A rotary feature on-machine measurement path adaptive optimization method

Abstract

The present application relates to the field of in-process measurement path planning, and proposes a kind of in-process measurement path adaptive optimization method of rotary feature.The present application carries out adaptive optimization to measurement path according to the geometric parameters of rotary feature of workpiece and the planning measurement point target section, measurement point number and measurement safety strategy and other parameters, and sets up adaptive circular arc between the measurement safety point corresponding to adjacent single measurement point to transition, to avoid the interference between measuring needle and rotary feature in moving process, cause the damage to measuring needle;At the same time, set adaptive circular arc to transition, can avoid the problem of interference between measuring needle and workpiece in moving process by increasing the number of measurement points or increasing the moving distance of measuring needle ball, the length of entire measurement path can be effectively shortened by optimizing measurement path through adaptive circular arc transition, improve the execution efficiency of in-process measurement, to reduce the use cost of machine tool.

Description

Technical Field

[0001] This invention relates to the field of in-machine measurement path planning, and in particular to an adaptive optimization method for in-machine measurement paths with turning characteristics. Background Technology

[0002] With the rapid development of in-machine measurement technology, it is increasingly being applied to defect detection and adaptive compensation machining of machined parts. A key step in in-machine measurement of workpieces is planning the in-machine measurement path for the target features on the workpiece. The quality of the in-machine measurement path directly affects the efficiency, accuracy, and reliability of the measurement results. Rotational features such as circles, cylinders, cones, spheres, and 3D tori are among the most common geometric features in machined parts, and their in-machine inspection results significantly influence the determination of the pass / fail status of related parts. Therefore, providing an in-machine measurement path optimization method for rotational features is an urgent need in the field of in-machine measurement technology.

[0003] Currently, in-machine measurement path planning for rotary features only generates measurement points by discretely arranging points of equal arc length in single or multiple cross-sectional circles. This is then combined with safety strategies and other relevant parameters to automatically generate the measurement path. Adjacent measurement points are connected by straight lines, without any optimization of the measurement path or simple optimization by adjusting the connection order of the measurement points. When the rotary feature is located in a special workpiece position and two adjacent measurement points are far apart, simply connecting them with straight lines easily leads to interference during measurement, damaging the probe. To avoid this interference, the number of measurement points is usually increased, or the safe distance for probe movement during measurement is increased to prevent interference between the probe and the workpiece. However, this method results in a lengthy measurement path and increased machine tool operating costs. Summary of the Invention

[0004] Therefore, the technical problem to be solved by the present invention is to overcome the problem that in the prior art, when generating the measurement path for the rotational characteristics of the workpiece, the measurement path is simply connected by a straight line through a safety point between two adjacent measurement points, which causes interference between the probe and the workpiece during the measurement process. In addition, the measurement path is not optimized to avoid interference, resulting in an excessively long measurement path, low detection efficiency, and high machine tool operating costs.

[0005] To address the aforementioned technical problems, this invention provides an adaptive optimization method for on-machine measurement path of rotational features, comprising:

[0006] Step 1: Set the number of measurement points on each target section; obtain the rotational characteristics of the workpiece to be measured and the geometric parameters of the target sections of the workpiece that need to be measured;

[0007] Step 2: Based on the rotational characteristics of the workpiece to be measured and the normal vector of the two-dimensional plane, determine the first rotational transformation matrix and the second rotational transformation matrix; position each target section on the XOY two-dimensional plane through the first rotational transformation matrix, so that the target section becomes a target section circle distributed on the two-dimensional plane; obtain the geometric parameters of the target section circle on the two-dimensional plane based on the geometric parameters of the target section in the three-dimensional coordinate system; obtain the measurement point set corresponding to each target section circle based on the number of measurement points in each target section;

[0008] Step 3: Set the measurement safety strategy parameters, which include the radius of the probe ball used in the measurement process and the safe distance of each measurement point on the target cross-section circle;

[0009] Step 4: Based on the coordinates of each measurement point in the measurement point set, determine the retraction vector of the probe's movement direction when the probe ball detects that measurement point. Combining the coordinates of each measurement point, the retraction vector of the probe's movement direction, and the radius of the probe ball, determine the measurement target point of the probe ball when measuring each measurement point. Based on the set safety distance for each measurement point, determine the coordinates of the corresponding safety measurement point for each measurement point.

[0010] Step 5: Repeat step 4 until all target cross-section circles have been processed, and obtain the measurement target point and measurement safety point of the probe ball on each target cross-section circle;

[0011] Step 6: To ensure that the probe ball does not interfere with the rotation feature during its movement to the next measurement safety point, an arc transition point is set between the current measurement safety point and the next measurement safety point according to the direction of the probe ball's movement. The angle at which the probe ball moves towards the arc transition point is the maximum central angle that the probe ball can cross in each movement; determine the maximum central angle that the probe ball can cross in each movement, i.e., the arc distance step length;

[0012] Step 7: Based on the maximum central angle that the probe ball can cross during its movement, and the angles formed by connecting the current measurement point and the next measurement point to the center of the target cross-section circle, determine the number of arc transition points between the current safe measurement point and the next safe measurement point, as well as the coordinates of each arc transition point, and obtain the corresponding set of arc transition points.

[0013] Step 8: Repeat steps 6 and 7 until, except for the last target cross-section circle measurement point, all the measurement safety points on the target cross-section circle have corresponding arc transition points between them and the next measurement safety point;

[0014] Step 9: Using the second rotation transformation matrix, measure the target points, safety points, and transition points (i.e., measurement path points) of all probe balls on each target cross section to obtain the measurement path points in the original three-dimensional coordinate system. On each target cross section, connect the probes in the order of safety point - target point - safety point - transition point to obtain the measurement path of the probe on each target cross section. Except for the last target cross section, connect the last measurement path point in each other target cross section with the initial measurement path point in the next target cross section to obtain the non-interference measurement path of the probes on all target cross sections.

[0015] In one embodiment of the present invention, in step 1, the number of measurement points is n, the rotation feature is the axial vector V(i,j,k); the center coordinates of the target cross section are O0(x,y,z), the radius is R, and in each target cross section...

[0016] In one embodiment of the present invention, in step 2, the first rotation transformation matrix M1 of the axial vector to the normal vector OZ(0,0,1) of the two-dimensional plane is:

[0017]

[0018] In step 9, the second rotation transformation matrix M2 is:

[0019]

[0020] Where β is the angle between the axial vector V and the vector OZ;

[0021] After transformation to a two-dimensional plane, the center coordinates of the target cross-section circle are O(x,y), the radius is R, and the arc parameter curve is C; the measurement point set Ωc{p} corresponding to the target cross-section circle i (x ci ,y ci Let |i=1,2...n}, where n measurement points are distributed on the circular arc curve C.

[0022] In one embodiment of the present invention, the radius of the probe ball is r, and the safe distance between each measuring point is Ωd = {d1, d2, ..., n}.

[0023] In one embodiment of the present invention, in step 4, a circle is constructed with the center O(x,y) of the target cross-section circle pointing to the measurement point p. i (x ci ,y ci The probe retraction vector N i (i,j)=(x ci -x,y ci -y), based on the internal and external properties of the rotation feature, when it is an outer circle, the probe retraction vector is N. iWhen the inner circle is denoted by N, the probe retraction vector is... i (i,j)=-N i (i,j).

[0024] In one embodiment of the present invention, in step 4, the measurement target point P of the probe ball is determined according to the probe ball radius r. ci For P ci =P i +r×N i According to the measurement point P i Determine the safe distance and the measurement point P. i Corresponding measurement safety point P di For P di =P ci +d×N i .

[0025] In one embodiment of the present invention, in step 6, to ensure that the probe ball does not interfere with the rotation feature during its movement, the probe ball is set to move along the return vector N. i directional retreat safety distance d i And the safe distance d i satisfy

[0026] Where α is the maximum central angle that the probe ball can cross in each movement under the condition of no interference, that is, the arc distance from the step; according to the safety distance d i Determine the maximum central angle that the probe ball can cross in each movement.

[0027] Taking into account the errors of the measurement system, the machining errors of the rotation characteristics, and other error factors, a safety factor δ is introduced to adjust the magnitude of α, where δ∈(0,1). After adjustment...

[0028] In one embodiment of the present invention, in step 7, the target cross-section circle center O(x,y) points to the current measurement point P. i vector U i (i,j) and pointing to the next measurement point P i+1 vector W i (i,j) determines the angle θ between the two vectors, that is, the central angle corresponding to the arc transition curve D formed between two adjacent measurement safety points is θ.

[0029] In one embodiment of the present invention, the number m of transition points on the circular arc transition curve D is determined based on the maximum central angle α that the probe ball can cross:

[0030] m = θ / α - 1, and m is an integer.

[0031] In one embodiment of the present invention, based on the center O(x,y) and vector U i (i,j), vector W i Given (i,j), the radius R of the target cross-section circle, and the radius r of the probe sphere, calculate the circular arc transition curve D. Distribute the above m circular arc transition points at equal intervals on the circular arc transition curve D to obtain the set of circular arc transition points Ωq{q i (x di ,y di )|i=1,2...m}.

[0032] The technical solution of the present invention has the following advantages compared with the prior art:

[0033] The in-machine measurement path optimization method of this invention adaptively optimizes the measurement path based on parameters such as rotation characteristics, geometric parameters of the target cross-section of the planned point, the number of measurement points, and measurement safety strategies. Furthermore, it sets adaptive arcs for transitions between adjacent single measurement points and their corresponding safety points, thereby preventing interference between the probe and the rotation characteristics during movement and thus avoiding damage to the workpiece. Simultaneously, setting adaptive arcs for transitions avoids addressing the problem of probe interference during movement by increasing the number of measurement points or the probe ball's movement distance. Optimizing the measurement path through adaptive arc transitions effectively shortens the overall measurement path length, improves the efficiency of in-machine measurement, and thus reduces the operating costs of the machine tool. Attached Figure Description

[0034] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0035] Figure 1 This is a flowchart of the adaptive optimization method for on-machine measurement path of rotational features provided in this embodiment of the invention;

[0036] Figure 2 This is a schematic diagram of adaptive optimization of the measurement path for the circular rotating feature section provided in an embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of the arc dispersion step length calculation provided in the embodiment of the present invention. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0039] Reference Figure 1 As shown, the in-machine measurement path optimization method provided by this invention includes:

[0040] Step 1: Set the number of measurement points on each target section; obtain the rotational characteristics of the workpiece to be measured and the geometric parameters of the target sections of the workpiece that need to be measured;

[0041] Step 2: Based on the rotational characteristics of the workpiece to be measured and the normal vector of the two-dimensional plane, determine the first rotational transformation matrix and the second rotational transformation matrix; position each target section on the XOY two-dimensional plane through the first rotational transformation matrix, so that the target section becomes a target section circle distributed on the two-dimensional plane; obtain the geometric parameters of the target section circle on the two-dimensional plane based on the geometric parameters of the target section in the three-dimensional coordinate system; obtain the measurement point set corresponding to each target section circle based on the number of measurement points in each target section;

[0042] Step 3: Set the measurement safety strategy parameters, which include the radius of the probe ball used in the measurement process and the safe distance of each measurement point on the target cross-section circle;

[0043] Step 4: Based on the coordinates of each measurement point in the measurement point set, determine the retraction vector of the probe's movement direction when the probe ball detects that measurement point. Combining the coordinates of each measurement point, the retraction vector of the probe's movement direction, and the radius of the probe ball, determine the measurement target point of the probe ball when measuring each measurement point. Based on the set safety distance for each measurement point, determine the coordinates of the corresponding safety measurement point for each measurement point.

[0044] Step 5: Repeat step 4 until all target cross-section circles have been processed, and obtain the measurement target point and measurement safety point of the probe ball on each target cross-section circle;

[0045] Step 6: To ensure that the probe ball does not interfere with the rotation feature during its movement to the next measurement safety point, an arc transition point is set between the current measurement safety point and the next measurement safety point according to the direction of the probe ball's movement. The angle at which the probe ball moves towards the arc transition point is the maximum central angle that the probe ball can cross in each movement; determine the maximum central angle that the probe ball can cross in each movement, i.e., the arc distance step length;

[0046] Step 7: Based on the maximum central angle that the probe ball can cross during its movement, and the angles formed by connecting the current measurement point and the next measurement point to the center of the target cross-section circle, determine the number of arc transition points between the current safe measurement point and the next safe measurement point, as well as the coordinates of each arc transition point, and obtain the corresponding set of arc transition points.

[0047] Step 8: Repeat steps 6 and 7 until, except for the last target cross-section circle measurement point, all the measurement safety points on the target cross-section circle have corresponding arc transition points between them and the next measurement safety point;

[0048] Step 9: Using the second rotation transformation matrix, measure the target points, safety points, and transition points (i.e., measurement path points) of all probe balls on each target cross section to obtain the measurement path points in the original three-dimensional coordinate system. On each target cross section, connect the probes in the order of safety point - target point - safety point - transition point to obtain the measurement path of the probe on each target cross section. Except for the last target cross section, connect the last measurement path point in each other target cross section with the initial measurement path point in the next target cross section to obtain the non-interference measurement path of the probes on all target cross sections.

[0049] In the specific path planning process, firstly, the axial vector V(i,j,k) of the rotation feature is determined; the center coordinates O0(x,y,z) and radius R of the target cross section are determined; the recommended national standards shown in Table 1 are consulted, and the measurement accuracy that the workpiece must meet is determined based on the application of the workpiece in practice; referring to the number of measurement points recommended by the British Standards Institution standard BS7172:1989 shown in Table 2 for several general surface features, the number of measurement points n in each target cross section is set. The number of measurement points recommended in Table 2 is based on the geometric characteristics of the workpiece to be measured, which, while meeting the measurement accuracy, also takes into account the measurement speed, providing a suitable recommended number of measurement points for workpiece measurement, ensuring measurement efficiency and avoiding deviations caused by too few measurement points.

[0050] Table 1. Tolerance grades and limit deviations for general tolerances of linear dimensions.

[0051]

[0052] Table 2. Number of measurement points for each feature recommended by British Standards Institution Standard BS7172:1989

[0053]

[0054] During the transformation of the target cross section into a two-dimensional plane through the first rotation transformation matrix, the center coordinates of the target cross section are multiplied by the first rotation transformation matrix M1 to obtain the target cross section circle corresponding to the target cross section on the two-dimensional plane, with the center coordinates being O(x,y), the radius being R, and the arc parameter curve being C.

[0055] The first rotation transformation matrix is ​​formed by the normal vector OZ(0,0,1) from the axial vector to the two-dimensional plane:

[0056]

[0057] Where β is the angle between the axial vector V and the vector OZ.

[0058] Based on the number n of measurement points on the target cross section, determine the corresponding set of measurement points Ωc{p} on the circle of the target cross section. i (xci ,y ci Let |i=1,2...n}, where n measurement points are distributed on the circular arc parametric curve C.

[0059] Set the measurement safety strategy parameters. During the measurement process, the radius of the probe ball used is r, and the safety distance of each measurement point is Ωd={d1,d2,...,n}.

[0060] Determine the retraction vector of the probe's movement direction when the probe ball detects the measurement point.

[0061] Based on the center of the target cross-section circle and the measurement point, determine the direction from the center O(x,y) of the target cross-section circle to the measurement point p. i (x ci ,y ci The retraction vector N of the probe ball in the direction of probe movement when it detects the measurement point. i (i,j)=(x ci -x,y ci -y), based on the internal and external attributes, when it is an outer circle, the retraction vector of the probe movement direction is N. i When the inner circle is denoted by N, the retraction vector N in the direction of probe movement. i (i,j)=-N i (i,j).

[0062] Based on the radius of the probe bulb, determine the target measurement point P of the probe bulb for each measurement. ci For P ci =P i +r×N i According to the measurement point P i Determine the safe distance and the measurement point P. i Corresponding measurement safety point P di And P di =P ci +d×N i .

[0063] Before starting the measurement, the probe ball is positioned at the safety point corresponding to the measurement point. After completing the measurement, the probe ball returns to the safety point corresponding to that measurement point and moves from there to the next safety point. To avoid interference between the probe ball and the rotation feature during this movement, the probe ball is required to move along the return vector N. i directional retreat safety distance d i To ensure that interference does not occur, this safety distance d is set. i satisfy

[0064] Where α is the maximum central angle that the probe ball can cross in each movement under the condition of no interference, i.e., the arc distance of the step; according to the safe distance d under the condition of no interference. i Determine the maximum central angle that the probe ball can traverse in each movement.

[0065] Combining the errors of the measurement system, the machining errors of the rotation characteristics, and other error factors, a safety factor δ is introduced to adjust the magnitude of α, where δ∈(0,1), resulting in the adjusted value as follows:

[0066] The target cross-section circle's center O(x,y) points to the current measurement point P. i vector U i (i,j) and pointing to the next measurement point P i+1 vector W i (i,j) determines the angle θ between the two vectors, that is, the angle between the current measurement target point of the probe ball and the measurement target point of the next probe ball is also θ, that is, the central angle corresponding to the arc transition curve formed between the current measurement safety point and the next measurement safety point is θ.

[0067] Based on the central angle θ and the maximum central angle α that the probe ball can cross in each movement, determine the number of transition points m on the circular transition curve:

[0068] m = θ / α - 1, and m is an integer.

[0069] Based on the center O(x,y) and vector U i (i,j), vector W i The circular transition curve D is calculated using (i,j), the radius R of the target cross-section circle, and the radius r of the probe sphere. The above m circular transition points are then evenly distributed on the circular transition curve D to obtain the set of circular transition points Ωq{q i (x di ,y di )|i=1,2...m}.

[0070] The measurement target points, measurement safety points, and arc transition points (i.e., measurement path points) of all probe balls on each target cross-section circle, as determined above, are transformed using the second rotation transformation matrix to obtain the measurement path points in the original three-dimensional coordinate system. On each target cross-section, the probes are connected in the order of measurement safety point - measurement target point - measurement safety point - transition point to obtain the measurement path of the probe on each target cross-section. The last measurement path point in each target cross-section (except the last one) is connected to the initial measurement path point in the next target cross-section to obtain the interference-free measurement path of the probes on all target cross-sections.

[0071] The second rotation transformation matrix M2 is:

[0072]

[0073] Where β is the angle between the axial vector V and the vector OZ.

[0074] During the measurement, the probe ball is first positioned at the measurement safety point corresponding to the initial measurement point, and then moves to the measurement target point corresponding to that measurement point; at the measurement target point, the probe ball completes the measurement; after completing the measurement at that point, the probe ball returns to the measurement safety point corresponding to that measurement point; the probe ball moves along the arc transition point between the measurement safety point and the next measurement safety point to the next measurement safety point for the next measurement; the above steps are repeated until the probe ball completes the measurement.

[0075] To verify the performance of this method, workpieces were selected for in-machine measurement:

[0076] Among them, the axial vector of the circle feature is V(0,0,1), the center coordinate of the target section is O0(0,0,0), the radius is R=20mm, the inner and outer attributes are outer circle, and the number of measurement points for each target section is 4.

[0077] Determine the first rotation transformation matrix from axial vector V(0,0,1) to vector OZ(0,0,1).

[0078] Multiply the center coordinates of the target section by the first rotation transformation matrix to transform the target section circle onto the XOY two-dimensional plane, and obtain the target section circle with the center coordinates of the target section circle being O(0,0). Based on the radius R, determine the arc parameter curve C.

[0079] Based on the number of measurement points (4) on each target cross-section, determine the measurement point set Ωc{p i (x ci ,y ci )|i=1,2,3,4}.

[0080] Set the safety strategy parameters, where the probe ball radius r = 3mm and the safety distance for each measurement point is Ωd = {2,2,2,2}.

[0081] Based on the center of the target cross-section circle and the position of the measurement point, the measurement target point and the measurement safety point of the probe ball corresponding to the measurement point are obtained.

[0082] Define the safety factor δ = 0.1, then

[0083] The central angle θ = 1.5708 rad corresponding to the circular transition curve formed between the current measurement safety point and the next measurement safety point is calculated, which allows us to determine the number of discrete points on the circular arc.

[0084] m = θ / α - 1 = 4.576;

[0085] Since m is an integer, we get m = 5.

[0086] The set of transition points Ωq{q of the circular arc is determined based on the number of discrete points of the circular arc. i (x di ,y di )|i=1,2,3,4,5}.

[0087] Except for the last target cross-section circular measurement point, perform the above steps sequentially on all measurement points to obtain the circular transition points between the measurement safety points.

[0088] All the obtained measurement path points are transformed to the original three-dimensional coordinate system through the second rotation transformation matrix to obtain the measurement path points and arc transition points corresponding to the three-dimensional coordinate system. All measurement path points and arc transition points are connected in the order of measurement safety point - measurement target point - measurement safety point - transition point. In addition, except for the final target section, the measurement path points at the end of each target section are connected to the initial measurement path points of the adjacent target sections to obtain a complete non-interference probe measurement path.

[0089] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0090] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0091] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0092] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0093] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An adaptive optimization method for on-machine measurement path of rotational characteristics, characterized in that, include: Step 1: Set the number of measurement points on each target section; obtain the rotational characteristics of the workpiece to be measured and the geometric parameters of the target sections of the workpiece that need to be measured; Step 2: Based on the rotational characteristics of the workpiece to be measured and the normal vector of the two-dimensional plane, determine the first rotational transformation matrix and the second rotational transformation matrix; position each target section on the XOY two-dimensional plane through the first rotational transformation matrix, so that the target section becomes a target section circle distributed on the two-dimensional plane; obtain the geometric parameters of the target section circle on the two-dimensional plane based on the geometric parameters of the target section in the three-dimensional coordinate system; obtain the measurement point set corresponding to each target section circle based on the number of measurement points in each target section; Step 3: Set the measurement safety strategy parameters, which include the radius of the probe ball used in the measurement process and the safe distance of each measurement point on the target cross-section circle; Step 4: Based on the coordinates of each measurement point in the measurement point set, determine the retraction vector of the probe's movement direction when the probe ball detects that measurement point. Combining the coordinates of each measurement point, the retraction vector of the probe's movement direction, and the radius of the probe ball, determine the measurement target point of the probe ball when measuring each measurement point. Based on the set safety distance for each measurement point, determine the coordinates of the corresponding safety measurement point for each measurement point. Step 5: Repeat step 4 until all target cross-section circles have been processed, and obtain the measurement target point and measurement safety point of the probe ball on each target cross-section circle; Step 6: To ensure that the probe ball does not interfere with the rotation feature during its movement to the next measurement safety point, an arc transition point is set between the current measurement safety point and the next measurement safety point according to the direction of the probe ball's movement. The angle at which the probe ball moves towards the arc transition point is the maximum central angle that the probe ball can cross in each movement; determine the maximum central angle that the probe ball can cross in each movement, i.e., the arc distance step length; Step 7: Based on the maximum central angle that the probe ball can cross during its movement, and the angles formed by connecting the current measurement point and the next measurement point to the center of the target cross-section circle, determine the number of arc transition points between the current safe measurement point and the next safe measurement point, as well as the coordinates of each arc transition point, and obtain the corresponding set of arc transition points. Step 8: Repeat steps 6 and 7 until, except for the last target cross-section circle measurement point, all the measurement safety points on the target cross-section circle have corresponding arc transition points between them and the next measurement safety point; Step 9: Using the second rotation transformation matrix, measure the target points, safety points, and transition points (i.e., measurement path points) of all probe balls on each target cross section to obtain the measurement path points in the original three-dimensional coordinate system. On each target cross section, connect the probes in the order of safety point - target point - safety point - transition point to obtain the measurement path of the probe on each target cross section. Except for the last target cross section, connect the last measurement path point in each other target cross section with the initial measurement path point in the next target cross section to obtain the non-interference measurement path of the probes on all target cross sections.

2. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 1, characterized in that: In step 1, the rotation feature is the axial vector V(i,j,k); the center coordinates of the target cross section are O0(x,y,z), the radius is R, and the number of measurement points in each target cross section is n.

3. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 2, characterized in that: In step 2, the first rotation transformation matrix M1 of the axial vector to the normal vector OZ(0,0,1) of the two-dimensional plane is: In step 9, the second rotation transformation matrix M2 is: Where β is the angle between the axial vector V and the vector OZ; After transformation to a two-dimensional plane, the center coordinates of the target cross-section circle are O(x,y), the radius is R, and the arc parameter curve is C; the measurement point set Ωc{p} corresponding to the target cross-section circle i (x ci ,y ci Let |i=1,2...n}, where n measurement points are distributed on the circular arc curve C.

4. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 3, characterized in that: The radius of the probe ball is r, and the safe distance for each measuring point is Ωd = {d1, d2, ..., n}.

5. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 4, characterized in that: In step 4, a circle is constructed with the center O(x,y) of the target cross-section circle pointing to the measurement point p. i (x ci ,y ci The probe retraction vector N i (i,j)=(x ci -x,y ci -y), based on the internal and external properties of the rotation feature, when it is an outer circle, the probe retraction vector is N. i When the inner circle is , the probe retraction vector N i (i,j)=-N i (i,j).

6. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 5, characterized in that: In step 4, the measurement target point P of the probe ball is determined based on the probe ball radius r. ci For P ci =P i +r×N i According to the measurement point P i Determine the safe distance from the measurement point P. i Corresponding measurement safety point P di For P di =P ci +d×N i .

7. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 6, characterized in that: In step 6, to ensure that the probe ball does not interfere with the rotation feature during its movement, the probe ball is set to move along the return vector N. i directional retreat safety distance d i And the safe distance d i satisfy Where α is the maximum central angle that the probe ball can cross in each movement under the condition of no interference, that is, the arc distance from the step; according to the safety distance d i Determine the maximum central angle that the probe ball can cross in each movement. Taking into account the errors of the measurement system, the machining errors of the rotation characteristics, and other error factors, a safety factor δ is introduced to adjust the magnitude of α, where δ∈(0,1). After adjustment...

8. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 7, characterized in that: In step 7, the target cross-section circle center O(x,y) points to the current measurement point P. i vector U i (i,j) and pointing to the next measurement point P i+1 vector W i (i,j) determines the angle θ between the two vectors, that is, the central angle corresponding to the arc transition curve D formed between two adjacent measurement safety points is θ.

9. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 8, characterized in that: Based on the maximum central angle α that the probe ball can cross, determine the number m of transition points on the circular transition curve D: And m is an integer.

10. The adaptive optimization method for on-machine measurement path of rotational characteristics according to claim 9, characterized in that: Based on the center O(x,y) and vector U i (i,j), vector W i Given (i,j), the radius R of the target cross-section circle, and the radius r of the probe sphere, calculate the circular arc transition curve D. Distribute the above m circular arc transition points at equal intervals on the circular arc transition curve D to obtain the circular arc transition point set Ωq{q i (x di ,y di )|i=1,2...m}.

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