CN115415886A - Inner wall optical surface polishing path calculation method - Google Patents
Inner wall optical surface polishing path calculation method Download PDFInfo
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- CN115415886A CN115415886A CN202211056314.4A CN202211056314A CN115415886A CN 115415886 A CN115415886 A CN 115415886A CN 202211056314 A CN202211056314 A CN 202211056314A CN 115415886 A CN115415886 A CN 115415886A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Abstract
The invention relates to the field of machining, in particular to a method for calculating an optical surface polishing path of an inner wall, which comprises the following steps: establishing a mechanical arm coordinate system parallel to the workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished; acquiring a polishing path basic vector by using the mechanical arm coordinate system; the polishing method can achieve the effect of removing surface machining textures, improves the surface quality, solves the problems that the space in removing the inner wall optical surface machining textures is small, the position is flexible, time and labor are wasted, and the process is uncontrollable due to the fact that manual polishing is needed to remove the textures.
Description
Technical Field
The invention relates to the field of machining, in particular to a method for calculating an optical surface polishing path of an inner wall.
Background
Precision and ultra-precision polishing is an effective post-treatment method for removing machining cutting textures, and is widely applied to machining post-treatment of optical surfaces and ultrahigh surface quality. The traditional method is only suitable for polishing the end surface of an open space, and is not suitable for polishing and removing the processing texture of the optical surface of the inner wall with narrow space and flexible optical surface orientation. Conventional polishing methods are mainly used for removing a processed texture on an optical surface of an end substrate. Rather than for machining removal of the inner wall optical surface. The removal of the inner wall optical surface machining texture faces the characteristic of flexible and variable surface orientation, so that a feasible inner wall polishing path calculation method is needed.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides the method for calculating the polishing path of the optical surface of the inner wall, which is characterized in that after a corresponding relation is established through a dual coordinate system, the polishing path is calculated based on the normal vector of the surface, the calculation precision is high, and the output path error is small.
In order to achieve the above object, the present invention provides a method for calculating an optical surface polishing path of an inner wall, comprising:
s1, establishing a mechanical arm coordinate system parallel to a workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished;
s2, obtaining a polishing path basic vector by using the mechanical arm coordinate system;
and S3, obtaining an inner wall optical surface polishing path by using the polishing path basic vector.
Preferably, the establishing a robot arm coordinate system parallel to the workpiece coordinate system to be polished by using the workpiece coordinate system to be polished includes:
determining an initial mechanical arm coordinate system X axis and an initial mechanical arm coordinate system Y axis which are parallel to the X axis and the Y axis of the workpiece coordinate system to be polished according to the X axis and the Y axis of the workpiece coordinate system to be polished;
determining the Z-axis direction of an initial mechanical arm coordinate system according to the direction of the polishing tool;
and establishing a mechanical arm coordinate system by utilizing the X axis, the Y axis and the Z axis of the initial mechanical arm coordinate system.
Preferably, the obtaining of the polishing path basis vector using the robot arm coordinate system includes:
acquiring an origin vector of the coordinate system of the mechanical arm and the coordinate of the workpiece to be polished by using the origin of the coordinate system of the mechanical arm and the origin of the coordinate system of the workpiece to be polished;
and using the original point vector of the mechanical arm coordinate system and the coordinate of the workpiece to be polished as a polishing path basic vector.
Preferably, the obtaining the inner wall optical surface polishing path by using the polishing path base vector comprises:
acquiring an initial polishing path point set of a workpiece to be polished by using the workpiece to be polished;
calculating a unit normal vector of each polishing path point in the polishing path point set by using a coordinate system of a workpiece to be polished;
calculating each initial polishing path point in the polishing path point set by using the unit normal vector of each polishing path point in the polishing path point set;
obtaining a set of trial-run polishing path points by using each initial polishing path point in the set of polishing path points;
carrying out spatial interference inspection by using the trial operation polishing path point set to obtain a polishing path point set of the workpiece to be polished;
and using the polishing path point set of the workpiece to be polished as an inner wall optical surface polishing path.
Further, the calculation formula for calculating the unit normal vector of each polishing path point in the polishing path point set by using the coordinate system of the workpiece to be polished is as follows:
F＝(x,y,z)＝0
wherein F = (x, y, z) is a surface equation analytical expression for each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished, and N = (u, v, w) is a unit normal vector for each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished.
Further, the calculation formula for calculating each initial polishing path point in the polishing path point set by using the unit normal vector of each polishing path point in the polishing path point set is as follows:
wherein (X, Y, Z) is the initial polishing path point, (u, v, w) is the unit normal vector of each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished, (X) p ，y p ，z p ) For polishing path points, (a, b, c) are polishing path basis vectors.
Further, obtaining a set of trial-run polishing waypoints using each initial polishing waypoint in the set of polishing waypoints comprises:
when the polishing tool points to the same axis as the Z axis of the mechanical arm coordinate system, calculating each trial operation polishing path point corresponding to the initial polishing path point by using each initial polishing path point in the polishing path point set;
and obtaining a set of trial run polishing path points by using the trial run polishing path points.
Further, the calculation formula for calculating each trial-run polishing path point corresponding to the initial polishing path point by using each initial polishing path point in the polishing path point set is as follows:
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)
α＝0,
wherein, (X, Y, Z, α, β, γ) is each trial-run polishing path point corresponding to the initial polishing path point, and (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished.
Further, the obtaining of the polishing path point set of the workpiece to be polished by performing spatial interference inspection using the trial-run polishing path point set includes:
and after performing visual simulation by using the test run polishing path point set, judging whether any point in the test run polishing path point set has spatial interference with the workpiece to be polished, if so, performing spatial interference priority processing on the test run polishing path point set, otherwise, outputting the test run polishing path point set as the polishing path point set of the workpiece to be polished.
Further, the preferentially processing the spatial interference on the set of trial-run polishing path points includes:
adjusting beta values of the trial-run polishing path points in the trial-run polishing path point set based on a spatial interference angle threshold value to obtain a trial-run polishing path point processing set;
after the visual simulation is carried out by utilizing the trial-run polishing path point processing set, judging whether any point in the trial-run polishing path point processing set has spatial interference with the workpiece to be polished, if so, returning to the step S1, otherwise, outputting the trial-run polishing path point processing set as a polishing path point set of the workpiece to be polished;
the spatial interference angle is an included angle between the polishing tool and a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished, and the threshold value of the spatial interference angle is not more than 20 degrees.
Compared with the closest prior art, the invention has the following beneficial effects:
the polishing path is calculated by establishing a dual coordinate system, so that the polishing tool is ensured to be always over against the surface of the workpiece to be polished, the polishing process is high in efficiency, meanwhile, the path is rechecked based on visual simulation to ensure that the calculation output of the path is accurate, and the workpiece to be polished cannot be damaged in the actual operation process.
Drawings
FIG. 1 is a flow chart of a method for calculating a polishing path of an optical surface of an inner wall according to the present invention;
FIG. 2 is a graph of the type of track of an optical surface polishing path for an inner wall according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a polishing tool state for an inner wall optical surface polishing path calculation practical application method provided by the present invention;
FIG. 4 is a trace diagram of a polishing path of an optical surface of an inner wall according to a practical application method of the present invention.
Detailed Description
The following provides a more detailed description of embodiments of the present invention, with reference to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1:
the invention provides a method for calculating an optical surface polishing path of an inner wall, as shown in fig. 1, comprising the following steps:
s1, establishing a mechanical arm coordinate system parallel to a workpiece coordinate system to be polished by utilizing the workpiece coordinate system to be polished;
s2, obtaining a polishing path basic vector by utilizing the mechanical arm coordinate system;
and S3, obtaining an inner wall optical surface polishing path by using the polishing path basic vector.
The step S1 specifically includes:
s1-1, determining an initial mechanical arm coordinate system X and an initial mechanical arm coordinate system Y which are parallel to the X and Y axes of a workpiece coordinate system to be polished according to the X and Y axes of the workpiece coordinate system to be polished;
s1-2, determining the Z-axis direction of an initial mechanical arm coordinate system according to the direction of a polishing tool;
and S1-3, establishing a mechanical arm coordinate system by utilizing X, Y and Z axes of the initial mechanical arm coordinate system.
The step S2 specifically includes:
s2-1, acquiring an origin vector of the coordinate system of the mechanical arm and the coordinate of the workpiece to be polished by using the origin of the coordinate system of the mechanical arm and the origin of the coordinate system of the workpiece to be polished;
and S2-2, using the origin point vector of the mechanical arm coordinate system and the coordinate of the workpiece to be polished as a polishing path basic vector.
Step S3 specifically includes:
s3-1, acquiring an initial polishing path point set of the workpiece to be polished by using the workpiece to be polished;
s3-2, calculating a unit normal vector of each polishing path point in the polishing path point set by using a coordinate system of a workpiece to be polished;
s3-3, calculating each initial polishing path point in the polishing path point set by using the unit normal vector of each polishing path point in the polishing path point set;
s3-4, obtaining a set of trial-run polishing path points by using each initial polishing path point in the set of polishing path points;
s3-5, performing spatial interference check by using the trial operation polishing path point set to obtain a polishing path point set of the workpiece to be polished;
and S3-6, using the polishing path point set of the workpiece to be polished as an inner wall optical surface polishing path.
The calculation formula of step S3-2 is as follows:
F＝(x,y,z)＝0
wherein F = (x, y, z) is a surface equation analytical expression for each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished, and N = (u, v, w) is a unit normal vector for each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished.
The calculation formula of step S3-3 is as follows:
wherein (X, Y, Z) is the initial polishing path point, (u, v, w) is the unit normal vector of each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished, (X) p ，y p ，z p ) For polishing path points, (a, b, c) is the polishing path base vector.
The step S3-4 specifically comprises the following steps:
s3-4-1, when the polishing tool points to the same axis as the Z axis of the mechanical arm coordinate system, calculating each trial run polishing path point corresponding to the initial polishing path point by using each initial polishing path point in the polishing path point set;
and S3-4-2, obtaining a set of trial operation polishing path points by using the trial operation polishing path points.
The calculation formula of step S3-4-1 is as follows:
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)
α＝0,
wherein, (X, Y, Z, α, β, γ) is each trial-run polishing path point corresponding to the initial polishing path point, and (u, v, w) is a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished.
The step S3-5 specifically comprises the following steps:
s3-5-1, after performing visual simulation by using the trial operation polishing path point set, judging whether any point in the trial operation polishing path point set has spatial interference with the workpiece to be polished, if so, performing spatial interference priority processing on the trial operation polishing path point set, and otherwise, outputting the trial operation polishing path point set as the polishing path point set of the workpiece to be polished.
The step S3-5-1 specifically comprises the following steps:
s3-5-1-1, adjusting beta values of all trial-run polishing path points in the trial-run polishing path point set based on a spatial interference angle threshold value to obtain a trial-run polishing path point processing set;
s3-5-1-2, after performing visual simulation by using the trial-run polishing path point processing set, judging whether any point in the trial-run polishing path point processing set has spatial interference with a workpiece to be polished, if so, returning to the step S1, otherwise, outputting the trial-run polishing path point processing set as a polishing path point set of the workpiece to be polished;
the spatial interference angle is an included angle between the polishing tool and a unit normal vector of each polishing path point in the polishing path point set based on the coordinate system of the workpiece to be polished, and the threshold value of the spatial interference angle is not more than 20 degrees.
Example 2:
the invention provides a practical application method for calculating an inner wall optical surface polishing path of an inner wall optical surface, which comprises the following steps:
s1: defining a mechanical arm motion coordinate system, wherein the mechanical arm motion coordinate system comprises but is not limited to using each axis of the mechanical arm as a motion coordinate system or using the motion of the tail end of the mechanical arm as a coordinate system, the coordinate system of the mechanical arm is selected to construct a coordinate system (XM, YM, ZM), the coordinate system of the workpiece is set to (XW, YW, ZW), the motion axis of the mechanical arm is adjusted to enable the tail end coordinate system of the mechanical arm to be parallel to each axis of the workpiece coordinate system, the pointing direction of the polishing tool is coincident with the ZM (or ZW) direction, the origin OM of the tail end coordinate system of the mechanical arm and the origin OW of the workpiece coordinate system in the state are set, and the vector OMOW can be expressed as the origin OW of the mechanical arm in the tail end coordinate system of the mechanical arm
O M O W ＝(a,b,c)
Wherein a is the distance between the center of the polishing tool and the end flange of the mechanical arm and the polishing head in the XM (or XW) direction, b is the distance between the center of the polishing tool and the end flange of the mechanical arm and the polishing head in the YM (or YW) direction, and c is the distance between the center of the polishing tool and the end flange of the mechanical arm and the polishing head in the ZM (or ZW) direction; the positive and negative of the axis of (XM, YM, ZM) or (XW, YW, ZW) are determined by the positive and negative directions of the axis.
S2: performing path point setting on the surface of the workpiece to be processed to form a processing track (x) of the tail end of the polishing head on the surface of the workpiece to be processed m ,y m ,z m ) The processing trajectory includes, but is not limited to, grid lines, spirals, arches, and other random trajectories.
In this embodiment, a practical application method for calculating the polishing path of the optical surface of the inner wall is used, and the sampling point trajectory is a zigzag trajectory as shown in fig. 2.
S3: to ensure that the polishing tool is treating the workpiece surface, the coordinates for the workpiece coordinate system are (x) p ,y p ,z p ) For the point of (a), calculating a surface normal vector N corresponding to the processing track point, wherein the calculation method can adopt but is not limited to an analytic geometric method of calculating a partial derivative by using a surface equation or a three-dimensional software modeling derivation, and calculating a unit normal vector N = (u, v, w);
s4: and generating coordinate instructions (X, Y, Z, alpha, beta and gamma) of the tail end of the mechanical arm required to move according to the processing track points. Because the length of the polishing tool in the embodiment is long, only the surface normal vector is considered to be in X in order to ensure that the polishing tool does not spatially interfere with the workpiece to be processed in the exposure process W Z W The projection of the plane ensures that the polishing tool is aligned with the normal vector of the surface to be processed, as shown in fig. 3. For coordinates of (x) in the object coordinate system p ,y p ,z p ) In a point ofThe coordinate command is calculated in the manner of
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)
β＝θ,α＝γ＝0
Wherein θ = arctan (u/w) is (x) from the surface of the workpiece to be machined p ,y p ,z p ) The normal vector of (a).
S5: inputting the coordinate points (X, Y, Z, alpha, beta and gamma) containing the track into a mechanical arm controller through a program command, controlling the mechanical arm to move by the controller, judging whether the polishing tool and the workpiece to be processed have space interference or not, if not, carrying out the next step, and if the processing steps of the space interference are as follows:
(1) The polishing tool contacts with the workpiece to be processed in the moving process, at this time, S4 may be entered first, and the β value is modified to achieve the effect of no interference, but it needs to be ensured that the included angle between the direction of the polishing head and the normal vector N of the surface of the workpiece to be processed is smaller than a certain threshold, which may be 20 ° in an embodiment.
(2) And in the case that S4 is not satisfied all the time, returning to S1 to modify the geometric dimension of the polishing tool and recalculating so as to satisfy the space non-interference requirement.
In this embodiment, a practical application method for calculating an optical surface polishing path of an inner wall of an optical surface of an inner wall is shown in fig. 4, where a motion coordinate trajectory of each position of the inner wall surface of a part to be polished is processed.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may 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, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may 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, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A method for calculating a polishing path for an optical surface of an inner wall, comprising:
s1, establishing a mechanical arm coordinate system parallel to a workpiece coordinate system to be polished by using the workpiece coordinate system to be polished;
s2, obtaining a polishing path basic vector by utilizing the mechanical arm coordinate system;
and S3, obtaining an inner wall optical surface polishing path by using the polishing path basic vector.
2. The method of claim 1, wherein the establishing a robot coordinate system parallel to the workpiece coordinate system to be polished using the workpiece coordinate system to be polished comprises:
determining an initial mechanical arm coordinate system X and an initial mechanical arm coordinate system Y which are parallel to the X and Y axes of the workpiece coordinate system to be polished according to the X and Y axes of the workpiece coordinate system to be polished;
determining the Z-axis direction of an initial mechanical arm coordinate system according to the direction of the polishing tool;
and establishing a mechanical arm coordinate system by utilizing the X, Y and Z axes of the initial mechanical arm coordinate system.
3. The method of claim 1, wherein obtaining a polishing path basis vector using the robot coordinate system comprises:
acquiring an origin vector of the coordinate system of the mechanical arm and the coordinate of the workpiece to be polished by using the origin of the coordinate system of the mechanical arm and the origin of the coordinate system of the workpiece to be polished;
and using the origin point vector of the mechanical arm coordinate system and the coordinate of the workpiece to be polished as a polishing path basic vector.
4. The method of claim 1, wherein obtaining the inner wall optical surface polishing path using the polishing path basis vector comprises:
acquiring an initial polishing path point set of a workpiece to be polished by using the workpiece to be polished;
calculating a unit normal vector of each polishing path point in the polishing path point set by using a coordinate system of a workpiece to be polished;
calculating each initial polishing path point in the polishing path point set by using the unit normal vector of each polishing path point in the polishing path point set;
obtaining a set of trial-run polishing path points by using each initial polishing path point in the set of polishing path points;
carrying out spatial interference inspection by using the trial operation polishing path point set to obtain a polishing path point set of the workpiece to be polished;
and using the polishing path point set of the workpiece to be polished as an inner wall optical surface polishing path.
5. The method of claim 4, wherein the calculation of the unit normal vector of each polishing path point in the set of polishing path points using the coordinate system of the workpiece to be polished is as follows:
F＝(x,y,z)＝0
where F = (x, y, z) is a surface equation analytical expression for each polishing path point in the set of polishing path points based on the workpiece coordinate system to be polished, and N = (u, v, w) is a unit normal vector for each polishing path point in the set of polishing path points based on the workpiece coordinate system to be polished.
6. The method of claim 4, wherein the calculation of each initial polishing path point in the set of polishing path points using the unit normal vector of each polishing path point in the set of polishing path points is as follows:
wherein (X, Y, Z) is the initial polishing path point, (u, v, w) is the unit normal vector of each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished, (X) p ，y p ，z p ) For polishing path points, (a, b, c) are polishing path basis vectors.
7. The method of claim 4, wherein obtaining a set of trial polishing waypoints using each initial polishing waypoint in the set of polishing waypoints comprises:
when the polishing tool points to the same axis as the Z axis of the mechanical arm coordinate system, calculating each trial-run polishing path point corresponding to the initial polishing path point by using each initial polishing path point in the polishing path point set;
and obtaining a set of trial run polishing path points by using the trial run polishing path points.
8. The method of claim 7, wherein the calculation of each of the trial polishing path points corresponding to the initial polishing path point using each of the initial polishing path points in the set of polishing path points is as follows:
(X,Y,Z)＝(x p ,y p ,z p )+(a,0,c)-(csinθ,0,ccosθ)-(acosθ,0,asinθ)
α＝0,
γ＝0
wherein, (X, Y, Z, α, β, γ) is each trial-run polishing path point corresponding to the initial polishing path point, and (u, v, w) is a unit normal vector of each polishing path point in the set of polishing path points based on the coordinate system of the workpiece to be polished.
9. The method of claim 4, wherein the step of obtaining a set of polishing waypoints for the workpiece to be polished by performing a spatial interference check using the set of trial-run polishing waypoints comprises:
and after performing visual simulation by using the trial operation polishing path point set, judging whether any point in the trial operation polishing path point set has spatial interference with the workpiece to be polished, if so, performing spatial interference priority processing on the trial operation polishing path point set, and otherwise, outputting the trial operation polishing path point set as the polishing path point set of the workpiece to be polished.
10. The method of claim 9, wherein the spatially-perturbed first-aid processing of the set of trial-run polishing path points comprises:
adjusting beta values of all trial-run polishing path points in the trial-run polishing path point set based on a spatial interference angle threshold value to obtain a trial-run polishing path point processing set;
after the visual simulation is carried out by utilizing the trial-run polishing path point processing set, judging whether any point in the trial-run polishing path point processing set has spatial interference with the workpiece to be polished, if so, returning to the step S1, otherwise, outputting the trial-run polishing path point processing set as a polishing path point set of the workpiece to be polished;
the spatial interference angle is an included angle between the polishing tool and a unit normal vector of each polishing path point in a polishing path point set based on a coordinate system of the workpiece to be polished, and the threshold value of the spatial interference angle is not more than 20 degrees.
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