Self-adaptive discretization method for segmented equal-angle cutter spiral line path

Abstract

The invention discloses a self-adaptive discretization method for a segmented equal-angle cutter spiral line path, and belongs to the technical field of optical product machining. Firstly, a spiral path of a cutter is planned according to a designed curved surface; initial parameters including a bow height error range and an increment angle are set, and a discrete angle of the first segmented area is obtained; adding the discrete angle of the current segmented area to the increment angle to obtain a discrete angle of a next segmented area; the bow height error is updated based on the discrete angle of the next segmented area, and the radius value of the next segmented area is obtained by adopting the dichotomy with the bow height error range as the constraint; and finally, iteratively acquiring a discrete angle and a radius value of each segmented region by segmented regions, and discretizing the spiral path by using the discrete angle and the radius value of each segmented region. Under the constraint of the bow height error range, the discrete angle is dynamically adjusted, and the machining precision of the complex curved surface can be effectively improved.

Description

Technical Field

[0001] The present application belongs to the technical field of optical product processing, and more specifically, relates to an adaptive discretization method for a segmented equi-angle tool spiral path. Background Art

[0002] Free-form optical components have significant advantages in beam control and optical system integration, and are therefore widely used in key areas such as advanced optoelectronics, detection, and communications. Free-form optical components with high surface accuracy are essential to ensure that optical systems continue to maintain high quality. However, the curvature changes of free-form surfaces are usually complex, and how to simultaneously ensure accuracy and efficiency during processing is a major challenge in the manufacturing field. Diamond cutting has high structural design freedom, higher material removal rate, and lower subsurface damage, and is therefore considered to be an effective free-form surface processing method. In this process, the CNC system uses interpolation algorithms and tool trajectory control to achieve the design requirements of the free-form surface. The tool trajectory usually evolves along the Archimedean spiral in space from the outermost area to the center of rotation, where a series of interaction points on the spiral are represented by a polar coordinate system, and these points are calculated based on the rotation angle and feed rate.

[0003] Traditional tool path spiral angle discretization methods mainly include the equal angle method and the equal arc length method. The problem with the equal angle method is that the outer circle point trajectory spacing is large, while the inner circle point trajectory spacing is small, resulting in inconsistent inner and outer circle processing accuracy. The problem with the equal arc length method is that the number of trajectory points in the inner circle is extremely small, and the dynamic characteristics of the spindle will be required to change the speed dynamically during processing. Subsequently, a dynamic discretization method combining the equal angle method and the equal arc length method has emerged. The equal arc length method is used for the outer circle, and the equal angle method is used for the inner circle. This method avoids the defects of both methods to a certain extent, but the bow height error cannot be controlled in this method. Summary of the invention

[0004] In response to the above defects or improvement needs of the prior art, the present application provides an adaptive discretization method for the spiral path of a segmented equi-angle tool, which aims to solve the problem that the dynamic discretization method of the spiral path in the existing free-form surface optical element processing technology cannot control the bow height error.

[0005] To achieve the above objectives, in a first aspect, the present application provides an adaptive discretization method for a segmented equi-angle tool helical path, which specifically includes the following steps:

[0006] Plan the spiral path of the tool according to the designed surface;

[0007] Set initial parameters including bow height error range and increment angle;

[0008] Obtaining a discrete angle of the first segmented area based on the bow height error range;

[0009] The discrete angle of the next segmented area is obtained by adding the incremental angle to the discrete angle of the current segmented area;

[0010] Update the bow height error based on the discrete angle of the next segmented area, and obtain the radius value of the next segmented area with the bow height error range as a constraint;

[0011] Iterate each segmented area to obtain the discrete angle and radius value of each segmented area;

[0012] The spiral path is discretized using discrete angle and radius values ​​for each segment region.

[0013] Preferably, the discrete angle of the first segmented area is obtained by the following steps:

[0014] (1) Obtain the three-dimensional coordinates of each discrete point through the number of discrete points NP;

[0015] (2) generating a plurality of interpolation points between adjacent discrete points, calculating the Z-axis differences between the plurality of interpolation points, and taking the maximum value of the Z-axis differences as the error of the adjacent discrete points;

[0016] (3) If the maximum value of the errors of all adjacent discrete points is greater than the upper limit of the bow height error range, the number of discrete points is increased and the process returns to step (1); otherwise, the discrete angle of the first segmented area is equal to 360° / NP.

[0017] Preferably, the step (1) is specifically:

[0018] (11) Obtain the polar coordinates of each discrete point according to the number of discrete points, where the polar coordinates of the i-th discrete point are (r(i), θ(i)):

[0019] r(i)=Rw-af×θ(i) / 360

[0020] θ(i)=(i-1)×(360° / NP)

[0021] Where r(i) is the radius coordinate, θ(i) is the angle coordinate; Rw=D / 2, D is the machining diameter of the spiral path; af is the feed amount per turn of the spiral path;

[0022] (12) Convert the polar coordinates of each discrete point into three-dimensional coordinates.

[0023] Preferably, the initial value of the number of discrete points is one of the initial parameters.

[0024] Preferably, the discrete angle of the next segmented area is obtained by adding the incremental angle to the discrete angle of the current segmented area, specifically:

[0025] θ i+1=θ i +Δθ

[0026] Among them, θ i and θ i+1 It is divided into discrete angles of the current segment area and the next segment area; Δθ is the incremental angle.

[0027] Preferably, the bow height error is updated based on the discrete angle of the next segmented area, and the radius value of the next segmented area is obtained with the bow height error range as a constraint, specifically:

[0028] Take 0 as the starting position and the radius of the current segment area as the ending position;

[0029] A binary search is used between the starting position and the ending position to find the radius value r of the next segmented area, so that the bow height error hmn obtained by substituting r into the bow height error function hmn=f(af,r,NP1) is within the bow height error range;

[0030] Where NP1 = 360 / θ i+1 ,θ i+1 is the discrete angle of the next segmented area; af is the feed amount per turn of the spiral path.

[0031] Preferably, after obtaining the discrete angle and radius value of the next segmented area, if the discrete angle θ of the next segmented area i+1 Satisfy the following formula:

[0032] θ i+1 ≥θ max

[0033] Then θ max as the discrete angle of all subsequent segmented areas, and θ max Update the bow height error, take the bow height error range as a constraint, and use the binary method to obtain the radius value as the radius value of all subsequent segmented areas; where θ max is the maximum step angle, one of the initial parameters;

[0034] Otherwise, continue to iterate each segmented area to obtain the discrete angle and radius values ​​of each segmented area.

[0035] In a second aspect, the present application provides an electronic device, comprising: a memory for storing programs; a processor for executing the programs stored in the memory, when the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0036] In a third aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0037] In a fourth aspect, the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0038] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art:

[0039] (1) The present application dynamically controls the discrete angle of each segment according to the set bow height range, ensuring that the error in the processing process is within an acceptable range; and through precise binary calculation, the radius value of the junction with the next area is accurately determined using binary calculation at each discrete angle calculation stage, ensuring that the starting bow height of each segment meets the requirements and greatly eliminating the bow height error of the discrete point.

[0040] (2) The present application can gradually adjust the angle during the processing process by dynamically adjusting discrete angle steps, thereby avoiding the need for the machine tool to frequently perform fast and high-precision dynamic adjustments and reducing the requirement for high-frequency response of the machine tool.

[0041] (3) The present application optimizes the setting of trajectory points through an adaptive dynamic adjustment mechanism, effectively avoiding the problem of surface unevenness caused by too many or too few discrete points in traditional methods, reducing redundant or repeated processing of trajectory points, and improving the efficiency of free-form surface processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of an adaptive discretization method of a segmented equi-angle tool spiral path provided in an embodiment of the present application.

[0043] Figure 2 It is a schematic diagram of the bow height provided in an embodiment of the present application.

[0044] Figure 3 It is a schematic diagram of discrete results displayed by a computer product provided in an embodiment of the present application.

[0045] Figure 4 It is a schematic diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0047] The terms "first" and "second" in the specification and claims herein are used to distinguish different objects rather than to describe a specific order of the objects. For example, a first segmented area and a second segmented area are used to distinguish different segmented areas rather than to describe a specific order of the segmented areas.

[0048] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0049] In the description of the embodiments of the present application, unless otherwise specified, “multiple” means two or more than two. For example, multiple interpolation points means two or more than two interpolation points.

[0050] like Figure 1 As shown, the embodiment of the present application implements an adaptive discretization method for a segmented equi-angle tool helical path, which specifically includes the following steps:

[0051] S1: Plan the spiral path of the tool according to the designed surface;

[0052] The spiral path and surface expression are used as the basic data of the discretization process. The feed amount per turn of the spiral path and the processing diameter of the spiral path can be obtained from the designed surface.

[0053] S2: Set the parameters according to the accuracy requirements;

[0054] Set the initial parameters including the bow height error range [eromin,eromax] and the incremental angle Δθ, as well as the discrete angle θ(1) of the first segment area and the maximum step angle θ max .

[0055] In this embodiment, the discrete angle θ1 of the first segment area is obtained by the following steps:

[0056] (1) The three-dimensional coordinates of each discrete point are obtained through the number of discrete points NP, specifically:

[0057] (11) Obtain the polar coordinates of each discrete point according to the number of discrete points, where the polar coordinates of the i-th discrete point are (r(i), θ(i)):

[0058] r(i)=Rw-af×θ(i) / 360

[0059] θ(i)=(i-1)×(360° / NP)

[0060] Where, Rw = D / 2, D is the processing diameter of the spiral path; af is the feed amount per turn of the spiral path;

[0061] (12) Convert the polar coordinates of each discrete point into three-dimensional coordinates.

[0062] (2) 50 interpolation points are generated between adjacent discrete points, the Z-axis differences between the 50 interpolation points are calculated, and the maximum value of the Z-axis differences is used as the error between the adjacent discrete points.

[0063] (3) If the maximum value of the errors of all adjacent discrete points is greater than the upper limit of the bow height error range, the number of discrete points is increased and the process returns to step (1); otherwise, θ1=360° / NP; specifically:

[0064] If max(hm)>eromax, then NP=NP+90, and return to step (1); otherwise θ1=360° / NP.

[0065] The bow height is the distance between the theoretical curve and the interpolation curve. Figure 2 As shown in the figure, in order to ensure the accuracy of the fitting curve during processing, the path curve must be a single peak interval within a single tool step, so the arc P(t i )P(t i+1 ) and the chord P(t i )P(t i+1 ) exists only at one point. i )P(t i+1 ) at a point P(t im ) is equal to the chord P(t i )P(t i+1 ), then this point is the point with the maximum bow height error within this step length.

[0066] The bow height error range includes setting the upper and lower limits of the overall bow height to control the maximum and minimum bow height of each section, ensuring that the bow height error during processing is within an acceptable range.

[0067] S3: The discrete angle of the next segmented area is obtained by adding the incremental angle to the discrete angle of the current segmented area, specifically:

[0068] θ i+1 =θ i +Δθ

[0069] Among them, θ i and θ i+1 It is divided into discrete angles of the current segment area and the next segment area; Δθ is the incremental angle.

[0070] S4: Update the bow height error based on the discrete angle of the next segmented area. With the bow height error range as the constraint, use the bisection method to obtain the radius value of the next segmented area;

[0071] Specifically, start from 0 as the starting position and the radius value of the current segmented area as the ending position;

[0072] Use the bisection method to search for the radius value r of the next segmented area between the starting position and the ending position, so that the bow height error hmm obtained by substituting r into the bow height error function hmm = f(af, r, NP1) is within the bow height error range;

[0073] Where, NP1 = 360 / θ i+1 , θ i+1 is the discrete angle of the next segmented area; af is the feed per revolution of the spiral path.

[0074] The specific bisection method is as follows:

[0075] Initially set rd(1) = R, rd(2) = 0, where R is the radius value of the current segmented area;

[0076] Take the midpoint of rd(1) and rd(2) as the radius value r of the next segmented area and substitute it into the bow height error function to calculate the bow height error hmm:

[0077] If hmm > eromax, it means that the density of the path is not enough and the radius needs to be reduced to increase the point density of the path. Update the path r of the next segmented area through the following formula:

[0078] rd(1) = r

[0079] r = (r + rd(2)) / 2

[0080] Continue to calculate the bow height error hmm until eromin < hmm < eromax is satisfied.

[0081] If hmm < eromin, it means that the path density is too large and the radius needs to be increased to reduce the point density of the path. At this time, update the path r of the next segmented area through the following formula:

[0082] rd(2) = r

[0083] r = (r + rd(1)) / 2

[0084] Continue to calculate the bow height error hmm until eromin < hmm < eromax is satisfied.

[0085] S5: After obtaining the discrete angle and radius value of the next segmented area, if the following formula is satisfied:

[0086] θ i+1 ≥ θmax

[0087] Then θ max as the discrete angle of all subsequent segmented areas, and θ max Update the bow height error, take the bow height error range as a constraint, and use the binary method to obtain the radius value as the radius value of all subsequent segmented areas; where θ max is the maximum step angle, one of the initial parameters;

[0088] Otherwise, continue to iterate each segmented area to obtain the discrete angle and radius values ​​of each segmented area.

[0089] S6: Discretize the spiral path using the discrete angle and radius values ​​of each segmented area.

[0090] like Figure 3 What is shown is a discrete result displayed by a computer program product provided in an embodiment of the present application, which is a computer program product for executing the method of the present application. Initial parameters such as bow height error range, incremental angle, maximum step angle, etc. are input into a computer program stored in the memory of an electronic device; after the processor of the electronic device executes the computer program, the discretization results of the spiral path and the radius values ​​of each area are displayed.

[0091] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device, such as Figure 4 As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430 and a communication bus 440, wherein the processor 410, the communication interface 420 and the memory 430 communicate with each other through the communication bus 440. The processor 410 may call the logic instructions in the memory 430 to execute the method in the above embodiment.

[0092] In addition, the logic instructions in the above-mentioned memory 430 can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application.

[0093] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0094] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0095] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0096] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0097] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a storage medium or transmitted through the storage medium. The computer instructions may be transmitted from a website site, a computer, a server or a data center to another website site, a computer, a server or a data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The storage medium may be any available medium that a computer can access or a data storage device such as a server or a data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid state disk (SSD)), etc.

[0098] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0099] The above content is easily understood by those skilled in the art. The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. An adaptive discretization method for a segmented equi-angle tool helical path, characterized in that: The specific steps include: Plan the spiral path of the tool according to the designed surface; Set initial parameters including bow height error range and increment angle; Obtaining a discrete angle of the first segmented area based on the bow height error range; The discrete angle of the next segmented area is obtained by adding the incremental angle to the discrete angle of the current segmented area; Update the bow height error based on the discrete angle of the next segmented area, and obtain the radius value of the next segmented area with the bow height error range as a constraint; Iterate each segmented area to obtain the discrete angle and radius value of each segmented area; The spiral path is discretized using discrete angle and radius values ​​for each segment region.

2. The adaptive discretization method according to claim 1, characterized in that: The discrete angle of the first segmented area is obtained by the following steps: (1) Obtain the three-dimensional coordinates of each discrete point through the number of discrete points NP; (2) generating a plurality of interpolation points between adjacent discrete points, calculating the Z-axis differences between the plurality of interpolation points, and taking the maximum value of the Z-axis differences as the error of the adjacent discrete points; (3) If the maximum value of the errors of all adjacent discrete points is greater than the upper limit of the bow height error range, the number of discrete points is increased and the process returns to step (1); otherwise, the discrete angle of the first segmented area is equal to 360° / NP.

3. The adaptive discretization method according to claim 2, characterized in that: The step (1) is specifically: (11) Obtain the polar coordinates of each discrete point according to the number of discrete points, where the polar coordinates of the i-th discrete point are (r(i), θ(i)): r(i)=Rw-af×θ(i) / 360 θ(i)=(i-1)×(360° / NP) Where r(i) is the radius coordinate, θ(i) is the angle coordinate; Rw=D / 2, D is the machining diameter of the spiral path; af is the feed amount per turn of the spiral path; (12) Convert the polar coordinates of each discrete point into three-dimensional coordinates.

4. The adaptive discretization method according to claim 2, characterized in that: The initial value of the number of discrete points is one of the initial parameters.

5. The adaptive discretization method according to claim 1, characterized in that: The discrete angle of the current segmented area plus the incremental angle is used to obtain the discrete angle of the next segmented area, specifically: i i+1 =θ i +Δθ Among them, θ i and θ i+1 It is divided into discrete angles of the current segment area and the next segment area; Δθ is the incremental angle.

6. The adaptive discretization method according to claim 1, characterized in that: The bow height error is updated based on the discrete angle of the next segmented area, and the radius value of the next segmented area is obtained with the bow height error range as a constraint, specifically: Take 0 as the starting position and the radius of the current segment area as the ending position; A binary search is used between the starting position and the ending position to find the radius value r of the next segmented area, so that the bow height error hmn obtained by substituting r into the bow height error function hmn=f(af,r,NP1) is within the bow height error range; Where NP1 = 360 / θ i+1 ,θ i+1 is the discrete angle of the next segmented area; af is the feed amount per turn of the spiral path.

7. The adaptive discretization method according to claim 1, characterized in that: After obtaining the discrete angle and radius value of the next segmented area, if the discrete angle θ of the next segmented area i+1 Satisfy the following formula: i i+1 ≥θ max Then θ max as the discrete angle of all subsequent segmented areas, and θ max Update the bow height error, take the bow height error range as a constraint, and use the binary method to obtain the radius value as the radius value of all subsequent segmented areas; where θ max is the maximum step angle, one of the initial parameters; Otherwise, continue to iterate each segmented area to obtain the discrete angle and radius values ​​of each segmented area.

8. An electronic device, characterized in that: include: Memory for storing computer programs; A processor, configured to execute the program stored in the memory. When the program stored in the memory is executed, the processor is configured to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, wherein when the computer program runs on a processor, the processor is enabled to execute the method according to any one of claims 1 to 7.

10. A computer program product, characterized in that When the computer program product runs on a processor, the processor is caused to execute the method according to any one of claims 1 to 7.

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