CN105045973A - Variable-arc-length adaptive sampling method - Google Patents
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Abstract
The present invention discloses a variable-arc-length adaptive sampling method and belongs to the technical field of CAD model measurement calculation methods for unknown curved surfaces for aircraft engine blades. The method comprises: performing initial measurement; performing data pre-processing; performing initial curved surface fitting; obtaining curvature information; determining a sampling mode; performing variable-arc-length adaptive sampling; and performing sampling data pre-processing and curved surface fitting to obtain an accurate model. According to the variable-arc-length adaptive sampling method, basic curvature information of an unknown curved surface is obtained by first-time measurement, and variable-arc-length adaptive sampling measurement of the curved surface is performed for the second time based on the curvature information, so that the accurate CAD model of the curved surface is reconstructed. The method has the advantages of high precision, no other auxiliary devices and easiness for implementation.
Description
Technical field
The present invention relates to a kind of adaptively sampled method of change arc length, belong to the technical field of the surface model survey calculation method of engine blade in mechano-electronic industry; Belong to the technical field of the Unknown curve surface cad model survey calculation method for blade of aviation engine specifically.
Background technology
Along with the development of aeronautical technology, more and more higher to aeromotor reliability requirement.Blade is as engine core parts, and condition of work badly very easily breaks down, and is therefore one of important means of raising engine reliability to the fault detect of engine blade.Ultrasonic non-destructive inspection techniques is because its directive property is good, penetration power is widely applied by force.In aeromotor automatic ultrasonic nondestructive detection system, ultrasonic transducer maintains static, and manipulator clamping blade does scanning campaign.Due to hyperacoustic characteristic, to remain that in scanning process ultrasonic transducer is perpendicular to blade surface; In order to meet above-mentioned requirements, the Motion trajectory of mechanical arm will based on blade cad model.But owing to relating to trade secret, user often can not obtain the cad model of blade from manufacturer, this just needs to use camber counter solution technology to obtain the cad model of blade.Spoon of blade reconstruct for unknown cad model is generally use survey instrument, measures, obtain blade surface data, carry out three-dimensionalreconstruction according to the data recorded to blade blade surface.
Camber counter solution refers to and records curved surface data information according to mock-up, constructs curved surface cad model.Namely utilize the three-dimensional data information of three-dimensional vision information equipment Inspection curved surface, go out to meet according to the curved surface data information structuring obtained the curved surface cad model that fitting precision requires.Can curved surface three-dimensional data information comprehensively reflect that curvature of curved surface changes, and has important impact for surface fitting precision.Can whether fitting surface be accurate, on find in Ultrasonic Detection process that surface defect has important impact.Therefore, in camber counter solution process, the method for sampling wants the precision that can improve camber counter solution.
The measuring method that current precision comparison is high is three coordinate measuring machine contact type measurement, and the blade for unknown cad model adopts unique step measuring method, and step-length is shorter, and measurement point is more, and the precision of surface reconstruction is higher.But this kind of method can not react the Curvature varying of curved surface, the data reconstruction precision obtained relative to adaptively sampled measurement in the same number of situation of sampled point is not high.
Summary of the invention
The present invention is directed to the deficiencies in the prior art, provide a kind of camber counter solution based on double measurement and become the adaptively sampled method of arc length; To realize in blade of aviation engine Ultrasonic Detection, for the situation of blade mathematics unknown-model, when sampled point number accurately can reflect curvature of curved surface, significantly improve the object of surface fitting precision.
For reach described object technical scheme of the present invention or method as follows.
A kind of adaptively sampled method of change arc length, comprises the steps:
Step one, three coordinate measuring machine prepares;
Step 2, initial measurement; Initial samples is carried out to blade, utilizes three coordinate measuring engine measurement minority to reflect the structure lines of blade shape;
Step 3, data prediction; Raw data pre-service;
Step 4, the initial matching of curved surface; From the cloud data of the structure lines obtained, import to the initial model reconstructing blade in reverse software;
Step 5, obtains curvature information; Curvature information is obtained based on curved surface initial model;
Step 6, determines sample mode; Determine that sample mode is for determining sample direction and direction of feed; Sample direction and step direction is determined according to vane curvature change; The direction that Curvature varying is large is defined as sample direction, and the direction that Curvature varying is little is defined as step direction;
Step 7, becomes arc length adaptively sampled; The coordinate of the adaptively sampled acquisition sampled point of arc length is become based on curvature information;
Step 8, sampled data pre-service; Becoming arc length discrete sampling point coordinate by calculating, arranging the sampling step length of three coordinate measuring machine in sample direction, it is adaptively sampled to carry out changes arc length, obtains cloud data of sampling;
Step 9, surface fitting obtains accurate model; The blade cloud data recorded by three coordinate measuring machine imports in reverse software and carries out model reconstruction, obtains the accurate cad model of blade, and the blade change arc length realizing Unknown Model is adaptively sampled.
This step 7 becomes that arc length is adaptively sampled is realized by following step:
(I) unique step stepping is adopted at step direction; The sample mode utilizing three coordinate measuring machine to determine in step 6 blade is sampled; When three coordinate measuring machine has been sampled to the structure lines in sample direction, will sample to next structure lines, the distance between these two structure lines is this step direction according in three coordinate measuring machine coordinate system, the direction unique step of certain coordinate axis moves a segment distance;
(II) in sample direction, adopt that arc length between the sampled point of curvature of curve general goal is little, that arc length is large between the sampled point at curvature little place requirement methodological principle realizes becoming arc length is adaptively sampled.
Should (II) realizes in sample direction the adaptively sampled process of change arc length into:
First, blade is measured for the first time to the initial model obtained, obtain the coordinate of a small amount of point in sampling location according to initial model, these coordinates put are imported in MATLAB software and carries out Cubic Spline Fitting and the function expression f obtaining every section of curve
1f
i, f
i+1... f
n, wherein n=1,2,3 ... natural number, i=1,2,3 ... the natural number of n;
Its two, based on curvature formulations 7
calculating the curvature information of every section of curve, just can obtain the curvature information of whole piece curve and the curvature maximum k of this section of curve by calculating
maxposition, wherein f " represents the second derivative of curvilinear function, the first order derivative of f ' expression curvilinear function;
Its three, according to formula 3l
i+1=(k
i+ c) l
i/ (k
i+1+ c) the interval arc length l at sampled point i+1 place can be calculated
i+1, wherein k
irepresent the curvature of certain point, l
ifor this point is to the interval arc length of next sampled point, c is positive number, i=0,1,2,3 ... n; Calculating sampled point interval arc length according to formula 3 is l
0l
il
n-1;
Its four, the coordinate being calculated each sampled point by the function expression of the sampled point interval arc length that calculates and curve is (x
0, y
0) ... (x
i, y
i) ... (x
n, y
n), wherein i=0,1,2,3 ... n;
This l
0for 1.5 times of the minimum measurement spacing of used three coordinate measuring machine,
This c value is set to this section of curvature of curve maximal value k of different arc
max0.8 times.
Total arc length l of this whole piece curve meets relation
There is the situation being greater than l, then this time point (x in the arc length sum that this interval arc length calculates gained
n, y
n) get the end points of curve.
The computing formula 6 of this arc length is
wherein y=f (x) represents the function of curve
Expression formula, y '=f ' (x) represents the first order derivative of curvilinear function, a and b is lower limit and the upper limit of x span; Utilize formula 6 and y=f (x) that the value of coordinate figure x and y can be calculated, just obtain the value of coordinate (x, y).
This cloud data is three-dimensional coordinate information; On this same structure line, the z coordinate of initial model sampled point is identical value with the z coordinate of the adaptively sampled point of change arc length.
The value of this z coordinate is the distance between two adjacent structure lines.
Adopt technical scheme of the present invention or method due to for spoon of blade reverse problem, propose based on lever principle and become the adaptively sampled method of arc length; And become the adaptively sampled strategy of arc length and method based on this Unknown curve surface reverse proposed based on double measurement; The camber counter solution that the present invention is based on double measurement becomes the adaptively sampled method of arc length.Three coordinate measuring machine first time is utilized just to measure minority key point data message to Unknown curve surface, simulate initial surface, obtain the basic curvature information of Unknown curve surface, carry out curved surface based on these curvature information second time and become the adaptively sampled measurement of arc length, thus reconstruct the accurate cad model of curved surface.Analog simulation test findings shows to utilize the precision of the adaptively sampled methods of arc length such as the surface accuracy of the adaptively sampled method reconstruct of change arc length of the present invention is better than, and without the need to other utility appliance, is easy to realize.
Accompanying drawing explanation
Fig. 1 is the schematic flow sheet that the present invention becomes the adaptively sampled method of arc length;
Fig. 2 is the structural representation of engine blade initial configuration line;
Fig. 3 is the cloud data schematic diagram of initial samples structure lines of the present invention;
Fig. 4 is the schematic diagram that the present invention utilizes initial configuration line and cloud data determination blade sampling policy;
Fig. 5 is that the present invention becomes the step direction of arc length sampling and the schematic diagram of sample direction;
Fig. 6 is the close-up schematic view in A, B region in Fig. 5;
Fig. 7 is the blade cloud data schematic diagram that the change arc length method of sampling of the present invention obtains;
Fig. 8 a is the view that in Fig. 4, structure lines 1 is arranged in coordinate axis;
Fig. 8 b is coordinate corresponding fitting function expression formula schematic diagram in Fig. 8 a;
Fig. 8 c is arc length and coordinate view between sampled point in Fig. 8 b;
Fig. 8 d is the end point structure schematic diagram of arc length of sampling in Fig. 8 c;
Fig. 8 e is structural representation when curvature of curve maximum point is in the middle of curve in Fig. 8 c;
Fig. 9 is curvature of the present invention and interval arc length corresponding relation schematic diagram.
Embodiment
Below in conjunction with accompanying drawing, technical scheme of the present invention or method are described in detail as follows, in order to comprehensive understanding.
As shown in Figure 1; A kind of adaptively sampled method of change arc length, comprises the steps:
Step one, three coordinate measuring machine prepares;
Step 2, initial measurement; Initial samples is carried out to blade, utilizes three coordinate measuring engine measurement minority to reflect the structure lines of blade shape; As shown in Figure 2; Initial samples carries out first time to blade exactly and measures, and three coordinate measuring machine is sampled to blade according to unique step, and sampled point number is less than secondary change arc length sampled point number.In sample direction, unique step sampling, step direction is also unique step.
Step 3, data prediction; Raw data pre-service;
Step 4, the initial matching of curved surface; From the cloud data of the structure lines obtained, import to the initial model reconstructing blade in reverse software; As shown in Figure 3;
Step 5, obtains curvature information; Curvature information is obtained based on curved surface initial model;
Step 6, determines sample mode; Determine that sample mode is for determining sample direction and direction of feed; Sample direction and step direction is determined according to vane curvature change; The direction that Curvature varying is large is defined as sample direction, and the direction that Curvature varying is little is defined as step direction; As shown in Fig. 4, Fig. 5, Fig. 6;
Step 7, becomes arc length adaptively sampled; The coordinate of the adaptively sampled acquisition sampled point of arc length is become based on curvature information;
Step 8, sampled data pre-service; Becoming arc length discrete sampling point coordinate by calculating, arranging the sampling step length of three coordinate measuring machine in sample direction, it is adaptively sampled to carry out changes arc length, obtains cloud data of sampling;
Step 9, surface fitting obtains accurate model; The blade cloud data recorded by three coordinate measuring machine imports in reverse software and carries out model reconstruction, obtains the accurate cad model of blade, and the blade change arc length realizing Unknown Model is adaptively sampled.As shown in Figure 7.
This step 7 becomes that arc length is adaptively sampled is realized by following step:
(I) unique step stepping is adopted at step direction; The sample mode utilizing three coordinate measuring machine to determine in step 6 blade is sampled; When three coordinate measuring machine has been sampled to the structure lines in sample direction, will sample to next structure lines, the distance between these two structure lines is this step direction according in three coordinate measuring machine coordinate system, the direction unique step of certain coordinate axis moves a segment distance;
(II) in sample direction, adopt that arc length between the sampled point of curvature of curve general goal is little, that arc length is large between the sampled point at curvature little place requirement methodological principle realizes becoming arc length is adaptively sampled.
Should (II) realizes in sample direction the adaptively sampled detailed process of change arc length into:
First, blade is measured for the first time to the initial model obtained, obtain the coordinate of a small amount of point in sampling location according to initial model, these coordinates put are imported in MATLAB software and carries out Cubic Spline Fitting and the function expression f obtaining every section of curve
1f
i, f
i+1... f
n, wherein n=1,2,3 ... natural number, i=1,2,3 ... the natural number of n;
Its two, based on curvature formulations 7
calculating the curvature information of every section of curve, just can obtain the curvature information of whole piece curve and the curvature maximum k of this section of curve by calculating
maxposition, wherein f " represent the second derivative of curvilinear function, the first order derivative of f ' expressions curvilinear function, while K
ii.e. k
i;
Its three, according to formula 3l
i+1=(k
i+ c) l
i/ (k
i+1+ c) the interval arc length l at sampled point i+1 place can be calculated
i+1, wherein k
irepresent the curvature of certain point, l
ifor this point is to the interval arc length of next sampled point, c is positive number, i=0,1,2,3 ... n; Calculating sampled point interval arc length respectively according to formula 3 is l
0l
il
n-1;
Its four, the coordinate being calculated each sampled point by the function expression of the sampled point interval arc length that calculates and curve is (x
0, y
0) ... (x
i, y
i) ... (x
n, y
n), wherein i=0,1,2,3 ... n;
This l
0for 1.5 times of the minimum measurement spacing of used three coordinate measuring machine,
This c value is set to this section of curvature of curve maximal value k of different arc
max0.8 times.
For c value choose further illustrate as follows: c gets a positive number here two effects, and first effect prevents the situation that curvature is zero.From formula k
il
i=k
i+1l
i+1(1) formula (k is developed
i+ c) l
i=(k
i+1+ c) l
i+1(2) add a parameter c in the middle of, suppose known k
i, l
iand k
i+1value, so can obtain l according to formula (1)
i+1=k
il
i/ k
i+1, work as k
i+1value when being zero, formula to calculate l
i+1, be nonsensical.The size of second effect c value can to regulate between sampled point arc length with the severe degree of Curvature varying.At formula l
i+1=(k
i+ c) l
i/ (k
i+1+ c) in (3), if known k
i, l
i, k
i+1what can calculate with the value of parameter c arrives l
i+1.Suppose that the value of c gets positive infinity, what so calculate according to formula (3) arrives l
i+1value and l
iidentical, because when c value gets positive infinity, k in formula (3)
i+ c=k
i+1+ c, does not so just reach the object that between sampled point, arc length changes with Curvature varying; If the value of c gets infinitesimal words, so work as k
i+1level off to zero time, the l calculated
i+1will be larger, between sampled point, arc length is just too violent with Curvature varying, and therefore the value of c must be moderate, generally gets k according to repeatedly calculating
max0.8 times.When needs diminish sampled point number, the value of c is suitably reduced, according to formula l
i=(k
max+ c) l
0/ (k
i+ c) (5) known, and when c reduces, arc length will increase with Curvature varying, and sampled point number reduces; When needs become sampled point number large, the value sampled point number suitably increasing c will increase.
Total arc length l of this whole piece curve meets relation
There is the situation being greater than l, then this time point (x in the arc length sum that this interval arc length calculates gained
n, y
n) get the end points of curve.
The computing formula 6 of this arc length is
wherein y=f (x) represents the function expression of curve, and y '=f ' (x) represents the first order derivative of curvilinear function, a and b is lower limit and the upper limit of x span; Utilize formula 6 and y=f (x) that the value of coordinate figure x and y can be calculated, just obtain the value of coordinate (x, y).
This cloud data is three-dimensional coordinate information; On this same structure line, the z coordinate of initial model sampled point is identical value with the z coordinate of the adaptively sampled point of change arc length.The value of this z coordinate is the distance between two adjacent structure lines.
Because Cubic Spline Fitting curve representation formula is the form of y=f (x), therefore the coordinate of match point must be the coordinate of point in two-dimensional space, needs to carry out accommodation to the three-dimensional coordinate of the point that leaf model extracts.
According to the initial model of blade, certain structure lines in sample direction extracts the coordinate of part point.As shown in Figure 8 a, coordinate is extracted in structure lines 1, these points are at three dimensions, therefore their coordinate is (x, y, z) three-dimensional coordinate form, but the coordinate figure of the coordinate one dimension of the point on same structure lines is identical, and the coordinate z value being point on structure lines 1 as the situation in Fig. 8 a is identical.The coordinate of these points can be expressed as (x
i, y
i, z), the identical point (x that these points can be found out on two-dimensional space of the coordinate z value due to these points
i, y
i) carry out computing, cubic spline function so just can be utilized to carry out matching.Finally unifiedly add an identical z value, then become three-dimensional point.
From initial model, extract coordinates of some points of certain segment structure line, these point coordinate are three-dimensional coordinates, but as above and Fig. 8 b explains, these coordinates putting certain one dimension are identical, suppose that these z-axis coordinates are identical here.Here the mathematic(al) representation of matched curve can just be carried out like that according to two-dimensional curve, i.e. the function expression of this curve in xy coordinate plane.Be input in MATLAB software by these coordinates put, call cubic spline function, simulate the function expression of every section of curve, suppose that certain section of curve is divided into 5 sections, the cubic spline function expression formula of every section is f
1~ f
5.
Curvature formulations (7) just can be utilized to calculate the coordinate of whole section of curvature of curve maximum and curvature maximum point after obtaining every section of curve cubic spline function expression formula.
According to formula in the present invention (5) and formula (6) (derivation is aftermentioned), value and the l of c are set
0value, utilize the coordinate of arc length between each sampled point of formulae discovery and point.
Between calculating sampling point arc length and sample point coordinate process in exist two kinds of situations:
As shown in Figure 8 c, the sampling arc length calculated according to formula (5) and (6) is at curve f for the first situation
3arc length in, then can utilize f
3function expression directly calculate the coordinate of this sampled point according to formula (6);
As shown in Figure 8 c, the sampling arc length calculated according to formula (5) and (6) is beyond curve f for the second situation
3arc length, arrived curve f
4scope in, when utilizing formula (6) calculating sampling point coordinate, arc length value corresponding in formula (6) should be the arc length that formula (5) calculates and deducts curve f
3whole section of arc length, and curvilinear function expression formula corresponding in formula (6) is f
4.
Obtain curve sample point coordinate for (x
i, y
i), wherein x
ivalue be stepping coordinate figure in three coordinate measuring machine sample direction, and the confidential measurement y of three-dimensional coordinates measurement
ivalue, obtain exact value.Finally obtain the coordinate figure (x through remeasuring
i, y
i), add original all identical z value, just obtain the accurate three-dimensional coordinate (x remeasured
i, y
i, z).
Two kinds of situations are existed for curvature and end points
Situation one: when the end points of the maximum point of curvature at curve, this is that the end points of final stage sampling arc length only has a kind of situation, as shown in figure 8d.
Situation two: curvature of curve maximum point, in the middle of curve, will be divided into two parts curve when calculating sampling point, as figure 8 e shows.Each section of curve is all be starting point with point of maximum curvature, regarding these two curves as independently line segment and carries out the calculating of sampled point arc length, according to said when calculating final stage sampled point in formula, getting another end points of curve.
In sum, the change arc length of realization is adaptively sampled is lever balance theory in physically based deformation, can obtain formula (1) k by the principle of lever balance
il
i=k
i+1l
i+1, wherein k
irepresent the curvature of certain point, l
ifor this point is to the interval arc length of next sampled point.This formula will keep setting up then works as k
irelative to k
i+1time large, then k
icorresponding sampled point detects arc length l
ibe less than k
i+1corresponding sampled point interval arc length l
i+1, the local sampled point interval that can realize curvature large is little, and the local sampled point interval that curvature is little is large, namely adaptively sampled.But this formula (1) exists the situation that curvature is zero, in order to make formula (1) have more ubiquity, curvature adds a positive number c simultaneously, then the new formula obtained (2) is (k
i+ c) l
i=(k
i+1+ c) l
i+1.In formula (2), if known k
i, l
i, c and k
i+1then obtain formula (3) l
i+1=(k
i+ c) l
i/ (k
i+1+ c).
For known mathematical model curve, curvature maximum and k can be calculated according to curvature formulations
maxwith the coordinate (x of corresponding point
0, y
0), setting k
maxcorresponding to next sampled point arc length be l
0, l
0value should slightly larger than the minimum sampling interval of three coordinate measuring machine.Coordinate (x a little can be calculated according to arc length formula
1, y
1), the curvature calculating this point is k
1, then point (x
1, y
1) to next sampled point (x
2, y
2) corresponding arc length l
1, the value of given c just can calculate formula l
1=(k
max+ c) l
0/ (k
1+ c) (4), i.e. formula (4).Therefore between sampled point, computing formula is l
i=(k
max+ c) l
0/ (k
i+ c) (5), then can calculate (x successively according to formula (5) and (6)
2, y
2) ..., (x
n, y
n) and l
2..., l
n-1.
As shown in Figure 9, for l
0arrange, this is the parameter wanting us to arrange voluntarily, and it is k
maxshould be corresponding sampled point interval arc length, therefore l
0smaller value (can sets itself).When calculating curvature of curve maximal value k
maxtime, also determine the coordinate of curvature maximum thereupon.
As Fig. 9, according to formula l
i=(k
max+ c) l
0/ (k
i+ c) (4), first known parameters has k
maxwith the coordinate (x of correspondence
0, y
0), value and the l of c are set
0value, work as l
0value be provided with after, according to arc length formula
(6) (the wherein first order derivative of the middle f ' signature song line function of formula (6), a and b is x span look lower limit and the upper limit) just can obtain l
0coordinate (the x that end points goes out
1, y
1), this point known
Coordinate (x
1, y
1) according to curvature formulations
(7) (f " represent the second derivative of curvilinear function, the first order derivative of f ' expression curvilinear function) just can obtain the curvature k of this point
1, so by k
max, l
0, k
1be updated in formula (4) with the value of c, just can draw l
1value.Obtain l
1value just can calculate the coordinate (x of his end points according to formula (6)
2, y
2) value, by (x
2, y
2) be updated to the curvature k that just can calculate this point in formula (7)
2, by k
max, l
0, k
2be updated in formula (5) with the value of c, just can obtain l
2value, circulate the interval arc length l that can constantly obtain between each sampled point successively
1l
il
n-1and the coordinate (x of the point of correspondence
1, y
1) ... (x
i, y
i) ... (x
n, y
n).
The computing formula of arc length is our previously mentioned formula
(6) (the wherein first order derivative of the middle f ' signature song line function of formula (6), a and b is x span look lower limit and the upper limit).Namely formula (6) also can be write as another kind of form
wherein y=f (x) represents the function expression of curve, and y '=f ' (x) represents the first order derivative of curvilinear function, and two kinds of forms are identical in mathematical meaning.Utilize formula (6) just can calculate coordinate figure x, again because y=f (x), just can obtain the value of y, just obtain the value of coordinate (x, y).
Claims (10)
1. become the adaptively sampled method of arc length, it is characterized in that comprising the steps:
Step one, three coordinate measuring machine prepares;
Step 2, initial measurement; Initial samples is carried out to blade, utilizes three coordinate measuring engine measurement minority to reflect the structure lines of blade shape;
Step 3, data prediction; Raw data pre-service;
Step 4, the initial matching of curved surface; From the cloud data of the structure lines obtained, import to the initial model reconstructing blade in reverse software;
Step 5, obtains curvature information; Curvature information is obtained based on curved surface initial model;
Step 6, determines sample mode; Determine that sample mode is for determining sample direction and direction of feed; Sample direction and step direction is determined according to vane curvature change; The direction that Curvature varying is large is defined as sample direction, and the direction that Curvature varying is little is defined as step direction;
Step 7, becomes arc length adaptively sampled; The coordinate of the adaptively sampled acquisition sampled point of arc length is become based on curvature information;
Step 8, sampled data pre-service; Becoming arc length discrete sampling point coordinate by calculating, arranging the sampling step length of three coordinate measuring machine in sample direction, it is adaptively sampled to carry out changes arc length, obtains cloud data of sampling;
Step 9, surface fitting obtains accurate model; The blade cloud data recorded by three coordinate measuring machine imports in reverse software and carries out model reconstruction, obtains the accurate cad model of blade, and the blade change arc length realizing Unknown Model is adaptively sampled.
2. as claimed in claim 1 become the adaptively sampled method of arc length, it is characterized in that this step 7 becomes that arc length is adaptively sampled to be realized by following step:
(I) unique step stepping is adopted at step direction; The sample mode utilizing three coordinate measuring machine to determine in step 6 blade is sampled; When three coordinate measuring machine has been sampled to the structure lines in sample direction, will sample to next structure lines, the distance between these two structure lines is this step direction according in three coordinate measuring machine coordinate system, the direction unique step of certain coordinate axis moves a segment distance;
(II) in sample direction, adopt that arc length between the sampled point of curvature of curve general goal is little, that arc length is large between the sampled point at curvature little place requirement methodological principle realizes becoming arc length is adaptively sampled.
3. as claimed in claim 2 become the adaptively sampled method of arc length, it is characterized in that this (II) realize in sample direction the adaptively sampled process of change arc length into:
First, blade is measured for the first time to the initial model obtained, obtain the coordinate of a small amount of point in sampling location according to initial model, these coordinates put are imported in MATLAB software and carries out Cubic Spline Fitting and the function expression f obtaining every section of curve
1f
i, f
i+1... f
n, wherein n=1,2,3 ... natural number, i=1,2,3 ... the natural number of n;
Its two, based on curvature formulations
calculating the curvature information of every section of curve, just can obtain the curvature information of whole piece curve and the curvature maximum k of this section of curve by calculating
maxposition, wherein f " represents the second derivative of curvilinear function, the first order derivative of f ' expression curvilinear function;
Its three, according to formula 3l
i+1=(k
i+ c) l
i/ (k
i+1+ c) the interval arc length l at sampled point i+1 place can be calculated
i+1, wherein k
irepresent the curvature of certain point, l
ifor this point is to the interval arc length of next sampled point, c is positive number, i=0,1,2,3 ... n; Calculating sampled point interval arc length according to formula 3 is l
0l
il
n-1;
Its four, the coordinate being calculated each sampled point by the function expression of the sampled point interval arc length that calculates and curve is (x
0, y
0) ... (x
i, y
i) ... (x
n, y
n), wherein i=0,1,2,3 ... n.
4. the adaptively sampled method of change arc length as claimed in claim 3, is characterized in that this l
0for 1.5 times of the minimum measurement spacing of used three coordinate measuring machine.
5. the adaptively sampled method of change arc length as claimed in claim 3, is characterized in that this c value is set to this section of curvature of curve maximal value k of different arc
max0.8 times.
6. the adaptively sampled method of change arc length as claimed in claim 3, is characterized in that total arc length l of this whole piece curve meets relation
7. the adaptively sampled method of change arc length as claimed in claim 6, is characterized in that the situation of l appears being greater than in the arc length sum of this interval arc length calculating gained, then this time point (x
n, y
n) get the end points of curve.
8. the adaptively sampled method of change arc length as claimed in claim 3, is characterized in that the computing formula 6 of this arc length is
wherein y=f (x) represents the function expression of curve, and y '=f ' (x) represents the first order derivative of curvilinear function, a and b is lower limit and the upper limit of x span; Utilize formula 6 and y=f (x) that the value of coordinate figure x and y can be calculated, just obtain the value of coordinate (x, y).
9. the adaptively sampled method of change arc length as claimed in claim 1, is characterized in that this cloud data is three-dimensional coordinate information; On this same structure line, the z coordinate of initial model sampled point is identical value with the z coordinate of the adaptively sampled point of change arc length.
10. the adaptively sampled method of change arc length as claimed in claim 9, is characterized in that the value of this z coordinate is the distance between two adjacent structure lines.
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