A method for calculating elastic-plastic contact stiffness of anisotropic fractal rough surfaces

Abstract

The present invention belongs to the field of mechanics, and discloses a method for calculating the elastic-plastic contact stiffness of anisotropic fractal rough surfaces; a single micro-convex contact model is established based on the anisotropic fractal rough surface, and a rough surface contact model is established by combining the island distribution probability micro-convex area distribution probability density function, thereby proposing a method for calculating the elastic-plastic contact stiffness of anisotropic fractal rough surfaces. This method effectively fills the gap in the existing anisotropic rough surface contact stiffness calculation method, directly shows the relationship between the critical deformation and the micro-convex grade and the influence on the contact stiffness, and provides a theoretical reference for the calculation of the service life, transmission efficiency and reliability of mechanical parts, and is suitable for large-scale use and promotion in industry.

Description

Technical Field

[0001] The invention belongs to the field of mechanics, and in particular relates to a method for calculating elastic-plastic contact stiffness of anisotropic fractal rough surface. Background Art

[0002] The surface of mechanical parts will show microscopic morphology such as stripes due to the influence of processing technology, friction and wear, making it anisotropic, which is quite different from the assumed smooth surface or isotropic surface. Research on anisotropic rough surfaces can effectively approximate the real surface, reduce the gap between nominal contact characteristics and real contact characteristics, and is conducive to the analysis of mechanical parts' service life, transmission efficiency, reliability and other characteristics.

[0003] There are already many research results on fractal rough surface simulation modeling and contact stiffness calculation in the existing technology. In these studies, the fitting technology has covered multi-dimensional and multi-directional rough surfaces. In addition, the research on the normal contact stiffness and time-varying contact stiffness of smooth, single rough and double rough surfaces has promoted the development of mechanical parts design conditions and contact characteristics. However, at present, the research on the contact stiffness of anisotropic fractal rough surfaces is not comprehensive. This research can effectively predict the working state and working characteristics of mechanical parts with obvious surface anisotropy, and provide a certain theoretical reference for the calculation of the service life, transmission efficiency, reliability and other aspects of mechanical parts. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating the elastic-plastic contact stiffness of anisotropic fractal rough surfaces, so as to solve the problem that there is a lack of such methods in the prior art, resulting in insufficient theoretical reference for the calculation of the service life, transmission efficiency and reliability of mechanical parts with anisotropic surfaces.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions to achieve the above problems:

[0006] A method for calculating elastic-plastic contact stiffness of anisotropic fractal rough surface comprises the following steps:

[0007] Step 1: Obtain the fractal parameters of the anisotropic fractal rough surface, including the transverse fractal dimension, the longitudinal fractal dimension, the transverse fractal roughness, and the longitudinal fractal roughness, which are respectively denoted as and 、 ;

[0008] Step 2: According to the fractal parameters and 、 ; Establish anisotropic fractal rough surface ;

[0009] Step 3, Anisotropic fractal rough surface , a single micro-convex body model before the rough surface contact deformation is established, and the single micro-convex body contour curve before the rough surface contact deformation is calculated based on it ;

[0010] According to the single convex body contour curve Calculate the curvature radius of the single asperity peak before the rough surface contact deformation 、 Single convex body height and the actual deformation of a single convex body ;

[0011] Step 4: The curvature radius of the single microconvex peak before the rough surface contact deformation 、 Single convex body height and the actual deformation of a single convex body Establish a single asperity contact model on rough surface;

[0012] Step 5, establishing a rough surface contact model based on the single asperity contact model of the rough surface and the asperity area distribution probability density function; determining the nominal contact area, nominal contact load and nominal contact stiffness of the anisotropic fractal rough surface.

[0013] The present invention also includes the following features:

[0014] Furthermore, in step 2, the anisotropic fractal rough surface is established using the following formula: :

[0015]

[0016] in:

[0017] represents anisotropic fractal rough surface;

[0018] and Respectively represent the coordinates of discrete points on the anisotropic fractal rough surface along the x-axis and y-axis;

[0019] Indicates the sampling length; represents the transverse fractal roughness; represents the longitudinal fractal roughness; represents the horizontal fractal dimension; Indicates the vertical fractal dimension; the value is between 1 and 2;

[0020] Indicates the asperity level;

[0021] Represents the spatial frequency, which satisfies the inverse of the wavelength;

[0022] and Represents a dimensionless coefficient.

[0023] Further, step 3 includes the following sub-steps;

[0024] Step 31, rough surface based on anisotropic fractal , a single micro-convex body model before the rough surface contact deformation is established, and the single micro-convex body contour curve before the rough surface contact deformation is calculated based on it ;

[0025] Step 32, using the following formula, calculate the radius of curvature of the peak of a single microconvex body before the rough surface is deformed by contact:

[0026]

[0027] in:

[0028] It represents the curvature radius of the single asperity peak before the rough surface is deformed in contact;

[0029] Step 33, take the single convex body contour curve before contact deformation The amplitude part is taken as the height of a single convex body, and its expression is as follows:

[0030]

[0031] in:

[0032] It represents the height of a single asperity before the rough surface is deformed in contact;

[0033] Step 34, using the following formula, calculate the actual deformation of the single micro-convex body before the rough surface contact deformation:

[0034]

[0035] in:

[0036] It represents the actual deformation of a single asperity before the rough surface contact deformation;

[0037] It indicates the actual height of a single convex body when it is compressed to a certain amount;

[0038] They respectively represent the coordinates of any point on the edge of the contact surface of a single micro-convex body on the x-axis and y-axis when the contact surface is a circle under a certain compression amount.

[0039] Further, step 4 includes the following sub-steps;

[0040] Step 41, use the following formulas to calculate the deformation of a single microconvex body in an elastic deformation state: , contact area , contact load and contact stiffness :

[0041] =

[0042] =π

[0043] = =

[0044]

[0045] in:

[0046] Indicates the average contact pressure;

[0047] represents the equivalent elastic modulus;

[0048] Step 42, when =kH When the single convex body reaches the critical state of elastic contact, the elastic critical deformation is calculated using the following formula , critical contact area and critical contact load :

[0049] =

[0050] = π

[0051] =

[0052] in,

[0053] k Represents the contact pressure coefficient of the bonding surface, satisfying k =0.454+0.41 , represents Poisson's ratio;

[0054] H Indicates the Vickers hardness of the softer material in contact, satisfying H= 2.8 s y ;

[0055] s y represents material stress;

[0056] Step 43, assume that the Poisson's ratios of the materials of the two contact surfaces are , The corresponding elastic modulus is , , the expression is as follows:

[0057]

[0058]

[0059] At this time, the single convexity level in the elastic state n The constraints of 1 are as follows:

[0060]

[0061] When the critical deformation of a single convex body = , enter the plastic contact state; use the following formula to calculate the critical deformation of the elastic-plastic contact state , critical contact area and critical contact load :

[0062]

[0063] Step 44, respectively determine the contact area of ​​a single convex body in the elastic-plastic contact state , contact load and contact stiffness Deformation Amount in Elastic-Plastic Contact State The expression is as follows:

[0064]

[0065]

[0066]

[0067] in, The deformation of a single convex body in elastic-plastic contact state;

[0068] At this time, the single asperity level of the elastic-plastic contact state n The constraints of 2 are as follows:

[0069] ;

[0070] Step 45, calculate the contact area of ​​the micro-convex body in the plastic state using the following formula: , contact load and contact stiffness :

[0071]

[0072] in, Represents the deformation amount of a single microplastic contact state.

[0073] Further, step 5 includes the following sub-steps;

[0074] Step 51, determine the probability density function based on the micro-convex body area distribution :

[0075]

[0076] in, D Indicates the fractal dimension of the rough surface, with a value of 2~3;

[0077] ;

[0078] in, represents the maximum cross-sectional area;

[0079] represents the fractal area expansion coefficient;

[0080] Step 52, calculate the nominal contact area of ​​the rough surface using the following formula :

[0081]

[0082] Among them, the nominal contact area of ​​the rough surface is the sum of the contact areas of single asperities of all levels;

[0083] represents the contact area of ​​all asperities in the elastic deformation state sum;

[0084] Represents the contact area of ​​all asperities in elastic-plastic contact state sum;

[0085] Represents the contact area of ​​all asperities in plastic contact sum;

[0086] Step 53, calculate the nominal contact load on the rough surface using the following formula ;

[0087]

[0088] Among them, the nominal contact load of the rough surface is the sum of the single asperity contact loads of all levels;

[0089] represents the contact load of all asperities in the elastic deformation state sum;

[0090] Represents the contact load of all asperities in elastic-plastic contact sum;

[0091] Represents the contact load of all asperities in plastic contact sum;

[0092] Indicates the nominal contact load on the rough surface;

[0093] Step 54, calculate the nominal contact stiffness of the rough surface using the following formula ;

[0094]

[0095] Among them, the nominal contact stiffness of the rough surface is the sum of the contact stiffness of all levels of single asperities;

[0096] Represents the contact stiffness of all asperities in the elastic deformation state sum;

[0097] Represents the contact stiffness of all asperities in elastic-plastic contact sum;

[0098] Represents the contact stiffness of all asperities in plastic contact sum.

[0099] Compared with the prior art, the present invention has the following technical effects:

[0100] The present invention provides a method for calculating the elastic-plastic contact stiffness of anisotropic fractal rough surfaces. Based on the anisotropic fractal rough surface, a single micro-convex contact model is established. In combination with the probability density function of the micro-convex area distribution, a rough surface contact model is established, thereby proposing a method for calculating the elastic-plastic contact stiffness of anisotropic fractal rough surfaces. This method effectively fills the gap in the existing methods for calculating the contact stiffness of anisotropic rough surfaces, directly demonstrates the relationship between the critical deformation and the micro-convex grade and the influence on the contact stiffness, and provides a theoretical reference for the calculation of the service life, transmission efficiency and reliability of mechanical parts, and is suitable for large-scale use and promotion in industry. DETAILED DESCRIPTION

[0101] It should be noted that all methods in the present invention, unless otherwise specified, all adopt methods known in the prior art. Specific embodiments of the present invention are given below. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent changes made on the basis of the technical solution of this application fall within the protection scope of the present invention.

[0102] A method for calculating elastic-plastic contact stiffness of anisotropic fractal rough surface comprises the following steps:

[0103] Step 1: Obtain the fractal parameters of the anisotropic fractal rough surface, including the transverse fractal dimension, the longitudinal fractal dimension, the transverse fractal roughness, and the longitudinal fractal roughness, which are respectively denoted as and 、 ;

[0104] Step 2: According to the fractal parameters and 、 ; Establish anisotropic fractal rough surface ;

[0105] Step 3, Anisotropic fractal rough surface , a single micro-convex body model before the rough surface contact deformation is established, and the single micro-convex body contour curve before the rough surface contact deformation is calculated based on it ;

[0106] According to the single convex body contour curve Calculate the curvature radius of the single asperity peak before the rough surface contact deformation 、 Single convex body height and the actual deformation of a single convex body ;

[0107] Step 4: The curvature radius of the single microconvex peak before the rough surface contact deformation 、Single convex body height and the actual deformation of a single convex body Establish a single asperity contact model on rough surface;

[0108] Step 5, establishing a rough surface contact model based on the single asperity contact model of the rough surface and the asperity area distribution probability density function; determining the nominal contact area, nominal contact load and nominal contact stiffness of the anisotropic fractal rough surface.

[0109] Furthermore, in step 2, the fractal function has a size consistency feature, and the anisotropic fractal rough surface is established using the following formula: :

[0110]

[0111] in:

[0112] represents anisotropic fractal rough surface;

[0113] and Respectively represent the coordinates of discrete points on the anisotropic fractal rough surface along the x-axis and y-axis;

[0114] Indicates the sampling length; represents the transverse fractal roughness; represents the longitudinal fractal roughness; represents the horizontal fractal dimension; Indicates the vertical fractal dimension; the value is between 1 and 2;

[0115] Indicates the asperity level;

[0116] Represents the spatial frequency, which satisfies the inverse of the wavelength;

[0117] and represents a dimensionless coefficient.

[0118] Further, step 3 includes the following sub-steps;

[0119] Step 31, Anisotropic fractal-based rough surface , a single micro-convex body model before the rough surface contact deformation is established, and the single micro-convex body contour curve before the rough surface contact deformation is calculated based on it ;

[0120] Step 32, using the following formula, calculate the radius of curvature of the peak of a single microconvex body before the rough surface is deformed by contact:

[0121]

[0122] in:

[0123] It represents the curvature radius of the peak of a single asperity before the rough surface is deformed in contact;

[0124] Step 33: Take the single convex body contour curve before contact deformation The amplitude part is the height of a single convex body, and its expression is as follows:

[0125]

[0126] in:

[0127] It represents the height of a single asperity before the rough surface is deformed in contact;

[0128] Step 34, using the following formula, calculate the actual deformation of the single micro-convex body before the rough surface contact deformation:

[0129]

[0130] in:

[0131] It represents the actual deformation of a single asperity before the rough surface contact deformation;

[0132] It indicates the actual height of a single convex body when it is compressed to a certain compression amount;

[0133] They respectively represent the coordinates of any point on the edge of the contact surface of a single micro-convex body on the x-axis and y-axis when the contact surface is a circle under a certain compression amount.

[0134] Further, step 4 includes the following sub-steps;

[0135] Step 41, use the following formulas to calculate the deformation of a single microconvex body in an elastic deformation state: , contact area , contact load and contact stiffness :

[0136] =

[0137] =π

[0138] = =

[0139]

[0140] in:

[0141] Indicates the average contact pressure;

[0142] represents the equivalent elastic modulus;

[0143] The simplified formula above is as follows:

[0144]

[0145] Step 42, when =kH When the single convex body reaches the critical state of elastic contact, the elastic critical deformation is calculated using the following formula , critical contact area and critical contact load :

[0146] =

[0147] = π

[0148] =

[0149] The simplified expression of the above formula is as follows:

[0150]

[0151] in,

[0152] k Represents the contact pressure coefficient of the bonding surface, satisfying k =0.454+0.41 , represents Poisson's ratio;

[0153] H Indicates the Vickers hardness of the softer material in contact, satisfying H =2.8 s y ;

[0154] s y represents material stress;

[0155] Step 43, assume that the Poisson's ratios of the materials of the two contact surfaces are , The corresponding elastic modulus is , , the expression is as follows:

[0156]

[0157] At this time, the single convexity level in the elastic state n The constraints of 1 are as follows:

[0158]

[0159] When the critical deformation of a single convex body = , enter the plastic contact state; use the following formula to calculate the critical deformation of the elastic-plastic contact state , critical contact area and critical contact load :

[0160]

[0161] Step 44, respectively determine the contact area of ​​a single convex body in the elastic-plastic contact state , contact load and contact stiffness Deformation Amount in Elastic-Plastic Contact State The expression is as follows:

[0162]

[0163]

[0164]

[0165] in, The deformation of a single convex body in elastic-plastic contact state;

[0166] At this time, the single asperity level of the elastic-plastic contact state n The constraints of 2 are as follows:

[0167]

[0168] Step 45, calculate the contact area of ​​the micro-convex body in the plastic state using the following formula: , contact load and contact stiffness :

[0169]

[0170] in, Represents the deformation amount of a single microplastic contact state.

[0171] When the contact area of ​​a single asperity satisfies A ≤ A 1c When , the micro-convex bodies are in elastic contact;

[0172] satisfy A 1c < A ≤ A 2c When , the micro-convex bodies are in elastic-plastic contact;

[0173] satisfy A > A 3c When , the micro-convex bodies come into plastic contact.

[0174] Furthermore,

[0175] Step 5 includes the following sub-steps:

[0176] Step 51, determine the probability density function based on the micro-convex body area distribution :

[0177]

[0178] in, D Indicates the fractal dimension of the rough surface, with a value of 2~3;

[0179] ;

[0180] in, represents the maximum cross-sectional area;

[0181] represents the fractal area expansion coefficient;

[0182] Step 52, calculate the nominal contact area of ​​the rough surface using the following formula :

[0183]

[0184] Among them, the nominal contact area of ​​the rough surface is the sum of the contact areas of single asperities of all levels;

[0185] represents the contact area of ​​all asperities in the elastic deformation state sum;

[0186] Represents the contact area of ​​all asperities in elastic-plastic contact state sum;

[0187] Represents the contact area of ​​all asperities in plastic contact sum;

[0188] Step 53, calculate the nominal contact load on the rough surface using the following formula ;

[0189]

[0190] Among them, the nominal contact load of the rough surface is the sum of the single asperity contact loads of all levels;

[0191] represents the contact load of all asperities in the elastic deformation state sum;

[0192] Represents the contact load of all asperities in elastic-plastic contact sum;

[0193] Represents the contact load of all asperities in plastic contact sum;

[0194] Indicates the nominal contact load on the rough surface;

[0195] Step 54, calculate the nominal contact stiffness of the rough surface using the following formula ;

[0196]

[0197] Among them, the nominal contact stiffness of the rough surface is the sum of the contact stiffness of all levels of single asperities;

[0198] Represents the contact stiffness of all asperities in the elastic deformation state sum;

[0199] Represents the contact stiffness of all asperities in elastic-plastic contact sum;

[0200] Represents the contact stiffness of all asperities in plastic contact sum.

Claims

1. A method for calculating elastic-plastic contact stiffness of anisotropic fractal rough surface, characterized in that: The following steps are involved: Step 1: Obtain the fractal parameters of the anisotropic fractal rough surface, including the transverse fractal dimension, the longitudinal fractal dimension, the transverse fractal roughness, and the longitudinal fractal roughness, which are respectively denoted as and 、 ; Step 2: According to the fractal parameters and 、 ; Establish anisotropic fractal rough surface ; Step 3: Anisotropic fractal rough surface , a single micro-convex body model before the rough surface contact deformation is established, and the single micro-convex body contour curve before the rough surface contact deformation is calculated based on it ; According to the single convex body contour curve Calculate the curvature radius of the single asperity peak before the rough surface contact deformation 、 Single convex body height and the actual deformation of a single convex body ; Step 4: The curvature radius of the single microconvex peak before the rough surface contact deformation 、 Single convex body height and the actual deformation of a single convex body Establish a single asperity contact model on rough surface; Step 5, establishing a rough surface contact model based on the rough surface single micro-convex body contact model and the micro-convex body area distribution probability density function; determining the nominal contact area, nominal contact load and nominal contact stiffness of the anisotropic fractal rough surface; In step 2, the anisotropic fractal rough surface is established using the following formula: : in: represents anisotropic fractal rough surface; and Respectively represent the coordinates of discrete points on the anisotropic fractal rough surface along the x-axis and y-axis; Indicates the sampling length; represents the transverse fractal roughness; represents the longitudinal fractal roughness; represents the horizontal fractal dimension; Indicates the vertical fractal dimension; the value is between 1 and 2; Indicates the asperity level; Represents the spatial frequency, which satisfies the inverse of the wavelength; and represents a dimensionless coefficient; Step 3 includes the following sub-steps: Step 31, rough surface based on anisotropic fractal , a single micro-convex body model before the rough surface contact deformation is established, and the single micro-convex body contour curve before the rough surface contact deformation is calculated based on it ; Step 32, using the following formula, calculate the radius of curvature of the peak of a single microconvex body before the rough surface is deformed by contact: in: It represents the curvature radius of the single asperity peak before the rough surface is deformed in contact; Step 33: Take the single convex body contour curve before contact deformation The amplitude part is taken as the height of a single convex body, and its expression is as follows: in: It represents the height of a single asperity before the rough surface is deformed in contact; Step 34, using the following formula, calculate the actual deformation of the single micro-convex body before the rough surface contact deformation: in: It represents the actual deformation of a single asperity before the rough surface contact deformation; It indicates the actual height of a single convex body when it is compressed to a certain compression amount; They represent the coordinates of any point on the edge of the contact surface of a single convex body on the x-axis and y-axis respectively when the contact surface is a circle under a certain compression amount; Step 4 includes the following sub-steps: Step 41, use the following formulas to calculate the deformation of the single microconvex body in the elastic deformation state: , contact area , contact load and contact stiffness : = =π = = in: Indicates the average contact pressure; represents the equivalent elastic modulus; Step 42, when =kH When the single convex body reaches the critical state of elastic contact, the elastic critical deformation is calculated using the following formula , critical contact area and critical contact load : = = π = in, k Represents the contact pressure coefficient of the bonding surface, satisfying k =0.454+0.41 , represents Poisson's ratio; H Indicates the Vickers hardness of the softer material in contact, satisfying H= 2.8 σ y ; σ y represents material stress; Step 43, assume that the Poisson's ratios of the materials of the two contact surfaces are , The corresponding elastic modulus is , , the expression is as follows: At this time, the single convexity level in the elastic state n The constraints of 1 are as follows: When the critical deformation of a single convex body = , enter the plastic contact state; use the following formula to calculate the critical deformation of the elastic-plastic contact state , critical contact area and critical contact load : ； Step 44, respectively determine the contact area of ​​the single convex body in the elastic-plastic contact state , contact load and contact stiffness Deformation Amount in Elastic-Plastic Contact State The expression is as follows: in, The deformation of a single convex body in elastic-plastic contact state; At this time, the single asperity level of the elastic-plastic contact state n The constraints of 2 are as follows: ； Step 45, calculate the contact area of ​​the micro-convex body in the plastic state using the following formula: , contact load and contact stiffness : in, represents the deformation of a single microplastic contact state; Step 5 includes the following sub-steps: Step 51, determine the probability density function based on the micro-convex body area distribution : in, D Indicates the fractal dimension of the rough surface, with a value of 2~3; ； in, represents the maximum cross-sectional area; represents the fractal area expansion coefficient; Step 52, calculate the nominal contact area of ​​the rough surface using the following formula : Among them, the nominal contact area of ​​the rough surface is the sum of the contact areas of single asperities of all levels; represents the contact area of ​​all asperities in the elastic deformation state sum; Represents the contact area of ​​all asperities in elastic-plastic contact state sum; Represents the contact area of ​​all asperities in plastic contact sum; Step 53, calculate the nominal contact load on the rough surface using the following formula ; Among them, the nominal contact load of the rough surface is the sum of the single asperity contact loads of all levels; represents the contact load of all asperities in the elastic deformation state sum; Represents the contact load of all asperities in elastic-plastic contact sum; Represents the contact load of all asperities in plastic contact sum; Indicates the nominal contact load on the rough surface; Step 54, calculate the nominal contact stiffness of the rough surface using the following formula ; Among them, the nominal contact stiffness of the rough surface is the sum of the contact stiffness of all levels of single asperities; Represents the contact stiffness of all asperities in the elastic deformation state sum; Represents the contact stiffness of all asperities in elastic-plastic contact sum; Represents the contact stiffness of all asperities in plastic contact sum.

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