CN107609231A - A kind of worm screw grinding worm surface microscopic topographic emulation mode and system - Google Patents
A kind of worm screw grinding worm surface microscopic topographic emulation mode and system Download PDFInfo
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Abstract
The present invention relates to Grinding Process to emulate field, disclose a kind of worm screw grinding worm surface microscopic topographic emulation mode and system, based on actual measurement wheel face, simulation result can be made more accurately so as to reduce gear-driven contact fatigue, further to improve service life.The present invention measures the part actual surface of worm abrasion wheel first, the shape characteristic parameter of worm abrasion wheel actual surface is calculated based on measurement result, and the full surface of worm abrasion wheel is reconstructed according to shape characteristic parameter, and reconstruction result is mapped on macroscopical curved surface, obtain worm abrasion wheel model；Then relative position of the worm abrasion wheel under by roll flute wheel coordinate system is calculated；It will in the form of a grid be divided to obtain by the final pattern of roll flute wheel workpiece surface, and calculated accordingly by the final structural parameters of roll flute wheel workpiece surface by the surface of mill gear workpieces again.
Description
Technical field
The present invention relates to Grinding Process to emulate field, more particularly to a kind of worm screw grinding worm surface microscopic topographic is imitated
True method and system.
Background technology
Gear grinding is to obtain the important method of high class gear, and wherein worm screw gear-grinding process is due to its high efficiency, in reality
Extensive utilization has been obtained in the processing of border.Because the flank of tooth microscopic appearance feature of worm screw grinding worm is tired to gear-driven contact
The performances such as labor, flex life, abrasion have a major impact, therefore, establish more accurate gear 3 d surface topography model for
The research of gear performance is significant.
Due to macroshape specific to gear and processing technology, the Mi-crocosmic forecast model of flat surface grinding, it is clear that and it is uncomfortable
For the flank of tooth surface microscopic topographic model, and at present for gear grinding surface microscopic topographic research it is less, and exist compared with
The defects of big.
Therefore, now need to provide one kind based on actual measurement wheel face, simulation result can be made more accurately to be passed so as to reduce gear
Dynamic contact fatigue, further improve the worm screw grinding worm surface microscopic topographic emulation mode and system of service life.
The content of the invention
Present invention aims at providing a kind of worm screw grinding worm surface microscopic topographic emulation mode and system, this method and
System is based on actual measurement wheel face, and simulation result can be made more accurately so as to reduce gear-driven contact fatigue, further to carry
High service life.
To achieve the above object, the invention provides a kind of worm screw grinding worm surface microscopic topographic emulation mode, including
Following steps：
The part actual surface of worm abrasion wheel is measured, the pattern of the worm abrasion wheel actual surface is calculated based on measurement result
Characteristic parameter, and the full surface of the worm abrasion wheel being reconstructed according to the shape characteristic parameter, and by reconstruction result
It is mapped on macroscopical curved surface, obtains the model of the worm abrasion wheel；
According to the worm abrasion wheel and the movement relation by mill gear workpieces, coordinate conversion matrix is established, obtains the snail
Relative position of the bar emery wheel under the wheel coordinate system by roll flute；
The surface by mill gear workpieces is divided in the form of a grid, calculating is all to be in the net region
Height value of the interior emery wheel data point in method direction of the net region central point along involute；
By the height value of each emery wheel data point compared with the elemental height of mesh point where the emery wheel data point,
New elemental height of the smaller value in both as mesh point is taken, obtains the final pattern by roll flute wheel workpiece surface, is counted
The final structural parameters by roll flute wheel workpiece surface are calculated, worm screw grinding worm surface is more accurately emulated with realizing.
To achieve the above object, the invention provides a kind of worm screw grinding worm surface microscopic topographic analogue system, including：
First module：For measuring the part actual surface of worm abrasion wheel, the worm abrasion wheel is calculated based on measurement result
The shape characteristic parameter of actual surface, and weight is carried out to the full surface of the worm abrasion wheel according to the shape characteristic parameter
Structure, and reconstruction result is mapped on macroscopical curved surface, obtain the model of the worm abrasion wheel；
Second unit：For according to the worm abrasion wheel and the movement relation by mill gear workpieces, establishing Coordinate Conversion square
Battle array, obtains relative position of the worm abrasion wheel under the wheel coordinate system by roll flute；
Third unit：For the surface by mill gear workpieces to be divided in the form of a grid, all places are calculated
In height value of the emery wheel data point in the net region in method direction of the net region central point along involute；
Unit the 4th：For by the initial of mesh point where the height value of each emery wheel data point and the emery wheel data point
Highly it is compared, takes new elemental height of the smaller value in both as mesh point, obtains described by roll flute wheel workpiece surface
Final pattern, calculate the final structural parameters by roll flute wheel workpiece surface, with realize to worm screw grinding worm surface more
Accurately emulation.
The invention has the advantages that：
The present invention provides a kind of worm screw grinding worm surface microscopic topographic emulation mode and system, and multiple quarter is measured first
To the microscopic appearance of worm abrasion wheel be reconstructed, and map that on worm screw curved surface, obtain based on actual measurement wheel face
Worm abrasion wheel microscopic appearance model, worm abrasion wheel and the movement relation by mill gear workpieces are then analyzed, obtains both contacts
Relation, further obtain by the final pattern of roll flute wheel workpiece surface, and be calculated by the most end form of roll flute wheel workpiece surface
Looks parameter；This method and system are based on actual measurement wheel face, can make simulation result more accurately so as to reducing gear-driven connect
Fatigue is touched, further improves service life.
Below with reference to accompanying drawings, the present invention is further detailed explanation.
Brief description of the drawings
Fig. 1 is the workflow schematic diagram of the preferred embodiment of the present invention；
Fig. 2 is the actual measurement worm abrasion wheel pattern schematic diagram of the preferred embodiment of the present invention；
Fig. 3 is the worm abrasion wheel pattern schematic diagram after the reconstruct of the preferred embodiment of the present invention；
Fig. 4 is the worm abrasion wheel model schematic of the preferred embodiment of the present invention；
Fig. 5 is the worm abrasion wheel of the preferred embodiment of the present invention and the movement relation schematic diagram by mill gear workpieces；
Fig. 6 is the worm abrasion wheel and the coordinate system diagram by mill gear workpieces that the preferred embodiment of the present invention is established；
Fig. 7 is that the surface mesh by mill gear workpieces of the preferred embodiment of the present invention divides schematic diagram；
Fig. 8 is the final pattern schematic diagram by roll flute wheel workpiece surface of the preferred embodiment of the present invention.
Embodiment
Embodiments of the invention are described in detail below in conjunction with accompanying drawing, but the present invention can be defined by the claims
Implement with the multitude of different ways of covering.
Embodiment 1
Referring to Fig. 1, the present embodiment provides a kind of worm screw grinding worm surface microscopic topographic emulation mode, including：
The part actual surface of worm abrasion wheel is measured, the pattern of the worm abrasion wheel actual surface is calculated based on measurement result
Characteristic parameter, and the full surface of the worm abrasion wheel being reconstructed according to the shape characteristic parameter, and by reconstruction result
It is mapped on macroscopical curved surface, obtains the model of the worm abrasion wheel；
According to the worm abrasion wheel and the movement relation by mill gear workpieces, coordinate conversion matrix is established, obtains the snail
Relative position of the bar emery wheel under the wheel coordinate system by roll flute；
The surface by mill gear workpieces is divided in the form of a grid, calculating is all to be in the net region
Height value of the interior emery wheel data point in method direction of the net region central point along involute；
By the height value of each emery wheel data point compared with the elemental height of mesh point where the emery wheel data point,
New elemental height of the smaller value in both as mesh point is taken, obtains the final pattern by roll flute wheel workpiece surface, is counted
The final structural parameters by roll flute wheel workpiece surface are calculated, worm screw grinding worm surface is more accurately emulated with realizing.
Specifically, by taking the emery wheel emulation of model 89A/F80K6v white fused alumina worm abrasion wheel as an example, to base in the present invention
Illustrated in the wheel face emulation of actual measurement；It is right by taking the worm wheel grinding technique on REISHAUER RZ400 lathes as an example
Envelope track in the present invention, workpiece surface wound is into illustrating.
First, multiple quarter is carried out to model 89A/F80K6v white fused alumina worm abrasion wheel using addition-type silicon rubber material,
Then the multiple pattern for carving obtained worm abrasion wheel is measured using model LSM700 laser confocal microscope, its
In, the eyepiece multiple of laser confocal microscope is 10x.The sampling interval is chosen as 2.5 μm to some 1cm x1cm of worm abrasion wheel
The surface topography of scope is measured, and standard deviation, skewness and the peak of worm abrasion wheel actual surface are calculated according to measurement result
State.
Then, macroshape is filtered off by eight multinomials, and appropriate noise reduction is carried out using firm Gaussian filter, obtained
To actual measurement worm abrasion wheel surface as shown in Figure 2.To obtained actual measurement worm abrasion wheel surface be filtered processing, it is necessary to explanation
It is that, because the process of filtering can cause the parameter on actual measurement worm abrasion wheel surface, e.g., skewness and kurtosis produce deviation, so
Need further to correct the parameter on actual measurement worm abrasion wheel surface after filtering process, use formula for：
In formula, SKηRepresent revised skewness, KηRepresent revised kurtosis, SKzRepresent the skewness before amendment, KzRepresent
Kurtosis before amendment, c represent data dot matrix z (i, j) total number, θaRepresent to choose from the data dot matrix z (i, j) the
A number, θbRepresent b-th of the number chosen from data dot matrix z (i, j), and θbFor θaAdjacent latter number.
Then, the parameter on revised actual measurement worm abrasion wheel surface is handled to obtain by Johnson converting systems
Non-gaussian sequence ηI+k, j+h, the auto-correlation function of calculating worm abrasion wheel actual surface：
In formula, z (i, j) represents the data dot matrix of the part actual surface of the worm abrasion wheel of measurement, and i represents the data
The row of dot matrix, j represent the data point matrix column, total line number of n representing matrixs, total columns of m representing matrixs, k expressions
The row k of autocorrelation matrix, l represent the l row of autocorrelation matrix.
And auto-correlation coefficient matrix α is calculated according to the nonlinear equation of auto-correlation functionk,l：
In formula, p represents the scope that the row of the data dot matrix can change, value 0,1 ... n-1；Q representing matrixs
The scope that can change of row, value 0,1 ... m-1.
Further, the microcosmic of the full surface of worm abrasion wheel is reconstructed according to auto-correlation coefficient matrix and non-gaussian sequence
Pattern level dot matrix：
Emery wheel 3 d surface topography is reconstructed according to characteristic parameter, obtains reconstruct wheel face as shown in Figure 3.
What deserves to be explained is above-mentioned calculating process is all calculating of each parameter in plane, it is contemplated that the macroscopic view of worm abrasion wheel
Shape, therefore, it is necessary to result of calculation obtained above is mapped on macroscopical curved surface, obtain final worm abrasion wheel model.Specifically
Ground, first calculate the surface equation of worm abrasion wheel：
In formula, x1、y1And z1Represent corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system, rbRepresent base radius,
λbEmery wheel lead angle is represented, β represents helix parameter, θσRepresent angle variables of the tooth surface parameters between 0-2 π.
Then, the position vector of worm abrasion wheel curved surface：
In formula,The position vector of worm abrasion wheel curved surface is represented,The direction vector of denotation coordination axle.
Then, the cooler normal vector of each point on the curved surface of worm abrasion wheel is confirmed：
In formula,Represent the unit normal of each point on worm abrasion wheel curved surface；
Due in above calculating process, the z that is obtained when the full surface of worm abrasion wheel is reconstructedI, jFor worm screw sand
The microscopic appearance level dot matrix of the full surface of wheel, therefore, it is necessary to by the height dot matrix along on worm abrasion wheel curved surface
The normal orientation of each point, it is mapped on actual worm abrasion wheel curved surface, relevant parameter is substituted into formula
WhereinExpression and zI, jThe position vector of the final worm abrasion wheel curved surface of corresponding point,Expression and zI, jCorresponding point
The position vector of worm abrasion wheel curved surface is represented,Represent worm abrasion wheel curved surface on zI, jThe cooler normal vector of corresponding point,
The worm abrasion wheel model diameter being calculated is 30mm, wherein, the model of worm abrasion wheel as shown in figure 4, what deserves to be explained is, snail
The position vector of bar emery wheel curved surface is exactly corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system.
Under the processing technology of worm screw grinding worm, worm abrasion wheel and by the movement relation of mill gear workpieces as shown in figure 5,
It is pointed out that Fig. 5 is section plan, and in figure, ω1Represent by the rotating speed of mill gear workpieces, ω0Represent worm abrasion wheel
Rotating speed, v represent feed speed, l0Represent worm abrasion wheel start grinding when center arrive gear upper surface distance, l expression snail
Distance of the bar wheel grinding Process-centric position to gear upper surface.In fact, there are many protrusions on worm abrasion wheel surface, i.e.
Emery wheel data point, that is, worm abrasion wheel be appreciated that for by numerous emery wheel group of data points into and being cylinder by mill gear workpieces
Shape.
Further, in order to analyze worm abrasion wheel and by between mill gear workpieces relative motion relation, it is necessary to establish out
Worm abrasion wheel and the coordinate system by mill gear workpieces, as shown in fig. 6, in figure, i0,j0,k0Represent s0Each reference axis of coordinate system is square
To unit vector, wherein, s0Represent the moving coordinates being connected with ground gear workpieces；i1,j1,k1Represent s1Coordinate system is respectively sat
The unit vector of parameter positive direction, wherein, s1Represent with installing the fixed coordinate system being connected by the frame of mill gear workpieces；i2,
j2,k2Represent s2The unit vector of each reference axis positive direction of coordinate system, wherein, s2Represent worm abrasion wheel and by mill gear workpieces it
Between auxiliary coordinates；i3,j3,k3Represent s3The unit vector of each reference axis positive direction of coordinate system, wherein, s3Represent and installation snail
The connected fixed coordinate system of the frame of bar emery wheel；i4,j4,k4Represent s4The unit vector of each reference axis positive direction of coordinate system, its
In, s4Represent the moving coordinate system being connected with worm abrasion wheel.
Then, the movement locus of worm abrasion wheel is predicted by program, specifically, inputs the rotating speed w of worm abrasion wheel0For
1300r/min, feed speed v are 1.5mm/min, and single feeding depth is 10 μm, and emery wheel feeding total depth is 100 μm, snail
The diameter d of bar emery wheel is 30mm.Existing parameter substitution Matrix Computation Formulas is obtained in t lower grinding wheel data point coordinates in tooth
Take turns the transformation matrix of coordinate system：
In formula,Represent the angle that turns over of worm abrasion wheel, E represent during initial installation worm abrasion wheel with by mill gear workpieces it
Between along emery wheel radial direction distance, haThe feeding distance of worm abrasion wheel is represented,The angle turned over by mill gear workpieces is represented,
In calculating process, existing parameter, which is substituted into Matrix Computation Formulas and calculated, can make calculating process more simple and efficient.
Then, the emery wheel data point set r on worm abrasion wheel, by Coordinate Conversion, it can be obtained and sat by mill gear workpieces
Point set r under mark system1：
r1=M43M32M21M10r；
It is possible to further according to worm abrasion wheel and by the relative motion relation between mill gear workpieces, it is determined that both it
Between contact relation, so as to obtain by the final pattern of roll flute wheel workpiece surface.Specifically, will be by mill gear workpieces referring to Fig. 7
Surface be divided into the net region with certain resolution, with matrix W p, q represents that transverse and longitudinal grid sequence number is respectively p, during q
Height value of the net region central point along involute method direction.
Input time t, calculate worm abrasion wheel and by mill gear workpieces under the motion of t, all emery wheel data points
Movement position, and take emery wheel data point and the set by the point interferenceed of the net region of roll flute wheel workpiece surface.Specifically,
Choose and EFGH-B is designated as by one of net region of roll flute wheel workpiece surfaceEBFBGBH, and calculate and all be in the grid regions
Emery wheel data point in domain, height value of the central point along involute method direction in net region.
Then, judge whether the height value of the net region medium plain emery wheel data point is less than the net corresponding to the emery wheel data point
The elemental height of lattice point, if it is less, replacing the elemental height of corresponding mesh point with the height of the emery wheel data point；It is if big
In then illustrating that emery wheel data point with being interfered by roll flute wheel workpiece surface, does not process.According to the step, to by roll flute
The point taken turns in all net regions of workpiece surface is calculated, and is calculated repeatedly within process time, finally give by
The final pattern of roll flute wheel workpiece surface is, it is necessary to explanation, under the motion for t that above-mentioned all steps are calculated,
By the final pattern of roll flute wheel workpiece surface, moved always due to worm abrasion wheel and by mill gear workpieces within process time,
So to be calculated repeatedly within process time, can just finally give by the final pattern of roll flute wheel workpiece surface, such as Fig. 8 institutes
Show.
Then, according to roughness Sa in national standard, Sq, RSmDefinition：
In formula, Sa represents to be represented by the three of mill gear workpieces by the three-dimensional appearance arithmetic mean height of mill gear workpieces, Sq
Tie up pattern arithmetic mean height, RSmRepresent to be represented by roll flute by the average headway of the profile irregularity of mill gear workpieces, A
The average headway of the profile irregularity of workpiece is taken turns, Z (x, y) is represented by the three-dimensional appearance data dot matrix of mill gear workpieces, m
Represent by the three-dimensional appearance data dot matrix of mill gear workpieces, SiRepresent by the three-dimensional appearance data dot matrix of mill gear workpieces.
Calculate accordingly by the final structural parameters of roll flute wheel workpiece surface, i.e. it is respectively Sa=to obtain workpiece surface roughness
0.72μm；Sq=0.8741 μm；RSm=37.24 μm.Worm screw grinding worm surface is more accurately emulated so as to realize.
Embodiment 2
Corresponding with above method embodiment, the present embodiment discloses a kind of worm screw grinding worm surface microscopic topographic emulation
System, including：
First module：For measuring the part actual surface of worm abrasion wheel, it is actual that worm abrasion wheel is calculated based on measurement result
The shape characteristic parameter on surface, and the full surface of worm abrasion wheel is reconstructed according to the shape characteristic parameter, and will weight
Structure result is mapped on macroscopical curved surface, obtains worm abrasion wheel model；
Second unit：For according to worm abrasion wheel and the movement relation by mill gear workpieces, establishing coordinate conversion matrix, obtaining
To relative position of the worm abrasion wheel under by roll flute wheel coordinate system；
Third unit：For will be divided in the form of a grid by the surface of mill gear workpieces, calculating is all to be in institute
State height value of the emery wheel data point in net region in method direction of the net region central point along involute；
Unit the 4th：For by the initial of mesh point where the height value of each emery wheel data point and the emery wheel data point
Highly it is compared, takes new elemental height of the smaller value in both as mesh point, obtain by roll flute wheel workpiece surface most
End form looks, the final structural parameters by roll flute wheel workpiece surface are calculated, it is more accurate to worm screw grinding worm surface to realize
Emulation.
The concrete processing procedure of above-mentioned each unit can refer to above method embodiment, repeat no more.
As described above, the present invention provides a kind of worm screw grinding worm surface microscopic topographic emulation mode and system, it is right first
The multiple microscopic appearance for carving the worm abrasion wheel that measurement obtains is reconstructed, and maps that on worm screw curved surface, obtains based on actual measurement
The worm abrasion wheel microscopic appearance model of wheel face, worm abrasion wheel and the movement relation by mill gear workpieces are then analyzed, is obtained
Both contact relations, are further obtained by the final pattern of roll flute wheel workpiece surface, and be calculated by mill gear workpieces table
The final structural parameters in face；This method and system are based on actual measurement wheel face, can make simulation result more accurately so as to reducing tooth
The contact fatigue of transmission is taken turns, further improves service life.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, for the skill of this area
For art personnel, the present invention can have various modifications and variations.Within the spirit and principles of the invention, that is made any repaiies
Change, equivalent substitution, improvement etc., should be included in the scope of the protection.
Claims (8)
1. a kind of worm screw grinding worm surface microscopic topographic emulation mode, it is characterised in that comprise the following steps：
The part actual surface of worm abrasion wheel is measured, the shape characteristic of the worm abrasion wheel actual surface is calculated based on measurement result
Parameter, and the full surface of the worm abrasion wheel is reconstructed according to the shape characteristic parameter, and reconstruction result is mapped
Onto macroscopical curved surface, the model of the worm abrasion wheel is obtained to carry out following processing：
According to the worm abrasion wheel and the movement relation by mill gear workpieces, coordinate conversion matrix is established, obtains the worm screw sand
Take turns the relative position under the wheel coordinate system by roll flute；
The surface by mill gear workpieces is divided in the form of a grid, the comprehensive relative position calculates the worm screw
Height of all emery wheel data points in the net region in method direction of the net region central point along involute on emery wheel
Angle value；
By the height value of each emery wheel data point compared with the elemental height of mesh point where the emery wheel data point, two are taken
New elemental height of the smaller value as mesh point in person, the final pattern by roll flute wheel workpiece surface is obtained, calculate institute
State by the final structural parameters of roll flute wheel workpiece surface, worm screw grinding worm surface is more accurately emulated with realizing.
2. worm screw grinding worm surface microscopic topographic emulation mode according to claim 1, it is characterised in that
The model for obtaining the worm abrasion wheel specifically includes following steps：
(1) actual surface of the worm abrasion wheel is carved again, measures the part actual surface of the worm abrasion wheel, and tie according to measurement
Fruit calculates standard deviation, skewness and the kurtosis of the worm abrasion wheel actual surface；
(2) auto-correlation function of the worm abrasion wheel actual surface is sought：
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In formula, z (i, j) represents the data dot matrix of the part actual surface of the worm abrasion wheel of measurement, and i represents data dot matrix
OK, j represents data point matrix column, and n represents total line number of data dot matrix, and m represents total columns of data dot matrix, and k is represented
The row k of data dot matrix, h represent the h row of data dot matrix；
(3) auto-correlation coefficient matrix α is calculated according to the nonlinear equation of the auto-correlation functionk,h, the nonlinear equation is：
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Arrange the scope that can change, value 0,1 ... m-1；
(4) result of calculation obtained to step (1) is filtered processing, and it is actual to correct the worm abrasion wheel after handling after filtering
The skewness and kurtosis on surface：
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<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>b</mi>
<mn>2</mn>
</msubsup>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
In formula, SKηRepresent revised skewness, KηRepresent revised kurtosis, SKzRepresent the skewness before amendment, KzRepresent amendment
Preceding kurtosis, c represent data dot matrix z (i, j) total number, θaRepresent a-th chosen from data dot matrix z (i, j)
Number, θbRepresent b-th of the number chosen from data dot matrix z (i, j)；
(5) institute is passed through as the input of Johnson converting systems using standard deviation, revised skewness and revised kurtosis
Non-gaussian sequence η is obtained after stating the conversion of Johnson converting systemsI+k, j+h；
(6) the microcosmic shape of the full surface of worm abrasion wheel is reconstructed according to the auto-correlation coefficient matrix and the non-gaussian sequence
Looks level dot matrix zI, j：
<mrow>
<msub>
<mi>z</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</msubsup>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>h</mi>
</mrow>
</msub>
<msub>
<mi>&eta;</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mi>k</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mi>h</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
(7) surface equation of worm abrasion wheel is calculated：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>r</mi>
<mi>b</mi>
</msub>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
<mo>+</mo>
<mi>u</mi>
<mi> </mi>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<msub>
<mi>&lambda;</mi>
<mi>b</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>r</mi>
<mi>b</mi>
</msub>
<msub>
<mi>sin&theta;</mi>
<mi>&sigma;</mi>
</msub>
<mo>+</mo>
<mi>u</mi>
<mi> </mi>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
<msub>
<mi>cos&theta;</mi>
<mi>&sigma;</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>u</mi>
<mi> </mi>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<msub>
<mi>&lambda;</mi>
<mi>b</mi>
</msub>
<mo>-</mo>
<mi>&beta;</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
In formula, x1、y1And z1Represent corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system, rbRepresent base radius, λbTable
Show emery wheel lead angle, β represents helix parameter, θσRepresent angle variables of the tooth surface parameters between 0-2 π；
Then, the position vector of worm abrasion wheel curved surface
<mrow>
<mover>
<mi>r</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mover>
<mi>i</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>+</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mover>
<mi>j</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>+</mo>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mover>
<mi>k</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>;</mo>
</mrow>
In formula,The position vector of worm abrasion wheel curved surface is represented,The direction vector of denotation coordination axle；
Confirm the cooler normal vector of each point on the curved surface of worm abrasion wheel：
<mrow>
<mover>
<mi>n</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mover>
<mi>i</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>+</mo>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mover>
<mi>j</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>-</mo>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
<mover>
<mi>k</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>;</mo>
</mrow>
In formula,Represent the cooler normal vector of each point on worm abrasion wheel curved surface；
(8) by the micro- of the full surface of the worm abrasion wheel reconstructed according to the auto-correlation coefficient matrix with the non-gaussian sequence
See pattern level dot matrix zI, jThe cooler normal vector of each point, is mapped to actual snail on along worm abrasion wheel curved surface
On bar emery wheel curved surface, worm abrasion wheel model is obtained：
In formula,Expression and zI, jThe position vector of the final worm abrasion wheel curved surface of corresponding point,Expression and zI, jIt is corresponding
The position vector of the expression worm abrasion wheel curved surface of point,Represent worm abrasion wheel curved surface on zI, jThe unit normal arrow of corresponding point
Amount.
3. worm screw grinding worm surface microscopic topographic emulation mode according to claim 2, it is characterised in that establish coordinate
Transition matrix includes：
<mrow>
<msub>
<mi>M</mi>
<mn>21</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>E</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>h</mi>
<mi>a</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>M</mi>
<mn>32</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
In formula,Represent the angle that the worm abrasion wheel turns over, E represent during initial installation the worm abrasion wheel with it is described by roll flute
Along the distance of emery wheel radial direction, h between wheel workpieceaThe feeding distance of worm abrasion wheel is represented,Expression is turned over by mill gear workpieces
Angle.
4. worm screw grinding worm surface microscopic topographic emulation mode according to any one of claims 1 to 3, it is characterised in that
It is described to obtain specifically including following steps by the final pattern of roll flute wheel workpiece surface：
(1) net region with certain resolution is divided into by roll flute wheel workpiece surface by described, chooses one of grid
Region is designated as EFGH-BEBFBGBH；
(2) record the worm abrasion wheel with it is described by mill gear workpieces under the motion of t, the worm abrasion wheel is in grid
Region EFGH-BEBFBGBHInterior all emery wheel data points, and each emery wheel data point is calculated in net region centrally along involute
Method direction height value；
(3) by the height value of each emery wheel data point and grid EFGH-BEBFBGBHIn corresponding mesh point elemental height carry out
Compare, take new elemental height of the smaller value in both as mesh point；
(4) repeat the above steps (1)-(3), calculates all grids by roll flute wheel workpiece surface after being divided into net region
Emery wheel data point in region is calculated, and obtains the final pattern by roll flute wheel workpiece surface.
A kind of 5. worm screw grinding worm surface microscopic topographic analogue system, it is characterised in that including：
First module：For measuring the part actual surface of worm abrasion wheel, it is actual that the worm abrasion wheel is calculated based on measurement result
The shape characteristic parameter on surface, and the full surface of the worm abrasion wheel is reconstructed according to the shape characteristic parameter, and
Reconstruction result is mapped on macroscopical curved surface, obtains the model of the worm abrasion wheel；
Second unit：For according to the worm abrasion wheel and the movement relation by mill gear workpieces, establishing coordinate conversion matrix, obtaining
To relative position of the worm abrasion wheel under the wheel coordinate system by roll flute；
Third unit：For the surface by mill gear workpieces to be divided in the form of a grid, calculating is all to be in institute
State height value of the emery wheel data point in net region in method direction of the net region central point along involute；
Unit the 4th：For by the elemental height of mesh point where the height value of each emery wheel data point and the emery wheel data point
Be compared, take new elemental height of the smaller value in both as mesh point, obtain it is described by roll flute wheel workpiece surface most
End form looks, the final structural parameters by roll flute wheel workpiece surface are calculated, it is more accurate to worm screw grinding worm surface to realize
Emulation.
6. worm screw grinding worm surface microscopic topographic analogue system according to claim 5, it is characterised in that
Worm abrasion wheel model is obtained in the first module and specifically includes following steps：
(1) actual surface of the worm abrasion wheel is carved again, measures the part actual surface of the worm abrasion wheel, and tie according to measurement
Fruit calculates standard deviation, skewness and the kurtosis of the worm abrasion wheel actual surface；
(2) auto-correlation function of the worm abrasion wheel actual surface is sought：
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>,</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<mi>i</mi>
<mo>)</mo>
<mo>(</mo>
<mi>m</mi>
<mo>-</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
</mfrac>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mi>i</mi>
</mrow>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mi>j</mi>
</mrow>
</msubsup>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>+</mo>
<mi>k</mi>
<mo>,</mo>
<mi>k</mi>
<mo>+</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula, z (i, j) represents the data dot matrix of the part actual surface of the worm abrasion wheel of measurement, and i represents data dot matrix
OK, j represents data point matrix column, and n represents total line number of data dot matrix, and m represents total columns of data dot matrix, and k is represented
The row k of data dot matrix, h represent the h row of data dot matrix；
(3) auto-correlation coefficient matrix α is calculated according to the nonlinear equation of the auto-correlation functionk,l, the nonlinear equation is：
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>,</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mi>p</mi>
</mrow>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mi>p</mi>
</mrow>
</msubsup>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>h</mi>
</mrow>
</msub>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mi>p</mi>
<mo>,</mo>
<mi>h</mi>
<mo>+</mo>
<mi>q</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
In formula, p represents the scope that the row of data dot matrix can change, value 0,1 ... n-1；Q represents data dot matrix
Arrange the scope that can change, value 0,1 ... m-1；
(4) result of calculation obtained to step (1) is filtered processing, and it is actual to correct the worm abrasion wheel after handling after filtering
The skewness and kurtosis on surface：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>SK</mi>
<mi>z</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>3</mn>
</msubsup>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</msup>
</mfrac>
<msub>
<mi>SK</mi>
<mi>&eta;</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>K</mi>
<mi>z</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>&eta;</mi>
</msub>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mn>6</mn>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>c</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>b</mi>
<mn>2</mn>
</msubsup>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>c</mi>
</msubsup>
<msubsup>
<mi>&theta;</mi>
<mi>a</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
In formula, SKηRepresent revised skewness, KηRepresent revised kurtosis, SKzRepresent the skewness before amendment, KzRepresent amendment
Preceding kurtosis, c represent data dot matrix z (i, j) total number, θaRepresent a-th chosen from data dot matrix z (i, j)
Number, θbRepresent b-th of the number chosen from data dot matrix z (i, j)；
(5) institute is passed through as the input of Johnson converting systems using standard deviation, revised skewness and revised kurtosis
Non-gaussian sequence η is obtained after stating the conversion of Johnson converting systemsI+k, j+h；
(6) the microcosmic shape of the full surface of worm abrasion wheel is reconstructed according to the auto-correlation coefficient matrix and the non-gaussian sequence
Looks level dot matrix zI, j：
<mrow>
<msub>
<mi>z</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</msubsup>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>h</mi>
</mrow>
</msub>
<msub>
<mi>&eta;</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mi>k</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mi>h</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
(7) surface equation of worm abrasion wheel is calculated：
<mrow>
<mfenced open='{' close=''>
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<msub>
<mi>r</mi>
<mi>b</mi>
</msub>
<mi>cos</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
<mo>+</mo>
<mi>u</mi>
<mi>cos</mi>
<msub>
<mi>&lambda;</mi>
<mi>b</mi>
</msub>
<mi>sin</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>r</mi>
<mi>b</mi>
</msub>
<mi>sin</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
<mo>+</mo>
<mi>u</mi>
<mi>cos</mi>
<msub>
<mi>&lambda;</mi>
<mi>b</mi>
</msub>
<mi>cos</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>u</mi>
<mi>sin</mi>
<msub>
<mi>&lambda;</mi>
<mi>b</mi>
</msub>
<mo>-</mo>
<mi>&beta;</mi>
<msub>
<mi>&theta;</mi>
<mi>&sigma;</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
In formula, x1、y1And z1Represent corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system, rbRepresent base radius, λbTable
Show emery wheel lead angle, β represents helix parameter, θσRepresent angle variables of the tooth surface parameters between 0-2 π；
Then, the position vector of worm abrasion wheel curved surface
<mrow>
<mover>
<mi>r</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mover>
<mi>i</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>+</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mover>
<mi>j</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>+</mo>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mover>
<mi>k</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>;</mo>
</mrow>
In formula,The position vector of worm abrasion wheel curved surface is represented,The direction vector of denotation coordination axle；
Confirm the cooler normal vector of each point on the curved surface of worm abrasion wheel：
<mrow>
<mover>
<mi>n</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mover>
<mi>i</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>+</mo>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mover>
<mi>j</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>-</mo>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
<mover>
<mi>k</mi>
<mo>&RightArrow;</mo>
</mover>
<mo>;</mo>
</mrow>
In formula,Represent the cooler normal vector of each point on worm abrasion wheel curved surface；
(8) by the micro- of the full surface of the worm abrasion wheel reconstructed according to the auto-correlation coefficient matrix with the non-gaussian sequence
See pattern level dot matrix zI, jThe cooler normal vector of each point, is mapped to actual snail on along worm abrasion wheel curved surface
On bar emery wheel curved surface, worm abrasion wheel model is obtained：
In formula,Expression and zI, jThe position vector of the final worm abrasion wheel curved surface of corresponding point,Expression and zI, jRelatively
The position vector for the expression worm abrasion wheel curved surface that should be put,Represent worm abrasion wheel curved surface on zI, jThe unit normal of corresponding point
Vector.
7. worm screw grinding worm surface microscopic topographic analogue system according to claim 6, it is characterised in that described second
Coordinate conversion matrix is established in unit to be included：
<mrow>
<msub>
<mi>M</mi>
<mn>21</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>E</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msub>
<mi>h</mi>
<mi>a</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>M</mi>
<mn>32</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>sin&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>cos&lambda;</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
In formula,Represent the angle that the worm abrasion wheel turns over, E represent during initial installation the worm abrasion wheel with it is described by roll flute
Along the distance of emery wheel radial direction, h between wheel workpieceaThe feeding distance of the worm abrasion wheel is represented,Represent by mill gear workpieces
The angle turned over.
8. according to any described worm screw grinding worm surface microscopic topographic analogue system of claim 5 to 7, it is characterised in that
Obtain specifically including following steps by the final pattern of roll flute wheel workpiece surface in Unit the 4th：
(1) net region with certain resolution is divided into by roll flute wheel workpiece surface by described, chooses one of grid
Region is designated as EFGH-BEBFBGBH；
(2) record the worm abrasion wheel with it is described by mill gear workpieces under the motion of t, the worm abrasion wheel is in grid
Region EFGH-BEBFBGBHInterior all emery wheel data points, and each emery wheel data point is calculated in net region centrally along involute
Method direction height value；
(3) by the height value of each emery wheel data point and grid EFGH-BEBFBGBHIn corresponding mesh point elemental height carry out
Compare, take new elemental height of the smaller value in both as mesh point；
(4) repeat the above steps (1)-(3), calculates all grids by roll flute wheel workpiece surface after being divided into net region
Emery wheel data point in region is calculated, and obtains the final pattern by roll flute wheel workpiece surface.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111967096A (en) * | 2020-06-09 | 2020-11-20 | 中南大学 | Design method of diamond roller and worm grinding wheel |
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| CN111967096A (en) * | 2020-06-09 | 2020-11-20 | 中南大学 | Design method of diamond roller and worm grinding wheel |
| CN111967096B (en) * | 2020-06-09 | 2022-07-15 | 中南大学 | Design method of diamond roller and worm grinding wheel |
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| CN107609231B (en) | 2019-08-30 |
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