CN107609231B - 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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- CN107609231B CN107609231B CN201710736399.3A CN201710736399A CN107609231B CN 107609231 B CN107609231 B CN 107609231B CN 201710736399 A CN201710736399 A CN 201710736399A CN 107609231 B CN107609231 B CN 107609231B
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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, simulation result can be made more accurate to reduce gear-driven contact fatigue, further increase service life based on actual measurement wheel face.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 be reconstructed according to full surface of the shape characteristic parameter to worm abrasion wheel, and reconstruction result is mapped on macroscopical curved surface, obtain worm abrasion wheel model；Then worm abrasion wheel is calculated by the relative position under roll flute wheel coordinate system；Again by being divided in the form of a grid by the surface of mill gear workpieces 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.
Description
Technical field
The present invention relates to Grinding Process emulation field more particularly to a kind of worm screw grinding worm surface microscopic topographic are imitative
True method and system.
Background technique
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.Since 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 of great significance.
Macroshape and processing technology as specific to gear, 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
Big defect.
Therefore, it now needs to provide one kind based on actual measurement wheel face, simulation result can be made more accurate to reduce gear biography
Dynamic contact fatigue further increases the worm screw grinding worm surface microscopic topographic emulation mode and system of service life.
Summary of the invention
It is an object of that present invention to provide 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, simulation result can be made more accurate to reduce gear-driven contact fatigue, further mentioned
High service life.
To achieve the above object, the present invention provides a kind of worm screw grinding worm surface microscopic topographic emulation modes, including
Following steps:
The part actual surface for measuring worm abrasion wheel, 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 by the movement relation of mill gear workpieces, coordinate conversion matrix is established, obtains the snail
Relative position of the bar grinding wheel under the wheel coordinate system by roll flute；
The surface by mill gear workpieces is divided in the form of a grid, is calculated all in the net region
Interior grinding wheel data point is in net region central point along the height value in the method direction of involute；
The height value of each grinding wheel data point is compared with the elemental height of mesh point where the grinding wheel data point,
The smaller value in the two is taken as the new elemental height of mesh point, 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 present invention provides a kind of worm screw grinding worm surface microscopic topographic analogue systems, comprising:
First unit: 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 according to full surface of the shape characteristic parameter to the worm abrasion wheel
Structure, and reconstruction result is mapped on macroscopical curved surface, obtain the model of the worm abrasion wheel；
Second unit: for establishing coordinate conversion square according to the worm abrasion wheel and by the movement relation of mill gear workpieces
Battle array, obtains relative position of the worm abrasion wheel under the wheel coordinate system by roll flute；
Third unit: for dividing the surface by mill gear workpieces in the form of a grid, all places are calculated
In the grinding wheel data point in the net region in net region central point along the height value in the method direction of involute；
Unit the 4th: for by the initial of the height value of each grinding wheel data point and mesh point where the grinding wheel data point
Height is compared, and is taken the smaller value in the two as the new elemental height of mesh point, is obtained described by roll flute wheel workpiece surface
Final pattern, the final structural parameters by roll flute wheel workpiece surface are calculated, to realize to worm screw grinding worm surface more
Accurately emulation.
The invention has the following advantages:
The present invention provides a kind of worm screw grinding worm surface microscopic topographic emulation mode and system, measures first multiple quarter
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
Then worm abrasion wheel microscopic appearance model analyzes worm abrasion wheel and by the movement relation of mill gear workpieces, obtains the contact of the two
Relationship is further obtained by the final pattern of roll flute wheel workpiece surface, and is 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, simulation result can be made more accurate to reduce gear-driven connect
Touching fatigue, further increases service life.
Below with reference to accompanying drawings, the present invention is described in further detail.
Detailed description of the invention
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 that the preferred embodiment of the present invention is established and the coordinate system diagram by mill gear workpieces；
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.
Specific embodiment
The embodiment of the present invention is described in detail below in conjunction with attached 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 modes, comprising:
The part actual surface for measuring worm abrasion wheel, 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 by the movement relation of mill gear workpieces, coordinate conversion matrix is established, obtains the snail
Relative position of the bar grinding wheel under the wheel coordinate system by roll flute；
The surface by mill gear workpieces is divided in the form of a grid, is calculated all in the net region
Interior grinding wheel data point is in net region central point along the height value in the method direction of involute；
The height value of each grinding wheel data point is compared with the elemental height of mesh point where the grinding wheel data point,
The smaller value in the two is taken as the new elemental height of mesh point, 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 emulation of the grinding wheel of the white fused alumina worm abrasion wheel of model 89A/F80K6v as an example, to base in the present invention
It is illustrated in the wheel face emulation of actual measurement；It is right by taking the worm wheel grinding technique on REISHAUER RZ400 lathe as an example
Envelope track in the present invention, workpiece surface wound is at being illustrated.
Firstly, multiple quarter is carried out using white fused alumina worm abrasion wheel of the addition-type silicon rubber material to model 89A/F80K6v,
Then it is measured using pattern of the laser confocal microscope of model LSM700 to the multiple worm abrasion wheel carved and obtained,
In, the eyepiece multiple of laser confocal microscope is 10x.Choosing the sampling interval is 2.5 μm to some 1cm x1cm of worm abrasion wheel
The surface topography of range measures, 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 carries out noise reduction appropriate using firm Gaussian filter, obtained
To actual measurement worm abrasion wheel surface as shown in Figure 2.Obtained actual measurement worm abrasion wheel surface is filtered, needs to illustrate
It is that, since the process of filtering can make the parameter for surveying worm abrasion wheel surface, e.g., skewness and kurtosis generate deviation, so
The parameter to actual measurement worm abrasion wheel surface is needed further to be corrected after filtering processing, using formula are as follows:
In formula, SKηIndicate revised skewness, KηIndicate revised kurtosis, SKzSkewness before indicating amendment, KzIt indicates
Kurtosis before amendment, c indicate the total number of data dot matrix z (i, j), θaIndicate to choose from the data dot matrix z (i, j) the
A number, θbIndicate 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 system
Non-gaussian sequence ηI+k, j+h, calculate the auto-correlation function of worm abrasion wheel actual surface:
In formula, z (i, j) indicates that the data dot matrix of the part actual surface of the worm abrasion wheel of measurement, i indicate the data
The row of dot matrix, j indicate the data point matrix column, total line number of n representing matrix, total columns of m representing matrix, k expression
The row k of autocorrelation matrix, l indicate the l column of autocorrelation matrix.
And auto-correlation coefficient matrix α is calculated according to the nonlinear equation of auto-correlation functionk,l:
In formula, p indicates the range that the row of the data dot matrix can change, value 0,1 ... n-1；Q representing matrix
The range that can change of column, 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:
Grinding wheel 3 d surface topography is reconstructed according to characteristic parameter, obtains reconstruct wheel face as shown in Figure 3.
It is worth noting that above-mentioned calculating process is all each parameter in the calculating of plane, it is contemplated that the macroscopic view of worm abrasion wheel
Shape, therefore, it needs for calculated result obtained above to be mapped on macroscopical curved surface, obtains final worm abrasion wheel model.Specifically
Ground first calculates the surface equation of worm abrasion wheel:
In formula, x1、y1And z1Indicate corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system, rbIndicate base radius,
λbIndicate that grinding wheel lead angle, β indicate helix parameter, θσIndicate angle variables of the tooth surface parameters between 0-2 π.
Then, the position vector of worm abrasion wheel curved surface:
In formula,Indicate the position vector of worm abrasion wheel curved surface,The direction vector of indicates coordinate axis.
Then, confirm the cooler normal vector of each point on the curved surface of worm abrasion wheel:
In formula,Indicate the unit normal of each point on worm abrasion wheel curved surface；
Due to the z in the above calculating process, 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 needs the height dot matrix along on worm abrasion wheel curved surface
The normal orientation of each point is mapped on actual worm abrasion wheel curved surface, relevant parameter is substituted into formulaWhereinExpression and zI, jThe position vector of the final worm abrasion wheel curved surface of corresponding point,Table
Show and zI, jThe position vector of the expression worm abrasion wheel curved surface of corresponding point,Indicate worm abrasion wheel curved surface on zI, jIt is corresponding
The cooler normal vector of point, the worm abrasion wheel model diameter being calculated are 30mm, wherein the model of worm abrasion wheel such as Fig. 4 institute
Show, it is worth noting that, the position vector of worm abrasion wheel curved surface is exactly corresponding seat of the worm abrasion wheel curved surface in rectangular coordinate system
Mark.
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 should be pointed out that Fig. 5 is section plan, and in figure, ω1It indicates by the revolving speed of mill gear workpieces, ω0Indicate worm abrasion wheel
Revolving speed, v indicate feed speed, l0Indicate distance of the center to gear upper surface, l expression snail when worm abrasion wheel starts grinding
Distance of the bar wheel grinding Process-centric position to gear upper surface.In fact, there are many protrusions on worm abrasion wheel surface, that is,
Grinding wheel data point, that is, worm abrasion wheel be understood that for by numerous grinding wheel group of data points at, and by mill gear workpieces be cylinder
Shape.
Further, it in order to analyze worm abrasion wheel and by between mill gear workpieces relative motion relation, needs to establish out
Worm abrasion wheel and by the coordinate system of mill gear workpieces, as shown in fig. 6, in figure, i0,j0,k0Indicate s0Each reference axis of coordinate system is square
To unit vector, wherein s0Indicate the moving coordinates being connected with ground gear workpieces；i1,j1,k1Indicate s1Coordinate system is respectively sat
The unit vector of parameter positive direction, wherein s1Indicate the fixed coordinate system being connected with installation by the rack of mill gear workpieces；i2,
j2,k2Indicate s2The unit vector of each reference axis positive direction of coordinate system, wherein s2Indicate worm abrasion wheel and by mill gear workpieces it
Between auxiliary coordinates；i3,j3,k3Indicate s3The unit vector of each reference axis positive direction of coordinate system, wherein s3It indicates and installation snail
The connected fixed coordinate system of the rack of bar grinding wheel；i4,j4,k4Indicate s4The unit vector of each reference axis positive direction of coordinate system,
In, s4Indicate the moving coordinate system being connected with worm abrasion wheel.
Then, predict that the motion profile of worm abrasion wheel specifically inputs the revolving speed w of worm abrasion wheel by program0For
1300r/min, feed speed v are 1.5mm/min, and single feeding depth is 10 μm, and grinding wheel feeding total depth is 100 μm, snail
The diameter d of bar grinding wheel is 30mm.Existing parameter substitution Matrix Computation Formulas is obtained in t moment lower grinding wheel data point coordinate in tooth
Take turns the transformation matrix of coordinate system:
In formula,Indicate the angle that turns over of worm abrasion wheel, E indicate when initial installation worm abrasion wheel with by mill gear workpieces it
Between along grinding wheel radial direction distance, haIndicate the feeding distance of worm abrasion wheel,Indicate the angle turned over by mill gear workpieces,
In calculating process, existing parameter, which is substituted into Matrix Computation Formulas calculating, can make calculating process more simple and efficient.
Then, the grinding wheel data point set r on worm abrasion wheel, is converted by coordinate, and available its is sat by mill gear workpieces
Point set r under mark system1:
r1=M43M32M21M10r；
It is possible to further determine the two according to worm abrasion wheel and by the relative motion relation between mill gear workpieces
Between contact relation, to obtain by the final pattern of roll flute wheel workpiece surface.It 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 indicates that transverse and longitudinal grid serial number is respectively p, when q
Height value of the net region central point along involute method direction.
Input time t calculates worm abrasion wheel and by mill gear workpieces under the movement of t moment, all grinding wheel data points
Movement position, and take grinding wheel data point with by the set for the point of the net region of roll flute wheel workpiece surface interferenceed.Specifically,
It chooses and EFGH-B is denoted as by one of net region of roll flute wheel workpiece surfaceEBFBGBH, and calculate all in the grid regions
Grinding 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 net corresponding to the grinding 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 grinding wheel data point；If big
In then illustrating that grinding wheel data point is not interfered with by roll flute wheel workpiece surface, be not processed.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 obtain by
The final pattern of roll flute wheel workpiece surface, it should be noted that above-mentioned all steps be calculated be t moment movement under,
By the final pattern of roll flute wheel workpiece surface, moved always within process time due to worm abrasion wheel and by mill gear workpieces,
So to be calculated repeatedly within process time, can just finally obtain by the final pattern of roll flute wheel workpiece surface, such as Fig. 8 institute
Show.
Then, according to roughness Sa in national standard, Sq, RSmDefinition:
In formula, Sa indicates that, by the three-dimensional appearance arithmetic mean height of mill gear workpieces, Sq is indicated by the three of mill gear workpieces
Tie up pattern arithmetic mean height, RSmIndicate that, by the average headway of the profile irregularity of mill gear workpieces, A is indicated by roll flute
The average headway of the profile irregularity of workpiece is taken turns, Z (x, y) is indicated by the three-dimensional appearance data dot matrix of mill gear workpieces, m
It indicates by the three-dimensional appearance data dot matrix of mill gear workpieces, SiIt indicates by the three-dimensional appearance data dot matrix of mill gear workpieces.
It is calculated accordingly by the final structural parameters of roll flute wheel workpiece surface, that is, obtaining workpiece surface roughness is respectively Sa=
0.72μm；Sq=0.8741 μm；RSm=37.24 μm.Worm screw grinding worm surface is more accurately emulated to realize.
Embodiment 2
Corresponding to the above method embodiment, the present embodiment discloses a kind of worm screw grinding worm surface microscopic topographic emulation
System, comprising:
First unit: for measuring the part actual surface of worm abrasion wheel, it is practical 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 weigh
Structure result is mapped on macroscopical curved surface, obtains worm abrasion wheel model；
Second unit: for establishing coordinate conversion matrix, obtaining according to worm abrasion wheel and by the movement relation of mill gear workpieces
To worm abrasion wheel by the relative position under roll flute wheel coordinate system；
Third unit: it for will be divided in the form of a grid by the surface of mill gear workpieces, calculates all in institute
State height value of the grinding wheel data point in net region in net region central point along the method direction of involute；
Unit the 4th: for by the initial of the height value of each grinding wheel data point and mesh point where the grinding wheel data point
Height is compared, and the smaller value in the two is taken to obtain by roll flute wheel workpiece surface most as the new elemental height of mesh point
End form looks calculate the final structural parameters by roll flute wheel workpiece surface, more acurrate 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
Then the worm abrasion wheel microscopic appearance model of wheel face is analyzed worm abrasion wheel and by the movement relation of mill gear workpieces, is obtained
The contact relation of the two is further obtained by the final pattern of roll flute wheel workpiece surface, and is calculated by mill gear workpieces table
The final structural parameters in face；This method and system are based on actual measurement wheel face, simulation result can be made more accurate to reduce tooth
The contact fatigue for taking turns transmission, further increases service life.
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field
For art personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair
Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (6)
1. a kind of worm screw grinding worm surface microscopic topographic emulation mode, which comprises the following steps:
The part actual surface for measuring worm abrasion wheel, 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 by the movement relation of 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
The height in method direction of all grinding wheel data points in the net region in net region central point along involute on grinding wheel
Angle value；
The height value of each grinding wheel data point is compared with the elemental height of mesh point where the grinding wheel data point, takes two
New elemental height of the smaller value as mesh point in person obtains the final pattern by roll flute wheel workpiece surface, calculates institute
It states by the final structural parameters of roll flute wheel workpiece surface, worm screw grinding worm surface is more accurately emulated with realizing；
Wherein, the model for obtaining the worm abrasion wheel specifically includes the following steps:
(1) actual surface for carving the worm abrasion wheel again measures the part actual surface of the worm abrasion wheel, and is tied 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:
In formula, z (i, j) indicates that the data dot matrix of the part actual surface of the worm abrasion wheel of measurement, i indicate data dot matrix
Row, j indicate that data point matrix column, n indicate total line number of data dot matrix, and m indicates that total columns of data dot matrix, k indicate
The row k of data dot matrix, h indicate the h column 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 are as follows:
In formula, p indicates the range that the row of data dot matrix can change, value 0,1 ... n-1；Q indicates data dot matrix
Arrange the range that can change, value 0,1 ... m-1；
(4) calculated result obtained to step (1) is filtered, and it is practical to correct the worm abrasion wheel after filtering processing
The skewness and kurtosis on surface:
In formula, SKηIndicate revised skewness, KηIndicate revised kurtosis, SKzSkewness before indicating amendment, KzIndicate amendment
Preceding kurtosis, c indicate the total number of data dot matrix z (i, j), θaIt indicates a-th chosen from data dot matrix z (i, j)
Number, θbIndicate b-th of the number chosen from data dot matrix z (i, j)；
(5) institute is passed through as the input of Johnson converting system using standard deviation, revised skewness and revised kurtosis
Non-gaussian sequence η is obtained after stating the conversion of Johnson converting systemI+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:
(7) surface equation of worm abrasion wheel is calculated:
In formula, x1、y1And z1Indicate corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system, rbIndicate base radius, λbTable
Show that grinding wheel lead angle, β indicate helix parameter, θσIndicate angle variables of the tooth surface parameters between 0-2 π, u is the base on flank of tooth surface
This parameter；
Then, the position vector of worm abrasion wheel curved surface
In formula,Indicate the position vector of worm abrasion wheel curved surface,The direction vector of indicates coordinate axis；
Confirm the cooler normal vector of each point on the curved surface of worm abrasion wheel:
In formula,Indicate 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 and the non-gaussian sequence
See pattern level dot matrix zI, jAlong the cooler normal vector of point each on worm abrasion wheel curved surface, it is mapped to actual snail
On bar grinding 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,Indicate worm abrasion wheel curved surface on zI, jThe unit normal of corresponding point
Vector.
2. worm screw grinding worm surface microscopic topographic emulation mode according to claim 1, which is characterized in that establish coordinate
Transition matrix includes:
In formula,Indicate the angle that the worm abrasion wheel turns over, E indicates when initial installation the worm abrasion wheel and described by roll flute
Take turns the distance between workpiece along grinding wheel radial direction, haIndicate the feeding distance of worm abrasion wheel,Expression is turned over by mill gear workpieces
Angle.
3. worm screw grinding worm surface microscopic topographic emulation mode according to claim 1 or 2, which is characterized in that
It is described obtain by the final pattern of roll flute wheel workpiece surface specifically includes the following steps:
(1) net region with certain resolution is divided by roll flute wheel workpiece surface by described, chooses one of grid
Region is denoted as EFGH-BEBFBGBH；
(2) record the worm abrasion wheel and it is described by mill gear workpieces under the movement of t moment, the worm abrasion wheel is in grid
Region EFGH-BEBFBGBHInterior all grinding wheel data points, and each grinding wheel data point is calculated at net region center along involute
Method direction height value；
(3) by the height value of each grinding wheel data point and grid EFGH-BEBFBGBHIn corresponding mesh point elemental height carry out
Compare, takes the smaller value in the two as the new elemental height of mesh point；
(4) repeat the above steps (1)-(3), calculates all grids by roll flute wheel workpiece surface after being divided into net region
Grinding wheel data point in region is calculated, and the final pattern by roll flute wheel workpiece surface is obtained.
4. a kind of worm screw grinding worm surface microscopic topographic analogue system characterized by comprising
First unit: for measuring the part actual surface of worm abrasion wheel, it is practical 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, the model of the worm abrasion wheel is obtained；
Second unit: for establishing coordinate conversion matrix, obtaining according to the worm abrasion wheel and by the movement relation of mill gear workpieces
To relative position of the worm abrasion wheel under the wheel coordinate system by roll flute；
Third unit: it for dividing the surface by mill gear workpieces in the form of a grid, calculates all in institute
State height value of the grinding wheel data point in net region in net region central point along the method direction of involute；
Unit the 4th: for by the elemental height of mesh point where the height value of each grinding wheel data point and the grinding wheel data point
Be compared, take the smaller value in the two as the new elemental height of mesh point, obtain it is described by roll flute wheel workpiece surface most
End form looks calculate the final structural parameters by roll flute wheel workpiece surface, more acurrate to worm screw grinding worm surface to realize
Emulation；
Wherein, obtain worm abrasion wheel model in the first unit specifically includes the following steps:
(1) actual surface for carving the worm abrasion wheel again measures the part actual surface of the worm abrasion wheel, and is tied 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:
In formula, z (i, j) indicates that the data dot matrix of the part actual surface of the worm abrasion wheel of measurement, i indicate data dot matrix
Row, j indicate that data point matrix column, n indicate total line number of data dot matrix, and m indicates that total columns of data dot matrix, k indicate
The row k of data dot matrix, h indicate the h column 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 are as follows:
In formula, p indicates the range that the row of data dot matrix can change, value 0,1 ... n-1；Q indicates data dot matrix
Arrange the range that can change, value 0,1 ... m-1；
(4) calculated result obtained to step (1) is filtered, and it is practical to correct the worm abrasion wheel after filtering processing
The skewness and kurtosis on surface:
In formula, SKηIndicate revised skewness, KηIndicate that revised kurtosis, SKz indicate the skewness before amendment, KzIndicate amendment
Preceding kurtosis, c indicate the total number of data dot matrix z (i, j), θaIt indicates a-th chosen from data dot matrix z (i, j)
Number, θbIndicate b-th of the number chosen from data dot matrix z (i, j)；
(5) institute is passed through as the input of Johnson converting system using standard deviation, revised skewness and revised kurtosis
Non-gaussian sequence η is obtained after stating the conversion of Johnson converting systemI+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:
(7) surface equation of worm abrasion wheel is calculated:
In formula, x1、y1And z1Indicate corresponding coordinate of the worm abrasion wheel curved surface in rectangular coordinate system, rbIndicate base radius, λbTable
Show that grinding wheel lead angle, β indicate helix parameter, θσIndicate angle variables of the tooth surface parameters between 0-2 π, u is the base on flank of tooth surface
This parameter；
Then, the position vector of worm abrasion wheel curved surface
In formula,Indicate the position vector of worm abrasion wheel curved surface,The direction vector of indicates coordinate axis；
Confirm the cooler normal vector of each point on the curved surface of worm abrasion wheel:
In formula,Indicate 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 and the non-gaussian sequence
See pattern level dot matrix zI, jAlong the cooler normal vector of point each on worm abrasion wheel curved surface, it is mapped to actual snail
On bar grinding 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,Indicate worm abrasion wheel curved surface on zI, jThe unit normal of corresponding point
Vector.
5. worm screw grinding worm surface microscopic topographic analogue system according to claim 4, which is characterized in that described second
Coordinate conversion matrix is established in unit includes:
In formula,Indicate the angle that the worm abrasion wheel turns over, E indicates when initial installation the worm abrasion wheel and described by roll flute
Take turns the distance between workpiece along grinding wheel radial direction, haIndicate the feeding distance of the worm abrasion wheel,It indicates by mill gear workpieces
The angle turned over.
6. worm screw grinding worm surface microscopic topographic analogue system according to claim 4 or 5, which is characterized in that
Obtained in Unit the 4th by the final pattern of roll flute wheel workpiece surface specifically includes the following steps:
(1) net region with certain resolution is divided by roll flute wheel workpiece surface by described, chooses one of grid
Region is denoted as EFGH-BEBFBGBH；
(2) record the worm abrasion wheel and it is described by mill gear workpieces under the movement of t moment, the worm abrasion wheel is in grid
Region EFGH-BEBFBGBHInterior all grinding wheel data points, and each grinding wheel data point is calculated at net region center along involute
Method direction height value；
(3) by the height value of each grinding wheel data point and grid EFGH-BEBFBGBHIn corresponding mesh point elemental height carry out
Compare, takes the smaller value in the two as the new elemental height of mesh point；
(4) repeat the above steps (1)-(3), calculates all grids by roll flute wheel workpiece surface after being divided into net region
Grinding wheel data point in region is calculated, and the final pattern by roll flute wheel workpiece surface is obtained.
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