CN108168479A - Circumferential distribution pore group position degree assessment method based on coordinate transform and array sort - Google Patents
Circumferential distribution pore group position degree assessment method based on coordinate transform and array sort Download PDFInfo
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- CN108168479A CN108168479A CN201810016125.1A CN201810016125A CN108168479A CN 108168479 A CN108168479 A CN 108168479A CN 201810016125 A CN201810016125 A CN 201810016125A CN 108168479 A CN108168479 A CN 108168479A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
Abstract
The invention discloses a kind of circumferential distribution pore group position degree assessment methods based on coordinate transform and array sort, a hole is as tangential benchmark optionally on the rotary type part to be measured with circumferential distribution pore group, obtain the location information of part circumferential distribution pore, and establish coordinate system, according to tolerance, the desired tolerance circle in each hole is found out;Be obtained under coordinate system the hole heart in hole away from and each hole heart line angle;Circle is drawn with the hole heart line in first hole, decile is carried out to intersecting arcs, group postrotational multigroup position in hole is determined with each Along ent;The position error in the hole in multigroup location hole group is obtained;Bubble sort is carried out, the accurate location degree error amount of hole in piece part group is obtained, the position degree of the rotary type part to be measured with circumferential distribution pore group is accurately evaluated.Wide range of measurement of the present invention, testing cost is low, and measurement efficiency is high, and processing mode is simple, without the direction for judging each hole and tangentially deviating, you can obtain the accurate location degree error in each hole.
Description
Technical field
The invention belongs to the technical field of quality detection of the rotary part with circumferential distribution pore group, and in particular to one
Circumferential distribution pore group position degree assessment method of the kind based on coordinate transform and array sort.
Background technology
In Mechanical Processing Industry, slewing parts are a kind of critically important parts, are widely used in automobile, aviation, ship
Circumference uniform distribution hole system is often distributed on this kind of part in the industries such as oceangoing ship and industrial robot, as shown in Figure 1, (a) represents band in figure
There is circumferential distribution pore group part schematic diagram, (b) represents the sectional view using part after rotation cutting, and (c) represents part tolerance band
Schematic diagram, to ensure the assembly relation between part, hole group generally requires the very accurate of processing.
Important component of the industrial robot as high-end intelligent manufacturing equipment, automatization level is high, and application places are wide,
It is the important support technology of advanced manufacturing industry.RV retarders and harmonic speed reducer be apply it is main on industrial robot joint
Two class retarders.RV retarders compared with harmonic speed reducer have larger fatigue strength, rigidity and service life, stable drive, thus its
It is widely used in industrial robot transmission system.RV retarders are by gear shaft, planetary gear, Cycloidal Wheel, pinwheel, crank axle, needle tooth
The compositions such as shell and planet carrier.Planet carrier and Cycloidal Wheel are as its important part (hereinafter referred to as part), and machining accuracy is to complete machine
Assembling quality, rotating accuracy and service life have direct influence.The position degree precision of the circle distribution axis hole hole group of part,
Load distribution, transmission capacity, fretting wear and the noise objective of retarder are directly affected, and then influences domestic robot industry
Development, therefore must assure that the position of position degree precision in hole system group between each hole and hole system relative to machining benchmark in processing
Degree of putting precision.
The measurement of domestic device to hole group position degree at present mainly has dedicated gauge and measurement of coordinates two ways with evaluation.Pass through
Dedicated gauge carries out workpiece qualification judgement, simple and easy to operate, but can only to evaluate workpiece qualified or not for the method, it is impossible to
Measure the exact value of position error.And three coordinate measuring machine is measurement of coordinates Typical Representative, can be accurately measured multiple
The location coordinate information of miscellaneous structure and hole group, but measurement beat is longer, it is of high cost, it is suitble to being inspected by random samples under the line of part, and
There are strict requirements to measuring environment, the on-line measurement to production line can not be met.In recent years, for certain part special measurement
The research of instrument has obtained significant progress, and this special purpose measuring instrument generally realizes data processing using software kit, for
Algorithm evaluation in terms of position degree is complex.
In actually detected, if selecting different hole as tangential positioning datum, the tangential deviation of same holes is general
Difference, this causes the final measurement error of workpiece larger, easily causes erroneous judgement.Traditional assessment method is directed to different design requirements,
By the way that carry out coordinate transform is translated or rotated under polar coordinates or rectangular coordinate system, circumferential apertures group position degree is assessed,
It needs to find the extreme point of rotation and judges direction of rotation during evaluation, direction of rotation and rotation angle and the tangential mistake in each hole
Difference is related, and due to the randomness of work pieces process, each each hole of workpiece is not known in tangential offset direction, the judgement of direction of rotation
The concrete condition for workpiece is needed, processing mode is complicated and changeable, is not easy to grasp.
Invention content
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that it provides a kind of based on coordinate
Transformation and the circumferential distribution pore group position degree assessment method of array sort, applied to dedicated location degree measuring instrument, are realized to having
The accurate evaluation of the position degree of the rotary part of circumferential distribution pore group.
The present invention uses following technical scheme:
Circumferential distribution pore group position degree assessment method based on coordinate transform and array sort, includes the following steps:
S1, optionally there is a hole on the rotary type part to be measured of circumferential distribution pore group as tangential benchmark, to obtain zero
The location information in m hole of part circle distribution, and coordinate system is established, according to tolerance, find out the desired tolerance circle in each hole;
Be obtained under S2, the coordinate system established in step S1 the hole heart in m hole away from and each hole heart line angle;
S3, circle is drawn with the hole heart line in first hole, intersected with its ideal position degree tolerance circle, n etc. is carried out to intersecting arcs
Point, group postrotational n groups position in hole is determined with each Along ent;
S4, translation rotating coordinate transformation is carried out to step S3, under new coordinate system, the m in n group location hole groups is obtained
The position error in a hole;
S5, bubble sort is carried out to step S4 results, the accurate location degree error amount of hole in piece part group is obtained, to circumference
The position degree of the rotary type part to be measured of distribution hole group is accurately evaluated.
Specifically, in step S1, using part outer circle to be measured as detection benchmark, using first hole on part to be measured as tangentially
Theoretical hole heart position and circle center line connecting are set as x-axis, establish cartesian coordinate system, find out the hole in m hole in a coordinate system by benchmark
Heart ideal position m (Xm', Ym'), it is that m Tolerance of Degree of position is made in the center of circle by radius, perfect apertures heart position of its Tolerance of Degree of position
Circle, the angle of theoretical hole heart line from each other is 360/m °, carries out data acquisition and obtains part circumferential distribution pore group to be measured
Location information, and construct the actual measurement center location m (X in m holem, Ym) and the outer circle center of circle Measured Coordinates (X0, Y0)。
Specifically, in step S2, according to the Measured Coordinates information of each hole center of circle in a coordinate system, actual measurement m is calculated
The hole heart in hole is away from LmIt is as follows:
Wherein, m (Xm, Ym) actual measurement center location for m hole, the Measured Coordinates in the outer circle center of circle are (X0, Y0)。
Further, m=3, according to the hole heart in 3 holes of actual measurement away from L1、L2、L3The hole heart line in 3 holes of actual measurement is calculated
Angle α12And α13It is as follows:
Specifically, in step S3, when each hole actual apertures heart away from and 2 times away from its difference absolute value of the theoretical hole heart be less than to be measured zero
During the Tolerance of Degree of position value of part circumferential apertures requirement, with the hole heart in first hole on part to be measured away from circular arc is made for radius, with its position
Degree of putting tolerance circle is intersecting, takes n Along ents in the intersecting arcs in tolerance circle, the position each put is followed successively by I counterclockwise1、
I2、...、In。
Specifically, in step S4, the hole heart line in m hole of determining angle is translated in a coordinate system first, makes outer circle
The center of circle is overlapped with coordinate origin, then it is rotated around coordinate origin, and the hole heart line in first hole is made first to rotate to I1Position
As initial position, under new coordinate system, the perfect apertures heart m (X in m holem', Ym') position is constant, obtain the hole heart in first hole
Then from initial position using Δ θ as rotation angle, it is rotated successively to I for the angle theta of line and x-axis2、......、InPosition,
The hole group of n kind different locations is can obtain, the hole heart that m hole of circle distribution is respectively obtained according to the hole group of n kind different locations is sat
Mark m (Xm", Ym") by being compared with perfect apertures heart position coordinates, calculates the position error in m hole of part circumference uniform distribution to be measured
fm。
Further, rotation angle Δ θ is:
Wherein:The hole heart line in first hole and the angle theta of x-axis are:
Wherein:L1For first hole actual apertures heart away from the design hole heart that, l is circumferential distribution pore away from.
Further, m=3, the 1 (X of hole heart coordinate in 3 holes of circle distribution1", Y1″)、2(X2", Y2″)、3(X3", Y3″)
It calculates as follows:
Wherein, α12And α13To survey the hole heart line angle in 3 holes, L1、L2、L3The actual apertures heart for three holes is away from l is
The design hole heart of circumferential distribution pore away from.
Further, m=3, the position error f in 3 circumference uniform distribution holes of part to be measured1、f2、f3For:
Specifically, in step S5, the n groups position that part circumference uniform distribution hole to be measured is in different rotary position is obtained by step S4
Degree of putting error is respectively ranked up the position degree in m hole in every group, and the maximum value extracted out in every group of data forms an array
W, element W1、W2、...、Wn, it is corresponding with n group position degrees, then the numerical value in array W is ranked up, finds out numerical value most
Small element Wi, corresponding i-th group of position degree is final required circumference uniform distribution hole relative to the part outer circle center of circle to be measured
Position error fm。
Compared with prior art, the present invention at least has the advantages that:
The present invention is based on coordinate transform and the circumferential distribution pore group position degree assessment method of array sort, setting based on part
Benchmark is counted as detection benchmark, by the desired tolerance in each hole of its circle distribution circle and the actual apertures heart away from intersecting arcs decile,
Determine the rotary course of hole group, the original position-information obtained to measuring device is handled.In part circle distribution to be measured
Hole it is uncertain in tangential offset direction, no matter select which hole as tangential benchmark, in multigroup spin data
After being ranked up comparison, the accurate position error in each hole can be obtained.
Further, each hole is gone out as detection baseline configuration using part benchmark outer circle to be measured and surveys center location and the outer circle center of circle
Measured Coordinates, avoid due to error caused by Reference misalignment, for subsequent coordinates transformation lay the foundation.
Further, according to Measured Coordinates information obtain the hole heart away from and hole heart line angle, can be by the hole heart away from whether surpassing
Requirement of going on a public errand directly judges whether part is qualified, and determine the position of hole group rotation transformation.
Further, the position error in hole is obtained in translation rotating coordinate transformation, sentences without progress rotation angle and direction
It is disconnected, translation rotation transformation is carried out in this way, and n groups hole group position error is obtained, it is convenient accurate, establish base to find optimal solution
Plinth.
Further, using bubble sort, after n groups hole group position error is obtained, array is carried out by ranking method
Sequence, can conveniently find makes group each hole true position error worst error value in hole be optimized to minimum position, you can is obtained
The optimal solution of hole group position degree.
In conclusion assessment method wide range of measurement of the present invention, testing cost is low, and measurement efficiency is high, and processing mode is simple,
It need not judge the direction that each hole tangentially deviates, you can obtain the accurate location degree error in each hole.
Below by drawings and examples, technical scheme of the present invention is described in further detail.
Description of the drawings
Fig. 1 is part circumferential distribution pore group Tolerance of Degree of position schematic diagram, wherein, (a) is with circumferential distribution pore group part
Schematic diagram, (b) are using the sectional view of part after rotation cutting, and (c) is hole in piece part group positional tolerance zone schematic diagram;
Fig. 2 is assessment method flow diagram of the present invention;
Fig. 3 is part circumferential distribution pore theory tolerance of the present invention circle and eyeball distribution schematic diagram;
Fig. 4 is intersecting arcs decile of the present invention and hole in piece part I1Rotation position schematic diagram;
Fig. 5 evaluates schematic diagram for part circumferential distribution pore group position degree of the present invention.
Specific embodiment
Referring to Fig. 2, the present invention provides a kind of circumferential distribution pore group position degrees based on coordinate transform and array sort
Assessment method includes the following steps:
S1, optionally there is a hole on the rotary type part to be measured of circumferential distribution pore group as tangential benchmark, to utilize measurement
Device carries out data acquisition, obtains the location information in m hole of part circle distribution, and establishes coordinate system, according to the tolerance of design
It is required that find out the desired tolerance circle in m hole;
Be obtained under S2, the coordinate system established in step S1 the hole heart in m hole away from and each hole heart line angle;
S3, circle is drawn with the hole heart line in first hole, intersected with its ideal position degree tolerance circle, n etc. is carried out to intersecting arcs
Point, group postrotational n groups position in hole is determined with each Along ent;
S4, translation rotating coordinate transformation is carried out to step S3, under new coordinate system, the m in n group location hole groups is obtained
The position error in a hole;
S5, bubble sort is carried out to result in step S4, the accurate location degree error amount of hole in piece part group is obtained, to having circle
The position degree of the rotary type part to be measured of all distribution hole groups is accurately evaluated.
Purpose, technical scheme and advantage to make the embodiment of the present invention are clearer, below in conjunction with the embodiment of the present invention
In attached drawing, the technical solution in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is
Part of the embodiment of the present invention, instead of all the embodiments.The present invention being described and shown in usually here in attached drawing is real
Applying the component of example can be arranged and be designed by a variety of different configurations.Therefore, the present invention to providing in the accompanying drawings below
The detailed description of embodiment be not intended to limit the range of claimed invention, but be merely representative of the selected of the present invention
Embodiment.Based on the embodiments of the present invention, those of ordinary skill in the art are obtained without creative efforts
The every other embodiment obtained, shall fall within the protection scope of the present invention.
Embodiment
It is specific to walk by RV retarder 320E planet carriers with the specific embodiment of the present invention is described for Cycloidal Wheel
It is rapid as follows:
S1, using planet carrier outer circle as detection benchmark, using first hole as tangential benchmark, by its theoretical hole heart position with
Circle center line connecting is set as x-axis, establishes cartesian coordinate system, finds out the 1 (X of ideal position of the three hole hole hearts in a coordinate system1', Y1′)、2
(X2', Y2') and 3 (X3', Y3'), it is that three position degree public affairs are made in the center of circle using its Tolerance of Degree of position as radius, perfect apertures heart position
Difference circle as shown in figure 3, the angle of theoretical hole heart line from each other is 120 degree, carries out data acquisition using measuring device, obtains
The location information of planet carrier circumferential distribution pore group is taken, and constructs the 1 (X of actual measurement center location in three holes1, Y1)、2(X2, Y2)、3
(X3, Y3) and the outer circle center of circle Measured Coordinates (X0, Y0), L in figure1、L2、L3Represent that hole 1, hole 2, hole 3 and part outer circle are real respectively
The distance in the center of circle is surveyed, i.e., the hole heart is away from α12Represent L1With L2Angle, α13Represent L1With L3Angle;
S2, the Measured Coordinates information according to each hole center of circle in a coordinate system, the angle α of the realistic hole heart line for surveying three holes12
And α13With the hole heart away from L1、L2And L3。
The hole heart in three hole of part is surveyed away from L1、L2And L3:
Survey the angle α of hole heart line12And α13, obtained by geometrical relationship:
Seek L1、L2And L3With the Δ L of difference of the perfect apertures heart away from L1、ΔL2With Δ L3If 2 | Δ L1|、2|ΔL2| and 2 | Δ
L3| middle any value is more than the Tolerance of Degree of position value of planet carrier circumferential apertures requirement, then how no matter the geometry picture frame of part rotate,
Position error is unqualified;
S3, when each hole actual apertures heart away from and the theoretical hole heart away from its difference absolute value 2 times (2 | Δ L1|、2|ΔL2| and 2 | Δ L3
|) less than the requirement of planet carrier circumferential apertures Tolerance of Degree of position value when, with the hole heart in 1 hole away from making circular arc for radius, with its position degree public affairs
Difference circle is intersecting, and n Along ents are taken in the intersecting arcs in tolerance circle, and (for 320E planet carriers and Cycloidal Wheel, when n=11 can obtain
Accurate position error value), the position each put is followed successively by I counterclockwise1、I2、...、I11, as shown in Figure 4;
S4, planet frame aperture group is subjected to translation rotation processing, forms new coordinate system, as shown in Figure 5:First by determining folder
The hole heart line in three holes at angle translates in a coordinate system, the outer circle center of circle is made to be overlapped with coordinate origin, then by it around coordinate origin
Rotation, makes the hole heart line in first hole first rotate to I1As initial position, three solid line lines represent at this time three for position
The position in a hole, and dotted line represents and measures the home position that initial data is formed, under new coordinate system, the perfect apertures heart in three holes
Position is constant, i.e. 1 (X1', Y1′)、2(X2', Y2') and 3 (X3', Y3'), then the hole heart line in first hole and the folder of x-axis at this time
Angle θ is:
In formula:L1For first hole actual apertures heart away from the design hole heart that, l is circumferential distribution pore away from;
Then from initial position using Δ θ as rotation angle, it is rotated successively to I2、......、I11Position can obtain 11
The hole group of kind different location, rotation angle Δ θ are:
In formula:N=1,2 ..., 11, be hole group rotation position number;
The geometrical relationship according to Fig. 5, when can calculate respectively in this 11 groups of positions, the hole heart in three holes of circle distribution
1 (X of coordinate1", Y1″)、2(X2", Y2″)、3(X3", Y3″):
The actual apertures heart is formed centrally the physical location degree circle of uncertainty with perfect apertures, i.e., three circles are the reality in each hole shown in Fig. 4
The circle of uncertainty, respective diameter value are its Tolerance of Degree of position, then can calculate planet carrier circle by being compared with perfect apertures heart position coordinates
The position error of all cloth holes, position error calculation formula are:
S5,11 groups of position errors that planet carrier circumference uniform distribution hole is in different rotary position are obtained by step S4, respectively
The position degree in three holes in every group is ranked up, extracts maximum value composition one array W, element W in every group of data out1、
W2、...、W11, it is corresponding with 11 groups of position degrees, then the numerical value in array W is ranked up, finds out the element of numerical value minimum
Wi, corresponding i-th group of position degree is that final required circumference uniform distribution hole is missed relative to the position degree in the planet carrier outer circle center of circle
Poor f1、f2、f3。
Assessment method of the present invention by taking planet carrier and Cycloidal Wheel of the joint of robot with RV retarder models 320E as an example, with
This algorithm is applied in its design basis --- Excircle machining face as benchmark is detected after measuring the data of circle distribution axis hole, without
Judge the direction that each hole tangentially deviates, you can obtain the accurate location degree error in each hole.
More than content is merely illustrative of the invention's technical idea, it is impossible to protection scope of the present invention is limited with this, it is every to press
According to technological thought proposed by the present invention, any change done on the basis of technical solution each falls within claims of the present invention
Protection domain within.
Claims (10)
1. the circumferential distribution pore group position degree assessment method based on coordinate transform and array sort, which is characterized in that including following
Step:
S1, optionally there is a hole on the rotary type part to be measured of circumferential distribution pore group as tangential benchmark, to obtain part circle
The location information in m hole of week distribution, and coordinate system is established, according to tolerance, find out the desired tolerance circle in each hole;
Be obtained under S2, the coordinate system established in step S1 the hole heart in m hole away from and each hole heart line angle;
S3, circle is drawn with the hole heart line in first hole, intersected with its ideal position degree tolerance circle, n deciles are carried out to intersecting arcs, with
Each Along ent determines the postrotational n groups position of hole group;
S4, translation rotating coordinate transformation is carried out to step S3, under new coordinate system, be obtained in m hole of n group location hole groups
Position error;
S5, bubble sort is carried out to step S4 results, the accurate location degree error amount of hole in piece part group is obtained, to circle distribution
The position degree of the rotary type part to be measured of hole group is accurately evaluated.
2. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 1
Method, which is characterized in that in step S1, using part outer circle to be measured as detection benchmark, using first hole on part to be measured as tangentially
Theoretical hole heart position and circle center line connecting are set as x-axis, establish cartesian coordinate system, find out the hole in m hole in a coordinate system by benchmark
Heart ideal position m (Xm',Ym'), it is that m Tolerance of Degree of position is made in the center of circle by radius, perfect apertures heart position of its Tolerance of Degree of position
Circle, the angle of theoretical hole heart line from each other is 360/m °, carries out data acquisition and obtains part circumferential distribution pore group to be measured
Location information, and construct the actual measurement center location m (X in m holem,Ym) and the outer circle center of circle Measured Coordinates (X0,Y0)。
3. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 1
Method, which is characterized in that in step S2, according to the Measured Coordinates information of each hole center of circle in a coordinate system, m hole of actual measurement is calculated
The hole heart away from LmIt is as follows:
Wherein, m (Xm,Ym) actual measurement center location for m hole, the Measured Coordinates in the outer circle center of circle are (X0,Y0)。
4. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 3
Method, which is characterized in that m=3, according to the hole heart in 3 holes of actual measurement away from L1、L2、L3The hole heart binding clip in 3 holes of actual measurement is calculated
Angle α12And α13It is as follows:
5. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 1
Method, which is characterized in that in step S3, when each hole actual apertures heart away from and the theoretical hole heart 2 times away from its difference absolute value be less than to be measured zero
During the Tolerance of Degree of position value of part circumferential apertures requirement, with the hole heart in first hole on part to be measured away from circular arc is made for radius, with its position
Degree of putting tolerance circle is intersecting, takes n Along ents in the intersecting arcs in tolerance circle, the position each put is followed successively by I counterclockwise1、I2、…、
In。
6. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 1
Method, which is characterized in that in step S4, the hole heart line in m hole of determining angle is translated in a coordinate system first, is made outer round
The heart is overlapped with coordinate origin, then it is rotated around coordinate origin, and the hole heart line in first hole is made first to rotate to I1Make position
For initial position, under new coordinate system, the perfect apertures heart m (X in m holem',Ym') position is constant, obtain the Kong Xinlian in first hole
Then from initial position using Δ θ as rotation angle, it is rotated successively to I for the angle theta of line and x-axis2、……、InPosition can obtain
To the hole group of n kind different locations, the hole heart coordinate m in m hole of circle distribution is respectively obtained according to the hole group of n kind different locations
(Xm”,Ym"), by being compared with perfect apertures heart position coordinates, calculate the position error f in m hole of part circumference uniform distribution to be measuredm。
7. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 6
Method, which is characterized in that rotation angle Δ θ is:
Wherein:The hole heart line in first hole and the angle theta of x-axis are:
Wherein:L1For first hole actual apertures heart away from the design hole heart that, l is circumferential distribution pore away from.
8. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 6
Method, which is characterized in that m=3, the 1 (X of hole heart coordinate in 3 holes of circle distribution1”,Y1”)、2(X2”,Y2”)、3(X3”,Y3") meter
It calculates as follows:
Wherein, α12And α13To survey the hole heart line angle in 3 holes, L1、L2、L3The actual apertures heart for three holes is away from l is circumference
The design hole heart of distribution hole away from.
9. a kind of circumferential distribution pore group position degree evaluation side based on coordinate transform and array sort according to claim 6
Method, which is characterized in that m=3, the position error f in 3 circumference uniform distribution holes of part to be measured1、f2、f3For:
It is 10. according to claim 1 a kind of based on the evaluation of the circumferential distribution pore group position degree of coordinate transform and array sort
Method, which is characterized in that in step S5, the n groups that part circumference uniform distribution hole to be measured is in different rotary position are obtained by step S4
Position error is respectively ranked up the position degree in m hole in every group, and the maximum value extracted out in every group of data forms a number
Group W, element W1、W2、…、Wn, it is corresponding with n group position degrees, then the numerical value in array W is ranked up, finds out numerical value most
Small element Wi, corresponding i-th group of position degree is final required circumference uniform distribution hole relative to the part outer circle center of circle to be measured
Position error fm。
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