CN113108750A - Four-oil-pad hydrostatic guideway motion precision evaluation method and system - Google Patents

Four-oil-pad hydrostatic guideway motion precision evaluation method and system Download PDF

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CN113108750A
CN113108750A CN202110378143.6A CN202110378143A CN113108750A CN 113108750 A CN113108750 A CN 113108750A CN 202110378143 A CN202110378143 A CN 202110378143A CN 113108750 A CN113108750 A CN 113108750A
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oil
pad
guide rail
hydrostatic
oil film
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查俊
李超
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XI'AN JIAOTONG UNIVERSITY SUZHOU ACADEMY
Xian Jiaotong University
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XI'AN JIAOTONG UNIVERSITY SUZHOU ACADEMY
Xian Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
    • G01B21/24—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes for testing alignment of axes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/08—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness for measuring thickness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile

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  • General Physics & Mathematics (AREA)
  • Magnetic Bearings And Hydrostatic Bearings (AREA)

Abstract

本发明一种四油垫静压导轨运动精度评价方法，能够对油垫中心距较大的四油垫静压导轨运动直线度进行计算；首先简化油垫中心距较大的静压导轨模型，并将静压导轨的导轨面误差进行数学表达，然后计算静压导轨面轮廓误差的油膜厚度，再建立考虑油垫中心距的油膜力计算模型和静压导轨静力学平衡方程，联立方程得到油垫中心距与导轨面轮廓误差波长的比值与运动直线度的对应关系，求解得到考虑油垫中心距的四油垫静压导轨运动直线度，从而更加准确的对四油垫静压导轨的运动直线度进行计算，能够判定滑块运动直线度误差，对四油垫静压导轨运动精度进行评价，从而为四油垫静压导轨精度设计提供了理论指导。

Figure 202110378143

The present invention is a method for evaluating the motion accuracy of the static pressure guide rail with four oil pads, which can calculate the motion straightness of the static pressure guide rail with a large oil pad center distance; The guideway surface error of the hydrostatic guideway is mathematically expressed, and then the oil film thickness of the hydrostatic guideway surface contour error is calculated, and the oil film force calculation model considering the center distance of the oil pad and the static pressure guideway static equilibrium equation are established, and the simultaneous equations are obtained. The corresponding relationship between the ratio of the oil pad center distance to the contour error wavelength of the guide rail surface and the motion straightness, the motion straightness of the four-oil pad hydrostatic guideway considering the center distance of the oil pad can be obtained by solving, so as to more accurately measure the motion straightness of the four-oil pad hydrostatic guideway. By calculating the motion straightness, the slider motion straightness error can be determined, and the motion accuracy of the four-oil pad hydrostatic guideway can be evaluated, thus providing theoretical guidance for the precision design of the four-oil-pad hydrostatic guideway.

Figure 202110378143

Description

Four-oil-pad hydrostatic guideway motion precision evaluation method and system
Technical Field
The invention relates to the field of hydrostatic guideway errors, in particular to a four-oil-pad hydrostatic guideway motion precision evaluation method and a four-oil-pad hydrostatic guideway motion precision evaluation system.
Background
The hydrostatic guideway is an important functional component of a precision, ultra-precision and three-coordinate measuring machine, and the motion straightness of a guideway slider has important influence on the precision of a machined and measured part. Therefore, the influence rule of the structural parameters of the hydrostatic guideway system on the motion straightness of the slide block needs to be researched, and a theoretical basis is provided for improving the motion straightness. When the structure size of the hydrostatic guideway oil pad is smaller, the hydrostatic guideway oil pad can be respectively simplified into a rigid small wheel, the ratio of the center distance of the oil pad to the profile error wavelength of the guideway surface is 0.5,1.5 and 2.5 … …, and the motion straightness error is zero. However, when the length of the hydrostatic guideway oil pad is large, the hydrostatic guideway oil pad cannot be simplified into a rigid small wheel, otherwise, the error evaluation of relevant structural parameters of the hydrostatic guideway oil pad can be caused, and the motion precision of the hydrostatic guideway with four oil pads cannot be improved.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a four-oil-pad hydrostatic guideway motion accuracy evaluation method and system, which are reasonable in design and simple in method, and can obtain the motion straightness of the four-oil-pad hydrostatic guideway when the center distance of oil pads is larger, thereby greatly improving the motion straightness accuracy of the hydrostatic guideway.
The invention is realized by the following technical scheme:
the four-oil pad hydrostatic guideway motion accuracy evaluation method comprises the following steps,
simplifying a four-oil-pad hydrostatic guideway model with a larger oil pad center distance according to preset conditions;
calculating to obtain a static pressure guide rail surface contour error equation according to the simplified four-oil pad static pressure guide rail model;
obtaining an oil film thickness equation at the oil sealing surface according to the theoretical oil film thickness and the static pressure guide rail surface profile error;
the four-oil-pad hydrostatic guide rail is equivalent to a quasi-static model, an oil film is equivalent to a linear spring unit, and an oil film supporting force equation of the oil pad when the guide rail sliding block moves is obtained according to the thickness of the oil film at the oil seal surface;
according to the balance between the resultant force of the oil film bearing force of each oil pad and the external load, keeping the balance state of the sliding block to obtain a static balance equation of the static pressure guide rail;
and (3) simultaneously establishing a hydrostatic guideway surface profile error equation, an oil film thickness equation, an oil film supporting force equation and a hydrostatic guideway static balance equation, solving to obtain the motion straightness of the hydrostatic guideway, and evaluating the motion precision of the hydrostatic guideway with four oil pads.
Preferably, the preset conditions include assuming that the profile error of the guide surface does not change in the width direction of the oil pad, and neglecting the profile error change of the guide surface in the width x direction of the slider.
Preferably, the static pressure guide rail surface contour error is obtained through calculation according to the simplified four-oil pad static pressure guide rail model, and is represented as follows through Fourier series fitting,
Figure BDA0003012088570000021
in the formula: e is the error amplitude, λ is the profile error wavelength,
Figure BDA0003012088570000022
is the phase angle and y is the guide surface profile length.
Preferably, the oil film thickness at the oil seal surface is obtained according to the theoretical oil film thickness and the static pressure guide surface profile error, and the method specifically comprises the following steps:
h(y)＝h0-fz(y)
in the formula: h is0Is the theoretical oil film thickness, fzAnd (y) is the static pressure guide surface contour error.
Preferably, the oil film supporting force of the oil pad when the rail slider moves is specifically expressed as follows,
Figure BDA0003012088570000023
in the formula: e.g. of the typej(y) is the linear displacement motion error at the center of the oil pad j; e.g. of the typez(y) is the linear displacement motion error of the slide block; thetaxIs the pitch angle error; thetayIs the roll angle error; f. ofej(y) is the action of the sliding block in the moving processThe variable quantity of the oil film bearing force on the oil pad j is determined by the thickness of the oil film at the oil sealing surface; f. ofbj(y) is the oil film bearing force on the oil pad j; a isj、bj、cjIs a directional coefficient, j is 1-4; f. ofjy(y) is the original supporting force of the oil pad when the slide block moves; m is the center distance of the oil pad in the Y direction; and n is the center distance of the oil pad in the X direction.
Preferably, the slider balance state is maintained according to the balance between the resultant force of the oil film bearing forces of the oil pads and the external load, so as to obtain a static balance equation of the hydrostatic guideway, which is specifically as follows:
Figure BDA0003012088570000031
in the formula (f)j(y) is the original supporting force of the oil pad when the slide block moves; m is the center distance of the oil pad in the Y direction; n is the center distance of the oil pad in the X direction; g is the self weight of the sliding block; w is the load at the machining position; mxIs the resultant moment in the X direction; myThe resultant moment in the Y direction; a isj，bjIs a directional coefficient, j is 1-4; m is1The distance between the machining position and the center of the slide block along the Y direction; n is1The distance between the machining position and the center of the slide block along the X direction.
Preferably, the simultaneous equations are solved to obtain the motion straightness of the hydrostatic guideway as follows:
ez＝B1·A1·(fe1+fe2+fe3+fe4-G-W)
in the formula, A is a slider structure parameter matrix; b is an oil film rigidity coefficient matrix; a. the1Is a first column vector, B1Is a first row vector; e.g. of the typezIs straightness; f. ofejJ is the variation of the oil film bearing force on the oil pad, and j is 1-4; g: self-weight of the sliding block; w: load at the machining location.
The four-oil-pad hydrostatic guideway motion accuracy evaluation system comprises,
the model simplifying module is used for simplifying the four-oil-pad hydrostatic guideway model with larger oil pad center distance according to preset conditions;
the guide rail surface contour error module is used for calculating to obtain a hydrostatic guide rail surface contour error equation according to the simplified four-oil-pad hydrostatic guide rail model;
the oil film thickness module is used for obtaining an oil film thickness equation at the oil sealing surface according to the theoretical oil film thickness and the static pressure guide rail surface profile error;
the oil film supporting force module is used for enabling the four oil pad hydrostatic guide rails to be equivalent to a quasi-static model, enabling the oil films to be equivalent to linear spring units, and obtaining an oil film supporting force equation of the oil pads when the guide rail sliding blocks move according to the thickness of the oil films at the oil sealing surfaces;
the static balance equation module is used for keeping the balance state of the sliding block according to the balance between the resultant force of the oil film bearing force of each oil pad and the external load to obtain a static balance equation of the static pressure guide rail;
and the straightness module is used for simultaneously establishing a hydrostatic guideway surface profile error equation, an oil film thickness equation, an oil film supporting force equation and a hydrostatic guideway static balance equation, solving to obtain the motion straightness of the hydrostatic guideway and evaluating the motion precision of the hydrostatic guideway with four oil pads.
Compared with the prior art, the invention has the following beneficial technical effects:
the four-oil-pad hydrostatic guideway motion accuracy evaluation method can calculate the motion straightness of the four-oil-pad hydrostatic guideway with larger oil pad center distance; the method comprises the steps of simplifying a hydrostatic guideway model with a large oil pad center distance, performing mathematical expression on a guideway surface error of the hydrostatic guideway, calculating the oil film thickness of a hydrostatic guideway surface profile error, establishing an oil film force calculation model considering the oil pad center distance and a hydrostatic guideway static equilibrium equation, combining the equations to obtain a corresponding relation between the ratio of the oil pad center distance to the guideway surface profile error wavelength and the motion straightness, and solving to obtain the four-oil-pad hydrostatic guideway motion straightness considering the oil pad center distance, so that the motion straightness of the four-oil-pad hydrostatic guideway is more accurately calculated, the slide block motion straightness error can be judged, the four-oil-pad hydrostatic guideway motion precision is evaluated, and theoretical guidance is provided for the four-oil-pad hydrostatic guideway precision design.
Drawings
FIG. 1 is a simplified schematic diagram of a hydrostatic guideway model with a large oil pad center distance according to an embodiment of the present invention;
FIG. 2 is a schematic view of the rail profile error and oil pad configuration of the present invention;
FIG. 3 is a schematic illustration of an equivalent mechanical model of the hydrostatic guideway in an example of the present invention;
in the figure: the oil pad 1, the first oil pad 11, the second oil pad 12, the slider 2, a width-direction oil film 21, a length-direction oil film 22, and the guide rail 3.
Detailed Description
The present invention will now be described in further detail with reference to specific examples, which are intended to be illustrative, but not limiting, of the invention.
The invention relates to a four-oil-pad hydrostatic guideway motion precision evaluation method considering an oil pad center distance, which comprises the following steps:
simplifying a four-oil-pad hydrostatic guideway model with a larger oil pad center distance according to preset conditions;
calculating to obtain a static pressure guide rail surface contour error equation according to the simplified four-oil pad static pressure guide rail model;
obtaining an oil film thickness equation at the oil sealing surface according to the theoretical oil film thickness and the static pressure guide rail surface profile error;
the four-oil-pad hydrostatic guide rail is equivalent to a quasi-static model, an oil film is equivalent to a linear spring unit, and an oil film supporting force equation of the oil pad when the guide rail sliding block moves is obtained according to the thickness of the oil film at the oil seal surface;
according to the balance between the resultant force of the oil film bearing force of each oil pad and the external load, keeping the balance state of the sliding block to obtain a static balance equation of the static pressure guide rail;
and (3) simultaneously establishing a hydrostatic guideway surface profile error equation, an oil film thickness equation, an oil film supporting force equation and a hydrostatic guideway static balance equation, solving to obtain the motion straightness of the hydrostatic guideway, and evaluating the motion precision of the hydrostatic guideway with four oil pads.
Specifically, the method comprises the following steps:
s1, aiming at the hydrostatic guide rail with larger oil pad size, simplifying the model of the guide rail slide block,the three-dimensional hydrostatic guide rail is simplified into a two-dimensional guide rail, a sliding block and an oil pad, so that analysis is convenient, and the analysis precision is not influenced in order to simplify the structure. As shown in fig. 1; a first oil pad 11 and a second oil pad 12; m is the center distance between the first oil pad 11 and the second oil pad 12; e.g. of the typez(y) is the displacement motion error of the slide block 13 line; λ is the guide surface profile error wavelength. The center distance of the oil pads is large, and the oil pads are a four-oil pad hydrostatic guideway model which cannot be simplified into small rigid wheels.
S2, assuming that the profile error of the guide surface does not change in the width direction of the oil pad, for example, the guide surface of the hydrostatic guide rail is usually divided into a plurality of sections, each section is equivalent to one oil pad, and the oil pad is provided with an oil film with certain rigidity; fig. 2 shows, among others, a width-direction oil film 21; a longitudinal oil film 22; laIs the length of the oil pad; luThe width of the oil sealing surface in the length direction of the oil pad; lbIs the width of the oil pad; lvThe width of the oil seal surface is the width of the oil pad in the width direction; bwIs the oil film discrete unit width; h is0Theoretical oil film thickness: f. ofz(y) is a guide surface profile tolerance error function;
wherein the profile error function can be fitted to a fourier series, and the rail surface profile error can be expressed as:
Figure BDA0003012088570000061
in the formula: e is the error amplitude, λ is the profile error wavelength,
Figure BDA0003012088570000062
is the phase angle and y is the guide surface profile length, where y is a variable.
S3, as shown in fig. 2, if the profile error variation of the guide surface along the slider width x direction is neglected, the oil film thickness at the oil seal surface at any position is:
h(y)＝h0-fz(y)
in the formula: h is0Is the theoretical oil film thickness, fzAnd (y) is a guide surface profile error.
Oil film of oil seal surfaceIs dispersed into N parts with width b along y directionwThe area of the ith unit is set as Ai, the total area of the oil film of the oil sealing surface is set as A, and when the far point o' of the oil pad is at any position, the thickness of the oil film corresponding to the unit is set as h (y)i)，yiThe average oil film thickness at the position corresponding to the ith cell is:
Figure BDA0003012088570000063
when o 'moves forward from the arbitrary position y, let the volume change amounts of oil films 1 and 2 be Δ V1 and Δ V1, respectively, and when o' moves from the arbitrary position y1 to y2, the change amount of the average oil film thickness is:
Figure BDA0003012088570000071
then o' at any position y, the average oil film thickness is:
Figure BDA0003012088570000072
s4, assuming that the lubricating oil is incompressible viscous fluid, the oil pressure p is suppliedsAnd the dynamic viscosity eta of the lubricating oil is constant, h (y) is replaced by ha (y), and the flow resistance of the oil sealing surface meets the following requirements:
Figure BDA0003012088570000073
if the flow resistance of the throttler is Rc(y), the working pressure of the oil chamber is:
Figure BDA0003012088570000074
the variation of the oil film bearing capacity is as follows:
fe(y)＝(p0(y)-p0(0))Ae
in the formula, AeIs the effective bearing area of the oil film.
When the guide rail sliding block moves, the four-oil-pad hydrostatic guide rail can be equivalent to a quasi-static model, and an oil film can be simplified into a linear spring unit, so that:
Figure BDA0003012088570000075
in the formula: e.g. of the typej(y) is the linear displacement motion error at the center of the oil pad j; e.g. of the typez(y) is the linear displacement motion error of the slide block; thetaxIs the pitch angle error; thetayIs the roll angle error; f. ofej(y) is the variation of the oil film bearing force acting on the oil pad j in the movement process of the sliding block; f. ofbj(y) is the oil film bearing force on the oil pad j; a isj、bj、cjIs a directional coefficient, j is 1-4; f. ofjThe (y) is the original supporting force of the oil pad when the slider is moving (distinguished from the oil film supporting force in consideration of the amount of change in the oil film supporting force).
S5, when the sliding block moves to any position, the resultant force of the oil film supporting forces of the oil pads is balanced with the external load, the resultant force and the resultant moment are always 0, the sliding block maintains a balanced state, as shown in fig. 3, the static balance equation of the hydrostatic guideway is:
Figure BDA0003012088570000081
wherein: k is a radical of1(y)-k4(y) oil film stiffness for four oil pads; e.g. of the type1(y)-e4(y) is the linear displacement motion error at the center of the oil pad of the four oil pads; f. ofj(y) is the original supporting force of the oil pad (different from the oil film supporting force considering the variation of the oil film supporting force) when the slider moves, f1(y)-f4(y) is the oil film bearing force of the four oil pads; m is the center distance between two oil pads in the Y direction; n: the center distance between the two oil pads in the X direction; g: self-weight of the sliding block; w: load at the machining location; m is1: the distance between the machining position and the center of the slide block along the Y direction; n is1: with machining position and centre of slide in X-directionA distance; mxIs the resultant moment in the X direction; myThe resultant moment in the Y direction; a isj，bjIs a directional coefficient, j is 1-4;
s6, combining the static pressure guide rail surface contour error equation, the oil film thickness equation, the oil film supporting force equation and the static pressure guide rail static equilibrium equation in the previous step, and solving the static pressure guide rail motion straightness as follows:
ez＝B1·A1·(fe1+fe2+fe3+fe4-G-W)
in the formula, A is a slider structure parameter matrix; b is an oil film rigidity coefficient matrix; cmIs a direction coefficient matrix; a. the-And B-Inverse matrices to matrices A and B, respectively, A1，A2And A3Is a column vector, B1，B2And B3Is a row vector.
Figure BDA0003012088570000082
Figure BDA0003012088570000091
Figure BDA0003012088570000092
The concrete application of linearity needs to be supplemented, and a simple calculation method cannot be protected as a patent subject.
The invention provides a four-oil-pad hydrostatic guideway motion accuracy evaluation method considering oil pad center distance. By utilizing the advantage of calculating the motion straightness of the four-oil-pad hydrostatic guide rail with the larger oil pad center distance, a four-oil-pad hydrostatic guide rail static analysis model considering the oil pad center distance is provided, and the slide block motion straightness error is solved, so that theoretical guidance is provided for hydrostatic guide rail precision design.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical solution according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (8)

1.四油垫静压导轨运动精度评价方法，其特征在于，包括，1. four oil pad hydrostatic guide rail motion accuracy evaluation method, is characterized in that, comprises, 根据预设条件，将油垫中心距较大的四油垫静压导轨模型进行简化；According to the preset conditions, the model of the hydrostatic guide rail with four oil pads with a large oil pad center distance is simplified; 根据简化后的四油垫静压导轨模型，计算得到静压导轨面轮廓误差方程；According to the simplified model of the hydrostatic guideway with four oil pads, the surface contour error equation of the hydrostatic guideway is calculated; 根据理论油膜厚度和静压导轨面轮廓误差，得到封油面处的油膜厚度方程；According to the theoretical oil film thickness and the contour error of the hydrostatic guideway surface, the oil film thickness equation at the oil sealing surface is obtained; 将四油垫静压导轨等效为准静态模型，油膜等效为线性弹簧单元，根据封油面处的油膜厚度，得到当导轨滑块运动时油垫的油膜支承力方程；The hydrostatic guide rail with four oil pads is equivalent to a quasi-static model, and the oil film is equivalent to a linear spring unit. According to the thickness of the oil film at the oil sealing surface, the oil film supporting force equation of the oil pad when the guide rail slider moves is obtained; 根据各油垫的油膜支承力合力与外载荷平衡，保持滑块平衡状态，得到静压导轨静力学平衡方程；According to the balance of the resultant force of the oil film supporting force of each oil pad and the external load, to maintain the balance state of the slider, the static balance equation of the static pressure guide rail is obtained; 联立静压导轨面轮廓误差方程、油膜厚度方程、油膜支承力方程和静压导轨静力学平衡方程，求解得到静压导轨运动直线度，对四油垫静压导轨运动精度进行评价。The hydrostatic guideway surface contour error equation, oil film thickness equation, oil film support force equation and static pressure guideway static balance equation are simultaneously solved to obtain the motion straightness of the hydrostatic guideway, and the motion accuracy of the four-oil pad hydrostatic guideway is evaluated. 2.根据权利要求1所述的四油垫静压导轨运动精度评价方法，其特征在于，所述预设条件，包括假设导轨面轮廓误差在油垫宽度方向不改变，以及忽略导轨面沿滑块宽度x方向的轮廓误差变化。2 . The method for evaluating the motion accuracy of a hydrostatic guide rail with four oil pads according to claim 1 , wherein the preset conditions include assuming that the guide rail surface contour error does not change in the width direction of the oil pad, and ignoring the sliding motion of the guide rail surface. 3 . Contour error variation in block width x direction. 3.根据权利1所述的四油垫静压导轨运动精度评价方法，其特征在于，所述根据简化后的四油垫静压导轨模型，计算得到静压导轨面轮廓误差，通过傅里叶级数拟合，表示如下，3. The method for evaluating the motion accuracy of the hydrostatic guide rail with four oil pads according to claim 1, characterized in that, according to the simplified model of the hydrostatic guide rail with four oil pads, the surface contour error of the hydrostatic guide rail is calculated and obtained by Fourier transform Series fitting, expressed as follows,
Figure FDA0003012088560000011
Figure FDA0003012088560000011
 式中：E为误差幅值，λ为轮廓误差波长，
Figure FDA0003012088560000012
为相位角，y为导轨面轮廓长度。where E is the error amplitude, λ is the contour error wavelength,
Figure FDA0003012088560000012
is the phase angle, and y is the profile length of the rail surface. 4.根据权利1所述的四油垫静压导轨运动精度评价方法，其特征在于，所述根据理论油膜厚度和静压导轨面轮廓误差，得到封油面处的油膜厚度，具体如下：4. The method for evaluating the motion accuracy of four oil pads hydrostatic guide rails according to claim 1, characterized in that, according to the theoretical oil film thickness and the hydrostatic guide rail surface profile error, the oil film thickness at the oil sealing surface is obtained, and the details are as follows: h(y)＝h0-fz(y)h(y)=h 0 -f z (y) 式中：h0为理论油膜厚度，fz(y)为静压导轨面轮廓误差。where h 0 is the theoretical oil film thickness, and f z (y) is the profile error of the hydrostatic guideway. 5.根据权利1所述的四油垫静压导轨运动精度评价方法，其特征在于，所述当导轨滑块运动时油垫的油膜支承力，具体表示如下，5. The method for evaluating the motion accuracy of a hydrostatic guide rail with four oil pads according to claim 1, wherein the oil film supporting force of the oil pad when the guide rail slider moves is specifically expressed as follows:
Figure FDA0003012088560000021
Figure FDA0003012088560000021
 式中：ej(y)为油垫j中心处的线位移运动误差；ez(y)为滑块线位移运动误差；θx为俯仰角误差；θy为滚转角误差；fej(y)为滑块运动过程中作用在油垫j上的油膜支承力变化量，由封油面处的油膜厚度确定；fbj(y)为油垫j上的油膜支承力；aj、bj、cj为方向系数，j＝1-4；fjy(y)为滑块运动时的油垫的原支承力；m为Y方向油垫中心距；n为X方向油垫中心距。In the formula: e j (y) is the linear displacement motion error at the center of the oil pad j; e z (y) is the linear displacement motion error of the slider; θ x is the pitch angle error; θ y is the roll angle error; f ej ( y) is the variation of the oil film support force acting on the oil pad j during the movement of the slider, which is determined by the thickness of the oil film at the oil sealing surface; f bj (y) is the oil film support force on the oil pad j; a j , b j , c j are the direction coefficients, j=1-4; f jy (y) is the original supporting force of the oil pad when the slider moves; m is the center distance of the oil pad in the Y direction; n is the center distance of the oil pad in the X direction. 6.根据权利1所述的四油垫静压导轨运动精度评价方法，其特征在于，所述根据各油垫的油膜支承力合力与外载荷平衡，保持滑块平衡状态，得到静压导轨静力学平衡方程，具体如下：6. The method for evaluating the motion accuracy of a hydrostatic guide rail with four oil pads according to claim 1, wherein the resultant force of the oil film supporting force of each oil pad is balanced with the external load, the slider is kept in a balanced state, and the static pressure guide rail static pressure is obtained. The mechanical equilibrium equation is as follows:
Figure FDA0003012088560000022
Figure FDA0003012088560000022
 式中，fj(y)为滑块运动时的油垫的原支承力；m为Y方向油垫中心距；n为X方向油垫中心距；G为滑块自重；W为加工位置处的载荷；Mx为X向的合力矩；My为Y向的合力矩；aj，bj为方向系数，j＝1-4；m1为加工位置和滑块中心沿Y方向的距离；n1为加工位置和滑块中心沿X方向的距离。In the formula, f j (y) is the original supporting force of the oil pad when the slider moves; m is the center distance of the oil pad in the Y direction; n is the center distance of the oil pad in the X direction; G is the dead weight of the slider; W is the processing position M x is the resultant moment in the X direction; M y is the resultant moment in the Y direction; a j , b j are the direction coefficients, j=1-4; m 1 is the distance between the machining position and the center of the slider along the Y direction ; n 1 is the distance between the machining position and the center of the slider along the X direction. 7.根据权利1所述的四油垫静压导轨运动精度评价方法，其特征在于，所述联立方程，求解得到静压导轨运动直线度，具体如下：7. The four-oil pad hydrostatic guide rail motion accuracy evaluation method according to claim 1, wherein the simultaneous equations are solved to obtain the motion straightness of the hydrostatic guide rail, and the details are as follows: ez＝B1·A1·(fe1+fe2+fe3+fe4-G-W)e z =B 1 ·A 1 ·(f e1 +f e2 +f e3 +f e4 -GW) 式中，A为滑块结构参数矩阵；B为油膜刚度系数矩阵；A1为第一列向量，B1为第一行向量；ez为直线度；fej为j油垫上的油膜支承力变化量，j＝1-4；G：滑块自重；W：加工位置处的载荷。In the formula, A is the slider structural parameter matrix; B is the oil film stiffness coefficient matrix; A 1 is the first column vector, B 1 is the first row vector; e z is the straightness; f ej is the oil film supporting force on the j oil pad Variation, j=1-4; G: the self-weight of the slider; W: the load at the processing position. 8.四油垫静压导轨运动精度评价系统，其特征在于，包括，8. The four-oil pad hydrostatic guide rail motion accuracy evaluation system is characterized in that, including, 模型简化模块，用于根据预设条件，将油垫中心距较大的四油垫静压导轨模型进行简化；The model simplification module is used to simplify the model of the four-oil pad hydrostatic guideway with a large oil pad center distance according to preset conditions; 导轨面轮廓误差模块，用于根据简化后的四油垫静压导轨模型，计算得到静压导轨面轮廓误差方程；The guide rail surface contour error module is used to calculate the hydrostatic guide rail surface contour error equation according to the simplified model of the four-oil pad hydrostatic guide rail; 油膜厚度模块，用于根据理论油膜厚度和静压导轨面轮廓误差，得到封油面处的油膜厚度方程；The oil film thickness module is used to obtain the oil film thickness equation at the oil sealing surface according to the theoretical oil film thickness and the contour error of the hydrostatic guide rail surface; 油膜支承力模块，用于将四油垫静压导轨等效为准静态模型，油膜等效为线性弹簧单元，根据封油面处的油膜厚度，得到当导轨滑块运动时油垫的油膜支承力方程；The oil film support force module is used to equiv force equation; 静力学平衡方程模块，用于根据各油垫的油膜支承力合力与外载荷平衡，保持滑块平衡状态，得到静压导轨静力学平衡方程；The static balance equation module is used to balance the resultant force of the oil film supporting force of each oil pad and the external load, maintain the balance state of the slider, and obtain the static balance equation of the static pressure guide rail; 直线度模块，用于联立静压导轨面轮廓误差方程、油膜厚度方程、油膜支承力方程和静压导轨静力学平衡方程，求解得到静压导轨运动直线度，对四油垫静压导轨运动精度进行评价。The straightness module is used to combine the surface contour error equation of the hydrostatic guideway, the oil film thickness equation, the oil film support force equation and the static pressure guideway static balance equation, and obtain the motion straightness of the hydrostatic guideway. Accuracy is evaluated.
CN202110378143.6A 2021-04-08 2021-04-08 Four-oil-pad hydrostatic guideway motion precision evaluation method and system Pending CN113108750A (en)

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Citations (2)

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CN102490077A (en) * 2011-12-06 2012-06-13 厦门大学 Vertical closed hydrostatic guideway perpendicularity error adjustment device
CN110142647A (en) * 2019-05-20 2019-08-20 华中科技大学 Device and method for real-time measurement of steady-state performance of hydrostatic guide rail

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CN102490077A (en) * 2011-12-06 2012-06-13 厦门大学 Vertical closed hydrostatic guideway perpendicularity error adjustment device
CN110142647A (en) * 2019-05-20 2019-08-20 华中科技大学 Device and method for real-time measurement of steady-state performance of hydrostatic guide rail

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