An adaptive discretization method for segmented constant angle tool helical curve path

Abstract

The application discloses a kind of adaptive discrete methods of segmented isometric tool helix path, belong to optical product processing technical field.The application first according to the design surface planning tool helix path;Again, set initial parameters including sag error range and increment angle, and obtain the discrete angle of first segmented region;Afterwards, the discrete angle of next segmented region is obtained by the discrete angle of current segmented region plus the increment angle;Again, based on the discrete angle of next segmented region, update sag error, with the sag error range as constraint, obtain the radius value of next segmented region using dichotomy;Finally, the discrete angle and radius value of each segmented region are obtained by iteration in segmented region, and the helix path is discretized using the discrete angle and radius value of each segmented region.The application can effectively improve the machining precision of complex surface under the constraint of sag error range, dynamically adjusts discrete angle.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of optical product processing, and more particularly relates to a self-adaptive discretization method for segmented constant-angle tool helical path. BACKGROUND

[0002] Freeform optical elements have significant advantages in beam manipulation and optical system integration, and are therefore widely used in advanced optoelectronic, detection and communication key fields. Freeform optical elements with high surface shape accuracy are essential to ensure that the optical system maintains high quality. However, the curvature of the freeform surface is usually complex, and how to ensure the accuracy and efficiency during the machining process is a major challenge in the manufacturing field. Diamond cutting has higher structural design freedom, higher material removal rate and lower subsurface damage, and is therefore considered an effective method for freeform surface machining. In this process, the CNC system uses interpolation algorithms and tool path control to achieve the design requirements of the freeform surface. The tool path usually evolves along a spatial Archimedean helix from the outermost region to the center of rotation, where a series of interaction points on the helix are represented by a polar coordinate system, which are calculated according to the rotation angle and feed rate.

[0003] The traditional helical path angle discretization method mainly includes constant-angle method and constant-arc-length method. The constant-angle method has the problem that the spacing between the outer circle point trajectories is large, and the spacing between the inner circle point trajectories is small, so the machining accuracy of the inner and outer circles is inconsistent. The constant-arc-length method has the problem that the number of trajectory points in the inner circle is very small, and it requires high dynamic characteristics to dynamically change the speed of the spindle during machining. Subsequently, a dynamic discretization method combining the constant-angle method and the constant-arc-length method was also proposed, which uses the constant-arc-length method for the outer circle and the constant-angle method for the inner circle, to some extent, avoiding the defects of the two methods, but this method cannot control the sag error. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a self-adaptive discretization method for segmented constant-angle tool helical path, which aims to solve the problem that the helical path dynamic discretization method cannot control the sag error in the existing freeform optical element machining technology.

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

[0006] Planning the helical path of the tool according to the design surface;

[0007] Setting initial parameters including the sag error range and the incremental angle;

[0008] Obtaining the discretization angle of the first segmented region based on the sag error range;

[0009] the discrete angle of the next segment region is obtained by adding the increment angle to the discrete angle of the current segment region;

[0010] the sag error is updated based on the discrete angle of the next segment region, and the radius value of the next segment region is obtained with the sag error range as a constraint;

[0011] the discrete angle and the radius value of each segment region are iteratively obtained segment by segment;

[0012] the spiral path is discretized using the discrete angle and the radius value of each segment region.

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

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

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

[0016] (3) if the maximum value in the errors of all adjacent discrete points is greater than the upper limit of the sag error range, increasing the number of discrete points and returning to step (1); otherwise, the discrete angle of the first segment region is equal to 360° / NP.

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

[0018] (11) obtaining the polar coordinates of each discrete point according to the number of discrete points, wherein the polar coordinates of the ith discrete point are (r(i), θ(i)):

[0019] r(i) = Rw- af x θ(i) / 360

[0020] θ(i) = (i-1) x (360° / NP)

[0021] wherein 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) converting 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 segment region is obtained by adding the increment angle to the discrete angle of the current segment region, specifically:

[0025] θ i+1= θ i + Δθ

[0026] wherein θ i and θ i+1 are discrete angles of the current segment area and the next segment area; and Δθ is an increment angle.

[0027] Preferably, the sag error is updated based on the discrete angle of the next segment area, and a radius value of the next segment area is obtained as a constraint of the sag error range, specifically as follows:

[0028] 0 is a starting position, and the radius value of the current segment area is a terminal position;

[0029] A bisection method is used to find the radius value r of the next segment area between the starting position and the terminal position, so that the sag error hmn obtained by substituting r into the sag error function hmn = f (af, r, NP1) is within the sag error range;

[0030] wherein NP1 = 360 / θ i+1 , θ i+1 is the discrete angle of the next segment area; and af is the feed per revolution of the helical path.

[0031] Preferably, after the discrete angle and the radius value of the next segment area are obtained, if the discrete angle θ i+1 of the next segment area satisfies the following formula:

[0032] θ i+1 ≥ θ max

[0033] θ max is taken as the discrete angle of all subsequent segment areas, and the sag error is updated with θ max , and a bisection method is used to obtain the radius value as the radius value of all subsequent segment areas as a constraint of the sag error range; wherein θ max is the maximum step angle, one of the initial parameters.

[0034] Otherwise, the discrete angle and the radius value of each segment area are obtained by iteration on a segment-by-segment basis.

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

[0036] In a third aspect, the present application provides a computer-readable storage medium, which stores a computer program, and when the computer program is run on a processor, the processor is caused to execute the method described in the first aspect or any possible implementation manner of the first aspect.

[0037] In a fourth aspect, the present application provides a computer program product, which, when running on a processor, causes the processor to execute the method described in the first aspect or any possible implementation manner of the first aspect.

[0038] Compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects in general:

[0039] (1) The present application dynamically controls the discrete angle of each segment according to the set bow height range, ensures that the error in the machining process is within an acceptable range, and accurately determines the radius value at the junction with the next region in each discrete angle calculation stage through accurate dichotomy, ensuring that the starting bow height of each segment meets the requirements and greatly eliminating the bow height error of the discrete points.

[0040] (2) The present application can gradually adjust the angle during the machining process through dynamic adjustment of the discrete angle step, avoiding the need for the machine tool to frequently perform rapid and high-precision dynamic adjustment, and reducing the requirement for high-frequency response of the machine tool.

[0041] (3) The present application optimizes the setting of the trajectory points through the adaptive dynamic adjustment mechanism, effectively avoids the uneven surface problem caused by too many or too few discrete points in the traditional method, reduces redundant machining or repeated machining of the trajectory points, and improves the free-form surface machining efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a flowchart of an adaptive discrete method of a segmented equiangular tool helix path provided by an embodiment of the present application.

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

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

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

[0046] In order to make the purpose, technical solutions and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not 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 objects. For example, "first segmented area" and "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 this 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 this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[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 segmented 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 machining 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 gaps between the 50 interpolation points are calculated, and the maximum value of the Z-axis gaps 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, increase the number of discrete points and return 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. When the arc P(t) in the curve P(t) i )P(t i+1 ) a point P(t im ) is equal to the slope of the tangent line 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: updating the camber error based on the discrete angle of the next sub-region, and obtaining the radius value of the next sub-region by dichotomy with the camber error range as a constraint;

[0071] Specifically, 0 is the starting position, and the radius value of the current sub-region is the end position;

[0072] The dichotomy is used to find the radius value r of the next sub-region between the starting position and the end position, so that the camber error hmm obtained by substituting r into the camber error function hmn=f(af,r,NP1) is within the camber error range;

[0073] Where NP1=360 / θ i+1 , θ i+1 is the discrete angle of the next sub-region, and af is the feed amount per revolution of the spiral path.

[0074] The dichotomy is specifically:

[0075] Initially, rd(1)=R and rd(2)=0, where R is the radius value of the current sub-region;

[0076] The midpoint of rd(1) and rd(2) is substituted into the camber error function to calculate the camber error hmm:

[0077] If hmm>eromax, it indicates that the density of the path is not enough, and the radius needs to be reduced to increase the point density of the path. The path r of the next sub-region is updated by:

[0078] rd(1)=r

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

[0080] The camber error hmm is continuously calculated until eromin<hmm<eromax is satisfied.

[0081] If hmm<eromin, it indicates 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, the path r of the next sub-region is updated by:

[0082] rd(2)=r

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

[0084] The camber error hmm is continuously calculated until eromin<hmm<eromax is satisfied.

[0085] S5: after obtaining the discrete angle and the radius value of the next sub-region, if the following formula is satisfied:

[0086] θ i+1 ≥θmax

[0087] then θ max is the discrete angle of the subsequent segmented region, and θ max updates the bow error, obtains the radius value as the radius value of the subsequent segmented region by using the dichotomy as the constraint of the bow error range; wherein θ max is the maximum step angle, one of the initial parameters;

[0088] Otherwise, continue to obtain the discrete angle and the radius value of each segmented region by iteration on a segmented region basis.

[0089] S6: discretizes the spiral path by using the discrete angle and the radius value of each segmented region.

[0090] As Figure 3 shown in the computer program product provided by the embodiment of the application, which is a computer program product for executing the method of the application, the initial parameters such as the bow error range, the incremental angle, and the maximum step angle are input in the computer program stored in the memory of the electronic device; the processor of the electronic device displays the discretization result of the spiral path and the radius value of each region after executing the computer program.

[0091] Based on the method in the above embodiment, the embodiment of the application provides an electronic device, as Figure 4 shown in the figure, which can include a processor 410, a communications interface 420, a memory 430, and a communications bus 440, wherein the processor 410, the communications interface 420, and the memory 430 complete mutual communication through the communications bus 440. The processor 410 can call the logic instructions in the memory 430 to execute the method in the above embodiment.

[0092] In addition, the logic instructions in the memory 430 described above can be implemented in the form of a software functional unit and sold or used as an independent product, which can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in the embodiments of the application.

[0093] Based on the method in the above embodiments, the embodiments of the present application provide a computer readable storage medium, which stores a computer program. When the computer program is run on a processor, the processor executes the method in the above embodiments.

[0094] Based on the method in the above embodiments, the embodiments of the present application provide a computer program product, which, when run on a processor, causes the processor to execute the method in the above embodiments.

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

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

[0097] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware or any combination thereof. When implemented by software, all or part of the embodiments can be implemented 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, all or part of the processes or functions described in the embodiments of the present application are generated. The computer can be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions can be stored in a storage medium or transmitted by the storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center through a wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) manner. The storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available medium can be a magnetic medium (for example, a floppy disk, a hard disk, a magnetic tape), an optical medium (for example, a DVD), or a semiconductor medium (for example, a solid state disk (SSD)) and the like.

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

[0099] It is easy for those skilled in the art to understand that the above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. An adaptive discretization method for a helical path of a segmented constant angle tool, characterized in that, Specifically comprising the following steps: According to the design surface planning tool helical path; Set the initial parameters including the bow height error range and the increment angle; Based on the bow height error range to obtain the discrete angle of the first sub-region; The discrete angle of the next sub-region is obtained by adding the increment angle to the discrete angle of the current sub-region; Based on the discrete angle of the next sub-region, update the bow height error, and obtain the radius value of the next sub-region with the bow height error range as the constraint; Iterate to obtain the discrete angle and radius value of each sub-region; Discretize the helical path using the discrete angle and radius value of each sub-region; The discrete angle of the first sub-region is obtained by the following steps: (1) by the number of discrete points obtaining three-dimensional coordinates of each discrete point; (2) Generate a plurality of interpolation points between adjacent discrete points, calculate the Z-axis difference between the plurality of interpolation points, and take the maximum value in the Z-axis difference 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 sag error range, then the number of discrete points is increased and step (1) is returned; otherwise the discrete angle of the first segmented region is equal to .

2. The adaptive discretization method of claim 1, wherein, The step (1) is specifically: (11) Obtain polar coordinates of each discrete point according to the number of discrete points, wherein the polar coordinates of the first discrete point is : r1= x1, θ1= arctan(y1 / x1) : wherein, is the radial coordinate, is the angular coordinate; , is the processing aperture of the helical path; is the advancement per turn of the helical path; (12) Convert the polar coordinates of each discrete point into three-dimensional coordinates.

3. The adaptive discretization method of claim 1, wherein, The initial value of the number of discrete points is one of the initial parameters.

4. The adaptive discretization method of claim 1, wherein, The discrete angle of the next sub-region is obtained by adding the increment angle to the discrete angle of the current sub-region, specifically: wherein, and discrete angles separating the current segment region and the next segment region; is an incremental angle.

5. The adaptive discretization method of claim 1, wherein, Based on the discrete angle of the next sub-region, update the bow height error, and obtain the radius value of the next sub-region with the bow height error range as the constraint, specifically: Take 0 as the starting position and the current sub-region radius value as the end position; A bisection method is used to find the next segment area radius value between the start and end positions such that Substitute the sag error function The resulting sag error is within the sag error range; wherein , is the discrete angle of the next segment region; is the amount of advancement per turn of the helical path.

6. The adaptive discretization method of claim 1, wherein, After obtaining the discrete angle and radius values of the next sub-division region, if the discrete angle of the next sub-division region satisfies the following equation: then the radius value of the subsequent all segmented areas is obtained by using dichotomy as the radius value of the subsequent all segmented areas, with the arch height error range as a constraint; wherein, as the discrete angle of all subsequent segmented areas, and the arch height error is updated, the radius value is obtained by using dichotomy as the radius value of the subsequent all segmented areas, with the arch height error range as a constraint; wherein, is the maximum step angle, one of the initial parameters; Otherwise, continue to iterate to obtain the discrete angle and radius value of each sub-region.

7. An electronic device, comprising: Comprise: Memory for storing computer programs; Processor for executing the program stored in the memory, when the program stored in the memory is executed, the processor is used to execute the method as claimed in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, characterized in that when the computer program runs on the processor, the processor executes the method as claimed in any one of claims 1-6.

9. A computer program product, characterised in that, When the computer program product runs on the processor, the processor executes the method as claimed in any one of claims 1-6.

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