Two-stage decay prediction method for ball screw preload

Abstract

The present invention discloses a two-stage decay prediction method for the preload force of a ball screw pair, and belongs to the technical field of research on the service performance of a ball screw pair. The present invention combines macroscopic geometric errors and microscopic contacts to model the decay process of the preload force of a ball screw pair, describes the geometric errors and calculates the wear depth of the first stage (rapid decay stage), corrects the formula for calculating the adhesive wear volume based on fractal theory, corrects the distribution function of the number of micro-convex bodies, calculates the volume of abrasive wear, and can more accurately describe the actual situation of the decay of the preload force, and more accurately predict the decay process of the preload force of a ball screw pair.

Description

Technical Field

[0001] The invention belongs to the technical field of ball screw pair service performance research, in particular to a two-stage decay prediction method for a ball screw pair preload force. Background Art

[0002] As one of the most critical parameters of a ball screw pair, preload affects its stiffness, precision and many other properties. However, due to wear during operation, the gap between the ball and the raceway will increase, resulting in a decrease in preload, which in turn affects the overall performance of the equipment. Therefore, establishing a calculation method for the preload decay of a ball screw pair is important for improving performance.

[0003] Current research mainly focuses on the uniform decay stage, directly or indirectly measuring the preload through different methods, and studying the impact of preload changes on other properties. However, due to the existence of macro-geometric errors in the raceway profile, ball screw pairs often exhibit two-stage degradation characteristics. Since the first stage usually accounts for about 20% of the entire preload decay process, the traditional method has poor prediction effect during actual use. To this end, the present invention proposes a two-stage decay prediction method for ball screw preload, which solves the problem that the existing method can only predict the uniform decay stage of the preload, and provides an important basis for calculating the degradation of the preload. Summary of the invention

[0004] The purpose of the present invention is to provide a two-stage decay prediction method for the preload force of a ball screw pair in view of the problems existing in the above-mentioned prior art.

[0005] The technical solution to achieve the purpose of the present invention is: a two-stage decay prediction method for the preload force of a ball screw pair, the method comprising the following steps:

[0006] Step 1: Calculate the initial preload force F of the ball screw pair based on Hertz theory p0 ;

[0007] Step 2: According to the wear mechanism of the ball screw pair, establish the overall model F of preload degradation p (t);

[0008] Step 3, calculating the actual force of the two nuts of the ball screw pair under the combined action of the preload force and the external load;

[0009] Step 4, modeling the geometric error of the screw, establishing a ball screw pair wear model considering the geometric error, and calculating the wear depth;

[0010] Step 5: Substitute the wear depth into the overall model F established in step 2 p (t), calculate the preload force F after wear p, substitute it into step 3, recalculate the actual forces of the two nuts, repeat steps 3 to 5 until the accumulated wear depth is equal to the peak value of the macro-geometric error, and obtain the preload force decay curve of the first stage, i.e., the rapid decay stage; the peak value of the macro-geometric error is the sum of the measured peak values ​​of the geometric errors;

[0011] Step 6, using fractal theory to model the raceway micro-profile and calculate the fractal parameters of the raceway surface;

[0012] Step 7, constructing a correction coefficient for the number of micro-convexities of the ball screw pair;

[0013] Step 8, calculating the actual contact area and load of the ball in combination with the correction coefficient of the number of micro-convex bodies of the ball screw pair;

[0014] Step 9, considering the elastic-plastic changes of the micro-convex body, the adhesive wear amount based on the fractal theory is calculated, and the abrasive wear amount is calculated according to the actual contact area and load;

[0015] Step 10, summing the adhesive wear and abrasive wear, establishing a wear model that takes microscopic contact characteristics into consideration, and calculating the wear depth;

[0016] Step 11: Substitute the wear depth from step 10 into the overall model F established in step 2 p (t), calculate the preload force F after wear p , substitute it into step 3, recalculate the actual force of the two nuts; repeat steps 8 to 11 until the number of revolutions reaches the set maximum value, and obtain the preload force decay curve of the second stage, i.e., the uniform decay stage

[0017] Compared with the prior art, the present invention has the following significant advantages: 1) By modeling the macro-geometric errors of the raceways, the contact conditions between the ball raceways are described more accurately, and the wear and preload decay conditions in the first stage (rapid decay stage) can be calculated more accurately; 2) A correction coefficient for the distribution density of fractal micro-protrusions of a ball screw pair is proposed, so that the calculation of the number of micro-protrusions is more accurate; 3) The adhesion wear volume calculation model based on fractal theory is corrected to be more in line with the actual situation of micro-protrusion deformation and wear; 4) By adding the abrasive wear volume calculation to the calculation of the wear amount in the second stage (uniform decay stage), the calculation of the wear amount in the second stage is made more accurate; 5) Based on the above results, a preload decay calculation model for a ball screw pair is established, so that the calculation results are more in line with the actual situation and more accurate.

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention is a flow chart of the two-stage decay prediction method of the preload force of a ball screw pair.

[0020] Figure 2 Schematic diagram of ball deformation under force.

[0021] Figure 3 Schematic diagram of the macro-geometric error of the raceway.

[0022] Figure 4 Schematic diagram of solving fractal parameters by structure function method, where (a) is the surface data before running-in, and (b) is the surface data after running-in.

[0023] Figure 5 Graph showing test and preload force decay prediction results in one embodiment. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0025] In one embodiment, in combination Figure 1 , a two-stage decay prediction method for a ball screw preload force is provided, the method comprising the following steps:

[0026] Step 1: Calculate the initial preload force F of the ball screw pair based on Hertz theory p0 ;

[0027] Step 2: According to the wear mechanism of the ball screw pair, establish the overall model F of preload degradation p (t);

[0028] Step 3, calculating the actual force of the two nuts of the ball screw pair under the combined action of the preload force and the external load;

[0029] Step 4, modeling the geometric error of the screw, establishing a ball screw pair wear model considering the geometric error, and calculating the wear depth;

[0030] Step 5: Substitute the wear depth into the overall model F established in step 2 p (t), calculate the preload force F after wear p , substitute it into step 3, recalculate the actual forces of the two nuts, repeat steps 3 to 5 until the accumulated wear depth is equal to the peak value of the macro-geometric error, and obtain the preload force decay curve of the first stage, i.e., the rapid decay stage; the peak value of the macro-geometric error is the sum of the measured peak values ​​of the geometric errors;

[0031] Step 6, using fractal theory to model the raceway micro-profile and calculate the fractal parameters of the raceway surface;

[0032] Step 7, constructing a correction coefficient for the number of micro-convexities of the ball screw pair;

[0033] Step 8, calculating the actual contact area and load of the ball in combination with the correction coefficient of the number of micro-convex bodies of the ball screw pair;

[0034] Step 9, considering the elastic-plastic changes of the micro-convex body, the adhesive wear amount based on the fractal theory is calculated, and the abrasive wear amount is calculated according to the actual contact area and load;

[0035] Step 10, summing the adhesive wear and abrasive wear, establishing a wear model that takes microscopic contact characteristics into consideration, and calculating the wear depth;

[0036] Step 11: Substitute the wear depth from step 10 into the overall model F established in step 2 p (t), calculate the preload force F after wear p , substitute it into step 3, and recalculate the actual forces of the two nuts; repeat steps 8 to 11 until the number of revolutions reaches the set maximum value, and obtain the preload force decay curve of the second stage, i.e., the uniform decay stage.

[0037] Further, in one embodiment, according to Hertz's theory, the normal load is proportional to the 3 / 2 power of the deformation. Figure 2 , the initial preload force F of the ball screw pair described in step 1 p0 The calculation formula is:

[0038]

[0039] In the formula, δ 0m'ni ,δ 0m'si They represent the normal deformation between the i-th ball and the nut and the screw raceway under the initial preload, m' represents the working nut A or the preload nut B, C kn and C kE is the structural constant, C E is the material constant, α m'ni , α m'si Respectively represent the contact angles between the ball and the nut, and between the ball and the screw raceway. represents the lead angle and M represents the number of balls.

[0040] Further, in one embodiment, the overall model F of the preload force degradation in step 2 is p (t) is:

[0041]

[0042] In the formula, Δδ m'ni , Δδ m'siRepresent the wear depth between the i-th ball and the nut raceway and the screw raceway respectively.

[0043] Further, in one embodiment, the calculation of the actual force of the two nuts of the ball screw pair under the combined action of the preload force and the external load in step 3 specifically includes:

[0044] When subjected to external load F a When the working nut A and the preloaded nut B are actually subjected to the load, the equation is:

[0045] F a =F p +F A -(F p -F B )=F A +F B

[0046] In the formula, F A and F B They are the increase / decrease of the working nut A and the preloaded nut B relative to the original preload force after loading; the coordination relationship between the axial force and deformation between the two nuts is expressed as follows:

[0047] The force on the working nut A can be regarded as the resultant force of M balls acting on the raceway:

[0048]

[0049] It can also be decomposed into the sum of the Hertz contact stress of the i-th ball and the forces of the remaining i-1 balls:

[0050]

[0051] Similarly, the force on the preload nut B also satisfies the following two relationships:

[0052]

[0053]

[0054] The relationship between Hertz contact stress and deformation is as follows:

[0055]

[0056] Where Z is the number of effective balls in a circle that bear the load, E is the elastic modulus, and A is n is the cross-sectional area of ​​the nut, P h is the screw lead, Q A1 and Q B1 Respectively represent the normal contact load of the first ball in the working nut A and the preloaded nut B, sinα A1 and sinαB1 Respectively represent the contact angle of the first ball in the working nut A and the preload nut B, δ 0m's1 and δ 0m'n1 Respectively represent the normal initial deformation of the first ball in the working nut A and the preloaded nut B;

[0057] Combined with the above formula, the actual forces of the two nuts under the action of preload and external load are obtained through iterative calculation.

[0058] Further, in one embodiment, the geometric error of the screw is modeled in step 4, a ball screw pair wear model considering the geometric error is established, and the wear depth is calculated, which specifically includes:

[0059] Step 4-1, according to Archard theory, the wear volume, i.e. the wear volume model of the ball screw pair considering geometric errors, is expressed as follows:

[0060]

[0061] In the formula, K represents the wear coefficient, Q represents the contact load, H represents the raceway hardness, and L sliding and V sliding They represent sliding distance and sliding speed respectively, N represents running-in revolutions, and w represents the angular velocity of the screw;

[0062] Step 4-2, the wear volume can be expressed by the contact area S and the wear depth h, recorded as W = S × h, then the wear rate dh is expressed as:

[0063]

[0064] According to Hertz theory, the contact surface between the ball and the raceway is an ellipse. Assuming that the contact area between the ball and the raceway in the same nut is equal, the total contact area S is proportional to the length of the minor semi-axis of the ellipse, and its proportionality coefficient is denoted as k. s , the wear rate is recorded as:

[0065]

[0066] In order to find the expression of b, it is necessary to model the raceway morphology considering the geometric error, which is described here by the sine function:

[0067] f i (x) = A i sin(2πx / L i +θ i )

[0068] In the formula, A i is the peak value corresponding to the i-th error curve, L i represents wavelength, θ irepresents the phase, i=1,2,...,u, and u is the number of geometric error categories. After superimposing the four error curves, the actual profile of the raceway can be expressed as:

[0069]

[0070] Because L i It is determined by the sampling length of the roughness meter, so u (the number of geometric error categories, considering waviness, profile error, pitch error, ball diameter error, then u is 4) L i can be regarded as equal. At this time, the actual profile considering the macroscopic geometric error can be regarded as a comprehensive sine function such as Figure 3 As shown, the formula is:

[0071] f(x)=Asin(2πx / L+θ)

[0072] Then the minor semi-axis b is expressed as:

[0073]

[0074] Where A is the peak value of the macroscopic geometric error, L is the wavelength, θ is the phase, b0 is the initialization length of the minor semi-axis, and N1 is the time it takes to wear out the peak value of the macroscopic geometric error in the first stage, i.e., the rapid decay stage;

[0075] The wear rate dh is converted to:

[0076]

[0077] The wear depth Δδ is calculated from this m'n'i for:

[0078]

[0079] Further, in one embodiment, in step 6, the fractal theory is used to model the microscopic profile of the raceway, the fractal parameters of the raceway surface are calculated, the contour features of the raceway surface before and after wear are collected by white light interferometer, and the profile data is processed by the structure function method. The obtained function is as shown in the attached figure. Figure 4 As shown, the fractal parameters D and G that characterize the rough surface are calculated using the following formula:

[0080] D=2-0.5k

[0081] lgG=(B-lgC) / 2(D-1)

[0082] Where k is the slope of lgS(τ)=(4-2D)lgτ+lgC+2(D-1)lgG, B is the intercept, S(τ) represents the power spectrum function of the raceway profile, and the calculation formula is:

[0083]

[0084] Where τ = nΔL, n is the sampling point count, ΔL is the sampling interval, N0 is the total number of samples, C = Γ(2D-3)sin[(D-1.5)π] / (4-2D)lnγ, and the calculation formula of the Γ function is: The final fractal parameters are the average values ​​before and after wear.

[0085] Furthermore, in one embodiment, the three factors affecting the number of contact micro-protrusions are: the elliptical area of ​​Hertzian contact, the theoretical contact area, and the equivalent radius of curvature between the two raceway surfaces. Combined with the exponential form of the original micro-protrusion distribution density function, the correction coefficient λ of the number of micro-protrusions of the ball screw pair is constructed as follows:

[0086]

[0087] In the formula, S ellipse is the elliptical area of ​​the Hertzian contact between the ball and the raceway, S0 is the area of ​​the ball diameter circle projected from the normal to the raceway, ρ is the comprehensive curvature radius, r and R are the ball radius and the curvature radius of the raceway respectively.

[0088] Further, in one embodiment, the calculation of the actual contact area and load of the ball in step 8 in combination with the correction coefficient of the number of micro-protrusions of the ball screw pair specifically includes:

[0089] Let the area of ​​a single microconvex body be a, and the area of ​​the largest microconvex body be a L , the critical area of ​​elastic-plastic deformation and plastic deformation of the micro-convex body is a pc , the critical area of ​​elastic deformation and elastic-plastic deformation of the micro-convex body is a ec According to the ratio of the maximum convex area to the two critical areas, the actual contact area and load of the ball are calculated, which are divided into the following types:

[0090] (1) When a L <a pc When all the micro-convex bodies are in a state of complete plastic deformation, the load on a single micro-convex body is P p =1.1K f σ y a,K f is the friction correction coefficient, μ is the friction coefficient, σ y is the yield strength;

[0091] The load on each ball is expressed as:

[0092]

[0093] The actual contact area of ​​the plastic deformation part is:

[0094]

[0095] in, The corrected asperity number is ψ is the domain expansion coefficient, E' is the equivalent elastic modulus;

[0096] (2) When a pc <a L <a ec When , some micro-convex bodies are in a completely plastic deformation state, while others are in an elastic-plastic state. The load on a single micro-convex body is The load on each ball is expressed as:

[0097]

[0098] The actual contact area of ​​the elastic-plastic deformation part is:

[0099]

[0100] in,

[0101] (3) When a ec <a L When , the micro-convex body has three deformation states: elastic, elastoplastic and plastic. The load on a single micro-convex body is

[0102] When D=1.5, the load on each ball is expressed as:

[0103]

[0104] When D≠1.5, the load on each ball is expressed as:

[0105]

[0106] The actual contact area of ​​the elastic deformation part is:

[0107]

[0108] Further, in one embodiment, the calculation of the adhesive wear amount based on fractal theory in step 9 specifically includes:

[0109] Taking into account the three deformation states of the micro-convex body (elastic, elastoplastic, and plastic), the original wear volume calculation formula that only considers the elastic and plastic deformation states is improved, and the revised formula is:

[0110] V adh =(1+γ e μ2 ) 1 / 2 (K e A e +K ep A ep +K p A p )L sliding

[0111] Where V adh is the adhesive wear amount, A e , A ep , A p They represent the contact area of ​​the micro-convex body that undergoes elastic, elastoplastic, and plastic deformation, respectively, and K e , K ep , K p Respectively represent the wear coefficients of elasticity, elastoplasticity, and plastic deformation, γ e It is an empirical parameter and takes the value of 9;

[0112] In step 9, the abrasive wear amount is calculated based on the actual contact area and load obtained, and the calculation formula is:

[0113]

[0114] Where V abr is the abrasive wear, K m is the abrasive wear coefficient.

[0115] Further, in one embodiment, the step 10 of summing the adhesive wear amount and the abrasive wear amount, establishing a wear amount model considering microscopic contact characteristics, and calculating the wear depth specifically includes:

[0116] The wear volume model considering the microscopic contact characteristics is established as follows:

[0117]

[0118] The wear depth is calculated based on the wear volume model:

[0119]

[0120] In the formula, A m'n'i Indicates the actual contact area between each ball and the raceway, A m'n'i =A e +A ep +A p , K′ n'i is the corrected contact coefficient of the ball screw pair, which characterizes the intermittent contact characteristics between the ball and the raceway of the ball screw pair. Where L n′ is the effective length of the raceway.

[0121] For example, in one of the embodiments, the method of the present invention is further verified and described. The two-stage ball screw preload decay model is verified by testing the preload decay process of a domestic manufacturer's DKFZD3210 model ball screw pair. The results are as follows: Figure 5 As shown. When only the traditional Archard theory is used, the calculated results drop rapidly, which is very different from the experimental results. Comparing the theoretical model that does not consider the elastic-plastic deformation area of ​​the micro-convex body and the abrasive wear with the experimental results, the theoretical value of the second stage is smaller, indicating that the wear volume of these two parts cannot be ignored.

[0122] In summary, the present invention combines macro-geometric errors and micro-contacts to model the preload decay process of a ball screw pair, describes the geometric errors and calculates the wear depth of the first stage (rapid decay stage), corrects the formula for calculating the adhesive wear volume based on fractal theory, corrects the micro-asperity number distribution function, and calculates the volume of abrasive wear. It can more accurately describe the actual situation of preload decay and make a more precise prediction of the preload decay process of a ball screw pair.

Claims

1. A two-stage decay prediction method for the preload force of a ball screw pair, characterized in that: The method comprises the following steps: Step 1: Calculate the initial preload force F of the ball screw pair based on Hertz theory p0 ; Step 2: According to the wear mechanism of the ball screw pair, establish the overall model F of preload degradation p (t); Step 3, calculating the actual force of the two nuts of the ball screw pair under the combined action of the preload force and the external load; Step 4, modeling the geometric error of the screw, establishing a ball screw pair wear model considering the geometric error, and calculating the wear depth; Step 5: Substitute the wear depth into the overall model F established in step 2 p (t), calculate the preload force F after wear p , substitute it into step 3, recalculate the actual forces of the two nuts, repeat steps 3 to 5 until the accumulated wear depth is equal to the peak value of the macro-geometric error, and obtain the preload force decay curve of the first stage, i.e., the rapid decay stage; the peak value of the macro-geometric error is the sum of the measured peak values ​​of the geometric errors; Step 6, using fractal theory to model the raceway micro-profile and calculate the fractal parameters of the raceway surface; Step 7, constructing a correction coefficient for the number of micro-convexities of the ball screw pair; Step 8, calculating the actual contact area and load of the ball in combination with the correction coefficient of the number of micro-convex bodies of the ball screw pair; Step 9, considering the elastic-plastic changes of the micro-convex body, the adhesive wear amount based on the fractal theory is calculated, and the abrasive wear amount is calculated according to the actual contact area and load; Step 10, summing the adhesive wear and abrasive wear, establishing a wear model that takes microscopic contact characteristics into consideration, and calculating the wear depth; Step 11: Substitute the wear depth from step 10 into the overall model F established in step 2 p (t), calculate the preload force F after wear p , substitute it into step 3, and recalculate the actual forces of the two nuts; repeat steps 8 to 11 until the number of revolutions reaches the set maximum value, and obtain the preload force decay curve of the second stage, i.e., the uniform decay stage; The initial preload force F of the ball screw pair described in step 1 p0 The calculation formula is: In the formula, δ 0m'ni , δ 0m'si They represent the normal deformation between the i-th ball and the nut and the screw raceway under the initial preload, m' represents the working nut A or the preload nut B, C kn and C kE is the structural constant, C E is the material constant, α m'ni , α m'si Respectively represent the contact angles between the ball and the nut, and between the ball and the screw raceway. represents the lead angle, M represents the number of balls; The overall model F of the preload degradation described in step 2 p (t) is: In the formula, Δδ m'ni , Δδ m'si Represent the wear depth between the i-th ball and the nut raceway and the screw raceway respectively.

2. The two-stage decay prediction method of the ball screw preload force according to claim 1 is characterized in that: Step 3 calculates the actual forces on the two nuts of the ball screw pair under the combined action of the preload force and the external load, specifically including: When subjected to external load F a When the working nut A and the preloaded nut B are actually subjected to the load, the equation is: F a =F p +F A -(F p -F B )=F A +F B In the formula, F A and F B They are the increase / decrease of the working nut A and the preloaded nut B relative to the original preload force after loading; the coordination relationship between the axial force and deformation between the two nuts is expressed as follows: The force on the working nut A can be regarded as the resultant force of M balls acting on the raceway: Similarly, the force on the preload nut B also satisfies the following two relationships: The relationship between Hertz contact stress and deformation is as follows: Where Z is the number of effective balls in a circle that bear the load, E is the elastic modulus, and A is n is the cross-sectional area of ​​the nut, P h is the screw lead, Q A1 and Q B1 Respectively represent the normal contact load of the first ball in the working nut A and the preloaded nut B, sinα A1 and sinα B1 Respectively represent the contact angle of the first ball in the working nut A and the preload nut B, δ 0m's1 and δ 0m'n1 Respectively represent the normal initial deformation of the first ball in the working nut A and the preloaded nut B; Combined with the above formula, the actual forces of the two nuts under the action of preload and external load are obtained through iterative calculation.

3. The two-stage decay prediction method of the ball screw preload force according to claim 2 is characterized in that: The force of the working nut A can be decomposed into the sum of the Hertzian contact stress of the i-th ball and the forces of the remaining i-1 balls:

4. The two-stage decay prediction method of the ball screw preload force according to claim 3 is characterized in that: Step 4 describes modeling the geometric error of the screw, establishing a ball screw pair wear model that takes into account the geometric error, and calculating the wear depth, specifically including: Step 4-1, according to Archard theory, the wear volume, i.e. the wear volume model of the ball screw pair considering geometric errors, is expressed as follows: In the formula, K represents the wear coefficient, Q represents the contact load, H represents the raceway hardness, and L sliding and V sliding They represent sliding distance and sliding speed respectively, N represents running-in revolutions, and w represents the angular velocity of the screw; Step 4-2, the wear volume can be expressed by the contact area S and the wear depth h, recorded as W = S × h, then the wear rate dh is expressed as: According to Hertz theory, the contact surface between the ball and the raceway is an ellipse. Assuming that the contact area between the ball and the raceway in the same nut is equal, the total contact area S is proportional to the length of the minor semi-axis of the ellipse, and its proportionality coefficient is denoted as k. s , the wear rate is recorded as: Among them, the raceway profile considering the geometric error is expressed by the sine function f(x): f(x)=Asin(2πx / L+θ) Then the minor semi-axis b is expressed as: Where A is the peak value of the macroscopic geometric error, L is the wavelength, θ is the phase, b0 is the initialization length of the minor semi-axis, and N1 is the time it takes to wear out the peak value of the macroscopic geometric error in the first stage, i.e., the rapid decay stage; The wear rate dh is converted to: The wear depth Δδ is calculated from this m'n'i for:

5. The two-stage decay prediction method of the preload force of a ball screw pair according to claim 4 is characterized in that: In step 6, the fractal theory is used to model the microscopic surface of the raceway and calculate the fractal parameters of the raceway surface. The calculation formula is: D=2-0.5k lgG=(B-lgC) / 2(D-1) Where k is the slope of lgS(τ)=(4-2D)lgτ+lgC+2(D-1)lgG, B is the intercept, S(τ) represents the power spectrum function of the raceway profile, and the calculation formula is: Where τ = nΔL, n is the sampling point count, ΔL is the sampling interval, N0 is the total number of samples, C = Γ(2D-3)sin[(D-1.5)π] / (4-2D)lnγ, and the calculation formula of the Γ function is:

6. The two-stage decay prediction method of the preload force of a ball screw pair according to claim 5, characterized in that: The correction coefficient λ of the number of micro-convex bodies of the ball screw pair in step 7 is: In the formula, S ellipse is the elliptical area of ​​the Hertzian contact between the ball and the raceway, S0 is the area of ​​the ball diameter circle projected from the normal to the raceway, ρ is the comprehensive curvature radius, r and R are the ball radius and the curvature radius of the raceway respectively.

7. The two-stage decay prediction method of the preload force of a ball screw pair according to claim 6, characterized in that: Step 8 combines the correction coefficient of the number of micro-convex bodies of the ball screw pair to calculate the actual contact area and load of the ball, which specifically includes: Let the area of ​​a single microconvex body be a, and the area of ​​the largest microconvex body be a L , the critical area of ​​elastic-plastic deformation and plastic deformation of the micro-convex body is a pc , the critical area of ​​elastic deformation and elastic-plastic deformation of the micro-convex body is a ec According to the ratio of the maximum micro-convex area to the two critical areas, the actual contact area and load of the ball are calculated and divided into the following types: (1) When a L <a pc When all the micro-convex bodies are in a state of complete plastic deformation, the load on a single micro-convex body is P p =1.1K f σ y a,K f is the friction correction coefficient, μ is the friction coefficient, σ y is the yield strength; The load on each ball is expressed as: The actual contact area of ​​the plastic deformation part is: in, The corrected asperity number is ψ is the domain expansion coefficient, E' is the equivalent elastic modulus; (2) When a pc <a L <a ec When , some micro-convex bodies are in a completely plastic deformation state, while others are in an elastic-plastic state. The load on a single micro-convex body is The load on each ball is expressed as: The actual contact area of ​​the elastic-plastic deformation part is: in, (3) When a ec <a L When , the micro-convex body has three deformation states: elastic, elastoplastic and plastic. The load on a single micro-convex body is When D=1.5, the load on each ball is expressed as: When D≠1.5, the load on each ball is expressed as: The actual contact area of ​​the elastic deformation part is:

8. The two-stage decay prediction method of the preload force of a ball screw pair according to claim 7, characterized in that: The calculation of adhesive wear based on fractal theory described in step 9 is as follows: V adh =(1+γ e m 2 ) 1 / 2 (K e A e +K ep A ep +K p A p )L sliding Where V adh is the adhesive wear amount, A e , A ep , A p They represent the contact area of ​​the micro-convex body that undergoes elastic, elastoplastic, and plastic deformation, respectively, and K e , K ep , K p Respectively represent the wear coefficients of elasticity, elastoplasticity, and plastic deformation, γ e is an empirical parameter; In step 9, the abrasive wear amount is calculated based on the actual contact area and load obtained, and the calculation formula is: Where V abr is the abrasive wear, K m is the abrasive wear coefficient.

9. The two-stage decay prediction method of the preload force of a ball screw pair according to claim 8, characterized in that: In step 10, the adhesive wear amount and the abrasive wear amount are summed, a wear amount model considering microscopic contact characteristics is established, and the wear depth is calculated, which specifically includes: The wear volume model considering the microscopic contact characteristics is established as follows: The wear depth is calculated based on the wear volume model: In the formula, A m'n'i Indicates the actual contact area between each ball and the raceway, A m'n'i =A e +A ep +A p , K n ' 'i is the corrected contact coefficient of the ball screw pair, which characterizes the intermittent contact characteristics between the ball and the raceway of the ball screw pair. Where L n′ is the effective length of the raceway.

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