CN101672637B - Digitizing detection method of complicated curved face - Google Patents
Digitizing detection method of complicated curved face Download PDFInfo
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- CN101672637B CN101672637B CN2009101962597A CN200910196259A CN101672637B CN 101672637 B CN101672637 B CN 101672637B CN 2009101962597 A CN2009101962597 A CN 2009101962597A CN 200910196259 A CN200910196259 A CN 200910196259A CN 101672637 B CN101672637 B CN 101672637B
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Abstract
The invention relates to a digitizing detection method of a complicated curved face. The method comprises the following steps: (1) extracting the geometric data of a CAD model of the complicated curved face, establishing an NURBS theoretical model of the complicated curved face, measuring a part object with the curved face by a three-coordinate measuring machine, digitizing the surface of the part to obtain the parameter of a measuring point; (2) establishing a binary nonlinear mathematical model with the minimum distance from the measuring point to an isoparametric line areas of the curved face by searching two groups of isoparametric line areas with isoparametric line structure proximate to the measuring point on the CAD curved face; and (3) calculating the shape error of the complicated curved face by a genetic algorithm to realize the error estimation of the complicated curved face. Compared with the prior art, the invention establishes an accurate curved face theoretical model, enhances the searching efficiency, can ensure the acquisition of a globally optimal solution and lightens the measuring intensity.
Description
Technical field
The present invention relates to Machine Design and detection technique field, especially relate to a kind of complex-curved digitizing detection method.
Background technology
Increasingly mature along with the develop rapidly of modern manufacturing industry and the design of CAD/CAM mean camber and process technology; The demand of complex curved surface parts such as hi-tech, high performance mechanized equipment such as thruster, screw pump, compressor, extruder, steam turbine, fan blower is increasing; They have in a plurality of essential industrys field of national economy such as military affairs, aviation, the energy, machinery, chemical industry, new material widely uses, and its manufacturing accuracy directly affects the serviceability and the quality of equipment.
Complex-curved shape error digitizing detects and is meant the measuring equipment measuring complex curved surface part that utilizes the advanced person, obtains curved surface part surface discrete data point, this data point is compared with designing a model of part, thereby detect mismachining tolerance.Digitizing detect provide an analysis to design a model and its final products between the method for the margin of error, can find whether each characteristic of part and size have the deviation flaw with respect to designing a model.Before part puts into production, the batch part is done initial workpiece detect, can check whether product has carried out the preparation of putting into production, in detection information, revise the defective that exists the processing.Because utilized the data of precision measurement and desirable profile to compare, can realize high precision, high efficiency detection, so complex-curved digitizing detection is had the important engineering meaning.
At present complex-curved digitizing is detected and remain traditional detection and modern detection method and deposit, the problem of existence mainly shows as:
(1) traditional complex-curved detection is to adopt model and actual curved surface to carry out the method for artificial comparison; This method need be made many models in kind; The quality that detects to a certain degree depends on individual knowledge level and experience; Labour intensity is big, detection time is long, accuracy of detection is low, is difficult to carry out information interchange with automatic control system and quality control system; In addition, existing dedicated test utensil can only detect certain some position of a certain product or product, does not have versatility.
(2) because the complicacy of complex-curved theoretical model; The research of a large amount of shape error evaluations concentrates in the research of ruled surface; To measuring the computational problem of distance from point to curved surface in the complex-curved shape error evaluation; The method that adopts the plane to approach is mostly carried out approximate processing, and calculated amount is big and precision is not high.
(3) in the existing wrap-around error computing method, the mathematical model that has does not meet minimal condition; Although what have meets minimal condition, in computation process, there is the approximate error of model, influence computational accuracy; The distance that directly will measure the point to curved surface discrete point that has is as wrap-around error, and do not calculate the normal direction distance of point to curved surface, and the high-precision requirement of this and Error Calculation has big gap.
What (4) have adopts STL to represent cad model; The directed distance of putting triangle grid model with original measurement is that spatial point is represented shape error to the triangular plate distance; And stl file is the data file of being come the approximate representation cad model by a series of triangular nets; For the steep excessively model of changes in surface, approach poor, error is very big.
(5) the employing measurement point that has is found the solution to the gradient method of B-spline surface distance, and gradient method and aforesaid method of steepest descent solving result are absorbed in the locally optimal solution in the primary iteration vertex neighborhood easily.
(6) great majority research at present is curved surface to be dispersed change into little grid plan, calculates measurement point then and evaluates complex-curved error to the minor increment of all little grid surfaces.Adopting the triangular plate of STL form to approach curved surface profile, also is present more common method to nearest triangular plate distance as wrap-around error according to measurement point, and the problem that these methods exist is that computational accuracy is not high enough.
(7) have with the distance of contour design point and corresponding measurement point as the error evaluation amount, but in actual measurement, can not guarantee measurement data points just and the design point that the CAD curved surface provides overlap, can not guarantee precision.
Because the shape error mathematical model that complex-curved shape error calculates by the Minimum Area method is very complicated, the utilization conventional calculation is difficult to direct calculating, usually adopts certain approximation method such as least square method to carry out indirect calculation.
Complex-curved digitizing detects problem because the complicacy of its shape error mathematical model is used conventional calculation to be difficult to directly find the solution, and adopted approximate method to calculate, and the resulting conclusion of different measuring methods is inconsistent.
Summary of the invention
The object of the invention be exactly provide in order to overcome the defective that above-mentioned prior art exists a kind of model accurately, search the complex-curved digitizing detection method that plain efficient is high, detection accuracy is good.
The object of the invention can be realized through following technical scheme:
A kind of complex-curved digitizing detection method is characterized in that, this method may further comprise the steps:
(1) geometric data of the complex-curved cad model of extraction is set up complex-curved NURBS theoretical model, utilizes three coordinate measuring machine that part curved surface in kind is carried out three-dimensional measurement again, with the piece surface digitizing, obtains the measurement point parameter;
(2) through parameter lines such as search on the CAD curved surface and measurement points nearest two groups, the binary nonlinear mathematical model of the regional minor increments of parameter line such as measurement point to curved surface is set up in zone such as the structure parameter line of etc.ing;
(3) the utilization genetic algorithm is come calculation of complex curve form error, realizes complex-curved error evaluation.
In the described step (1) during the NURBS theoretical model of complex structure curved surface,, calculate the data point on the nurbs surface of u, v parameter correspondence according to U and the V knot vector on two parametric directions of cad model.
When setting up the binary nonlinear mathematical model in the described step (2); To each measurement point, select 2 nearest points in curved surface u parameter line direction, the point that on two v parameter lines at these 2 places, selects 2 nearest u parameters to equate then; Wait the parameter line zone by these of four some structures; The intersection point of surface normal and curved surface that guaranteed measurement point to four somes orderings, is found out less u in four points in these four determined rectangular areas of point
a, v
aParameter value and bigger u
b, v
bParameter value.
When using genetic algorithm in the described step (3), at variable range [u
a, u
b] and [v
a, v
b] interior search and the point of measurement point apart from minimum, the parameter value of this point is u
*, v
*, measurement point is the mismachining tolerance of part curve form to the distance of this point.
Compared with prior art, the present invention has the following advantages:
(1) accurately sets up curved face theoretical model: the theoretical model of CAD curved surface that utilized the NURBS construction of function; Simultaneously in the feasible zone of its knot vector parameter; Utilize u, v parameter as optimization variable, set up and calculated the two yuan nonlinear mathematical models of measurement point to CAD curved surface minor increment.
(2) improve search efficiency: propose the method for solving that division waits the parameter line zone; At first seek parameter line zones such as near the CAD curved surface u of measurement point, v; Through parameter line zones such as the nearest u of structure on the CAD curved surface and measurement point, v, as the hunting zone, simultaneously; Propose parameter line regional extents such as the segmentation node parameter dwindles, improved search efficiency.
(3) guarantee to obtain globally optimal solution: the utilization genetic algorithm is calculated the minor increment of measurement point to the CAD curved surface, and this method ability global optimizing only need be utilized target function value, need not derivative operation, has simplified computation process greatly.Can overcome the deficiency of traditional numerical optimization, this method detection accuracy is good, precision is high, strong robustness, detects for complex-curved digitizing to have important use value.
(4) alleviate measured intensity: native system has alleviated measuring operation personnel's labour intensity, and the analysis to measure result has improved the measurement accuracy automatically.
Description of drawings
Fig. 1 is the process flow diagram of this method;
Fig. 2 is near the area schematic such as parameter line such as grade the measurement point.
1 is measurement point among the figure, and 2 is apart from the nearest point of measurement point on the curved surface.
Embodiment
Below in conjunction with accompanying drawing and specific embodiment the present invention is elaborated.
Embodiment
A kind of complex-curved digitizing detection method, its flow process is as shown in Figure 1, and this method may further comprise the steps:
(1) geometric data of the complex-curved cad model of extraction is set up complex-curved NURBS theoretical model, utilizes the three-dimensional measurement curved surface part in kind again, with the piece surface digitizing, obtains the measurement point parameter;
(2), set up the binary nonlinear mathematical model of zone such as the parameter line of measuring point to curved surface minor increments through parameter lines such as parameter line structure zones such as search on the CAD curved surface and measurement points nearest two groups;
(3) the utilization genetic algorithm is come calculation of complex curve form error, realizes complex-curved error evaluation.
Adopt the NURBS method to describe the theoretical model of CAD curved surface, two knot vector U of nurbs surface and V have the unit square field of definition 0≤u of standard usually, v≤1, and this field of definition is divided into (m-k+1) * (n-l+1) individual sub-rectangle by its internal segment dotted line.Nurbs surface is the reasonable parametric polynomial curved surface of a kind of burst of special shape, and wherein each subsurface sheet is defined in that certain has on the sub-rectangular domain of non-zero area in the unit square.
The step of calculation of complex curve form error is generally speaking:
(1) calculates the minor increment of all measurement points to the CAD curved surface
{dst
i|i＝0，1，...，n}
(2) calculate the maximal value of each minor increment
dst
max＝max{dst
i|i＝0，1，...，n}
(3) peaked 2 times of Minimum Areas that promptly contain the desirable profile equidistant surface of whole measuring points, this is the shape error of curved surface.
f＝2×dst
max (1)
Can know that by complex-curved shape error calculation procedure the key of complex-curved shape error evaluation is to calculate the distance of measurement point to the CAD curved surface.A measurement point m
i(x
i, y
i, z
i) (i=0,1 ..., n) on nurbs surface, must find a nearest some p
i *(p
x(u
i *, v
i *), p
y(u
i *, v
i *), p
z(u
i *, v
i *)), this point was the surface normal of measurement point and the intersection point of curved surface.Therefore, it is exactly to each measurement point that complex-curved shape error calculates, one group of u of search on the CAD curved surface
*, v
*Value, make point on their pairing curved surfaces to the distance of corresponding measurement point for minimum, this is that measurement point arrives complex-curved distance.In view of the above, the objective function of measurement distance from point to curved surface is:
I=0 wherein, 1 ..., n, n are measure dot number.
The key of calculation of complex curve form error is certain measurement point of computer memory to the minor increment of its CAD curved surface, promptly will on the CAD curved surface, search for a bit, make its and this measurement point apart from minimum.
For the parameter value among CAD curved surface knot vector U and the V; Calculate each parameter corresponding to the data point coordinate on the curved surface; Certain measurement point is compared with these data points, seeks out four the net surfaces lattice points nearest with measurement point, and guarantee these four net points u lines such as two groups with etc. on the v line; Make them corresponding to two groups of parameter values, i.e. [u among u and the v
a, u
b] and [v
a, v
b]; These two groups of parameter determining one sub regions of curved surface; Native system such as is referred to as at the parameter line zone, must be positioned at this zone, search of utilization genetic algorithm and the closest approach [u of measurement point apart from minimum in these parameter line regional extents then with point on the nearest curved surface of measurement point
*, v
*]; The distance of the two is promptly measured the distance of point to curved surface; As shown in Figure 2, wait the parameter line zone for the dash area among the figure, wait the parameter line dividing region to dwindle the hunting zone of genetic algorithm; Help improving computing velocity, be based on the calculation procedure that waits the regional measurement point of parameter line to CAD curved surface minor increment:
(1) reads in the geological information of cad model curved surface, construct its nurbs surface theoretical model,, calculate the data point on the corresponding nurbs surface of u, v parameter according to U and the V knot vector on its two parametric directions;
(2) to each measurement point; At 2 nearest points of curved surface u parameter line direction finding; On two v parameter lines at these 2 places, seek the point that 2 nearest u parameters equate then; Wait the parameter line zone by this of four somes structure, the intersection point of surface normal and curved surface that guaranteed measurement point is in these 4 determined rectangular areas of point;
(3) to 4 some orderings, find out less u in 4 points
a, v
aParameter value and bigger u
b, v
bParameter value;
(4) use genetic algorithm, at variable range [u
a, u
b] and [v
a, v
b] the interior searching and the minimum point 2 of measurement point 1 distance, its parameter value is u
*, v
*
Measurement point is the mismachining tolerance of part curve form to the distance of this point.
Claims (1)
1. a complex-curved digitizing detection method is characterized in that, this method may further comprise the steps:
(1) geometric data of the complex-curved cad model of extraction is set up complex-curved NURBS theoretical model, utilizes three coordinate measuring machine that part curved surface in kind is carried out three-dimensional measurement again, with the piece surface digitizing, obtains the measurement point parameter;
(2) through parameter lines such as search on the CAD curved surface and measurement points nearest two groups, the binary nonlinear mathematical model of the regional minor increments of parameter line such as measurement point to curved surface is set up in zone such as the structure parameter line of etc.ing;
(3) the utilization genetic algorithm is come calculation of complex curve form error, realizes complex-curved error evaluation;
In the described step (1) during the NURBS theoretical model of complex structure curved surface,, calculate the data point on the nurbs surface of u, v parameter correspondence according to U and the V knot vector on two parametric directions of cad model; When setting up the binary nonlinear mathematical model in the described step (2); To each measurement point, select 2 nearest points in curved surface u parameter line direction, the point that on two v parameter lines at these 2 places, selects 2 nearest u parameters to equate then; Wait the parameter line zone by these of four some structures; The intersection point of surface normal and curved surface that guaranteed measurement point to four somes orderings, is found out less u in four points in these four determined rectangular areas of point
a, v
aParameter value and bigger u
b, v
bParameter value; When using genetic algorithm in the described step (3), at variable range [u
a, u
b] and [v
a, v
b] interior search and the point of measurement point apart from minimum, the parameter value of this point is u
*, v
*, measurement point is the mismachining tolerance of part curve form to the distance of this point;
Adopt the NURBS method to describe the theoretical model of CAD curved surface; Two knot vector U of nurbs surface and V have the unit square field of definition 0≤u of standard usually; V≤1; This field of definition is divided into (m-k+1) * (n-l+1) individual sub-rectangle by its internal segment dotted line, and nurbs surface is the reasonable parametric polynomial curved surface of a kind of burst of special shape, and wherein each subsurface sheet is defined in that certain has on the sub-rectangular domain of non-zero area in the unit square;
The step of calculation of complex curve form error is generally speaking:
(1) calculates the minor increment of all measurement points to the CAD curved surface
{dst
i|i＝0，1，...，n}
(2) calculate the maximal value of each minor increment
dst
max＝max{dst
i|i＝0，1，...，n}
(3) peaked 2 times of Minimum Areas that promptly contain the desirable profile equidistant surface of whole measuring points, this is the shape error of curved surface;
f＝2×dst
max (1)
Can know that by complex-curved shape error calculation procedure the key of complex-curved shape error evaluation is to calculate the distance of measurement point to the CAD curved surface, a measurement point m
i(x
i, y
i, z
i) (i=0,1 ..., n) on nurbs surface, must find a nearest point
This point was the surface normal of measurement point and the intersection point of curved surface, and therefore, it is exactly to each measurement point that complex-curved shape error calculates, one group of u of search on the CAD curved surface
*, v
*Value, make point on their pairing curved surfaces to the distance of corresponding measurement point for minimum, this is that measurement point arrives complex-curved distance, in view of the above, the objective function of measuring distance from point to curved surface is:
I=0 wherein, 1 ..., n, n are measure dot number;
The key of calculation of complex curve form error is certain measurement point of computer memory to the minor increment of its CAD curved surface, promptly will on the CAD curved surface, search for a bit, make its and this measurement point apart from minimum;
For the parameter value among CAD curved surface knot vector U and the V; Calculate each parameter corresponding to the data point coordinate on the curved surface; Certain measurement point is compared with these data points, seeks out four the net surfaces lattice points nearest with measurement point, and guarantee these four net points u lines such as two groups with etc. on the v line; Make them corresponding to two groups of parameter values, i.e. [u among u and the v
a, u
b] and [v
a, v
b]; These two groups of parameter determining one sub regions of curved surface; The parameter line zone such as be referred to as, must be positioned at this zone, search of utilization genetic algorithm and the closest approach [u of measurement point in these parameter line regional extents then apart from minimum with point on the nearest curved surface of measurement point
*, v
*], the distance of the two is promptly measured the distance of point to curved surface, waits the parameter line dividing region to dwindle the hunting zone of genetic algorithm, helps improving computing velocity, based on the calculation procedure that waits the regional measurement point of parameter line to CAD curved surface minor increment is:
(1) reads in the geological information of cad model curved surface, construct its nurbs surface theoretical model,, calculate the data point on the corresponding nurbs surface of u, v parameter according to U and the V knot vector on its two parametric directions;
(2) to each measurement point; At 2 nearest points of curved surface u parameter line direction finding; On two v parameter lines at these 2 places, seek the point that 2 nearest u parameters equate then; Wait the parameter line zone by this of four somes structure, the intersection point of surface normal and curved surface that guaranteed measurement point is in these 4 determined rectangular areas of point;
(3) to 4 some orderings, find out less u in 4 points
a, v
aParameter value and bigger u
b, v
bParameter value;
(4) use genetic algorithm, at variable range [u
a, u
b] and [v
a, v
b] the interior searching and the point of measurement point apart from minimum, its parameter value is u
*, v
*
Measurement point is the mismachining tolerance of part curve form to the distance of this point.
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