CN106709207B - Method for determining normal contact stiffness of loaded combination part by considering interaction influence of asperities on rough surface - Google Patents
Method for determining normal contact stiffness of loaded combination part by considering interaction influence of asperities on rough surface Download PDFInfo
- Publication number
- CN106709207B CN106709207B CN201710029431.4A CN201710029431A CN106709207B CN 106709207 B CN106709207 B CN 106709207B CN 201710029431 A CN201710029431 A CN 201710029431A CN 106709207 B CN106709207 B CN 106709207B
- Authority
- CN
- China
- Prior art keywords
- contact
- fractal
- normal
- rough surface
- stiffness
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 230000003993 interaction Effects 0.000 title claims abstract description 30
- 238000000034 method Methods 0.000 title claims abstract description 29
- 239000000463 material Substances 0.000 claims abstract description 26
- 238000004364 calculation method Methods 0.000 claims abstract description 11
- 238000012876 topography Methods 0.000 claims abstract description 10
- 238000011160 research Methods 0.000 claims description 10
- 238000005315 distribution function Methods 0.000 claims description 9
- 230000000694 effects Effects 0.000 claims description 9
- 238000005070 sampling Methods 0.000 claims description 8
- 238000006073 displacement reaction Methods 0.000 claims description 7
- 238000000611 regression analysis Methods 0.000 claims description 6
- 238000012512 characterization method Methods 0.000 claims description 5
- 230000008901 benefit Effects 0.000 abstract description 4
- 230000007547 defect Effects 0.000 abstract description 2
- 238000005516 engineering process Methods 0.000 description 3
- 238000003754 machining Methods 0.000 description 3
- 230000009471 action Effects 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
- 238000007619 statistical method Methods 0.000 description 2
- 230000008859 change Effects 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000005489 elastic deformation Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000012417 linear regression Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000000877 morphologic effect Effects 0.000 description 1
- 239000007779 soft material Substances 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000013179 statistical model Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012800 visualization Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Abstract
The invention provides a method for determining normal contact stiffness of a loaded joint part by considering interaction influence of asperities on a rough surface, which comprises the following steps: measuring the micro-topography data of the contact surface, obtaining the micro-profile data of the contact surface at the joint part by using a three-dimensional profile measuring instrument, extracting the position coordinates of the vertexes of the micro-protrusions in the length direction, and simulating the micro-protrusion form of the rough surface; establishing a relation between the normal load and the contact stiffness; calculating fractal parameters of the contact surface, and performing theoretical calculation on the extracted data by using a structural function method to obtain the fractal dimension and the scale coefficient of the surface; and finally calculating the normal contact stiffness of the joint part by substituting the parameter values of the materials according to the steps. The invention provides a novel method for determining the normal contact stiffness of a joint surface, overcomes the defect that the calculation result of the traditional method based on the fractal theory is inaccurate under the heavy load condition, and has the advantages of strong reliability, close to the actual condition, small calculation amount, improved calculation efficiency and the like.
Description
Technical Field
The invention relates to a method for determining normal contact stiffness of a mechanical joint, in particular to a method for determining normal contact stiffness of a loaded joint by considering interaction influence of asperities on a rough surface.
Background
The increasing development of industrial technology puts higher demands on the precision and integration of machining equipment, and the further improvement of machining precision does not depart from the wide application of mechanical coupling technology. The contact rigidity of the mechanical joint part is an important component of the overall rigidity of the mechanical structure, and has a very significant influence on the dynamic characteristics of large-scale mechanical equipment. The study of foreign scholars shows that in a common lathe, the deformation of a slide carriage and a tool rest accounts for 40 percent of the total deformation of the lathe, and the deformation ratio of a guide rail joint part is as high as 30 percent; meanwhile, for a single-arm double housing planer, when the joint surface of the tool rest and the upright post is assumed to be completely rigid, the integral rigidity of the planer can be improved by even 39%. Therefore, in order to improve the working accuracy of the machining equipment, it is necessary to predict the stiffness characteristic of the joint portion at the design stage. Theoretical calculation of the rigidity of the joint part and experimental research technology appear.
For the research of the contact rigidity of the joint surface, on one hand, part of researchers establish a statistical microcontact model of the mechanical joint surface on the basis of the hertzian contact theory from the point of statistics. The research finds that the height distribution of the rough surface microprotrusions is approximate to Gaussian distribution, and provides a solid theoretical basis for the research of the dynamic characteristics of the mechanical joint; on the other hand, a learner establishes a fractal contact model based on a fractal function representing a rough surface profile curve and an island area distribution function, the model divides the contact state of the rough surface into an elastic deformation stage and a plastic deformation stage, researches are carried out from the angle of a functional relation between a normal load and a contact area, and the influence of the resolution of a measuring instrument and the length of a sample is avoided on the analysis result.
Although the research scholars at home and abroad continuously make efforts, the normal contact rigidity model of the joint part is always developed and perfected. However, when the mechanical joint is subjected to a large load, a large error still exists in calculating the contact rigidity value by using the existing rough surface contact model. The main reasons for this are: when the mechanical joint part bears a large load, the microprotrusions on the rough surface are seriously deformed, and the assumption that the deformation action of the microprotrusions in the fractal contact model is independent from each other and the assumption that the curvature radius of the peaks of the microprotrusions on the rough surface in the statistical model is the same are not true. In fact, in the case where the mechanical joint is subjected to a large normal load, the interaction force between the asperities of the contact surface dominates and cannot be ignored. Therefore, under heavy load, the joint contact stiffness cannot be accurately calculated using the foregoing theoretical method.
Disclosure of Invention
In light of the above-identified problems, a method for determining the normal contact stiffness of a loaded joint is provided that takes into account the effects of asperity interactions. The method mainly improves the accuracy of the contact model by measuring the micro-topography data of the contact surface, establishing the relation between the normal load and the contact rigidity, calculating the fractal parameter of the contact surface and calculating the normal contact rigidity of the joint part.
The technical means adopted by the invention are as follows:
a method of determining the normal contact stiffness of a loaded joint taking into account the effects of asperity interactions, comprising the steps of:
s1, measuring the microscopic topography data of the contact surface, obtaining the microscopic contour data of the contact surface at the joint part by using a three-dimensional contour measuring instrument, extracting the position coordinates of the vertexes of the microprotrusions in the length direction, and simulating the microprotrusion form of the rough surface;
s2, establishing a relationship between the normal load and the contact stiffness, specifically including,
s21, establishing a relation between a normal load and a contact area, converting two joint surfaces of the loaded joint part into a rigid smooth plane to be in contact with a rough plane, and considering the deformation caused by elastic factors after the interaction of the microprotrusions; according to the Hertz contact theory, the total load of the contact surface can be obtained after the curvature radius and the elastic-plastic deformation of the micro convex body are comprehensively considered, and a fractal contact model is obtained;
s22, establishing a normal contact stiffness model, and deducing the total stiffness value of the bonding surface of the microprotrusions according to the load deformation function of the microprotrusions;
s3, calculating fractal parameters of the contact surface, theoretically calculating the data extracted in the step S1 by using a structure function method to obtain the fractal dimension and the scale coefficient of the surface, specifically comprising,
s31, establishing a structure function, and defining the increment variance of the rough surface profile characterization function as the structure function;
s32, obtaining surface fractal parameters, calculating corresponding structure function values according to discrete signals of the contour curve in different scales, and performing regression analysis on a fitting curve to obtain a fractal dimension and a scale coefficient of the determined surface;
s33, the joint surface is equivalent, the mechanical joint surface is composed of two rough surfaces which are contacted with each other, and the contact of the two mechanical surfaces is equivalent to the contact between an elastic rough surface and a rigid plane in consideration of the research convenience and scientificity;
and S4, substituting the material parameter values into the finally calculated normal contact stiffness of the joint part according to the steps.
Further, in step S21, the amount of deformation due to the elastic factor after the influence of the microprotrusion interaction is taken into consideration as z-dn, as seen from the fractal contact model,
z+δ‘-dn＝δ，
then
z-dn＝δ-δ‘，
According to the Hertz contact theory, the total load of the contact surface can be obtained by comprehensively considering the curvature radius of the micro-convex body and the elastic-plastic deformation:
wherein, P is normal load; d is the fractal dimension of the rough surface; g is a scale coefficient; e is the combined modulus of elasticity of the two contact surfaces: (
E1、E2、v1、v2Respectively representing the elastic modulus and the Poisson ratio of materials forming the two parts of the combined surface), wherein a is the contact area of a contact point; a iscIs the critical contact area (a)c＝G2(2E/H)2/(D-1))；alThe maximum contact point area; sigmayThe yield strength of the softer material in the two contact surfaces; kcTo compareHardness H and yield strength sigma of soft materialyCorrelation coefficient (H ═ K)cσy)；
After substituting the distribution function n (a) of the microprotrusions, the integral can obtain a fractal contact model considering the interaction influence between the microprotrusions:
further, in step S22, substituting and deriving the relationship of the dimple radius to contact area, an expression for the individual dimple contact stiffness k can be derived:
substituting the micro-convex body distribution function to obtain a total rigidity value K of the joint surface:
namely, it is
Further, in step S31, the expression of the structure function is:
s(τ)＝<[Z(x+τ)-Z(x)]2>，
wherein, z (x) is a rough surface profile characterization function, τ is an arbitrary selected value of data interval, x is a profile displacement coordinate, and the discretized structural function expression is as follows:
wherein, Δ L is the sampling interval, L is the sampling length, and N is the number of acquisition points.
Further, in step S32, specifically, corresponding structure functions are calculated according to the discrete signals of the profile curves at different scales τThe values of each discrete value are plotted in log s-lg tau log coordinates, lgS (tau) and lg tau are found to be in linear correlation, and the slope k of a fitting curve can be obtained by regression analysissSatisfies the following conditions:
ks＝4-2D，
and the intercept B thereof satisfies:
B＝lg CG2(D-1)，
for a certain surface constant C:
and gamma is a constant larger than 1, and for a random surface which obeys normal distribution, the fractal dimension and the scale coefficient of a determined surface can be obtained by taking gamma as 1.5.
Further, in step S33, the equivalent elastic rough surface structure function is as follows:
s(τ)＝s′(τ)+s″(τ)；
namely, it is
In the formula, s '(tau) and s' (tau) respectively represent the structural functions of the two rough contact surfaces; d1、D2Representing fractal dimensions, G, of two rough surface profiles1、G2Representing the scale factor, C, of the profile of two rough surfaces1、C2And obtaining the fractal parameters of the equivalent elastic rough surface for constants related to the respective fractal parameters of the two surfaces.
Further, step S4 specifically includes,
s41, substituting the material parameter value and the fractal parameter value of the equivalent elastic rough surface calculated in the step S33 into the critical contact area formula in the step S21 to obtain the critical contact area ac；
S42, calculating the maximum contact area, and substituting the normal load, the critical contact area, the fractal parameter of the equivalent elastic rough surface and the material parameter born by the joint partStep S21, the fractal contact model considering the interaction effect between the microprotrusions is proposed to obtain the maximum contact area al；
S43, calculating the normal contact stiffness, and calculating the parameters of the two rough surface materials, the fractal parameter value of the equivalent elastic rough surface calculated in the step S3 and the critical contact area acMaximum contact area alThe normal contact stiffness of the mechanical joint can be calculated by substituting the contact stiffness model proposed in step S2.
Compared with the existing method for determining the contact rigidity of the joint surface, the method has the following advantages that:
1. the method provides a new method for determining the normal contact stiffness of the joint surface, fully considers the influence of the interaction phenomenon between the asperities on the contact stiffness of the rough surface, and overcomes the defect that the calculation result is inaccurate under the heavy load condition in the traditional method based on the fractal theory.
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 micro-convex body, has the advantage of scale independence, has the calculation accuracy which is not influenced by the resolution of the measuring instrument, and has wider application range and higher reliability compared with the original statistical method.
3. Compared with the traditional finite element method, the method comprehensively considers the profile characteristics of the rough surface, is closer to the actual condition, has smaller calculated amount and stronger operability, and improves the 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 needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic view of the contact deformation of a loaded rough surface.
Fig. 2 shows the surface topography of the top surface 1 in an embodiment of the invention.
Fig. 3 shows the surface topography of the lower surface 2 in an embodiment of the invention.
Fig. 4 is a graph of contact stiffness versus normal contact load as proposed by the present invention.
FIG. 5 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 objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a contact deformation diagram of the microprotrusions studied in accordance with the present invention is equivalent to a contact of an ideal rigid surface with a complex rough surface. As can be seen in the figure, δ represents the distance between the peak of the asperity of the rough surface before loading and the mean plane of the asperity after loading, δ' represents the distance between the mean plane of the asperity before and after loading, z is the distance between the peak of the asperity before loading and the mean plane, d is the distance between the mean plane of the asperity before loading, and dn is the distance between the mean plane of the asperity after loading.
Referring to fig. 2 and fig. 3, there are shown local micro-topography maps in μm for two rough contact surfaces of a mechanical joint according to an embodiment of the present invention, respectively.
FIG. 4 is a graph showing the relationship between normal contact stiffness and normal contact load for different surfaces in a non-dimensionalized manner, taking into account the influence of the interaction between asperities on the contact surface.
Fig. 5 shows a fitting curve obtained by performing linear regression analysis on discrete points of two contact surfaces in a log-log coordinate system according to the discrete form of the structural function of the two contact surfaces in an embodiment of the invention without a scale interval.
The invention is described in detail below with reference to the attached drawing figures:
s1, measuring the micro-topography data of the contact surface
And acquiring microscopic contour data of the contact surface at the joint part by using a three-dimensional contour measuring instrument, extracting position coordinates of the vertexes of the microprotrusions in the length direction, and simulating the microprotrusion form of the rough surface in MATLAB software. The surface topography post-processed by numerical software in this example is shown in fig. 2 and 3.
S2, establishing the relation between the normal load and the contact rigidity
S21, establishing the relation between the normal load and the contact area
As shown in FIG. 1, the two bonding surfaces of the loaded bonding portion can be converted into a rigid smooth surface contacting a rough surface. The amount of deformation caused by elastic factors after considering the influence of microprotrusion interaction is z-dn.
For the convenience of research, the conventional fractal contact model ignores the influence of the interaction between the microprotrusions, and it can be seen from fig. 1 that the approximation z-d is δ assuming that the average plane of the microprotrusions is constant. In practice, however, the average plane of the asperities is shifted by δ 'due to the interaction between the asperities, so that the average plane of the asperities is shifted by δ' as a whole, and the height z of the asperities from the average plane to the peak is an independent morphological parameter of the asperities and does not change with the decrease in the average plane of the asperities, so that the amount of deformation caused by the elastic factor is z-dn, which is not z-d proposed in the conventional fractal contact model.
From FIG. 1, it can be seen that
z+δ‘-dn＝δ，
So that there are
z-dn＝δ-δ‘，
According to the theory of elasticity of Ferussac, the average planar deformation of the microprotrusions in Hertz contact due to the deforming action of the microprotrusions is
The total displacement of the rough surface after loading is therefore:
wherein P is the normal load and E is the combined modulus of elasticity of the two contact surfaces: (
E1、E2、v1、v2Respectively, the modulus of elasticity and the poisson's ratio of the materials constituting the two parts of the bonding surface).
Further, it is possible to obtain:
while the microprotrusion contact area radius r may be expressed as:
the functional relationship between the radius R of the contact area of the microprotrusions and the radius R of curvature of the microprotrusions, and the normal displacement δ can be obtained:
r2＝Rδ，
the functional relationship between the contact area a of the microprotrusions and the normal displacement δ can be derived from the relationship between the contact area a of the microprotrusions and the contact radius r:
a＝πr2＝πRδ，
further, it is found that:
obtaining the relation between the normal load and the contact area of the microprotrusions:
according to the classical typing contact theory, the relationship between the profile height and the coordinates of the sampling position can be expressed by a function z (x) with self-affine property:
where x represents the sampling position coordinates and z (x) is the profile height of the matte surface.
The radius of curvature of the microprotrusions can thus be found:
in the formula, D is the fractal dimension of the rough surface, and G is the scale coefficient.
Substituting the curvature radius expression into a normal load and micro-convex body contact area relational expression to obtain a contact rigidity model when the rough surface is elastically deformed after consideration of the interaction factors of the micro-convex bodies:
according to the traditional fractal contact model, the relationship between the load and the contact area when the rough surface is plastically deformed is as follows:
P＝Kcσya，
in the formula, KcHardness H and yield strength sigma of softer materialyCorrelation coefficient (H ═ K)cσy)。
After the elastic-plastic deformation factor is comprehensively considered, the relationship between the normal load and the contact area can be expressed as follows:
wherein E is the combined modulus of elasticity of the two contact surfaces: (
E1、E2、v1、v2Respectively representing the elastic modulus and the Poisson ratio of materials forming the two parts of the combined surface), wherein a is the contact area of a contact point;acis the critical contact area (a)c＝G2(2E/H)2/(D-1))；alThe maximum contact point area.
According to the fractal contact theory, the distribution function of the area of the microprotrusions can be expressed as:
after substituting the distribution function of the microprotrusions into the relational expression of the normal load and the contact area of the microprotrusions, integrating to obtain a fractal contact model considering the interaction influence among the microprotrusions:
s22, establishing a normal contact stiffness model
According to the derived relationship between normal load and normal displacement:
derivation can yield the relationship between the stiffness and deflection of a single microprotrusion:
the above formula can be expressed as:
whereas for normal load P the following relationship exists:
therefore, the rigidity deformation relation of the single microprotrusion body can meet the following requirements:
the total stiffness value of the whole joint surface can be obtained by integration:
substituting the distribution function of the area of the micro convex body to obtain:
after considering the interaction effect between the microprotrusions, the relationship between the normal load and the contact stiffness of the contact surfaces of different microtopography after dimensionless is shown in FIG. 4.
S3, determining the fractal parameter of the joint surface
And (4) theoretically calculating the data extracted in the step (S1) by using a structure function method so as to obtain the fractal dimension and the scale coefficient of the surface.
S31, establishing a structure function
The incremental variance of the rough surface profile characterization function z (x) is typically defined as a structure function, expressed as:
s(τ)＝<[Z(x+τ)-Z(x)]2>＝CG2(D-1)τ(4-2D)，
where τ is an arbitrarily selected value of the data interval and x is the profile displacement coordinate.
And then acquiring data of the peak position of the acquired fixed-direction microprotrusions by using a surface profile measuring instrument, substituting the acquired data into the structural function expression, and finishing the calculation of the discretization structural function of the specific surface.
And the discretized structural function expression is as follows:
wherein Δ L is the sampling interval, L is the sampling length, and N is the number of acquisition points.
S32, obtaining surface fractal parameters
Corresponding structure function values are calculated according to discrete signals of the profile curve with different scales tau, each discrete value is drawn in lg s-lg tau double logarithmic coordinates, lgS (tau) and lg tau are found to be in linear correlation, and the slope k of a fitting curve can be obtained through regression analysissSatisfies the following conditions:
ks＝4-2D，
and the intercept B thereof satisfies:
B＝lgCG2(D-1)，
for a certain rough surface, the constant C can be expressed as:
for the second euler integral, γ is a constant greater than 1, and for a random surface that follows a normal distribution, γ is taken to be 1.5.
The fractal dimension and the scale factor of the two contact surfaces can be obtained thereby.
S33, equivalent of joint surface
With respect to the mechanical rough surface fractal contact model established in step S21, the specific contact form and deformation between the peaks and valleys on the topography of the two contacting rough surfaces are difficult to predict, and therefore, considering the convenience and scientificity of research, the contact of two mechanical surfaces is equivalent to the contact between one elastic rough surface and one rigid plane.
The equivalent elastic rough surface structure function is as follows:
s(τ)＝s′(τ)+s″(τ)，
namely, it is
In the formula, s '(tau) and s' (tau) respectively represent the structural functions of the two rough contact surfaces; d1、D2Representing fractal dimensions, G, of two rough surface profiles1、G2Representing the scale factor, C, of the profile of two rough surfaces1、C2Is prepared by reacting withAnd (3) constants relevant to respective fractal parameters of the two surfaces.
The fractal dimension and the scale coefficient of the surface profile of the equivalent elastic rough surface can be obtained through the formula.
S4, calculating the normal contact stiffness of the joint part
S41, calculating the critical contact area
Substituting the material parameter value and the fractal parameter value of the equivalent elastic rough surface calculated in the step S3 into the critical contact area formula in the step S2 to obtain the critical contact area ac。
S42, calculating the maximum contact point area
Substituting the normal load, critical contact area, fractal parameter of the elastic rough surface and material parameter of the joint into the fractal contact model considering the interaction effect between the microprotrusions in step S21 to obtain the maximum contact area al。
S43, determining the normal contact stiffness
The parameters of the two rough surface materials, the fractal parameter value of the equivalent elastic rough surface calculated in the step S3 and the critical contact area acMaximum contact area alThe normal contact stiffness of the mechanical joint can be calculated by substituting the contact stiffness model proposed in step S2.
Examples
Taking two different rough surfaces as an example, the micro surface morphologies of the local areas of the two rough surfaces after the numerical software simulation are respectively shown in fig. 2 and fig. 3. The material parameters of the contact surface 1 are as follows: modulus of elasticity E1130Gpa, poisson's ratio v10.3 yield strength σy1300MPa, hardness H11200 MPa; the material parameters of the contact surface 2 are as follows: modulus of elasticity E2130Gpa, poisson's ratio v20.3 yield strength σy2260MPa, hardness H2740 MPa. Normal load P applied to the joint portion is 1 × 104Pa。
The number of the acquisition points is set to be 500, and the acquired profile height data is substituted into a discrete structural function expression to draw the two contact surfacesThe discretization of the structural function image and the regression analysis in the log-log coordinates can obtain the slope and intercept of the fitted curve, and the visualization result is shown in fig. 5. Further, according to step S32, it is found that the fractal dimension of the two contact surfaces is 1.207 and the scale factor of the surface 1 is 5.0X 10-17m, face 2 has a scale factor of 5.7X 10-19m。
From step S33, it can be seen that:
D＝D1＝D2，
then there are:
substituting the fractal parameters of two contact surfaces can obtain the fractal dimension D of 1.207, G7.109 × 10-17m, thereby equating the problem of two rough surface contact as an ideal rigid smooth surface in contact with a complex rough surface.
And substituting the normal load, the fractal parameter values and the material parameter values into the contact stiffness model proposed in the step S2 to obtain the contact stiffness of the joint surface.
Wherein for critical contact area acSatisfies the following conditions:
ac＝G2(2E/H)2/(D-1)，
substituting equivalent fractal parameter and material parameter to calculate the critical contact area ac＝1.976×10-8m2。
And for the maximum contact area alSubstituting the normal load, the critical contact area, the hardness coefficient, the equivalent fractal parameter of the rough surface profile and the material parameter into the fractal contact model in the step S21 to calculate the maximum contact area al＝1.980×10-5m2。
The normal contact stiffness K of the bonding surface of this example was determined to be 3.051 × 109N/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 (6)
1. A method of determining the normal contact stiffness of a loaded joint taking into account the effects of asperity interactions, comprising the steps of:
s1, measuring the microscopic topography data of the contact surface, obtaining the microscopic contour data of the contact surface at the joint part by using a three-dimensional contour measuring instrument, extracting the position coordinates of the vertexes of the microprotrusions in the length direction, and simulating the microprotrusion form of the rough surface;
s2, establishing a relationship between the normal load and the contact stiffness, specifically including,
s21, establishing a relation between a normal load and a contact area, converting two joint surfaces of the loaded joint part into a rigid smooth plane to be in contact with a rough plane, and considering the deformation caused by elastic factors after the interaction of the microprotrusions; according to the Hertz contact theory, the total load of the contact surface can be obtained after the curvature radius and the elastic-plastic deformation of the micro convex body are comprehensively considered, and a fractal contact model is obtained;
s22, establishing a normal contact stiffness model, and deducing the total stiffness value of the bonding surface of the microprotrusions according to the load deformation function of the microprotrusions;
s3, calculating fractal parameters of the contact surface, theoretically calculating the data extracted in the step S1 by using a structure function method to obtain the fractal dimension and the scale coefficient of the surface, specifically comprising,
s31, establishing a structure function, and defining the increment variance of the rough surface profile characterization function as the structure function;
s32, obtaining surface fractal parameters, calculating corresponding structure function values according to discrete signals of the contour curve in different scales, and performing regression analysis on a fitting curve to obtain a fractal dimension and a scale coefficient of the determined surface;
s33, the joint surface is equivalent, the mechanical joint surface is composed of two rough surfaces which are contacted with each other, and the contact of the two mechanical surfaces is equivalent to the contact between an elastic rough surface and a rigid plane in consideration of the research convenience and scientificity;
s4, substituting the parameter values of the materials into the parameters of the final calculation of the normal contact stiffness of the joint part according to the steps;
in step S21, the amount of deformation due to the elastic factor after considering the influence of the microprotrusion interaction is z-dn, as seen from the fractal contact model,
z+δ‘-dn＝δ，
then
z-dn＝δ-δ‘，
Wherein δ represents the distance between the peak of the microprotrusion of the rough surface before loading and the rigid plane after loading, δ' represents the distance between the average planes of the microprotrusions before and after loading, z is the distance between the peak of the microprotrusion before loading and the average plane, d is the distance between the rigid plane and the average plane of the microprotrusion before loading, and dn is the distance between the rigid plane and the average plane of the microprotrusion after loading;
according to the Hertz contact theory, the total load of the contact surface can be obtained by comprehensively considering the curvature radius of the micro-convex body and the elastic-plastic deformation:
wherein, P is normal load; d is the fractal dimension of the rough surface; g is a scale coefficient; e is the combined modulus of elasticity of the two contact surfaces
E1、E2、v1、v2Respectively representing the elastic modulus and the Poisson ratio of materials forming the two parts of the combined surface, wherein a is the contact area of a contact point; a iscIs the critical contact area ac＝G2(2E/H)2/(D-1)；alThe maximum contact point area; sigmayIs a softer material in two contact surfacesThe yield strength of the material; kcHardness H and yield strength sigma of softer materialyIs equal to Kcσy(ii) a n (a) is a microprotrusion distribution function;
after substituting the distribution function n (a) of the microprotrusions, the integral can obtain a fractal contact model considering the interaction influence between the microprotrusions:
2. the method for determining the normal contact stiffness of a loaded joint considering the interaction effect of asperities on a rough surface as recited in claim 1, wherein in step S22, the relationship of asperity radius to contact area is substituted and derived to derive the expression for the contact stiffness k of a single asperity:
substituting the micro-convex body distribution function to obtain a total rigidity value K of the joint surface:
namely, it is
3. The method for determining the normal contact stiffness of a loaded joint considering the interaction effect of asperities of claim 2 wherein in step S31 the expression of the structure function is:
s(τ)＝<[Z(x+τ)-Z(x)]2>，
wherein, z (x) is a rough surface profile characterization function, τ is an arbitrary selected value of data interval, x is a profile displacement coordinate, and the discretized structural function expression is as follows:
wherein, Δ L is the sampling interval, L is the sampling length, N is the number of acquisition points, and i is the initial counting unit of the calculation formula.
4. The method for determining the normal contact stiffness of a loaded joint in consideration of the interaction effect of asperities on a rough surface, as claimed in claim 3, wherein in step S32, the values of the structural functions are calculated from the discrete signals of the profile curve at different scales τ, and each discrete value is plotted in lg S-lg τ log coordinates, wherein lgS (τ) is found to be linearly related to lg τ, and the slope k of the fitted curve is obtained by regression analysissSatisfies the following conditions:
ks＝4-2D，
and the intercept B thereof satisfies:
B＝lgCG2(D-1)，
for a certain surface constant C:
and gamma is a constant larger than 1, and for a random surface which obeys normal distribution, the fractal dimension and the scale coefficient of a determined surface can be obtained by taking gamma as 1.5.
5. The method for determining the normal contact stiffness of a loaded joint considering the interaction between asperities as recited in claim 4, wherein in step S33, the equivalent elastic asperity structure function is as follows:
s(τ)＝s′(τ)+s″(τ)；
namely, it is
In the formula, s '(tau) and s' (tau) respectively represent the structural functions of the two rough contact surfaces; d1、D2Representing fractal dimensions, G, of two rough surface profiles1、G2Representing the scale factor, C, of the profile of two rough surfaces1、C2And obtaining the fractal parameters of the equivalent elastic rough surface for constants related to the respective fractal parameters of the two surfaces.
6. The method for determining the normal contact stiffness of a loaded joint considering the influence of asperity interactions according to claim 5, wherein step S4 specifically comprises,
s41, substituting the material parameter value and the fractal parameter value of the equivalent elastic rough surface calculated in the step S33 into the critical contact area formula in the step S21 to obtain the critical contact area ac；
S42, calculating the maximum contact area, substituting the normal load, the critical contact area, the fractal parameter of the equivalent elastic rough surface and the material parameter born by the joint into the fractal contact model considering the interaction influence between the microprotrusions, which is put forward in the step S21, to obtain the maximum contact area al；
S43, calculating the normal contact stiffness, and calculating the parameters of the two rough surface materials, the fractal parameter value of the equivalent elastic rough surface calculated in the step S3 and the critical contact area acMaximum contact area alThe normal contact stiffness of the mechanical joint can be calculated by substituting the contact stiffness model proposed in step S2.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710029431.4A CN106709207B (en) | 2017-01-16 | 2017-01-16 | Method for determining normal contact stiffness of loaded combination part by considering interaction influence of asperities on rough surface |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710029431.4A CN106709207B (en) | 2017-01-16 | 2017-01-16 | Method for determining normal contact stiffness of loaded combination part by considering interaction influence of asperities on rough surface |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106709207A CN106709207A (en) | 2017-05-24 |
| CN106709207B true CN106709207B (en) | 2020-06-16 |
Family
ID=58907520
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710029431.4A Expired - Fee Related CN106709207B (en) | 2017-01-16 | 2017-01-16 | Method for determining normal contact stiffness of loaded combination part by considering interaction influence of asperities on rough surface |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106709207B (en) |
Families Citing this family (29)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107423497B (en) * | 2017-07-12 | 2018-07-24 | 中南大学 | A kind of rough surface micro-bulge approximating method and system |
| CN108052756B (en) * | 2017-12-22 | 2021-04-06 | 太原科技大学 | Method for determining joint surface contact parameters based on FFT |
| CN108304641B (en) * | 2018-01-29 | 2021-06-25 | 北京航空航天大学 | Design method for heat resistance of high-energy-capacity dry friction element |
| CN108829909A (en) * | 2018-04-12 | 2018-11-16 | 西安建筑科技大学 | A kind of faying face modeling method considering rough surface percent ripple and micro-bulge interaction |
| CN108829915A (en) * | 2018-04-24 | 2018-11-16 | 武汉科技大学 | A kind of evaluation method of coarse aggregates surface texture roughness |
| CN108613922B (en) * | 2018-04-26 | 2021-02-19 | 东北大学 | Bonding surface static friction factor three-dimensional fractal prediction method considering adhesive force |
| CN108846154B (en) * | 2018-04-26 | 2022-04-26 | 东北大学 | Three-dimensional fractal prediction method for thermal contact resistance of joint surface by considering deformation of microprotrusion matrix |
| CN109408909B (en) * | 2018-09-30 | 2022-12-13 | 中南大学 | Three-dimensional rough surface micro-convex body fitting method |
| CN109446655B (en) * | 2018-10-30 | 2023-06-13 | 东北大学 | Three-dimensional fractal prediction method for normal contact stiffness of double fractal bonding surface |
| CN109829224B (en) * | 2019-01-25 | 2020-08-11 | 北京科技大学 | Method for calculating tangential contact stiffness of rough elastic interface |
| CN109960883B (en) * | 2019-03-28 | 2023-04-25 | 北京工业大学 | Fractal theory-based contact stiffness calculation method for inclined angle-containing joint surface |
| CN110083960B (en) * | 2019-05-06 | 2023-04-07 | 沈阳建筑大学 | Design method of spring contact of area array packaging central processing unit interface |
| CN110328575B (en) * | 2019-05-09 | 2020-07-28 | 东北大学 | Prediction method for polished surface morphology of optical hard and brittle material |
| CN110427656B (en) * | 2019-07-10 | 2021-07-27 | 清华大学 | Split type TBM cutter head joint characteristic scale measuring method and system |
| CN110532669B (en) * | 2019-08-26 | 2022-09-13 | 西安建筑科技大学 | Method for modeling contact stiffness of mechanical joint surface |
| CN110631520B (en) * | 2019-10-09 | 2023-08-01 | 青岛科信信息科技有限公司 | Method for measuring roughness of soft sticky body by improved non-contact optical interferometry |
| CN111177842B (en) * | 2020-01-03 | 2022-09-09 | 中铁第四勘察设计院集团有限公司 | Method and device for determining dynamic characteristics of shield tunnel segment contact surface and storage medium |
| CN111523259B (en) * | 2020-03-09 | 2023-03-21 | 北京航空航天大学 | Scanning electron microscope structure modeling method based on joint surface virtual material method |
| CN111353234B (en) * | 2020-03-11 | 2023-03-28 | 西安建筑科技大学 | Method and system for constructing rough surface contact model considering micro-convex body interaction |
| CN111382481B (en) * | 2020-03-11 | 2024-02-13 | 深圳万知达科技有限公司 | Modeling method and system for normal stiffness of joint surface by considering interaction of microprotrusions |
| CN111781134B (en) * | 2020-07-09 | 2023-03-21 | 中国人民解放军国防科技大学 | Measuring method and measuring system for normal contact parameter of joint surface |
| CN112257193B (en) * | 2020-09-27 | 2023-09-26 | 沈阳建筑大学 | Characterization method of curved surface texture |
| CN112395754B (en) * | 2020-11-12 | 2023-02-28 | 清华大学 | Dynamic weakening prediction method for rigidity of mechanical connection structure joint surface |
| CN112597608B (en) * | 2020-12-25 | 2023-03-14 | 清华大学 | Mechanical joint surface tangent-normal coupling mechanical modeling method |
| CN112926131B (en) * | 2021-01-26 | 2022-11-29 | 中车青岛四方机车车辆股份有限公司 | Method and device for determining pneumatic load of vehicle |
| CN112949123B (en) * | 2021-02-06 | 2022-11-11 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Method for establishing relation between point contact force load and deformation by considering coating influence |
| CN113190926B (en) * | 2021-04-20 | 2023-02-10 | 西安理工大学 | Modeling method for microprotrusion contact containing nonmetallic inclusions |
| CN114925498B (en) * | 2022-04-24 | 2023-05-05 | 西南交通大学 | Rapid calculation method for normal load of three-dimensional elastoplastic wheel track by considering curvature transition |
| CN114894115B (en) * | 2022-05-16 | 2024-04-02 | 西安交通大学 | Optical in-situ measurement method for rough surface indentation depth |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102608167A (en) * | 2012-02-20 | 2012-07-25 | 西安交通大学 | Method for determining normal contact stiffness of fixed joint surface |
| EP2748746A1 (en) * | 2011-08-25 | 2014-07-02 | The Government of the United States of America as represented by the Secretary of the Navy | An algorithm and a method for characterizing surfaces with fractal nature |
-
2017
- 2017-01-16 CN CN201710029431.4A patent/CN106709207B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2748746A1 (en) * | 2011-08-25 | 2014-07-02 | The Government of the United States of America as represented by the Secretary of the Navy | An algorithm and a method for characterizing surfaces with fractal nature |
| CN102608167A (en) * | 2012-02-20 | 2012-07-25 | 西安交通大学 | Method for determining normal contact stiffness of fixed joint surface |
Non-Patent Citations (3)
| Title |
|---|
| 基于分形几何与接触力学理论的结合面法向接触刚度计算模型;杨红平等;《机械工程学报》;20130105;第102-106页 * |
| 基于分形理论的结合面接触特性分析;王鹏程;《中国优秀硕士学位论文全文数据库 工程科技Ⅰ辑》;20160115;第B022-382页 * |
| 基于基底长度的粗糙表面分形接触模型的构建与分析;丁雪兴等;《摩擦学学报》;20140731;第341-346页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106709207A (en) | 2017-05-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106709207B (en) | Method for determining normal contact stiffness of loaded combination part by considering interaction influence of asperities on rough surface | |
| CN103926156B (en) | A kind of three-dimensional rock structural face shears mechanical behavior multifractal appraisal procedure | |
| WO2018086160A1 (en) | Rough surface-based three-dimensional contact stiffness calculation method for spur gear | |
| CN109269892B (en) | Method and system for measuring elastic modulus of polymer | |
| Warren et al. | A fractal model for the rigid-perfectly plastic contact of rough surfaces | |
| CN104834806A (en) | Joint roughness coefficient size effect sampling representativeness evaluation method | |
| CN109472071B (en) | Three-dimensional fractal prediction method for static friction coefficient of joint surface | |
| CN102054122A (en) | Haptic texture rendering method based on practical measurement | |
| Larsson et al. | Inelastic flattening of rough surfaces | |
| CN110457795A (en) | High-rise charming appearance and behaviour displacement state appraisal procedure neural network based | |
| CN115408783A (en) | Construction method of digital twin-based multi-level information assembly model | |
| CN109829224B (en) | Method for calculating tangential contact stiffness of rough elastic interface | |
| CN103439030B (en) | Texture force measuring method in a kind of haptic feedback | |
| CN109446655B (en) | Three-dimensional fractal prediction method for normal contact stiffness of double fractal bonding surface | |
| CN112231921A (en) | Contact rigidity modeling method for fixed mechanical joint part | |
| Mu et al. | Study on rough surfaces: A novel method for high-precision simulation and interface contact performances analysis | |
| CN112926210A (en) | Fixed joint contact damping three-dimensional fractal prediction method | |
| CN112395754B (en) | Dynamic weakening prediction method for rigidity of mechanical connection structure joint surface | |
| CN104122205A (en) | Method for measuring residual stress by using uplift amount of indentation | |
| CN101799275A (en) | Ultra-precision online measuring method of diameter of bearing ball | |
| Zhou et al. | Three-dimensional asperity model of rough surfaces based on valley–peak ratio of the maximum peak | |
| CN104462202A (en) | Soil consolidation coefficient model and establishing method thereof | |
| CN107169200A (en) | A kind of computational methods for determining cylindrical boundary rigidity | |
| CN114969630A (en) | Method and device for predicting friction coefficient of rough fractal surface under normal load | |
| CN110532669B (en) | Method for modeling contact stiffness of mechanical joint surface |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200616 |