CN108846154B - Three-dimensional fractal prediction method for thermal contact resistance of joint surface by considering deformation of microprotrusion matrix - Google Patents
Three-dimensional fractal prediction method for thermal contact resistance of joint surface by considering deformation of microprotrusion matrix Download PDFInfo
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Abstract
The invention provides a joint surface contact thermal resistance three-dimensional fractal prediction method considering deformation of a microprotrusion matrix, and relates to the technical field of mechanical joint surfaces. The method comprises the steps of firstly, replacing a two-dimensional fractal function with a three-dimensional fractal function of the surface appearance of a joint surface which is closer to the actual condition, and expressing the contact deformation of a microprotrusion body by the amplitude difference of the peak and the trough of the three-dimensional function; then calculating the elastic critical deformation and the critical contact area of the microprotrusion body in the elastic deformation stage and the deformation of the microprotrusion body matrix; and finally, establishing the relation between the total normal load of the joint surface and the contact area and the relation between the total normal load of the joint surface and the total contact thermal resistance of the joint surface. According to the joint surface contact thermal resistance three-dimensional fractal prediction method considering the deformation of the microprotrusion matrix, the obtained joint surface contact thermal resistance is more accurate and closer to the actual situation, and theoretical basis can be provided for the contact thermal resistance of the joint surface in mechanical thermal state analysis.
Description
Technical Field
The invention relates to the technical field of mechanical joint surfaces, in particular to a joint surface contact thermal resistance three-dimensional fractal prediction method considering deformation of a microprotrusion matrix.
Background
In the manufacture and assembly of machine tools or various types of mechanical equipment, the mechanical structure is generally not a continuous whole and comprises a large number of parts, and the contact surfaces between the assembled parts are called joint surfaces. In the working process of the mechanical equipment, each component, each part and the whole mechanical equipment are all under the action of various heat sources, so that a certain temperature field is formed in the component, and the mechanical joint surface inevitably generates thermal deformation, thereby affecting the overall performance of the mechanical structure. Therefore, theoretically, the contact behavior of the joint surface is studied, and the thermal characteristics of the joint surface can be predicted in the design stage, which is very important for improving the stability and the processing precision of the mechanical processing equipment.
For the research of the contact thermal resistance of the joint surface, on the basis of the classical Hertz contact theory (Hertz), a part of scholars assume that the height distribution of the convex bodies of the joint surface is approximately Gaussian distributed and start from the angle of statistics, and establish a microscopic statistical contact model of the contact thermal resistance of the mechanical joint surface; the other part of scholars establishes a contact thermal resistance fractal contact model of the mechanical joint surface by utilizing an area distribution function and a fractal function representing the surface appearance of the joint surface based on a fractal theory, thereby avoiding the defect that the microscopic statistical contact model is influenced by the resolution and the sampling length of a surface appearance measuring instrument.
Although the thermal contact resistance model of the mechanical joint surface is continuously developed and perfected under the continuous efforts of domestic and foreign scholars, the thermal contact resistance between the joint surfaces calculated by using the existing thermal contact resistance model still has larger errors under the heavy load condition. The main reasons for this are: the existing joint surface thermal contact resistance calculation model does not consider the influence of the deformation of a micro-convex body matrix, and under a heavy load condition, the influence of the matrix deformation generated by the interaction of the micro-convex bodies between the joint surfaces on the calculation of the thermal contact resistance is large and cannot be ignored; meanwhile, the existing mechanical joint surface contact thermal resistance calculation model neglects the characteristic of fractal distribution of the three-dimensional surface of the microprotrusion. Therefore, under heavy load conditions, the contact thermal resistance of the joint surface cannot be accurately calculated by using the conventional theoretical method.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a joint surface contact thermal resistance three-dimensional fractal prediction method considering the deformation of a microprotrusion substrate, so that the contact thermal resistance of the joint surface is calculated under a heavy load condition.
The joint surface contact thermal resistance three-dimensional fractal prediction method considering the deformation of the microprotrusion matrix comprises the following steps:
δ＝2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3D)/2
wherein, delta is the contact deformation of a single microprotrusion body on the surface of the joint surface, gamma is a frequency density related parameter, gamma is more than 1, 1.5 is generally taken, D is the fractal dimension of the surface of the joint surface, D is more than 2 and less than 3, G is the fractal scale coefficient of the surface of the joint surface, and a is the actual elastic contact area of the single microprotrusion body on the surface of the joint surface;
step 2.1, according to the classical hertzian contact theory, when two rough surfaces of the joint surface contact each other, an equivalent microprotrusion rough surface contacts a smooth rigid plane to represent, and then the actual elastic contact area a of a single microprotrusion of the joint surface is the cross-sectional area of a single microprotrusion deformed on the equivalent rough surface and the rigid plane, as shown in the following formula:
a＝πRδ
wherein R is the curvature radius of a single microprotrusion body on the surface of the joint surface;
2.2, calculating the elastic critical deformation and the elastic critical contact area of a single microprotrusion body on the surface of the joint surface in an elastic deformation stage;
the elastic critical deformation of the single microprotrusion body is shown by the following formula:
δc＝(kφ)2π(5-D)/22(3D-15)/2G2-Da(D-1)/2(lnγ)-1/2
wherein k is the yield strength sigma of the softer material in the two contact materials with the joint surfaceyCoefficient relating to hardness H, relationship between the threeComprises the following steps: k σ H ═ k σy；φ＝σyE is the coefficient of material properties, E is the equivalent elastic modulus of the two contact materials of the joint surface,
E1、E2respectively representing the modulus of elasticity, v, of the two contact materials of the faying surface1、v2Respectively representing the Poisson's ratio of two contact materials on the joint surface;
the elastic critical contact area of the single microprotrusion is shown by the following formula:
ac＝(kφ)2/(2-D)π(4-D)/(2-D)2(3D-13)/(2-D)G2(lnγ)1/(D-2)；
said micro-protrusions are uniformly distributed on the nominal contact area of the bonding surface, so that for an elastic half-space body, a point (x, y) on the surface with an area size of 2a ' × 2a ' is subjected to a uniform pressure p acting on the surface according to the Leff's equationmThe magnitude of the generated deformation is shown in the following formula:
the area is (2 a')2The micro-protrusions are equivalent to the area of a circular micro-protrusion, then
Wherein P iseA normal load is applied to a single microprotrusion body which is elastically deformed;
further, according to the fractal theory, the amount of deformation ξ of the matrix due to the microprotrusion interaction is shown by the following formula:
wherein a is the actual elastic contact area of a single microprotrusion, and E is the equivalent elastic modulus of the two contact materials of the joint surface;
step 4.1, establishing the relation between the normal load borne by a single microprotrusion body in different deformation areas and the contact area of the single microprotrusion body;
according to the fractal theory, the relationship between the normal load borne by a single microprotrusion body in different deformation areas and the contact area of the single microprotrusion body is as follows:
(1) when the microprotrusions are in resilient contact:
in fractal theory, the contact deformation of a single microprotrusion body due to normal loading is:
δ＝s-d
wherein s is the height of a single microprotrusion body based on the plane of the microprotrusion body substrate before normal load application, and d is the distance between the plane of the microprotrusion body substrate before normal load application and the smooth rigid plane;
based on the elastic theory, for the local area bearing the load, the deformation of the matrix generated by the interaction of the microprotrusions is xi, so that the distance between the equivalent rough surface and the smooth rigid plane is increased, and therefore, the deformation of the single microprotrusion caused by the elastic factor is s-d', and then
s-d′＝δ-ξ
Wherein d' is the distance between the plane of the microprotrusion substrate and the smooth rigid plane after the normal load is applied;
according to classical hertzian contact theory, the load on a single microprotrusion body in elastic deformation is related to its actual elastic contact area by the following equation:
the curvature radius R of the microprotrusions is set to 2(3D-11)/2π(1-D)/2G2-Da(D-1)/2(lnγ)-1/2Substituting the formula to obtain:
(2) when the microprotrusions are in plastic contact:
Pp＝kσyap
wherein, PpThe load on the individual microprotrusions being plastically deformed, apIs the actual plastic contact area of the microprotrusions;
4.2, establishing a relation between the total normal load borne by the joint surface and the contact area of the joint surface;
according to the fractal theory, the relationship between the total normal load borne by the joint surface and the contact area is shown as the following formula:
wherein, alIs the maximum contact area of a single microprotrusion, acIs the elastic critical contact area of a single microprotrusion body;
according to the fractal theory, the relationship between the total normal load of the joint surface and the total contact thermal resistance of the joint surface is shown as the following formula:
wherein R 'is the contact thermal resistance on the rough joint surface, k' is a constant related to the thermal conductivity of the two contact materials,
k1、k2respectively the thermal conductivity, k, of the two contact materialsfIs the thermal conductivity of the air between the voids,
substituting the thickness of the joint surface void space into a contact thermal resistance expression on a rough joint surface to obtain:
wherein h is the average value of the heights of the micro-convex bodies of the two contact planes of the joint surface,
is the real contact area of two contact planes of the junction surface, AaThe nominal contact area of two contact planes of the joint surface;
and (4) combining a thermal contact resistance formula on the rough joint surface with a relation between the total normal load and the contact area of the joint surface in the step 4.2, and establishing a relation between the total normal load and the total thermal contact resistance of the joint surface based on the three-dimensional fractal function.
According to the technical scheme, the invention has the beneficial effects that: compared with the traditional method based on statistics and a two-dimensional fractal function, the three-dimensional fractal prediction method for the contact thermal resistance of the bonding surface with consideration of the deformation of the microprotrusion matrix adopts the three-dimensional fractal function to represent the microprotrusion morphology of the rough bonding surface, and is more consistent with the actual situation, so that the prediction result is more accurate. Meanwhile, the influence of the deformation of the matrix on the contact thermal resistance caused by the interaction of the microprotrusions under the heavy load condition is fully considered, and the defect that the contact thermal resistance of the joint surface is calculated inaccurately by the existing method based on the fractal theory is overcome.
Drawings
FIG. 1 is a flowchart of a joint surface contact thermal resistance three-dimensional fractal prediction method considering the deformation of a microprotrusion substrate according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a three-dimensional fractal function representing a shape of a microprotrusion of a rough joint surface according to an embodiment of the present invention;
FIG. 3 is a schematic view of equivalent contact deformation of a surface of a bonding surface according to an embodiment of the present invention;
FIG. 4 is a graph showing the relationship between the dimensionless normal load and the dimensionless thermal contact resistance of the bonding surface under the two conditions of considering the deformation of the microprotrusion substrate and neglecting the deformation of the microprotrusion substrate according to the embodiment of the present invention;
fig. 5 is a graph illustrating a relationship between a dimensionless normal load and a dimensionless contact thermal conductance of a bonding surface under two conditions of considering deformation of a microprotrusion substrate and neglecting deformation of the microprotrusion substrate according to an embodiment of the present invention.
Wherein, 1, loading the base plane of the front microprotrusion body; 2. loading the base plane of the micro convex body; 3. a smooth rigid plane; 4. equivalent asperity roughness surface.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A joint surface contact thermal resistance three-dimensional fractal prediction method considering deformation of a microprotrusion substrate is shown in FIG. 1 and comprises the following steps:
δ＝2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
wherein, delta is the contact deformation of a single microprotrusion body on the surface of the joint surface, gamma is a frequency density related parameter, gamma is more than 1, 1.5 is generally taken, D is the fractal dimension of the surface of the joint surface, D is more than 2 and less than 3, G is the fractal scale coefficient of the surface of the joint surface, and a is the actual elastic contact area of the single microprotrusion body on the surface of the joint surface;
in the embodiment, a two-dimensional fractal W-M function describing a surface profile curve of the joint surface is improved into a three-dimensional fractal W-M function describing a fractal curved surface of the surface profile curve of the joint surface. The parameters for the given equivalent matte surface are: fractal scale coefficient G of joint surface 1.05 × 10-8m, the fractal dimension D is 2.437, the parameter gamma related to the frequency density of the surface topography of the bonding surface is 1.5, and the obtained three-dimensional topography of the surface of the bonding surface is shown in FIG. 2.
step 2.1, according to the classical hertzian contact theory, when two rough surfaces of the joint surface contact each other, as shown in fig. 3, an equivalent microprotrusion rough surface 4 contacts a smooth rigid plane 3 to represent, and then the actual elastic contact area a of a single microprotrusion of the joint surface is the cross-sectional area of a single microprotrusion deformed on the equivalent rough surface 4 and the rigid smooth plane 3, as shown in the following formula:
a＝πRδ
wherein R is the curvature radius of a single microprotrusion body on the surface of the joint surface;
2.2, calculating the elastic critical deformation and the elastic critical contact area of a single microprotrusion body on the surface of the joint surface in an elastic deformation stage;
the elastic critical deformation of the single microprotrusion body is shown by the following formula:
δc＝(kφ)2π(5-D)/22(3D-15)/2G2-Da(D-1)/2(lnγ)-1/2
wherein k is the yield strength sigma of the softer material in the two contact materials with the joint surfaceyThe relation between the coefficient related to the hardness H and the hardness H is as follows: k σ H ═ k σy；φ＝σyE is the coefficient of material properties, E is the equivalent elastic modulus of the two contact materials of the joint surface,
E1、E2respectively representing the modulus of elasticity, v, of the two contact materials of the faying surface1、v2Respectively representing the Poisson's ratio of two contact materials on the joint surface;
the elastic critical contact area of the single microprotrusion is shown by the following formula:
ac＝(kφ)2/(2-D)π(4-D)/(2-D)2(3D-13)/(2-D)G2(lnγ)1/(D-2)；
in this embodiment, the hardness of the two contact materials on the surface of the bonding surface is H1＝H2＝4.19×109pa, bulletA modulus of elasticity of E1＝E2＝2.07×1011Pa, Poisson's ratio v1＝v2The elastic critical contact area of the individual microprotrusions calculated as 0.29 is ac＝6.8327×10-9m2。
said micro-protrusions are uniformly distributed on the nominal contact area of the bonding surface, so that for an elastic half-space body, a point (x, y) on the surface with an area size of 2a ' × 2a ' is subjected to a uniform pressure p acting on the surface according to the Leff's equationmThe magnitude of the generated deformation is shown in the following formula:
the area is (2 a')2The micro-protrusions are equivalent to the area of a circular micro-protrusion, then
Wherein P iseA normal load is applied to a single microprotrusion body which is elastically deformed;
further, according to the fractal theory, the amount of deformation ξ of the matrix due to the microprotrusion interaction is shown by the following formula:
wherein a is the actual elastic contact area of a single microprotrusion, and E is the equivalent elastic modulus of the two contact materials of the joint surface;
step 4.1, establishing the relation between the normal load borne by a single microprotrusion body in different deformation areas and the contact area of the single microprotrusion body;
according to the fractal theory, the relationship between the normal load borne by a single microprotrusion body in different deformation areas and the contact area of the single microprotrusion body is as follows:
(1) when the microprotrusions are in resilient contact:
in fractal theory, the contact deformation of a single microprotrusion body due to normal loading is:
δ＝s-d
wherein s is the height of a single microprotrusion body based on the plane of the microprotrusion body substrate before normal load application, and d is the distance between the plane of the microprotrusion body substrate before normal load application and the smooth rigid plane;
based on the elastic theory, for the local area bearing the load, the deformation of the matrix generated by the interaction of the microprotrusions is xi, so that the distance between the equivalent rough surface and the smooth rigid plane is increased, and therefore, the deformation of the single microprotrusion caused by the elastic factor is s-d', and then
s-d′＝δ-ξ
Wherein d' is the distance between the plane of the microprotrusion substrate and the smooth rigid plane after the normal load is applied;
according to classical hertzian contact theory, the load on a single microprotrusion body in elastic deformation is related to its actual elastic contact area by the following equation:
the curvature radius R of the microprotrusions is set to 2(3D-11)/2π(1-D)/2G2-Da(D-1)/2(lnγ)-1/2Substituting the formula to obtain:
(2) when the microprotrusions are in plastic contact:
Pp＝kσyap
wherein, PpThe load on the individual microprotrusions being plastically deformed, apIs the actual plastic contact area of the microprotrusions;
4.2, establishing a relation between the total normal load borne by the joint surface and the contact area;
according to the fractal theory, the relationship between the total normal load borne by the joint surface and the contact area is shown as the following formula:
wherein, alIs the maximum contact area of a single microprotrusion, acIs the elastic critical contact area of a single microprotrusion body;
according to the fractal theory, the relationship between the total normal load of the joint surface and the total contact thermal resistance of the joint surface is shown as the following formula:
wherein R 'is the contact thermal resistance on the rough joint surface, k' is a constant related to the thermal conductivity of the two contact materials,
k1、k2respectively the thermal conductivity, k, of the two contact materialsfIs the thermal conductivity of the air between the voids,
substituting the thickness of the joint surface void space into a contact thermal resistance expression on a rough joint surface to obtain:
wherein h is the average value of the heights of the micro-convex bodies of the two contact planes of the joint surface,
is the real contact area of two contact planes of the junction surface, AaFor two contact surfaces of the joint surfaceA nominal contact area of the face;
and (4) combining a thermal contact resistance formula on the rough joint surface with a relation between the total normal load and the contact area of the joint surface in the step 4.2, and establishing a relation between the total normal load and the total thermal contact resistance of the joint surface based on the three-dimensional fractal function.
In this embodiment, the load is large, so the influence of the air medium thermal resistance can be ignored, and the average value h of the heights of the two contact plane microprotrusions is 1.016 × 10-5m, true contact area Ar＝6.4072×10-5m2Thermal conductivity k of two contact materials1＝k244W/(m DEG C), the fractal dimension D of the bonding surface is 2.437, and the fractal scale coefficient G is 1.05X 10-8m, the parameter gamma related to the surface frequency density of the combined surface is 1.5, and the maximum contact point area a of a single microprotrusionl＝5.0213×10-5m2Finally calculating the thermal contact resistance of the joint surface as R0.0050W/(m)2·K)。
In this embodiment, the relationship between the dimensionless normal load of the joint surface and the dimensionless thermal contact resistance is shown in fig. 4, and it can be seen from the figure that the joint surface thermal contact resistance considering the deformation of the microprotrusion substrate is larger than the joint surface thermal contact resistance neglecting the deformation of the microprotrusion substrate, because the deformation of the microprotrusion substrate increases the distance between the equivalent rough surface and the smooth rigid plane, the joint surface thermal contact resistance can be increased by the mechanism of generation of the thermal contact resistance; and with the increase of the normal load, the deformation of the microprotrusion substrate is more obvious, so the difference between the thermal contact resistance considering the deformation of the microprotrusion substrate and the thermal contact resistance neglecting the deformation is increased.
In this embodiment, in order to more clearly reflect the influence of the deformation of the microprotrusion substrate on the contact thermal resistance, a relationship between a dimensionless normal load and a dimensionless contact thermal conductance is also given, as shown in fig. 5, it can be seen from the figure that the deformation of the microprotrusion substrate is more obvious with the increase of the normal load, so that the difference between the contact thermal conductance considering the deformation of the microprotrusion substrate and the contact thermal conductance neglecting the deformation increases.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (3)
1. A joint surface contact thermal resistance three-dimensional fractal prediction method considering deformation of a microprotrusion matrix is characterized by comprising the following steps of: the method comprises the following steps:
step 1, simulating a three-dimensional profile of a bonding surface microprotrusion: replacing a two-dimensional fractal function with a three-dimensional fractal function closer to the actual surface topography of the joint surface, and expressing the contact deformation of the microprotrusions by the amplitude difference between the peaks and the troughs of the three-dimensional fractal function, wherein the formula is as follows:
δ＝2(11-3D)/2GD-2(lnγ)1/2π(D-3)/2a(3-D)/2
wherein, delta is the contact deformation of a single microprotrusion body on the surface of the joint surface, gamma is a frequency density related parameter, gamma is more than 1, 1.5 is taken, D is the fractal dimension of the surface of the joint surface, 2< D <3, G is the fractal scale coefficient of the surface of the joint surface, and a is the actual elastic contact area of the single microprotrusion body on the surface of the joint surface;
step 2, respectively calculating the deformation and the critical contact area of a single microprotrusion body on the surface of the joint surface in the elastic deformation stage;
step 3, calculating the matrix deformation of the micro-convex body on the surface of the joint surface;
step 4, establishing a relation between the total normal load of the joint surface and the contact area of the joint surface;
step 5, establishing a relation between the total normal load of the joint surface and the total contact thermal resistance of the joint surface;
the specific method of the step 2 comprises the following steps:
step 2.1, according to the classical hertzian contact theory, when two rough surfaces of the joint surface contact each other, an equivalent microprotrusion rough surface contacts a smooth rigid plane to represent, and then the actual elastic contact area a of a single microprotrusion of the joint surface is the cross-sectional area of a single microprotrusion deformed on the equivalent rough surface and the rigid plane, as shown in the following formula:
a＝πRδ
wherein R is the curvature radius of a single microprotrusion body on the surface of the joint surface;
2.2, calculating the elastic critical deformation and the elastic critical contact area of a single microprotrusion body on the surface of the joint surface in an elastic deformation stage;
the elastic critical deformation of the single microprotrusion body is shown by the following formula:
δc＝(kφ)2π(5-D)/22(3D-15)/2G2-Da(D-1)/2(lnγ)-1/2
wherein k is the yield strength sigma of the softer material in the materials in contact with the joint surfaceyThe relation between the coefficient related to the hardness H and the hardness H is as follows: k σ H ═ k σy；φ＝σyE is the coefficient of material properties, E is the equivalent elastic modulus of the two contact materials of the joint surface,
E1、E2respectively, the modulus of elasticity, v, of the two contact materials of the faying surface1、ν2Respectively representing the Poisson's ratio of two contact materials on the joint surface;
the elastic critical contact area of the single microprotrusion is shown by the following formula:
ac＝(kφ)2/(2-D)π(4-D)/(2-D)2(3D-13)/(2-D)G2(lnγ)1/(D-2)
the specific method of the step 3 comprises the following steps:
said micro-protrusions are uniformly distributed on the nominal contact area of the bonding surface, so that for an elastic half-space body, a point (x, y) on the surface with an area size of 2a ' × 2a ' is subjected to a uniform pressure p acting on the surface according to the Leff's equationmThe magnitude of the generated deformation is shown in the following formula:
the area is (2 a')2The micro-protrusions are equivalent to the area of a circular micro-protrusion, then
Wherein P iseA normal load is applied to a single microprotrusion body which is elastically deformed;
further, according to the fractal theory, the amount of deformation ξ of the matrix due to the microprotrusion interaction is shown by the following formula:
wherein a is the actual elastic contact area of a single microprotrusion, and E is the equivalent elastic modulus of the two contact materials of the bonding surface.
2. The joint surface contact thermal resistance three-dimensional fractal prediction method considering the deformation of the microprotrusion substrate as claimed in claim 1, wherein: the specific method of the step 4 comprises the following steps:
step 4.1, establishing the relation between the normal load borne by a single microprotrusion body in different deformation areas and the contact area of the single microprotrusion body;
according to the fractal theory, the relationship between the normal load borne by a single microprotrusion body in different deformation areas and the contact area of the single microprotrusion body is as follows:
(1) when the microprotrusions are in resilient contact:
in fractal theory, the contact deformation of a single microprotrusion body due to normal loading is:
δ＝s-d
wherein s is the height of a single microprotrusion body based on the plane of the microprotrusion body substrate before normal load application, and d is the distance between the plane of the microprotrusion body substrate before normal load application and the smooth rigid plane;
based on the elastic theory, for the local area bearing the load, the deformation of the matrix generated by the interaction of the microprotrusions is xi, so that the distance between the equivalent rough surface and the smooth rigid plane is increased, and therefore, the deformation of the single microprotrusion caused by the elastic factor is s-d', and then
s-d′＝δ-ξ
Wherein d' is the distance between the plane of the microprotrusion substrate and the smooth rigid plane after the normal load is applied;
according to classical hertzian contact theory, the load on a single microprotrusion body in elastic deformation is related to its actual elastic contact area by the following equation:
the curvature radius R of the microprotrusions is set to 2(3D-11)/2π(1-D)/2G2-Da(D-1)/2(lnγ)-1/2Substituting the formula to obtain:
(2) when the microprotrusions are in plastic contact:
Pp＝kσyap
wherein, PpThe load on the individual microprotrusions being plastically deformed, apIs the actual plastic contact area of the microprotrusions;
4.2, establishing a relation between the total normal load borne by the joint surface and the contact area;
according to the fractal theory, the relationship between the total normal load borne by the joint surface and the contact area is shown as the following formula:
wherein, alIs the maximum contact area of a single microprotrusion, acIs the elastic critical contact area of a single microprotrusion.
3. The joint surface contact thermal resistance three-dimensional fractal prediction method considering the deformation of the microprotrusion substrate as claimed in claim 2, wherein: the specific method of the step 5 comprises the following steps:
according to the fractal theory, the relationship between the total normal load of the joint surface and the total contact thermal resistance of the joint surface is shown as the following formula:
wherein R 'is the contact thermal resistance on the rough joint surface, k' is a constant related to the thermal conductivity of the two contact materials,
k1、k2respectively the thermal conductivity, k, of the two contact materialsfIs the thermal conductivity of the air between the voids,
substituting the thickness of the joint surface void space into a contact thermal resistance expression on a rough joint surface to obtain:
wherein h is the average value of the heights of the micro-convex bodies of the two contact planes of the joint surface,
is the real contact area of two contact planes of the junction surface, AaThe nominal contact area of two contact planes of the joint surface;
and (4) combining a thermal contact resistance formula on the rough joint surface with a relation between the total normal load and the contact area of the joint surface in the step 4.2, and establishing a relation between the total normal load and the total thermal contact resistance of the joint surface based on the three-dimensional fractal function.
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