CN110619164A - Modeling method for friction coefficient of contact surface based on fractal theory and Florida theory - Google Patents

Abstract

The invention discloses a modeling method of a contact surface friction coefficient based on a fractal theory and a Florida theory. And then solving the real contact area and the contact load through piecewise integration according to the elastic/plastic deformation stage of the material, and deducing a friction coefficient model of the contact surface by using the Florida theory on the basis. And finally, a reliable bolt fastening scheme is developed, and theoretical support is provided for the lifting of the assembly technology of the heavy numerical control machine tool. The microscopic topography of the joint surface directly affects the size of the real contact area of the mechanical joint and the distribution of the contact load, further resulting in a change in the friction coefficient of the contact surface. The friction coefficient of the bearing surface of the bolt influences the distribution of the bolt pre-tightening torque, so that the bolt rigidity is changed.

Description

A calculation of friction coefficient of contact surface based on fractal theory and Florida theory modeling method

technical field

The invention belongs to the field of assembly characteristics of foundation bolts for heavy-duty machine tools, and relates to a friction coefficient modeling method of a contact surface at a microscopic angle, considering the elastic/plastic deformation stage of a material, and deriving the contact surface based on fractal theory and Florida theory The true coefficient of friction model for .

Background technique

The coefficient of friction not only affects the heat transfer and electrical conductivity of the structure, but also has a direct impact on the stability, safety and reliability of the mechanical structure, especially in the ultra-precision/precision fields (aviation, aerospace and five-axis and heavy machine tools, etc. ) play a decisive role. In order to accelerate the realization of Made in China 2025, especially breakthroughs in some high-end technology fields, the core of which is to improve the performance of aviation/aerospace engines and the precision of high-end machine tools. The mechanical properties of these assemblies are affected by the coefficient of surface friction. At the same time, the assembly is connected by bolts, in other words, the study of the bolt contact area is the key. The illustrated invention is based on the modeling of the surface friction coefficients in the area of bolted connections in the field of heavy machine tools.

Contents of the invention

The key of the invention is to establish the connection between the microscopic surface features and the friction coefficient, and propose a calculation method for the surface friction coefficient based on the fractal theory and the Florida theory.

The technical solution of the present invention is a modeling method based on the fractal theory and the Florida theory of the contact surface friction coefficient. The specific implementation process of the method is as follows,

Step 1 assumes that the geometric characteristics of each truncated surface of the rough surface are similar, and the three-dimensional shape is characterized by the two-dimensional W-M function as follows:

Step 2 Since the microscopic features of the rough surface contain a large number of asperities, the contact between metals is actually the interaction between each asperity. Under the action of external load, the single asperity will deform, and the deformation is

δ＝2G ^(D-2) (lnγ) ^1/2 (2r') ^(3-D) (2)

Step 3. According to the force closed-loop and deformation coordination relationship, when the material is in the elastic stage and plastic stage, the contact load and contact area of a single asperity are known;

Step 3.1 The material is about to undergo plasticity, which marks the transformation of the asperity from elastic to elastic-plastic deformation. The critical value of the elastic displacement δ _c and the critical value of the cross-sectional area of the asperity a _c ' are

Step 3.2 The material is elastically deformed. According to the Hertz contact, the contact load f _e and the contact area a _e can be known

In step 3.3, the material will undergo complete plastic deformation, and the contact area a _p and contact load f _p of the asperities are respectively:

a _p =2πRδ=a' (7)

f _p =Ha _p (8)

In step 4, the contact point formed by cutting the rough surface horizontally by a smooth plane is used to establish the island distribution function of the contact point, and then:

The contact parameters of the nominal surface in step 5 include the surface contact load and the real contact area through the integration and summation of the single asperity:

(1) When the cross-sectional area a' of a single asperity is in the range of a _c '<a'<a' _l , the real contact area A _re and contact load F _e of the contact surface are calculated by integral:

(2) When the cross-sectional area a' of a single asperity is 0<a'<a' _c , the real area A _rp and the contact load F _p represent:

Step 6 Under the action of external force, the asperity between metals will undergo elastic deformation and plastic deformation, so the total load F and total contact area _Ar of the contact surface are expressed as:

Step 7 During the elastic/plastic deformation of the material, the real contact area and contact load of the bonding surface are as above. The contact area/contact load size and distribution have an important influence on the surface friction coefficient. Considering that the coefficient of friction is affected by the geometric features of the rough surface, as well as the interaction and deformation of asperities, the interaction of fragments and the separation effect of the furrow, as well as the normal load and the division of the contact area between different contact bodies, the establishment The Florida model is represented as follows

μ＝(1-β)μ _a +βμ _ap +μ _d (16)

Among them, the formula (16) is composed of three parts, which are the adhesion coefficient of μ _a , the furrow coefficient of μ _ap and the wear coefficient of μ _d , which can be written as

Substituting Equations (14), (15) and Equations (17)-(19) into Equation (16) can calculate the true friction coefficient of the joint surface.

Compared with the prior art, the present invention explains the real friction coefficient of the contact surface from a microcosmic point of view, and takes into account the principle of action between the asperities, fundamentally solves the calculation of the friction coefficient, in order to predict the real friction coefficient of the contact surface The coefficient of friction provides theoretical support.

Description of drawings

Figure 1. Three-dimensional topography of rough surface.

Figure 2 Two-dimensional W-M function profile.

Fig. 3 Geometric deformation diagram of a single asperity.

Fig. 4. Schematic diagram of the contact principle on a rough surface.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments.

The technical solution of the present invention is a modeling method based on the fractal theory and the Florida theory of the friction coefficient of the contact surface. The specific implementation process of the method is as follows. Step 1 Yan and Komvopoulos believe that the geometric features of the rough surface satisfy disorder and self-affine. and roughness (Figure 1). In order to simplify the problem, it is artificially assumed that the geometric characteristics of each truncated surface are similar, so the two-dimensional W-M function is used to characterize the three-dimensional shape as follows (Fig. 2):

Step 2 Since the microscopic features of the rough surface contain a large number of asperities, the contact between metals is actually the interaction between each asperity. Under the action of external load, the single asperity will deform (Fig. 3), and its deformation is

δ＝2G ^(D-2) (lnγ) ^1/2 (2r') ^(3-D) (2)

Step 3 According to the force closed-loop and deformation coordination relationship, when the material is in the elastic stage and plastic stage, the contact load and contact area of a single asperity can be known

Step 3.1Chang et al. proposed that the material is about to undergo plasticity, which marks the transformation of the asperity from elastic to elastic-plastic deformation. The critical value of the elastic displacement δ _c and the critical value of the cross-sectional area of the asperity a _c ' are

Step 3.2 The material is elastically deformed. According to the Hertz contact, the contact load f _e and the contact area a _e can be known

Step 3.3 The material will undergo complete plastic deformation. At this stage, the asperity contact area a _p and contact load f _p

a _p =2πRδ=a' (7)

f _p =Ha _p (8)

Step 4. Mandelbrot et al. cut the contact point formed by a smooth plane horizontally on the rough surface, which is similar to the island formed by cutting the earth’s surface through the sea level, establish the island distribution function of the contact point, and then develop it through Wang and Komvopoulos

Step 5 The contact parameters of the nominal surface include the surface contact load and the real contact area obtained by integral and summation of a single asperity

(1) When the cross-sectional area a' of a single asperity is in the range of a _c '<a'<a' _l , the real contact area A _re and contact load F _e of the contact surface are calculated by integral

(2) When the cross-sectional area a' of a single asperity is 0<a'<a' _c , the real area A _rp and the contact load F _p represent

Step 6 Under the action of external force, the asperity between metals will undergo elastic deformation and plastic deformation, so the total load F and the total contact area _Ar of the contact surface are represented by

Step 7 During the elastic/plastic deformation of the material, the real contact area and contact load of the bonding surface are as above. The contact area/contact load size and distribution have an important influence on the surface friction coefficient. Consider that the coefficient of friction is affected by the geometry of the rough surface. Zhang et al. considered the interaction and deformation of asperities, the interaction of fragments and the separation effect of furrows (Fig. 4), as well as the division of normal loads (and contact areas) between different contact bodies, and established the Florida model expressed as follows

μ＝(1-β)μ _a +βμ _ap +μ _d (16)

Among them, the formula (16) is composed of three parts, which are the adhesion coefficient of μ _a , the furrow coefficient of μ _ap and the wear coefficient of μ _d , which can be written as

Substituting Equations (14), (15) and Equations (17)-(19) into Equation (16) can calculate the true friction coefficient of the joint surface.

Compared with the prior art, the present invention explains the real friction coefficient of the contact surface from a microscopic point of view, and takes into account the principle of action between the asperities, fundamentally solves the calculation of the friction coefficient, and predicts the real friction coefficient of the contact surface. Coefficients provide theoretical support.

Parameter interpretation: a' is the cut-off area of a single asperity (m ² );

a _l ' is the maximum cut-off area of a single asperity (m ² );

a _c 'is the critical cut-off area of a single asperity (m ² );

a _e is the elastic deformation contact area of single asperity (m ² );

a _p is the plastic deformation contact area of single asperity (m ² );

A _re is the real contact area of elastic deformation (m ² );

A _rp is the real contact area of plastic deformation (m ² );

A _r is the real contact area of the contact surface, A _r =A _a +A _ap +A _d (m ² );

D is the fractal dimension;

E is the equivalent Young's modulus, E=((1-υ ₁ ² )/E ₁ +(1-υ ₂ ² )/E ₂ ) ^-1 (Elastic modulus of E ₁ , E ₂ materials) (Pa );

f(t) is the friction correlation function, f(t)=1-[2ln(1+t)-t]/ln(1-t ² );

f _e is the elastic contact load of single asperity (N);

f _p is the plastic contact load of single asperity (N);

F _e is the elastic deformation contact load (N);

F _p is the plastic deformation contact load (N);

F is the total contact load (N) of the contact surface;

G is the characteristic roughness (m);

H is the hardness of the softer material, H=2.8σ _y (Pa);

R is the equivalent radius of curvature of the asperity,

S ₁ and S ₂ are the shear strength (pa) of the material, H=6S(Pa);

z ₀ is the distance from the asperity peak point to the equivalent plane (m);

β is the asperity contact area percentage under compression, and its range is 0.5-1;

γ is the surface characteristic constant, its value is 1.5;

μ is the coefficient of friction;

τ _a1 and τ _a2 are the shear stress of the material in the asperity adhesion area, τ _a1 = τ _a2 = K _a N ^0.5 (N number of contact points per unit area; K _a is the adhesion coefficient, its value is generally 0.05J/m ² to 1J/ ^m2 ) (Pa);

ν is the Poisson's ratio of the material;

ψ is the local expansion coefficient.

Claims (1)

1. A modeling method based on fractal theory and the contact surface friction coefficient of Florida theory, it is characterized in that: the concrete implementation process of this method is as follows, Step 1 assumes that the geometric characteristics of each truncated surface of the rough surface are similar, and the three-dimensional shape is characterized by the two-dimensional W-M function as follows: Step 2 Since the microscopic features of the rough surface contain a large number of asperities, the contact between metals is actually the interaction between each asperity; under the action of an external load, a single asperity will deform, and the deformation amount is δ＝2G ^(D-2) (lnγ) ^1/2 (2r') ^(3-D) (2) Step 3. According to the force closed-loop and deformation coordination relationship, when the material is in the elastic stage and plastic stage, the contact load and contact area of a single asperity are known; Step 3.1 The material is about to undergo plasticity, which marks the transformation of the asperity from elastic to elastic-plastic deformation. The critical value of the elastic displacement δ _c and the critical value of the cross-sectional area of the asperity a _c ' are Step 3.2 The material undergoes elastic deformation; according to the Hertzian contact, its contact load f _e and contact area a _e can be known In step 3.3, the material will undergo complete plastic deformation, and the contact area a _p and contact load f _p of the asperities are respectively: a _p =2πRδ=a' (7) f _p =Ha _p (8) In step 4, the contact point formed by cutting the rough surface horizontally by a smooth plane is used to establish the island distribution function of the contact point, and then: The contact parameters of the nominal surface in step 5 include the surface contact load and the real contact area through the integration and summation of the single asperity: (1) When the cross-sectional area a' of a single asperity is in the range of a _c '<a'<a' _l , the real contact area A _re and contact load F _e of the contact surface are calculated by integral: (2) When the cross-sectional area a' of a single asperity is 0<a'<a' _c , the real area A _rp and the contact load F _p represent: Step 6 Under the action of external force, the asperity between metals will undergo elastic deformation and plastic deformation, so the total load F and total contact area _Ar of the contact surface are expressed as: Step 7 During the elastic/plastic deformation of materials, the real contact area and contact load of the bonding surface are as above; the size and distribution of contact area/contact load have an important influence on the surface friction coefficient; considering that the friction coefficient is affected by the rough surface geometric characteristics The influence of , as well as the interaction and deformation of asperities, the interaction of fragments and the separation effect of furrows, as well as the normal load and the division of contact areas between different contact bodies, the Florida model is established as follows μ＝(1-β)μ _a +βμ _ap +μ _d (16) Among them, the formula (16) is composed of three parts, which are the adhesion coefficient of μ _a , the furrow coefficient of μ _ap and the wear coefficient of μ _d , which can be written as Substituting Equations (14), (15) and Equations (17)-(19) into Equation (16) can calculate the true friction coefficient of the joint surface.