CN112926210A - Fixed joint contact damping three-dimensional fractal prediction method - Google Patents

Fixed joint contact damping three-dimensional fractal prediction method Download PDF

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CN112926210A
CN112926210A CN202110256490.1A CN202110256490A CN112926210A CN 112926210 A CN112926210 A CN 112926210A CN 202110256490 A CN202110256490 A CN 202110256490A CN 112926210 A CN112926210 A CN 112926210A
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李祥
孙万
兰国生
张学良
冀成龙
李声祺
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Taiyuan University of Science and Technology
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Abstract

The invention discloses a fixed joint contact damping three-dimensional fractal prediction method, which comprises the following steps: firstly, measuring micro-topography data of contact surfaces, and obtaining characteristic fractal parameters of the two contact surfaces, namely fractal dimension and fractal roughness parameters, by a structure function method; based on a fractal theory, considering the influence of friction factors and the deformation process of the microprotrusions, enabling the normal contact dynamic model of the joint surface to be equivalent to a spring and a viscous damper, and establishing a fixed joint surface normal contact damping model; determining the static friction factor of the joint surface according to the existing method; substituting the characteristic fractal parameters, normal load, material parameter values and static friction factor of the equivalent rough surface into the model to calculate the maximum cross-sectional contact area of all micro-convex bodies on the junction surface; and substituting the static friction factor of the joint surface, the maximum cross-sectional contact area, the external excitation frequency, the parameter values of the material and the characteristic fractal parameter of the equivalent rough surface into the model to calculate the normal contact damping of the joint part. The invention provides a three-dimensional fractal prediction method for contact damping of a fixed mechanical joint part, which considers the influence of friction factors and the deformation process of a microprotrusion body, ensures that the established model is irrelevant to the quality of a joint surface matrix and better accords with the actual contact condition, and can provide theoretical basis for predicting and controlling the normal damping of a precise mechanical joint surface.

Description

Fixed joint contact damping three-dimensional fractal prediction method
Technical Field
The invention belongs to the technical field of joint surface contact deformation mechanism research, and particularly relates to a method for mechanical joint surface contact damping modeling.
Background
Generally, various machines are assembled by a plurality of parts, and all parts, components and assemblies are contacted with each other to form a large number of joint surfaces. In the macroscopic world, the surfaces of parts that appear smooth and flat exhibit in fact rough surface contours whose shape is complex, so that the actual joint surface consists of asperities of different sizes and shapes. When the surfaces of the two parts are contacted, some of the microprotrusions between the bonding surfaces are contacted, and some of the microprotrusions between the bonding surfaces are not contacted. Some of the microprotrusions that make contact undergo elastic deformation, some undergo elastoplastic deformation, and some undergo plastic deformation. Under the action of static load, the multiple micro-convex bodies which are elastically and plastically deformed between the joint surfaces have the capacity of resisting deformation and show the static rigidity characteristic between the joint surfaces. Under the action of dynamic load, normal or tangential relative displacement can occur between two contact surfaces, so that the elastic and elastic-plastic micro-convex bodies store energy, and meanwhile, the plastic-deformation micro-convex bodies consume energy, and the contact rigidity and the contact damping between the joint surfaces are shown. Research shows that the contact damping of the joint surface accounts for more than 90% of the total mechanical damping, and the joint surface damping is far larger than the damping of mechanical parts. The mechanical joint has a very close and complex relationship with the static characteristics, vibration and vibration control and dynamic characteristics of the mechanical structure. Therefore, the research on the rigidity and the damping characteristic of the mechanical joint surface provides good theoretical basis and guidance for the structural design of mechanical products, the dynamic optimization of mechanical systems and the surface processing method, and has important significance in both theoretical and practical applications
At present, the existing joint surface contact rigidity models are more, the normal contact damping models are fewer, and most of the existing models are established under a two-dimensional contact curve, which is not consistent with the actual three-dimensional characteristics of the joint surface; the influence of friction factors is not considered in the existing models; it is worth noting that the existing model does not distinguish between the work done by elastic stress (when the deformation amount is smaller than the critical deformation amount) and the work done by plastic stress (when the deformation amount is larger than the critical deformation amount) on the microprotrusions in the plastic state, and the energy consumption of the microprotrusions is calculated by only using the plastic energy consumption. Aiming at the defects, a three-dimensional fractal prediction method for contact damping of a fixed mechanical joint part is provided. Compared with the rough surface statistical parameters of the statistical model, the rough surface fractal parameters in the fractal model are not influenced by the sampling length and the resolution of a testing instrument, and have the characteristic of objective and unique certainty. The model is more suitable for the actual condition of the contact surface, and can provide a theoretical basis for further research of the joint surface.
Disclosure of Invention
The invention aims to provide a fixed mechanical joint contact damping three-dimensional fractal prediction method to solve one or more technical problems. The modeling method considers the influence of friction factors and the deformation process of the micro-convex body, and the established fixed joint surface normal contact damping model is irrelevant to the joint surface matrix quality, so that the theoretical model can better accord with the actual situation, and can be used for predicting the contact damping of the fixed mechanical joint surface.
In order to achieve the purpose, the invention adopts the following technical scheme:
a three-dimensional fractal prediction method for contact damping of a fixed mechanical joint part is characterized by comprising the following steps:
1) measuring the micro-topography data of the contact surfaces, and obtaining characteristic fractal parameters of the two contact surfaces, namely fractal dimension and fractal roughness parameters, by a structure function method;
calculating a corresponding structure function value according to discrete signals of the contour curve of different scales, wherein the structure function is defined as the incremental variance of the rough surface contour function, and the expression is as follows:
Figure BDA0002967562300000022
where τ represents the data step in the horizontal direction, which can be any value, z (x) represents the measured value of the surface profile, DsThe fractal dimension number of the section outline on the three-dimensional rough surface is expressed, and the relation of the fractal dimension number and the fractal D of the three-dimensional rough surface is D ═ Ds+1, coefficient C satisfies the relation
Figure BDA0002967562300000021
Wherein Γ represents the second type euler integral, and G represents the fractal roughness parameter.
The fractal parameter of the equivalent rough surface can be obtained by the formula (2)
Se(τ)＝S1(τ)+S2(τ) (2)
Wherein S is1(τ) and S2(τ) structural functions representing the profile of the two rough surfaces, Se(τ) represents the structure function of the equivalent rough surface profile.
Taking logS (τ) on both sides of equation of formula (1) at the same time is (4-2D)s) log τ + logC, so that logS (τ) is linear with log τ, and the fractal dimension can be determined by the slope k of the line, based on regression analysis of the fitted curve from the structural function valuessIs obtained by calculation, ks＝4-2DsFractal roughness can be obtained by the intercept B of a straight line, where B is logC.
2) Establishing a single microprotrusion contact model by combining a W-M function, and determining the deformation amount and the radius of the microprotrusion; obtaining contact parameters of a single microprotrusion body according to a Hertz theory, wherein the parameters comprise elastic critical deformation, energy storage, energy consumption, contact rigidity and contact load;
a single spherical microprotrusion contact model was created in combination with an improved W-M function that more accurately describes three-dimensional rough surfaces as shown in FIG. 2, according to Hertz's theory of contact, when two rough surfaces of the faying surface contact each other, the two rough surfaces are converted into an equivalent rough surface and an equivalent rough surfaceWhen the rigid smooth surfaces are contacted with each other, the contact deformation of the single microprotrusions on the equivalent rough surface is
Figure BDA0002967562300000031
Wherein a ' is the cross-sectional area of the microprotrusion, the contact radius is r ', the relation between a ' and the real contact area a (the contact radius is r) of the microprotrusion is 2a, D is the fractal dimension of the rough surface,
Figure BDA0002967562300000032
wherein gamma is the spatial frequency of the random profile, the general value is 1.5, and G is a fractal roughness parameter; the radius of the single microprotrusion on the equivalent rough surface is
Figure BDA0002967562300000033
The individual microprotrusion contact parameters can be obtained according to hertz theory: the elastic critical contact deformation of the single microprotrusion body is
Figure BDA0002967562300000034
Wherein σyFor the yield strength σ of the softer of the mutually contacting materialsy＝H/2.8；kμFor the correction coefficient of friction, there can be divided into two cases, in which when 0. ltoreq. mu. ltoreq.0.3, ku1-0.228 μ; when mu is more than or equal to 0.3 and less than or equal to 0.9, ku＝0.932exp[-1.58(μ-0.3)]Wherein μ is the coefficient of friction; a resilient contact load of
Figure BDA0002967562300000035
Wherein E is the combined elastic modulus E ═ 1/[ (1-upsilon) of the two contact materials1 2)/E1+(1-υ2 2)/E2]，E1And E2Respectively, the modulus of elasticity, upsilon, of the two contact materials1And upsilon2Respectively the poisson's ratio of the two contact materials; plastic contact load of P p2 pi HR δ, where H is the hardness of the softer of the two contact materials; only the resiliently deformed microprotrusions have normal stiffness by definition of stiffness
Figure BDA0002967562300000036
When the final state of the single microprotrusion body is elastic contact, the deformation amount of the equivalent microprotrusion body is always in the elastic deformation stage from 0 to delta, so that the stored elastic potential energy is
Figure BDA0002967562300000041
When the final state of the individual asperities is plastic contact, the amount of equivalent asperity deformation ranges from 0 to δcIn the elastic deformation phase, from deltacDelta. is in the plastic deformation phase, so that the energy consumed is
Figure BDA0002967562300000042
3) Expanding the single microprotrusion contact model established in the step 2) to the whole mechanical joint surface by combining a contact area distribution density function to obtain a calculation expression of normal load, normal stiffness, energy storage and energy consumption of the whole joint surface, and equating the normal contact dynamic characteristics of the fixed joint surface to a spring and a viscous damper to establish a joint surface normal contact damping model;
according to the fractal theory, the distribution function of the micro-contact cross-sectional area of the joint surface can be obtained as
Figure BDA0002967562300000043
Wherein a isl' is the largest cross-sectional contact area of all asperities.
Deriving normal load P of the whole joint surface according to the single microprotrusion contact model and the distribution function of the microprotrusion cross-sectional areanNormal stiffness KnEnergy storage WeEnergy consumption WdIs a calculation expression of
Figure BDA0002967562300000044
Figure BDA0002967562300000045
Figure BDA0002967562300000046
Figure BDA0002967562300000047
Wherein, acIs the critical contact area of bonding surface microprotrusions, when delta/deltacWhen 1, the critical cross-sectional area is obtained
Figure BDA0002967562300000048
The normal contact dynamic characteristics of the fixed joint surface are equivalent to a spring and a viscous damper, as shown in figure 3, and the fixed joint surface can be obtained
Figure BDA0002967562300000052
Wherein t is time; cnNormal contact damping for the joint surface; f (t) ═ Pncos (ω t) is a normal dynamic contact load acting on the joint surface, wherein ω is an angular frequency ω of 2 pi f, and f is an external excitation frequency; x (t) ═ Xncos(ωt-θn) Is the normal dynamic contact relative displacement between the joint surfaces, wherein thetanIs the initial phase; thus, η ═ Wd/We＝|fcx(t)|/|fkx(t)|＝Cnω/KnEta is damping loss factor, then
Figure BDA0002967562300000051
4) Determining the static friction factor of the combining surface according to a three-dimensional fractal model [ J ] of combined surface static friction factor of Languosheng, Zhang-school-good, Wenshuhua, cattle certification, Chengyuenghui, Languosheng, university of Taiyuan, 2013,34(06):451-455. ";
5) calculating the maximum cross-sectional contact area of all the micro-convex bodies on the joint surface;
substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1) and the static friction factor, the normal load and the material parameter values obtained in the step 4) into the model built in the step 3) to calculate the maximum cross-sectional contact area of all the micro-convex bodies on the joint surface.
6) Calculating the normal contact damping of the joint part;
substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1), the static friction factor obtained in the step 4), the maximum cross-section contact area obtained in the step 5), the external excitation frequency and the parameter values of the material into the model built in the step 3) to calculate the normal contact damping of the joint part.
Compared with the existing method for determining the contact rigidity of the joint surface, the method has the following advantages that:
1. the method considers the influence of friction factors and the deformation process of the micro-convex body (for the micro-convex body in a plastic state, when the deformation is smaller than the critical deformation, the work is done by elastic stress, and when the deformation is larger than the critical deformation, the work is done by plastic stress, so the energy loss of the micro-convex body is the sum of the work done by the elastic stress and the work done by the plastic stress, not only the plastic energy consumption), and the established fixed joint surface normal contact damping model is independent of the joint surface matrix quality, so that the theoretical model can better accord with the actual situation.
2. The method gets rid of the assumption that the traditional statistical method is based on the consistency of the curvature radius of the rough surface microprotrusion, and the characteristic fractal parameters in the fractal model are the unification of surface multi-scale similarity measurement and absolute measurement, so that the method has the characteristic of multi-scale fractal measurement and also keeps the advantages of intuition and conciseness of the conventional roughness parameters.
3. Compared with the traditional finite element method, the method has the characteristics of smaller calculated amount, strong operability and high calculation efficiency.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; it is obvious that the drawings in the following description are some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
Fig. 1 is a calculation flowchart of a fixed mechanical joint contact damping three-dimensional fractal prediction method according to an embodiment of the present invention.
Fig. 2 shows the ideal rigid plane in contact with the microprotrusions.
FIG. 3 is a junction surface dynamics model.
FIG. 4 is a discretized structure function of the contact surface in log-log coordinates for an embodiment of the invention.
Detailed Description
In order to make the purpose, technical effect and technical solution of the embodiments of the present invention clearer, the following clearly and completely describes the technical solution of the embodiments of the present invention with reference to the drawings in the embodiments of the present invention; it is to be understood that the described embodiments are only some of the embodiments of the present invention. Other embodiments, which can be derived by one of ordinary skill in the art from the disclosed embodiments without inventive faculty, are intended to be within the scope of the invention.
The invention is described in further detail below with reference to the figures and examples.
The invention relates to a modeling method for contact rigidity of a fixed mechanical joint part, which specifically comprises the following steps:
step 1: and measuring the micro-topography data of the contact surfaces, and obtaining characteristic fractal parameters of the two contact surfaces, namely fractal dimension and fractal roughness parameters, by a structure function method.
Calculating a corresponding structure function value according to discrete signals of the contour curve of different scales, wherein the structure function is defined as the incremental variance of the rough surface contour function, and the expression is as follows:
Figure BDA0002967562300000061
where τ represents the data step in the horizontal direction, which can be any value, z (x) represents the measured value of the surface profile, DsThe fractal dimension number of the section outline on the three-dimensional rough surface is expressed, and the relation of the fractal dimension number and the fractal D of the three-dimensional rough surface is D ═ Ds+1, coefficient C satisfies the relation
Figure BDA0002967562300000071
Wherein Γ represents the second type euler integral, and G represents the fractal roughness parameter.
The fractal parameter of the equivalent rough surface can be obtained by the formula (2)
Se(τ)＝S1(τ)+S2(τ) (4)
Wherein S is1(τ) and S2(τ) structural functions representing the profile of the two rough surfaces, Se(τ) represents the structure function of the equivalent rough surface profile.
Taking logS (τ) on both sides of equation of formula (1) at the same time is (4-2D)s) log τ + logC, so that logS (τ) is linear with log τ, and the fractal dimension can be determined by the slope k of the line, based on regression analysis of the fitted curve from the structural function valuessIs obtained by calculation, ks＝4-2DsFractal roughness can be obtained by the intercept B of a straight line, where B is logC.
Step 2: establishing a single microprotrusion contact model by combining a W-M function, and determining the deformation amount and the radius of the microprotrusion; obtaining single microprotrusion contact parameters according to Hertz's theory, including elastic critical deformation, energy storage, energy dissipation, contact stiffness, and contact load.
A contact model of a single spherical microprotrusion is established in combination with an improved W-M function which can more accurately describe a three-dimensional rough surface, as shown in figure 2, according to the Hertz's contact theory, when two rough surfaces of a bonding surface are in contact with each other, the two rough surfaces are converted into an equivalent rough surface which is in contact with a rigid smooth plane, and the contact deformation of the single microprotrusion on the equivalent rough surface is
Figure BDA0002967562300000072
Wherein a ' is the cross-sectional area of the microprotrusion, the contact radius is r ', the relation between a ' and the real contact area a (the contact radius is r) of the microprotrusion is 2a, D is the fractal dimension of the rough surface,
Figure BDA0002967562300000073
wherein gamma is the spatial frequency of the random profile, the general value is 1.5, and G is a fractal roughness parameter; the radius of the single microprotrusion on the equivalent rough surface is
Figure BDA0002967562300000074
The individual microprotrusion contact parameters can be obtained according to hertz theory: the elastic critical contact deformation of the single microprotrusion body is
Figure BDA0002967562300000075
Wherein σyFor the yield strength σ of the softer of the mutually contacting materialsy＝H/2.8；kμWhen the static friction coefficient of the joint surface is not less than 0 mu and not more than 0.3, k is the correction coefficient of the friction forceu1-0.228 μ; when mu is more than or equal to 0.3 and less than or equal to 0.9, ku＝0.932exp[-1.58(μ-0.3)]Wherein μ is the coefficient of friction; a resilient contact load of
Figure BDA0002967562300000081
Wherein E is the combined elastic modulus E ═ 1/[ (1-upsilon) of the two contact materials1 2)/E1+(1-υ2 2)/E2]，E1And E2Respectively, the modulus of elasticity, upsilon, of the two contact materials1And upsilon2Respectively the poisson's ratio of the two contact materials; plastic contact load of Pp2 pi HR δ, where H is the hardness of the softer of the two contact materials; only the resiliently deformed microprotrusions have normal stiffness by definition of stiffness
Figure BDA0002967562300000082
When the final state of the single microprotrusion body is elastic contact, the deformation amount of the equivalent microprotrusion body is always in the elastic deformation stage from 0 to delta, so that the stored elastic potential energy is
Figure BDA0002967562300000083
When the final state of the individual asperities is plastic contact, the amount of equivalent asperity deformation ranges from 0 to δcIn the elastic deformation phase, from deltacDelta. is in the plastic deformation phase, so that the energy consumed is
Figure BDA0002967562300000084
And step 3: expanding the single micro-convex body contact model established in the step 2) to the whole mechanical joint surface by combining a contact area distribution density function, obtaining a calculation expression of normal load, normal stiffness, energy storage and energy consumption of the whole joint surface, and equating the normal contact dynamic characteristics of the fixed joint surface to a spring and a viscous damper to establish a joint surface normal contact damping model.
According to the fractal theory, the distribution function of the micro-contact cross-sectional area of the joint surface can be obtained as
Figure BDA0002967562300000085
Wherein a'lThe largest cross-sectional contact area among all asperities.
Deriving normal load P of the whole joint surface according to the single microprotrusion contact model and the distribution function of the microprotrusion cross-sectional areanNormal stiffness KnEnergy storage WeEnergy consumption WdIs a calculation expression of
Figure BDA0002967562300000086
Figure BDA0002967562300000087
Figure BDA0002967562300000091
Figure BDA0002967562300000092
Wherein, ac' is the critical contact area of bonding surface microprotrusions, when delta/deltacWhen 1, the critical cross-section is obtainedHas a cross-sectional area of
Figure BDA0002967562300000093
The normal contact dynamic characteristics of the fixed joint surface are equivalent to a spring and a viscous damper, as shown in figure 3, and the fixed joint surface can be obtained
Figure BDA0002967562300000095
Wherein t is time; cnNormal contact damping for the joint surface; f (t) ═ Pncos (ω t) is a normal dynamic contact load acting on the joint surface, wherein ω is an angular frequency ω of 2 pi f, and f is an external excitation frequency; x (t) ═ Xncos(ωt-θn) Is the normal dynamic contact relative displacement between the joint surfaces, wherein thetanIs the initial phase; thus, η ═ Wd/We＝|fcx(t)|/|fkx(t)|＝Cnω/KnEta is the damping loss factor, i.e
Figure BDA0002967562300000094
And 4, step 4: the static friction factor of the combining surface is determined according to a three-dimensional fractal model [ J ] of combined surface static friction factor of Languosheng, Zhang-school-good, Wenshuhua, cattle certification, Chengyou, Languosheng, university of Taiyuan, 2013,34(06):451-455.
And 5: and (3) substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step (1), the static friction factor obtained in the step (4), the normal load and the parameter values of the material into the model built in the step (3) to calculate the maximum cross-sectional contact area of all the micro-convex bodies on the joint surface.
Step 6: substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1, the static friction factor obtained in the step 4, the maximum cross-sectional contact area obtained in the step 5, the external excitation frequency and the parameter values of the material into the model built in the step) to calculate the normal contact damping of the joint part.
Examples
Taking two different rough surfaces as an example, the materials of the two rough contact surfaces are cast iron, and the characteristic parameter of the material is H1＝H2＝231Mpa,E1＝E2＝130Gpa,υ1＝υ20.25; nominal contact area of the bonding surface is Aa＝11200mm2Normal load P applied to the jointn＝1.0213MPa。
The number of the acquisition points is set to be 500, the acquired profile height data is substituted into the discretized structural function expression, then discretized structural function images of the two contact surfaces can be drawn, the slope and intercept of a fitting curve can be obtained through regression analysis in a log-log coordinate, and the visualization result is shown in fig. 4. Further, the fractal dimension D of the plane 0 can be obtained according to the step 1s1.3690, D is 2.3690, and the fractal roughness parameter is 7.4325 × 10-13Fractal dimension D of m, plane 2s1.4548, D is 2.4548, and the fractal roughness parameter is 3.7481 × 10-10m, equivalent fractal dimension D of junction surfaces1.4381, D is 2.4381, and the fractal roughness parameter is 2.3984 × 10-10m, thereby equating the problem of two rough surface contact as an ideal rigid smooth surface in contact with a complex rough surface.
According to the literature, the static friction factor of the combined surface is determined to be 0.2314 according to the three-dimensional fractal model of combined surface static friction factor J of Languosheng and Taiyuan university, 2013,34(06) 451 and 455.
Firstly, substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1), the static friction factor obtained in the step 4) and the parameter values of the materials into the model established in the step 3) to calculate the critical cross-sectional contact area a of the joint surfacec′＝5.832×10-6(ii) a Secondly, substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1) and the static friction factor, the normal load, the parameter values of the material and the critical cross-section contact surface obtained in the step 4) into the model established in the step 3) to calculate the maximum cross-section contact area a of all the micro-convex bodies on the joint surfacel＝2.7586×10-5(ii) a Substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1), the static friction factor obtained in the step 4), the maximum cross-section contact area obtained in the step 5), the parameter values of the material and the critical cross-section contact surface into the step3) The built model calculates the normal contact rigidity K of the joint partn＝3.8679×108N/m and damping loss factor eta is 8.4395; finally, calculating the normal contact damping C of the joint part according to the established model and the external excitation frequency valuen＝1.0391×107N·s/m。
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled 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; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A fixed joint contact damping three-dimensional fractal prediction method is characterized by comprising the following steps:
1) measuring the micro-topography data of the contact surfaces, and obtaining characteristic fractal parameters of the two contact surfaces, namely fractal dimension and fractal roughness parameters, by a structure function method;
2) establishing a single microprotrusion contact model by combining a W-M function, and determining the deformation amount and the radius of the microprotrusion; obtaining contact parameters of a single microprotrusion body according to a Hertz theory, wherein the parameters comprise elastic critical deformation, energy storage, energy consumption, contact rigidity and contact load;
3) expanding the single micro-convex body contact model established in the step 2) to the whole mechanical joint surface by combining a contact area distribution density function, obtaining a calculation expression of normal load, normal stiffness, energy storage and energy consumption of the whole joint surface, and equating the normal contact dynamic characteristics of the fixed joint surface to a spring and a viscous damper to establish a joint surface normal contact damping model;
4) determining the static friction factor of the joint surface according to the existing method;
5) substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1) and the static friction factor, the normal load and the material parameter values obtained in the step 4) into the model built in the step 3) to calculate the maximum cross-sectional contact area of all the micro-convex bodies on the joint surface;
6) substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1), the static friction factor obtained in the step 4), the maximum cross-section contact area obtained in the step 5), the external excitation frequency and the parameter values of the material into the model built in the step 3) to calculate the normal contact damping of the joint part.
2. The fixed mechanical joint contact damping three-dimensional fractal prediction method as claimed in claim 1, wherein in step 1), the fractal dimension and fractal roughness at the joint surface are calculated by a structure function method, corresponding structure function values are calculated according to discrete signals of profile curves of different scales, the structure function is defined as the incremental variance of the rough surface profile function, and the expression is as follows:
Figure FDA0002967562290000011
where τ represents the data step in the horizontal direction, which can be any value, z (x) represents the measured value of the surface profile, DsThe fractal dimension number of the section outline on the three-dimensional rough surface is expressed, and the relation of the fractal dimension number and the fractal D of the three-dimensional rough surface is D ═ Ds+1, coefficient C satisfies the relation
Figure FDA0002967562290000012
Wherein gamma represents a second Euler integral, and G represents a fractal roughness parameter; the two sides of the equation of the formula (1) are simultaneously logarithmized
Figure FDA0002967562290000013
Therefore, log S (tau) is linear with log tau, and the fractal dimension can be determined by the slope k of the straight line according to the regression analysis of the fitted curve of the structural function valuessIs obtained by calculation, ks＝4-2DsFractal roughness can be obtained by the intercept B of a straight line, where B is logC. Fractal parameters of equivalent rough surfacesThe number can be obtained by the formula (2)
Se(τ)＝S1(τ)+S2(τ) (2)
Wherein S is1(τ) and S2(τ) structural functions representing the profile of the two rough surfaces, Se(τ) represents the structure function of the equivalent rough surface profile.
3. The method as claimed in claim 1, wherein in step 2), the improved W-M function describing the three-dimensional rough surface more accurately is combined to create a single spherical microprotrusion contact model as shown in FIG. 2. according to Hertz's theory of contact, when two rough surfaces of the bonding surface contact each other, the two rough surfaces are converted into an equivalent rough surface and a rigid smooth surface, and the contact deformation of the single microprotrusion on the equivalent rough surface is equal to
Figure FDA0002967562290000021
Wherein a ' is the cross-sectional area of the microprotrusion, the contact radius is r ', the relation between a ' and the real contact area a (the contact radius is r) of the microprotrusion is 2a, D is the fractal dimension of the rough surface,
Figure FDA0002967562290000022
wherein gamma is the spatial frequency of the random profile, the general value is 1.5, and G is a fractal roughness parameter; the radius of the single microprotrusion on the equivalent rough surface is
Figure FDA0002967562290000023
4. The fixed mechanical joint contact damping three-dimensional fractal prediction method as claimed in claim 1, wherein in step 2), single microprotrusion contact parameters are obtained according to hertz theory: elastic critical contact deformation amount of
Figure FDA0002967562290000024
Wherein σyFor the yield strength σ of the softer of the mutually contacting materialsy＝H/2.8；kμWhen mu is not less than 0 and not more than 0.3, k is a correction coefficient of frictionu1-0.228 μ; when mu is more than or equal to 0.3 and less than or equal to 0.9, ku＝0.932exp[-1.58(μ-0.3)]Wherein μ is the coefficient of friction; a resilient contact load of
Figure FDA0002967562290000025
Wherein E is the combined elastic modulus E ═ 1/[ (1-upsilon) of the two contact materials1 2)/E1+(1-υ2 2)/E2]，E1And E2Respectively, the modulus of elasticity, upsilon, of the two contact materials1And upsilon2Respectively the poisson's ratio of the two contact materials; plastic contact load of Pp2 pi HR δ, where H is the hardness of the softer of the two contact materials; only the resiliently deformed microprotrusions have normal stiffness by definition of stiffness
Figure FDA0002967562290000031
When the final state of the single microprotrusion body is elastic contact, the deformation amount of the equivalent microprotrusion body is always in the elastic deformation stage from 0 to delta, so that the stored elastic potential energy is
Figure FDA0002967562290000032
When the final state of the individual asperities is plastic contact, the amount of equivalent asperity deformation ranges from 0 to δcIn the elastic deformation phase, from deltacDelta. is in the plastic deformation phase, so that the energy consumed is
Figure FDA0002967562290000033
5. The method for predicting the contact damping three-dimensional fractal of the fixed mechanical joint part as claimed in claim 1, wherein in the step 3), the distribution function of the micro-contact cross-sectional area of the joint surface is
Figure FDA0002967562290000034
Wherein a'lThe largest cross-sectional contact area among all asperities.
6. The fixed mechanical joint contact damping three-dimensional fractal prediction method as claimed in claim 1, wherein in step 3), the normal load P of the whole joint surface is derivednNormal stiffness KnEnergy storage WeEnergy consumption WdIs a calculation expression of
Figure FDA0002967562290000035
Figure FDA0002967562290000036
Figure FDA0002967562290000037
Figure FDA0002967562290000038
Wherein, acIs the critical contact area of bonding surface microprotrusions, when delta/deltacWhen 1, the critical cross-sectional area is obtained
Figure FDA0002967562290000039
7. The fixed mechanical joint contact damping three-dimensional fractal prediction method as claimed in claim 1, wherein in step 3), a joint surface normal contact damping model is established;
the normal contact dynamic characteristics of the fixed joint surface are equivalent to spring and viscosityThe damper can be obtained as shown in FIG. 3
Figure FDA0002967562290000041
Wherein t is time; cnNormal contact damping for the joint surface; f (t) ═ Pncos (ω t) is a normal dynamic contact load acting on the joint surface, wherein ω is an angular frequency ω of 2 pi f, and f is an external excitation frequency; x (t) ═ Xncos(ωt-θn) Is the normal dynamic contact relative displacement between the joint surfaces, wherein thetanIs the initial phase; thus, η ═ Wd/We＝|fcx(t)|/|fkx(t)|＝Cnω/KnWhere η is damping loss factor, then
Figure FDA0002967562290000042
8. The three-dimensional fractal prediction method for the contact damping of the fixed mechanical joint part as claimed in claim 1, wherein in step 4), the joint surface static friction factor is determined according to the literature "Yidonghua, Zhang schang, Wenshuhua, cattle testimony, Chengyou, Languosheng, joint surface static friction factor three-dimensional fractal model [ J ] Taiyuan science university report 2013,34(06): 451-" 455 ".
9. The fixed mechanical joint contact damping three-dimensional fractal prediction method as claimed in claim 1, wherein in step 5), the maximum cross-sectional contact area of all micro-protrusions on the joint surface is calculated; substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1) and the static friction factor, the normal load and the material parameter values obtained in the step 4) into the model built in the step 3) to calculate the maximum cross-sectional contact area of all the micro-convex bodies on the joint surface.
10. The fixed mechanical joint contact damping three-dimensional fractal prediction method as claimed in claim 1, wherein in step 6), joint normal contact damping is calculated; substituting the characteristic fractal parameters of the equivalent rough surface obtained in the step 1), the static friction factor obtained in the step 4), the maximum cross-section contact area obtained in the step 5), the external excitation frequency and the parameter values of the material into the model built in the step 3), and calculating the normal contact damping of the joint part.
CN202110256490.1A 2021-03-09 2021-03-09 Fixed joint contact damping three-dimensional fractal prediction method Pending CN112926210A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113552062A (en) * 2021-07-22 2021-10-26 成都理工大学 Rock crack surface three-dimensional morphology representation-based crack surface friction coefficient calculation method
CN113567744A (en) * 2021-07-27 2021-10-29 浙江理工大学 Method for calculating contact resistance of electric connector under storage condition

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113552062A (en) * 2021-07-22 2021-10-26 成都理工大学 Rock crack surface three-dimensional morphology representation-based crack surface friction coefficient calculation method
CN113552062B (en) * 2021-07-22 2022-07-29 成都理工大学 Rock crack surface three-dimensional morphology representation-based crack surface friction coefficient calculation method
CN113567744A (en) * 2021-07-27 2021-10-29 浙江理工大学 Method for calculating contact resistance of electric connector under storage condition
CN113567744B (en) * 2021-07-27 2024-02-27 浙江理工大学 Method for calculating contact resistance of electric connector under storage condition

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