Method and system for evaluating static performance and reliability of ball screw

Abstract

The invention discloses a method and system for evaluating the static performance and reliability of a ball screw, and the method comprises the steps: correcting an internal force balance equation of adjacent balls in consideration of the same contact states of the balls and a raceway; establishing a mapping relation between an assembly condition and a contact mechanism, and calculating a contact angle between a ball and a raceway under an assembly error; correcting an internal force balance equation of adjacent balls by considering different assembly conditions; determining boundary conditions of a ball internal force balance equation, correcting an axial force balance equation in the ball screw, and determining judgment conditions of unloaded balls under different assembly conditions; and carrying out reliability evaluation on the static performance of the ball screw under different assembly conditions based on the judgment conditions.

Description

Background Art

[0002] Ball screws are widely used in CNC machine tools due to their high transmission accuracy and good dynamic characteristics. The static characteristics under different assembly conditions, namely, axial contact stiffness and fatigue life, have a significant impact on transmission accuracy and dynamic characteristics. At the same time, the reliability assessment of static characteristics of high-end machine tools has always been an important research topic. However, due to the limitations of assembly technology, the assembly conditions of ball screws will have a significant impact on their static characteristics. Therefore, it is necessary to evaluate the static characteristics and reliability of ball screws under different assembly conditions.

[0003] There is a load distribution calculation method based on Hooke's law, and the influence of ball geometric error on load distribution is analyzed. There is also a ball screw analysis method considering turning torque, which analyzes the influence of ball screw deflection and radial displacement on load distribution and fatigue life. However, the deformation coordination relationship of adjacent balls is not considered when calculating load distribution, and the deflection direction of the ball screw is not considered comprehensively. And on the basis of considering the flexibility of the ball screw, the ball load distribution curve under different external loads and the influence of different ball precision on load distribution are analyzed. It includes the establishment of a ball screw fatigue life model under bidirectional external loads, and the analysis of the influence of axial external loads and radial external loads on the fatigue life of the ball screw.

[0004] However, the above studies are all based on the condition of perfect assembly of ball screws, which is obviously not realistic due to human assembly errors. The influence of different assembly conditions on the static performance of ball screws is ignored, as well as the diversity of assembly conditions of ball screws caused by different users in different application environments and the influence of assembly conditions on the reliability of static characteristics of ball screws are ignored. Therefore, a static characteristic analysis and reliability evaluation method of ball screws under different assembly conditions is proposed. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method and system for evaluating the static performance and reliability of a ball screw in response to the deficiencies in the above-mentioned prior art, so as to solve the technical problem that the static characteristics of the ball screw cannot be calculated and the reliability of the static characteristics cannot be analyzed under different assembly conditions.

[0006] The present invention adopts the following technical solutions:

[0007] A method for evaluating the static performance and reliability of a ball screw comprises the following steps:

[0008] Considering the same contact state between the ball and the raceway, the internal force balance equation of adjacent balls is modified;

[0009] Establish the mapping relationship between assembly conditions and contact mechanism, and calculate the contact angle between the ball and the raceway under assembly error;

[0010] Considering different assembly conditions, the internal force balance equation of adjacent balls is modified; the boundary conditions of the ball internal force balance equation are determined, the axial force balance equation in the ball screw is modified, and the judgment conditions of unloaded balls under different assembly conditions are determined;

[0011] The reliability of the static performance of the ball screw under different assembly conditions is evaluated based on the judgment conditions.

[0012] Preferably, considering that the contact state of the balls and raceways is the same, the internal force balance equation of adjacent balls is modified as follows:

[0013] Establish the deformation coordination equation of adjacent balls;

[0014] Use Hertz's formula to calculate the contact load between the ball and the raceway;

[0015] Calculate the ball internal forces of the jth nut unit and the jth screw unit;

[0016] Transformation of axial deformation and normal deformation between ball raceways;

[0017] Calculate the axial deformation of the jth nut unit and the jth screw unit using Hooke's law;

[0018] Axial force balance equation in a ball screw;

[0019] The internal force balance equation of adjacent balls is obtained by combining the deformation coordination equation of adjacent balls, the contact load between the balls and the raceways, the transformation of the axial deformation and normal deformation between the ball raceways, and the axial deformation of the jth nut unit and the jth screw unit.

[0020] On the basis of considering the same contact state between the ball and the raceway, the internal force balance equation of the adjacent balls is modified.

[0021] Preferably, the internal force balance equation of adjacent balls is corrected as follows:

[0022]

[0023] Among them, Q (j-1) is the contact load between the j-1th ball and the raceway, Q j is the contact load between the jth ball and the raceway, α (j-1) is the contact angle between the j-1th ball and the raceway, α j is the contact angle between the jth ball and the raceway, Q m is the contact load between the mth ball and the raceway, α m is the contact angle between the mth ball and the raceway, F a j is the axial internal force of adjacent balls, U jis the axial deformation coefficient, K is the Hertzian contact coefficient, and λ is the helix angle.

[0024] Preferably, a mapping relationship between assembly conditions and contact mechanisms is established, and the contact angle between the ball and the raceway under assembly error is calculated as follows:

[0025] Calculate the displacement of the center of curvature of the raceway under radial assembly error;

[0026] Calculate the transformation of the axial deflection angle in the screw axis plane and the helix plane;

[0027] Calculate the displacement of the center of curvature of the raceway under the assembly error of the deflection angle around the x-axis;

[0028] Calculate the displacement of the center of curvature of the raceway under the assembly error of the deflection angle around the y-axis;

[0029] Calculate the contact angle between the ball and the raceway under three assembly errors.

[0030] Preferably, the contact angle α between the ball and the raceway under the three assembly errors is j for:

[0031]

[0032] Where α0 is the initial contact angle of the ball screw, r n is the radius of curvature of the nut raceway, r s is the radius of curvature of the screw raceway, D b is the radius of the ball, δ normj Yes, L2xj is the radial displacement of the center of curvature of the screw raceway of the jth ball caused by the assembly error of the deflection angle around the x-axis, l L2yj is the radial displacement of the center of curvature of the screw raceway corresponding to the jth ball caused by the assembly error of the deflection angle around the y-axis, δ r0 is the radial assembly error, is the position angle of the ball.

[0033] Preferably, the determination conditions for determining the unloaded ball under different assembly conditions are specifically:

[0034] Calculate the distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway under different assembly conditions;

[0035] Determine whether the balls in the ball screw are in a non-contact state;

[0036] When the balls between the pth and qth balls are not loaded, the deformation coordination equation between the pth ball and the qth ball is obtained based on the deformation coordination equation of the adjacent balls;

[0037] After considering different assembly conditions, the internal force balance equation of adjacent balls is modified;

[0038] Determine the boundary conditions of the ball internal force equilibrium equation;

[0039] Correction of the axial force balance equation in the ball screw.

[0040] Preferably, determining whether the balls in the ball screw are in a non-contact state is specifically as follows:

[0041]

[0042] Among them, when U j When the condition is satisfied, the ball is in an unloaded state. is the axial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, is the radial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, is the straight-line distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, U 1j is the first judgment condition, U 2j It is the second judgment condition.

[0043] Preferably, the reliability evaluation of the static performance of the ball screw under different assembly conditions is performed based on the judgment conditions as follows:

[0044] Calculate the axial contact stiffness of the ball screw;

[0045] Calculate the fatigue life of ball screws;

[0046] User-oriented reliability evaluation index

[0047] The reliability of the axial contact stiffness of the ball screw and the reliability of the fatigue life of the ball screw are calculated according to the reliability evaluation index;

[0048] By traversing the range of assembly conditions to determine the axial contact stiffness reliability and fatigue life reliability of the ball screw under different combinations of assembly conditions, the maximum allowable range of assembly conditions without reliability failure can be obtained. According to the order in which the maximum range of assembly conditions reaches the set range, the assembly conditions that are most sensitive to the reliability of the axial contact stiffness and fatigue life of the ball screw are obtained.

[0049] Preferably, the axial contact stiffness reliability of the ball screw and the fatigue life reliability of the ball screw are calculated as follows:

[0050]

[0051] Among them, k bs is the axial contact stiffness of the ball screw when there is no assembly error, T bs is the fatigue life of the ball screw when there is no assembly error, is the axial contact stiffness of the ball screw under different assembly conditions, It refers to the fatigue life of the ball screw under different assembly conditions, χ1 is the reliability evaluation index of the axial contact stiffness, and χ2 is the reliability evaluation index of the fatigue life. is the reliability of the axial contact stiffness, It is the reliability of fatigue life.

[0052] In a second aspect, an embodiment of the present invention provides a ball screw static performance and reliability evaluation system, comprising:

[0053] The parameter module considers that the contact state between the ball and the raceway is the same and modifies the internal force balance equation of adjacent balls;

[0054] The calculation module establishes the mapping relationship between assembly conditions and contact mechanisms, and calculates the contact angle between the ball and the raceway under assembly errors;

[0055] The judgment module considers different assembly conditions and corrects the internal force balance equation of adjacent balls; determines the boundary conditions of the ball internal force balance equation, corrects the axial force balance equation in the ball screw, and determines the judgment conditions of unloaded balls under different assembly conditions;

[0056] The evaluation module performs reliability evaluation on the static performance of the ball screw under different assembly conditions based on the judgment conditions.

[0057] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned ball screw static performance and reliability evaluation method when executing the computer program.

[0058] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, including a computer program, which, when executed by a processor, implements the steps of the above-mentioned ball screw static performance and reliability evaluation method.

[0059] In a fifth aspect, a chip comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for evaluating the static performance and reliability of a ball screw when executing the computer program.

[0060] In a sixth aspect, an embodiment of the present invention provides an electronic device, comprising a computer program, which, when executed by the electronic device, implements the steps of the above-mentioned method for evaluating the static performance and reliability of a ball screw.

[0061] Compared with the prior art, the present invention has at least the following beneficial effects:

[0062] A method for evaluating the static performance and reliability of a ball screw is provided. On the basis of considering that the contact state of the ball and the raceway is the same, the internal force balance equation of adjacent balls is established according to the deformation coordination equation of adjacent balls, the Hertz contact formula, the axial deformation and normal deformation transformation formula, and the axial deformation formula of the screw and nut unit. By considering the assembly conditions: the influence of radial assembly error, assembly error around the x-axis rotation angle, and assembly error around the y-axis deflection angle on the raceway curvature center, a contact angle formula between the ball and the raceway under the assembly conditions considering the three assembly errors is established. Based on the screw raceway curvature center and the nut under different assembly conditions, the contact angle formula between the ball and the raceway is established. The distance between the center of raceway curvature and the ball contact state judgment formula is proposed, the ball deformation coordination equation when unloaded balls exist and the correction method of the adjacent ball internal force balance equation are given, and the boundary conditions of the adjacent ball internal force balance equation are given; the calculated ball contact load is used to calculate the axial contact stiffness of the ball screw and the fatigue life of the ball screw, and the calculation method of the axial contact stiffness reliability of the ball screw and the fatigue life of the ball screw under different assembly conditions is given; the calculation process of the axial contact stiffness reliability of the ball screw and the fatigue life of the ball screw is given, and the update process of the ball non-contact state is given.

[0063] Furthermore, the deformation coordination equation of adjacent balls is established to take into account the actual situation that the ball load is inversely proportional to the load-bearing surface of the ball screw; the deformation coordination equation of adjacent balls is simplified by considering the same contact state of the ball and the raceway. The deformation coordination equation of adjacent balls is established by using the Hertz contact formula, the axial deformation and normal deformation transformation formula, and the axial deformation formula of the screw and nut unit; the internal force balance equation of adjacent balls is simplified based on the axial force balance equation and the same contact state of the ball and the raceway.

[0064] Furthermore, the mapping relationship between assembly conditions and contact mechanisms is established to consider the influence of radial assembly error, x-axis deflection angle assembly error, and y-axis deflection angle assembly error on the contact mechanism. Through the mapping relationship, the contact angle between the ball and the raceway under different assembly conditions is accurately established; the analysis method of the raceway curvature center is used to calculate the axial displacement of the raceway curvature center corresponding to the radial assembly error, and the axial and radial displacements of the raceway curvature center corresponding to the x-axis and y-axis rotation angle assembly errors, and the contact angle formula between the ball and the raceway under three assembly errors is established.

[0065] Furthermore, the judgment formula of the contact state of unloaded balls is adopted to evaluate the contact state of balls under different assembly conditions, so that the static performance calculation of ball screws under different conditions is more accurate; according to the distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway under different assembly conditions, the judgment formula of the contact state of balls is proposed. When there are unloaded balls, the modified ball deformation coordination equation and the internal force balance equation of adjacent balls are established, and the boundary conditions of the internal force balance equation of adjacent balls are proposed.

[0066] Furthermore, the static performance reliability of the ball screw is calculated based on the reliability evaluation index. The static performance reliability of the ball screw under different assembly conditions is calculated by the traversal method, and the assembly condition sensitivity of the ball screw is obtained; the axial contact stiffness of the ball screw and the fatigue life of the ball screw are calculated based on the ball contact load and contact angle, and the calculation method of the axial contact stiffness reliability of the ball screw and the fatigue life of the ball screw under different assembly conditions is given. Subsequently, the static performance reliability of the ball screw is calculated based on the reliability evaluation index, and then the assembly condition sensitivity of the ball screw is obtained.

[0067] It can be understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0068] In summary, the present invention improves the internal force balance equation of adjacent balls, establishes the mapping relationship between assembly conditions and contact mechanisms, and proposes ball state judgment conditions under different assembly conditions, which can effectively calculate the static performance of the ball screw under different assembly conditions; at the same time, based on the static performance reliability index, a static performance reliability evaluation method for the ball screw under different assembly conditions is proposed.

[0069] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0071] Figure 1 It is a flow chart of the present invention;

[0072] Figure 2 This is a comparison diagram with the existing method under the effect of assembly error around the y-axis deflection angle;

[0073] Figure 3 This is a comparison diagram with the existing method under the effect of radial assembly error;

[0074] Figure 4 This is the analysis diagram of the influence of assembly conditions on axial contact stiffness;

[0075] Figure 5 This is an analysis diagram of the impact of assembly conditions on fatigue life;

[0076] Figure 6 The reliability diagram of the axial contact stiffness of the ball screw, where (a) is the radial assembly error of 25 μm, and (b) is the radial assembly error of -25 μm;

[0077] Figure 7 The fatigue life reliability diagram of the ball screw, where (a) is the radial assembly error of 25 μm, and (b) is the radial assembly error of -25 μm;

[0078] Figure 8 A schematic diagram of a computer device provided by an embodiment of the present invention;

[0079] Fig. 9 The block diagram of a chip provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0080] 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 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.

[0081] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0082] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0083] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0084] It should be understood that, although the terms first, second, third, etc. may be used to describe preset ranges, etc. in the embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0085] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0086] Various structural schematic diagrams of the embodiments disclosed in the present invention are shown in the accompanying drawings. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0087] See also Figure 1 The present invention provides a method for evaluating the static performance and reliability of a ball screw, comprising the following steps:

[0088] S1, internal force balance equation of adjacent balls based on the same contact state between balls and raceways;

[0089] S101, establishing deformation coordination equations of adjacent balls;

[0090] Δ nj +Δ sj =δ na(j-1) -δ naj +δ sa(j-1) -δ saj

[0091] Among them, Δnj is the axial deformation of the jth nut unit, Δ sj is the axial deformation of the j-th screw unit, δ na(j-1) is the axial contact deformation between the j-1th ball and the nut raceway, δ sa(j-1) is the axial contact deformation between the j-1th ball and the screw raceway, δ naj is the axial contact deformation between the jth ball and the nut raceway, δ saj is the axial contact deformation between the jth ball and the screw raceway.

[0092] S102. Calculate the contact load between the ball and the raceway using the Hertz formula;

[0093]

[0094] Among them, Q sj is the contact load between the jth ball and the screw raceway, Q nj is the contact load between the jth ball and the nut raceway, δ snormj is the normal deformation between the jth ball and the screw raceway, δ nnormj is the normal deformation between the jth ball and the nut raceway, K s and K n is the Hertz contact coefficient.

[0095] S103, calculating the ball internal force of the j-th nut unit and the j-th screw unit;

[0096]

[0097] Among them, F a is the axial load of the ball screw. Q sm is the contact load between the mth ball and the screw raceway, Q nm is the contact load between the mth ball and the nut raceway, α sm is the contact angle between the mth ball and the screw raceway, α nm is the contact angle between the mth ball and the nut raceway, and λ is the helix angle of the ball screw.

[0098] S104, transformation of axial deformation and normal deformation between ball raceways;

[0099]

[0100] Among them, α nj is the contact angle between the jth ball and the nut raceway, α sj is the contact angle between the jth ball and the screw raceway.

[0101] S105. Calculate the axial deformation of the j-th nut unit and the j-th screw unit using Hooke's law;

[0102]

[0103] Among them, U sj is the deformation coefficient between the ball and the screw raceway, U nj It is the deformation coefficient between the ball and the nut raceway.

[0104] S016, axial force balance equation in ball screw;

[0105]

[0106] Among them, Z n is the number of balls in the ball screw.

[0107] S107, combining the deformation coordination equation of adjacent balls in step S101, the Hertz contact formula in step S102, the normal deformation and axial deformation transformation formula in step S104, and the axial deformation formula in step S105, to obtain the internal force balance equation of adjacent balls;

[0108]

[0109] Among them, U j is the axial deformation coefficient, Q s(j-1) is the contact load between the j-1th ball and the screw raceway, Q n(j-1) is the contact load between the j-1th ball and the nut raceway, α s(j-1) is the contact angle between the j-1th ball and the screw raceway, α sj is the contact angle between the jth ball and the screw raceway, α n(j-1) is the contact angle between the j-1th ball and the nut raceway, α nj is the contact angle between the jth ball and the nut raceway.

[0110] S108, on the basis of considering that the contact state between the balls and the raceway is the same, correcting the internal force balance equation of the adjacent balls in step S107;

[0111]

[0112] Among them, Q (j-1) is the contact load between the j-1th ball and the raceway, Q j is the contact load between the jth ball and the raceway, α (j-1) is the contact angle between the j-1th ball and the raceway, α j is the contact angle between the jth ball and the raceway, Q m is the contact load between the mth ball and the raceway, αm is the contact angle between the mth ball and the raceway.

[0113] S2. Establishing the mapping relationship between assembly conditions and contact mechanisms;

[0114] S201, calculating the raceway curvature center displacement under radial assembly error;

[0115]

[0116] Among them, δ r0 is the radial displacement of the center of curvature of the raceway of the first ball, is the position angle of the ball.

[0117] S202, calculating the transformation of the axial deflection angle in the screw axis plane and the helix plane;

[0118]

[0119] in, is the deflection angle around the y-axis in the plane of the helix, is the deflection angle around the y-axis in the plane of the screw axis, is the deflection angle around the x-axis in the plane of the helix, It is the deflection angle around the x-axis in the plane of the screw axis.

[0120] S203, calculating the displacement of the center of curvature of the raceway under the assembly error of the deflection angle around the x-axis;

[0121]

[0122] Among them, l L1xj is the axial displacement of the center of curvature of the screw raceway corresponding to the jth ball caused by the assembly error of the deflection angle around the x-axis, l L2xj is the radial displacement of the center of curvature of the screw raceway of the jth ball caused by the assembly error of the deflection angle around the x-axis, R j is the trajectory radius of the screw raceway’s center of curvature.

[0123] S204, calculating the displacement of the center of curvature of the raceway under the assembly error of the deflection angle around the y-axis;

[0124]

[0125] Among them, l L1yj is the axial displacement of the center of curvature of the screw raceway corresponding to the jth ball caused by the assembly error of the deflection angle around the y-axis, l L2yj It is the radial displacement of the center of curvature of the screw raceway corresponding to the jth ball caused by the assembly error of the deflection angle around the y-axis.

[0126] S205. Calculate the contact angle between the ball and the raceway under three assembly errors.

[0127]

[0128] Where α0 is the initial contact angle of the ball screw, r n is the radius of curvature of the nut raceway, r s is the radius of curvature of the screw raceway, D b is the radius of the ball.

[0129] S3. Determination criteria for unloaded balls under different assembly conditions;

[0130] S301. Calculate the distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway under different assembly conditions:

[0131]

[0132] in, is the axial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, is the radial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, It is the straight-line distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway.

[0133] S302, judging whether the balls in the ball screw are in a non-contact state according to the following formula;

[0134]

[0135] WhenU j When it is satisfied, the ball is in an unloaded state.

[0136] S303, when the balls between the pth and qth balls are not loaded, the deformation coordination equation between the pth ball and the qth ball is obtained based on the deformation coordination equation of the adjacent balls in step S101;

[0137] Δ nq +Δ sq =δ sap +δ nap -δ saq -δ naq

[0138] Among them, Δ nq is the axial deformation of the qth nut unit, Δ sq is the axial deformation of the qth screw unit, δ nap is the axial contact deformation between the pth ball and the nut raceway, δ sap is the axial contact deformation between the pth ball and the screw raceway, δ naqis the axial contact deformation between the qth ball and the nut raceway, δ saq Axial contact deformation between the qth ball and the screw raceway.

[0139] S304, after considering different assembly conditions, correct the internal force balance equation of adjacent balls in step S108;

[0140]

[0141] S305, determining the boundary conditions of the ball internal force balance equation in step S304;

[0142]

[0143] S306, correcting the axial force balance equation in the ball screw in step S106;

[0144]

[0145] S4. Reliability evaluation of static performance of ball screw under different assembly conditions.

[0146] S401. Calculate the axial contact stiffness of the ball screw;

[0147]

[0148] Among them, Q au is the contact load between the uth ball and the raceway, δ nau is the normal deformation between the u-th ball and the nut raceway, δ sau is the normal deformation between the u-th ball and the screw raceway, k su is the axial contact stiffness between the u-th ball and the screw raceway, k nu is the axial contact stiffness between the u-th ball and the nut raceway, k bs is the axial contact stiffness of the ball screw.

[0149] S402, calculate the fatigue life of the ball screw;

[0150]

[0151] Where σ0 is the fatigue limit, σ0 = 2450N / mm 2 , N0 is the cycle base of steel, N0 = 10 8 . m is the contact coefficient of steel, m = 3. d m is the pitch diameter of the screw, σ max is the maximum contact stress of the ball, and α is the contact angle corresponding to the maximum contact stress of the ball. bs is the fatigue life of the ball screw.

[0152] S403, User-oriented reliability evaluation index

[0153] According to the specific needs of different users, the stiffness reliability and fatigue life reliability evaluation index of users is proposed. The index is determined by the user's specified allowable stiffness failure range χ1 and fatigue life failure range χ2.

[0154] S404, calculating the axial contact stiffness reliability of the ball screw and the fatigue life reliability of the ball screw according to the reliability evaluation index;

[0155]

[0156] Among them, k bs Refers to the axial contact stiffness of the ball screw when there is no assembly error, T bs Refers to the fatigue life of the ball screw when there is no assembly error. Refers to the axial contact stiffness of the ball screw under different assembly conditions. Refers to the fatigue life of the ball screw under different assembly conditions.

[0157] S405. The axial contact stiffness reliability and fatigue life reliability of the ball screw under different combinations of assembly conditions are determined by traversal within the range of assembly conditions, so as to obtain the maximum allowable range of assembly conditions without reliability failure. According to the order in which the maximum range of assembly conditions reaches the set range, the assembly conditions that are most sensitive to the reliability of the axial contact stiffness and fatigue life of the ball screw are obtained.

[0158] The specific calculation process of a ball screw static performance and reliability evaluation method of the present invention is as follows:

[0159] Input the geometric parameters, axial load, and assembly conditions of the ball screw;

[0160] Calculate the contact angles of different balls under the current assembly conditions using the formula in step S205;

[0161] Use the formula in step S108 to calculate the internal force balance equation of adjacent balls;

[0162] Use the formula in step S302 to determine whether the ball is in a non-contact state. If the ball is in a non-contact state, use step S304 to correct the formula in step S108, use step S306 to correct the formula in step S106, and set the boundary conditions of the formula in step S304 in step S305;

[0163] Otherwise, the formulas in step S305, step S304 and step S306 are combined to solve the contact load of the ball using Newton's iteration method;

[0164] The axial contact stiffness of the ball screw is calculated according to the formula in step S401, and the fatigue life of the ball screw is calculated according to the formula in step S402;

[0165] According to the stiffness failure range and the fatigue life failure range, the formula in step S404 is used to calculate the ball screw axial contact stiffness reliability and the ball screw fatigue life reliability under the given failure range.

[0166] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as a system, method or program product. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software, which may be collectively referred to herein as a "circuit", "module" or "platform".

[0167] In another embodiment of the present invention, a ball screw static performance and reliability evaluation system is provided, which can be used to implement the above-mentioned ball screw static performance and reliability evaluation method. Specifically, the ball screw static performance and reliability evaluation system includes a parameter module, a calculation module, a determination module and an evaluation module.

[0168] Among them, the parameter module considers that the contact state of the ball and the raceway is the same, and corrects the internal force balance equation of adjacent balls;

[0169] The calculation module establishes the mapping relationship between assembly conditions and contact mechanisms, and calculates the contact angle between the ball and the raceway under assembly errors;

[0170] The judgment module considers different assembly conditions and corrects the internal force balance equation of adjacent balls; determines the boundary conditions of the ball internal force balance equation, corrects the axial force balance equation in the ball screw, and determines the judgment conditions of unloaded balls under different assembly conditions;

[0171] The evaluation module performs reliability evaluation on the static performance of the ball screw under different assembly conditions based on the judgment conditions.

[0172] In another embodiment of the present invention, a terminal device is provided, the terminal device includes a processor and a memory, the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, graphics processing units (GPU), tensor processing units (TPU), digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding functions; the processor described in the embodiment of the present invention can be used for the operation of the static performance and reliability evaluation method of the ball screw, including:

[0173] Considering that the contact state of the ball and the raceway is the same, the internal force balance equation of the adjacent balls is corrected; the mapping relationship between the assembly condition and the contact mechanism is established, and the contact angle between the ball and the raceway under the assembly error is calculated; considering different assembly conditions, the internal force balance equation of the adjacent balls is corrected; the boundary conditions of the ball internal force balance equation are determined, the axial force balance equation in the ball screw is corrected, and the judgment conditions for unloaded balls under different assembly conditions are determined; based on the judgment conditions, the reliability of the static performance of the ball screw under different assembly conditions is evaluated.

[0174] See also Figure 8 , the terminal device is a computer device, and the computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, the ball screw static performance and reliability evaluation method in the embodiment is implemented. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit in the ball screw static performance and reliability evaluation system in the embodiment are implemented. To avoid repetition, it is not described one by one here.

[0175] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Figure 8 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0176] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, graphics processing units (GPU), tensor processing units (TPU), digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0177] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the computer device 60.

[0178] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0179] See also Fig. 9 The terminal device is an electronic device 600, which is in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0180] The storage unit stores program codes, which can be executed by the processing unit 610, so that the processing unit 610 performs the steps according to various exemplary embodiments of the present invention described in the above method section of this specification. For example, the processing unit 610 can perform the following steps: Figure 1 Follow the steps shown in .

[0181] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 6201 and / or a cache memory unit 6202 , and may further include a read-only memory unit (ROM) 6203 .

[0182] The storage unit 620 may also include a program / utility 6204 having a set (at least one) of program modules 6205, such program modules 6205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0183] Bus 630 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0184] The electronic device 600 may also communicate with one or more external devices 700 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or communicate with any device that enables the electronic device 600 to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed via an input / output (I / O) interface 650. Furthermore, the electronic device 600 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) via a network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 via a bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms, etc.

[0185] In another embodiment of the present invention, the present invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs. It should be noted that the computer-readable storage medium here can be a high-speed RAM memory, or a non-volatile memory (Non-VolatileMemory), such as at least one disk memory.

[0186] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the ball screw static performance and reliability evaluation method in the above embodiment; the processor may load and execute the following steps:

[0187] Considering that the contact state of the ball and the raceway is the same, the internal force balance equation of the adjacent balls is corrected; the mapping relationship between the assembly condition and the contact mechanism is established, and the contact angle between the ball and the raceway under the assembly error is calculated; considering different assembly conditions, the internal force balance equation of the adjacent balls is corrected; the boundary conditions of the ball internal force balance equation are determined, the axial force balance equation in the ball screw is corrected, and the judgment conditions for unloaded balls under different assembly conditions are determined; based on the judgment conditions, the reliability of the static performance of the ball screw under different assembly conditions is evaluated.

[0188] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can usually be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0189] Comparison with existing methods

[0190] Comparison 1:

[0191] See also Figure 2, and compared the ball contact load under the assembly error around the y-axis deflection angle. The ball screw parameters are: nominal diameter 20mm, ball diameter 4.763mm, lead 8mm, raceway curvature radius 2.477mm, number of columns × number of rows 3 × 1, contact angle 45°, number of balls 86. Axial load 4000N. The ball deflection angle is 0.0046°. Compared with the existing method, the ball contact load close to the loaded surface in this method is larger, because this method calculates the ball contact load based on the deformation coordination equation of adjacent balls.

[0192] Comparison 2:

[0193] See also Figure 3 , and compared the ball contact load under radial assembly error. The ball screw parameters are: nominal diameter 40mm, ball diameter 6mm, lead 20mm, raceway curvature radius 3.3mm, number of columns × number of rows 2×1, contact angle 45°, number of balls 42. Axial load 6170N. The radial assembly error is 40μm. Compared with this method, the influence of radial assembly error is not considered in the existing method. The ball contact load of this method is in the form of a sinusoidal distribution, which is due to the uneven distribution of the ball contact load caused by the radial assembly error.

[0194] Simulation Analysis

[0195] See also Figure 4 and Figure 5 , the axial contact stiffness and fatigue life of the ball screw are analyzed. The parameters of the ball screw are nominal diameter 25mm, ball diameter 3.175mm, lead 5mm, raceway curvature radius 1.651mm, number of columns × number of rows 2.5 × 1, contact angle 45°, number of balls 62. Axial load 600N. Under the action of different pairs of assembly errors around the x-axis deflection angle, assembly errors around the y-axis deflection angle, and radial assembly errors, the axial contact stiffness and fatigue life of the ball screw have obvious changes. Although the magnitudes of the two are different, the change trends are similar.

[0196] See also Figure 6 and Figure 7 , the reliability of axial contact stiffness and fatigue life of ball screw were analyzed. The parameters of ball screw are: nominal diameter 25mm, ball diameter 3.175mm, lead 5mm, raceway curvature radius 1.651mm, number of columns × number of rows 2.5 × 1, contact angle 45°, number of balls 62. Axial load 600N.

[0197] exist Figure 6 middle, Figure 6 (a) The radial assembly error is 25μm, Figure 6(b) The radial assembly error is -25μm. The results show that the range of axial accuracy reliability under positive radial assembly error is larger. Figure 6 (a) and Figure 6 In (b), the change of the assembly error around the deflection angle of the x-axis has the same influence on the change trend of the axial contact stiffness. The combination of positive radial assembly error and negative deflection angle around the y-axis, and negative radial assembly error and positive deflection angle around the y-axis is less likely to cause a decrease in the reliability of the axial contact stiffness.

[0198] exist Figure 7 middle, Figure 7 (a) The radial assembly error is 25μm, Figure 7 (b) The radial assembly error is -25μm. The influence of the assembly error on the axial contact stiffness reliability and fatigue life reliability is the same. Figure 6 and Figure 7 It can be concluded that the impact of assembly error on the reliability of axial contact stiffness is much greater than its impact on fatigue life reliability.

[0199] In summary, the static performance and reliability evaluation method and system of a ball screw of the present invention, compared with the existing method, takes into account the situation that the ball contact load is inversely proportional to the distance of the ball screw load surface, and analyzes the influence of the assembly error around the y-axis deflection angle and the radial assembly error on the contact load. And the static performance of the ball screw under different assembly conditions is evaluated; the internal force balance equation of adjacent balls is improved, the mapping relationship between the assembly conditions and the contact mechanism is established, and the ball state judgment conditions under different assembly conditions are proposed, which can effectively calculate the static performance of the ball screw under different assembly conditions. At the same time, based on the static performance reliability index, a static performance reliability evaluation method of the ball screw under different assembly conditions is proposed. It can efficiently calculate the static performance of the ball screw under different assembly conditions and evaluate the reliability of the static performance of the ball screw. It can be widely used in non-standard equipment, machine tool equipment, and aerospace equipment, and has great potential.

[0200] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0201] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0202] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0203] In the embodiments provided by the present invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are only schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0204] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0205] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0206] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0207] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0208] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0209] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0210] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for evaluating the static performance and reliability of a ball screw, characterized in that: The following steps are involved: Considering the same contact state between the ball and the raceway, the internal force balance equation of adjacent balls is modified; Establish the mapping relationship between assembly conditions and contact mechanism, and calculate the contact angle between the ball and the raceway under assembly error; Considering different assembly conditions, the internal force balance equation of adjacent balls is modified; Determine the boundary conditions of the ball internal force balance equation, correct the axial force balance equation in the ball screw, and determine the judgment conditions for unloaded balls under different assembly conditions; The reliability of the static performance of the ball screw under different assembly conditions is evaluated based on the judgment conditions.

2. The ball screw static performance and reliability evaluation method according to claim 1, characterized in that: Considering that the contact state of the ball and the raceway is the same, the internal force balance equation of the adjacent balls is modified as follows: Establish the deformation coordination equation of adjacent balls; Use Hertz's formula to calculate the contact load between the ball and the raceway; Calculate the ball internal forces of the jth nut unit and the jth screw unit; Transformation of axial deformation and normal deformation between ball raceways; Calculate the axial deformation of the jth nut unit and the jth screw unit using Hooke's law; Axial force balance equation in a ball screw; The internal force balance equation of adjacent balls is obtained by combining the deformation coordination equation of adjacent balls, the contact load between the balls and the raceways, the transformation of the axial deformation and normal deformation between the ball raceways, and the axial deformation of the jth nut unit and the jth screw unit. On the basis of considering the same contact state between the ball and the raceway, the internal force balance equation of the adjacent balls is modified.

3. The ball screw static performance and reliability evaluation method according to claim 2, characterized in that: The corrected internal force balance equation of adjacent balls is as follows: Among them, Q (j-1) is the contact load between the j-1th ball and the raceway, Q j is the contact load between the jth ball and the raceway, α (j-1) is the contact angle between the j-1th ball and the raceway, α j is the contact angle between the jth ball and the raceway, Q m is the contact load between the mth ball and the raceway, α m is the contact angle between the mth ball and the raceway, F a j is the axial internal force of adjacent balls, U j is the axial deformation coefficient, K is the Hertzian contact coefficient, and λ is the helix angle.

4. The ball screw static performance and reliability evaluation method according to claim 1, characterized in that: The mapping relationship between assembly conditions and contact mechanisms is established, and the contact angle between the ball and the raceway under assembly error is calculated as follows: Calculate the displacement of the center of curvature of the raceway under radial assembly error; Calculate the transformation of the axial deflection angle in the screw axis plane and the helix plane; Calculate the displacement of the center of curvature of the raceway under the assembly error of the deflection angle around the x-axis; Calculate the displacement of the center of curvature of the raceway under the assembly error of the deflection angle around the y-axis; Calculate the contact angle between the ball and the raceway under three assembly errors.

5. The ball screw static performance and reliability evaluation method according to claim 4, characterized in that: Contact angle α between ball and raceway under three assembly errors j for: Where α0 is the initial contact angle of the ball screw, r n is the radius of curvature of the nut raceway, r s is the radius of curvature of the screw raceway, D b is the radius of the ball, δ normj Yes, L2xj is the radial displacement of the center of curvature of the screw raceway of the jth ball caused by the assembly error of the deflection angle around the x-axis, l L2yj is the radial displacement of the center of curvature of the screw raceway corresponding to the jth ball caused by the assembly error of the deflection angle around the y-axis, δ r0 is the radial assembly error, is the position angle of the ball.

6. The ball screw static performance and reliability evaluation method according to claim 1, characterized in that: The specific criteria for determining the unloaded ball under different assembly conditions are: Calculate the distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway under different assembly conditions; Determine whether the balls in the ball screw are in a non-contact state; When the balls between the pth and qth balls are not loaded, the deformation coordination equation between the pth ball and the qth ball is obtained based on the deformation coordination equation of the adjacent balls; After considering different assembly conditions, the internal force balance equation of adjacent balls is modified; Determine the boundary conditions of the ball internal force equilibrium equation; Correction of the axial force balance equation in the ball screw.

7. The ball screw static performance and reliability evaluation method according to claim 6, characterized in that: To determine whether the balls in the ball screw are in a non-contact state, specifically: Among them, when U j When the condition is satisfied, the ball is in an unloaded state. is the axial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, is the radial distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, is the straight-line distance between the center of curvature of the screw raceway and the center of curvature of the nut raceway, U 1j is the first judgment condition, U 2j It is the second judgment condition.

8. The ball screw static performance and reliability evaluation method according to claim 1, characterized in that: The reliability evaluation of the static performance of the ball screw under different assembly conditions is carried out based on the judgment conditions: Calculate the axial contact stiffness of the ball screw; Calculate the fatigue life of ball screws; User-oriented reliability evaluation index The reliability of the axial contact stiffness of the ball screw and the reliability of the fatigue life of the ball screw are calculated according to the reliability evaluation index; By traversing the range of assembly conditions to determine the axial contact stiffness reliability and fatigue life reliability of the ball screw under different combinations of assembly conditions, the maximum allowable range of assembly conditions without reliability failure can be obtained. According to the order in which the maximum range of assembly conditions reaches the set range, the assembly conditions that are most sensitive to the reliability of the axial contact stiffness and fatigue life of the ball screw are obtained.

9. The ball screw static performance and reliability evaluation method according to claim 8, characterized in that: The reliability of the axial contact stiffness of the ball screw and the reliability of the fatigue life of the ball screw are calculated as follows: Among them, k bs is the axial contact stiffness of the ball screw when there is no assembly error, T bs is the fatigue life of the ball screw when there is no assembly error, is the axial contact stiffness of the ball screw under different assembly conditions, It refers to the fatigue life of the ball screw under different assembly conditions, χ1 is the reliability evaluation index of the axial contact stiffness, and χ2 is the reliability evaluation index of the fatigue life. is the reliability of the axial contact stiffness, It is the reliability of fatigue life.

10. A ball screw static performance and reliability evaluation system, characterized in that: include: The parameter module considers that the contact state between the ball and the raceway is the same and modifies the internal force balance equation of adjacent balls; The calculation module establishes the mapping relationship between assembly conditions and contact mechanisms, and calculates the contact angle between the ball and the raceway under assembly errors; The judgment module considers different assembly conditions and corrects the internal force balance equation of adjacent balls; Determine the boundary conditions of the ball internal force balance equation, correct the axial force balance equation in the ball screw, and determine the judgment conditions for unloaded balls under different assembly conditions; The evaluation module performs reliability evaluation on the static performance of the ball screw under different assembly conditions based on the judgment conditions.

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