Polishing path control method, readable storage medium and polishing equipment
By optimizing the polishing path spacing and idle travel path, the problems of low efficiency and poor consistency in traditional polishing methods are solved, achieving more efficient polishing and quality stability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HONGFUJIN PRECISION ELECTRONICS ZHENGZHOU
- Filing Date
- 2026-01-29
- Publication Date
- 2026-05-12
AI Technical Summary
Traditional robotic polishing methods are inefficient and cannot guarantee consistent processing. Furthermore, five-axis polishing machines suffer from overlapping and redundant polishing paths and efficiency loss during idle strokes when processing complex curved surfaces.
By generating a target polishing scheme, adjusting the spacing between adjacent polishing paths and the size relationship between the mounting surface and the working surface, the polishing path control method is optimized by reducing polishing path overlap and empty strokes.
It improves the efficiency of polishing equipment, reduces non-processing travel distance, shortens processing time, improves the consistency of workpiece surface quality and equipment uptime, and reduces the defect rate.
Smart Images

Figure CN122007990A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of polishing technology, and in particular to a polishing path control method, a readable storage medium, and a polishing apparatus using the polishing path control method. Background Technology
[0002] With the increasing demands for surface quality in precision components from modern manufacturing, polishing has become an increasingly important process for achieving high-gloss finishes. Traditional robotic polishing methods can only process a single workpiece at a time, limiting efficiency and making it difficult to guarantee processing consistency. Five-axis polishing machines, with their multi-degree-of-freedom collaborative control capabilities, are widely used in aerospace, automotive manufacturing, and medical device industries.
[0003] However, two key efficiency bottlenecks were discovered in actual mass production environments: (1) Redundancy of polishing path: When machining complex curved surfaces, the polishing path generated by traditional programming has an overlap area of 10%-15%, which causes the grinding head to repeatedly stay in the already processed area; (2) Idle travel efficiency loss: After the equipment completes the processing of a single workpiece, the non-processing movement time to return to the standby position accounts for 3%-5% of the single workpiece cycle, and the motion trajectory has not been optimally calculated. Summary of the Invention
[0004] In view of this, this application provides a polishing path control method, a readable storage medium, and a polishing device to improve the working efficiency of the polishing device.
[0005] This application provides a polishing path control method applied to a polishing device, the polishing device including a grinding head for mounting consumables, the grinding head having a mounting surface that directly contacts the consumables, and the surface of the consumables that directly contacts the workpiece being a working surface; the polishing path control method includes: obtaining polishing parameters based on an initial polishing scheme; obtaining a first polishing path, a second polishing path, and an idle stroke path according to the polishing parameters, wherein the first polishing path and the second polishing path have a distance d between them; generating a target polishing scheme according to the distance d, the size of the mounting surface, and the size of the working surface, and outputting polishing scheme modification information according to the idle stroke path; and driving the grinding head and the consumables to polish the workpiece based on the target polishing scheme.
[0006] A second aspect of this application provides a readable storage medium storing a computer program that, when read, implements the steps of the polishing path control method as described above.
[0007] A third aspect of this application provides a polishing apparatus, comprising: a control device including a memory and a controller electrically connected to each other, the memory storing a computer program, the controller being configured to read the computer program to enable the polishing apparatus to perform the steps of the polishing path control method described above; a drive device electrically connected to the control device; and a grinding head for fixing consumables and controlled by the drive device to polish the workpiece based on the target polishing scheme.
[0008] The aforementioned polishing path control method, readable storage medium, and polishing equipment can obtain the first polishing path, the second polishing path, and the idle stroke path based on the polishing parameters in the initial polishing scheme. On the one hand, it adjusts the relationship between the spacing d between adjacent polishing paths and the dimensions of the mounting surface and the working surface to generate the target polishing scheme. On the other hand, it outputs polishing scheme modification information based on the idle stroke path. While ensuring polishing quality, it can improve the polishing efficiency of the polishing equipment by reducing polishing path overlap and reducing idle stroke, respectively. Attached Figure Description
[0009] Figure 1 This is a schematic diagram of the module structure of the polishing equipment according to an embodiment of this application.
[0010] Figure 2 for Figure 1 A schematic diagram of the structure with consumables installed on the intermediate grinding head.
[0011] Figure 3 This is a flowchart illustrating the steps of the polishing path control method according to an embodiment of this application.
[0012] Figure 4 This is a schematic diagram showing the positional relationship between the grinding head, consumables, and polishing path.
[0013] Figure 5 This is a schematic diagram of the polishing path in the initial polishing scheme displayed by the software simulation.
[0014] Figure 6 This is a schematic diagram of the polishing path in the target polishing scheme displayed by the software simulation.
[0015] Figure 7 This is a schematic diagram of the modification information for the empty travel path generated in step S3.
[0016] Figure 8 This is a schematic diagram illustrating the process of polishing a workpiece using an initial polishing scheme.
[0017] Figure 9 This is a schematic diagram illustrating the process of polishing a workpiece using a target polishing scheme. Detailed Implementation
[0018] Please see Figure 1The polishing equipment 100 of this application embodiment includes a control device 110, a drive device 120, and a grinding head 130. The control device 110 is electrically connected to the drive device 120, and the drive device 120 is controlled by the control device 110 to drive the grinding head 130 to polish the surface of the workpiece along a pre-set polishing path. The polishing equipment 100 of this application embodiment is a five-axis polishing equipment, which can achieve the polishing of planar or complex curved surfaces through the coordinated motion of five axes (including three linear feed axes X, Y, and Z and two rotary axes A and C). The polishing equipment 100 may also include a worktable for fixing the workpiece to be polished, various sensors for real-time feedback of working information during the operation of the polishing equipment 100, a dust removal device for dust removal during the operation of the polishing equipment 100, etc., which will not be described in detail here.
[0019] Please see Figure 2 In one embodiment, the drive grinding head 130 is generally cylindrical and has a mounting surface 131. The mounting surface 131 is used to mount the consumable 200, for example, by attaching it to the surface. The consumable 200 is generally disc-shaped and has a working surface 201. Both the mounting surface 131 and the working surface 201 are circular, and the line connecting their centers is perpendicular to both the mounting surface 131 and the working surface 201. During the operation of the polishing equipment 100, the drive device 120 drives the grinding head 130 to rotate at high speed around the center of the mounting surface 131, thereby causing the consumable 200 to rotate synchronously around the working surface 201. Physical grinding, or "polishing," is achieved by utilizing the friction between the working surface 201 and the workpiece surface.
[0020] Before processing, a CNC program can be imported into the polishing equipment 100. The CNC program provides a polishing solution and may include motion trajectory, cutting parameters (such as spindle speed and feed rate), and process instructions. During processing, the polishing equipment 100 can control the working process of the grinding head 130 based on the CNC program, such as controlling the movement speed and movement path of the grinding head 130.
[0021] Traditional polishing methods may suffer from excessive overlap in polishing paths or excessive idle strokes, resulting in low polishing efficiency. This application provides a polishing path control method that improves polishing efficiency by reducing polishing path overlap and idle strokes. The polishing path control method provided in this application is applied to the polishing equipment 100 described above. Please refer to... Figure 3 The polishing path control method in this application includes: Step S1: Obtain polishing parameters based on the initial polishing scheme; Step S2: Obtain a first polishing path, a second polishing path, and an idle stroke path according to the polishing parameters, wherein there is a spacing d between the first polishing path and the second polishing path; Step S3: Generate a target polishing scheme based on the spacing d, the dimensions of the mounting surface, and the dimensions of the working surface; and output polishing scheme modification information based on the empty travel path; and Step S4: Drive the grinding head and the consumable to polish the workpiece based on the target polishing scheme.
[0022] Before step S1, an initial polishing scheme is imported manually by the user or automatically by the system. This initial polishing scheme is also an initial CNC program. In one embodiment, step S1 includes a numerical definition step, a line processing step, and a parameter extraction step.
[0023] In the numerical definition step, the definitions of each value read from the initial polishing scheme are determined. Specifically, coordinate parameters X, Y, and Z (3D coordinates), rotation parameters A and C (rotation angles), process parameters F (feed rate), S (spindle speed), and K (tool number), and line number identifier Line (G-code line number) can be defined. The aforementioned coordinate parameters X, Y, and Z (3D coordinates), rotation parameters A and C (rotation angles), process parameters F (feed rate), S (spindle speed), K (tool number), and line number identifier Line (G-code line number) are the polishing parameters obtained according to the initial polishing scheme.
[0024] In the line processing step, each line of G code in the initial polishing scheme is identified. For each line of G code, comments need to be cleaned (removing the comment content after semicolons and parentheses), whitespace needs to be removed (removing whitespace characters such as leading and trailing spaces and tabs), and blank line checks need to be performed (if an empty string is obtained after cleanup, the line processing is skipped).
[0025] The parameter extraction steps include: a. Row number extraction (purpose: write coordinates directly based on row number): For each line of string, record the current row number; b. Coordinate and process parameter extraction: Matching the following parameter patterns: Coordinate parameters: X, Y, Z followed by numbers (can include negative signs and decimal points); Rotation parameters: A, C followed by numbers (can include a minus sign and a decimal point); Speed parameter: F followed by a number (feed rate).
[0026] Special parameters: S parameter: can match ordinary numbers or variable references (such as @1); K parameter: Integer value (tool number).
[0027] c. Parameter value conversion: Data type conversion based on the matching results. Polishing parameters (X,Y,Z,A,C,F): Convert the string to a floating-point number.
[0028] Special handling for S-parameters: If it starts with "@" (such as @1), keep it as a string (variable reference); otherwise, convert it to a floating-point number (actual numerical value).
[0029] K parameter: Convert to integer type.
[0030] In one embodiment, the polishing parameters obtained in step S1 can be shown in the following table: Table 1 In step S2, the polishing path and the idle travel path are calculated and obtained based on the polishing parameters read above. In one embodiment, during the operation of the polishing equipment 100, the grinding head 130 and the consumable 200 polish the surface of the workpiece row by row. That is, in this case, the entire polishing trajectory includes at least two independent, spaced, and parallel polishing paths. In one embodiment, the spacing d between each pair of adjacent polishing paths is equal. During the operation of the polishing equipment 100, the grinding head 130 and the consumable 200 not only need to move during the polishing process, but the movement path of the grinding head 130 and the consumable 200 in the non-polishing state is defined as the idle travel path in this embodiment. The polishing path and the idle travel path are described below.
[0031] First, regarding the polishing path, in one embodiment, the polishing path of the grinding head 130 and the consumable 200 is a straight path. In step S2, the general straight line equation of each polishing path can be calculated based on the coordinate parameters in the polishing parameters. This general straight line equation is used to characterize the position of each polishing path, and the spacing d between each pair of adjacent polishing paths can be calculated based on this general straight line equation.
[0032] Specifically, for each set of coordinate parameters (X, Y, Z), it represents the three-dimensional coordinates of the polishing point during the polishing process. The polishing point is defined as the center of the working surface 201 of the consumable 200. During the polishing process, the line connecting all points traversed by the center of the working surface 201 forms the polishing path. The general linear equation of the polishing path can be expressed as: MX + NY + P = 0. By selecting three sets of coordinate parameters for each polishing path from Table 1, parameters M, N, and P can be solved, thus obtaining the specific expression for the general linear equation of each polishing path.
[0033] Taking the calculation of at least the first polishing path M1*X+N1*Y+P1=0 and the second polishing path M2*X+N2*Y+P2=0 as an example, the spacing between the first polishing path and the second polishing path... The spacing between each pair of adjacent polishing paths can be calculated using the method described above.
[0034] Secondly, for empty travel paths, this application provides the following methods for determination: a. Detect consecutive identical coordinate points. If the X / Y / Z coordinate values of adjacent program segments are not completely identical, and the feed rate (F value) is high (e.g., >12000mm / min), it indicates an idle stroke; b. Z-axis sudden rise determination: When the Z-axis suddenly rises to the safe plane (e.g., >10mm), and the subsequent XY coordinate changes, it is considered an avoidance maneuver. c. Non-machining motion of the rotary axis: Large-angle rotation (e.g., >30°) of the A / C axis without cutting parameters (e.g., spindle speed S=0) is mostly idle travel; d. Idle travel typically uses G00 rapid positioning or G01 high-speed feed; e. Movement without a spindle start command (M03 / M04) or at speed S=0 must be a no-stroke; f. If the pressure control command (e.g., #10701==[1-0.5*#618]) is not activated on the five-axis polishing machine, even if the coordinates change, it may be a pointless movement.
[0035] When any of the above-mentioned cases (af) are detected, it can be determined as an empty path, and the code at the empty path can be marked.
[0036] In the case of a five-axis polishing device 100, the polishing device 100 can polish both flat and curved surfaces. However, during the use of the device, it has been found that the aforementioned technical problem of "excessive overlap of polishing paths or excessive idle strokes" is more likely to occur when polishing flat surfaces. Therefore, in one embodiment, the polishing efficiency is mainly improved for polishing flat surfaces.
[0037] Therefore, before step S2, the process further includes: determining whether the initial polishing scheme is planar movement based on the polishing parameters. If the determination is yes, it indicates that the movement of the grinding head 130 and consumable 200 in the current initial polishing scheme is planar movement, and the subsequent step S2 is executed. If the determination is yes, it indicates that the movement of the grinding head 130 and consumable 200 in the current initial polishing scheme is not planar movement, and the subsequent steps are no longer executed.
[0038] In one embodiment, the specific determination method is as follows: when only one or two values of the coordinate parameters XYZ of each polishing point remain unchanged, and the rotation parameter AC is constant, it is determined to be planar movement; otherwise, it is determined to be non-planar movement. For example, the polishing parameters shown in Table 2 below are the case of planar movement, while the parameters shown in Table 3 below are the case of non-planar movement.
[0039] Table 2 Table 3 In step S3, in the first aspect: a target polishing scheme is generated based on the spacing d, the size of the mounting surface 131, and the size of the working surface 201. Specifically, it includes: generating a preset numerical range according to the size of the mounting surface and the size of the working surface; when the spacing d is within the preset numerical range, generating a target polishing scheme consistent with the initial polishing scheme; and when the spacing d is outside the preset numerical range, moving the position of the first polishing path and / or the second polishing path to generate a target polishing scheme different from the initial polishing scheme.
[0040] Please refer to Figure 4 , in an embodiment, a preset numerical range is generated according to the radii of the mounting surface 131 and the working surface 201. The radius of the mounting surface 131 is denoted as r, the radius of the working surface 201 is denoted as R, R > r, and the preset numerical range is defined as R + r to 2R.
[0041] When R + r < d < 2R, it is considered that the spacing d is within the preset numerical range. At this time, there is no need to change the polishing path, and the target polishing scheme is consistent with the initial polishing scheme. When d ≤ R + r or d ≥ 2R, it is considered that the spacing d is outside the preset numerical range. At this time, the polishing path needs to be adjusted so that the spacing d is within the preset numerical range.
[0042] For example, when it is necessary to adjust the spacing d between the first polishing path L1 and the second polishing path L2, at least one of the first polishing path L1 and the second polishing path L2 is selected to be translated along a straight line direction. The straight line direction is perpendicular to the first polishing path L1 and the second polishing path L2. In an embodiment, it is only necessary to select to translate only one of the first polishing path L1 and the second polishing path L2 along a straight line direction.
[0043] Specifically, substitute the foregoing formula into the numerical range R + r < d < 2R, , multiply both sides of the inequality by (always positive), and the relationship between P1 and P2 can be obtained: . Determine the adjusted polishing path according to the numerical ranges of P1 and P2. The above is a numerical range. In an embodiment, the intermediate value of this numerical range can be specifically selected.
[0044] For example, in one embodiment, if R=5 and r=3, the general linear equations of the two polishing paths calculated according to the initial polishing scheme are expressed as 4X-3Y+30=0 and 4X-3Y+60=0, respectively. The preset numerical range should be 8 to 10, meaning P1 and P2 must satisfy: 40<|P1-P2|<50. Substituting the values of P1 (30) and P2 (60) into the above general linear equations, it is clear that this numerical range is not met. Therefore, it is determined that one of the polishing paths needs to be moved. The range of the P value (denoted as P3) of the moved polishing path should be: P3∈(−20,−10)∪(70,80). If the P value of the subsequent polishing path (e.g., there is a third polishing path, a fourth polishing path, etc.) is greater than P1, then the value of P3 should be between 70 and 80; otherwise, the value of P3 should be between -20 and -70.
[0045] After step S3, a visual polishing path diagram can be output based on the target polishing scheme. For example, a Cartesian coordinate system can be established using Python matplotlib, and the polishing paths in the initial polishing scheme and the target polishing scheme can be visualized by connecting each path point in sequence. The polishing path in the initial polishing scheme is shown in the attached diagram. Figure 5 As shown, the polishing path in the target polishing scheme is referenced. Figure 6 As shown in the diagram. The vertical blue lines represent the polishing path, the horizontal blue lines represent the movement path when changing lines, and the diagonal blue lines represent the idle travel path.
[0046] In step S3, the second aspect involves outputting empty travel path modification information based on the empty travel path. Unlike directly outputting the modified target polishing scheme, the adjustment of the empty travel path, due to the need to consider issues such as space avoidance with other structures, does not directly output the modified empty travel scheme. Instead, it only outputs the empty travel path modification information, marking the suggested modifications and informing the user. The user can then refer to this empty travel path modification information for specific modifications. For example, see the attached image for the output empty travel path modification information. Figure 7 As shown, mark the corresponding line G code where the adjustment is suggested directly.
[0047] Figure 8 This is a schematic diagram of the polishing path in an initial polishing scheme. Figure 9 This is a schematic diagram of the polishing path in the target polishing scheme generated by the polishing path control method of this application embodiment. See also... Figure 8 and Figure 9It can be seen that the initial polishing scheme has a small spacing between adjacent polishing paths, resulting in a large overlap area between two adjacent polishing paths during the polishing process. In the target polishing scheme, while ensuring that no workpiece 300 is missed during polishing, the spacing between two adjacent polishing paths is significantly reduced compared to the initial polishing scheme, which helps to reduce the overlap area between two adjacent polishing paths. Figure 8 and Figure 9 For example, because the overlap area between two adjacent polishing paths is different, the following method is adopted: Figure 8 In the case of the initial polishing scheme, the entire polishing trajectory includes 8 polishing paths, which means it needs to be polished 8 times. Figure 9 Under the target polishing scheme, the entire polishing trajectory includes 7 polishing paths, meaning it requires 7 polishing passes. This effectively shortens polishing time and improves polishing efficiency.
[0048] The polishing path control method and polishing equipment 100 of this application embodiment can obtain a first polishing path, a second polishing path and an idle stroke path according to the polishing parameters in the initial polishing scheme. On the one hand, the relationship between the spacing d between adjacent polishing paths and the dimensions of the mounting surface and the working surface is adjusted to generate a target polishing scheme. On the other hand, polishing scheme modification information is output according to the idle stroke path. On the one hand, the polishing efficiency of the polishing equipment 100 can be improved by reducing polishing path overlap and reducing idle stroke, respectively, while ensuring polishing quality.
[0049] Verified in actual production lines, the polishing path control method and polishing equipment 100 of this application can optimize non-processing travel distance by 23.5%, reduce processing time for the same workpiece by approximately 6.25%, decrease the defect rate of large flat surfaces by 1.9%, increase the overall uptime of a single polishing equipment 100 by 3%, and reduce equipment investment by 15% for the same production capacity requirements. Furthermore, the surface quality consistency of the workpiece is improved, and the roughness fluctuation range is narrowed from ±0.02μm to ±0.01μm.
[0050] This application also provides a non-volatile computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements any step of the above-described polishing path control method.
[0051] The control device 110 of this application embodiment includes a memory and a processor electrically connected to each other. The memory stores a computer program, which, when read by the processor, enables the control device 110 to execute any step of the polishing path control method described above.
[0052] When the above-described polishing path control method is implemented and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above-described embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement any step of the above-described polishing path control method. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable storage medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.
[0053] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the sample processing system, connecting all parts of the system via various interfaces and lines.
[0054] The memory is used to store the computer programs and / or modules. The processor implements various functions of the sample processing system by running or executing the computer programs and / or modules stored in the memory and by calling data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, image playback function, etc.), etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, RAM, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.
[0055] Those skilled in the art should recognize that the above embodiments are only used to illustrate this application and are not intended to limit this application. Any appropriate changes and variations made to the above embodiments within the essential spirit and scope of this application fall within the scope of protection claimed in this application.
Claims
1. A polishing path control method, characterized in that, The polishing equipment includes a grinding head for mounting consumables, the grinding head having a mounting surface that directly contacts the consumables, and the consumables including a working surface for directly contacting the workpiece; The polishing path control method includes: Obtain polishing parameters based on the initial polishing scheme; A first polishing path, a second polishing path, and an idle stroke path are obtained based on the polishing parameters, wherein there is a spacing d between the first polishing path and the second polishing path; A target polishing scheme is generated based on the spacing d, the dimensions of the mounting surface, and the dimensions of the working surface, and polishing scheme modification information is output based on the empty travel path; and The grinding head and the consumables are driven to polish the workpiece based on the target polishing scheme.
2. The polishing path control method as described in claim 1, characterized in that, The step of obtaining the first polishing path and the second polishing path according to the polishing parameters includes: when the initial polishing scheme is determined to be planar movement according to the polishing parameters, at least a first polishing path and a second polishing path that are spaced apart from each other are calculated based on the initial polishing scheme.
3. The polishing path control method as described in claim 2, characterized in that, The polishing parameters include the polishing point coordinates and rotation parameters of the grinding head; the step of determining that the initial polishing scheme is planar movement based on the polishing parameters includes: when some coordinate values of the polishing point coordinates remain constant and the rotation parameters remain constant, it is determined that the grinding head moves along the plane.
4. The polishing path control method as described in claim 1, characterized in that, The step of generating a target polishing scheme based on the spacing d, the mounting surface size, and the working surface size includes: A preset numerical range is generated based on the dimensions of the mounting surface and the working surface. When the spacing d is within the preset value range, a target polishing scheme consistent with the initial polishing scheme is generated; and When the spacing d is outside the preset value range, the positions of the first polishing path and / or the second polishing path are moved to generate a target polishing scheme that is different from the initial polishing scheme.
5. The polishing path control method as described in claim 4, characterized in that, Both the mounting surface and the working surface are circular, and the preset value range is from R+r to 2R, where R>r, R is the diameter of the working surface, and r is the diameter of the mounting surface.
6. The polishing path control method as described in claim 4, characterized in that, The step of moving the position of the first polishing path and / or the second polishing path includes: translating the position of the first polishing path and / or the second polishing path along a straight line.
7. The polishing path control method according to any one of claims 1-6, characterized in that, The first polishing path and the second polishing path are straight paths.
8. The polishing path control method according to any one of claims 1-6, characterized in that, The first polishing path and the second polishing path are parallel to each other.
9. A readable storage medium, characterized in that, The system contains a computer program that, when read, implements the steps of the polishing path control method as described in any one of claims 1-8.
10. A polishing device, characterized in that, include: A control device includes a memory and a controller electrically connected to each other, the memory storing a computer program, and the controller being used to read the computer program to cause the polishing equipment to perform the steps of the polishing path control method as described in any one of claims 1-8; The drive unit is electrically connected to the control unit; as well as A grinding head, used to hold consumables, is controlled by the drive device to polish the workpiece based on the target polishing scheme.