Calculation method of contact stiffness of accelerometer joint considering temperature effect

Abstract

The present invention provides a method for calculating the contact stiffness of an accelerometer joint considering the influence of temperature, including: measuring the rough surface of the accelerometer joint, calculating the fractal characteristic parameters of the rough surface, obtaining the fractal dimension and fractal roughness of the rough surface based on the fractal characteristic parameters; constructing an isotropic fractal rough surface based on the fractal dimension and fractal roughness; establishing a micro-convex body model under the action of temperature, using the micro-convex body model to analyze the contact parameters of different deformation stages; generalizing the micro-convex body model to the entire accelerometer joint, and obtaining the total normal contact load and normal contact stiffness of the accelerometer joint under the influence of temperature. The present invention uses a fractal function to construct a rough surface of the joint to calculate the contact stiffness of the accelerometer joint, and establishes a fractal model of the normal contact load and normal contact stiffness of the joint under the action of temperature, thereby realizing an effective prediction of the contact state of the joint under the action of temperature during service.

Description

Technical Field

[0001] The invention belongs to the technical field of research on contact deformation mechanism of joint surfaces, and in particular relates to a method for calculating contact stiffness of a joint part of an accelerometer taking temperature influence into consideration. Background Art

[0002] Inertial navigation is a precision navigation technology with the characteristics of high precision, real-time, reliability and independence. It is widely used in high-end equipment such as satellites, aircraft, and rockets. As the core component of the inertial navigation system, the accelerometer provides the carrier with information such as speed and attitude. The performance level of the accelerometer plays a decisive role in the navigation accuracy of the overall equipment. However, by analyzing its manufacturing, assembly and service stages, it is found that when the manufacturing accuracy and initial assembly accuracy meet the process requirements, due to the coupling of service physical fields such as external heat, external force, and vibration, the contact state of the joint will change at the microscopic scale, which will lead to fluctuations in product performance. Taking the service temperature field as an example, the temperature range of the accelerometer working environment is -55 to 80℃. The change in temperature causes the core components to respond at different scales. This response first occurs at the microscopic scale, and the resulting thermal expansion, thermal deformation, thermal stress and other phenomena cause the joint load to change and the components to deform. Specifically, the core components of the accelerometer, the differential capacitance sensor plates, are not in ideal surface-to-surface contact, but are actually point-to-point or point-to-surface contact. Under the action of external force, the contact interface has a certain normal contact stiffness, and the stiffness is related to the load and the actual contact area. When the ambient temperature changes and the load changes, the interface contact stiffness is inconsistent with the stiffness at room temperature. Under the influence of multi-factor coupling constraints, the deformation of the interface changes, which in turn causes the small gap between the capacitance sensor plates to change, resulting in unstable accelerometer bias and affecting its performance. Therefore, it is necessary to analyze the changes in the contact performance of the accelerometer joint after assembly under multi-factor coupling constraints with temperature.

[0003] At present, the calculation methods for contact stiffness of joints at home and abroad are mainly based on studying the contact behavior of micro-convex bodies on rough surfaces. The GW model proposed by Greenwood and Williamson, from a statistical point of view, believes that the micro-convex bodies on rough surfaces have a constant radius of curvature and a Gaussian distribution of height. The Hertz contact theory is used to calculate the relationship between the normal load and the contact area in the elastic deformation stage, so as to obtain the contact parameters of the joint. The statistical parameters of this calculation method are affected by the resolution and sampling length of the measuring instrument and are not objective. Due to the self-similar and scale-independent characteristics of fractal geometry, subsequent scholars applied fractal theory to the analysis of contact characteristics of rough surfaces based on the Weierstrass-Mandelbrot (WM) function, and developed MB fractal contact theory, WK fractal model, and YK fractal contact model, resulting in most subsequent studies based on these three models for further expansion and application to suit the contact analysis of micro-convex bodies at different deformation stages.

[0004] Judging from the current research status at home and abroad, most of the existing methods for calculating the contact stiffness of joints use fractal theory to characterize rough surfaces. There are still some deficiencies in the calculation methods of the contact stiffness of rough interfaces, including: calculating the contact load and stiffness of the joints at different deformation stages, less consideration of the effect of temperature on the contact performance of the joints, and difficulty in clarifying the influence of the physical field of the service state on the product performance. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the calculation method of rough interface contact stiffness in the prior art, and to provide a method for calculating the contact stiffness of the accelerometer joint taking into account the influence of temperature. The method takes into account the influence of the ambient temperature of the accelerometer when in service on the contact stiffness of its joint, which helps to analyze the influence of temperature on the contact performance between the joint surfaces and the functional properties of the product under service.

[0006] To achieve the above purpose, the technical solution provided by the present invention is:

[0007] A method for calculating contact stiffness of an accelerometer joint considering temperature influence, comprising:

[0008] Step 1, measuring the rough surface of the accelerometer joint, calculating the fractal characteristic parameters of the rough surface, and obtaining the fractal dimension and fractal roughness of the rough surface based on the fractal characteristic parameters;

[0009] Step 2: constructing an isotropic fractal rough surface based on the fractal dimension and the fractal roughness;

[0010] Step 3: Establish a micro-asperity model under the action of temperature, and use the micro-asperity model to analyze the contact parameters at different deformation stages; wherein the micro-asperity model is a micro-asperity thermo-elastic-plastic normal contact load and normal contact stiffness model, and different deformation stages include elastic deformation stage, elastic-plastic deformation stage and plastic deformation stage;

[0011] Step 4: Extend the asperity model to the entire accelerometer joint to obtain the total normal contact load and normal contact stiffness of the accelerometer joint under the influence of temperature.

[0012] As a further limitation of the present invention, the step 1 comprises:

[0013] The profile data of the rough surface of the accelerometer joint is measured by a three-dimensional profile measuring instrument, and the surface topography data of the rough surface is recorded in the form of discrete height samples;

[0014] The fractal characteristic parameters of the rough surface are calculated, and the fractal dimension and fractal roughness are calculated using a structure function.

[0015] As a further limitation of the present invention, in step 1, the process of recording the surface topography data includes:

[0016] Assume that the number of sampling points of surface topography data is , the discrete height sample data of the surface morphology is , For sampling point Towards coordinates, then Discrete height sample data of sampling points It is expressed as:

[0017]

[0018] In the formula, Indicates Sampling points Towards coordinates, Indicates Surface profile height at each sampling point;

[0019] The discrete height sample data of the surface topography The incremental equation is set as the structure function , expressed as:

[0020]

[0021] In the formula, < > means finding the average value, Representation and interval The surface height value, represents an arbitrarily chosen value for the data interval, represents the count of sampling points, Indicates The surface profile height of the sampling points, represents the relationship coefficient between the structure function and the fractal parameter, represents the fractal roughness, represents the fractal dimension;

[0022] Take the logarithm of both ends of equation (2), perform least squares fitting on the structure function, and get the slope of the fitting line: and the intercept , from the slope of the straight line Determining the fractal dimension , expressed as: ; By the intercept Determining fractal roughness , expressed as: .

[0023] As a further limitation of the present invention, the expression of the fractal rough surface in step 2 is:

[0024] z x,y &=L G L D - 2 lnγ M ∑ m=1 M ∑ n=0 n max c D - 3 n &× cos ϕ m,n - cos [ 2π c n x 2 + y 2 1 2 L × cos tan - 1 y x - πm M + ϕ m,n ]

[0025] In the formula, represents the surface topography height, Indicates sampling point Towards coordinates, Indicates sampling point Towards coordinates, represents the sampling length, represents the fractal roughness, represents the fractal dimension, represents the surface frequency density, represents the number of superimposed peaks of the reconstructed surface, represents the upper bound of the surface frequency index, represents the surface frequency index, Indicates the sequence number of the reconstructed surface superposition peak, Indicated in [0,2π] Random phases evenly distributed within the range.

[0026] As a further limitation of the present invention, the step three further comprises:

[0027] The contact of the fractal rough surface is assumed to be the contact between a rough surface and a rigid ideal plane, and the asperity model is the contact between a spherical asperity and a rigid ideal plane;

[0028] Based on the fractal rough surface and the convex body model, the step three specifically includes:

[0029] The contact deformation of the micro-asperities in the micro-asperity model includes an elastic deformation stage, specifically:

[0030] Thermoelastic normal contact load caused by thermal stress factors during the elastic deformation stage It is expressed as: ;

[0031] In the formula, represents the normal mechanical load in the elastic deformation stage, represents the normal load caused by thermal stress factors in the elastic deformation stage, represents the micro-contact cross-sectional area of ​​the micro-asperity; represents the linear expansion coefficient, represents the equivalent elastic modulus, Indicates temperature difference;

[0032] In the elastic deformation stage, the thermoelastic normal contact stiffness of the micro-asperity is The expression is:

[0033]

[0034] In the formula, represents the thermo-elastoplastic normal contact load right The first derivative of Indicates the deformation of the micro-convex body right The first derivative of represents the thermo-elastoplastic normal contact load Deformation of the micro-convex body The first derivative of .

[0035] As a further limitation of the present invention, based on the fractal rough surface and the micro-convex body model, the step three specifically includes:

[0036] The contact deformation of the micro-asperities in the micro-asperity model also includes elastic-plastic deformation and plastic deformation, specifically:

[0037] (1) Elastic-plastic deformation includes: The first stage of elastic-plastic deformation , the second stage of elastic-plastic deformation ; is the deformation amount, is the critical elastic deformation of the micro-convex body; where:

[0038] The expression of the first stage of elastic-plastic deformation is:

[0039]

[0040] In the formula, It represents the thermal elastic-plastic normal contact load caused by thermal stress factors in the first stage of elastic-plastic deformation. represents the normal elastic-plastic mechanical load in the first stage of elastic-plastic deformation, represents the normal load caused by thermal stress factors in the first stage of elastic-plastic deformation, represents the correlation factor, Indicates hardness;

[0041] The expression of the second stage of elastic-plastic deformation is:

[0042]

[0043] In the formula, It represents the thermal elastic-plastic normal contact load caused by thermal stress factors in the second stage of elastic-plastic deformation. represents the normal elastic-plastic mechanical load in the second stage of elastic-plastic deformation, It represents the normal load caused by thermal stress factor in the second stage of elastic-plastic deformation;

[0044] In the first stage of elastic-plastic deformation, the thermo-elastic-plastic normal contact stiffness of the micro-asperity is The expression is:

[0045]

[0046] In the second stage of elastic-plastic deformation, the thermo-elastic-plastic normal contact stiffness of the micro-asperity is The expression is:

[0047]

[0048] (2) Plastic deformation includes: During the plastic deformation stage, the thermoplastic normal contact load caused by thermal stress factors It is expressed as:

[0049]

[0050] In the formula, represents the normal plastic mechanical load in the plastic deformation stage, represents the normal load caused by thermal stress factors in the plastic deformation stage, is the yield strength;

[0051] In the plastic deformation stage, the thermoplastic normal contact stiffness of the micro-asperity is .

[0052] As a further limitation of the present invention, the step 4 further comprises:

[0053] Based on the convex body model, the total normal contact load and normal contact stiffness of the accelerometer joint are established, where:

[0054] Asperity micro-contact cross-sectional area size distribution function The expression is:

[0055]

[0056] In the formula, represents the area expansion factor of the microcontact size distribution, represents the maximum micro-contact cross-sectional area;

[0057] Critical elastic micro-contact cross-sectional area The expression is:

[0058]

[0059] The total normal contact load of the accelerometer joint is the sum of the loads causing elastic, elastoplastic and plastic deformation, reflecting the influence of temperature change on the overall normal total load of the contact part. When the total normal contact load of the accelerometer joint is The expression is:

[0060]

[0061] The advantages of the present invention are:

[0062] The present invention uses fractal functions to construct a rough surface of a joint to calculate the contact stiffness of an accelerometer joint, comprehensively considers the influence of thermal deformation and thermal stress of the accelerometer joint caused by the service temperature load on the contact state of the accelerometer joint, and for the three deformation stages of elasticity, elastoplasticity and plasticity of the joint, establishes a fractal model of the normal contact load and normal contact stiffness of the joint under the action of temperature, thereby achieving effective prediction of the contact state of the joint under the action of temperature during service, making the theoretical model closer to the actual situation, and providing an accurate contact model for the performance research of long-period inertial devices, so as to promote the accurate prediction of the system assembly accuracy.

[0063] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0065] Figure 1 :A flow chart of a method for calculating contact stiffness of an accelerometer joint considering temperature influence provided by the present invention;

[0066] Figure 2: Simulated microscopic surface morphology of the contact surface of the accelerometer joint provided by the present invention;

[0067] Figure 3 : Rough surface contact and simplified contact model diagram provided by the present invention;

[0068] Figure 4 : Example model diagram provided by the present invention;

[0069] Figure 5 : Double logarithmic plot of the structure function provided by the present invention;

[0070] Figure 6 : Material property parameters of the two contact surfaces provided by the present invention. DETAILED DESCRIPTION

[0071] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0072] See also Figure 1 The embodiment of the present invention provides a method for calculating the contact stiffness of an accelerometer joint considering the influence of temperature, which specifically includes the following steps:

[0073] Step 1: measure the rough surface of the accelerometer joint, calculate the fractal characteristic parameters of the rough surface, and obtain the fractal dimension and fractal roughness of the rough surface based on the fractal characteristic parameters.

[0074] Step 1 of the embodiment of the present invention includes: using a three-dimensional profilometer to measure the profile data of the rough surface of the accelerometer joint, and recording the surface morphology data of the rough surface in the form of discrete height samples; calculating the fractal characteristic parameters of the rough surface, and using the structure function to calculate the fractal dimension and fractal roughness.

[0075] Specifically, in step 1, the process of recording surface topography data includes:

[0076] Assume that the number of sampling points of surface topography data is , the discrete height sample data of the surface morphology is , For sampling point Towards coordinates, then Discrete height sample data of sampling points It is expressed as:

[0077]

[0078] In the formula, Indicates Sampling points Towards coordinates, Indicates Surface profile height at each sampling point;

[0079] Calculate fractal characteristic parameters and use structure function to calculate fractal dimension and fractal roughness . The discrete height sample data of the surface morphology The incremental equation is set as the structure function , expressed as:

[0080]

[0081] In the formula, < > means finding the average value, Representation and interval The surface height value, represents an arbitrarily chosen value for the data interval, represents the count of sampling points, represents the relationship coefficient between the structure function and the fractal parameter, , Represents fractal roughness. The larger the value, the rougher the surface. Represents the fractal dimension of the rough surface contour. The larger the value, the smoother the rough surface. represents the gamma function, expressed as , Indicates the surface frequency density. Based on the consideration of surface flatness and frequency density distribution, it is generally taken as .

[0082] Taking the logarithm of both ends of equation (2), we can get

[0083]

[0084] Fit the structure function to a straight line using the least squares method to obtain the slope of the straight line and the intercept . From the slope of the straight line Determining the fractal dimension , fractal dimension With slope The relationship is expressed as: ; Fractal roughness With intercept The relationship is expressed as: . Fit the structure function to a straight line using the least squares method to obtain the slope of the straight line and the intercept . Use Python to simulate the rough surface micro-convex morphology, such as Figure 2 shown.

[0085] Step 2: Construct an isotropic fractal rough surface based on fractal dimension and fractal roughness.

[0086] In the construction process of the fractal rough surface in the above step 2 of the embodiment of the present invention, the expression is:

[0087] z x,y &=L G L D-2 lnγ M ∑ m=1 M ∑ n=0 n max c D-3 n &× cos ϕ m,n - cos [ 2π c n x 2 + y 2 1 2 L × cos tan - 1 y x - πm M + ϕ m,n ]

[0088] In the formula, represents the surface topography height, Indicates the sampling point Towards coordinates, Indicates the sampling point Towards coordinates, represents the sampling length, represents the fractal roughness, represents the fractal dimension, represents the surface frequency density, represents the number of superimposed peaks of the reconstructed surface, Represents the surface frequency index, setting the highest frequency to , The upper limit is n max = int [ log L / L S / logγ] , represents the measurement scale (determined by the resolution of the instrument), int […] Indicates the maximum integer value of the number in the brackets. Indicates the sequence number of the reconstructed surface superposition peak, starting from Start taking numbers. Indicated in [0,2π] Random phases evenly distributed within the range.

[0089] The fractal roughness obtained in step 1 and fractal dimension Substitute the above formula and use Python to simulate the convex morphology of the rough surface.

[0090] Step 3: Establish a micro-asperity model under the action of temperature, and use the micro-asperity model to analyze the contact parameters at different deformation stages; wherein the micro-asperity model is a micro-asperity normal contact load and normal contact stiffness model, and different deformation stages include elastic deformation stage, elastoplastic deformation stage and plastic deformation stage.

[0091] On the basis of the above step three, step three of the embodiment of the present invention also includes: assuming the contact of the fractal rough surface as the contact between a rough surface and a rigid ideal plane, and the micro-convex body model as the contact between a spherical micro-convex body and a rigid ideal plane. During the service of the product, as the ambient temperature changes, the originally connected joints produce constraints and restrictions, and thermal stress is generated between the contact surfaces; moreover, the contact analysis under the influence of temperature in the embodiment of the present invention, compared with the contact analysis without thermal stress, only adds the temperature load, and the other aspects are exactly the same. Therefore, the embodiment of the present invention changes the normal contact load Divided into mechanical loads Loads due to thermal stress , ;

[0092] Thermoelastic normal contact load caused by thermal stress factors during elastic deformation stage Expressed as ; In the formula, represents the normal mechanical load in the elastic deformation stage, It represents the normal load caused by thermal stress factors in the elastic deformation stage, and the expression is ; In the formula, represents the linear expansion coefficient, represents the equivalent elastic modulus, Represents the temperature difference, Represents the actual micro-contact cross-sectional area of ​​the micro-convex body in the elastic deformation stage.

[0093] Equivalent elastic modulus formula

[0094] In the formula, represents the elastic modulus of a contact surface, represents the elastic modulus of the other contact surface, represents the Poisson's ratio corresponding to a contact surface, Represents the Poisson's ratio corresponding to the other contact surface.

[0095] Based on the Hertz contact theory, the actual micro-contact cross-sectional area of ​​the micro-convex body in the elastic deformation stage is obtained and normal mechanical load in the elastic deformation stage They are:

[0096] ,

[0097] In the formula, represents the radius of curvature of the microconvex body, represents the equivalent elastic modulus, represents the deformation of the microconvex body, according to Figure 3 The geometric relationship is obtained by the Pythagorean theorem , where Represents the radius of the actual micro-contact area of ​​the micro-asperity.

[0098] In the embodiment of the present invention, the actual micro-contact cross-sectional area of ​​the micro-convex body during the elastic deformation stage is and micro-contact cross-sectional area The relationship is: Normal load caused by thermal stress factors during elastic deformation It is expressed as: .

[0099] The contact deformation of the micro-asperities in the micro-asperity model includes the elastic deformation stage, specifically:

[0100] Thermoelastic normal contact load caused by thermal stress factors during the elastic deformation stage It is expressed as:

[0101] In the formula, represents the normal mechanical load in the elastic deformation stage, represents the normal load caused by thermal stress factors in the elastic deformation stage, represents the micro-contact cross-sectional area of ​​the micro-convex body, represents the linear expansion coefficient, represents the equivalent elastic modulus, Indicates temperature difference;

[0102] Thermoelastic normal contact stiffness of asperities in the elastic deformation stage The expression is:

[0103]

[0104] In the formula, represents the thermo-elastoplastic normal contact load right The first derivative of Indicates the deformation of the micro-convex body right The first derivative of represents the thermo-elastoplastic normal contact load Deformation of the micro-convex body The first derivative of .

[0105] More specifically, based on the fractal rough surface and the asperity model, step three of the embodiment of the present invention further includes: the contact deformation of the asperities in the asperity model also includes elastic-plastic deformation and plastic deformation, specifically:

[0106] (1) Elastic-plastic deformation includes: when the deformation of the micro-convex body is greater than the elastic critical deformation, the material begins to yield and the micro-convex body enters the elastic-plastic deformation stage. It is expressed as:

[0107]

[0108] in, represents the correlation factor, which is the hardness and yield strength Ratio.

[0109] When the deformation In the range, the microconvex body is in the elastic-plastic deformation stage. When the deformation is , the yield area of ​​the microconvex body is located below the contact surface. As the load gradually increases, the yield area below the contact surface gradually expands. When the deformation amount is When , the yield area expands to the entire contact surface. Therefore, in the elastic-plastic deformation stage, the actual micro-contact cross-sectional area of ​​the micro-convex body is , Normal mechanical load and normal loads due to thermal stresses It is divided into the following two stages:

[0110] The first stage of elastic-plastic deformation , the second stage of elastic-plastic deformation ;in:

[0111] The expression of the first stage of elastic-plastic deformation is:

[0112]

[0113] In the formula, It represents the thermal elastic-plastic normal contact load caused by thermal stress factors in the first stage of elastic-plastic deformation. represents the normal elastic-plastic mechanical load in the first stage of elastic-plastic deformation, represents the normal load caused by thermal stress factors in the first stage of elastic-plastic deformation, represents the correlation factor, Indicates hardness;

[0114] The expression of the second stage of elastic-plastic deformation is:

[0115]

[0116] In the formula, It represents the thermal elastic-plastic normal contact load caused by thermal stress factors in the second stage of elastic-plastic deformation. represents the normal elastic-plastic mechanical load in the second stage of elastic-plastic deformation, It represents the normal load caused by thermal stress factor in the second stage of elastic-plastic deformation;

[0117] In the first stage of elastic-plastic deformation, the thermo-elastic-plastic normal contact stiffness of the micro-asperity is The expression is:

[0118]

[0119] In the second stage of elastic-plastic deformation, the thermo-elastic-plastic normal contact stiffness of the micro-asperity is The expression is:

[0120]

[0121] When the deformation increases to When the deformation of the micro-convex body When , it enters the stage of complete plastic deformation. In the plastic deformation stage, the thermoplastic normal contact load of the micro-convex body The expression is:

[0122] , ,

[0123] In the formula, represents the normal mechanical load borne by the micro-convex body during the plastic deformation stage, represents the normal load caused by thermal stress on the micro-convex body during the plastic deformation stage, It represents the actual micro-contact area of ​​micro-convex body in the plastic deformation stage;

[0124] Normal mechanical load on the asperity The expression is:

[0125] ,

[0126] In the formula, It represents the actual micro-contact area of ​​micro-convex body in the plastic deformation stage;

[0127] Normal plastic mechanical load during plastic deformation stage It is expressed as:

[0128]

[0129] In the formula, represents the micro-contact cross-sectional area of ​​the micro-convex body, where:

[0130]

[0131] Plastic deformation includes: During the plastic deformation stage, the thermoplastic normal contact load caused by thermal stress factors It is expressed as:

[0132]

[0133] In the formula, represents the normal plastic mechanical load in the plastic deformation stage, represents the normal load caused by thermal stress factors in the plastic deformation stage, Represents yield strength.

[0134] In the plastic deformation stage, the calculation of normal contact stiffness does not include the micro-convex body that has undergone plastic deformation. Therefore, in the plastic deformation stage, the thermoplastic normal contact stiffness of the micro-convex body is .

[0135] Step 4: Extend the micro-convex body model to the entire accelerometer joint to obtain the total normal contact load and normal contact stiffness of the accelerometer joint under the influence of temperature.

[0136] Based on the above step 4, more specifically, step 4 of the embodiment of the present invention further includes:

[0137] Based on the convex body model, the total normal contact load and normal contact stiffness of the accelerometer joint are established, where:

[0138] Asperity micro-contact cross-sectional area size distribution function The expression is:

[0139]

[0140] In the formula, represents the fractal dimension, represents the area expansion factor of the microcontact size distribution, represents the maximum micro-contact cross-sectional area, represents the micro-contact cross-sectional area of ​​the micro-asperity; Through the dichotomy method, it is obtained and obeys the following relationship:

[0141]

[0142] when ,get , that is, the critical elastic micro-contact cross-sectional area , critical elastic micro-contact cross-sectional area The expression is:

[0143]

[0144] Will and Divide them and we get

[0145] .

[0146] when When a ` ∈[0, a c ` )+[ a c ` , a L ` ] , in the integral interval a ` ∈[ a c ` , a L ` ] Inside, there is , at this time, the microconvex body undergoes elastic deformation; in the integral interval According to the elastic-plastic and plastic deformation stages, and The relationship between the integral interval is further divided into [0, ( 1 110 ) 1 (D-1) a c ` ] , [ 1 110 1 D-1 a c ` , ( 1 6 ) 1 (D-1) a c ` ] , Three intervals. a ` ∈ [ 0, ( 1 110 ) 1 (D-1) a c ` ] When , the microconvex body is in the plastic deformation stage; when a ` ∈[ ( 1 110 ) 1 (D-1) a c ` , ( 1 6 ) 1 (D-1) a c ` ] When , the microconvex body is in the second elastic-plastic deformation stage; when When , the micro-convex body is in the first elastic-plastic deformation stage.

[0147] From the above, we can see that when the micro-contact cross-sectional area is smaller, due to the curvature radius of the micro-convex body Micro-contact cross-sectional area Therefore, the curvature radius of the micro-convex body decreases as the micro-contact cross-sectional area decreases. As the curvature radius decreases, the critical elastic deformation The lower the micro-contact cross-sectional area, the easier it is for the micro-contact to undergo plastic deformation. On the contrary, when the micro-contact cross-sectional area is larger, the micro-contact is more likely to undergo elastic deformation.

[0148] The total normal contact load of the accelerometer joint in the embodiment of the present invention is the sum of the loads causing elastic, elastoplastic and plastic deformations, which can reflect the influence of temperature change on the overall normal total load of the contact part. When the total normal contact load of the accelerometer joint is The relationship between the normal contact load of the micro-protrusion and the micro-contact cross-sectional area size distribution function of the micro-protrusion at different deformation stages in step three is expressed as follows:

[0149] .

[0150] when When Directly substitute into the above formula and then integrate. ,and When , integrate the above formula and expand it to get:

[0151] .

[0152] In the embodiment of the present invention, the contact deformation of the accelerometer joint portion is in the elastic and elastoplastic deformation stage, and the convex body has a normal contact stiffness. When the total normal contact stiffness of the accelerometer joint is is the sum of the stiffness in the elastic stage and the elastoplastic stage, expressed as:

[0153]

[0154] According to the above disclosed method for calculating the contact stiffness of the accelerometer joint considering the influence of temperature, an example of calculating the contact stiffness of the accelerometer joint is described as follows:

[0155] Calculate the contact stiffness of the joint under the influence of temperature. The contact between two parts constitutes the joint, such as Figure 4 In the model shown, Part_A is 20mm×20mm in length and 0.5mm in thickness, and Part_B is 20mm×20mm in length and 1mm in thickness. The surface of Part_A is considered as an ideal smooth rigid plane, and the surface of Part_B is considered as a rough surface. Assuming that the temperature of Part_A remains unchanged, the ambient temperature only raises the temperature of the other part Part_B in contact with it, thus generating different temperature differences at the contact points. Set the initial temperature to 20℃ and the service ambient temperature to 50℃. The joint is a rough surface contact, and the contact stiffness of the joint under the influence of service temperature is calculated. The material properties are as follows: Figure 6 The material property parameters of the two contact surfaces are shown.

[0156] The surface morphology is scanned using a three-dimensional profile scanner, and the discrete height samples obtained by sampling are substituted into the structure function formula of the above method of the embodiment of the present invention, and a double logarithmic image is drawn. The fitting curve is obtained according to the least squares method. The result is as follows: Figure 5 As shown. Then calculate the fractal dimension Fractal Roughness , critical elastic micro-contact cross-sectional area , Calculated by dichotomy , the load is set to When the maximum micro-contact cross-sectional area is obtained According to the specific implementation process, the parameters such as fractal dimension, fractal roughness and material properties are introduced into the above steps of the embodiment of the present invention, and the normal contact stiffness of this example is obtained as .

[0157] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope of the present invention.

Claims

1. A method for calculating the contact stiffness of an accelerometer joint considering the influence of temperature, characterized in that: include: Step 1, measuring the rough surface of the accelerometer joint, calculating the fractal characteristic parameters of the rough surface, and obtaining the fractal dimension and fractal roughness of the rough surface based on the fractal characteristic parameters; Step 2: constructing an isotropic fractal rough surface based on the fractal dimension and the fractal roughness; Step 3: Establish a micro-asperity model under the action of temperature, and use the micro-asperity model to analyze the contact parameters at different deformation stages; wherein the micro-asperity model is a micro-asperity normal contact load and normal contact stiffness model, and different deformation stages include an elastic deformation stage, an elastic-plastic deformation stage, and a plastic deformation stage; Step 4: generalize the asperity model to the entire accelerometer joint to obtain the total normal contact load and normal contact stiffness of the accelerometer joint under the influence of temperature; Wherein, the step 3 establishes the normal contact load and normal contact stiffness model of the micro-convex body under the action of temperature. Specifically: the normal contact load p is divided into the mechanical load p m Loads due to thermal stress p t , p=p m +p t ; Thermoelastic normal contact load p caused by thermal stress factors during the elastic deformation stage e (a ` ) is expressed as: In the formula, p me (a ` ) represents the normal mechanical load in the elastic deformation stage, p te (a ` ) represents the normal load caused by thermal stress factors in the elastic deformation stage, a ` represents the micro-contact cross-sectional area of ​​the micro-convex body, α represents the linear expansion coefficient, E represents the equivalent elastic modulus, and ΔT represents the temperature difference; Thermoelastic normal contact stiffness k of the asperity in the elastic deformation stage ne The expression is: In the formula, represents the thermo-elastoplastic normal contact load p e (a ` ) ` The first derivative of represents the deformation of the microconvex body δ(a ` ) ` The first derivative of represents the thermo-elastoplastic normal contact load p e (a ` ) for the deformation of the microconvex body δ(a ` )’s first-order derivative; The first stage of elastic-plastic deformation c ≤δ<6δ c , the second stage of elastic-plastic deformation 6δ c ≤δ≤110δ c ;in: The expression of the first stage of elastic-plastic deformation is: In the formula, p ep1 (a ` ) represents the thermal elastic-plastic normal contact load caused by thermal stress factors in the first stage of elastic-plastic deformation, p mep1 (a ` ) represents the normal elastic-plastic mechanical load in the first stage of elastic-plastic deformation, p tep1 (a ` ) represents the normal load caused by thermal stress factors in the first stage of elastic-plastic deformation, K represents the correlation factor, and H represents the hardness; The expression of the second stage of elastic-plastic deformation is: In the formula, p ep2 (a ` ) represents the thermal elastic-plastic normal contact load caused by thermal stress factors in the second stage of elastic-plastic deformation, p mep2 (a ` ) represents the normal elastic-plastic mechanical load in the second stage of elastic-plastic deformation, p tep2 (a ` ) represents the normal load caused by thermal stress factors in the second stage of elastic-plastic deformation; In the first stage of elastic-plastic deformation, the thermo-elastic-plastic normal contact stiffness k of the micro-convex body is nep1 The expression is: In the second stage of elastic-plastic deformation, the thermo-elastic-plastic normal contact stiffness k of the micro-asperity is nep2 The expression is: In the plastic deformation stage, the thermoplastic normal contact load p of the micro-convex body is p The expression is: p p =p mp +p tp ,p mp =Kσ y a p , In the formula, p mp represents the normal mechanical load borne by the micro-convex body during the plastic deformation stage, p tp represents the normal load caused by thermal stress on the micro-convex body during the plastic deformation stage, a p It represents the actual micro-contact area of ​​micro-convex body in the plastic deformation stage; Normal plastic mechanical load p in the plastic deformation stage mp (a ` ) is expressed as: p mp (and ` )=Kσ y and ` In the formula, a ` represents the micro-contact cross-sectional area of ​​the micro-asperity; In the plastic deformation stage, the thermoplastic normal contact load p caused by thermal stress factors p (a ` ) is expressed as: p p (a ` )=p mp (a ` )+p tp (a ` )=Kσ y a ` +αEΔTa ` In the formula, p mp (a ` ) represents the normal plastic mechanical load in the plastic deformation stage, p tp (a ` ) represents the normal load caused by thermal stress factors in the plastic deformation stage, σ y represents yield strength; In the plastic deformation stage, the thermoplastic normal contact stiffness k of the micro-convex body is np =0.

2. The method for calculating the contact stiffness of the accelerometer joint considering the temperature influence according to claim 1, characterized in that: The step one comprises: The profile data of the rough surface of the accelerometer joint is measured by a three-dimensional profile measuring instrument, and the surface topography data of the rough surface is recorded in the form of discrete height samples; The fractal characteristic parameters of the rough surface are calculated, and the fractal dimension and fractal roughness are calculated using a structure function.

3. The method for calculating the contact stiffness of the accelerometer joint considering the temperature influence according to claim 2, characterized in that: In the step 1, the process of recording the surface topography data includes: Assume that the number of sampling points of the surface topography data is N, the discrete height sample data of the surface topography is z(x), and x is the x-coordinate of the sampling point. Then the discrete height sample data z(x) of the i-th sampling point is i ) is expressed as: z(x i ) = z i (i = 0, 1, 2, …, N - 1) Equation (1) In the formula, x i represents the x-coordinate of the i-th sampling point, z i Represents the surface profile height of the i-th sampling point; The incremental equation of the discrete height sample data z(x) of the surface topography is set as the structure function S(τ), which is expressed as: In the formula, <> means finding the average value, z(x+τ) means the surface height value with an interval of τ from x, τ means an arbitrarily selected value of the data interval, n0 means the count of the sampling points, represents the surface profile height of the i+n0th sampling point, C ` represents the relationship coefficient between the structure function and the fractal parameters, G represents the fractal roughness, and D represents the fractal dimension; Take the logarithm of both ends of equation (2), perform least squares fitting on the structure function, and obtain the slope k and intercept b of the fitting line. The fractal dimension D is determined by the slope k of the line, which is expressed as: The fractal roughness G is determined by the intercept b and is expressed as:

4. The method for calculating the contact stiffness of an accelerometer joint considering the influence of temperature according to claim 1, characterized in that: The expression of the fractal rough surface in step 2 is: In the formula, z(x,y) represents the surface topography height, x represents the x-coordinate of the sampling point, y represents the y-coordinate of the sampling point, L represents the sampling length, G represents the fractal roughness, D represents the fractal dimension, γ represents the surface frequency density, M represents the number of superimposed peaks of the reconstructed surface, and n represents the sampling length. max represents the upper bound of the surface frequency index, n represents the surface frequency index, m represents the sequence number of the reconstructed surface superposition peak, φ m,n represents a random phase uniformly distributed in the range [0,2π].

5. The method for calculating the contact stiffness of the accelerometer joint considering the temperature influence according to claim 4, characterized in that: The step three also includes: The contact of the fractal rough surface is assumed to be the contact between a rough surface and a rigid ideal plane, and the asperity model is the contact between a spherical asperity and a rigid ideal plane.

6. The method for calculating the contact stiffness of an accelerometer joint considering the influence of temperature according to claim 1, characterized in that: The step 4 also includes: Based on the convex body model, the total normal contact load and normal contact stiffness of the accelerometer joint are established, where: The distribution function of the microcontact cross-sectional area of ​​microprotrusions n(a ` ) is: n(a ` )=0.5Dψ 1-0.5D a L `0.5D a `-1-0.5D Where ψ represents the area expansion factor of the micro-contact size distribution, a L ` represents the maximum micro-contact cross-sectional area; Critical elastic micro-contact cross-sectional area a c ` The expression is: The total normal contact load of the accelerometer joint is preferably the sum of the loads causing elastic, elastoplastic and plastic deformation, reflecting the influence of temperature change on the overall normal total load of the contact part. L ` >a c ` When the total normal contact load p(a L ` >a c ` ) is expressed as:

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