CN110355690A - It is a kind of towards the roll flute error modeling of crushing precision and compensation method - Google Patents
It is a kind of towards the roll flute error modeling of crushing precision and compensation method Download PDFInfo
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- CN110355690A CN110355690A CN201910752515.XA CN201910752515A CN110355690A CN 110355690 A CN110355690 A CN 110355690A CN 201910752515 A CN201910752515 A CN 201910752515A CN 110355690 A CN110355690 A CN 110355690A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
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Abstract
The invention discloses a kind of towards the roll flute error modeling of crushing precision and compensation method.Firstly, being based on crushing system geometric error and Forward kinematics, crushing system geometric error-spatial error model is established；Then, consider crushing envelope movement and finishing contact conditions, construct crushing error model, disclose geometric error to the mapping principle of crushing precision；Subsequently, crushing error-tooth surface error model, influence of the quantitative analysis items crushing system geometric error to precision of grinding teeth are further established based on conjugation Principle of Grinding and Cutting；It finally solves to obtain the explicit algorithm expression formula of dresser shaft actual motion instruction using ideal cutting location data and conditioning system geometric error, realizes the roll flute error compensation towards crushing precision.Dresser shaft actual motion instruction of the present invention solves, and is calculated using offline high-performance computer, therefore error compensation strategy of the present invention has many advantages, such as versatility, easily implements.
Description
Technical field
It is especially a kind of towards crushing essence the present invention relates to NC Machine Error analysis and Accuracy Control field
The roll flute error modeling of degree and compensation method.
Background technique
Formation teeth-grinding carries out grinding finishing using grinding wheel cylindrical surface.CNC gear profile grinder includes two subsystems,
The crushing system being made of diamond roller-grinding wheel and the plunge grinding system being made of grinding wheel-gear blank.In crushing
In system, since grinding wheel, diamond roller are there are installation error, dresser shaft exists simultaneously installation error and kinematic error, grinding wheel
Deviation namely crushing error are inevitably generated between practical profile and ideal profile after finishing.Crushing error is into
The important sources of shape Gear-grinding Machining Errors can directly rerun a movie onto processing tooth-formation of gear, can also influence in grinding process indirectly
Abrasion of grinding wheel speed, grinding force, grinding heat, grinding vibration etc., and then influence precision of grinding teeth and efficiency.
To guarantee gear grinding precision, existing some scholars carried out error modeling for crushing system, and research is repaired
Influence of the quasi-static error to crushing error in whole system, and further analyze the damage to precision of grinding teeth.However, existing
Research only focuses on the influence of individual event or several grinding wheel installation errors to roll flute profile accuracy mostly, lacks and repairs to other grinding wheels
Whole system geometric error, including diamond roller installation error, dresser shaft straightness error and dresser shaft kinematic error, are led to sand
The comprehensive modeling for taking turns rounding error, naturally also lacks the roll flute error modeling being led to these crushing error sources.That is,
Existing crushing error model and roll flute error model are comprehensive to the inadequate system of the analysis in error source, can not effectively quantify point
Analyse influence of all crushing system geometric errors to precision of grinding teeth.In addition, also lacking the roll flute towards crushing precision
Error compensation strategy.
Summary of the invention
In view of this, the purpose of the present invention is to provide a kind of roll flute error modelings towards crushing precision and compensation
Method can be based on crushing system geometric error source analysis, construct crushing error model and precision of grinding teeth model,
To influence of the quantitative analysis items geometric error to precision of grinding teeth；Furthermore, it is possible to based on established model and practical reverse movement
Method calculates the dresser shaft actual motion instruction for considering error compensation, realizes that precision of grinding teeth is promoted.
In order to achieve the above objectives, the invention provides the following technical scheme:
It is provided by the invention towards the roll flute error modeling of crushing precision and compensation method, comprising the following steps:
Step 1: crushing system geometric error-crushing error modeling, the specific steps are as follows:
(1) crushing system geometric error is determined；
(2) crushing system geometric error-spatial error model is established；
(3) according to crushing envelope movement and finishing contact conditions, crushing error model is constructed；
Step 2: crushing error-tooth surface error is established based on grinding system Forward kinematics and conjugation Principle of Grinding and Cutting
Model；
Step 3: it solves to obtain dresser shaft actual motion instruction using ideal cutting location data and conditioning system geometric error
Calculation expression；And the roll flute error compensation towards crushing precision is obtained according to calculation expression.
Further, the crushing system geometric error includes the installation error and dresser shaft of grinding wheel, diamond roller
Kinematic error.
Further, the crushing system geometric error-spatial error model is established according to following formula:
△P(y,w,E23×1)=T15(y,w,E23×1)Pt-T15(y, w, 023×1)Pt；
Wherein,
△P(y,w,E23×1) indicate crushing system geometric error uniform space error；
The NC instruction of y expression Y dresser shaft；
The NC instruction of w expression W dresser shaft；
023×1Indicate that the equal value of conditioning system error is 0；
E23×1=(g1,g2,…,g23) indicate conditioning system error collection,
Pt=[0,0,0]TIndicate the center of the diamond roller in diamond roller coordinate system；
T15(y,w,E23×1) indicate diamond roller to grinding wheel coordinate system attained pose transformation matrix；
T15(y, w, 023×1) indicate diamond roller to grinding wheel coordinate system ideal module and carriage transformation matrix.
Further, the subcoordinate system in the crushing system includes grinding wheel coordinate system and Y axis coordinate system, is sat from grinding wheel
The real transform matrix of mark system to Y axis coordinate system is that position auto―control, grinding wheel installation pose error matrix, grinding wheel are installed by grinding wheel
Motion pose matrix, grinding wheel movement position and attitude error matrix successively connect multiplied arrive；
The grinding wheel installs position auto―control are as follows:
Wherein,
Tp21Installation position auto―control of the expression grinding wheel to Y axis coordinate system；
d1Indicate grinding wheel center in the x negative sense d of Y-axis zero-bit1At distance；
The grinding wheel installs pose error matrix are as follows:
Wherein,
Tpe21Installation pose error matrix of the expression grinding wheel to Y axis coordinate system；
δWxIndicate grinding wheel x to installation linearity error；
δWyIndicate grinding wheel y to installation linearity error；
δWzIndicate grinding wheel z to installation linearity error；
εWxIndicate grinding wheel x to setting angle error；
εWzIndicate grinding wheel z to setting angle error；
Module and carriage transformation matrix of the grinding wheel to Y axis coordinate system are as follows:
Wherein,
T21Attained pose transformation matrix of the expression grinding wheel to Y axis coordinate system；
Tm21=I4×4Indicate grinding wheel movement position auto―control；
Tme21=I4×4Indicate grinding wheel movement position and attitude error matrix；
I4×4Indicate 4 × 4 unit matrix.
Further, the subcoordinate system in the crushing system includes bistrique rack coordinate system and Y axis coordinate system, it is described from
Attained pose transformation matrix of the Y axis coordinate system to bistrique rack coordinate system are as follows:
Wherein,
T32Attained pose transformation matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
Tp32Installation position auto―control of the expression Y axis coordinate system to bistrique rack coordinate system；
Tpe32Installation pose error matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
Tm32Motion pose matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
Tme32Motion pose error matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
d2Indicate Y-axis zero-bit in the z negative sense d at bistrique frame center2At distance；
The NC instruction of y expression Y-axis；
δx(y) indicate Y-axis x to movement linearity error；
δy(y) indicate Y-axis y to movement linearity error；
δz(y) indicate Y-axis z to movement linearity error；
εx(y) indicate Y-axis x to movement angle error；
εy(y) indicate Y-axis y to movement angle error；
εz(y) indicate Y-axis z to movement angle error；Or
Subcoordinate system in the crushing system includes bistrique rack coordinate system and W axis coordinate system, from W axis coordinate system to
The attained pose transformation matrix of bistrique rack coordinate system is calculated according to following formula:
Wherein,
T34Attained pose transformation matrix of the expression W axis to bistrique rack coordinate system；
Tp34Installation position auto―control of the expression W axis to bistrique rack coordinate system；
Tpe34Installation pose error matrix of the expression W axis to bistrique rack coordinate system；
Tm34Motion pose matrix of the expression W axis to bistrique rack coordinate system；
Tme34Installation pose error matrix of the expression W axis to bistrique rack coordinate system；
εz(w) indicate W axis z to movement angle error；
εy(w) indicate W axis y to movement angle error；
εx(w) indicate W axis x to movement angle error；
δz(w) indicate W axis z to movement linearity error；
δx(w) indicate W axis x to movement linearity error；
δy(w) indicate W axis y to movement linearity error；
d3Indicate W axis zero-bit in the x negative sense d at bistrique frame center3At distance, d3=d1；
εWYIndicate the between centers error of perpendicularity of W axis and Y-axis；
The NC instruction of w expression W axis；
Or
Subcoordinate system in the crushing system includes diamond roller coordinate system and W axis coordinate system, from diamond
The attained pose transformation matrix of idler wheel coordinate system to W axis coordinate system is calculated according to following formula:
Wherein,
T45Attained pose transformation matrix of the expression diamond roller to W axis coordinate system；
Tp45Installation position auto―control of the expression diamond roller to W axis coordinate system；
Tpe45Installation pose error matrix of the expression diamond roller to W axis coordinate system；
Tm45Motion pose matrix of the expression diamond roller to W axis coordinate system；
Tme45Motion pose error matrix of the expression diamond roller to W axis coordinate system；
εRzIndicate diamond roller z to movement angle error；
εRxIndicate diamond roller x to movement angle error；
δRxIndicate diamond roller x to movement linearity error；
δRyIndicate diamond roller y to movement linearity error；
δRzIndicate diamond roller z to movement linearity error；
d4Indicate diamond roller center in the y forward direction d of W axis zero-bit4At distance；
Or
Subcoordinate system in the crushing system includes diamond roller coordinate system and grinding wheel coordinate system, from diamond
The attained pose transformation matrix of idler wheel coordinate system to grinding wheel coordinate system is calculated according to following formula:
X0=w [εWY-εy(y)]-y[εWz+εz(y)]-d2εy(y)+d4[εWz+εz(y)-εz(w)]-δWx-δx(y)+δx(w)+
δRx
Y0=-y+d4+w[εWx+εx(y)]+d2[εWx+εx(y)]+d3εz(y)-δWy-δy(y)+δy(w)+δRy
Z0=w+d2+y[εWx+εx(y)]-d3εy(y)-d4[εWx+εx(y)-εx(w)]-δWz-δz(y)+δz(w)+δRz
Wherein,
T15Attained pose transformation matrix of the expression diamond roller to grinding wheel coordinate system.
Further, the building of the crushing error model is established according to according to following formula:
Wherein,
△raq(E23×1) indicate crushing profile error of coordinate；
△naq(E23×1) indicate that crushing profile method swears error；
△yaqIndicate crushing profile y-coordinate error；
△zaqIndicate crushing profile z coordinate error；
△nyaqIndicate that crushing profile y method swears error；
△nzaqIndicate that crushing profile z method swears error；
raq(E23×1) indicate the practical axle sectional shape coordinate of grinding wheel；
naq(E23×1) indicate the practical axle sectional shape method arrow of grinding wheel；
rWIndicate grinding wheel ideal axle sectional shape coordinate；
nWIndicate grinding wheel ideal axle sectional shape method arrow；
△yaq(E23×1) indicate the practical axle sectional shape y-coordinate error of grinding wheel；
△zaq(E23×1) indicate the practical axle sectional shape z coordinate error of grinding wheel；
△nyaq(E23×1) indicate that the practical axle sectional shape y method of grinding wheel swears error；
△nzaq(E23×1) indicate that the practical axle sectional shape z method of grinding wheel swears error；
yaq(E23×1) indicate the practical axle sectional shape y-coordinate of grinding wheel；
zaq(E23×1) indicate the practical axle sectional shape z coordinate of grinding wheel；
nyaq(E23×1) indicate the practical axle sectional shape y method arrow of grinding wheel；
nzaq(E23×1) indicate the practical axle sectional shape z method arrow of grinding wheel；
yWIndicate grinding wheel ideal axle sectional shape y-coordinate；
zWIndicate grinding wheel ideal axle sectional shape z coordinate；
nWyIndicate grinding wheel ideal axle sectional shape y method arrow；
nWzIndicate grinding wheel ideal axle sectional shape z method arrow.
Further, the tooth surface error model in the crushing error-tooth surface error model is established according to following formula:
Wherein, δ nTS(k, j) indicates the normal error of j-th of discrete point of kth contact line, k=1,2 ..., λ, j=
1,2,...,n；
It indicates；
Indicate the actual coordinate of j-th of discrete point of kth contact line；
Indicate the ideal coordinates of j-th of discrete point of kth contact line；
Indicate the ideal method arrow of j-th of discrete point of kth contact line.
Further, it is characterised in that: the calculation expression of the dresser shaft actual motion instruction in the step 3 is as follows:
Wherein,
x0Indicate the ideal x coordinate at diamond roller center in grinding wheel coordinate system；
y0Indicate the ideal y-coordinate at diamond roller center in grinding wheel coordinate system；
z0Indicate the ideal z coordinate at diamond roller center in grinding wheel coordinate system.
The beneficial effects of the present invention are:
The present invention provides a kind of towards the roll flute error modeling of crushing precision and compensation method.Firstly, being based on sand
The definition of conditioning system geometric error and conditioning system Forward kinematics are taken turns, crushing system geometric error-space error is established
Model, influence relationship of the reflection geometric error to finishing motion profile；Then, consider crushing envelope movement and finishing contact
Condition constructs crushing error model, discloses geometric error to the mapping principle of crushing precision；Subsequently, based on mill
It cuts system forward kinematics and conjugation Principle of Grinding and Cutting further establishes crushing error-tooth surface error model, to quantify point
Analyse influence of every crushing system geometric error to precision of grinding teeth；Finally to guarantee that diamond roller ideal cutting location data is
Target solves to obtain the explicit algorithm table of dresser shaft actual motion instruction using ideal cutting location data and conditioning system geometric error
Up to formula, to realize the roll flute error compensation towards crushing precision.Dresser shaft actual motion instruction of the present invention is asked
Solution, is calculated using offline high-performance computer, independent of the data-handling capacity of numerically-controlled machine tool itself, therefore this
Inventing the error compensation strategy being related to has many advantages, such as versatility, easily implements.
Other advantages, target and feature of the invention will be illustrated in the following description to a certain extent, and
And to a certain extent, based on will be apparent to those skilled in the art to investigating hereafter, Huo Zheke
To be instructed from the practice of the present invention.Target of the invention and other advantages can be realized by following specification and
It obtains.
Detailed description of the invention
In order to keep the purpose of the present invention, technical scheme and beneficial effects clearer, the present invention provides following attached drawing and carries out
Illustrate:
Fig. 1 is formation teeth-grinding lathe basic structure.
Fig. 2 is crushing system coordinate system and error term.
Fig. 3 is crushing schematic diagram.
Fig. 4 is crushing profile error schematic diagram.
Fig. 5 is roll flute error modeling and compensation method flow chart towards crushing precision.
In figure, 11 indicate that gear, 12 indicate that grinding wheel, 13 indicate diamond roller；31 it is dressing track, 32 is turning centre
Track, 33 be grinding wheel profile, 34 be idler wheel center, 35 be turning centre；41 be practical profile, 42 be ideal profile, 43 is method
To error.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings and specific examples, so that those skilled in the art can be with
It better understands the present invention and can be practiced, but illustrated embodiment is not as a limitation of the invention.
It is provided in this embodiment towards the roll flute error modeling of crushing precision and compensation method, comprising the following steps:
Step 1: crushing system geometric error-crushing error modeling；
(1) crushing system geometric error defines
As shown in Figure 1, formation teeth-grinding lathe includes two relatively independent subsystems, crushing system and formation teeth-grinding
System.The former is made of grinding wheel, diamond roller, bistrique frame, W/Y dresser shaft, and the latter is by grinding wheel, gear blank, base, X/Z/A/C
It is ground axis composition.Crushing system and plunge grinding system are relatively independent, not by gear blank and grinding motion axis (X/Z/A/C)
The influence of installation error and kinematic error.As shown in fig. 1, wherein 11 indicate that gear, 12 indicate that grinding wheel, 13 indicate diamond
Idler wheel.
Crushing system geometric error includes the kinematic error of grinding wheel, the installation error of diamond roller and dresser shaft,
Bounce caused by shaft hole matching tolerance when installation error mostlys come from grinding wheel, diamond roller installation；Kinematic error is then main
Caused by the manufacturing defect of dresser shaft, so that generating deviation between attained pose and ideal pose when dresser shaft moves.For convenient for point
Analysis, crushing systematic error conclude sequence such as table 1.
The sequence of 1 crushing system geometric error of table and definition
Wherein,
g1~g5It indicates grinding wheel installation error, both led to roll flute error indirectly by influencing crushing precision, also by
Plunge grinding processing directly affects precision of grinding teeth；
g6~g11Indicate Y-axis kinematic error, including 3 location errors and 3 rotation errors；Bistrique frame is in crushing
It is taken as in journey reference frame (RCS), it is ideal error free；
g12~g18Successively indicate 1 installation error and 6 kinematic errors of W axis；
g19~g23Indicate diamond roller installation error.
Wherein, it is driven due to grinding wheel central symmetry and by electro spindle and carries out high speed rotation, the y of grinding wheel installation is to rotation error
Influence to crushing and formation teeth-grinding is negligible；Similarly, the y of diamond roller installation also can be ignored to rotation error.
Further, since crushing process nature is grinding wheel radial direction dressing process, can be considered y, z-plane Combined process, grinding wheel it is tangential (
That is x to) slight error, have no effect on finishing after the practical profile of grinding wheel.
(2) crushing system geometric error-spatial error model
As shown in Fig. 2, Fig. 2 is crushing system coordinate system and error term, based on homogeneous transform matrix theory and forward direction
Kinematics can establish the module and carriage transformation matrix between adjacent coordinates system respectively.With grinding wheel coordinate system to the position orientation relation of Y axis coordinate system
For, real transform matrix between the two can be installed position auto―control by grinding wheel, grinding wheel installs pose error matrix, grinding wheel movement position
Appearance matrix, grinding wheel movement position and attitude error matrix successively connect multiplied arrive.Specifically, grinding wheel installs position auto―control are as follows:
Wherein, d1Indicate grinding wheel center in the x negative sense d of Y-axis zero-bit1At distance.
Grinding wheel installs pose error matrix are as follows:
Wherein, δWx,δWy,δWz,εWx,εWzIndicate grinding wheel installation error, the actual coordinates and reason after representing grinding wheel installation
Think the departure degree between coordinate system, error defines in ideal grinding wheel coordinate system after mounting, direction and machine tool motion axis one
It causes.
Grinding wheel movement position auto―control: Tm21=I4×4
Grinding wheel movement position and attitude error matrix: Tme21=I4×4
Therefore, attained pose transformation matrix of the grinding wheel to Y axis coordinate system are as follows:
Similarly, with d2Indicate Y-axis zero-bit in the z negative sense d at bistrique frame center2At distance；The NC instruction of Y-axis is indicated with y,
The available attained pose transformation matrix from Y-axis to bistrique frame:
With d3Indicate W axis zero-bit in the x negative sense d at bistrique frame center3At distance, d3=d1；With εWYIndicate the axis of W axis and Y-axis
Between the error of perpendicularity；The NC instruction of W axis is indicated with w, the available attained pose transformation matrix from W axis to bistrique frame:
With d4Indicate diamond roller center in the y forward direction d of W axis zero-bit4It is available from diamond roller to W at distance
The attained pose transformation matrix of axis:
Therefore, it is based on roll flute kinematic chain (workpiece chain 3-2-1 and cutter chain 3-4-5), considers that crushing system geometry misses
Difference, from diamond roller to the attained pose transformation matrix of grinding wheel coordinate system are as follows:
T15=(T21)-1×(T32)-1×T34×T45
=(Tp21Tpe21Tm21Tme21)-1(Tp32Tpe32Tm32Tme32)-1(Tp34Tpe34Tm34Tme34)(Tp45Tpe45Tm45Tme45)
=(Tpe21 -1Tp21 -1)(Tme32 -1Tm32 -1Tp32 -1)(Tp34Tpe34Tm34Tme34)(Tp45Tpe45)
Since error value is smaller, ignore error multiplication second order and the above higher order term, simultaneously because d3=d1, can be by T15Change
Letter are as follows:
Wherein:
X0=w [εWY-εy(y)]-y[εWz+εz(y)]-d2εy(y)+d4[εWz+εz(y)-εz(w)]-δWx-δx(y)+δx(w)+
δRx
Y0=-y+d4+w[εWx+εx(y)]+d2[εWx+εx(y)]+d3εz(y)-δWy-δy(y)+δy(w)+δRy
Z0=w+d2+y[εWx+εx(y)]-d3εy(y)-d4[εWx+εx(y)-εx(w)]-δWz-δz(y)+δz(w)+δRz
If with E23×1=(g1,g2,…,g23) indicating conditioning system error collection, the center of diamond roller is rolled in diamond
P is represented by wheel coordinate systemt=[0,0,0]T, then it can establish crushing system geometric error-spatial error model:
△P(y,w,E23×1)=T51(y,w,E23×1)Pt-T51(y, w, 023×1)Pt
(3) crushing error modeling
As shown in figure 3, during crushing, grinding wheel keeps constant speed rotation, diamond roller counter-rotating and along pre-
Fixed track carries out finishing envelope movement to grinding wheel, and when dressing track refers to crushing, diamond roller central point is sat in grinding wheel
Motion profile in mark system；When diamond roller cutting envelope surface refers to the spinning of idler wheel cutting point and moves along dressing track
The swept surface of formation.As shown in Figure 3, wherein 31 be dressing track, 32 be turning centre track, 33 be grinding wheel profile, 34 be
Idler wheel center, 35 are turning centre.
If indicating grinding wheel profile parameter with u, profile coordinate is represented by rW(u)=[0, yW(u),zW(u),1]T, unit
Method arrow is represented by nW(u)=[0, nWx(u),nWy(u),0]T.Dressing track is regarded as grinding wheel ideal axle sectional shape first along exterior feature
Shape normal direction translates idler wheel radius of clean-up rc, then along half of idler wheel thickness b of idler wheel axial translationR/ 2, finally rolled along idler wheel radial translation
Take turns radius rRIt obtains.Dressing track on the right of grinding wheel when profile finishing, in grinding wheel coordinate system are as follows:
Based on position auto―control transformation theory, may be expressed as:
The linkage track of the dressing track namely Y, W axis, therefore the pose between diamond roller coordinate system and grinding wheel coordinate system
Transformation matrix is also the function of grinding wheel profile parameter u, is represented by T15(u)。
During crushing, the cutting circular arc of diamond roller is rotated around roller axis.In diamond roller coordinate system
In, if set the angle that idler wheel turning centre is rotated around roller axis asThen turning centre rotary track C1Are as follows:
It may also indicate that are as follows:
Wherein,
Indicate track C1Coordinate；
xRcIndicate track C1X coordinate；
Indicate track C1Y-coordinate；
Indicate track C1Z coordinate.
Therefore, when idler wheel turning centre is moved along dressing track, the envelope track plane S of turning centre1And its per unit system arrow,
It may be expressed as: in grinding wheel coordinate system
Wherein,
Indicate the envelope track plane S of turning centre1Coordinate；
Indicate the envelope track plane S of turning centre1Per unit system arrow.When crushing, between turning centre and cutting point
There are radius of clean-up r in normal directioncOffset, therefore the space envelope curved surface S of cutting point2With the envelope track plane of turning centre
S1Between there is also normal direction offsets.In grinding wheel coordinate system, idler wheel cuts envelope surface S2Are as follows:
Wherein,
Indicate the space envelope curved surface S of cutting point2Coordinate；
Indicate the space envelope curved surface S of cutting point2Per unit system arrow.
If grinding wheel axle sectional shape is rotated around grinding wheel axis, grinding wheel outer surface S can be formed3.If grinding wheel rotation angle is
φ, then grinding wheel outer surface S3Are as follows:
Wherein,
Indicate grinding wheel outer surface S3Coordinate；
Indicate grinding wheel outer surface S3Per unit system arrow；
Tr(φ) indicates grinding wheel spin matrix:
When crushing, idler wheel cuts envelope surface S2It is contacted between grinding wheel outer surface for line.Since grinding wheel outer surface is
The method arrow of the surface of revolution, wheel face arbitrary point must intersect with grinding wheel axis, so idler wheel cuts envelope surface and wheel face
Modify contact conditions are as follows: the point on cutting envelope surface, Ruo Qifa arrow intersect with grinding wheel axis, then the point is crushing contact
Point, i.e.,
Wherein,
Indicate S2X coordinate；
Indicate S2Z coordinate；
Indicate S2X to per unit system swear；
Indicate S2Z to per unit system swear.According to finishing contact conditions, grinding wheel outer surface and idler wheel cutting packet can be acquired
The contact line and per unit system of network curved surface are sweared:
Wherein,
rclIndicate the coordinate of contact line；
xcl,ycl,zclIndicate the x of contact line, y, z coordinate；
nclIndicate the per unit system arrow of contact line；
nxcl,nycl,nzclIndicate that the x of contact line, y, z are sweared to per unit system.
If it is projected on grinding wheel axial cross section around the rotation of grinding wheel axis, grinding wheel axle sectional shape and its per unit system can be obtained
Arrow,
Wherein,
raqIndicate grinding wheel axle sectional shape coordinate；
yaq,zaqIndicate the y of grinding wheel axle sectional shape, z coordinate；
naqIndicate the per unit system arrow of grinding wheel axle sectional shape；
nyaq,nzaqIndicate that the y of grinding wheel axle sectional shape, z are sweared to per unit system.As shown in Figure 4, wherein 41 be practical profile, 42
It is normal error for ideal profile, 43；Conditioning system geometric error is considered, by the practical axle sectional shape of grinding wheel and ideal axle sectional shape
Make difference relatively, crushing error can be obtained.
Wherein,
Step 2: crushing error-tooth surface error modeling；
Using the grinding wheel after finishing, roll flute processing is carried out, the practical axle sectional shape of grinding wheel after finishing uses raq(u) and
naq(u) combine when being indicated, the practical grinding wheel in grinding wheel coordinate system (TCS) may be expressed as:
Wherein,
rwtIndicate practical grinding wheel coordinate；
nwtIndicate practical grinding wheel per unit system arrow.
During formation teeth-grinding, ignore the installation error and kinematic error to roll flute base and grinding motion axis (X/Z/A/C),
Only consider grinding wheel installation error (δ present in crushing systemWx、δWy、δWz、εWx、εWz), the influence to grinding accuracy.
As shown in Figure 1, being based on roll flute propulsion chain (W-Y-A-Z-X-R-C-G) and homogeneous transform matrix, can establish
Characterization is from grinding wheel to 4 × 4 matrixes of the pose transformation relation gear coordinate system:
Wherein, A indicates grinding wheel established angle, equal in magnitude with gear helical angle；X indicate the center between grinding wheel and gear away from；Y
The y of expression grinding wheel is to movement, Y=0 during roll flute；C indicate gear rotate angle, Z indicate grinding wheel with gear rotate and on
The distance risen, value are equal to pC, and p indicates helix parameter.
Due to only considering grinding wheel installation error, the movement relation between remaining each adjacent component is thought of as perfect condition, because
Module and carriage transformation matrix between this adjacent component coordinate system is respectively as follows:
Thus it can be calculated, from grinding wheel coordinate system to the ideal transformation relationship of gear coordinate system are as follows:
Grinding wheel installation error is considered, from grinding wheel coordinate system to the real transform relationship of gear coordinate system are as follows:
The practical grinding wheel in gear coordinate system (GCS) may be expressed as: as a result,
Due to grinding wheel parameter it is known that according to conjugation Grinding Contact condition following equation can be listed:
F=(kw×rww+pkw)·nww=0
Wherein, kwIndicate gear axial direction unit vector；rww、nwwRespectively indicate grinding wheel coordinate vector in gear coordinate system and
Per unit system arrow；P indicates helix parameter；F indicates conjugation Grinding Contact function.
It is λ grinding cutter location that the equidistant discretization in track will be ground as a result, can phase using dichotomy or Newton iteration method
It should solve respectively and obtain λ item ideal and practical contact line, respectively with rlwi,nlwiAnd rlwa,nlwaIt indicates, wherein every contact line packet
Containing n discrete point.Thus, it is possible to establish grinding tooth surface error model:
Wherein, δ nTS(k, j) indicates the normal error of j-th of discrete point of kth contact line, k=1,2 ..., λ, j=
1,2,...,n。
Based on tooth surface error model, flank profil, teeth directional precision information are extracted using simple algebraic operation.If end is cut
The Norma l deviation of discrete contact points extracts on face, available total profile deviation information；If by index cylinder tooth trace on from
The Norma l deviation for dissipating contact point extracts, available spiral deviation information.Profile accuracy can refer to ISO 1328-1-
1997 standards are evaluated, and evaluation index includes tooth profile total deviation (Fα), profile geometry deviation (ffα) and flank profil slope deviation
(fHα)；Similarly, teeth directional precision evaluation index includes helix total deviation (Fβ), helix shape deviation (ffβ) and spiral line slope
Deviation (fHβ)。
So far, which can be with quantitative analysis items crushing system geometric error to the shadow of precision of grinding teeth
It rings, can both analyze individual event geometric error to the independent effect relationship of roll flute accuracy class, multinomial geometric error opposite grinding can also be analyzed
The coupling effect of tooth accuracy class.
Step 3: the roll flute error compensating method towards crushing precision
To guarantee crushing precision, crushing system geometric error is minimized or eliminated to the shadow of precision of grinding teeth
It rings, proposes the error compensating method based on practical inverse kinematics.This method is to guarantee the ideal cutting location data of diamond roller
For target, expressed by the explicit algorithm that ideal cutting location data and conditioning system geometric error solve dresser shaft actual motion instruction
Formula, to realize error compensation.
Since the center of diamond roller is represented by P in diamond roller coordinate systemt=[0,0,0]TIf by Buddha's warrior attendant
Ideal position data of the center of stone idler wheel in grinding wheel coordinate system are set as Pw=[x0,y0,z0]T, should meet between the two following
Mapping relations:
[Pw,1]T=T15[Pt,1]T
The formula can be turned to further:
T32T21[x0,y0,z0,1]T=T34T45[0,0,0,1]T
In addition, can be turned to based on the translation features separation theorem that piecemeal calculates:
Tme32T21[x0,y0,z0,1]T-Tp23Tp34Tpe34Tme34T45[0,0,0,1]T=[0 ,-y, 0,0]T+Tp23Tp34Tpe34
[0,0,w,0]T
Wherein,
Therefore, above formula can indicate are as follows:
To which the dresser shaft actual motion instruction calculation expression under the influence of geometric error can be obtained:
It is former with the dresser shaft actual motion instruction substitution being calculated in actual crushing and Grinding Process
Instruction generates new numerical control code, and the formation teeth-grinding error compensation towards crushing precision can be realized in movement, so that roll flute
Precision is promoted.
It is provided in this embodiment towards the roll flute error modeling of crushing precision and compensation method, can be repaired based on grinding wheel
Whole system geometric error source analysis constructs crushing error model and precision of grinding teeth model, so that quantitative analysis items are several
What influence of the error to precision of grinding teeth；Error is considered furthermore, it is possible to calculate based on established model and practical inverse kinematics method
The dresser shaft actual motion of compensation instructs, and realizes that precision of grinding teeth is promoted.
Embodiment described above is only to absolutely prove preferred embodiment that is of the invention and being lifted, protection model of the invention
It encloses without being limited thereto.Those skilled in the art's made equivalent substitute or transformation on the basis of the present invention, in the present invention
Protection scope within.Protection scope of the present invention is subject to claims.
Claims (8)
1. a kind of towards the roll flute error modeling of crushing precision and compensation method, it is characterised in that: the following steps are included:
Step 1: crushing system geometric error-crushing error modeling, the specific steps are as follows:
(1) crushing system geometric error is determined；
(2) crushing system geometric error-spatial error model is established；
(3) according to crushing envelope movement and finishing contact conditions, crushing error model is constructed；
Step 2: crushing error-tooth surface error model is established based on grinding system Forward kinematics and conjugation Principle of Grinding and Cutting；
Step 3: it solves to obtain the calculating of dresser shaft actual motion instruction using ideal cutting location data and conditioning system geometric error
Expression formula；And the roll flute error compensation towards crushing precision is obtained according to calculation expression.
2. the method as described in claim 1, it is characterised in that: the crushing system geometric error includes grinding wheel, Buddha's warrior attendant
The installation error of stone idler wheel and the kinematic error of dresser shaft.
3. the method as described in claim 1, it is characterised in that: the crushing system geometric error-spatial error model
It is established according to following formula:
△P(y,w,E23×1)=T15(y,w,E23×1)Pt-T15(y, w, 023×1)Pt；
Wherein,
△P(y,w,E23×1) indicate crushing system geometric error uniform space error；
The NC instruction of y expression Y dresser shaft；
The NC instruction of w expression W dresser shaft；
023×1Indicate that the equal value of conditioning system error is 0；
E23×1=(g1,g2,…,g23) indicate conditioning system error collection,
Pt=[0,0,0]TIndicate the center of the diamond roller in diamond roller coordinate system；
T15(y,w,E23×1) indicate diamond roller to grinding wheel coordinate system attained pose transformation matrix；
T15(y, w, 023×1) indicate diamond roller to grinding wheel coordinate system ideal module and carriage transformation matrix.
4. the method as described in claim 1, it is characterised in that: the subcoordinate system in the crushing system includes that grinding wheel is sat
Mark system and Y axis coordinate system, the real transform matrix from grinding wheel coordinate system to Y axis coordinate system be by grinding wheel install position auto―control,
Grinding wheel installation pose error matrix, grinding wheel movement position auto―control, grinding wheel movement position and attitude error matrix successively connect multiplied arrive；
The grinding wheel installs position auto―control are as follows:
Wherein,
Tp21Installation position auto―control of the expression grinding wheel to Y axis coordinate system；
d1Indicate grinding wheel center in the x negative sense d of Y-axis zero-bit1At distance；
The grinding wheel installs pose error matrix are as follows:
Wherein,
Tpe21Installation pose error matrix of the expression grinding wheel to Y axis coordinate system；
δWxIndicate grinding wheel x to installation linearity error；
δWyIndicate grinding wheel y to installation linearity error；
δWzIndicate grinding wheel z to installation linearity error；
εWxIndicate grinding wheel x to setting angle error；
εWzIndicate grinding wheel z to setting angle error；
Module and carriage transformation matrix of the grinding wheel to Y axis coordinate system are as follows:
Wherein,
T21Attained pose transformation matrix of the expression grinding wheel to Y axis coordinate system；
Tm21=I4×4Indicate grinding wheel movement position auto―control；
Tme21=I4×4Indicate grinding wheel movement position and attitude error matrix；
I4×4Indicate 4 × 4 unit matrix.
5. the method as described in claim 1, it is characterised in that: the subcoordinate system in the crushing system includes bistrique frame
Coordinate system and Y axis coordinate system, it is described from Y axis coordinate system to the attained pose transformation matrix of bistrique rack coordinate system are as follows:
Wherein,
T32Attained pose transformation matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
Tp32Installation position auto―control of the expression Y axis coordinate system to bistrique rack coordinate system；
Tpe32Installation pose error matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
Tm32Motion pose matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
Tme32Motion pose error matrix of the expression Y axis coordinate system to bistrique rack coordinate system；
d2Indicate Y-axis zero-bit in the z negative sense d at bistrique frame center2At distance；
The NC instruction of y expression Y-axis；
δx(y) indicate Y-axis x to movement linearity error；
δy(y) indicate Y-axis y to movement linearity error；
δz(y) indicate Y-axis z to movement linearity error；
εx(y) indicate Y-axis x to movement angle error；
εy(y) indicate Y-axis y to movement angle error；
εz(y) indicate Y-axis z to movement angle error；
Or
Subcoordinate system in the crushing system includes bistrique rack coordinate system and W axis coordinate system, from W axis coordinate system to bistrique
The attained pose transformation matrix of rack coordinate system is calculated according to following formula:
Wherein,
T34Attained pose transformation matrix of the expression W axis to bistrique rack coordinate system；
Tp34Installation position auto―control of the expression W axis to bistrique rack coordinate system；
Tpe34Installation pose error matrix of the expression W axis to bistrique rack coordinate system；
Tm34Motion pose matrix of the expression W axis to bistrique rack coordinate system；
Tme34Installation pose error matrix of the expression W axis to bistrique rack coordinate system；
εz(w) indicate W axis z to movement angle error；
εy(w) indicate W axis y to movement angle error；
εx(w) indicate W axis x to movement angle error；
δz(w) indicate W axis z to movement linearity error；
δx(w) indicate W axis x to movement linearity error；
δy(w) indicate W axis y to movement linearity error；
d3Indicate W axis zero-bit in the x negative sense d at bistrique frame center3At distance, d3=d1；
εWYIndicate the between centers error of perpendicularity of W axis and Y-axis；
The NC instruction of w expression W axis；
Or
Subcoordinate system in the crushing system includes diamond roller coordinate system and W axis coordinate system, from diamond roller
The attained pose transformation matrix of coordinate system to W axis coordinate system is calculated according to following formula:
Wherein,
T45Attained pose transformation matrix of the expression diamond roller to W axis coordinate system；
Tp45Installation position auto―control of the expression diamond roller to W axis coordinate system；
Tpe45Installation pose error matrix of the expression diamond roller to W axis coordinate system；
Tm45Motion pose matrix of the expression diamond roller to W axis coordinate system；
Tme45Motion pose error matrix of the expression diamond roller to W axis coordinate system；
εRzIndicate diamond roller z to movement angle error；
εRxIndicate diamond roller x to movement angle error；
δRxIndicate diamond roller x to movement linearity error；
δRyIndicate diamond roller y to movement linearity error；
δRzIndicate diamond roller z to movement linearity error；
d4Indicate diamond roller center in the y forward direction d of W axis zero-bit4At distance；
Or
Subcoordinate system in the crushing system includes diamond roller coordinate system and grinding wheel coordinate system, from diamond roller
The attained pose transformation matrix of coordinate system to grinding wheel coordinate system is calculated according to following formula:
X0=w [εWY-εy(y)]-y[εWz+εz(y)]-d2εy(y)+d4[εWz+εz(y)-εz(w)]-δWx-δx(y)+δx(w)+δRx
Y0=-y+d4+w[εWx+εx(y)]+d2[εWx+εx(y)]+d3εz(y)-δWy-δy(y)+δy(w)+δRy
Z0=w+d2+y[εWx+εx(y)]-d3εy(y)-d4[εWx+εx(y)-εx(w)]-δWz-δz(y)+δz(w)+δRz
Wherein,
T15Attained pose transformation matrix of the expression diamond roller to grinding wheel coordinate system.
6. the method as described in claim 1, it is characterised in that: the building of the crushing error model is according to according to following
Formula is established:
Wherein,
△raq(E23×1) indicate crushing profile error of coordinate；
△naq(E23×1) indicate that crushing profile method swears error；
△yaqIndicate crushing profile y-coordinate error；
△zaqIndicate crushing profile z coordinate error；
△nyaqIndicate that crushing profile y method swears error；
△nzaqIndicate that crushing profile z method swears error；
raq(E23×1) indicate the practical axle sectional shape coordinate of grinding wheel；
naq(E23×1) indicate the practical axle sectional shape method arrow of grinding wheel；
rWIndicate grinding wheel ideal axle sectional shape coordinate；
nWIndicate grinding wheel ideal axle sectional shape method arrow；
△yaq(E23×1) indicate the practical axle sectional shape y-coordinate error of grinding wheel；
△zaq(E23×1) indicate the practical axle sectional shape z coordinate error of grinding wheel；
△nyaq(E23×1) indicate that the practical axle sectional shape y method of grinding wheel swears error；
△nzaq(E23×1) indicate that the practical axle sectional shape z method of grinding wheel swears error；
yaq(E23×1) indicate the practical axle sectional shape y-coordinate of grinding wheel；
zaq(E23×1) indicate the practical axle sectional shape z coordinate of grinding wheel；
nyaq(E23×1) indicate the practical axle sectional shape y method arrow of grinding wheel；
nzaq(E23×1) indicate the practical axle sectional shape z method arrow of grinding wheel；
yWIndicate grinding wheel ideal axle sectional shape y-coordinate；
zWIndicate grinding wheel ideal axle sectional shape z coordinate；
nWyIndicate grinding wheel ideal axle sectional shape y method arrow；
nWzIndicate grinding wheel ideal axle sectional shape z method arrow.
7. the method as described in claim 1, it is characterised in that: the flank of tooth in the crushing error-tooth surface error model
Error model is established according to following formula:
Wherein, δ nTS(k, j) indicates the normal error of j-th of discrete point of kth contact line, k=1,2 ..., λ, j=1,
2,...,n；
It indicates；
Indicate the actual coordinate of j-th of discrete point of kth contact line；
Indicate the ideal coordinates of j-th of discrete point of kth contact line；
Indicate the ideal method arrow of j-th of discrete point of kth contact line.
8. the method as described in claim 1, it is characterised in that: the calculating of the dresser shaft actual motion instruction in the step 3
Expression formula is as follows:
Wherein,
x0Indicate the ideal x coordinate at diamond roller center in grinding wheel coordinate system；
y0Indicate the ideal y-coordinate at diamond roller center in grinding wheel coordinate system；
z0Indicate the ideal z coordinate at diamond roller center in grinding wheel coordinate system.
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| CN114091210A (en) * | 2021-12-13 | 2022-02-25 | 山东大学 | Generating grinding tooth surface distortion prediction model construction method considering tooth profile modification |
| CN114091210B (en) * | 2021-12-13 | 2024-05-10 | 山东大学 | Method for constructing generated grinding tooth surface distortion prediction model taking tooth profile modification into consideration |
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