CN115415886B - Method for calculating polishing path of optical surface of inner wall - Google Patents

Abstract

The invention relates to the field of mechanical processing, and in particular to a method for calculating the polishing path of an inner wall optical surface, which includes: using the coordinate system of the workpiece to be polished to establish a robot arm coordinate system parallel to the coordinate system of the workpiece to be polished; using the robot arm coordinate system to obtain the polishing Path basic vector; using the polishing path basic vector to obtain the inner wall optical surface polishing path, the inner wall optical surface distributed on the side wall can be polished, and the polishing method can achieve the effect of surface processing texture removal, improve surface quality, and solve the inner wall optical surface problem. The space required for surface processing texture removal is small, the location is flexible, and the texture removal requires manual hand polishing, which is time-consuming and labor-intensive, and the process is uncontrollable.

Description

A method for calculating the polishing path of inner wall optical surfaces

Technical field

The invention relates to the field of mechanical processing, and in particular to a method for calculating the polishing path of an inner wall optical surface.

Background technique

Precision and ultra-precision polishing is an effective post-processing method for machining cutting texture removal and is widely used in optical surfaces and post-machining treatments with ultra-high surface quality. The traditional method is only suitable for polishing the end surface of the open space. It is not suitable for polishing and removing the processing texture of the inner wall optical surface, which has narrow space restrictions and flexible optical surface orientation. Previous polishing methods were mainly used to remove the processing texture on the optical surface of the end-face substrate. It is not used for processing and removing the optical surface of the inner wall. The removal of optical surface processing texture of the inner wall faces the flexible and uncertain characteristics of the surface orientation, so a practical method for calculating the inner wall polishing path is needed.

Contents of the invention

In view of the shortcomings of the existing technology, the present invention provides a method for calculating the polishing path of the inner wall optical surface. After establishing the corresponding relationship through dual coordinate systems, the polishing path is calculated based on the surface normal vector, and the calculation accuracy is high and the output path error is small.

In order to achieve the above objectives, the present invention provides a method for calculating the polishing path of the inner wall optical surface, which includes:

S1. Use the coordinate system of the workpiece to be polished to establish a robot arm coordinate system parallel to the coordinate system of the workpiece to be polished;

S2. Use the robot arm coordinate system to obtain the basic vector of the polishing path;

S3. Use the basic vector of the polishing path to obtain the polishing path of the inner wall optical surface.

Preferably, using the coordinate system of the workpiece to be polished to establish a robot arm coordinate system parallel to the coordinate system of the workpiece to be polished includes:

Determine the X and Y axes of the initial robot arm coordinate system parallel to the X and Y axes of the workpiece coordinate system to be polished based on the X and Y axes of the workpiece coordinate system to be polished;

Determine the Z-axis direction of the initial robot arm coordinate system according to the polishing tool pointing;

The robot arm coordinate system is established using the X, Y, and Z axes of the initial robot arm coordinate system.

Preferably, using the robot coordinate system to obtain the basic vector of the polishing path includes:

Using the origin of the robot arm coordinate system and the origin of the workpiece coordinate system to be polished to obtain the origin vectors of the robot arm coordinate system and the workpiece coordinates to be polished;

The origin vector of the robot arm coordinate system and the coordinates of the workpiece to be polished is used as the basic vector of the polishing path.

Preferably, using the polishing path basic vector to obtain the inner wall optical surface polishing path includes:

Use the workpiece to be polished to obtain the initial polishing path point set of the workpiece to be polished;

Calculate the unit normal vector of each polishing path point in the polishing path point set using the coordinate system of the workpiece to be polished;

Calculating each initial polishing path point in the polishing path point set using the unit normal vector of each polishing path point in the polishing path point set;

Using each initial polishing path point in the polishing path point set to obtain a trial run polishing path point set;

Use the trial run polishing path point set to perform spatial interference inspection to obtain the polishing path point set of the workpiece to be polished;

The set of polishing path points of the workpiece to be polished is used as the 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 using the coordinate system of the workpiece to be polished is as follows:

F＝(x,y,z)＝0

Among them, F = (x, y, z) is the analytical expression of the surface equation of 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 the analytical expression of the surface equation based on the coordinate system of the workpiece to be polished. The unit normal vector of each polishing path point in the polishing path point set of the system.

Further, the calculation formula for calculating each initial polishing path point in the polishing path point set using the unit normal vector of each polishing path point in the polishing path point set is as follows:

Among them, (X, Y, Z) is the initial polishing path point, (u, v, w) is the 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, (x _p , y _p , z _p ) are the polishing path points, (a, b, c) are the polishing path basic vectors.

Further, using each initial polishing path point in the polishing path point set to obtain the trial run polishing path point set includes:

When the polishing tool points in the same direction as the Z-axis of the robot arm coordinate system, each initial polishing path point in the polishing path point set is used to calculate each trial run polishing path point corresponding to the initial polishing path point;

A set of trial run polishing path points is obtained using each of 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 using each initial polishing path point in the polishing path point set is as follows:

β＝arccos w,γ＝0

(X,Y,Z)=(x _p ,y _p ,z _p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)

α=0,

Among them, (X, Y, Z, α, β, γ) are the trial run polishing path points corresponding to the initial polishing path point, (u, v, w) are the polishing path points in the set based on the workpiece coordinate system to be polished. The unit normal vector of the polished path point.

Further, using the trial run polishing path point set to perform spatial interference inspection to obtain the polishing path point set of the workpiece to be polished includes:

After visual simulation using the trial run polishing path point set, determine whether any point in the trial run polishing path point set has spatial interference with the workpiece to be polished. If so, perform spatial interference priority processing on the trial run polishing path point set. Otherwise, output Trial run the polishing path point set as the polishing path point set of the workpiece to be polished.

Further, the spatial interference priority processing of the trial run polishing path point set includes:

Adjust the β value of each trial polishing path point in the trial polishing path point set based on the spatial interference angle threshold to obtain a trial polishing path point processing set;

After visual simulation is performed using the trial run polishing path point processing set, it is determined whether any point in the trial run polishing path point processing set has spatial interference with the workpiece to be polished. If so, return to step S1. Otherwise, output the trial run polishing path point. The processing set is used as a set of polishing path points for the workpiece to be polished;

Among them, the spatial interference angle is the angle between the polishing tool and the 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 spatial interference angle threshold is no more than 20 degrees.

Compared with the closest existing technology, the present invention has the following beneficial effects:

By establishing a dual coordinate system to calculate the polishing path, it is ensured that the polishing tool is always facing the surface of the workpiece to be polished, making the polishing process highly efficient. At the same time, rechecking based on visual simulation ensures that the calculation output of the path is accurate and will not be polished during the actual operation. Damage to the workpiece.

Description of the drawings

Figure 1 is a flow chart of a method for calculating the polishing path of an inner wall optical surface provided by the present invention;

Figure 2 is a polishing path trajectory type diagram of a practical application method for calculating the polishing path of an inner wall optical surface provided by the present invention;

Figure 3 is a schematic diagram of the polishing tool state of a practical application method for calculating the polishing path of an inner wall optical surface provided by the present invention;

Figure 4 is a polishing path trajectory diagram of a practical application method for calculating the polishing path of an inner wall optical surface provided by the present invention.

Detailed ways

The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

In order to make the purpose, 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 in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

Example 1:

The invention provides a method for calculating the polishing path of the inner wall optical surface, as shown in Figure 1, including:

S1. Use the coordinate system of the workpiece to be polished to establish a robot arm coordinate system parallel to the coordinate system of the workpiece to be polished;

S2. Use the robot arm coordinate system to obtain the basic vector of the polishing path;

S3. Use the basic vector of the polishing path to obtain the polishing path of the inner wall optical surface.

Step S1 specifically includes:

S1-1. Determine the X and Y axes of the initial robot arm coordinate system parallel to the X and Y axes of the workpiece coordinate system to be polished based on the X and Y axes of the workpiece coordinate system to be polished;

S1-2. Determine the Z-axis direction of the initial robot arm coordinate system based on the polishing tool pointing;

S1-3. Establish a robot arm coordinate system using the X, Y, and Z axes of the initial robot arm coordinate system.

Step S2 specifically includes:

S2-1. Use the origin of the robot arm coordinate system and the origin of the workpiece coordinate system to be polished to obtain the origin vectors of the robot arm coordinate system and the workpiece coordinates to be polished;

S2-2. Use the origin vector of the robot arm coordinate system and the coordinates of the workpiece to be polished as the basic vector of the polishing path.

Step S3 specifically includes:

S3-1. Use the workpiece to be polished to obtain the initial polishing path point set of the workpiece to be polished;

S3-2. Calculate the unit normal vector of each polishing path point in the polishing path point set using the coordinate system of the workpiece to be polished;

S3-3. Calculate each initial polishing path point in the polishing path point set using the unit normal vector of each polishing path point in the polishing path point set;

S3-4. Use each initial polishing path point in the polishing path point set to obtain a trial run polishing path point set;

S3-5. Use the trial run polishing path point set to perform spatial interference inspection to obtain the polishing path point set of the workpiece to be polished;

S3-6. Use the set of polishing path points of the workpiece to be polished as the polishing path of the inner wall optical surface.

The calculation formula of step S3-2 is as follows:

F＝(x,y,z)＝0

Among them, F = (x, y, z) is the analytical expression of the surface equation of 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 the analytical expression of the surface equation based on the coordinate system of the workpiece to be polished. The unit normal vector of each polishing path point in the polishing path point set of the system.

The calculation formula of step S3-3 is as follows:

Among them, (X, Y, Z) is the initial polishing path point, (u, v, w) is the 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, (x _p , y _p , z _p ) are the polishing path points, (a, b, c) are the polishing path basic vectors.

Step S3-4 specifically includes:

S3-4-1. When the polishing tool points to the same Z-axis as the robot arm coordinate system, use each initial polishing path point in the polishing path point set to calculate each trial run polishing path point corresponding to the initial polishing path point;

S3-4-2. Use each of the trial operation polishing path points to obtain a set of trial operation polishing path points.

The calculation formula of step S3-4-1 is as follows:

β＝arccos w,γ＝0

(X,Y,Z)=(x _p ,y _p ,z _p )+(a,0,c)-(c sinθ,0,c cosθ)-(a cosθ,0,a sinθ)

α=0,

Among them, (X, Y, Z, α, β, γ) are the trial run polishing path points corresponding to the initial polishing path point, (u, v, w) are the polishing path points in the set based on the workpiece coordinate system to be polished. The unit normal vector of the polished path point.

Step S3-5 specifically includes:

S3-5-1. After visual simulation using the trial run polishing path point set, determine whether any point in the trial run polishing path point set has spatial interference with the workpiece to be polished. If so, perform spatial interference on the trial run polishing path point set. Prioritize processing, otherwise, output the trial run polishing path point set as the polishing path point set of the workpiece to be polished.

Step S3-5-1 specifically includes:

S3-5-1-1. Adjust the β value of each trial polishing path point in the trial polishing path point set based on the spatial interference angle threshold to obtain a trial polishing path point processing set;

S3-5-1-2. After using the trial run polishing path point processing set to perform visual simulation, determine whether any point in the trial run polishing path point processing set has spatial interference with the workpiece to be polished. If so, return to step S1. Otherwise, output the trial run polishing path point processing set as the polishing path point set of the workpiece to be polished;

Among them, the spatial interference angle is the angle between the polishing tool and the 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 spatial interference angle threshold is no more than 20 degrees.

Example 2:

The invention provides a practical application method for calculating the polishing path of the inner wall optical surface, which includes:

S1: Define the robot arm motion coordinate system. The robot arm motion coordinate system includes but is not limited to using each axis of the robot arm as the motion coordinate system or using the motion of the end of the robot arm as the coordinate system. The coordinate system of the present invention selects the axis of the robot arm. The movement of the end constructs a coordinate system, recorded as (XM, YM, ZM), and the coordinate system of the workpiece is set to (XW, YW, ZW). Adjust the motion axis of the manipulator so that the coordinate system of the end of the manipulator and the workpiece coordinate system are The axes are parallel, and the direction pointed by the polishing tool coincides with the ZM (or ZW) direction. Set the origin OM of the end coordinate system of the robot arm and the origin OW of the workpiece coordinate system in this state. The vector of the vector OMOW is in the end coordinate system of the robot arm. The following can be expressed as

O _M O _W =(a,b,c)

Among them, a is the distance between the polishing tool and the center of the flange at the end of the robot arm and the polishing head in the XM (or XW) direction, b is the distance between the polishing tool and the center of the flange at the end of the robot arm and the polishing head in the YM (or YW) direction. c is the distance between the polishing tool and the center of the flange at the end of the robot arm to the polishing head in the ZM (or ZW) direction; its positive and negative are determined by the positive and negative directions of the coordinate axes of (XM, YM, ZM) or (XW, YW, ZW) Depends.

S2: Set path points on the surface of the workpiece to be processed to form a processing trajectory (x _m , y _m , z _m ) of the end of the polishing head on the surface of the workpiece to be processed. The processing trajectory includes but is not limited to grid lines, spiral lines, and bows. Glyphs and other random trajectories.

In this embodiment, a practical application method for calculating the polishing path of the inner wall optical surface of the inner wall optical surface, the sampling point trajectory, as shown in Figure 2, adopts an arcuate trajectory.

S3: In order to ensure that the polishing tool is facing the surface of the workpiece to be processed, for the point in the workpiece coordinate system with coordinates (x _p , y _p , z _p ), calculate the surface normal vector N corresponding to the processing trajectory point. The calculation method can be Using but not limited to the analytical geometry method of using surface equations to obtain partial derivatives or using three-dimensional software modeling and derivation, the unit normal vector N = (u, v, w) is calculated;

S4: Generate the coordinate instructions (X, Y, Z, α, β, γ) required for the movement of the end of the robot arm based on the processing trajectory points. Since the length of the polishing tool in this embodiment is long, in order to ensure that there is no spatial interference between the polishing tool and the workpiece to be processed during the exposure process, only the projection of the surface normal vector on the X _W Z _W plane is considered at this time to ensure that the polishing tool is in the correct position. The normal vector of the surface to be processed is shown in Figure 3. For a point with coordinates (x _p ,y _p ,z _p ) in the workpiece coordinate system, the calculation method of its coordinate command is:

(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

Among them, θ = arctan (u/w) is determined by the normal vector of the workpiece surface to be processed at (x _p , y _p , z _p ).

S5: Input the trajectory coordinate points (X, Y, Z, α, β, γ) to the robot arm controller through program instructions. The controller controls the movement of the robot arm to determine whether there is spatial interference between the polishing tool and the workpiece to be processed. , if there is no spatial interference, proceed to the next step. If there is spatial interference, the processing steps are as follows:

(1) The polishing tool comes into contact with the workpiece to be processed during movement. At this time, you can enter S4 first and modify the β value to achieve a non-interference effect. However, you need to ensure that the angle between the direction of the polishing head at this time and the normal vector N of the surface of the workpiece to be processed is ensured. Less than a certain threshold, which may be 20° in an embodiment.

(2) If S4 is still not satisfied, return to S1 to modify the geometric dimensions of the polishing tool and recalculate it so that the spatial non-interference requirements are met.

In this embodiment, a practical application method for calculating the polishing path of the inner wall optical surface of the inner wall optical surface, the movement coordinate trajectory of each position of the inner wall surface processing of the part to be polished is shown in Figure 4.

Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the 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, etc.) 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 process and/or block in the flowchart illustrations and/or block diagrams, and combinations of processes and/or blocks in the flowchart illustrations 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 device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device produce a use A device for realizing the functions specified in one process or multiple processes of the flowchart and/or one block or multiple blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory that causes a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction means, the instructions The device implements the functions specified in a process or processes of the flowchart and/or a block or blocks of the block diagram.

These computer program instructions may also be loaded onto a computer or other programmable data processing device, causing a series of operating steps to be performed on the computer or other programmable device to produce computer-implemented processing, thereby executing on the computer or other programmable device. Instructions provide steps for implementing the functions specified in a process or processes of a flowchart diagram and/or a block or blocks of a block diagram.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that the present invention can still be modified. Modifications or equivalent substitutions may be made to the specific embodiments, and any modifications or equivalent substitutions that do not depart from the spirit and scope of the invention shall be covered by the scope of the claims of the invention.

Claims (8)

1. A method for calculating the polishing path of the inner wall optical surface, which is characterized by including: S1. Use the coordinate system of the workpiece to be polished to establish a robot arm coordinate system parallel to the coordinate system of the workpiece to be polished; S2. Use the robot arm coordinate system to obtain the basic vector of the polishing path; S3. Use the basic vector of the polishing path to obtain the polishing path of the inner wall optical surface; S3-1. Use the workpiece to be polished to obtain the initial polishing path point set of the workpiece to be polished; S3-2. Calculate the unit normal vector of each polishing path point in the polishing path point set using the coordinate system of the workpiece to be polished; S3-3. Calculate each initial polishing path point in the polishing path point set using the unit normal vector of each polishing path point in the polishing path point set; The calculation formula of S3-3 is as follows: Among them, (X, Y, Z) is the initial polishing path point, (u, v, w) is the 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, (x _p , y _p , z _p ) are the polishing path points, (a, b, c) are the polishing path basic vectors; S3-4. Use each initial polishing path point in the polishing path point set to obtain a trial run polishing path point set; S3-5. Use the trial run polishing path point set to perform spatial interference inspection to obtain the polishing path point set of the workpiece to be polished; S3-6. Use the set of polishing path points of the workpiece to be polished as the polishing path of the inner wall optical surface. 2. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 1, wherein the use of the workpiece coordinate system to be polished to establish a robot arm coordinate system parallel to the workpiece coordinate system to be polished includes: Determine the X and Y axes of the initial robot arm coordinate system parallel to the X and Y axes of the workpiece coordinate system to be polished based on the X and Y axes of the workpiece coordinate system to be polished; Determine the Z-axis direction of the initial robot arm coordinate system according to the polishing tool pointing; The robot arm coordinate system is established using the X, Y, and Z axes of the initial robot arm coordinate system. 3. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 1, characterized in that using the robot arm coordinate system to obtain the polishing path basic vector includes: Using the origin of the robot arm coordinate system and the origin of the workpiece coordinate system to be polished to obtain the origin vectors of the robot arm coordinate system and the workpiece coordinates to be polished; The origin vector of the robot arm coordinate system and the coordinates of the workpiece to be polished is used as the basic vector of the polishing path. 4. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 1, wherein the unit normal vector of each polishing path point in the polishing path point set is calculated using the workpiece coordinate system to be polished. The formula is as follows: F＝(x,y,z)＝0 Among them, F = (x, y, z) is the analytical expression of the surface equation of 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 the analytical expression of the surface equation based on the coordinate system of the workpiece to be polished. The unit normal vector of each polishing path point in the polishing path point set of the system. 5. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 1, characterized in that, using each initial polishing path point in the polishing path point set to obtain the trial run polishing path point set includes: When the polishing tool points in the same direction as the Z-axis of the robot arm coordinate system, each initial polishing path point in the polishing path point set is used to calculate each trial run polishing path point corresponding to the initial polishing path point; A set of trial run polishing path points is obtained using each of the trial run polishing path points. 6. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 5, characterized in that each initial polishing path point in the polishing path point set is used to calculate each trial run polishing path point corresponding to the initial polishing path point. The calculation formula is as follows: β＝arccosw,γ＝0 (X,Y,Z)＝(x _p ,y _p ,z _p )+(a,0,c)-(csinθ,0,ccosθ)-(acosθ,0,asinθ) α=0, γ=0 Among them, (X, Y, Z, α, β, γ) are the trial run polishing path points corresponding to the initial polishing path point, (u, v, w) are the polishing path points in the set based on the workpiece coordinate system to be polished. The unit normal vector of the polished path point. 7. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 1, wherein the set of polishing path points of the workpiece to be polished is obtained by performing spatial interference inspection using the trial run polishing path point set: After visual simulation using the trial run polishing path point set, determine whether any point in the trial run polishing path point set has spatial interference with the workpiece to be polished. If so, perform spatial interference priority processing on the trial run polishing path point set. Otherwise, output Trial run the polishing path point set as the polishing path point set of the workpiece to be polished. 8. A method for calculating the polishing path of an inner wall optical surface as claimed in claim 7, wherein the spatial interference priority processing of the trial run polishing path point set includes: Adjust the β value of each trial polishing path point in the trial polishing path point set based on the spatial interference angle threshold to obtain a trial polishing path point processing set; After visual simulation is performed using the trial run polishing path point processing set, it is determined whether any point in the trial run polishing path point processing set has spatial interference with the workpiece to be polished. If so, return to step S1. Otherwise, output the trial run polishing path point. The processing set is used as a set of polishing path points for the workpiece to be polished; Among them, the spatial interference angle is the angle between the polishing tool and the 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 spatial interference angle threshold is no more than 20 degrees.