Calculation method of friction torque of ball screw pair suitable for different application occasions

Abstract

The invention discloses a ball screw pair friction torque calculation method suitable for different application occasions, and relates to the technical field of ball screw pair transmission performance calculation, and the method comprises the following steps: analyzing the contact characteristics of a ball and a contact raceway, and obtaining the contact stress and contact load at the contact position; the lubricating condition of the ball screw pair is determined by analyzing an oil film at the contact position; calculating friction coefficients of ball contact positions under different lubrication conditions; after the friction coefficient corresponding to the current lubricating condition is selected, the friction torque under the action of the axial load and the friction torque generated by lubricating are calculated; and calculating the friction torque of the ball screw pair based on the friction torque under the action of the axial load and the friction torque generated by lubrication. According to the method, the friction torque under the action of the axial load and the friction torque generated by lubrication are calculated through contact characteristic analysis and oil film analysis, the friction torque of the ball screw pair applied to different places can be accurately calculated, and the method has important significance on bearing characteristic analysis of the ball screw pair.

Description

[0001] This application is a divisional application. The application number of the original application is 202310619773.7, the application date is May 30, 2023, and the name of the invention is "A method for calculating the friction torque of a ball screw pair considering lubrication conditions." Technical Field

[0002] The present invention relates to the technical field of ball screw pair transmission performance calculation, and more specifically to a method for calculating the friction torque of a ball screw pair suitable for different application occasions. Background Art

[0003] As the core transmission component of CNC machine tools, the transmission characteristics of ball screw pairs will directly affect the transmission stability of the transmission system, thereby affecting the quality of the processed products. The contact between the ball and the screw shaft raceway, and the ball and the nut raceway is affected by their contact state. The contact state determines the transmission performance of the ball screw pair. The parameters that can directly characterize the contact state are of great significance to the improvement of the transmission performance of the ball screw pair. The axial load acting on the screw pair is manifested as a friction torque, but the friction torque is not only the product of the contact load and the contact coefficient. In different applications, the lubrication conditions of the ball screw pair are very different. The lubrication conditions are closely related to the friction torque value of the ball screw pair. The viscous friction of the lubricant has a great influence on the friction torque of the ball screw pair, and the friction coefficient of the ball screw pair at low speed and medium and high speed conditions has a large difference. Therefore, providing a method for calculating the friction torque of a ball screw pair suitable for different applications is a problem that technicians in this field need to solve urgently. Summary of the invention

[0004] In view of this, the present invention provides a method for calculating the friction torque of a ball screw pair suitable for different application scenarios. In order to solve the problem that the friction torque of the ball screw pair has a large difference from the theoretical value due to different lubrication conditions in different application scenarios, the contact characteristics of the ball and the contact raceway and the oil film at the contact point are analyzed, and the friction torque of the ball screw pair is calculated taking the lubrication conditions into consideration.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for calculating the friction torque of a ball screw pair suitable for different application scenarios comprises the following steps:

[0007] S1. Analyze the contact characteristics between the ball and the contact raceway to obtain the contact stress and contact load at the contact point;

[0008] S2. Determine the lubrication condition of the ball screw pair by analyzing the oil film at the contact point;

[0009] S3, calculate the friction coefficient of the ball contact under different lubrication conditions;

[0010] S4, after selecting the friction coefficient corresponding to the current lubrication condition, calculate the friction torque under the axial load and the friction torque generated by lubrication;

[0011] S5. Calculate the friction torque of the ball screw pair based on the friction torque under the axial load and the friction torque generated by lubrication.

[0012] Optionally, the contact characteristic analysis in S1 is to regard the contact between the ball and the raceway as a contact ellipse contact of two contact bodies, the contact stress at the contact point is calculated according to the contact ellipse distribution, and the contact load Q at the contact point is the integral of the contact pressure on the contact ellipsoid.

[0013] Optionally, the relationship between the contact stress and contact deformation at the contact point is:

[0014]

[0015] in,

[0016]

[0017] Where p(x,y) is the contact stress variation function on the contact ellipse, δ(x,y) is the contact deformation variation function on the contact ellipse, and p max is the maximum contact stress, δ max is the maximum contact deformation; x and y are the ordinate and abscissa of the rectangular coordinate system of the contact ellipse, respectively; a is the length of the major semi-axis of the contact ellipse, b is the length of the minor semi-axis of the contact ellipse, and δ * is the dimensionless contact strain, E' is the equivalent elastic modulus, ρ is the curvature, and Q is the contact load at the contact point.

[0018] Optionally, S2 is specifically:

[0019] The Reynolds equation is used to describe the relationship between oil film thickness and lubricant viscosity:

[0020]

[0021] In the formula, ρ r is the density of the lubricant, η is the dynamic viscosity of the lubricant, h r is the oil film thickness, p is the oil film pressure, and t is the motion lubrication time;

[0022] Calculate the center oil film thickness h c and minimum oil film thickness h min :

[0023]

[0024] Where U is the dimensionless velocity parameter; G is the dimensionless material parameter; W is the dimensionless load coefficient; k eis the ellipticity, which is the ratio of the length of the major semi-axis of the contact ellipse, a, to the length of the minor semi-axis of the contact ellipse, b; R x is the comprehensive curvature radius in the normal plane of the contact point;

[0025] Calculate the oil film lubrication parameter Λ and determine the lubrication friction state of the two contact surfaces:

[0026]

[0027] In the formula, σ 1 , σ 2 are the roughness of the corresponding contact surfaces respectively; when Λ≤1, the lubrication state of the contact surface is boundary lubrication; when 1<Λ<3, the lubrication state of the contact surface is partial elastic fluid lubrication; when Λ≥3, the lubrication state of the contact surface is full oil film elastic fluid lubrication.

[0028] Optionally, the dynamic viscosity η of the lubricant varies nonlinearly with the oil film pressure p:

[0029]

[0030] Where η o is the standard dynamic viscosity of the lubricant, ν 0 is the kinematic viscosity of the lubricant base oil at standard atmospheric pressure and 40°C, p 0 is the pressure coefficient, α v is the viscosity-pressure coefficient of the lubricant, z r is the vertical coordinate of the contact ellipse space rectangular coordinate system;

[0031] Lubricant density ρ r As the oil film pressure p changes:

[0032]

[0033] In the formula, ρ 0 is the standard density of the lubricant.

[0034] Optional, S3 is:

[0035] The lubrication conditions of the ball screw pair are divided into the first lubrication condition and the second lubrication condition. Under the first lubrication condition, part of the ball contact is in the boundary lubrication state, and part of the ball contact is in the partial elastic fluid lubrication state. The first equivalent friction coefficient μ of the ball screw pair as a whole is directly calculated. eq1 :

[0036]

[0037] Where Λ is the oil film lubrication parameter, and f(Λ) is the oil film lubrication parameter variation function: f(Λ) = 1.2Λ 0.64 / (1+0.37Λ1.26 ), F f is the Coulomb friction force, Ω is the area separated by the oil film, τ is the shear stress generated by the lubricant, μ d is the friction coefficient of direct contact, Q d is the load on the direct contact area, S d is the contact area;

[0038] Under the second lubrication condition, part of the ball contact is in a partial elastic fluid lubrication state, and part of the ball contact is in a full oil film elastic fluid lubrication state. The second equivalent friction coefficient μ eq2 for:

[0039] μ eq2 =μ EHL +μ l

[0040] In the formula, μ EHL is the friction coefficient of the elastic fluid lubrication zone, μ l It is the basic friction coefficient when Coulomb friction and elastic fluid lubrication friction exist simultaneously.

[0041] Optional, friction moment M under axial load in S4 f for:

[0042]

[0043] μ is the selected friction coefficient, α i is the contact angle of the ith ball, λ is the ball track control parameter of the screw; d m is the nominal diameter of the ball, D W is the nominal diameter of the screw, p i is the contact stress of the i-th ball;

[0044] The friction torque generated by lubrication is M v :

[0045]

[0046] Where M vi is the friction torque of a single ball in the ball screw pair, v s is the kinematic viscosity of the lubricant in the ball-screw shaft raceway contact, a si 、b si are the lengths of the major and minor axes of the corresponding ball-screw shaft raceway contact ellipse, a ni 、b ni are the lengths of the major and minor axes of the corresponding ball-nut raceway contact ellipse, h si 、h ni are the oil film thickness corresponding to the ball-screw shaft raceway contact and the ball-nut raceway contact, ηsi , η ni They are the dynamic viscosity of the lubricant corresponding to the ball-screw shaft raceway contact and the ball-nut raceway contact, respectively.

[0047] Optionally, the friction torque of the ball screw pair is the sum of the friction torque under the axial load and the friction torque generated by lubrication.

[0048] It can be seen from the above technical solutions that, compared with the prior art, the present invention provides a method for calculating the friction torque of a ball screw pair suitable for different application scenarios, which has the following beneficial effects:

[0049] 1. The present invention combines Hertz contact theory and the principle of force deformation to analyze the spatial function of the contact ellipse to obtain the contact stress and contact deformation function formula, so as to facilitate the calculation of the friction torque under the subsequent axial load;

[0050] 2. The present invention performs fluid lubrication analysis on the contact elastic body, uses elastic fluid lubrication theory to analyze the rolling of the ball on the raceway, ball-ball sliding, and ball-raceway sliding, and analyzes the oil film at the contact to determine the lubrication conditions, so as to better use an accurate lubrication calculation method;

[0051] 3. The friction coefficient between the ball and raceway contact surface is very different at different movement speeds. Generally speaking, the friction coefficient of the ball screw pair at low speed and medium and high speed is quite different. Analyzing the friction coefficient of the ball screw pair in the two cases makes the calculation of the friction torque generated by lubrication more accurate.

[0052] 4. The present invention proposes that the friction torque of the ball screw pair is divided into the friction torque under the action of the axial load and the friction torque generated by lubrication, which can be well combined with its application site for targeted calculation, making the calculated value of the friction torque more reliable and accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0054] Figure 1 It is a flow chart of the method for calculating the friction torque of a ball screw pair of the present invention;

[0055] Figure 2 It is a schematic diagram of the contact body between the ball and the raceway of the present invention;

[0056] Figure 3 The curve diagram of the influence of the oil film thickness on the contact surface of the ball screw pair of the present invention and the pressure conditions;

[0057] Figure 4 The figure is a curve diagram of the equivalent friction coefficient and rotation speed variation of the ball screw pair of the present invention. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] The embodiment of the present invention discloses a method for calculating the friction torque of a ball screw pair suitable for different application scenarios, such as Figure 1 As shown, the following steps are included:

[0060] S1. Analyze the contact characteristics between the ball and the contact raceway to obtain the contact stress and contact load at the contact point;

[0061] S2. Determine the lubrication condition of the ball screw pair by analyzing the oil film at the contact point;

[0062] S3, calculate the friction coefficient of the ball contact under different lubrication conditions;

[0063] S4, after selecting the friction coefficient corresponding to the current lubrication condition, calculate the friction torque under the axial load and the friction torque generated by lubrication;

[0064] S5. Calculate the friction torque of the ball screw pair based on the friction torque under the axial load and the friction torque generated by lubrication.

[0065] Furthermore, the contact characteristic analysis in S1 regards the contact between the ball and the raceway as a contact ellipse contact of two contact bodies, the contact stress at the contact point is calculated according to the contact ellipse distribution, and the contact load Q at the contact point is the integral of the contact pressure on the contact ellipsoid.

[0066] Furthermore, the relationship between the contact stress and contact deformation at the contact point is:

[0067]

[0068] in,

[0069]

[0070] Where p(x,y) is the contact stress variation function on the contact ellipse, δ(x,y) is the contact deformation variation function on the contact ellipse, and p max is the maximum contact stress, δ maxis the maximum contact deformation; x and y are the ordinate and abscissa of the rectangular coordinate system of the contact ellipse, respectively; a is the length of the major semi-axis of the contact ellipse, b is the length of the minor semi-axis of the contact ellipse, and δ * is the dimensionless contact strain, E' is the equivalent elastic modulus, ρ is the curvature, and Q is the contact load at the contact point.

[0071] Furthermore, S2 is specifically:

[0072] The Reynolds equation is used to describe the relationship between oil film thickness and lubricant viscosity:

[0073]

[0074] In the formula, ρ r is the density of the lubricant, η is the dynamic viscosity of the lubricant, the unit is Pa·s, h r is the oil film thickness, p is the oil film pressure, and t is the motion lubrication time;

[0075] In this embodiment, the ball screw pair is under steady-state isothermal conditions, and the boundary conditions p = 0, Solve the Reynolds equation. The state of the lubricant in the ball screw pair is represented by the distribution of the oil film formed between the contact surfaces. The Reynolds equation shows that the thickness of the oil film is related to the dynamic viscosity, density, and pressure conditions of the lubricant. The dynamic viscosity η and density ρ of the lubricant are r The influence of the oil film thickness on the contact surface of the ball screw pair and the pressure conditions is as follows: Figure 3 As shown in the figure, in the Hertz contact area (elastic contact area), the oil film thickness is stable and unchanged. The oil film thickness in this area is h c , which is the central oil film thickness and also the basic oil film thickness; at the same time, it can be seen that the change law of elastic fluid pressure in the Hertz contact area is basically the same as the change law of Hertz stress, and the values ​​are not much different; at the exit of the contact area, the contact surfaces are no longer in contact, and the contact stress disappears, causing the elastic fluid pressure to suddenly increase and then decrease rapidly. Therefore, the oil film at the exit of the contact area has a necking phenomenon (that is, the oil film thickness suddenly decreases and then increases). At this time, the oil film thickness has a minimum value of h min Generally speaking, h min =3h / 4.

[0076] Calculate the center oil film thickness h c and minimum oil film thickness h min :

[0077]

[0078] Where U is the dimensionless velocity parameter; G is the dimensionless material parameter; W is the dimensionless load coefficient; k eis the ellipticity, which is the ratio of the length of the major semi-axis of the contact ellipse, a, to the length of the minor semi-axis of the contact ellipse, b; R x is the comprehensive curvature radius in the normal plane of the contact point, and its value is the sum of the curvatures of the contact normal plane (ρ 11 +ρ 22 ) is the reciprocal of .

[0079] Calculate the oil film lubrication parameter Λ and determine the lubrication friction state of the two contact surfaces:

[0080]

[0081] In the formula, σ 1 , σ 2 are the roughness of the corresponding contact surfaces respectively; when Λ≤1, the lubrication state of the contact surface is boundary lubrication; when 1<Λ<3, the lubrication state of the contact surface is partial elastic fluid lubrication; when Λ≥3, the lubrication state of the contact surface is full oil film elastic fluid lubrication.

[0082] In this embodiment, the lubricating oil film thickness h r It is related to the movement speed of the contact surface, and the movement speed of the contact surface also determines the friction state. The oil film lubrication parameter Λ is generally used to judge the lubrication friction state of the two contact surfaces. The lubrication friction state curves of each friction stage are as follows: Figure 2 shown.

[0083] Furthermore, the dynamic viscosity η of the lubricant changes nonlinearly with the change of the oil film pressure p:

[0084]

[0085] Where η o is the standard dynamic viscosity of the lubricant, ν 0 is the kinematic viscosity of the lubricant base oil at standard atmospheric pressure and 40°C, p 0 is the pressure coefficient, α v is the viscosity-pressure coefficient of the lubricant, z r is the vertical coordinate of the contact ellipse space rectangular coordinate system;

[0086] Lubricant density ρ r As the oil film pressure p changes:

[0087]

[0088] In the formula, ρ 0 is the standard density of the lubricant.

[0089] Furthermore, S3 is specifically:

[0090] The lubrication conditions of the ball screw pair are divided into the first lubrication condition and the second lubrication condition, such as Figure 4As shown, in this embodiment, the first lubrication condition is low-speed operation, and the second lubrication condition is medium-high speed operation; there is a certain regularity in the change of the equivalent friction coefficient of the ball screw pair and the speed. Figure 4 The turning point in the ball screw pair is divided into low speed and medium-high speed. Different lubricants and different roughness will make Figure 4 The turning points of the curves correspond to different rotation speeds.

[0091] Under the first lubrication condition, part of the ball contact is in the boundary lubrication state, and part of the ball contact is in the partial elastic fluid lubrication state. The first equivalent friction coefficient μ of the ball screw pair as a whole is directly calculated. eq1 :

[0092]

[0093] Where Λ is the oil film lubrication parameter, and f(Λ) is the oil film lubrication parameter variation function: f(Λ) = 1.2Λ 0.64 / (1+0.37Λ 1.26 ), F f is the Coulomb friction force, Ω is the area separated by the oil film, τ is the shear stress generated by the lubricant, μ d is the friction coefficient of direct contact, Q d is the load on the direct contact area, S d is the contact area;

[0094] Furthermore, the lubrication friction state is complex in this state, so the overall friction coefficient of the ball screw pair can be directly calculated during analysis. Under the low-speed operation of the first lubrication condition, the thickness of the oil film formed by the lubricant between the contact surfaces is h r It is very small and cannot completely separate the two contact surfaces. Therefore, most of the contact area is direct contact between the two contact surfaces. The Coulomb friction generated by direct contact is generally greater than the friction in the oil film separation area. At this time, the friction between the contact surfaces is approximately:

[0095]

[0096] Under the second lubrication condition, part of the ball contact is in a partial elastic fluid lubrication state, and part of the ball contact is in a full oil film elastic fluid lubrication state. The second equivalent friction coefficient μ eq2 for:

[0097] μ eq2 =μ EHL +μ l

[0098] In the formula, μ EHL is the friction coefficient of the elastic fluid lubrication zone, μ l It is the basic friction coefficient when Coulomb friction and elastic fluid lubrication friction exist simultaneously.

[0099] Furthermore, as the speed increases, the oil film thickness h r It also gradually increases, and the ball-raceway friction enters the stage of full-partial fluid lubrication and full fluid lubrication. In this friction stability stage, the friction force increases with the increase of speed. The oil film has stabilized and the friction coefficient between the contact surfaces is also stable and does not change. It increases with the increase of Hertz contact pressure. In this stage, the friction force between the contact surfaces is mainly elastic fluid lubrication viscosity, and Coulomb friction only exists at the contact edge. The magnitude of Coulomb friction is:

[0100] F f =μ l Q l +τ·S d

[0101] In the formula, Q l is the load on the contact surface under the second lubrication condition.

[0102] The friction coefficient calculation formula of the elastic fluid lubrication area is:

[0103] μ EHL =μ min -μ l

[0104] μ EHL It can be approximated as:

[0105]

[0106] According to the equivalent friction coefficient under the first lubrication condition, the basic friction coefficient μ can be obtained. l .

[0107] Furthermore, the friction torque M under the axial load in S4 f for:

[0108]

[0109] μ is the selected friction coefficient, α i is the contact angle of the ith ball, λ is the ball track control parameter of the screw; d m is the nominal diameter of the ball, D W is the nominal diameter of the screw, p i is the contact stress of the i-th ball; the friction torque of the ball screw pair under axial load is composed of the friction torque of each ball.

[0110] The friction torque generated by lubrication is M v :

[0111]

[0112] Where M viis the friction torque of a single ball in the ball screw pair, v s is the kinematic viscosity of the lubricant in the ball-screw shaft raceway contact, a si 、b si are the lengths of the major and minor axes of the corresponding ball-screw shaft raceway contact ellipse, a ni 、b ni are the lengths of the major and minor axes of the corresponding ball-nut raceway contact ellipse, h si 、h ni are the oil film thickness corresponding to the ball-screw shaft raceway contact and the ball-nut raceway contact, η si , η ni They are the dynamic viscosity of the lubricant corresponding to the ball-screw shaft raceway contact and the ball-nut raceway contact, respectively.

[0113] Furthermore, under different speed conditions, the equivalent friction coefficient between the ball and the raceway is different, and the magnitude of the lubrication friction torque is related to the lubricant type and the speed. According to the lubrication condition analysis results in S2, the calculation formula for the viscous friction torque of a single ball in the ball screw pair is:

[0114]

[0115] The viscous friction torque of a ball screw pair is the sum of the viscous friction torques of all balls.

[0116] Furthermore, the friction torque of the ball screw pair is the sum of the friction torque under the axial load and the friction torque caused by lubrication: M 0 =M f +M v .

[0117] In this embodiment, the basic structural parameters of the planetary roller screw pair used are shown in Table 1 below:

[0118] Table 1

[0119] parameter Numeric <![CDATA[Ball diameter r W / mm]]> 3.969 <![CDATA[Nominal diameter d of ball screw pair m / mm]]> 28 <![CDATA[Curvature radius r of nut raceway n / mm]]> 2.381 <![CDATA[Curvature radius r of the lead screw raceway s / mm]]> 2.143 <![CDATA[Effective length l of lead screw measurement s / mm]]> 132 Helix angle λ / (°) 3.90 <![CDATA[Initial contact angle α on the lead screw side s0 / (°)]]> 45 <![CDATA[Initial contact angle α on the nut side n0 / (°)]]> 24 <![CDATA[Lead P h / mm]]> 6 Number of cycles × number of columns 5×1 Number of balls per turn N 22 <![CDATA[Single - turn effective load - bearing number z 1 > 18 Total number of balls H 110 Friction factor μ 0.003 Elastic modulus E / MPa <![CDATA[2.11×10 5 ]]> Poisson's ratio 0.3

[0120] The ball screw pair is used at a rotation speed of 40 rpm. Combined with the parameters in Table 1, the calculation method of the present invention is used to calculate the friction torque under the axial load and the friction torque generated by lubrication, and the actual friction torque value is measured by experiment. The specific values ​​are shown in Table 2 below:

[0121] Table 2

[0122]

[0123]

[0124] In summary, the method for calculating the friction torque of a ball screw pair taking into account the lubrication conditions provided by the present invention takes into account the influence of different lubrication conditions on the friction torque of the ball screw pair, and calculates the friction torque under the action of the axial load and the friction torque generated by lubrication through contact characteristic analysis and oil film analysis. The friction torque of the ball screw pair used in different places can be accurately calculated, which is of great significance to the load-bearing characteristic analysis of the ball screw pair.

[0125] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0126] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the friction torque of a ball screw pair suitable for different application occasions, characterized in that: The following steps are involved: S1. Analyze the contact characteristics between the ball and the contact raceway to obtain the contact stress and contact load at the contact point; S2. Determine the lubrication condition of the ball screw pair by analyzing the oil film at the contact point; S3, calculate the friction coefficient of the ball contact under different lubrication conditions; S4, after selecting the friction coefficient corresponding to the current lubrication condition, calculate the friction torque under the axial load and the friction torque generated by lubrication; S5, calculating the friction torque of the ball screw pair based on the friction torque under the axial load and the friction torque generated by lubrication; S3 is specifically: The lubrication conditions of the ball screw pair are divided into the first lubrication condition and the second lubrication condition. Under the first lubrication condition, part of the ball contact is in the boundary lubrication state, and part of the ball contact is in the partial elastic fluid lubrication state. The first equivalent friction coefficient μ of the ball screw pair as a whole is directly calculated. eq1 : Where Λ is the oil film lubrication parameter, and f(Λ) is the oil film lubrication parameter variation function: f(Λ) = 1.2Λ 0.64 / (1+0.37Λ 1.26 ), F f is the Coulomb friction force, τ is the shear stress generated by the lubricant, μ d is the friction coefficient of direct contact, Q is the contact load at the contact point, Q d is the load on the direct contact area, S d is the contact area; Under the low-speed operation of the first lubrication condition, the thickness of the oil film formed by the lubricant between the contact surfaces cannot completely separate the two contact surfaces. The Coulomb friction force generated by direct contact is greater than the friction force in the oil film separation area. At this time, the Coulomb friction force between the contact surfaces is: Where, Ω is the area separated by the oil film; Under the second lubrication condition, part of the ball contact is in a partial elastic fluid lubrication state, and part of the ball contact is in a full oil film elastic fluid lubrication state. The second equivalent friction coefficient μ eq2 for: m eq2 =μ EHL +m l In the formula, μ EHL is the friction coefficient of the elastic fluid lubrication zone, μ l is the basic friction coefficient when Coulomb friction and elastic fluid lubrication friction exist simultaneously; In the friction stability stage under the second lubrication condition, the friction force increases with the increase of the speed, the oil film is stable, and the friction coefficient between the contact surfaces is also stable and unchanged. The friction force between the contact surfaces is mainly the elastic fluid lubrication viscosity force, and the Coulomb friction force only exists at the contact edge. The magnitude of the Coulomb friction force is: F f =μ l ·Q l +τ·S d In the formula, Q l is the load on the contact surface under the second lubrication condition; The friction coefficient calculation formula of the elastic fluid lubrication area is: According to the first equivalent friction coefficient under the first lubrication condition, the basic friction coefficient μ is obtained. l .

2. A method for calculating the friction torque of a ball screw pair suitable for different application scenarios according to claim 1, characterized in that: The contact characteristic analysis in S1 regards the contact between the ball and the raceway as the contact ellipse contact of two contact bodies. The contact stress at the contact point is calculated according to the contact ellipse distribution, and the contact load Q at the contact point is the integral of the contact pressure on the contact ellipsoid.

3. A method for calculating the friction torque of a ball screw pair suitable for different application scenarios according to claim 2, characterized in that: The relationship between the contact stress and contact deformation at the contact point is: in, Where p(x,y) is the contact stress variation function on the contact ellipse, δ(x,y) is the contact deformation variation function on the contact ellipse, and p max is the maximum contact stress, δ max is the maximum contact deformation; x and y are the ordinate and abscissa of the rectangular coordinate system of the contact ellipse, respectively; a is the length of the major semi-axis of the contact ellipse, b is the length of the minor semi-axis of the contact ellipse, and δ * is the dimensionless contact strain, E' is the equivalent elastic modulus, ρ is the curvature, and Q is the contact load at the contact point.

4. The method for calculating the friction torque of a ball screw pair suitable for different application scenarios according to claim 2, characterized in that: S2 is specifically: The Reynolds equation is used to describe the relationship between oil film thickness and lubricant viscosity: In the formula, ρ r is the density of the lubricant, η is the dynamic viscosity of the lubricant, h r is the oil film thickness, p is the oil film pressure, t is the motion lubrication time; x and y are the ordinate and abscissa of the contact ellipse rectangular coordinate system respectively; Calculate the center oil film thickness h c and minimum oil film thickness h min : Where U is the dimensionless velocity parameter; G is the dimensionless material parameter; W is the dimensionless load coefficient; ke is the ellipticity, which is the ratio of the length of the major semi-axis of the contact ellipse a to the length of the minor semi-axis of the contact ellipse b; R x is the comprehensive curvature radius in the normal plane of the contact point; Calculate the oil film lubrication parameter Λ and determine the lubrication friction state of the two contact surfaces: In the formula, σ1 and σ2 are the roughness of the corresponding contact surfaces respectively; when Λ≤1, the lubrication state of the contact surface is boundary lubrication; when 1<Λ<3, the lubrication state of the contact surface is partial elastic fluid lubrication; when Λ≥3, the lubrication state of the contact surface is full oil film elastic fluid lubrication.

5. The method for calculating the friction torque of a ball screw pair suitable for different application scenarios according to claim 4, characterized in that: The dynamic viscosity η of the lubricant changes nonlinearly with the change of the oil film pressure p: Where η o is the standard dynamic viscosity of the lubricant, ν0 is the kinematic viscosity of the lubricant base oil at standard atmospheric pressure and 40°C, p0 is the pressure coefficient, α v is the viscosity-pressure coefficient of the lubricant, z r is the vertical coordinate of the contact ellipse space rectangular coordinate system; Lubricant density ρ r As the oil film pressure p changes: Where ρ0 is the standard density of the lubricant.

6. The method for calculating the friction torque of a ball screw pair suitable for different application occasions according to claim 1, characterized in that: Friction moment M under axial load in S4 f for: Where μ is the selected friction coefficient, α i is the contact angle of the ith ball, λ is the ball track control parameter of the screw; d m is the nominal diameter of the ball, D W is the nominal diameter of the screw, p i is the contact stress of the ith ball, H is the total number of balls; The friction torque generated by lubrication is M v : Where M vi is the friction torque of a single ball in the ball screw pair, v s is the kinematic viscosity of the lubricant in the ball-screw shaft raceway contact, a si , b si are the lengths of the major and minor axes of the corresponding ball-screw shaft raceway contact ellipse, a ni , b ni are the lengths of the major and minor axes of the corresponding ball-nut raceway contact ellipse, h si 、h ni are the oil film thickness corresponding to the ball-screw shaft raceway contact and the ball-nut raceway contact, η si , η ni They are the dynamic viscosity of the lubricant corresponding to the ball-screw shaft raceway contact and the ball-nut raceway contact, respectively.

7. A method for calculating the friction torque of a ball screw pair suitable for different application scenarios according to any one of claims 1 to 6, characterized in that: The friction torque of the ball screw pair is the sum of the friction torque under the axial load and the friction torque generated by lubrication.

Images