CN109387363A - A kind of ball screw assembly, positioning accuracy decline prediction technique - Google Patents

A kind of ball screw assembly, positioning accuracy decline prediction technique Download PDF

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CN109387363A
CN109387363A CN201811232526.7A CN201811232526A CN109387363A CN 109387363 A CN109387363 A CN 109387363A CN 201811232526 A CN201811232526 A CN 201811232526A CN 109387363 A CN109387363 A CN 109387363A
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ball screw
screw assembly
ball
feeding
positioning accuracy
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CN109387363B (en
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程强
齐宝宝
闫俊
徐文祥
仲光宇
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Beijing University of Technology
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    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms

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Abstract

The invention discloses a kind of ball screw assembly, positioning accuracy decline prediction techniques, it include: ball screw assembly, positioning accuracy regression analysis, the ball screw assembly, strain energy distributional analysis of quasicontinuum influence of crust deformation, the foundation and forecast analysis of ball screw assembly, positioning accuracy degenerated mode under difference feeding operating condition, based on Quasi continuum theory, determine that its strain energy is distributed according to the microdeformation feature of the wear surface of ball screw assembly, consider the different feeding operating conditions of ball screw assembly, establish the index wear model of ball screw assembly, according to macro-micro- multi-scale method, the useful life of the positioning accuracy retentivity of ball screw assembly, is predicted.The present invention establishes a set of realization precision, precision stability Coordination Evaluation, merges the precision evaluation system of perforation, has the significance taken over from the past and set a new course for the future.

Description

A kind of ball screw assembly, positioning accuracy decline prediction technique
Technical field
It is failed prediction technique the present invention provides a kind of based on macro-micro- multiple dimensioned machine tool ball screw pair positioning accuracy, Belong to Ball Bearing Lead Screw Fit technical field.
Background technique
Ball screw assembly, plays critical effect in transmitting power and the motion mode conversion of the equipment such as numerically-controlled machine tool, The positioning accuracy of ball screw assembly, influences the machining accuracy of numerically-controlled machine tool very big.Ball screw assembly, can occur during military service Abrasion, abrasion are the principal element for causing its positioning accuracy to fail, and the direct factor for causing positioning accuracy to fail.It is a kind of new The considerations of type, positioning accuracies decline prediction techniques of the ball screw assembly, under different feeding operating conditions invents, based on quasi-continuous Jie Matter is theoretical, determines that its strain energy is distributed according to the microdeformation feature of the wear surface of ball screw assembly, considers ball screw assembly, Different feeding operating conditions, the index wear model of ball screw assembly, is established, according to macro-micro- multi-scale method, to ball-screw The useful life of secondary positioning accuracy retentivity is predicted.
The present invention establishes a set of realization precision, precision is kept to abrasion is excavated to the function influence mechanism of precision stability Property Coordination Evaluation, merge the precision evaluation system of perforation, there is the significance taken over from the past and set a new course for the future.
Summary of the invention
It is an object of the present invention to provide a kind of ball screw assembly, positioning accuracy decline prediction techniques, comprising: ball screw assembly, is fixed Under position precision regression analysis, the ball screw assembly, strain energy distributional analysis of quasicontinuum influence of crust deformation, different feeding operating conditions The foundation and forecast analysis of ball screw assembly, positioning accuracy degenerated mode.
The technical solution adopted by the present invention is a kind of ball screw assembly, positioning accuracy decline prediction technique, realizes this method Step includes the following:
S1, ball screw assembly, positioning accuracy regression analysis；
S2, it is based on Quasi continuum theory, considered under quasicontinuum influence of crust deformation, analysis ball screw assembly, wear surface Strain energy distribution；
S3, the different foundation and forecast analysis for feeding the ball screw assembly, positioning accuracy degenerated mode under operating condition.
Detailed description of the invention
Fig. 1 ball screw assembly, state of wear schematic diagram.
Fig. 2 quasi-continuum method schematic diagram.
Fig. 3 quasicontinuum system variant gradient schematic diagram.
Coupling Deformation gradient schematic diagram in Fig. 4 quasicontinuum system.
Fig. 5 considers deformation gradient schematic diagram in the quasicontinuum system of diffusion.
Frayed deformation gradient schematic diagram in Fig. 6 quasicontinuum system.
Fig. 7 ball screw assembly, feeds schematic diagram.
The probability density function of Fig. 8 ξ.
Fig. 9 feeds total amount and amount of feeding Relationship of Coefficients.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is described in detail.
The step of a kind of ball screw assembly, positioning accuracy fails prediction technique, realizes this method include the following:
Step 1 ball screw assembly, positioning accuracy regression analysis
The decline of ball screw assembly, precision is mainly as caused by wearing.There are positioning accuracy errors, angle for ball screw assembly, Error and parallelism error etc. are spent due to abrasion, cause its precision that fade characteristics is presented.The error of ball screw assembly, is made Analysis: ball screw assembly, directly results in the positioning accuracy error in horizontal plane and in vertical plane and increases after abrasion.Ball Lead screw pair is as shown in Figure 1 due to contact condition caused by wearing.
The abrasion of ball screw assembly, causes it to fail in the precision in tri- directions X, Y, Z.Assuming that the ball in raceway Number is m, then arc length l of the ball in lead screw raceways1-m, arc length l in nut rolling wayn1-mIt is respectively as follows:
Wherein, βsmIt is all balls central angle corresponding on lead screw raceway, βnmIt is all balls on nut rolling way Corresponding central angle, X ' (β), Y ' (β), Z'(β) ball centre of sphere parametric equation X (β), Y (β), Z (β) first derivative.
If the initial position where ball in lead screw raceway is xsi, ball and all contact micro-bulges of lead screw raceway are along lead screw The average deviation of hand of spiral regression straight line is ebs(xsi)；If the initial position where ball in nut rolling way is xni, ball with All contact micro-bulges of nut rolling way are e along the average deviation of nut screw direction regression straight linebn(xni), then ball screw assembly, Positioning accuracy measured value g in feed directionfd(xi) indicate are as follows:
If the positioning accuracy error of ball screw assembly, in feed direction is Gfd, GfdIndicate all micro convex point skewed popularities point The sum of positive and negative maximum of cloth reflects the degenerative process of ball screw assembly, feed accuracy and the feature of raceway face pattern, divides Cloth situation is closely related.
The ball screw assembly, strain energy of step 2 quasicontinuum influence of crust deformation is distributed
The abrasion of ball screw assembly, directly affects raceway face shape characteristic, the microprocess of abrasion is considered, according to ball Lead screw pair abrasion surface microdeformation characteristic determines its strain energy distribution situation.Quasi-continuum method is used, to establish rolling The secondary microcosmic wear model of ballscrew.
When contact surface is by preload, it is microcosmic on be divided into regional area and non local region.Subject to as shown in Figure 2 Continuum Methods schematic diagram.
In Fig. 2, the core space in deformation loaded is all elected to be all atoms to represent atom, in deformation The lesser region of gradient chooses several atoms conducts and represents atom.
According to quasicontinuum method, then the derivation of energy formula of ball screw assembly, quasicontinuum system are as follows:
Wherein,Subject to continuum system coupling local continuous part and the static load of non local atomic component answer The summation of power energy,Subject to continuum system obtain the summation that external loading is done work,For quasicontinuum system The summation of the linear elasticity stress energy of system local continuous part, is calculated by following formula:
In formula, NcnAtomicity, Λ are represented for continuumφFor the volume of unit cn,It is close for unit strain energy Degree,Subject to continuum system local continuous region total deformation gradient.
Wherein,Subject to the non local atomic component of continuum system interatomic Potentials can summation, It is calculated by following formula:
In formula, NnlaAtomicity, W are represented for non local atomic regionnlaFor weight function, EnlaFor SW (Stillinger- Weber) potential energy.EnlaWith the relationship of the power on atom k are as follows:
In formula, rrwFor all atoms in atom k adjacent ranges, size is generally taken as 2-3 times of atomic radius.
Ball screw assembly, is during military service, since the effect of outer work condition causes it to wear.According to quasi-continuous Medium system part and non local resolution principle, it is believed that in ball screw assembly, wear process, quasicontinuum system partial zones The change rate of the total deformation gradient in domain is definite value δφ, pass throughIt is calculated.Assuming that when ball screw assembly, is loaded Afterwards, the element deformation gradient distribution in quasicontinuum system is as shown in Figure 3.
In Fig. 3, ψ is deformational displacement amount, and χ is the proportionality coefficient of atomic region, and χ ψ is the range of non local atomic region,For the minimal deformation gradient value of local continuous unit,For the maximum distortion gradient of non local atomic component unit, It is smaller for the total deformation gradient change rate of local continuous unit and be definite value, if its variation slope be tan β.By Fig. 3 Known to:
Wherein, Q is the coefficient of non local atomic component exponential equation, nχOriginal for non local atomic component exponential equation refers to Number.
After preload unloading, deformational displacement amount of the ball screw assembly, in quasicontinuum system cannot be completely extensive It is multiple.According to local and non local regional determination theorem, coupling unit gradient change rate can be obtained greater than local continuous region by Fig. 3 Gradient change rate, it is at 0, as shown in Figure 4 that atomic region, which is extended to gradient change rate,.
In Fig. 4, η is empty rate elongation, and η χ ψ is the range of non local atomic region after empty extend, in conjunction with binomial theorem pair Exponential part is simplified, and can be obtained:
Wherein, nηEmpty for non local atomic component exponential equation extends proportion index, in combination with lattice in quantification theory Relaxation theory acquires.
Consider the influence of diffusion process, it is believed that after atom divergence loss, the distal end exponential curve of non local atomic region is returned Contracting, as shown in Figure 5.
In Fig. 5, k is diffusion coefficient, kηχψFor the range in diffusing atom region, in conjunction with binomial theorem to exponential part into Row simplifies, and can obtain:
Wherein, nkFor the diffusion proportion index of atomic component exponential equation.
Ball screw assembly, wears the loss that will lead to material, and the loss of material will affect atomic ratio coefficient χ and atom Proportion index nχ, the empty extended exponential equation in the material loss part of continuum is approximate, as shown in Figure 6.
In Fig. 6, σ ψ is loss amount, and σ is that continuous part loses ratio, carries out letter to exponential part in conjunction with binomial theorem Change, can obtain:
Wherein, R is the constant term coefficient of exponential equation continuous part.
Step 3 difference feeds the foundation and forecast analysis of the ball screw assembly, positioning accuracy degenerated mode under operating condition
By the analysis of deformation gradient distribution in alignment continuum system, if quasicontinuum system atomic part is vertical In σ sectional area be Aal, continuous part is λ A perpendicular to the sectional area of σal, λ is proportionality coefficient.Based on coupled characteristic and expansion Dissipating influences, and it is impaired in ball screw assembly, quasicontinuum system to consider that abrasion causes, can obtain unidirectional quasicontinuum system and connect The simplification derivation of energy formula of continuous part and atomic component:
Wherein, ntFor abrasion index, it is calculated by following formula:
nt=nχ+nη+nk (14)
According to quasicontinuum method principle and the principle of virtual work, the displacement of quasicontinuum system unit equalization point is true by following formula It is fixed:
It is obtained by formula (15):
Based on binomial theorem abbreviation and after the reduction of fractions to a common denominator:
Wherein,Change it is relatively small, since continuous part loss ratio σ is relatively large, but linear elasticity region The loss of energy has little influence on the exponential distribution of atomic region, main to influence constant term coefficient. Middle χ is with respect to other quantity grade.In conclusion based on quasicontinuum principle and exponential approximation it is assumed that ball screw assembly, is taking During labour, index variation is presented with accumulative abrasion number in abrasion loss.Assuming that ball screw assembly, is by steady contact wear Number be C, ball screw assembly, continuum system concentrated wear amount Δ d can be obtainedbWith contact wear number CbBetween relationship Formula:
Wherein, QbFor the exponential part atomic region coefficient of waste under ball screw assembly, brittleness loading conditions, RbFor ball wire The exponential part continuum coefficient of waste under thick stick pair brittleness loading conditions, KbFor the bullet under ball screw assembly, brittleness loading conditions Property part wears coefficient, nχbFor the original index of non local atomic component exponential equation, nηbFor non local atomic component exponential equation Empty extend proportion index, nkbFor the diffusion proportion index of atomic component exponential equation.
During ball screw assembly, is in toughness wear stage, then the empty rate elongation of atomic component is not present, i.e., does not examine Consider the empty of non local atomic component exponential equation and extends proportion index nη, the wearing depth Δ d of ball screw assembly, can be obtainedtWith abrasion Number CtBetween relational expression:
Wherein, QtFor the exponential part atomic region coefficient of waste under ball screw assembly, toughness loading conditions, KtFor ball wire The elastic part coefficient of waste under thick stick pair toughness loading conditions, nχtFor the original index of non local atomic component exponential equation, nktFor The diffusion proportion index of atomic component exponential equation.
During military service, lead screw can be worn ball screw assembly, with nut.Due to machine tool processing workpiece size Difference, the amount of feeding for causing ball screw assembly, each are different.It is illustrated in figure 7 amount of feeding schematic diagram of the nut relative to lead screw.
By Fig. 7: assuming that feeding sum of ball screw assembly, during military service is N, nut relative to lead screw it is minimum into It is f to amountmin, nut is f relative to the maximum amount of feeding of lead screwmax, amount of feeding f Normal Distribution.Introduce feeding coefficient of discharge ξ, 0≤ξ≤1, ξ are a stochastic variables, for measuring the different degrees of of the ball screw assembly, amount of feeding.
Ball screw assembly, feeding mode influences the distribution of its abrasion loss, according to practical military service operating condition, ball screw assembly, into To the basic Normal Distribution of coefficient of discharge ξ ((a) shown in) in such as Fig. 8, negative skewness distribution (shown in (b) in such as Fig. 8) and Three kinds of states of positive skewness distribution (shown in (c) in such as Fig. 8).Normal distribution indicates smaller in actual condition and larger feeding distance Shared specific gravity is small, and negative skewness distribution indicates that actual condition is partial to large inflow, and positive skewness distribution indicates that actual condition is biased to In the small amount of feeding.
Assuming that ball screw assembly, is respectively Ω according to the feeding total amount of three kinds of modes in identical active timea、Ωb、 Ωc, then total amount Ω is fedaWith the feeding coefficient of discharge ξ of normal distributionaRelationship such as Fig. 9 in (a) shown in, feed total amount ΩbWith The feeding coefficient of discharge ξ of negative skewness distributionbRelationship such as Fig. 9 in (b) shown in, feed total amount ΩcWith the amount of feeding of positive skewness distribution Coefficient ξcRelationship such as Fig. 9 in (c) shown in.
Ball screw assembly, is during military service, and in conjunction with Fig. 9, different feeding modes leads to its asperity contact number not Together, so as to cause its wearing character difference.The strain energy loss calculating process for the micro-bulge that contacts with each other every time is simplified, is tied Box-like (4), (18) and (19) obtain the expression formula of the straight line degree measurement point simplified in ball screw assembly, direction of feed
sfd(xi)≈Λxi w (20)
In formula (20), Λ is the coefficient of waste under ball screw assembly, difference loading conditions, and w is that ball screw assembly, difference is loaded In the case of abrasion proportion index, when ball screw assembly, be in brittleness it is loaded when, have:
When ball screw assembly, be in toughness it is loaded when, have:
Military service and feeding mode with ball screw assembly, the frequency of exposure in different location micro-bulge can be presented not Together.The frequency of exposure of micro-bulge is constantly accumulative, and the different degrees of wear is presented in the micro-bulge in different location.In conjunction with Fig. 1 with Formula (20), according to the geometrical relationship of straightness in the wearing depth and direction of feed of ball screw assembly, the feeding of ball screw assembly, Precision stability general formula is expressed as follows:
Sfd≈Sfd0(xi)tw (23)
Wherein, Sfd0For the initial feed accuracy value of ball screw assembly, SfdFor the reality after ball screw assembly, military service a period of time When feed accuracy value, t be ball screw assembly, active time, w be ball screw assembly, grinding away over time index.

Claims (2)

  1. The prediction technique 1. a kind of ball screw assembly, positioning accuracy fails, it is characterised in that: the step of realizing this method include the following:
    S1, ball screw assembly, positioning accuracy regression analysis；
    S2, it is based on Quasi continuum theory, considered under quasicontinuum influence of crust deformation, analyze the strain of ball screw assembly, wear surface It can distribution；
    S3, the different foundation and forecast analysis for feeding the ball screw assembly, positioning accuracy degenerated mode under operating condition.
  2. The prediction technique 2. a kind of ball screw assembly, positioning accuracy according to claim 1 fails, which is characterized in that realizing should The step of method includes the following:
    Step 1 ball screw assembly, positioning accuracy regression analysis
    The decline of ball screw assembly, precision is mainly as caused by wearing；There are positioning accuracy error, angles to miss for ball screw assembly, Difference and parallelism error etc. cause its precision that fade characteristics is presented due to abrasion；Analysis is made to the error of ball screw assembly: Ball screw assembly, directly results in the positioning accuracy error in horizontal plane and in vertical plane and increases after abrasion；
    The abrasion of ball screw assembly, causes it to fail in the precision in tri- directions X, Y, Z；Assuming that the ball number in raceway It is m, then arc length l of the ball in lead screw raceways1-m, arc length l in nut rolling wayn1-mIt is respectively as follows:
    Wherein, βsmIt is all balls central angle corresponding on lead screw raceway, βnmIt is that all balls institute on nut rolling way is right The central angle answered, X ' (β), Y ' (β), Z'(β) ball centre of sphere parametric equation X (β), Y (β), Z (β) first derivative；
    If the initial position where ball in lead screw raceway is xsi, ball and all contact micro-bulges of lead screw raceway are along lead screw spiral The average deviation of direction regression straight line is ebs(xsi)；If the initial position where ball in nut rolling way is xni, ball and nut All contact micro-bulges of raceway are e along the average deviation of nut screw direction regression straight linebn(xni), then ball screw assembly, into To the positioning accuracy measured value g on directionfd(xi) indicate are as follows:
    If the positioning accuracy error of ball screw assembly, in feed direction is Gfd, GfdIndicate all micro convex point skewed popularity distributions just The sum of negative maximum reflects the degenerative process of ball screw assembly, feed accuracy and feature, the distribution situation of raceway face pattern It is closely related；
    The ball screw assembly, strain energy of step 2 quasicontinuum influence of crust deformation is distributed
    The abrasion of ball screw assembly, directly affects raceway face shape characteristic, the microprocess of abrasion is considered, according to ball-screw Pair abrasion surface microdeformation characteristic determines its strain energy distribution situation；Quasi-continuum method is used, to establish ball wire The secondary microcosmic wear model of thick stick；
    When contact surface is by preload, it is microcosmic on be divided into regional area and non local region；
    Core space in deformation loaded is all elected to be all atoms to represent atom, is in the lesser area of deformation gradient Domain chooses several atoms conducts and represents atom；
    According to quasicontinuum method, then the derivation of energy formula of ball screw assembly, quasicontinuum system are as follows:
    Wherein,Subject to continuum system coupling local continuous part and non local atomic component dead-load stress can Summation,Subject to continuum system obtain the summation that external loading is done work,Subject to continuum system part The summation of the linear elasticity stress energy of continuous part, is calculated by following formula:
    In formula, NcnAtomicity, Λ are represented for continuumφFor the volume of unit cn,For unit strain energy density, Subject to continuum system local continuous region total deformation gradient；
    Wherein,Subject to the non local atomic component of continuum system interatomic Potentials can summation, by following formula It is calculated:
    In formula, NnlaAtomicity, W are represented for non local atomic regionnlaFor weight function, EnlaFor SW potential energy；EnlaOn atom k The relationship of power are as follows:
    In formula, rrwFor all atoms in atom k adjacent ranges, size is taken as 2-3 times of atomic radius；
    Ball screw assembly, is during military service, since the effect of outer work condition causes it to wear；According to quasicontinuum System part and non local resolution principle, it is believed that in ball screw assembly, wear process, quasicontinuum system regional area The change rate of total deformation gradient is definite value δφ, pass throughIt is calculated；
    ψ is deformational displacement amount, and χ is the proportionality coefficient of atomic region, and χ ψ is the range of non local atomic region,Connect for part The minimal deformation gradient value of continuous unit,For the maximum distortion gradient of non local atomic component unit, part is connected The total deformation gradient change rate of continuous unit is smaller and is definite value, if the slope of its variation is tan β；
    Wherein, Q is the coefficient of non local atomic component exponential equation, nχFor the original index of non local atomic component exponential equation；
    After preload unloading, deformational displacement amount of the ball screw assembly, in quasicontinuum system cannot be restored completely；η is Empty rate elongation, η χ ψ are the range of non local atomic region after empty extend, and are simplified in conjunction with binomial theorem to exponential part, It can obtain:
    Wherein, nηEmpty for non local atomic component exponential equation extends proportion index, in combination with lattice relaxation reason in quantification theory By acquiring；
    Consider the influence of diffusion process, it is believed that after atom divergence loss, the distal end exponential curve of non local atomic region bounces back, k For diffusion coefficient, k η χ ψ is the range in diffusing atom region, simplifies in conjunction with binomial theorem to exponential part, can obtain:
    Wherein, nkFor the diffusion proportion index of atomic component exponential equation；
    Ball screw assembly, wears the loss that will lead to material, and the loss of material will affect atomic ratio coefficient χ and atomic ratio Index nχ, the empty extended exponential equation in the material loss part of continuum is approximate；
    σ ψ is loss amount, and σ is that continuous part loses ratio, simplifies in conjunction with binomial theorem to exponential part, can obtain:
    Wherein, R is the constant term coefficient of exponential equation continuous part；
    Step 3 difference feeds the foundation and forecast analysis of the ball screw assembly, positioning accuracy degenerated mode under operating condition
    By the analysis of deformation gradient distribution in alignment continuum system, if quasicontinuum system atomic part is perpendicular to σ Sectional area be Aal, continuous part is λ A perpendicular to the sectional area of σal, λ is proportionality coefficient；Based on coupled characteristic and diffusion shadow It rings, it is impaired in ball screw assembly, quasicontinuum system to consider that abrasion causes, the unidirectional continuous portion of quasicontinuum system can be obtained Divide the simplification derivation of energy formula with atomic component:
    Wherein, ntFor abrasion index, it is calculated by following formula:
    nt=nχ+nη+nk (14)
    According to quasicontinuum method principle and the principle of virtual work, the displacement of quasicontinuum system unit equalization point is determined by following formula:
    It is obtained by formula (15):
    Based on binomial theorem abbreviation and after the reduction of fractions to a common denominator:
    Wherein,Change it is relatively small, since continuous part loss ratio σ is relatively large, but linear elasticity region energy Loss have little influence on the exponential distribution of atomic region, it is main to influence constant term coefficient；Middle χ phase To other quantity grade；In conclusion based on quasicontinuum principle and exponential approximation it is assumed that ball screw assembly, is in military service process In, index variation is presented with accumulative abrasion number in abrasion loss；Assuming that number of the ball screw assembly, by steady contact wear For C, ball screw assembly, continuum system concentrated wear amount Δ d can be obtainedbWith contact wear number CbBetween relational expression:
    Wherein, QbFor the exponential part atomic region coefficient of waste under ball screw assembly, brittleness loading conditions, RbFor ball screw assembly, The exponential part continuum coefficient of waste under brittleness loading conditions, KbFor the elastic portion under ball screw assembly, brittleness loading conditions Divide the coefficient of waste, nχbFor the original index of non local atomic component exponential equation, nηbFor the void of non local atomic component exponential equation Extend proportion index, nkbFor the diffusion proportion index of atomic component exponential equation；
    During ball screw assembly, is in toughness wear stage, then the empty rate elongation of atomic component is not present, i.e., does not consider non- The empty of local atomic part index number equation extends proportion index nη, the wearing depth Δ d of ball screw assembly, can be obtainedtWith abrasion number CtBetween relational expression:
    Wherein, QtFor the exponential part atomic region coefficient of waste under ball screw assembly, toughness loading conditions, KtFor ball screw assembly, The elastic part coefficient of waste under toughness loading conditions, nχtFor the original index of non local atomic component exponential equation, nktFor atom The diffusion proportion index of part index number equation；
    During military service, lead screw can be worn ball screw assembly, with nut；Due to the difference of machine tool processing workpiece size, The amount of feeding for causing ball screw assembly, each is different；
    Assuming that feeding sum of ball screw assembly, during military service is N, nut is f relative to the minimum amount of feeding of lead screwmin, Nut is f relative to the maximum amount of feeding of lead screwmax, amount of feeding f Normal Distribution；Introduce feeding coefficient of discharge ξ, 0≤ξ≤1, ξ It is a stochastic variable, for measuring the different degrees of of the ball screw assembly, amount of feeding；
    Ball screw assembly, feeding mode influences the distribution of its abrasion loss, according to practical military service operating condition, the amount of feeding of ball screw assembly, The basic Normal Distribution of coefficient ξ, negative skewness distribution and positive skewness are distributed three kinds of states；Normal distribution indicates in actual condition Smaller small with specific gravity shared by larger feeding distance, negative skewness distribution indicates that actual condition is partial to large inflow, positive skewness point Cloth indicates that actual condition is partial to the small amount of feeding；
    Assuming that ball screw assembly, is respectively Ω according to the feeding total amount of three kinds of modes in identical active timea、Ωb、Ωc；
    For ball screw assembly, during military service, different feeding modes causes its asperity contact number different, so as to cause it Wearing character is different；The strain energy loss calculating process for the micro-bulge that contacts with each other every time is simplified, convolution (4), (18) With (19), the expression formula of the straight line degree measurement point simplified in ball screw assembly, direction of feed is obtained
    sfd(xi)≈Λxi w (20)
    In formula (20), Λ is the coefficient of waste under ball screw assembly, difference loading conditions, and w is ball screw assembly, difference loading conditions Under abrasion proportion index, when ball screw assembly, be in brittleness it is loaded when, have:
    When ball screw assembly, be in toughness it is loaded when, have:
    Difference can be presented in military service and feeding mode with ball screw assembly, the frequency of exposure in different location micro-bulge；It is micro- The frequency of exposure of convex body is constantly accumulative, and the different degrees of wear is presented in the micro-bulge in different location；Convolution (20), according to The feed accuracy retentivity of the geometrical relationship of straightness in the wearing depth and direction of feed of ball screw assembly, ball screw assembly, is logical It is formulated as follows:
    Sfd≈Sfd0(xi)tw (23)
    Wherein, Sfd0For the initial feed accuracy value of ball screw assembly, SfdFor ball screw assembly, be on active service a period of time after it is real-time into To accuracy value, t is the active time of ball screw assembly, and w is the grinding away over time index of ball screw assembly,.
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