CN113011041A - Rolling linear guide rail pair pretightening force recession calculation method considering microcosmic contact characteristic - Google Patents

Rolling linear guide rail pair pretightening force recession calculation method considering microcosmic contact characteristic Download PDF

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CN113011041A
CN113011041A CN202110355980.7A CN202110355980A CN113011041A CN 113011041 A CN113011041 A CN 113011041A CN 202110355980 A CN202110355980 A CN 202110355980A CN 113011041 A CN113011041 A CN 113011041A
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rolling
raceway
guide rail
linear guide
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CN113011041B (en
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周长光
任士豪
冯虎田
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Nanjing University of Science and Technology
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Abstract

The invention discloses a rolling linear guide rail pair pretightening force recession calculation method considering microcosmic contact characteristics, which comprises the following steps of: determining the pre-tightening force of the rolling linear guide rail pair, and calculating the normal load borne by the upper and lower rows of roller paths of the guide rail pair under the combined action of the pre-tightening force and the external load based on the Hertz theory; extracting a fractal parameter of the surface of the guide rail pair raceway based on a structural function method; based on an MB fractal model, calculating the contact area of the contact surface of the rolling body and the raceway by combining the corrected density distribution function of the microprotrusions, and calculating the stress of the rolling body; establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway by using an Archard wear principle, obtaining a rolling linear guide rail pair pretightening force recession calculation model from the wear loss calculation model, and calculating the rolling linear guide rail pair pretightening force recession by using the model. The invention improves the accuracy of the pre-tightening force calculation result of the rolling linear guide rail pair and better guides the process and the design application of related functional components.

Description

Rolling linear guide rail pair pretightening force recession calculation method considering microcosmic contact characteristic
Technical Field
The invention belongs to the technical field of research on service performance of a rolling linear guide rail pair, and particularly relates to a rolling linear guide rail pair pretightening force decline calculation method considering microcosmic contact characteristics.
Background
In order to eliminate the reverse clearance and improve the dynamic characteristic, the pre-tightening force is applied to various occasions of the rolling linear guide rail pair by increasing the size of the rolling body, however, the pre-tightening force of the rolling linear guide rail pair is gradually reduced due to relative sliding between the rolling body and the roller path, and the dynamic characteristic of the numerical control machine tool is further reduced, so that the establishment of the pre-tightening force decline calculation method of the rolling linear guide rail pair plays an important role in researching the dynamic characteristic of the numerical control machine tool.
At present, related researches on the rolling linear guide rail pair mainly focus on establishing a model for processing the load capacity, the friction characteristic and the thermal behavior of the rolling linear guide rail pair. The research on the decay of the pretightening force is less, the related direction mainly lies in the related calculation related to the abrasion, and the decay calculation deep to the pretightening force is less. And the existing wear calculation does not consider the microcosmic contact between the rolling bodies and the raceways and the intermittent wear behavior between the rolling bodies and the raceways.
Disclosure of Invention
The invention aims to provide a rolling linear guide rail pair pretightening force recession calculation method considering microcosmic contact characteristics, aiming at the problems in the prior art.
The technical solution for realizing the purpose of the invention is as follows: a rolling linear guide rail pair pretightening force decline calculation method considering microcosmic contact characteristics comprises the following steps:
step 1, determining the pretightening force of the rolling linear guide rail pair by combining the definition of the pretightening force in the ball screw pair, and then calculating the normal load borne by the upper and lower rows of roller paths of the rolling linear guide rail pair under the combined action of the pretightening force and an external load based on the Hertz theory;
step 2, extracting a fractal parameter of the surface of the rolling linear guide rail pair raceway based on a structural function method;
step 3, calculating the contact area of the contact surface of the rolling body and the raceway by combining the corrected density distribution function of the microprotrusion body based on the MB fractal model; considering three deformation stages of elasticity, elastoplasticity and plasticity of the micro-convex body of the raceway, calculating the stress of the rolling body by combining the corrected density distribution function of the micro-convex body and by sectional integration;
and 4, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway by using the Archard wear principle, obtaining a pre-tightening force recession calculation model of the rolling linear guide rail pair from the wear loss calculation model, and calculating the pre-tightening force recession of the rolling linear guide rail pair by using the model.
Further, the pre-tightening force of the rolling linear guide rail pair in the step 1 is as follows:
Figure BDA0003003839460000021
in the formula, Fp0Is the pre-tightening force in the initial condition, n is the number of rolling bodies in each row, Q0ij(b-c)The normal contact load of the ith row jth rolling body and the slide block roller path is represented by i, 1,2,3,4,
Figure BDA0003003839460000022
wherein KH(b-c)And delta0ij(b-c)Respectively Hertz contact coefficient and initial deformation between the rolling body and the sliding block raceway, gammaiThe contact angle of the rolling bodies in the ith row and the raceway is shown.
Further, step 1 calculates normal loads borne by upper and lower rows of raceways of the rolling linear guide rail pair under the combined action of a pretightening force and an external load based on the Hertz theory, and specifically comprises the following steps:
when in use
Figure BDA0003003839460000023
When all the rolling bodies are loaded, when
Figure BDA0003003839460000024
When the rolling elements in the lower row are to be unloaded, the normal contact load acting on each rolling element satisfies the following equation:
Figure BDA0003003839460000025
and then combining the relationship among the normal loads obtained by the Hertz theoretical elastic deformation relationship in the following formula, so that the normal loads borne by the upper and lower rows of raceways of the rolling linear guide rail pair under the combined action of the pre-tightening force and the external loading load can be obtained:
Figure BDA0003003839460000026
in the formula, Qij(b-n')N 'r in the case of a guide track raceway, n' c in the case of a slider raceway, n being the number of rolling elements per row, and FVFor applying vertical loads, FpIs a pre-tightening force, Q0The rolling elements are subjected to normal force under the condition of only pre-tightening force.
Further, the step 2 of extracting the fractal parameter of the surface of the rolling linear guide rail pair raceway based on the structural function method specifically includes:
extracting the complexity D of the rough surface and the characteristic length scale G of the rough surface, wherein the calculation formulas are respectively as follows:
Figure BDA0003003839460000027
Figure BDA0003003839460000028
where k and b are the slope and intercept of lgS (τ) ═ 4-2D) lg τ + lgC +2(D-1) lgG, respectively, meaning that k ═ 4-2D and b ═ lgC +2(D-1) lgG, where S (τ) is the power spectrum of the two-dimensional height parameter of the raceway surface, τ ═ n Δ L, where n is the count of the sampling points, Δ L is the sampling interval, C ═ Γ (2D-3) sin [ (D-1.5) pi ═ L, and]l (4-2D) ln gamma, gamma () is a gamma function, in the real number domain
Figure BDA0003003839460000031
S (τ) is obtained by the equation:
Figure BDA0003003839460000032
n is the total number of samples, z()Is the height of the sampling point.
Further, the modified microprotrusion density distribution function of step 3 is:
n'(a)＝λn(a)＝DaL D/2/2aD/2+1
wherein λ is a correction coefficient:
Figure BDA0003003839460000033
in the formula, ShFor the Hertz contact area, R, of the individual rolling elements with the racewaysbIs the radius of the raceway, rbN' (a) is a modified microprotrusion density distribution function, n (a) is a microprotrusion density distribution function representing the number of microprotrusions having an area greater than a, aLR represents the radius of curvature of the point of contact, R being the radius of the top edge of the microprotrusion.
Further, in step 3, based on the MB fractal model, the contact area between the rolling element and the raceway contact surface is calculated by combining the corrected density distribution function of the microprotrusions, and the calculation formula is as follows:
Figure BDA0003003839460000034
in the formula, AijThe contact area of the ith row and the jth rolling element is shown.
Further, in step 3, considering three deformation stages of elasticity, elastoplasticity and plasticity of the raceway microprotrusions, calculating the stress of the rolling body by combining the corrected microprotrusion density distribution function through piecewise integration, specifically comprising:
(1) when a isL＜apcThe microprotrusions being in a fully plastic deformed state, the contact load P of a single microprotrusionpComprises the following steps:
Pp＝kσSa，k＝3
the load Q of each rolling elementi′jComprises the following steps:
Figure BDA0003003839460000035
wherein σSIs the yield limit of the raceway, apcIs the plastic critical area of the microprotrusions,
Figure BDA0003003839460000041
Figure BDA0003003839460000042
m is the strain hardening index, E is the equivalent elastic modulus,
Figure BDA0003003839460000043
wherein E1And E2The elastic modulus, μ, of the two materials respectively1And mu2Respectively the poisson ratio of the two materials;
(2) when a ispc＜aL＜aecThe microprotrusions are in plastic deformation and elastic-plastic deformation states, and the contact load P of a single microprotrusionepComprises the following steps:
Figure BDA0003003839460000044
the load Q of each rolling elementi′jComprises the following steps:
Figure BDA0003003839460000045
wherein the content of the first and second substances,
Figure BDA0003003839460000046
r represents the radius of curvature of the contact point, R being the radius of the top edge of the microprotrusion; a isecIs the elastic critical area of the microprotrusions,
Figure BDA0003003839460000047
(3) when a isL＞aecThe micro-convex body has three of complete plastic deformation, elastic plastic deformation and elastic deformationDeformation state, contact load P of individual microprotrusionseComprises the following steps:
Figure BDA0003003839460000048
the load Q of each rolling elementi′jComprises the following steps:
Figure BDA0003003839460000049
wherein:
Figure BDA0003003839460000051
Figure BDA0003003839460000052
Figure BDA0003003839460000053
Figure BDA0003003839460000054
Figure BDA0003003839460000055
further, step 4, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling element and the raceway by using the arch wear principle, and obtaining a rolling linear guide pair pretightening force decline calculation model accordingly, which specifically comprises the following steps:
step 4-1, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway, specifically:
calculating the abrasion loss of a single rolling body to a roller pathΔδij(b-n')：
Figure BDA0003003839460000056
Then, establishing a wear calculation model considering microcosmic contact and intermittent wear behaviors between the rolling bodies and the raceways, namely summing the wear of each rolling body to obtain the total wear of the rolling bodies to the single-row raceways:
Figure BDA0003003839460000057
in the formula, b-n 'represents the rolling element b with respect to the raceway n', where n 'is r in the case of a guide raceway and n' is c, Δ δ in the case of a slider racewayij(b-n')Is the wear depth between the j-th rolling element and the raceway of the i-th row, K'n'iIn order to be an effective contact coefficient,
Figure BDA0003003839460000058
bn′iminor semi-axis of ellipse of contact of rolling body with racewayn′The effective stroke length of the guide rail or the slide block roller path; k(b-n')For dimensionless coefficients related to material and lubrication conditions, Qij(b-n')Is the normal contact force between the jth rolling body and the raceway of the ith row, delta t is running and time, Vij(b-n')The sliding speed between the jth rolling element and the rolling track of the ith row, H is the hardness of the soft material, Aij(b-n')The contact area of the jth rolling body in the ith row and the raceway; delta deltai(b-n′)The total abrasion depth between the ith row of rolling bodies and the raceway is shown, and n is the number of balls borne by a single row;
and 4-2, combining the model and the pre-tightening force of the rolling linear guide rail pair in the step 1 to obtain a rolling linear guide rail pair pre-tightening force recession calculation model, which is as follows:
Figure BDA0003003839460000061
in the formula, Fp(t) is the pre-tightening force at the moment of operation t, KH(b-c)The hertzian contact coefficient between the rolling elements and the roller track of the slide is p 1, m 2 or p 3, m 4, delta0pj(b-c)And delta0mj(b-c)Initial deformation, delta, of the p-th row and the m-th row of rolling elements to the slide block raceway before running out0pj(b-r)And delta0mj(b-r)The initial deformation, delta, of the p-th row and the m-th row of rolling elements before running and running of the guide rail racewayp(b-c)And deltam(b-c)Total wear depth, delta, of rolling elements of p-th and m-th rows on the slider trackp(b-r)And deltam(b-r)Total wear depth, gamma, of the rolling elements of the p-th and m-th rows on the raceway of the guide railmThe contact angle of the rolling element in the m-th row.
Compared with the prior art, the invention has the following remarkable advantages: 1) according to the invention, the upper and lower rows of forces of the rolling linear guide rail pair are distinguished, so that the subsequent calculation of the abrasion loss of the roller path is divided into the upper and lower rows, and the calculation result is more accurate and accords with the reality; 2) according to the method, a fractal theory is utilized, microcosmic contact is considered, and a correction coefficient is introduced to correct a density distribution function, so that a corrected result is more suitable for the contact condition of a rolling linear guide rail pair, and the final contact area is more accurately calculated; 3) according to the invention, the intermittent wear behavior in the wear process of the rolling linear guide rail pair is considered by introducing the effective contact coefficient, so that the wear condition is more practical; 4) by combining the results, a rolling linear guide rail pair pretightening force decline model is established, so that the decline process of the pretightening force is more accurate and reasonable in calculation.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flow chart of a method for calculating the pre-tightening force decay of a rolling linear guide rail pair in consideration of microcosmic contact characteristics.
Fig. 2 is a stress and deformation diagram of the rolling direct guide rail pair.
Fig. 3 is a two-dimensional profile of the raceway surface.
Fig. 4 is a schematic diagram of a structural function method for solving fractal parameters.
FIG. 5 is a graph of test and pretension decay prediction results in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, with reference to fig. 1, a rolling linear guide pair pretension decay calculation method considering micro-contact characteristics is provided, the method includes the following steps:
step 1, determining the pretightening force of the rolling linear guide rail pair by combining the definition of the pretightening force in the ball screw pair, and then calculating the normal load borne by the upper and lower rows of roller paths of the rolling linear guide rail pair under the combined action of the pretightening force and an external load based on the Hertz theory;
step 2, extracting a fractal parameter of the surface of the rolling linear guide rail pair raceway based on a structural function method;
step 3, calculating the contact area of the contact surface of the rolling body and the raceway by combining the corrected density distribution function of the microprotrusion body based on the MB fractal model; considering three deformation stages of elasticity, elastoplasticity and plasticity of the micro-convex body of the raceway, calculating the stress of the rolling body by combining the corrected density distribution function of the micro-convex body through sectional integration, wherein the stress of the rolling body is balanced with an external load;
and 4, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway by using the Archard wear principle, obtaining a pre-tightening force recession calculation model of the rolling linear guide rail pair from the wear loss calculation model, and calculating the pre-tightening force recession of the rolling linear guide rail pair by using the model.
Further, in one embodiment, in step 1, the pretightening force of the rolling linear guide rail pair is determined by combining the definition of the pretightening force in the ball screw pair, and specifically, the pretightening force is determined by:
(a) the direction of the pre-tightening force is parallel to the direction of the vertical load (the ball screw is generally subjected to the axial load, and the rolling linear guide rail pair is generally subjected to the vertical load);
(b) when no vertical load is applied, the pretightening force acts on the upper row of rolling elements and the lower row of rolling elements to form a pair of equal and opposite forces;
(c) when a vertical load is applied, the acting force of the pretightening force on the upper row of rolling bodies is increased, and the acting force on the lower row of rolling bodies is reduced.
Based on the above, as shown in fig. 2, the pre-tightening force of the rolling linear guide pair is:
Figure BDA0003003839460000071
in the formula, Fp0Is the pre-tightening force in the initial condition, n is the number of rolling bodies in each row, Q0ij(b-c)The normal contact load of the ith row jth rolling body and the slide block roller path is represented by i, 1,2,3,4,
Figure BDA0003003839460000072
wherein KH(b-c)And delta0ij(b-c)Respectively Hertz contact coefficient and initial deformation between the rolling body and the sliding block raceway, gammaiThe contact angle of the rolling bodies in the ith row and the raceway is shown.
Further, in one embodiment, the step 1 of calculating, based on the Hertz theory, normal loads applied to the upper and lower rows of raceways of the rolling linear guide rail pair under the combined action of the pretightening force and the external load specifically includes:
when in use
Figure BDA0003003839460000081
When all the rolling bodies are loaded, when
Figure BDA0003003839460000082
When the rolling elements in the lower row are to be unloaded, the normal contact load acting on each rolling element satisfies the following equation:
Figure BDA0003003839460000083
and then combining the relationship among the normal loads obtained by the Hertz theoretical elastic deformation relationship in the following formula, and determining the normal loads borne by the upper and lower rows of raceways of the rolling linear guide rail pair under the combined action of the pretightening force and the external load by the deformation condition of the raceways after being stressed as shown in FIG. 2:
Figure BDA0003003839460000084
in the formula, Qij(b-n')N 'r in the case of a guide track raceway, n' c in the case of a slider raceway, n being the number of rolling elements per row, and FVFor applying vertical loads, FpIs a pre-tightening force, Q0The rolling elements are subjected to normal force under the condition of only pre-tightening force.
Further, in one embodiment, the extracting of the fractal parameter of the surface of the raceway of the rolling linear guide rail pair based on the structural function method in step 2 specifically includes:
a two-dimensional contour of a raceway surface is extracted through a white light interferometer or a roughness meter and is shown in figure 3, a fitted straight line is obtained by processing data through a structural function method and is shown in figure 4, the complexity D of the rough surface and the characteristic length scale G of the rough surface are extracted through the slope and the intercept of the straight line, and the calculation formulas are respectively as follows:
Figure BDA0003003839460000085
Figure BDA0003003839460000086
where k and b are the slope and intercept of lgS (τ) ═ 4-2D) lg τ + lgC +2(D-1) lgG, respectively, meaning that k ═ 4-2D and b ═ lgC +2(D-1) lgG, where S (τ) is the power spectrum of the two-dimensional height parameter of the raceway surface, τ ═ n Δ L, where n is the count of the sampling points, Δ L is the sampling interval, C ═ Γ (2D-3) sin [ (D-1.5) pi ═ L, and]l (4-2D) ln gamma, gamma () is a gamma function, in the real number domain
Figure BDA0003003839460000091
S (τ) is obtained by the equation:
Figure BDA0003003839460000092
n is the total number of samples, z()Is the height of the sampling point.
Further, in one embodiment, the modified microprotrusion density distribution function of step 3 is:
n'(a)＝λn(a)＝DaL D/2/2aD/2+1
wherein λ is a correction coefficient:
Figure BDA0003003839460000093
in the formula, ShFor the Hertz contact area, R, of the individual rolling elements with the racewaysbIs the radius of the raceway, rbN' (a) is a modified microprotrusion density distribution function, n (a) is a microprotrusion density distribution function representing the number of microprotrusions having an area greater than a, aLR represents the radius of curvature of the point of contact, R being the radius of the top edge of the microprotrusion.
Further, in one embodiment, the contact area of the rolling element and the raceway contact surface is calculated based on the MB fractal model in step 3 by combining the modified density distribution function of the microprotrusions, and the calculation formula is as follows:
Figure BDA0003003839460000094
in the formula, AijThe contact area of the ith row and the jth rolling element is shown.
Further, in one embodiment, the step 3 of calculating the stress of the rolling element by a piecewise integral in combination with the corrected distribution function of the density of the asperities in consideration of three deformation stages of elasticity, elastoplasticity and plasticity of the raceway asperities specifically includes:
here, the three deformation stages of the microprotrusions, including elasticity, elastoplasticity, and plasticity, are specifically:
plastic critical area a of the structural microprotrusionspcAnd elastic critical area aecThe elasticity of the microprotrusions due to plastic deformation (microprotrusions I: a < a) according to the area of contact apc) Elastoplasticity (microprotrusions ii: a ispc＜a＜aec) And plasticity (microprotrusion iii: a > aec)
(1) When a isL＜apcThe microprotrusions being in a fully plastic deformed state, the contact load P of a single microprotrusionpComprises the following steps:
Pp＝kσSa，k＝3
the load Q of each rolling elementi′jComprises the following steps:
Figure BDA0003003839460000101
wherein σSIn rolling linear guide rail pairs, σ is the yield limit of the softer materialSIs the yield limit of the raceway, apcIs the plastic critical area of the microprotrusions,
Figure BDA0003003839460000102
Figure BDA0003003839460000103
m is the strain hardening index, E is the equivalent elastic modulus,
Figure BDA0003003839460000104
wherein E1And E2The elastic modulus, μ, of the two materials respectively1And mu2Respectively the poisson ratio of the two materials;
(2) when a ispc＜aL＜aecThe microprotrusions are in plastic deformation and elastic-plastic deformation states, and the contact load P of a single microprotrusionepComprises the following steps:
Figure BDA0003003839460000105
the load Q of each rolling elementi′jComprises the following steps:
Figure BDA0003003839460000106
wherein the content of the first and second substances,
Figure BDA0003003839460000107
r represents the radius of curvature of the contact point, R being the radius of the top edge of the microprotrusion; a isecIs the elastic critical area of the microprotrusions,
Figure BDA0003003839460000108
(3) when a isL＞aecThe microprotrusions have three deformation states of plastic deformation, elastic-plastic deformation and elastic deformation, and the contact load P of a single microprotrusioneComprises the following steps:
Figure BDA0003003839460000109
the load Q of each rolling elementi′jComprises the following steps:
Figure BDA0003003839460000111
wherein:
Figure BDA0003003839460000112
Figure BDA0003003839460000113
Figure BDA0003003839460000114
Figure BDA0003003839460000115
Figure BDA0003003839460000116
further, in one embodiment, the step 4 of establishing a wear calculation model considering the microcosmic contact and intermittent wear behavior between the rolling element and the raceway by using the arch wear principle, and obtaining a rolling linear guide pair pretightening force decline calculation model therefrom specifically includes:
step 4-1, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway, specifically:
calculating the abrasion loss delta of single rolling body to racewayij(b-n')：
Figure BDA0003003839460000117
Then, establishing a wear calculation model considering microcosmic contact and intermittent wear behaviors between the rolling bodies and the raceways, namely summing the wear of each rolling body to obtain the total wear of the rolling bodies to the single-row raceways:
Figure BDA0003003839460000118
in the formula, b-n 'represents the rolling element b with respect to the raceway n', where n 'is r in the case of a guide raceway and n' is c, Δ δ in the case of a slider racewayij(b-n')Is the wear depth between the j-th rolling element and the raceway of the i-th row, K'n'iFor the effective contact coefficient (here, intermittent wear between the rolling bodies and the raceways, only the parts of the raceways in contact with the rolling bodies wear during a certain operating time, the main wear areasIs the overlap region between the contact region of maximum hertzian contact stress and the specific wear region, thus introducing an effective contact coefficient; because the stroke of the slide block is smaller, the effective contact coefficient of the slide block roller path is larger than that of the guide rail roller path, which also shows that the abrasion degree of the slide block is larger than that of the guide rail in the same time,
Figure BDA0003003839460000121
bn′iminor semi-axis of ellipse of contact of rolling body with racewayn′The effective stroke length of the guide rail or the slide block roller path; k(b-n')For dimensionless coefficients related to material and lubrication conditions, Qij(b-n')Is the normal contact force between the jth rolling body and the raceway of the ith row, delta t is running and time, Vij(b-n')The sliding speed between the jth rolling element and the rolling track of the ith row, H is the hardness of the soft material, Aij(b-n')The contact area of the jth rolling body in the ith row and the raceway; delta deltai(b-n′)The total abrasion depth between the ith row of rolling bodies and the raceway is shown, and n is the number of balls borne by a single row;
and 4-2, combining the model and the pre-tightening force of the rolling linear guide rail pair in the step 1 to obtain a rolling linear guide rail pair pre-tightening force recession calculation model, which is as follows:
Figure BDA0003003839460000122
in the formula, Fp(t) is the pre-tightening force at the moment of operation t, KH(b-c)The hertzian contact coefficient between the rolling elements and the roller track of the slide is p 1, m 2 or p 3, m 4, delta0pj(b-c)And delta0mj(b-c)Initial deformation, delta, of the p-th row and the m-th row of rolling elements to the slide block raceway before running out0pj(b-r)And delta0mj(b-r)The initial deformation, delta, of the p-th row and the m-th row of rolling elements before running and running of the guide rail racewayp(b-c)And deltam(b-c)Total wear depth, delta, of rolling elements of p-th and m-th rows on the slider trackp(b-r)And deltam(b-r)Scrolling for the p-th and m-th columns, respectivelyTotal wear depth, gamma, of the body to the track racewaymThe contact angle of the rolling element in the m-th row.
As a specific example, the invention tests the pre-tightening force recession process of a guide rail pair of DA45CL model of a certain domestic manufacturer through experiments, and verifies the accuracy of the pre-tightening force recession prediction model of the rolling linear guide rail pair, and as a result, as shown in FIG. 5, due to the intermittent wear behavior between the rolling elements and the roller paths, the actual wear depth in the rolling linear guide rail pair is far smaller than that calculated previously. Thus, when the effective contact coefficient K 'is not introduced'n'i(far less than 1), the model has much faster prediction of the decay of the pretightening force and the TAO model than the experimental result. Due to the special surface condition of the two curved rough surfaces of the raceway-linear guide pair, the actual contact and wear area is slightly lower than previously thought, resulting in a smaller wear depth of the raceway surfaces. Therefore, when the correction coefficient λ (slightly less than 1) is not introduced, the reduction rate of the predicted preload of the model is slightly lower than the experimental result. When K 'is introduced'n'iAnd lambda later, the predicted pretension of the model becomes very close to the experimental results.
In the invention, fractal theory is applied to the contact between the rolling element and the raceway, a correction coefficient lambda is introduced to correct a density distribution function, and an effective contact coefficient K 'is introduced'n'iThe intermittent wear behavior between the rolling bodies and the raceways is considered, and the situation that the stress of the upper and lower rows of raceways is inconsistent under the condition of external loading is considered, so that a brand-new rolling linear guide rail pair pretightening force decline model is established, and the decline situation of the pretightening force of the rolling linear guide rail pair can be more accurately predicted.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. A rolling linear guide rail pair pretightening force decline calculation method considering microcosmic contact characteristics is characterized by comprising the following steps of:
step 1, determining the pretightening force of the rolling linear guide rail pair by combining the definition of the pretightening force in the ball screw pair, and then calculating the normal load borne by the upper and lower rows of roller paths of the rolling linear guide rail pair under the combined action of the pretightening force and an external load based on the Hertz theory;
step 2, extracting a fractal parameter of the surface of the rolling linear guide rail pair raceway based on a structural function method;
step 3, calculating the contact area of the contact surface of the rolling body and the raceway by combining the corrected density distribution function of the microprotrusion body based on the MB fractal model; considering three deformation stages of elasticity, elastoplasticity and plasticity of the micro-convex body of the raceway, calculating the stress of the rolling body by combining the corrected density distribution function of the micro-convex body and by sectional integration;
and 4, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway by using the Archard wear principle, obtaining a pre-tightening force recession calculation model of the rolling linear guide rail pair from the wear loss calculation model, and calculating the pre-tightening force recession of the rolling linear guide rail pair by using the model.
2. The method for calculating the decay of the pre-tightening force of the rolling linear guide rail pair in consideration of the microcontact characteristic as claimed in claim 1, wherein the pre-tightening force of the rolling linear guide rail pair in step 1 is as follows:
Figure FDA0003003839450000011
in the formula, Fp0Is the pre-tightening force in the initial condition, n is the number of rolling bodies in each row, Q0ij(b-c)The normal contact load of the ith row jth rolling body and the slide block roller path is represented by i, 1,2,3,4,
Figure FDA0003003839450000012
wherein KH(b-c)And delta0ij(b-c)Are respectively Hertz connectedCoefficient of contact and initial deformation, gamma, between rolling body and slide trackiThe contact angle of the rolling bodies in the ith row and the raceway is shown.
3. The method for calculating the pre-tightening force decline of the rolling linear guide rail pair in consideration of the microcosmic contact characteristic as claimed in claim 2, wherein the step 1 of calculating the normal load on the upper and lower rows of raceways of the rolling linear guide rail pair under the combined action of the pre-tightening force and the external load based on the Hertz theory specifically comprises:
when in use
Figure FDA0003003839450000013
When all the rolling bodies are loaded, when
Figure FDA0003003839450000014
When the rolling elements in the lower row are to be unloaded, the normal contact load acting on each rolling element satisfies the following equation:
Figure FDA0003003839450000021
and then combining the relationship among the normal loads obtained by the Hertz theoretical elastic deformation relationship in the following formula, so that the normal loads borne by the upper and lower rows of raceways of the rolling linear guide rail pair under the combined action of the pre-tightening force and the external loading load can be obtained:
Figure FDA0003003839450000022
in the formula, Qij(b-n')Is the normal contact load between the jth rolling element b and the raceway n ' of the ith row, n ' ═ r in the case of a rail raceway and n ' ═ c in the case of a slider raceway, n is the number of rolling elements per row, and FVFor applying vertical loads, FpIs a pre-tightening force, Q0The rolling elements are subjected to normal force under the condition of only pre-tightening force.
4. The method for calculating the pre-tightening force decline of the rolling linear guide rail pair in consideration of the microcontact characteristic as claimed in claim 3, wherein the step 2 of extracting the fractal parameter of the surface of the raceway of the rolling linear guide rail pair based on the structural function method specifically comprises:
extracting the complexity D of the rough surface and the characteristic length scale G of the rough surface, wherein the calculation formulas are respectively as follows:
Figure FDA0003003839450000023
Figure FDA0003003839450000024
where k and b are the slope and intercept of lgS (τ) ═ 4-2D) lg τ + lgC +2(D-1) lgG, respectively, meaning that k ═ 4-2D and b ═ lgC +2(D-1) lgG, where S (τ) is the power spectrum of the two-dimensional height parameter of the raceway surface, τ ═ n Δ L, where n is the count of the sampling points, Δ L is the sampling interval, C ═ Γ (2D-3) sin [ (D-1.5) pi ═ L, and]l (4-2D) ln gamma, gamma () is a gamma function, in the real number domain
Figure FDA0003003839450000025
S (τ) is obtained by the equation:
Figure FDA0003003839450000026
n is the total number of samples, z()Is the height of the sampling point.
5. The method for calculating the pre-tightening force decay of the rolling linear guide rail pair considering the microcontact characteristic as claimed in claim 4, wherein the modified microprotrusion density distribution function in step 3 is:
n'(a)＝λn(a)＝DaL D/2/2aD/2+1
wherein λ is a correction coefficient:
Figure FDA0003003839450000031
in the formula, ShFor the Hertz contact area, R, of the individual rolling elements with the racewaysbIs the radius of the raceway, rbN' (a) is a modified microprotrusion density distribution function, n (a) is a microprotrusion density distribution function representing the number of microprotrusions having an area greater than a, aLR represents the radius of curvature of the point of contact, R being the radius of the top edge of the microprotrusion.
6. The method for calculating the pre-tightening force recession of the rolling linear guide rail pair considering the microcosmic contact characteristic as claimed in claim 5, wherein the contact area of the rolling element and the raceway contact surface is calculated based on the MB fractal model in step 3 by combining the corrected density distribution function of the microprotrusions, and the calculation formula is as follows:
Figure FDA0003003839450000032
in the formula, AijThe contact area of the ith row and the jth rolling element is shown.
7. The method for calculating the pre-tightening force decline of the rolling linear guide rail pair considering the microcontact characteristic as claimed in claim 6, wherein in step 3, the stress of the rolling element is calculated by combining the corrected density distribution function of the micro-convex body through piecewise integration in consideration of three deformation stages of elasticity, elastoplasticity and plasticity of the micro-convex body of the raceway, and specifically comprises the following steps:
(1) when a isL＜apcThe microprotrusions being in a fully plastic deformed state, the contact load P of a single microprotrusionpComprises the following steps:
Pp＝kσSa，k＝3
the load Q of each rolling elementi′jComprises the following steps:
Figure FDA0003003839450000033
wherein σSIs the yield limit of the raceway, apcIs the plastic critical area of the microprotrusions,
Figure FDA0003003839450000034
Figure FDA0003003839450000035
m is the strain hardening index, E is the equivalent elastic modulus,
Figure FDA0003003839450000036
wherein E1And E2The elastic modulus, μ, of the two materials respectively1And mu2Respectively the poisson ratio of the two materials;
(2) when a ispc＜aL＜aecThe microprotrusions are in plastic deformation and elastic-plastic deformation states, and the contact load P of a single microprotrusionepComprises the following steps:
Figure FDA0003003839450000041
load Q 'of each rolling element'ijComprises the following steps:
Figure FDA0003003839450000042
wherein the content of the first and second substances,
Figure FDA0003003839450000043
r represents the radius of curvature of the contact point, R being the radius of the top edge of the microprotrusion; a isecIs the elastic critical area of the microprotrusions,
Figure FDA0003003839450000044
(3) when a isL＞aecMicro, microThe convex body has three deformation states of plastic deformation, elastic-plastic deformation and elastic deformation, and the contact load P of single micro convex bodyeComprises the following steps:
Figure FDA0003003839450000045
load Q 'of each rolling element'ijComprises the following steps:
Figure FDA0003003839450000046
wherein:
Figure FDA0003003839450000047
Figure FDA0003003839450000048
Figure FDA0003003839450000049
Figure FDA0003003839450000051
Figure FDA0003003839450000052
8. the method for calculating the pre-tightening force recession of the rolling linear guide pair in consideration of the microcontact characteristic as claimed in claim 7, wherein the step 4 is to establish a wear amount calculation model in consideration of microcontact and intermittent wear behaviors between the rolling element and the raceway by using the Archard wear principle, and to obtain the rolling linear guide pair pre-tightening force recession calculation model therefrom, and specifically comprises:
step 4-1, establishing a wear loss calculation model considering microcosmic contact and intermittent wear behaviors between the rolling body and the raceway, specifically:
calculating the abrasion loss delta of single rolling body to racewayij(b-n')：
Figure FDA0003003839450000053
Then, establishing a wear calculation model considering microcosmic contact and intermittent wear behaviors between the rolling bodies and the raceways, namely summing the wear of each rolling body to obtain the total wear of the rolling bodies to the single-row raceways:
Figure FDA0003003839450000054
in the formula, b-n 'represents the rolling element b with respect to the raceway n', where n 'is r in the case of a guide raceway and n' is c, Δ δ in the case of a slider racewayij(b-n')Is the wear depth between the j-th rolling element and the raceway of the i-th row, K'n'iIn order to be an effective contact coefficient,
Figure FDA0003003839450000055
bn′iminor semi-axis of ellipse of contact of rolling body with racewayn′The effective stroke length of the guide rail or the slide block roller path; k(b-n')For dimensionless coefficients related to material and lubrication conditions, Qij(b-n')Is the normal contact force between the jth rolling body and the raceway of the ith row, delta t is running and time, Vij(b-n')The sliding speed between the jth rolling element and the rolling track of the ith row, H is the hardness of the soft material, Aij(b-n')The contact area of the jth rolling body in the ith row and the raceway; delta deltai(b-n′)The total abrasion depth between the ith row of rolling bodies and the raceway is shown, and n is the number of balls borne by a single row;
and 4-2, combining the model and the pre-tightening force of the rolling linear guide rail pair in the step 1 to obtain a rolling linear guide rail pair pre-tightening force recession calculation model, which is as follows:
Figure FDA0003003839450000061
in the formula, Fp(t) is the pre-tightening force at the moment of operation t, KH(b-c)The hertzian contact coefficient between the rolling elements and the roller track of the slide is p 1, m 2 or p 3, m 4, delta0pj(b-c)And delta0mj(b-c)Initial deformation, delta, of the p-th row and the m-th row of rolling elements to the slide block raceway before running out0pj(b-r)And delta0mj(b-r)The initial deformation, delta, of the p-th row and the m-th row of rolling elements before running and running of the guide rail racewayp(b-c)And deltam(b-c)Total wear depth, delta, of rolling elements of p-th and m-th rows on the slider trackp(b-r)And deltam(b-r)Total wear depth, gamma, of the rolling elements of the p-th and m-th rows on the raceway of the guide railmThe contact angle of the rolling element in the m-th row.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113792451A (en) * 2021-08-16 2021-12-14 东南大学 Rolling linear guide rail pair static rigidity calculation and structural parameter design method
CN115660224A (en) * 2022-12-12 2023-01-31 南京理工大学 Pre-tightening dragging force prediction method of roller linear guide rail pair

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106017889A (en) * 2016-06-22 2016-10-12 北京工业大学 Test device and detection method for detecting comprehensive performance degradation of rolling linear guideway pair
CN110095280A (en) * 2019-04-29 2019-08-06 南京理工大学 A kind of linear rolling guide resultant wear coefficient testing method
CN110725861A (en) * 2019-09-17 2020-01-24 浙江工业大学 Method for applying pre-tightening force of ball linear guide rail pair

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106017889A (en) * 2016-06-22 2016-10-12 北京工业大学 Test device and detection method for detecting comprehensive performance degradation of rolling linear guideway pair
CN110095280A (en) * 2019-04-29 2019-08-06 南京理工大学 A kind of linear rolling guide resultant wear coefficient testing method
CN110725861A (en) * 2019-09-17 2020-01-24 浙江工业大学 Method for applying pre-tightening force of ball linear guide rail pair

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113792451A (en) * 2021-08-16 2021-12-14 东南大学 Rolling linear guide rail pair static rigidity calculation and structural parameter design method
CN113792451B (en) * 2021-08-16 2022-11-11 东南大学 Rolling linear guide rail pair static rigidity calculation and structural parameter design method
CN115660224A (en) * 2022-12-12 2023-01-31 南京理工大学 Pre-tightening dragging force prediction method of roller linear guide rail pair
CN115660224B (en) * 2022-12-12 2023-03-17 南京理工大学 Pre-tightening dragging force prediction method of roller linear guide rail pair

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