CN108803497A - A kind of modeling method of guiding error-moving component position and attitude error mapping model - Google Patents
A kind of modeling method of guiding error-moving component position and attitude error mapping model Download PDFInfo
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/4097—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by using design data to control NC machines, e.g. CAD/CAM
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
The invention discloses a kind of modeling methods of guiding error-moving component position and attitude error mapping model, the described method comprises the following steps：Establish the Elastic Contact model of rolling element and guide rail roller surface and sliding block roller surface；Establish the error transfer function model of single sliding block；The mapping model of moving component position and attitude error and guiding error is established, and provides the definition method of homogenization coefficient.The present invention can specify the error-correction model mechanism of rolling guide-rail pairs, determine specific error-correction model ratio, quantitative in lathe Top-Down Design to instruct Tolerance assignment, reduce manufacturing cost, effectively control rigging error, improve assembly yield.
Description
Technical field
The present invention relates to numerically-controlled machine tool rigging errors to transmit and optimization field, especially a kind of straight-line rolling guide set guide rail
The modeling method of error-moving component position and attitude error mapping model.
Background technology
In lathe assembling process, each parts can all have certain error, cause the part position after assembly inclined
From ideal position.For lathe, final goal is to ensure the machining accuracy of lathe；And the kinematic accuracy of workbench is direct
Influence the machining accuracy of lathe.Therefore, to ensure the kinematic accuracy of workbench in Machine Tool design, manufacture and installation process.
In a practical situation, caused by the kinematic accuracy of workbench is often the straightness error by guide rail, this is because
Under the action of load, corresponding juxtaposition metamorphose can occur for the rolling element at rolling guide faying face, cause the association of geometric error
It adjusts, be superimposed and offset, to show the transitive relation between guiding error and workbench position and attitude error.Therefore, no matter for
Machine tool accuracy designs or the control of rigging error, and the guarantee of guide rail mounting precision is all highly important.
Currently, the linear of workpiece motion s chain end component position and attitude error and geometric error source can be established with many-body theory
Mapping model, to instruct lathe end precision to the Tolerance assignment of the kinematic accuracy of each kinematic pair.However, being arrived for kinematic pair
Rolling guide installation base surface this assembling link can not exacting tolerances distribution, main cause is the error-correction model machine of rolling guide-rail pairs
It manages unknown.
Existing research is all to carry out Tolerance assignment using rolling guide-rail pairs as Rigid-body System, leads to accuracy Design very not
Accurately, and enterprise can only determine the homogenizing ratio of rolling guide by experience or experiment, so that it is determined that guide rail installation base surface
Scraping precision, but this method can not be carried out in Machine Tool design and fabrication stage.So kinematic pair installs base to rolling guide
Error-correction model mechanism between face becomes the bottleneck problem of geometric precision of machine tool Top-Down Design with analysis method.
Prediction for straight-line rolling guide set moving component position and attitude error and rolling guide-rail pairs Panel-corrected Model, it is domestic
Outer scholar had a more in-depth study, but not yet clear rolling guide-rail pairs error-correction model mechanism at present, and will roll
Guideway is handled as rigid body, the Top-Down Design for instructing lathe of no standard measure.
Invention content
In order to solve the problems in the existing technology, the present invention provides a kind of guiding error-moving component position and attitude error
The modeling method of mapping model overcomes the problems, such as that precision is low in Machine Tool design in the prior art, manufacture and installation process.
The technical scheme is that：A kind of modeling method of guiding error-moving component position and attitude error mapping model, packet
Include following steps：
(1) relationship of contact and juxtaposition metamorphose between rolling element and roller surface is determined based on Hertzian contact theory；
(2) according to the geometrical model of rolling element and roller surface juxtaposition metamorphose, the expression formula of single rolling element deformation is solved,
The bearing capacity of single sliding block is solved based on Hertzian contact theory, introduces transmission function, is defined transmission function and is missed for different guide rails
Under difference frequency, the bearing capacity of single sliding block and the ratio of guiding error；
(3) according to the space mechanical model of the rolling guide-rail pairs under guiding error excitation state and sliding block and workbench
Between rigid displacement TRANSFER MODEL, establish the Linear Mapping model of moving component position and attitude error and guiding error, and provide
Change the definition method of coefficient.
The modeling procedure of step (2) the single sliding block error transfer function model is：
(1) the bilateral juxtaposition metamorphose of rolling element and roller surface is reduced to single edge contact deformation, finds out single rolling element
Deflection；
(2) contact force of the single rolling element found out according to Hertzian contact theory, and found out by force resolution and synthesis
The bearing capacity of single sliding block；
(3) bearing capacity suffered by different guiding error frequency sliding blocks is calculated, and is compared with guiding error, is obtained
Go out the bearing capacity of sliding block and guiding error be under same frequency be that wavelength is identical, the identical or opposite SIN function of phase；
(4) influence for quantitative description wavelength to kinematic pair error, introduces the concept of transmission function, establishes single sliding block
Bearing capacity and guiding error between linear function TRANSFER MODEL.
The Linear Mapping model of step (3) the moving component position and attitude error and guiding error is：
In formula, δx(z)、δy(z)、εx(z)、εy(z) and εz(z) be respectively moving component along x to displacement error, along y
To displacement error, along x to angular errors, along y to angular errors and along z to angular errors；Xi, YcAnd ZkFor work
The distance of platform and two center of sliding block in the direction x, y and z；eijFor guide rail four direction straightness error；Kx(0) and Ky(0)
Respectively Static stiffness of the sliding block in the directions x and y；Kx(ω) and Ky(ω) is transmission function.
The definition method of step (3) homogenization coefficient is：
In formula, ne|xAnd ne|yRespectively rolling guide-rail pairs x and the straightness error in the directions y are homogenized ratio, ex(ω) and ey
(ω) is respectively error amount of the guide rail raceway surface error in the directions x and y.
Beneficial effects of the present invention are：Present invention is disclosed the error-correction model mechanism of straight-line rolling guide set, determine error
The definition method of homogenizing ratio contributes to the action rule of further analytical error homogenizing influence factor, and quantitative instructs guide rail
Scraping and assembly reduce manufacturing cost, improve assembly yield.
Description of the drawings
Fig. 1 is the rolling guide-rail pairs illustraton of model of the present invention；
Fig. 2 is the geometrical model of rolling element and roller surface juxtaposition metamorphose；
Fig. 3 is the corresponding diagram of guiding error and sliding block bearing capacity under different guiding error wavelength；
Fig. 4 is bearing capacity caused by the straightness error of guide rail SIN function form；
Fig. 5 is the space mechanical model of rolling guide-rail pairs；
Fig. 6 is guide rail layout；
Fig. 7 is the raceway surface error at table core；
Fig. 8 is the x straightness errors being calculated by mapping model；
Fig. 9 is the y straightness errors being calculated by mapping model；
Figure 10 is the Run-out error being calculated by mapping model；
Figure 11 is the pitch error being calculated by mapping model；
Figure 12 is the roll error being calculated by mapping model；
Figure 13 is that calculated x straightness errors are homogenized ratio；
Figure 14 is that calculated y straightness errors are homogenized ratio.
Specific implementation mode
To make the object, technical solutions and advantages of the present invention clearer, with reference to the accompanying drawings and examples to the present invention
Embodiment be described in further detail.
(1) the Elastic Contact model of rolling element and guide rail roller surface and sliding block roller surface is established
The present invention by taking the workbench of THK SRG R45 linear rolling tracks and designed, designed as an example, model as shown in Figure 1,
Panel-corrected Model is happened at three faying faces, and one is sliding block and workbench by bolted fixed combinating surface, one
It is the movable faying face that sliding block is connected with guide rail by rolling element, the other is four sliding blocks and workbench are by bolted fixation
Faying face.The guiding error that the present invention studies refers to the error that guide rail is mounted on after basal plane, that is, guide rail itself processing and manufacturing
The result of error and the effect of basal plane error coupler.Assume further that the assembly of workbench and Four-slider composition is ideal fit body,
Ignore the connection function of bolt.
According to Hertzian contact theory it is found that with roller surface elastic contact deformation, contact stress and deformation value occur for rolling element
Relationship be,
In formula, normal loads of the Q between roller and roller surface, R is the radius of roller, δnFor roller center and roller surface
Opposite approach amount, ν1And ν2The respectively Poisson's ratio of roller and roller surface, E1And E2The respectively springform of roller and roller surface
Amount.
Roller and raceway are generally Steel material, their elasticity modulus is identical with Poisson's ratio, i.e.,：
E1=E2=E (2)
υ1=υ2=υ
Therefore, in engineer application, through frequently with Palmgren empirical equations,
In formula, l is the length of roller.
(2) the error transfer function model of single sliding block is established
Assuming that guide rail raceway surface error is distributed in periodic SIN function, only guide rail roller surface has error, rolling element
For elastomer, Fig. 2 is the geometrical model of rolling element and roller surface juxtaposition metamorphose, and there are four the straightness error e in direction for guide railij
(z).Assuming that the error amount of roller surface four direction is mean value, then the bearing capacity of sliding block can be in force balance state.
ex(z)=e11(z)|x=e12(z)|x=e21(z)|x=e22(z)|x (4)
ey(z)=e11(z)|y=e12(z)|y=e21(z)|y=e22(z)|y (5)
In Fig. 2, ArWith A'rIt is the ideal contact point of rolling element and guide rail roller surface and practical contact point, AbWith A'bIt is rolling
Ideal contact point and practical contact point of the kinetoplast with sliding block roller surface, it is assumed that the curvature of guide rail raceway groove and sliding block raceway groove
Radius is identical, β0It is desired contact angle and the actual contact angle with β ', i, j indicate the quadrant where roller surface.
For ease of calculation, by the contact point A of rolling element and guide rail roller surfacebIt is fixed, bilateral juxtaposition metamorphose is reduced to
Single edge contact deforms,
Vy,ij(z)=lrcosβ0+(-1)jey,k(z) (7)
Vx,ij(z)=lrsinβ0+(-1)jex,k(z) (8)
In formula (6)-(8), ξij,kFor the deformation values of single rolling element, g is the Interference size of roller, lrIt is roller and two
Raceway contact point AbAnd ArBetween initial distance.
According to Hertzian contact theory, the stress for the sliding block that guide rail linearity error generates can be expressed as
According to Hertzian contact theory：
Fe,ijk(z)=(2C)-10/9(ξijk(z))10/9 (10)
In formula (10)-(12), Fe,ijkIt is the Hertz contact power of single rolling element, p is the number of single-row roller, fe(z) it is
The bearing capacity of single sliding block.
Assuming that ωbIt is the frequency that wavelength is equal to length, i.e. ωb=2 π/lb, lbIt is length, by ωbAs base
Frequently, error frequency ω is normalized, holding suffered by different guiding error frequency sliding blocks is calculated according to formula (9)
Power is carried, as shown in fig. 3, it was found that the bearing capacity f that sliding block is subject toe(z) it is identical as guiding error wavelength, phase is identical or opposite
SIN function, that is to say, that in entire stroke, sliding block bearing capacity fe(z) certain with the ratio of guiding error e (z).It is studied
Model ignore dynamic response.
Therefore, when guide rail roller surface has the straightness error e (z) of SIN function form, bearing capacity that sliding block is subject to
fe(z) with it with same modality, as shown in Figure 4.
In order to effectively analyze the error-correction model mechanism of rolling guide-rail pairs, the concept of transmission function is introduced, letter is transmitted in definition
Number K (z) is the stress f of single sliding block under different guiding error wavelength ratioe(z) relationship between guiding error e (z).
Based on sliding block bearing capacity fe(z) with the certain characteristic of the ratio of guiding error e (z), in order to quantitative description wavelength to kinematic pair miss
Dependent variable is changed to ω by the influence of difference, and K (ω) is the ratio of sliding block stress and guiding error under different error frequencies.
(3) mapping model of moving component position and attitude error and guiding error is established, and provides the definition method of homogenization coefficient.
Guiding error is expanded into Fourier space of the period equal to rail length L：
In formula (14), auAnd buFor the Fourier coefficient of guiding error.
The stress f of single sliding blockeik(z) it can be expressed as：
Assuming that the rigidity of four sliding blocks is identical with size, ignore the deformation of workbench and the dead weight of rolling guide-rail pairs,
Under the excitation of guiding error, system is in force balance state.As shown in figure 5, the position and attitude error δ of rolling guide-rail pairs 5-DOFx
(z)、δy(z)、εx(z)、εy(z) and εz(z) power and torque equilibrium equation is as follows：
fx,ik(z)=fex,ik(z)-Kx(0)xik(z) (17)
fy,ik(z)=fey,ik(z)-Ky(0)yik(z) (19)
In formula (16)-formula (22), fx,ik(z) and fy,ik(z) sliding block guiding error excitation under suffered by the directions x and y
Resultant force, fex,ik(z) and fey,ik(z) it is respectively suffered contact force in x and y direction of the sliding block under guiding error excitation,
Kx(0) and Ky(0) it is respectively Static stiffness of the sliding block in the directions x and y, m is the number of sliding block.
The distance X of workbench and two center of sliding block in the direction x, y and zi, YcAnd ZkIt can be expressed as：
L in formula (23), (24)x、lzIt is distance of two centers in x and z directions respectively.
The displacement x in x and y direction of the sliding block under guiding error excitationik(z) and yik(z) it is：
yik(z)=δy(z)-Ziεx(z)+Xiεz(z) (25)
xik(z)=δx(z)+Ziεy(z)+Ycεz(z) (26)
δ in formula (25), (26)x(z) and δy(z) it is respectively straightness error of the workbench in the directions x and y, εx(z)、εy
(z) and εz(z) it is roll error, pitch error and the Run-out error of guide rail.
The matrix equation of moving component 5-DOF position and attitude errors can be obtained by arrangement：
In formula (27)
K1=2mKy(0)
K4=2mYcKx(0)
K6=2mYcKx(0)
K7=2mKx(0)
Above formula is further converted, it can be with workbench position and attitude error and the more intuitive expression formula of guiding error：
According to the equation of equilibrium of power and torque, it can be deduced that the position and attitude error δ that workbench five is tieed upx(z)、δy(z)、εx(z)、
εy(z) and εz(z), the position and attitude error of workbench can be obtained by measuring, by inverse operation, scraping required for can finding out
The error e (z) of guide rail.
Define the ratio n of the position and attitude error and corresponding rails error of moving componenteFor the homogenization coefficient of Panel-corrected Model,
Expression formula is as follows：
In formula (30), (31), ne|xAnd ne|yRespectively the straightness error in the directions x and y is homogenized ratio, ex(ω) and ey
(ω) is respectively error amount of the guide rail raceway surface error in the directions x and y.
In order to verify the correctness of mapping model, the workbench of guide rail slide block and designed, designed to THK SRG R45 into
Row calculates, and guide rail layout is as shown in Figure 6, wherein elastic modulus E=206000MPa of guide rail and sliding block, Poisson's ratio υ=0.3,
Kx(0)=987N/ μm, Ky(0)=3000N/ μm, roll body length l=12mm, sliding block quantity m=4, lx=474mm, lz=
441mm, desired contact angle beta0=45 °, the number p=21 of single-row roller leads L=1200mm, it is assumed that left rail roller surface is wrong
Difference, right guide rail roller surface is error free, the raceway surface error of left railRight guide rail
Roller surface error e11(z)=e12(z)=e21(z)=e22(z)=0 9 discrete points, are taken on the stroke of 1200mm, every
150mm is calculated once, and the raceway surface error wherein at table core is as shown in fig. 7, the mapping model provided according to formula (29)
X straightness errors, y straightness errors, Run-out error, pitch error and the roll error being calculated as shown in Fig. 8-Figure 12,
According to the definition method for the homogenization coefficient that formula (30)-(31) provide, calculated x straightness errors homogenizing ratio and y straightness
Error-correction model ratio is as illustrated in figs. 13-14.
By calculation shows that, when left rail is error free, and right guide rail has error, there are error-correction model to show for rolling guide-rail pairs
As that is, workbench position and attitude error is less than guide rail raceway surface error.
It will be appreciated by those skilled in the art that attached drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
It is for illustration only, it can not represent the quality of embodiment.The foregoing is merely presently preferred embodiments of the present invention, not limiting this
Invention, all within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in this hair
Within bright protection domain.
Claims (4)
1. a kind of modeling method of guiding error-moving component position and attitude error mapping model, which is characterized in that including following step
Suddenly：
(1) relationship of contact and juxtaposition metamorphose between rolling element and roller surface is determined based on Hertzian contact theory；
(2) according to the geometrical model of rolling element and roller surface juxtaposition metamorphose, the expression formula of single rolling element deformation is solved, is based on
Hertzian contact theory solves the bearing capacity of single sliding block, introduces transmission function, and it is different guiding errors frequency to define transmission function
Under rate, the bearing capacity of single sliding block and the ratio of guiding error；
(3) according between the space mechanical model and sliding block and workbench of the rolling guide-rail pairs under guiding error excitation state
The TRANSFER MODEL of rigid displacement, establishes the Linear Mapping model of moving component position and attitude error and guiding error, and provides homogenizing system
Several definition methods.
2. a kind of modeling method of guiding error according to claim 1-moving component position and attitude error mapping model, special
Sign is that the modeling procedure of step (2) the single sliding block error transfer function model is：
(1) the bilateral juxtaposition metamorphose of rolling element and roller surface is reduced to single edge contact deformation, finds out the deformation of single rolling element
Amount；
(2) contact force of the single rolling element found out according to Hertzian contact theory, and found out individually by force resolution and synthesis
The bearing capacity of sliding block；
(3) bearing capacity suffered by different guiding error frequency sliding blocks is calculated, and is compared with guiding error, obtains cunning
It is that wavelength is identical that the bearing capacity of block, which is under same frequency with guiding error, the identical or opposite SIN function of phase；
(4) influence for quantitative description wavelength to kinematic pair error, introduces the concept of transmission function, establishes holding for single sliding block
Carry the linear function TRANSFER MODEL between power and guiding error.
3. a kind of modeling method of guiding error according to claim 1-moving component position and attitude error mapping model, special
Sign is that the Linear Mapping model of step (3) the moving component position and attitude error and guiding error is：
In formula, δx(z)、δy(z)、εx(z)、εy(z) and εz(z) be respectively moving component along x to displacement error, along y to
Displacement error, along x to angular errors, along y to angular errors and along z to angular errors；Xi, YcAnd ZkFor workbench and
Distance of two center of sliding block in the direction x, y and z；eijFor guide rail four direction straightness error；Kx(0) and Ky(0) respectively
Static stiffness for sliding block in the directions x and y；Kx(ω) and Ky(ω) is transmission function.
4. a kind of modeling method of guiding error according to claim 1-moving component position and attitude error mapping model, special
Sign is that the definition method of step (3) homogenization coefficient is：
In formula, ne|xAnd ne|yRespectively rolling guide-rail pairs x and the straightness error in the directions y are homogenized ratio, ex(ω) and ey(ω) point
Not Wei guide rail raceway surface error the directions x and y error amount.
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Application publication date: 20181113 |