CN108613922A - A kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength - Google Patents
A kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength Download PDFInfo
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Abstract
The present invention provides a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength, is related to Machine Joint Surfaces technical field.The two-dimensional fractal function for describing faying face surface topography is improved to three-dimensional fractal function by this method first, and the difference of this function trough and wave crest is used in combination to indicate juxtaposition metamorphose amount.Calculate separately again elastic deformation stage, the faying face surface micro-bulge in elastic-plastic deformation stage deflection and critical contact area；The relationship of total normal load, total adhesion strength, total circumferential load and faying face contact area suffered by calculations incorporated face simultaneously.Finally establish the relationship between faying face static friction factor and normal load, circumferential load and adhesion strength.The faying face static friction factor three-dimensional fractal prediction technique provided by the invention for considering adhesion strength, obtained faying face static friction factor is highly reliable, closer to actual conditions, can provide theoretical foundation for the static friction factor of prediction, control precision machinery faying face.
Description
Technical field
The present invention relates to Machine Joint Surfaces technical field more particularly to a kind of faying face static friction factors considering adhesion strength
Three-dimensional fractal prediction technique.
Background technology
Lathe and most of complicated mechanical engineering equipment also include a large amount of parts, dress other than structural body
It is known as faying face with the contact surface between parts, or is engaging portion.Machine Joint Surfaces can not be kept away due to the effect of external load
The generation friction phenomenon exempted from, to influence the overall performance of mechanical structure.Therefore the touching act of faying face is theoretically studied,
The frictional behavior that faying face is predicted in the design phase, for improving working efficiency, stability and the processing essence of machining equipment
Degree is particularly important.
Research for faying face static friction factor, a part of scholar is on the basis of classical Hertzian contact theory, it is assumed that
The height of faying face micro-bulge is distributed approximate Gaussian distribution and from statistical angle, establishes the quiet of Machine Joint Surfaces and rubs
Wipe factor microcomputer statistical contact model；Another part scholar is based on fractal theory, utilizes point of characterization Rough Surface Profile curve
Shape function and island area distribution function establish the static friction factor Fractal Contact model of Machine Joint Surfaces, avoid microcosmic system
The shortcomings that meter 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 static friction factor models of Machine Joint Surfaces constantly development,
It is perfect, but still have larger mistake using the static friction factor between existing static friction factor model calculations incorporated face under fully loaded transportation condition
Difference.Itself main reason is that：Under fully loaded transportation condition, the adhesion strength between faying face is affected to static friction factor calculating, no
It can ignore；Meanwhile existing machinery faying face static friction factor computation model has ignored the spy of micro-bulge three-dimensional surface fractal cloth
Point.Therefore under fully loaded transportation condition, the static friction factor of faying face can not be accurately calculated using existing theoretical method.
Invention content
In view of the drawbacks of the prior art, the present invention provides a kind of faying face static friction factor three-dimensional fractal considering adhesion strength
Prediction technique realizes the calculating of Machine Joint Surfaces static friction factor under fully loaded transportation condition.
A kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength, includes the following steps：
The three-dimensional appearance of step 1, simulation faying face surface micro-bulge：The two-dimensional fractal letter of faying face surface topography will be described
Number is improved to three-dimensional fractal function, and the trough that this function is used in combination indicates that the contact of the single micro-bulge of faying face becomes with the difference of wave crest
Shape amount δ, shown in following formula：
δ=2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
Wherein, G is the Fractal scale coefficient on faying face surface, and D is the fractal dimension on faying face surface, and 2 ＜ D ＜ 3, γ are
Parameter related with faying face surface topography frequency density, γ>1, it is that the single micro-bulge in faying face surface is practical generally to take 1.5, a
Elastic Contact area；
Step 2 calculates separately elastic deformation stage, elastic-plastic deformation stage, the deformation of the single micro-bulge in faying face surface
Amount and critical contact area, specific method are：
Step 2.1, according to Hertzian contact theory, when two rough surface of faying face contacts with each other, by two rough surfaces convert
It contacts with each other for an equivalent rough surface and a rigid smooth plane, 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 single micro-bulge, and δ is the juxtaposition metamorphose amount of single micro-bulge；
Step 2.2, the elastic critical deflection and elastic critical contact area for calculating single micro-bulge；
The elastic critical deflection δ of the single micro-bulgecThe following formula of calculating shown in：
Wherein, kμFor the modifying factor of frictional force, φ is material property coefficient；
The elastic critical contact area a of the single micro-bulgecThe following formula of calculating shown in：
It further finds out, the one area critical contact area a of elastoplasticity of single micro-bulgept1Shown in following formula：
apt1=1101/(2-D)ac；
The two area critical contact area a of elastoplasticity of single micro-bulgept2Shown in following formula：
apt2=61/(2-D)ac；
The relationship of the contact area of total normal load and faying face suffered by step 3, calculations incorporated face；
According to fractal theory, work as al＞ acAnd when D ≠ 2.5, the contact surface of total normal load P and faying face suffered by faying face
Shown in the following formula of long-pending relationship：
Work as al＞ acAnd when D=2.5, the following formula of contact area relationship of total normal load P and faying face suffered by faying face
It is shown：
Wherein, alFor single micro-bulge Maximum Contact point area, k is to be bent with softer material in two contact material of faying face
Take intensity σyWith the relevant coefficients of hardness H, the relationship between three is：H=k σy；E is the equivalent bullet of two contact material of faying face
Property modulus,E1、E2The elasticity modulus of two contact materials, ν are indicated respectively1、ν2Two contact materials are indicated respectively
The Poisson's ratio of material；
The relationship of total adhesion strength and faying face contact area, specific method suffered by step 4, calculations incorporated face are：
Step 4.1, the adhesion strength for establishing the single micro-bulge in different distortion section are in contact with it the relationship of area；
According to fractal theory, the relationship that the adhesion strength of the single micro-bulge in different distortion section is in contact with it area is：
(1) in relief area, δ/δcThe adhesion strength of ＜ 0, single micro-bulge are in contact with it the following formula institute of relationship of area
Show：
(2) in perfect elasticity area, 0 ＜ δ/δc＜ 1, the relationship that the adhesion strength of single micro-bulge is in contact with it area are public as follows
Shown in formula：
(3) in one area of elastoplasticity, 1 ＜ δ/δc＜ 6, the relationship that the adhesion strength of single micro-bulge is in contact with it area are public as follows
Shown in formula：
(4) in 2nd area of elastoplasticity, 6 ＜ δ/δc＜ 110, the relationship that the adhesion strength of single micro-bulge is in contact with it area are as follows
Shown in formula：
Wherein, FsiFor the adhesion strength of the single micro-bulge under different distortion section, i=1 ..., 4, Δ γ ' is adhesion strength
Can, ε is intermolecular distance；
Step 4.2, the relationship for establishing faying face total adhesion strength and faying face contact area；
According to fractal theory, shown in the following formula of relationship of the total adhesion strength of faying face with faying face contact area：
Wherein,
Wherein, AnFor faying face nominal contact area,For the face of faying face contact point
Product distribution function, FsiFor the adhesion strength of the single micro-bulge under different distortion section, Δ γ ' is adhesion strength energy；
The relationship of total circumferential load and faying face contact area suffered by step 5, calculations incorporated face；
According to fractal theory, the relationship of total circumferential load and faying face contact area suffered by faying face is：
Work as al＞ acAnd when D ≠ 2.5, total circumferential load suffered by faying face is with faying face contact area relational expression：
Work as al＞ acAnd when D=2.5, total circumferential load suffered by faying face is with faying face contact area relational expression：
Step 6, the total normal load P for establishing faying face static friction factor μ and faying face, total circumferential load Q and total adhesion
Power FsBetween relationship, shown in following formula：
As shown from the above technical solution, the beneficial effects of the present invention are：A kind of consideration adhesion strength provided by the invention
Faying face static friction factor three-dimensional fractal prediction technique, with it is traditional based on the method for finite element and two-dimensional fractal theory compared with,
Faying face surface topography is characterized using three-dimensional fractal function, closer to actual conditions, while keeping prediction result more acurrate.Meanwhile
The method of the present invention has fully considered influence of the faying face adhesion strength to static friction factor under fully loaded transportation condition, overcome it is existing based on point
The disadvantage of the method calculations incorporated face static friction factor inaccuracy of shape theory.
Description of the drawings
Fig. 1 is a kind of faying face static friction factor three-dimensional fractal prediction side considering adhesion strength provided in an embodiment of the present invention
The flow chart of method；
Fig. 2 is faying face surface topography three-dimensional fractal schematic diagram provided in an embodiment of the present invention；
Fig. 3 is faying face stress diagram provided in an embodiment of the present invention；
Fig. 4 is static friction factor and dimensionless method when three-dimensional surface fractal dimension provided in an embodiment of the present invention takes different value
To the relational graph of load；
Fig. 5 is consideration adhesion strength provided in an embodiment of the present invention, does not consider three kinds of adhesion strength and static friction factor test value
In the case of static friction factor and total normal load relational graph.
Wherein, 1, rigid smooth plane；2, equivalent rough surface.
Specific implementation mode
With reference to the accompanying drawings and examples, the specific implementation mode of the present invention is described in further detail.Implement below
Example is not limited to the scope of the present invention for illustrating the present invention.
The present embodiment uses the faying face static friction factor three of the consideration adhesion strength of the present invention by taking certain Machine Joint Surfaces as an example
Dimension fractal prediction method calculates the static friction factor of the faying face.
A kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength, as shown in Figure 1, including following step
Suddenly：
The three-dimensional appearance of step 1, simulation faying face surface micro-bulge：The two-dimensional fractal letter of faying face surface topography will be described
Number is improved to three-dimensional fractal function, and the trough that this function is used in combination indicates that the contact of the single micro-bulge of faying face becomes with the difference of wave crest
Shape amount δ, shown in following formula：
δ=2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
Wherein, G is the Fractal scale coefficient on faying face surface, and D is the fractal dimension on faying face surface, and 2 ＜ D ＜ 3, γ are
Parameter related with faying face surface topography frequency density, γ>1, it is that the single micro-bulge in faying face surface is practical generally to take 1.5, a
Elastic Contact area；
In the present embodiment, the two-dimensional fractal W-M functions for describing faying face surface outline curves are improved to description faying face
The three-dimensional fractal W-M functions of Surface Fractal curved surface.Give equivalent rough surface parameter be：The Fractal scale coefficient on faying face surface
G=2.01 × 10-9There are related parameter γ=1.5 in m, fractal dimension D=2.501 with faying face surface topography frequency density, obtain
Faying face three-dimensional surface shape is as shown in Figure 2.
Step 2 calculates separately elastic deformation stage, elastic-plastic deformation stage, the deformation of the single micro-bulge in faying face surface
Amount and critical contact area, specific method are：
Step 2.1, according to Hertzian contact theory, when two rough surface of faying face contacts with each other, as shown in figure 3, thick by two
Rough surface conversion is that an equivalent rough surface 2 contacts with each other with a rigid smooth plane 1, then the single micro-bulge in faying face surface is real
Border Elastic Contact area 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 single micro-bulge, and δ is the juxtaposition metamorphose amount of single micro-bulge；
Step 2.2, the elastic critical deflection and elastic critical contact area for calculating single micro-bulge；
The elastic critical deflection δ of the single micro-bulgecThe following formula of calculating shown in：
Wherein, kμFor the modifying factor of frictional force, φ is material property coefficient；
The elastic critical contact area a of the single micro-bulgecThe following formula of calculating shown in：
It further finds out, the one area critical contact area a of elastoplasticity of single micro-bulgept1Shown in following formula：
apt1=1101/(2-D)ac；
The two area critical contact area a of elastoplasticity of single micro-bulgept2Shown in following formula：
apt2=61/(2-D)ac；
In the present embodiment, material property coefficient φ=σy/ E, two contact surface material parameter of faying face are respectively：One contact
The material parameter in face is：Elastic modulus E1=197GPa, Poisson's ratio ν1=0.3, yield strength σy1=346MPa, hardness H1=
478MPa；The material parameter of another contact surface is：Elastic modulus E2=205GPa, Poisson's ratio ν2=0.3, yield strength σy2=
353MPa, hardness H2=500MPa, the elastic critical contact area a of calculated single micro-bulgec=5.986319 × 10- 10m2。
The relationship of the contact area of total normal load and faying face suffered by step 3, calculations incorporated face；
According to fractal theory, work as al＞ acAnd when D ≠ 2.5, the contact surface of total normal load P and faying face suffered by faying face
Shown in the following formula of long-pending relationship：
Work as al＞ acAnd when D=2.5, the following formula of contact area relationship of total normal load P and faying face suffered by faying face
It is shown：
Wherein, alFor single micro-bulge Maximum Contact point area, k is to be bent with softer material in two contact material of faying face
Take intensity σyWith the relevant coefficients of hardness H, the relationship between three is：H=k σy；E is the equivalent bullet of two contact material of faying face
Property modulus,E1、E2The elasticity modulus of two contact materials, ν are indicated respectively1、ν2Two contact materials are indicated respectively
The Poisson's ratio of material；
In the present embodiment, it is applied to the normal load P=100kN of faying face, calculates single micro-bulge Maximum Contact point
Area al=2.293740 × 10-4m2。
The relationship of total adhesion strength and faying face contact area, specific method suffered by step 4, calculations incorporated face are：
Step 4.1, the adhesion strength for establishing the single micro-bulge in different distortion section are in contact with it the relationship of area；
According to fractal theory, the relationship that the adhesion strength of the single micro-bulge in different distortion section is in contact with it area is：
(1) in relief area, δ/δcThe adhesion strength of ＜ 0, single micro-bulge are in contact with it the following formula institute of relationship of area
Show：
(2) in perfect elasticity area, 0 ＜ δ/δc＜ 1, the relationship that the adhesion strength of single micro-bulge is in contact with it area are public as follows
Shown in formula：
(3) in one area of elastoplasticity, 1 ＜ δ/δc＜ 6, the relationship that the adhesion strength of single micro-bulge is in contact with it area are public as follows
Shown in formula：
(4) in 2nd area of elastoplasticity, 6 ＜ δ/δc＜ 110, the relationship that the adhesion strength of single micro-bulge is in contact with it area are as follows
Shown in formula：
Wherein, FsiFor the adhesion strength of the single micro-bulge under different distortion section, i=1 ..., 4, Δ γ ' is adhesion strength
Can, ε is intermolecular distance；
Step 4.2, the relationship for establishing faying face total adhesion strength and faying face contact area；
According to fractal theory, shown in the following formula of relationship of the total adhesion strength of faying face with faying face contact area：
Wherein,
Wherein, AnFor faying face nominal contact area,For the face of faying face contact point
Product distribution function, FsiFor the adhesion strength of the single micro-bulge under different distortion section, Δ γ ' is adhesion strength energy；
In the present embodiment, faying face nominal contact area A is takenn=3.440610 × 10-3m2, adhesion strength energy Δ γ '=
3.2erg/cm2, intermolecular distance ε=4 × 10-10M calculates the total adhesion strength F of faying faces=2169.500842N.
The relationship of total circumferential load and faying face contact area suffered by step 5, calculations incorporated face；
According to fractal theory, the relationship of total circumferential load and faying face contact area suffered by faying face is：
Work as al＞ acAnd when D ≠ 2.5, total circumferential load suffered by faying face is with faying face contact area relational expression：
Work as al＞ acAnd when D=2.5, total circumferential load suffered by faying face is with faying face contact area relational expression：
In the present embodiment, the total circumferential load Q=45318.214N of faying face is calculated.
Step 6, the total normal load P for establishing faying face static friction factor μ and faying face, total circumferential load Q and total adhesion
Power FsBetween relationship, shown in following formula：
Faying face static friction factor μ=0.463232 in the present embodiment, the pass of static friction factor and dimensionless normal load
System is as shown in figure 4, as seen from the figure, under different faying face Surface Fractal Dimensions, with the increase of dimensionless normal load, tie
The static friction factor in conjunction face increases therewith, when dimensionless normal load is smaller, static friction factor shadow of the adhesion strength to faying face
Sound is smaller, and when dimensionless normal load is larger, adhesion strength is affected to the static friction factor of faying face.
The present embodiment also will account for adhesion strength and ignore the result of calculation with total normal direction of static friction factor in the case of adhesion strength
The relationship of load and document " Tian Hong-liang, Liu Fong, Zhao Chun-hua, et al.Predication
investigation on static tribological performance of metallic material
surfaces-theoretical model[J].Journal of Vibration and Shock,2014,3(1):209-
The test value of static friction factor and the relationship of total normal load are compared in 220. ", as shown in figure 5, it can be seen from the figure that
Under fully loaded transportation condition, adhesion strength is affected to faying face static friction factor, while the calculated results of the present invention and examination
The difference for testing value is also smaller.
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, it will be understood by those of ordinary skill in the art that：It still may be used
To modify to the technical solution recorded in previous embodiment, either which part or all technical features are equal
It replaces；And these modifications or replacements, model defined by the claims in the present invention that it does not separate the essence of the corresponding technical solution
It encloses.
Claims (6)
1. a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength, it is characterised in that：Including following step
Suddenly：
The three-dimensional appearance of step 1, simulation faying face surface micro-bulge：The two-dimensional fractal function for describing faying face surface topography is changed
The juxtaposition metamorphose amount of the single micro-bulge of faying face is indicated into the difference for three-dimensional fractal function, trough and wave crest that this function is used in combination
δ, shown in following formula：
δ=2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
Wherein, G is the Fractal scale coefficient on faying face surface, and D is the fractal dimension on faying face surface, and 2 ＜ D ＜ 3, γ are and knot
The related parameter of conjunction face surface topography frequency density, γ>1, it is the single micro-bulge actual elastic in faying face surface generally to take 1.5, a
Contact area；
Step 2 calculates separately elastic deformation stage, elastic-plastic deformation stage, the deflection of the single micro-bulge in faying face surface with
Critical contact area；
The relationship of the contact area of total normal load and faying face suffered by step 3, calculations incorporated face；
The relationship of total adhesion strength and faying face contact area suffered by step 4, calculations incorporated face；
The relationship of total circumferential load and faying face contact area suffered by step 5, calculations incorporated face；
Between step 6, the total normal load for establishing faying face static friction factor and faying face, total circumferential load and total adhesion strength
Relationship.
2. a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength according to claim 1,
It is characterized in that：The specific method of the step 2 is：
Step 2.1, according to Hertzian contact theory, when two rough surface of faying face contacts with each other, two rough surfaces are converted into one
Equivalent rough surface contacts with each other with a rigid smooth plane, 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 single micro-bulge, and δ is the juxtaposition metamorphose amount of single micro-bulge；
Step 2.2, the elastic critical deflection and elastic critical contact area for calculating single micro-bulge；
The elastic critical deflection δ of the single micro-bulgecThe following formula of calculating shown in：
Wherein, kμFor the modifying factor of frictional force, φ is material property coefficient；
The elastic critical contact area a of the single micro-bulgecThe following formula of calculating shown in：
It further finds out, the one area critical contact area a of elastoplasticity of single micro-bulgept1Shown in following formula：
apt1=1101/(2-D)ac；
The two area critical contact area a of elastoplasticity of single micro-bulgept2Shown in following formula：
apt2=61/(2-D)ac。
3. a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength according to claim 2,
It is characterized in that：The specific method of the step 3 is：
According to fractal theory, work as al＞ acAnd when D ≠ 2.5, the contact area of total normal load P and faying face suffered by faying face
Shown in the following formula of relationship：
Work as al＞ acAnd when D=2.5, the following formula institute of the contact area relationship of total normal load P and faying face suffered by faying face
Show：
Wherein, alFor single micro-bulge Maximum Contact point area, k is strong with the surrender of softer material in two contact material of faying face
Spend σyWith the relevant coefficients of hardness H, the relationship between three is：H=k σy；E is the Equivalent Elasticity mould of two contact material of faying face
Amount,E1、E2The elasticity modulus of two contact materials, ν are indicated respectively1、ν2Two contact materials are indicated respectively
Poisson's ratio.
4. a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength according to claim 3,
It is characterized in that：The specific method of the step 4 is：
Step 4.1, the adhesion strength for establishing the single micro-bulge in different distortion section are in contact with it the relationship of area；
According to fractal theory, the relationship that the adhesion strength of the single micro-bulge in different distortion section is in contact with it area is：
(1) in relief area, δ/δcThe adhesion strength of ＜ 0, single micro-bulge are in contact with it shown in the following formula of relationship of area：
(2) in perfect elasticity area, 0 ＜ δ/δcThe adhesion strength of ＜ 1, single micro-bulge are in contact with it the following formula institute of relationship of area
Show：
(3) in one area of elastoplasticity, 1 ＜ δ/δcThe adhesion strength of ＜ 6, single micro-bulge are in contact with it the following formula institute of relationship of area
Show：
(4) in 2nd area of elastoplasticity, 6 ＜ δ/δcThe adhesion strength of ＜ 110, single micro-bulge are in contact with it the following formula of relationship of area
It is shown：
Wherein, FsiFor the adhesion strength of the single micro-bulge under different distortion section, i=1 ..., 4, Δ γ ' is adhesion strength energy, and ε is
Intermolecular distance；
Step 4.2, the relationship for establishing faying face total adhesion strength and faying face contact area；
According to fractal theory, shown in the following formula of relationship of the total adhesion strength of faying face with faying face contact area：
Wherein,
Wherein, AnFor faying face nominal contact area,For the area distributions of faying face contact point
Function, FsiFor the adhesion strength of the single micro-bulge under different distortion section, Δ γ ' is adhesion strength energy.
5. a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength according to claim 4,
It is characterized in that：The specific method of the step 5 is：
According to fractal theory, the relationship of total circumferential load and faying face contact area suffered by faying face is：
Work as al＞ acAnd when D ≠ 2.5, total circumferential load suffered by faying face is with faying face contact area relational expression：
Work as al＞ acAnd when D=2.5, total circumferential load suffered by faying face is with faying face contact area relational expression：
6. a kind of faying face static friction factor three-dimensional fractal prediction technique considering adhesion strength according to claim 5,
It is characterized in that：Total normal load P, the total circumferential load Q of faying face static friction factor μ and faying face described in step 6 and total adhesion
Power FsBetween the following formula of relationship shown in：
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| 殷东华等: ""结合面静摩擦因数三维分形模型"", 《太原科技学报》 * |
| 潘五九等: ""考虑三维结合部形貌的静摩擦因数非线性分形模型"", 《东北大学学报》 * |
| 秦磊等: ""考虑粘着力的结合面静摩擦系数统计模型"", 《太原科技大学学报》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109472071A (en) * | 2018-10-30 | 2019-03-15 | 东北大学 | A kind of faying face confficient of static friction three-dimensional fractal prediction technique |
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| CN108613922B (en) | 2021-02-19 |
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