CN110500969B - An in-situ measurement planning method for complex surfaces with high steepness - Google Patents

Abstract

The invention relates to an in-situ measurement and planning method for a high-steepness complex curved surface, belonging to the field of curved surface measurement, and relates to an in-situ measurement and planning method for a high-steepness complex curved surface. In this method, the non-equidistant transverse cross-section contours of complex surfaces are first generated with equal illumination angles as constraints, combined with the longitudinal cross-sectional contours to obtain a full-surface grid scanning measurement path, and the extraction is based on the average curvature change in the two parameter directions. Surface concave and convex features, generate local encrypted scan contours. Then, according to the equal illumination angle and the obtained scanning path, a multi-segment stitching measurement motion planning is performed to obtain the motion trajectory of the sensor reference point. Finally, the measurement declination inspection of the optical probe is carried out to complete the in-situ measurement planning of complex curved surfaces. The method realizes in-situ scanning path generation and measurement motion planning for complex surfaces with high steepness, ensures the measurement accuracy of the feature area, reduces the dynamic measurement error caused by the multi-axis linkage of the machine tool, and is reliable and versatile.

Description

An in-situ measurement planning method for complex surfaces with high steepness

technical field

The invention belongs to the field of curved surface measurement, and particularly relates to an in-situ measurement planning method for a complex curved surface with high steepness.

Background technique

In some high-end equipment, there is a large class of complex free-form surfaces with high steepness, and their surfaces have concave and convex features. The guarantee of the machining contour accuracy of this type of surface should be based on the state obtained by its in-situ precision measurement, and the machining error compensation should be adjusted. The in-situ measurement process is based on the motion of the machine tool, and according to the planned scanning path, the non-contact high-precision displacement sensor is used to obtain the surface data of the part, and then the geometry of the complex surface is reflected. Therefore, reasonable planning of the scanning path and the measurement motion of the machine tool is an important guarantee to meet the requirements of measurement accuracy and efficiency.

For the coordinate detection of such high-steep complex surfaces and aspheric surfaces, equidistant section contours are often used as scanning paths. However, the horizontal equidistant section contour method leads to relatively sparse trajectories near the poles, and the longitudinal equiangular section contour method leads to the inability to fully express the surface area away from the center, especially for high-steep free-form surfaces with concave-convex features on the surface. The distribution of measuring points in the area is sparse, and the measurement accuracy is difficult to guarantee. On the other hand, the high steepness of complex surfaces and the curvature changes of local concave-convex features require the spatial attitude of the optical probe to change, and it is difficult to measure the surface shape in-situ. Therefore, it is necessary to find an in-situ measurement suitable for high-steep complex surfaces. planning method.

In 2017, He Wantao et al. invented a scanning path planning method based on laser ranging based on dense point cloud acquisition of blade in the invention patent CN105627923B, which segmented and extended the profile curve of the blade profile, and generated it according to the segmented curve. The path is measured and the average of the normal angles of the measurement area is used as the measurement angle. This method is mainly used for scanning path planning for off-line detection of blade profile, and does not consider the movement of the measurement platform and the influence of movement errors on the measurement results. In 2019, Wang Liuning et al. invented a method for creating measurement points based on online measurement technology in the invention patent CN106202843B. By obtaining the information of points, lines or surfaces on the model to be processed, the surface is divided into multiple parts according to isoparametric lines. For each part, the measurement points on each surface patch are created by means of equal distribution points, and the measurement path is generated in the online measurement system. This method is difficult to ensure the measurement accuracy of concave-convex features on high-steep free-form surfaces.

SUMMARY OF THE INVENTION

The main technical problem to be solved by the present invention is to overcome the shortcomings of the above methods, and to meet the requirements of in-situ measurement of complex curved surfaces with high precision and high efficiency, a method for in-situ measurement and planning of complex curved surfaces with high steepness is invented. In this method, the non-equidistant transverse cross-section contour lines are generated by taking the equal illumination angle as a constraint, which solves the problem of sparse measurement trajectories near the poles caused by the large longitudinal height difference of the high-steep surface. The generated non-equidistant transverse section lines and longitudinal section lines are combined to obtain a full-surface grid scanning measurement path, which improves the expression integrity of key areas of high-steep complex surfaces and aspheric parts, such as poles and equatorial regions. The surface concave and convex features are extracted according to the average curvature of the surface, and local encrypted scanning contour lines are generated to ensure the measurement accuracy of the feature area. According to the equal illumination angle, the machine tool measurement motion trajectory that takes into account the incident angle of the sensor beam is generated, which avoids the frequent indexing of the probe, and reduces the dynamic error caused by the multi-axis linkage of the machine tool. In situ measurement.

The technical scheme adopted in the present invention is an in-situ measurement and planning method for a high-steepness complex curved surface, which is characterized in that, in the measurement planning method, firstly, the central axis of the high-steepness complex curved surface is used as a reference direction, and according to a given equal illumination angle size, calculate the iso-illuminance line containing the aspheric surface in the reference direction, and use its corresponding non-equidistant section contour as the initial scanning path of the high-steep complex surface; secondly, generate an equal distance between two adjacent section contour lines The cross-sectional contour line is used to obtain the transverse scanning path; according to the given angle index value, the longitudinal cross-sectional contour line is calculated to obtain the longitudinal scanning path; then, the average curvature of the surface is calculated, and the concave-convex feature boundary line is extracted based on the rate of change of the average curvature, The scanning path is encrypted in the feature area; finally, multi-segment measurement motion planning is carried out according to the generated scanning path, and the measurement declination inspection is carried out to complete the in-situ measurement planning of complex surfaces. The specific steps of the method are as follows:

Step 1 Generate initial scan path

First, the maximum steepness angle α of the containing aspheric surface A of the high-steepness complex surface S is calculated, which is used to guide the selection of the equal illumination angle. The maximum steepness angle α is the included angle between the normal direction of any point on the circle l _eq of the edge section of the mouth of the containing aspheric surface A and the direction of the central axis. Then, according to the angle, the initial iso-illuminance angle and angle increment are reasonably selected to calculate the iso-illuminance line containing the aspheric surface A.

Given the initial equal illumination angle β ₀ , under this equal illumination angle, the points on the inclusive aspheric surface A with the same illumination are calculated as:

为单位参考向量，计算获得相同光照度的点，形成初始等照度线l₀。Among them, P(u, v) is any point on the inclusive aspheric surface A; u, v are the curve coordinate parameters;

is a unit reference vector, calculate the points that obtain the same illuminance, and form the initial iso-illuminance line l ₀ .

According to the measurement accuracy requirements and the allowable incident angle range of the sensor beam, the angle increment Δβ is set to obtain a set of equal illumination angles {β _i |i=0,1,2,...,n},

β _i =β ₀ +i×Δβ (2)

Among them, Δβ>0, β _i ≤α, n is the number of equal illumination angles.

Finally, in the same way as the initial iso-illuminance line calculation, the iso-illuminance line set {l _i | _i =0,1, 2,...,n}. Extract the height values of each iso-illuminance line, and further calculate the non-equidistant section profile on the high-steep complex surface S based on the obtained height set {hi | _i =0,1,2,...,n} Line set {L _i |i=0,1,2,...,n}, which is used as the initial scan path.

Step 2 Generate a horizontal scan path

Generate equidistant section contour lines between two adjacent initial scanning paths, and set the number of transverse section contour lines added between every two adjacent initial scanning paths to be N _add , then the distance between equidistant sections {d _i | i=0,1,2,...,n-1} is:

The height set {h _ij |i = 0, 1, 2, ..., n, j = 1, 2, ..., N _add } of the increased transverse section contour lines is calculated as follows:

h _ij = _hi +j·d _i (4)

Calculate the equidistant between the initial scanning paths according to the set of heights of the increased transverse section contour lines {h _ij |i=0,1,2,...,n,j=1,2,...,N _add } Cross-sectional contour line set {L _ij |i=0,1,2,...,n,j=1,2,...,N _add }, where L _ij represents the i-th and i+1-th initial The jth transverse cross-sectional contour line inserted between scan paths. Thus, the initial scan path set {L _i |i=0,1,2,...,n} and the equidistant section contour set {L _ij |i=0,1,2,...,n, _j =1, ₂ , .

Step 3 Generate vertical scan path

According to the given angle index value θ, a set of section planes HP of the central axis of the complex curved surface S with high steepness are generated; the complex curved surface S with high steepness is intercepted by the set of section planes HP to obtain the longitudinal scanning path L _Z . The generated horizontal scanning path L _H and the vertical scanning path L _Z form a grid-like full-surface scanning measurement path L _Global of a complex curved surface S with high steepness.

Step 4 Generate a local area scan path for surface bumps

According to the parameter expression of the complex surface S with high steepness, a discrete parameter grid matrix P is constructed. The curve coordinates corresponding to the parameter grid nodes P _ij in the discrete parameter grid matrix P are (u _i , v _j ), i= 1,2,3,...,n, j=1,2,3,...,m. Calculate the average curvature H of the high-steepness complex surface S at each parameter grid node P _ij (u _i , v _j ), determine the average curvature change threshold Th, and determine the concave-convex feature area according to the average curvature change threshold Th.

The average curvature H is calculated according to the first and second fundamental quantities of the high-steepness complex surface S, and the calculation formula is:

Among them, E, F, and G are the first fundamental quantities of the high-steepness complex surface S, and L, M, and N are the second fundamental quantities of the high-steepness complex surface S.

Then, the average curvature change threshold Th is determined, and the concave-convex feature area is determined according to the average curvature change threshold Th; first, according to the average curvature change values in the two parameter directions, the average curvature change ratio components in the two parameter directions are calculated, respectively υH _u (u _i ,v _j ) and υH _v (u _i ,v _j ) are calculated according to the following equations:

Then, the average curvature change ratios of the two directions are synthesized to obtain the average curvature change ratio υH(u _i ,v _j ) of the high-steep complex surface S. The calculation formula is:

Then, obtain the maximum value of the average curvature change ratio υH(u _i ,v _j ) of each discrete parameter grid line along the two parameter directions, and set the minimum value of each maximum value as the average curvature change threshold Th, which is

According to the set average curvature change threshold Th, the parameter grid nodes belonging to the feature region are determined, and the nodes whose average curvature change ratio υH(u _i ,v _j ) is greater than the average curvature change threshold Th are regarded as points in the concave-convex feature region, It is marked as "1", and other nodes are marked as "0", thus generating the concave-convex feature matrix B _ij , specifically:

Finally, the feature separation curve is determined according to the obtained concave-convex feature matrix B _ij , and the boundary tracking algorithm of the eight-direction chain code is adopted, that is, the boundary curve of the concave-convex feature is extracted by using the starting point coordinates and the direction of the boundary point of the feature separation curve. A sequence SC representing the characteristic separation curve is thus formed.

利用这组局部纵向等角度截平面

截取高陡度复杂曲面S，并以特征分离曲线的序列SC为边界，得到局部纵向扫描路径

In the concave-convex feature area, a set of local longitudinal equal-angle section planes of the central axis of the complex surface S with high steepness are generated

Use this set of local longitudinal equiangular section planes

Intercept the high-steep complex surface S, and take the sequence SC of feature separation curves as the boundary to obtain the local longitudinal scanning path

Step 5 In-situ measurement motion planning

According to the obtained iso-illuminance angle set {β _i |i=0,1,2,...,n}, the full-surface scanning measurement path L _Global and the local scanning measurement path L _Local , the in-situ measurement motion planning is carried out, and the sensor rotation is obtained. The trajectory of the center point.

进行测量时，保证光学测头的光轴与高陡度复杂曲面S的中心轴线夹角为β_i，对位于等照度角β_i和β_i+1之间的纵向截面轮廓线进行连续扫描测量；当光学测头运动至等照度角为β_i+1的位置时，保证光学测头的光轴与高陡度复杂曲面S的中心轴线夹角为β_i+1，对位于等照度角β_i+1和β_i+2之间的纵向截面轮廓线进行连续扫描测量，由此实现高陡度复杂曲面S的纵向截面轮廓线的分段式扫描测量。When measuring along the transverse scanning path L _H , ensure that the optical axis of the optical probe is along the normal direction of the containing aspheric surface A of the highly steep complex curved surface S. Along longitudinal scan path L _Z and local longitudinal scan path

During the measurement, ensure that the angle between the optical axis of the optical probe and the central axis of the high-steep complex surface S is β _i , and continuously scan and measure the longitudinal cross-sectional contour line between the equal illumination angles β _i and β _i+1 . ; When the optical probe moves to the position where the equal illumination angle is β _i+1 , ensure that the optical axis of the optical probe and the central axis of the high-steep complex curved surface S are at an angle of β _i+1 ; The longitudinal cross-sectional contour line between _i+1 and β _i+2 is continuously scanned and measured, thereby realizing the segmented scanning measurement of the longitudinal cross-sectional contour line of the complex curved surface S with high steepness.

Step 6 Measure the declination angle inspection

Check whether the normal included angle γ between the optical axis of the optical probe and the high-steep complex curved surface S at each scanning sampling point exceeds the allowable deflection angle of the optical probe. When measuring along the transverse scan path L _H , the included angle γ _h is calculated according to the following formula:

为包容非球面A上任意一点的单位法向量，

为高陡度复杂曲面S 上任意一点的单位法向量。在沿纵向扫描路径L_Z和局部纵向扫描路径

进行分段扫描测量时，在每一段纵向截面轮廓线上，夹角γ_z根据下式计算：in,

is the unit normal vector containing any point on the aspheric surface A,

is the unit normal vector of any point on the high-steep complex surface S. along the longitudinal scan path L _Z and the local longitudinal scan path

When performing segmental scanning measurement, on the contour line of each longitudinal section, the included angle _γz is calculated according to the following formula:

为单位参考向量。in,

is the unit reference vector.

If the included angles γ _h and γ _z at each scanning sampling point are within the allowable declination range of the optical probe, it means that the planned scanning path and measurement motion are valid; otherwise, the angle increment Δβ set in step 1 needs to be reduced .

Step 7 Generate an in-situ measurement program

生成机床坐标系下的传感器回转中心坐标，创建G指令文件，给定机床运动参数与各轴运动指令，并保存为txt文件。According to the obtained grid-like full-surface scan measurement path L _Global and local longitudinal scan path

Generate the coordinates of the center of rotation of the sensor in the machine tool coordinate system, create a G command file, give the machine tool motion parameters and the motion commands of each axis, and save it as a txt file.

The beneficial effect of the present invention is that in the method, the non-equidistant transverse cross-sectional contour line is generated with the equal illumination angle as the constraint condition, and the generated non-equidistant transverse cross-sectional line and the longitudinal cross-sectional line are combined to obtain a full-surface grid scanning Measurement path. It solves the problem of sparse measurement trajectories near the poles caused by the large longitudinal height difference of high-steep surfaces, and the problems that the high-steep regions and concave-convex feature regions of surfaces cannot be fully expressed due to the use of equidistant cross-sectional contour lines as scanning paths. According to the equal illumination angle, the machine tool measurement motion trajectory that takes into account the incident angle of the sensor beam is generated, which avoids the frequent indexing of the probe, and effectively avoids the rotary table from participating in coordinate extraction, reducing the nonlinear error caused by its interpolation motion. , to ensure the measurement accuracy of the feature area. The movement direction of scanning measurement is specified, which avoids the measurement error caused by the backlash of the linear axis; at the same time, the dynamic error caused by the multi-axis linkage of the machine tool is reduced, and the key areas of high-steep complex surfaces and aspherical parts are improved, such as poles, Expression integrity in the equatorial region. The method has strong versatility, and can realize precise and fast in-situ measurement of high-steep surface parts on multi-axis CNC machine tools or coordinate measuring machines.

Description of drawings

Accompanying drawing 1—flow chart of the planning method of the present invention;

局部纵向扫描路径；l_eq-包容非球面A口部边缘截面圆；

包容非球面A口部边缘截面圆l_eq上任意点的单位法向量；

单位参考向量；α-高陡度复杂曲面S的包容非球面A的最大陡度角α；Accompanying drawing 2 - scanning path planning schematic diagram, wherein: L _H - horizontal scanning path, L _Z - vertical scanning path,

Partial longitudinal scan path; l _eq - a circle containing the edge section of the mouth of the aspheric surface A;

The unit normal vector of any point on the circle l _eq of the edge section at the mouth of the containing aspheric surface A;

Unit reference vector; α - the maximum steepness angle α of the containing aspheric surface A of the high-steepness complex surface S;

第i条横向扫描路径，Bⁱ-第i条横向扫描路径的最小包容圆，O-最小包容圆的圆心，P-第i条横向扫描路径上的测点，T-测点P处对应的最小包容圆法线方向；Figure 3 - Schematic diagram of lateral measurement motion planning, in which: 1-optical probe, a-centerline of optical probe 1,

The i-th transverse scan path, B ⁱ - the minimum inclusive circle of the i-th transverse scan path, O - the center of the minimum inclusive circle, P - the measuring point on the i-th transverse scan path, T - the corresponding measurement point P Minimum inclusive circle normal direction;

第一条纵向扫描路径L_Z1内第i-1段扫描线的起始控制点，

第一条纵向扫描路径L_Z1内第i段扫描线的起始控制点，T_i-1-第一条纵向扫描路径L_Z1内第i-1段扫描线的测量方向矢量，T_i-第一条纵向扫描路径L_Z1内第i段扫描线的测量方向矢量；Accompanying drawing 4 - Schematic diagram of transverse measurement motion planning, wherein: L _Z1 - the first longitudinal scanning path, τ _i-1 - the i-1th scanning line in the first longitudinal scanning path L _Z1 , τ _i - the first scanning line the i-th scanning line in the longitudinal scanning path L _Z1 ,

The starting control point of the scan line of the i-1th segment in the first longitudinal scan path L _Z1 ,

The starting control point of the i-th scanning line in the first longitudinal scanning path L _Z1 , T _i-1 - the measurement direction vector of the i-1 scanning line in the first longitudinal scanning path L _Z1 , T _i - the i-th scanning line The measurement direction vector of the i-th scanning line in a longitudinal scanning path L _Z1 ;

Figure 5 - Schematic diagram of the test for measuring the declination angle γ _h , where: γ _max - the maximum declination angle allowed by the optical probe.

Detailed ways

The specific embodiments of the present invention will be described in detail with reference to the technical solutions and the accompanying drawings.

In this embodiment, the high-steepness complex curved surface S used is a free-form surface with concave-convex-convex features on the surface, a height of 52.5 mm, a diameter of 100 mm, and a total of 4 non-rotationally symmetrical concave features in the circumferential direction. Accompanying drawing 1 is the flow chart of the planning method of the present invention, and the specific steps of in-situ measurement planning of this curved surface are as follows:

Step 1 Generate initial scan path

与单位参考向量

之间的夹角，本实施例中的最大陡度角α为61.5367°，如附图2所示。然后计算包容非球面A上任意一点P(u,v)的单位法向量为

选择高陡度复杂曲面S或其包容非球面A的中心轴线作为参考方向，本实施例中的参考方向在工件坐标系中为[0,0,1]，给定初始等照度角β₁＝0.6046°，根据式(1)计算获得相同光照度的点，形成初始等照度线l₀。根据测量精度要求与传感器光束允许的入射角度范围，给定角度增量Δβ＝4°，利用式(2)得到等照度角集合{β_i|i＝0,1,2,...,14}。最后，与计算初始等照度线同理，根据等照度角集合{β_i|i＝0,1,2,...,14}计算得到等照度线集合{l_i|i＝0,1,2,...,14}。提取各条等照度线的高度值，得到高度集合 {h_i|i＝0,1,2,...,14}，表1列出计算得到的15条等照度线高度值。First, calculate the maximum steepness angle α of the containing aspheric surface A of the high-steep complex surface S. The maximum steepness angle α is the unit normal vector of any point on the circle l _eq of the edge section at the mouth of the containing aspheric surface A.

with the unit reference vector

The angle between them, the maximum steepness angle α in this embodiment is 61.5367°, as shown in FIG. 2 . Then calculate the unit normal vector containing any point P(u, v) on the aspheric surface A as

The central axis of the high-steep complex surface S or its containing aspheric surface A is selected as the reference direction. The reference direction in this embodiment is [0, 0, 1] in the workpiece coordinate system, and the initial equal illumination angle β ₁ = 0.6046°, according to formula (1), the points of the same illuminance are calculated to form the initial iso-illuminance line l ₀ . According to the measurement accuracy requirements and the allowable incident angle range of the sensor beam, given the angle increment Δβ=4°, the equal illumination angle set {β _i |i=0,1,2,...,14 can be obtained by using the formula (2). }. Finally, in the same way as the calculation of the initial iso-illuminance line, the set of iso-illuminance lines {l _i | _i =0,1, 2,...,14}. Extract the height values of each iso-illuminance line to obtain a height set {hi | _i =0,1,2,...,14}, and Table 1 lists the calculated height values of the 15 iso-illuminance lines.

Table 1 The height value h _i (mm) of the iso-illuminance line containing the aspheric surface A

According to the height set {h _i |i=0,1,2,...,14}, the non-equidistant section contours on the complex surface S with high steepness are calculated and used as the initial scanning path {L _i |i =0,1,2,...,14}.

Step 2 Generate a horizontal scan path

Equidistant cross-sectional contour lines are generated between two adjacent initial scanning paths. In this embodiment, the number N _add of transverse cross-sectional contour lines added between two adjacent initial scanning paths is 2. According to the height set of the increased transverse cross-sectional contour lines {h _ij |i=0,1,2,...,14,j=1,2} Calculated to obtain the set of equidistant cross-sectional contour lines between the initial scanning paths{L _ij |i=0,1,2, ...,14,j=1,2}, where L _ij represents the j-th transverse cross-sectional contour line inserted between the i-th and the i+1-th iso-illuminance line corresponding to the initial scanning path. Thus, the initial scan path set {L _i |i=0,1,2,...,14} and the equidistant section contour set {L _ij |i=0,1,2,...,14, j=1, 2} together form 43 transverse scanning paths L _H of the complex curved surface S with high steepness. Table 2 lists the calculated height values of the lateral scan path.

Table 2. Height value of transverse scanning path of high-steep complex surface S (mm)

Step 3 Generate vertical scan path

Given the angle division value θ=20°, a set of section planes HP of the central axis of the complex curved surface S with high steepness are generated. Using this set of section planes HP to take the complex curved surface S with high steepness, the longitudinal scanning path L _Z is obtained, 18 in total. The generated horizontal scanning path L _H and the vertical scanning path L _Z form a grid-like full-surface scanning measurement path L _Global of a complex curved surface S with high steepness.

Step 4: Extract the surface bump and volt features and generate a local scan path

According to the parameter expression of the complex surface S with high steepness, a discrete parameter grid matrix P is constructed. The curve coordinates corresponding to the parameter grid nodes P _ij in the discrete parameter grid matrix P are (u _i , v _j ), i= 1,2,3,...,n, j=1,2,3,...,m. Calculate the average curvature H of the high-steep complex surface S at each parameter grid node P _ij (u _i , v _j ) according to formula (5), determine the average curvature change threshold Th, and determine the concave-convex feature according to the average curvature change threshold Th area.

The method for determining the average curvature change threshold Th is as follows: first, according to the average curvature change values in the two parameter directions, the average curvature change ratio components in the two parameter directions are calculated by using equations (6) and (7), which are respectively recorded as υH _u (u _i , v _j ) and υH _v (u _i , v _j ), then, according to formula (8), the average curvature change ratios in the two directions are synthesized to obtain the average curvature change ratio υH ( u _i ,v _j ). Then, use the formula (9) to obtain the maximum value of the average curvature change ratio υH(u _i ,v _j ) of each discrete parameter grid line along the two parameter directions, and set the minimum value among the maximum values as the average Curvature change threshold Th.

According to the set average curvature change threshold Th, the parameter grid nodes belonging to the feature region are determined, and the nodes whose average curvature change ratio υH(u _i ,v _j ) is greater than the average curvature change threshold Th are regarded as points in the concave-convex feature region, It is marked as "1" and other nodes are marked as "0" to generate a bump feature matrix B _ij . Finally, the feature separation curve is determined according to the obtained concave-convex feature matrix B _ij , and the boundary curve of the concave-convex feature is extracted by the boundary tracking algorithm of the eight-direction chain code. A sequence SC representing the characteristic separation curve is thus formed.

利用这组局部纵向等角度截平面

截取高陡度复杂曲面S，并以特征分离曲线的序列SC为边界，得到局部纵向扫描路径

In the concave-convex feature area, generate a set of high-steep complex surfaces S or local longitudinal equal-angle section planes containing the central axis of the aspheric surface A

Use this set of local longitudinal equiangular section planes

Intercept the high-steep complex surface S, and take the sequence SC of feature separation curves as the boundary to obtain the local longitudinal scanning path

The generated scanning measurement path is shown in Figure 2.

Step 5 In-situ measurement motion planning

According to the obtained iso-illuminance angle set {β _i |i=0,1,2,...,n}, the full-surface scanning measurement path L _Global and the local scanning measurement path L _Local , the in-situ measurement motion planning is carried out, and the sensor rotation is obtained. The trajectory of the center point.

进行测量时，计算在每一个测点P处对应的最小包容圆Bⁱ的法线方向T，并调整光学测头1的中心线a沿着该方向测量，如附图3所示。along the i-th lateral scan path

During measurement, calculate the normal direction T of the smallest inclusive circle B ⁱ corresponding to each measuring point P, and adjust the centerline a of the optical probe 1 to measure along this direction, as shown in FIG. 3 .

进行测量时，以第一条纵向扫描路径L_Z1为例，如附图4所示。光学测头1运动至第一条纵向扫描路径L_Z1内第i-1段扫描线的起始控制点

并自动调整光学测头1的中心线 a与第一条纵向扫描路径L_Z1内第i-1段扫描线的测量方向矢量T_i-1重合，保证光学测头1的光轴与高陡度复杂曲面S的中心轴线夹角为β_i-1。光学测头 1连续运动至第一条纵向扫描路径L_Z1内第i段扫描线的起始控制点

使光学测头1的中心线a与第一条纵向扫描路径L_Z1内第i段扫描线的测量方向矢量T_i重合，保证光学测头的光轴与高陡度复杂曲面S的中心轴线夹角为β_i。光学测头1沿第一条纵向扫描路径L_Z1内的各段扫描线依次测量。Along longitudinal scan path L _Z and local longitudinal scan path

When measuring, take the first longitudinal scanning path L _Z1 as an example, as shown in FIG. 4 . The optical probe 1 moves to the starting control point of the i-1th scanning line in the first longitudinal scanning path L _Z1

And automatically adjust the center line a of the optical probe 1 to coincide with the measurement direction vector T _i- 1 of the scan line i-1 in the first longitudinal scanning path L _Z1 to ensure that the optical axis of the optical probe 1 and the high steepness The included angle of the central axis of the complex surface S is β _i-1 . The optical probe 1 moves continuously to the starting control point of the i-th scanning line in the first longitudinal scanning path L _Z1

Make the center line a of the optical probe 1 coincide with the measurement direction vector T _i of the i-th scanning line in the first longitudinal scanning path L _Z1 , and ensure that the optical axis of the optical probe is clamped with the central axis of the complex curved surface S with high steepness. The angle is β _i . The optical probe 1 measures sequentially along each segment of the scanning line in the first longitudinal scanning path L _Z1 .

Step 6 Measure the declination inspection

进行分段扫描测量时，根据式(12)，计算得夹角γ_z的最大值为 14.8478°。夹角γ_h和γ_z均小于光学测头的允许偏角，生成的测量路径与规划的测量运动有效。Check whether the normal included angle γ between the optical axis of the optical probe and the high-steep complex curved surface S at each scanning sampling point exceeds the allowable deflection angle of the optical probe. In this embodiment, the allowable deflection angle of the optical probe is ±30°. When measuring along the lateral scanning path L _H , according to formula (11), the maximum value of γ _h is calculated to be 20.0427°, as shown in FIG. 5 . along the longitudinal scan path L _Z and the local longitudinal scan path

When performing segmented scanning measurement, according to formula (12), the maximum value of the included angle γ _z is calculated to be 14.8478°. The included angles γ _h and γ _z are both smaller than the allowable declination angle of the optical probe, and the generated measurement path is valid with the planned measurement movement.

Step 7 Generate an in-situ measurement program

生成机床坐标系下的传感器回转中心坐标，创建G指令文件，给定机床运动参数与各轴运动指令，并保存为txt文件。According to the obtained grid-like full-surface scan measurement path L _Global and local longitudinal scan path

Generate the coordinates of the center of rotation of the sensor in the machine tool coordinate system, create a G command file, give the machine tool motion parameters and the motion commands of each axis, and save it as a txt file.

The invention realizes the in-situ scanning path generation and measurement motion planning of high-steep and complex curved surfaces, effectively avoids the rotary table from participating in coordinate extraction, reduces the dynamic error caused by the multi-axis linkage of the machine tool, and ensures the measurement accuracy of the characteristic area. The expression integrity of key areas (such as poles and equatorial regions) of high-steep complex surfaces and aspherical parts is improved, the automatic generation of in-situ measurement programs is completed, and precise and fast in-situ measurement of high-steep complex surfaces is realized.

Claims (1)

1. a high-steepness complex curved surface in-situ measurement planning method, it is characterized in that, in the measurement planning method, at first with the central axis of the high-steepness complex curved surface as the reference direction, according to the given equal illumination angle size, calculate and obtain this The iso-illuminance line of the aspheric surface is included in the reference direction, and the corresponding non-equidistant section contour line is used as the initial scanning path of the high-steep complex surface; secondly, the equidistant section contour line is generated between two adjacent section contour lines, and the transverse section contour line is obtained. Scanning path; according to the given angle index value, calculate the longitudinal section contour line to obtain the longitudinal scanning path; then, calculate the average curvature of the surface, extract the concave-convex feature boundary line based on the change rate of the average curvature, and encrypt the scan in the feature area Finally, according to the generated scanning path, carry out multi-segment stitching measurement motion planning, and carry out measurement declination inspection to complete the in-situ measurement planning of complex surfaces; the specific steps of the planning method are as follows: The first step is to generate the initial scan path First, calculate the maximum steepness angle α of the containing aspheric surface A of the high-steep complex surface S; then, according to the angle, reasonably select the initial iso-illuminance angle and angle increment, which are used to calculate the iso-illuminance line of the containing aspheric surface A; Given the initial equal illumination angle β ₀ , under this equal illumination angle, the points on the inclusive aspheric surface A with the same illumination are calculated as:

Among them, P(u, v) is any point on the inclusive aspheric surface A; u, v are the curve coordinate parameters;

is the unit reference vector, calculate the points that obtain the same illuminance, and form the initial iso-illuminance line l ₀ ; Set the angle increment Δβ to obtain a set of equal illumination angles {β _i |i=0,1,2,...,n}, β _i =β ₀ +i×Δβ (2) Among them, Δβ>0, β _i ≤α, n is the number of iso-illuminance angles; the same as the initial iso-illuminance line calculation, according to the set of iso-illuminance angles {β _i |i=0,1,2,...,n } Calculate the set of iso-illuminance lines {l _i |i=0,1,2,...,n}; extract the height value of each iso-illuminance line, according to the obtained height set {h _i |i=0,1 ,2,...,n}, the non-equidistant cross-sectional contour set {L _i |i=0,1,2,...,n} on the complex surface S with high steepness is obtained by further calculation, which is taken as initial scan path; Step 2 Generate a horizontal scan path Generate equidistant section contour lines between two adjacent initial scanning paths, and set the number of transverse section contour lines added between every two adjacent initial scanning paths to be N _add , then the distance between equidistant sections {d _i | i=0,1,2,...,n-1} is:

The height set {h _ij |i = 0, 1, 2, ..., n, j = 1, 2, ..., N _add } of the increased transverse section contour lines is calculated as follows: h _ij = _hi +j·d _i (4) The equidistant between the initial scan paths is calculated according to the set of heights of the increased transverse section contour lines {h _ij |i=0,1,2,...,n,j=1,2,...,N _add } Cross-sectional contour line set {L _ij |i=0,1,2,...,n,j=1,2,...,N _add }, where L _ij represents the i-th and i+1-th initial The j-th transverse section contour line inserted between the scan paths; thus, the initial set of scan paths {L _i |i=0,1,2,...,n} and the set of equidistant section contour lines {L _ij | _i = ₀ , 1, 2, . Step 3 Generate a vertical scan path According to the given angle index value θ, generate a group of section planes HP of the central axis of the complex curved surface S with high steepness; use this group of section planes HP to intercept the complex curved surface S with high steepness to obtain the longitudinal scanning path _LZ ; generate The horizontal scanning path L _H and the longitudinal scanning path L _Z form a grid-like full-surface scanning measurement path L _Global of a complex curved surface S with high steepness; The fourth step is to generate a local area scan path for surface bumps According to the parameter expression of the complex surface S with high steepness, a discrete parameter grid matrix P is constructed. The curve coordinates corresponding to the parameter grid nodes P _ij in the discrete parameter grid matrix P are (u _i , v _j ), i= 1,2,3,...,n, j=1,2,3,...,m; calculate the high-steepness complex surface S at each parameter grid node P _ij (u _i ,v _j ) the average curvature H, determine the average curvature change threshold Th, and determine the concave-convex feature area according to the average curvature change threshold Th; The average curvature H is calculated according to the first and second fundamental quantities of the high-steepness complex surface S, and the calculation formula is:

Among them, E, F, G are the first fundamental quantities of the high-steepness complex surface S, and L, M, N are the second fundamental quantities of the high-steepness complex surface S; Determine the average curvature change threshold Th, and determine the concave-convex feature area according to the average curvature change threshold Th; first, according to the average curvature change values in the two parameter directions, calculate the average curvature change ratio components in the two parameter directions, which are υH _u ( u _i ,v _j ) and υH _v (u _i ,v _j ) are calculated according to the following formulas:

The average curvature change ratio of the two directions is synthesized to obtain the average curvature change ratio υH(u _i ,v _j ) of the high-steep complex surface S. The calculation formula is:

Obtain the maximum value of the average curvature change ratio υH(u _i , v _j ) of each discrete parameter grid line along the two parameter directions, and set the minimum value of each maximum value as the average curvature change threshold Th, that is,

According to the set average curvature change threshold Th, the parameter grid nodes belonging to the feature region are determined, and the nodes whose average curvature change ratio υH(u _i ,v _j ) is greater than the average curvature change threshold Th are regarded as points in the concave-convex feature region, It is marked as "1", and other nodes are marked as "0", thus generating the concave-convex feature matrix B _ij , specifically:

Finally, the feature separation curve is determined according to the obtained concave-convex feature matrix B _ij , and the boundary tracking algorithm of the eight-direction chain code is used, that is, the boundary curve of the concave-convex feature is extracted by using the starting point coordinates and the direction of the boundary point of the feature separation curve; the sequence SC of the characteristic separation curves; In the concave-convex feature area, a set of local longitudinal equal-angle section planes of the central axis of the complex surface S with high steepness are generated

Use this set of local longitudinal equiangular section planes

Intercept the high-steep complex surface S, and take the sequence SC of feature separation curves as the boundary to obtain the local longitudinal scanning path

Step 5 In-situ measurement motion planning According to the obtained iso-illuminance angle set {β _i |i=0,1,2,...,n}, the full-surface scanning measurement path L _Global and the local scanning measurement path L _Local , the in-situ measurement motion planning is carried out, and the sensor rotation is obtained. The trajectory of the center point; When measuring along the transverse scanning path L _H , ensure that the optical axis of the optical probe is along the normal direction of the containing aspheric surface A of the highly steep and complex curved surface S; along the longitudinal scanning path L _Z and the local longitudinal scanning path

During the measurement, ensure that the angle between the optical axis of the optical probe and the central axis of the high-steep complex surface S is β _i , and continuously scan and measure the longitudinal cross-sectional contour line between the equal illumination angles β _i and β _i+1 . ; When the optical probe moves to the position where the equal illumination angle is β _i+1 , ensure that the optical axis of the optical probe and the central axis of the high-steep complex curved surface S are at an angle of β _i+1 ; The longitudinal section contour between _i+1 and β _i+2 is continuously scanned and measured, thereby realizing the segmented scanning measurement of the longitudinal section contour of the complex curved surface S with high steepness; The sixth step is to measure the declination angle test Check whether the normal angle γ between the optical axis of the optical probe and the high-steep complex curved surface S at each scanning sampling point exceeds the allowable deflection angle of the optical probe; when measuring along the lateral scanning path L _H , the included angle γ _h is calculated according to the following formula,

in,

is the unit normal vector containing any point on the aspheric surface A,

is the unit normal vector of any point on the high-steep complex surface S; along the longitudinal scan path L _Z and the local longitudinal scan path

When performing segmental scanning measurement, on the contour line of each longitudinal section, the included angle _γz is calculated according to the following formula,

in,

is the unit reference vector; if the included angles γ _h and γ _z at each scanning sampling point are within the allowable declination range of the optical probe, it means that the planned scanning path and measurement motion are valid; otherwise, the setting in step 1 needs to be reduced The angle increment Δβ of ; Step 7 Generate an in-situ measurement program According to the obtained grid-like full-surface scan measurement path L _Global and local longitudinal scan path

Generate the coordinates of the center of rotation of the sensor in the machine tool coordinate system, create a G command file, give the machine tool motion parameters and the motion commands of each axis, and save it as a txt file.

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