CN105653842B - Construction method of geometric error model of rolling guide rail feeding system - Google Patents
Construction method of geometric error model of rolling guide rail feeding system Download PDFInfo
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- CN105653842B CN105653842B CN201510974996.0A CN201510974996A CN105653842B CN 105653842 B CN105653842 B CN 105653842B CN 201510974996 A CN201510974996 A CN 201510974996A CN 105653842 B CN105653842 B CN 105653842B
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Abstract
The invention provides a modeling method for a force deformation error of a feeding system, which aims at a machine tool feeding system with a linear rolling guide rail as a bearing and guiding mechanism and comprehensively considers the coupling influence of the precision and the rigidity of the guide rail on the precision of the feeding system under the action of an external force. Firstly, estimating the contact rigidity of the guide rail by an equivalent load method, secondly, establishing a stress balance equation of the workbench which takes the slide block as a support, thirdly, determining the geometric deformation relation of each slide block according to the rigid hypothesis of the workbench, supplementing the equation according to the physical relation column between deformation and force, and finally, simultaneously establishing the equations to solve the force deformation error of the feeding system. The invention fills the blank of the coupling influence of the precision and the rigidity of the guide rail on the precision of the feeding system under the action of external force, and has good application prospect for researching the force error of the machine tool.
Description
Technical Field
The invention relates to the field of machine tool feeding system rigidity and precision research, in particular to a construction method of a rolling guide rail feeding system geometric error model and an acquisition method of the rolling guide rail feeding system geometric error.
Background
The feeding system of the numerical control machine tool is a key component influencing the precision of the numerical control machine tool, and the quality and the performance of the feeding system have great influence on the machining precision, the precision retentivity and the reliability of the numerical control machine tool. The geometric accuracy of the feeding system can be called as geometric error mainly from errors of parts of the feeding system and deformation of the parts of the feeding system caused by forced fit of external force, heat, geometric errors among the parts of the feeding system and assembly errors, and the deformation is finally transmitted to the working table or the main shaft to form the geometric error of the feeding system.
In the space described by the cartesian coordinate system, the motion of the numerically controlled machine tool can be measured in 6 geometric errors generated by 6 degrees of freedom. The function of the guide rail is to control the 5 degrees of freedom of the moving part, moving only in the required direction, so that the guide rail error is considered as the main source of the geometric error of the feeding system.
The linear rolling guide rail has the advantages of high motion sensitivity, high positioning precision, small traction force, small abrasion, simple and convenient lubrication and maintenance and the like, gradually replaces the traditional sliding linear guide rail (except for heavy-load machine tools), and becomes an important functional part of the current numerical control machine tool. The guide rail precision comprises guide rail guiding precision, rigidity and the like. The rigidity of the guide rail comprises the self rigidity and the contact rigidity of the guide rail, and the rolling contact belongs to a weak rigidity link compared with the self rigidity of the guide rail, so the rigidity of the guide rail is generally referred to as the contact rigidity of a guide rail sliding block pair. In the influence of the guide rail precision on the precision of the feeding system, only the influence of the guide rail guide precision on the motion precision, namely the straightness of the guide rail and the parallelism between the guide rails, is often emphasized. The influence of the guide rail rigidity on the accuracy of the feeding system is biased to static analysis, namely the motion accuracy of the feeding system is solved mainly through analysis of the load of the feeding system, distribution of stress of each slide block and analysis of the rigidity of the guide rail slide block pair. The influence of the guide rail precision on the precision of the feeding system is the result of the combined action of the guide rail guiding precision and the guide rail rigidity, the current research fails to indicate the mechanism of the influence of the guide rail precision on the system precision, the influence of the external force action on the system precision assumes that the contact pressure of a joint part is uniformly distributed, and the deformation and the contact load generated by forced matching due to the precision of the guide rail are not considered.
Disclosure of Invention
The invention aims to provide a construction method of a geometric error model of a rolling guide rail feeding system and an acquisition method of the geometric error of the rolling guide rail feeding system, aiming at a machine tool feeding system taking a linear rolling guide rail as a bearing and guiding mechanism, and comprehensively considering the coupling influence of the precision and rigidity of the guide rail on the precision of the feeding system under the action of external force.
The above object of the invention is achieved by the features of the independent claims, the dependent claims developing the features of the independent claims in alternative or advantageous ways.
In order to achieve the above object, the present invention provides a method for constructing a geometric error model of a rolling guide feeding system, comprising: firstly, estimating the contact rigidity of a guide rail by an equivalent load method, secondly, establishing a stress balance equation of a workbench which takes a slide block as a support, then determining the geometric deformation relation of each slide block according to the rigidity assumption of the workbench, supplementing an equation according to the physical relation column between deformation and force, and finally solving the force deformation error of a feeding system by a simultaneous equation.
It should be understood that all combinations of the foregoing concepts and additional concepts described in greater detail below can be considered as part of the inventive subject matter of this disclosure unless such concepts are mutually inconsistent. In addition, all combinations of claimed subject matter are considered a part of the presently disclosed subject matter.
The foregoing and other aspects, embodiments and features of the present teachings can be more fully understood from the following description taken in conjunction with the accompanying drawings. Additional aspects of the present invention, such as features and/or advantages of exemplary embodiments, will be apparent from the description which follows, or may be learned by practice of specific embodiments in accordance with the teachings of the present invention.
Drawings
The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. Embodiments of various aspects of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of the feed system error model of the present invention.
Fig. 2 is a schematic view of a feed system guide rail-table unit.
FIG. 3 is a schematic view of a radial loading of a rail-slider pair.
Fig. 4 is a schematic diagram of the moment applied to the guide rail sliding block pair.
Fig. 5 is a schematic view of radial reaction force of each slider.
FIG. 6 is a schematic view of a z-axis displacement of a slider.
FIG. 7 is a schematic view showing the y-axis positional shift of the slider.
Detailed Description
In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.
In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily intended to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, and that the concepts and embodiments disclosed herein are not limited to any embodiment. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.
According to a preferred embodiment of the present invention, the present invention models the force deformation error of a four-block rail-table unit, as shown in FIG. 2, using pre-stressed rail-slide pairs to achieve a nearly linear slide force deformation characteristic. The guide rail precision and the stress of the workbench in the model are used as input, wherein the guide rail precision comprises the initial position error of the slide block and the contact rigidity of the guide rail slide block pair, and the stress of the workbench can be converted into the force and the torque of an action point at the center of the workbench. And outputting a geometric error formed by the slide block and the workbench finally, namely outputting the model as a workbench error under the joint influence of the guide rail precision and stress, namely other 5 errors except the axial position error.
Referring to fig. 1, the method for constructing the geometric error model of the rolling guide feeding system specifically includes the following steps:
step A: the method for modeling the contact rigidity of the guide rail by the equivalent load method comprises the following specific steps:
step A-1: and establishing a coordinate system direction, wherein the axial motion direction is taken as an x axis, the radial vertical direction perpendicular to the x axis is taken as a z axis, and the transverse direction is taken as a y axis.
Step A-2: and calculating the rotational stiffness of the sliding block pair by an equivalent load method according to the radial stiffness K subjected to linearization processing.
Taking the slider type with a contact angle of 45 degrees and symmetrically distributed raceways along the transverse direction and the longitudinal direction as an example, the longitudinal stiffness and the transverse stiffness of the slider type are the same according to a formula, that is, the bearing capacity in 4 directions is the same, as shown in fig. 3. Assuming that the longitudinal rigidity and the transverse rigidity of the slide block pair are K, namely Kz＝KyK. The ability of the slider to resist moment deformation is called the rotational stiffness, and as shown in FIG. 4, the rotational stiffness K is denoted by Kx',Ky',Kz'。
When the slide block is subjected to axial torque MCWhile the slide block is subjected to torsion angular deformation phix. The effect is equivalent to each row of roller paths bearing a force F perpendicular to the line connecting the roller paths and the slider shaft. Transverse spacing l of raceway2Longitudinal spacing of raceways l2The included angle between the connecting line of the roller path and the sliding block shaft and the horizontal direction is theta, and F can be decomposed into longitudinal component force FzAnd a transverse component Fy. Assuming that the two raceways on the same side in the transverse direction and the longitudinal direction satisfy the assumption of linear stiffness, and the stiffness of the two raceways on the single side is half of the overall stiffness, a relationship in the following formula can be obtained:
torque MCDeformation of torsion angle phixCan be expressed as
The torsional stiffness about the x-axis can be expressed as
When the slide block is subjected to pitching torque MAWhen the slide block generates a pitch angle deformation phiy. Linear stiffness is assumed to be satisfied longitudinally and the discrete arrangement of the balls is not counted. Can be combined withThe acting force is equivalent to linear gradual load distributed along the axial direction, and the deformation relation of the force of the length of the roller path is expressed as
Torque MADeformation of torsion angle phiyCan be expressed as
Pitch stiffness about the y-axis can be expressed as
Similarly, the torsional pendulum stiffness about the z-axis can be expressed as
And B: establishing a deformation relation between a workbench stress balance equation and each sliding block:
step B-1: with Fx,Fy,Fz,Mx,My,MzRepresenting an external force acting on the center of the table at Ri，SiShowing the support reaction forces of the side effect of the rail slide in the z-direction and the y-direction of the table, M is shown in FIG. 5ix,Miy,MizThe torques generated by the deformation in three directions of the slider are shown, wherein (i is 1,2,3 and 4).
Step B-2: establishing an equilibrium equation:
step B-3: since the table rigidity is much greater than the contact rigidity, the table is regarded as a rigid body. The position relationship of each slide relative to the reference can be represented by fig. 6 and 7, and is expressed by the following equation:
in the formula, deltaiIndicating the z-offset, δ, of the slider relative to a reference linei' denotes the y-offset of the slider with respect to the reference line, phiix,φiy,φizThe rotation angle of each slide block relative to the reference axial direction is shown, wherein (i is 1,2,3 and 4).
And C: establishing a supplementary equation according to the rigidity of the guide rail sliding block pair and the guide rail error:
initial offset of slider is delta0i,δ0'i,φ0ix,φ0iy,φ0izThe relative positional deviation amount is δri,δr'i,φrix,φriy,φrizThis is shown in fig. 6 and 7, where (i ═ 1,2,3, 4). The linear relation between the relative position offset and the pose change of the slide block can be obtained
Step D: and (3) simultaneous equation sets, solving the stress condition of each sliding block:
in the formula (I), the compound is shown in the specification,respectively representing the resultant bending moments of the 4 sliding blocks around the x-axis direction and the y-axis direction, and the bending moment of each sliding block can be represented by the following formula
In the formula (I), the compound is shown in the specification,the resultant bending moment of 4 sliders around the z-axis direction can be expressed by the following formula
Step E: solving the geometric error formed by the slide block and the workbench:
step E-1: solving for the relative position offset of the slider
[δri,δr'i,φrix,φriy,φriz]T＝K-1[Ri,Si,Mix,Miy,Miz]T
Step E-2: solving the resulting geometric error of the stage
According to the disclosure, a person skilled in the art can develop a corresponding program according to the content of the disclosure and run the program on a computer system, so as to implement the steps and effects of the embodiment of the method for constructing the geometric error model of the rolling guide feeding system.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.
Claims (2)
1. A method for constructing a geometric error model of a rolling guide rail feeding system is characterized by comprising the following steps: firstly, estimating the contact rigidity of a guide rail by an equivalent load method, secondly establishing a stress balance equation of a workbench supported by a slide block, then determining the geometric deformation relation of each slide block according to the rigidity assumption of the workbench, supplementing an equation according to the physical relation column between deformation and force, and finally solving the force deformation error of a feeding system by a simultaneous equation;
the method specifically comprises the following steps:
step A: the method for modeling the contact rigidity of the guide rail by the equivalent load method comprises the following specific steps of A-1 to A-2:
step A-1: establishing a coordinate system direction, taking the axial motion direction as an x axis, taking a radial vertical direction perpendicular to the x axis as a z axis, and taking the transverse direction as a y axis;
step A-2: calculating the rotational stiffness of the sliding block pair by an equivalent load method according to the radial stiffness K subjected to linearization processing; for the slider type with the contact angle of 45 degrees and the raceways symmetrically distributed along the z-axis direction and the y-axis direction, the rigidity in the z-axis direction is the same as that in the y-axis direction, namely the bearing capacity in 4 directions is the same, and the rigidity value of the slider pair along two directions is assumed to be K, namely Kz＝KyThe ability of the slider to resist moment deformation is called the rotational stiffness, Kx',Ky',Kz'；
When the slide block is subjected to axial torque MCWhile the slide block is subjected to torsion angular deformation phixThe action is equivalent to that each row of rolling paths bear a force F vertical to the connecting line of the rolling paths and the sliding block shaft, and the distance l between the rolling paths along the y-axis direction is set1The distance between the raceways in the z-axis2The included angle between the connecting line of the roller path and the sliding block shaft and the horizontal direction is theta, and F can be decomposed into component force F along the z-axis directionzAnd a component force F in the y-axis directionyAssuming that the two raceways along the z-axis direction and along the y-axis direction have the same side and satisfy the linear stiffness, and the stiffness of the two raceways on one side is half of the overall stiffness, the relationship in the following formula can be obtained:
torque MCDeformation of torsion angle phixThe relationship of (c) can be expressed as:
the torsional stiffness about the x-axis can be expressed as:
when the slide block is subjected to pitching torque MAWhen the slide block generates a pitch angle deformation phiyAssuming that linear stiffness is satisfied along the z-axis direction, and the discrete arrangement of the balls is not counted, the acting force can be equivalent to a linear gradual load distributed along the axial direction, and the force deformation relationship of the length of the raceway is l, which can be expressed as:
torque MADeformation of torsion angle phiyThe relationship of (c) can be expressed as:
the pitch stiffness about the y-axis can be expressed as:
similarly, the torsional pendulum stiffness about the z-axis can be expressed as:
and B: establishing a deformation relation between a stress balance equation of the workbench and each sliding block, wherein the method comprises the following steps B-1 to B-3:
step B-1: with Fx,Fy,Fz,Mx,My,MzRepresenting an external force acting on the center of the table at Ri，SiShowing the reaction forces of the side effects of the rail slide in the z-and y-directions of the table, Mix,Miy,MizShowing the change of the slide in three directionsForming a torque generated, wherein i ═ 1,2,3, 4;
step B-2: establishing an equilibrium equation:
step B-3: since the stiffness of the table is much greater than the contact stiffness, the table is considered as a rigid body and is represented by the following equation:
in the formula, deltaiIndicating the z-offset, δ, of the slider relative to a reference linei' denotes the y-offset of the slider with respect to the reference line, phiix,φiy,φizThe rotation angle of each slide block relative to the reference axial direction is shown, wherein i is 1,2,3, 4;
and C: establishing a supplementary equation according to the rigidity of the guide rail sliding block pair and the guide rail error:
initial offset of slider is delta0i,δ′0i,φ0ix,φ0iy,φ0izThe relative positional deviation amount is δri,δ′ri,φrix,φriy,φrizWherein i is 1,2,3, 4; the linear relation between the relative position offset and the pose change of the slide block can be obtained
Step D: and (3) simultaneous equation sets, solving the stress condition of each sliding block:
in the formula (I), the compound is shown in the specification,respectively showing the combination of the 4 sliders in the x-axis direction and the y-axis directionThe bending moment applied to each slider can be represented by the following formula:
in the formula (I), the compound is shown in the specification,the resultant bending moment of 4 sliders around the z-axis direction can be expressed by the following formula
Step E: and solving the final formed geometric error of the slide block and the workbench, including E-1 to E-2:
step E-1: solving for the relative position offset of the slider
[δri,δ′ri,φrix,φriy,φriz]T＝K-1[Ri,Si,Mix,Miy,Miz]T
Step E-2: solving the resulting geometric error of the stage
2. A geometric error acquisition method of a rolling guide rail feeding system is characterized by comprising the following steps:
step 1, constructing a geometric error model of a rolling guide rail feeding system according to the method of claim 1;
and 2, inputting the model established in the step 1 by taking the guide rail precision and the stress of the workbench as input, and outputting a geometric error formed by the slide block and the workbench finally, wherein the guide rail precision comprises an initial position error of the slide block and the contact rigidity of a guide rail slide block pair, and the stress of the workbench is converted into a force and a torque of an action point at the center of the workbench.
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| CN109766511B (en) * | 2018-12-05 | 2020-07-28 | 北京理工大学 | Contact relation model considering deformation error and assembly error calculation method |
| CN110725861B (en) * | 2019-09-17 | 2020-10-27 | 浙江工业大学 | Method for applying pre-tightening force of ball linear guide rail pair |
| CN112558500A (en) * | 2020-12-14 | 2021-03-26 | 山东建筑大学 | Modeling and simulation method for crawler-type guide rail dual-drive micro-feeding servo system |
| CN113275977B (en) * | 2021-06-07 | 2022-02-11 | 中国工程物理研究院激光聚变研究中心 | Method for determinacy compensating shape error of guide rail of aspheric optical element processing machine tool |
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