal theory, is combined using area distributions function and characterization
The fractal function of face surface topography establishes the thermal contact resistance Fractal Contact model of Machine Joint Surfaces, so as to avoid microcomputer statistical
The shortcomings that contact model is influenced by measuring surface form instrumental resolution and sampling length.
Although at home and abroad under the unremitting effort of scholar, the thermal contact resistance model of Machine Joint Surfaces develops constantly always
Perfect, but still have larger mistake using the thermal contact resistance between existing thermal contact resistance model calculations incorporated face under fully loaded transportation condition
Difference.Itself main reason is that：Existing faying face thermal contact resistance computation model does not account for the influence of micro-bulge matrix deformation,
Under fully loaded transportation condition, micro-bulge interaction generates matrix deformation and is affected to contact thermal resistance calculation between faying face, cannot
Ignore；Meanwhile existing machinery faying face thermal contact resistance computation model has ignored the characteristics of micro-bulge three-dimensional surface fractal cloth.Cause
The thermal contact resistance of faying face can not be accurately calculated using existing theoretical method under fully loaded transportation condition for this.
Summary of the invention
In view of the drawbacks of the prior art, the present invention provides a kind of faying face thermal contact resistance three of consideration micro-bulge matrix deformation
Fractal prediction method is tieed up, realizes the thermal contact resistance in the calculations incorporated face under fully loaded transportation condition.
The faying face thermal contact resistance three-dimensional fractal prediction technique for considering the deformation of micro-bulge matrix, includes the following steps：
Step 1, the three-D profile for simulating faying face micro-bulge：Use three closer to faying face surface topography actual conditions
It ties up fractal function and substitutes two-dimensional fractal function, and by the wave crest and trough of this three-dimensional fractal function of the juxtaposition metamorphose amount of micro-bulge
Difference in magnitude indicate, shown in following formula：
δ=2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3D)/2
Wherein, δ be the single micro-bulge in faying face surface juxtaposition metamorphose amount, γ be frequency density relevant parameter, γ > 1,
Generally taking 1.5, D is the fractal dimension on faying face surface, and 2 < D < 3, G are the Fractal scale coefficient on faying face surface, and a is to combine
The single micro-bulge actual elastic contact area in face surface；
Step 2 calculates separately elastic deformation stage, the deflection of the single micro-bulge in faying face surface and critical contact face
Product, specific method are：
Step 2.1, according to classical Hertzian contact theory, it is equivalent micro- with one when two rough surface of faying face contacts with each other
Convex body rough surface indicates with a smooth rigid plane contact, then the single micro-bulge actual elastic contact surface in faying face surface
Product a is the area of section that the single micro-bulge deformed on equivalent rough surface intersects with rigid smooth plane, shown in following formula：
A=π R δ
Wherein, R is the radius of curvature of the single micro-bulge in faying face surface；
Step 2.2, the single micro-bulge in calculations incorporated face surface elastic deformation stage elastic critical deflection and elasticity
Critical contact area；
The elastic critical deflection of the single micro-bulge, shown in following formula：
δc=(k φ)2π(5-D)/22(3D-15)/2G2-Da(D-1)/2(lnγ)-1/2
Wherein, k is the yield strength σ with softer material in two contact material of faying faceyCoefficient relevant with hardness H, three
Relationship between person is：H=k σy；φ=σy/ E is material property coefficient, and E is the Equivalent Elasticity mould of two contact material of faying face
Amount,E1、E2Respectively indicate the elasticity modulus of two contact material of faying face, v1、v2Respectively indicate faying face
The Poisson's ratio of two contact materials；
The elastic critical contact area of the single micro-bulge, shown in following formula：
ac=(k φ)2/(2-D)π(4-D)/(2-D)2(3D-13)/(2-D)G2(lnγ)1/(D-2)；
The matrix deflection of step 3, calculations incorporated face surface micro-bulge；
The micro-bulge is evenly distributed on the nominal contact area of faying face, then according to Loew equation, for a bullet
Property semi-infinite body, size be the surface 2a ' × 2a ' on a bit (x, y) by the homogeneous pressure p acted on surfacemInstitute
Shown in the following formula of deflection size of generation：
It is (2a ') by area2Micro-bulge be equivalent to area be a round dimpling bulk area, thenWherein PeFor
Normal load suffered by the single micro-bulge of flexible deformation；
In turn, according to fractal theory, micro-bulge interaction causes shown in the following formula of deflection ξ of its matrix：
Wherein, a is single micro-bulge actual elastic contact area, and E is the equivalent elastic modulus of two contact material of faying face；
Step 4 establishes relationship between the total normal load of faying face and faying face contact area, and specific method is：
Step 4.1 establishes the relationship that normal load suffered by the single micro-bulge in different distortion area is in contact with it area；
According to fractal theory, the relationship that normal load suffered by the single micro-bulge in different distortion area is in contact with it area is：
(1) when micro-bulge is in Elastic Contact：
In fractal theory, single micro-bulge is due to the juxtaposition metamorphose amount that normal load acts on and generates：
δ=s-d
Wherein, s is to apply the single micro-bulge height before normal load on the basis of micro-bulge base plane, and d is to apply
Micro-bulge base plane before normal load is at a distance from smooth rigid plane；
Based on elastic theory, for load bearing regional area, the matrix deflection that micro-bulge interaction generates is
ξ, so that the distance between equivalent rough surface and smooth rigid plane are increased, therefore the single micro-bulge as caused by elasticity factor
Deflection be s-d ', then
S-d '=δ-ξ
Wherein, d ' be apply normal load after micro-bulge base plane at a distance from smooth rigid plane；
According to classical Hertzian contact theory, the single micro-bulge institute in flexible deformation is loaded with its practical Elastic Contact
Shown in the following formula of the relationship of area：
By radius of curvature R=2 of micro-bulge(3D-11)/2π(1-D)/2G2-Da(D-1)/2(lnγ)-1/2Above formula is substituted into obtain：
(2) when micro-bulge is in plastic contact：
Pp=k σyap
Wherein, PpIt is loaded for the single micro-bulge of plastic deformation, apFor the practical plastic contact area of micro-bulge；
Step 4.2, the relationship for establishing total normal load and faying face contact area suffered by faying face；
According to fractal theory, shown in the following formula of relationship of total normal load and contact area suffered by faying face：
Wherein, alFor single micro-bulge Maximum Contact point area, acFor single micro-bulge elastic critical contact area；
Step 5 establishes relationship between the total normal load of faying face and the total thermal contact resistance of faying face；
The following formula institute of relationship according to fractal theory, between the total normal load of faying face and the total thermal contact resistance of faying face
Show：
Wherein, R ' is the thermal contact resistance on coarse faying face, and k ' is constant related with two contact material thermal coefficients,k1、k2Respectively two contact material thermal coefficients, kfThe thermal coefficient of air between gap,
For faying face void space thickness, the thermal contact resistance expression formula substituted on coarse faying face is obtained：
Wherein, h is the average value of two contact plane micro-bulge height of faying face,It is connect for faying face two
Touch the real contact area of plane, AaFor the nominal contact area of two contact plane of faying face；
By the thermal contact resistance formula on coarse faying face and total normal load and contact area suffered by faying face in step 4.2
Relational expression simultaneous, establish between the total normal load of faying face based on three-dimensional fractal function and the total thermal contact resistance of faying face
Relationship.
As shown from the above technical solution, the beneficial effects of the present invention are：Consideration micro-bulge matrix provided by the invention becomes
The faying face thermal contact resistance three-dimensional fractal prediction technique of shape, compared with tradition is based on the method for statistics and two-dimensional fractal function,
The micro-bulge pattern that coarse faying face surface is characterized using three-dimensional fractal function is more consistent with actual conditions, makes prediction result more
Accurately.Meanwhile having fully considered that micro-bulge interaction causes the deformation of its matrix to the influence of thermal contact resistance under fully loaded transportation condition,
Overcome the disadvantage of the existing method calculations incorporated face contact thermal resistance inaccuracy based on fractal theory.
Detailed description of the invention
Fig. 1 is the faying face thermal contact resistance three-dimensional fractal prediction of consideration micro-bulge matrix deformation provided in an embodiment of the present invention
The flow chart of method；
Fig. 2 is the micro-bulge pattern provided in an embodiment of the present invention that coarse faying face surface is characterized using three-dimensional fractal function
Schematic diagram；
Fig. 3 is the equivalent juxtaposition metamorphose schematic diagram in faying face surface provided in an embodiment of the present invention；
Fig. 4 is that consideration micro-bulge matrix provided in an embodiment of the present invention deforms and ignore micro-bulge matrix two kinds of situations of deformation
The dimensionless normal load of lower faying face and the relational graph of dimensionless thermal contact resistance；
Fig. 5 is that consideration micro-bulge matrix provided in an embodiment of the present invention deforms and ignore micro-bulge matrix two kinds of situations of deformation
The dimensionless normal load of lower faying face and the relational graph of dimensionless contact conductane.
Wherein, 1, the preceding micro-bulge base plane of load；2, micro-bulge base plane after loading；3, smooth rigid plane；4,
Equivalent micro-bulge rough surface.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Implement below
Example is not intended to limit the scope of the invention for illustrating the present invention.
The faying face thermal contact resistance three-dimensional fractal prediction technique of micro-bulge matrix deformation is considered, as shown in Figure 1, including following
Step：
Step 1, the three-D profile for simulating faying face micro-bulge：Use three closer to faying face surface topography actual conditions
It ties up fractal function and substitutes two-dimensional fractal function, and by the wave crest and trough of this three-dimensional fractal function of the juxtaposition metamorphose amount of micro-bulge
Difference in magnitude indicate, shown in following formula：
δ=2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
Wherein, δ be the single micro-bulge in faying face surface juxtaposition metamorphose amount, γ be frequency density relevant parameter, γ > 1,
Generally taking 1.5, D is the fractal dimension on faying face surface, and 2 < D < 3, G are the Fractal scale coefficient on faying face surface, and a is to combine
The single micro-bulge actual elastic contact area in face surface；
In the present embodiment, the two-dimensional fractal W-M function for describing faying face surface outline curves is improved to description faying face
The three-dimensional fractal W-M function of Surface Fractal curved surface.The parameter for giving equivalent rough surface is：Faying face Surface Fractal scale coefficient G
=1.05 × 10-8M, fractal dimension D=2.437, parameter related with faying face surface topography frequency density γ=1.5 obtain
Faying face three-dimensional surface shape is as shown in Figure 2.
Step 2 calculates separately elastic deformation stage, the deflection of the single micro-bulge in faying face surface and critical contact face
Product, specific method are：
Step 2.1, according to classical Hertzian contact theory, when two rough surface of faying face contacts with each other, as shown in figure 3, with
One equivalent micro-bulge rough surface 4 is contacted with a smooth rigid plane 3 to indicate, then the single micro-bulge in faying face surface is real
Border Elastic Contact area a is the section face that the single micro-bulge deformed on equivalent rough surface 4 intersects with rigid smooth plane 3
Product, shown in following formula：
A=π R δ
Wherein, R is the radius of curvature of the single micro-bulge in faying face surface；
Step 2.2, the single micro-bulge in calculations incorporated face surface elastic deformation stage elastic critical deflection and elasticity
Critical contact area；
The elastic critical deflection of the single micro-bulge, shown in following formula：
δc=(k φ)2π(5-D)/22(3D-15)/2G2-Da(D-1)/2(lnγ)-1/2
Wherein, k is the yield strength σ with softer material in two contact material of faying faceyCoefficient relevant with hardness H, three
Relationship between person is：H=k σy；φ=σy/ E is material property coefficient, and E is the Equivalent Elasticity mould of two contact material of faying face
Amount,E1、E2Respectively indicate the elasticity modulus of two contact material of faying face, v1、v2Respectively indicate faying face
The Poisson's ratio of two contact materials；
The elastic critical contact area of the single micro-bulge, shown in following formula：
ac=(k φ)2/(2-D)π(4-D)/(2-D)2(3D-13)/(2-D)G2(lnγ)1/(D-2)；
In the present embodiment, two contact material hardness of faying face surface is H1=H2=4.19 × 109Pa, elasticity modulus E1
=E2=2.07 × 1011Pa, Poisson's ratio v1=v2=0.29, the elastic critical contact area for the single micro-bulge being calculated is
ac=6.8327 × 10-9m2。
The matrix deflection of step 3, calculations incorporated face surface micro-bulge；
The micro-bulge is evenly distributed on the nominal contact area of faying face, then according to Loew equation, for a bullet
Property semi-infinite body, size be the surface 2a ' × 2a ' on a bit (x, y) by the homogeneous pressure p acted on surfacemInstitute
Shown in the following formula of deflection size of generation：
It is (2a ') by area2Micro-bulge be equivalent to area be a round dimpling bulk area, thenWherein PeFor
Normal load suffered by the single micro-bulge of flexible deformation；
In turn, according to fractal theory, micro-bulge interaction causes shown in the following formula of deflection ξ of its matrix：
Wherein, a is single micro-bulge actual elastic contact area, and E is the equivalent elastic modulus of two contact material of faying face；
Step 4 establishes relationship between the total normal load of faying face and faying face contact area, and specific method is：
Step 4.1 establishes the relationship that normal load suffered by the single micro-bulge in different distortion area is in contact with it area；
According to fractal theory, the relationship that normal load suffered by the single micro-bulge in different distortion area is in contact with it area is：
(1) when micro-bulge is in Elastic Contact：
In fractal theory, single micro-bulge is due to the juxtaposition metamorphose amount that normal load acts on and generates：
δ=s-d
Wherein, s is to apply the single micro-bulge height before normal load on the basis of micro-bulge base plane, and d is to apply
Micro-bulge base plane before normal load is at a distance from smooth rigid plane；
Based on elastic theory, for load bearing regional area, the matrix deflection that micro-bulge interaction generates is
ξ, so that the distance between equivalent rough surface and smooth rigid plane are increased, therefore the single micro-bulge as caused by elasticity factor
Deflection be s-d ', then
S-d '=δ-ξ
Wherein, d ' be apply normal load after micro-bulge base plane at a distance from smooth rigid plane；
According to classical Hertzian contact theory, the single micro-bulge institute in flexible deformation is loaded with its practical Elastic Contact
Shown in the following formula of the relationship of area：
By radius of curvature R=2 of micro-bulge(3D-11)/2π(1-D)/2G2-Da(D-1)/2(lnγ)-1/2Above formula is substituted into obtain：
(2) when micro-bulge is in plastic contact：
Pp=k σyap
Wherein, PpIt is loaded for the single micro-bulge of plastic deformation, apFor the practical plastic contact area of micro-bulge；
Step 4.2, the relationship for establishing total normal load and contact area suffered by faying face；
According to fractal theory, shown in the following formula of relationship of total normal load and contact area suffered by faying face：
Wherein, alFor single micro-bulge Maximum Contact point area, acFor single micro-bulge elastic critical contact area；
Step 5 establishes relationship between the total normal load of faying face and the total thermal contact resistance of faying face；
The following formula institute of relationship according to fractal theory, between the total normal load of faying face and the total thermal contact resistance of faying face
Show：
Wherein, R ' is the thermal contact resistance on coarse faying face, and k ' is constant related with two contact material thermal coefficients,k1、k2Respectively two contact material thermal coefficients, kfThe thermal coefficient of air between gap,
For faying face void space thickness, the thermal contact resistance expression formula substituted on coarse faying face is obtained：
Wherein, h is the average value of two contact plane micro-bulge height of faying face,It is connect for faying face two
Touch the real contact area of plane, AaFor the nominal contact area of two contact plane of faying face；
By the thermal contact resistance formula on coarse faying face and total normal load and contact area suffered by faying face in step 4.2
Relational expression simultaneous, establish between the total normal load of faying face based on three-dimensional fractal function and the total thermal contact resistance of faying face
Relationship.
In the present embodiment, load is larger, therefore can ignore the influence of air dielectric thermal resistance, takes two contact plane micro-bulges high
Average value h=1.016 × 10 of degree-5M, real contact area Ar=6.4072 × 10-5m2, two contact material thermal coefficient k1=
k2=44W/ (m DEG C), fractal dimension D=2.437 on faying face surface, Fractal scale coefficient G=1.05 × 10-8M, with combination
Related parameter γ=1.5 of face surface frequency density, single micro-bulge Maximum Contact point area al=5.0213 × 10-5m2, finally
Calculate faying face thermal contact resistance be R=0.0050W/ (m2·K)。
In the present embodiment, faying face dimensionless normal load and dimensionless thermal contact resistance relationship are as shown in figure 4, can by figure
Know, consider that the faying face thermal contact resistance of micro-bulge matrix deformation is greater than the faying face thermal contact resistance for ignoring the deformation of micro-bulge matrix,
This is because the deformation of micro-bulge matrix increases the distance between equivalent rough surface and smooth rigid plane, thus by contacting
It will increase faying face thermal contact resistance known to the mechanism of production of thermal resistance；And with the increase of normal load, the deformation of micro-bulge matrix
It is more obvious, therefore consider that difference will increase between the thermal contact resistance of micro-bulge matrix deformation and the thermal contact resistance for ignoring deformation.
In the present embodiment, in order to which more specific reaction micro-bulge matrix deforms the influence to thermal contact resistance, nothing is given
Dimension normal load and dimensionless contact conductane relationship, as shown in figure 5, as seen from the figure with the increase of normal load, micro-bulge
The deformation of matrix is more obvious, therefore considers difference meeting between the contact conductane of micro-bulge matrix deformation and the contact conductane for ignoring deformation
Increase.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that：It still may be used
To modify to technical solution documented by previous embodiment, or some or all of the technical features are equal
Replacement；And these are modified or replaceed, model defined by the claims in the present invention that it does not separate the essence of the corresponding technical solution
It encloses.
Claims (5)
1. a kind of faying face thermal contact resistance three-dimensional fractal prediction technique for considering the deformation of micro-bulge matrix, it is characterised in that：Including
Following steps：
Step 1, the three-D profile for simulating faying face micro-bulge：Use the three-dimensional point closer to faying face surface topography actual conditions
Shape function substitutes two-dimensional fractal function, and by juxtaposition metamorphose the amount wave crest of this three-dimensional fractal function and the width of trough of micro-bulge
Value difference indicates, shown in following formula：
δ=2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
Wherein, δ be the single micro-bulge in faying face surface juxtaposition metamorphose amount, γ be frequency density relevant parameter, γ > 1, generally
Taking 1.5, D is the fractal dimension on faying face surface, and 2 < D < 3, G are the Fractal scale coefficient on faying face surface, and a is faying face table
The single micro-bulge actual elastic contact area in face；
Step 2 calculates separately elastic deformation stage, the deflection and critical contact area of the single micro-bulge in faying face surface；
The matrix deflection of step 3, calculations incorporated face surface micro-bulge；
Step 4 establishes relationship between the total normal load of faying face and faying face contact area；
Step 5 establishes relationship between the total normal load of faying face and the total thermal contact resistance of faying face.
2. the faying face thermal contact resistance three-dimensional fractal prediction technique according to claim 1 for considering the deformation of micro-bulge matrix,
It is characterized in that：The specific method of the step 2 is：
Step 2.1, according to classical Hertzian contact theory, when two rough surface of faying face contacts with each other, with an equivalent micro-bulge
Rough surface indicates with a smooth rigid plane contact, then the single micro-bulge actual elastic contact area a in faying face surface
For the area of section that the single micro-bulge deformed on equivalent rough surface intersects with rigid smooth plane, shown in following formula：
A=π R δ
Wherein, R is the radius of curvature of the single micro-bulge in faying face surface；
Step 2.2, the single micro-bulge in calculations incorporated face surface elastic deformation stage elastic critical deflection and elastic critical
Contact area；
The elastic critical deflection of the single micro-bulge, shown in following formula：
δc=(k φ)2π(5-D)/22(3D-15)/2G2-Da(D-1)/2(lnγ)-1/2
Wherein, k is and the yield strength σ with softer material in two contact material of faying faceyCoefficient relevant with hardness H, three it
Between relationship be：H=k σy；φ=σy/ E is material property coefficient, and E is the equivalent elastic modulus of two contact material of faying face,E1、E2Respectively indicate the elasticity modulus of two contact material of faying face, v1、v2Respectively indicate faying face two
The Poisson's ratio of contact material；
The elastic critical contact area of the single micro-bulge, shown in following formula：
ac=(k φ)2/(2-D)π(4-D)/(2-D)2(3D-13)/(2-D)G2(lnγ)1/(D-2)。
3. the faying face thermal contact resistance three-dimensional fractal prediction technique according to claim 2 for considering the deformation of micro-bulge matrix,
It is characterized in that：The specific method of the step 3 is：
The micro-bulge is evenly distributed on the nominal contact area of faying face, then according to Loew equation, for an elasticity half
Space body, size are a bit (x, y) on the surface 2a ' × 2a ' by the homogeneous pressure p acted on surfacemIt is produced
The following formula of deflection size shown in：
It is (2a ') by area2Micro-bulge be equivalent to area be a round dimpling bulk area, thenWherein PeFor elasticity
Normal load suffered by the single micro-bulge of deformation；
In turn, according to fractal theory, micro-bulge interaction causes shown in the following formula of deflection ξ of its matrix：
Wherein, a is single micro-bulge actual elastic contact area, and E is the equivalent elastic modulus of two contact material of faying face.
4. the faying face thermal contact resistance three-dimensional fractal prediction technique according to claim 3 for considering the deformation of micro-bulge matrix,
It is characterized in that：The specific method of the step 4 is：
Step 4.1 establishes the relationship that normal load suffered by the single micro-bulge in different distortion area is in contact with it area；
According to fractal theory, the relationship that normal load suffered by the single micro-bulge in different distortion area is in contact with it area is：
(1) when micro-bulge is in Elastic Contact：
In fractal theory, single micro-bulge is due to the juxtaposition metamorphose amount that normal load acts on and generates：
δ=s-d
Wherein, s is to apply the single micro-bulge height before normal load on the basis of micro-bulge base plane, and d is to apply normal direction
Micro-bulge base plane before load is at a distance from smooth rigid plane；
Based on elastic theory, for load bearing regional area, the matrix deflection that micro-bulge interaction generates is ξ, from
And the distance between equivalent rough surface and smooth rigid plane are increased, therefore the change of the single micro-bulge as caused by elasticity factor
Shape amount is s-d ', then
S-d '=δ-ξ
Wherein, d ' be apply normal load after micro-bulge base plane at a distance from smooth rigid plane；
According to classical Hertzian contact theory, the single micro-bulge institute in flexible deformation is loaded with its practical Elastic Contact area
The following formula of relationship shown in：
By radius of curvature R=2 of micro-bulge(3D-11)/2π(1-D)/2G2-Da(D-1)/2(lnγ)-1/2Above formula is substituted into obtain：
(2) when micro-bulge is in plastic contact：
Pp=k σyap
Wherein, PpIt is loaded for the single micro-bulge of plastic deformation, apFor the practical plastic contact area of micro-bulge；
Step 4.2, the relationship for establishing total normal load and contact area suffered by faying face；
According to fractal theory, shown in the following formula of relationship of total normal load and contact area suffered by faying face：
Wherein, alFor single micro-bulge Maximum Contact point area, acFor single micro-bulge elastic critical contact area.
5. the faying face thermal contact resistance three-dimensional fractal prediction technique according to claim 4 for considering the deformation of micro-bulge matrix,
It is characterized in that：The specific method of the step 5 is：
According to fractal theory, shown in the following formula of relationship between the total normal load of faying face and the total thermal contact resistance of faying face：
Wherein, R ' is the thermal contact resistance on coarse faying face, and k ' is constant related with two contact material thermal coefficients,
k1、k2Respectively two contact material thermal coefficients, kfThe thermal coefficient of air between gap,
For faying face void space thickness, the thermal contact resistance expression formula substituted on coarse faying face is obtained：
Wherein, h is the average value of two contact plane micro-bulge height of faying face,For two contact plane of faying face
Real contact area, AaFor the nominal contact area of two contact plane of faying face；
By the pass of thermal contact resistance formula and total normal load and contact area suffered by faying face in step 4.2 on coarse faying face
It is formula simultaneous, establishes the pass between the total normal load of faying face based on three-dimensional fractal function and the total thermal contact resistance of faying face
System.
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