A multi-objective optimization method, apparatus, equipment, and medium for a double-sided grinding and polishing process.

Abstract

This invention provides a multi-objective optimization method, apparatus, equipment, and medium for a double-sided grinding and polishing process, relating to the field of double-sided grinding and polishing parameter optimization technology. It includes: S1, obtaining the equipment parameters of the double-sided grinding and polishing equipment; S2, constructing a multi-objective optimization model based on the equipment parameters and an initial optimization model built upon the kinematic model of the double-sided grinding and polishing equipment. The multi-objective optimization model uses the grinding disc rotation speed n as the criterion. p Center wheel speed n s The workpiece eccentricity d is used as the optimization variable. The multi-objective optimization model takes surface quality uniformity, grinding disc wear uniformity, material removal rate, processing stability, and consistency of double-sided material removal as optimization objectives. S3, using the particle swarm optimization algorithm, with the grinding disc rotation speed n... p Center wheel speed n s The coordinates of the iterative particles are used to solve for the workpiece eccentricity d, obtaining multiple sets of solutions for the optimization variables. S4. Based on the multiple sets of solutions for the optimization variables, the preferred solutions for each optimization objective and the globally optimal solution that satisfies all optimization objectives are selected.

Description

Technical Field

[0001] This invention relates to the field of double-sided grinding and polishing parameter optimization technology, and more specifically, to a multi-objective optimization method, apparatus, equipment, and medium for double-sided grinding and polishing processes. Background Technology

[0002] With the rapid development of the optoelectronics and 3C industries, the demand for thin-film components such as ceramic substrates, glass panels, and semiconductor substrates is increasing, and the requirements are becoming more stringent. These components require not only high surface quality but also high shape accuracy in their applications. Double-sided grinding and polishing is the main method for achieving efficient and precise machining of these thin-film components.

[0003] Double-sided grinding and polishing is a process that simultaneously processes the upper and lower surfaces of a part by applying pressure and relative rotation speed to upper and lower grinding and polishing discs. Double-sided grinding not only offers high processing efficiency, enabling rapid and high-precision machining of the upper and lower surfaces of parts, but also effectively ensures the shape accuracy of the parts. Therefore, double-sided grinding and polishing is a key process for ensuring the processing accuracy and efficiency of various thin-film parts in the optoelectronics and 3C industries.

[0004] In double-sided grinding and polishing, the workpiece undergoes complex planetary motion relative to the grinding and polishing discs. Its trajectory is influenced by numerous parameters, including the rotational speeds of the upper and lower grinding and polishing discs, the rotational speed of the central wheel, the number of teeth in each component of the planetary gear train, the workpiece's placement, and the grinding pressure. The selection of processing parameters significantly impacts the uniformity of workpiece surface quality, the uniformity of grinding disc wear, the material removal rate, the stability of the processing, and the consistency of material removal on both sides. Existing technologies optimize for a single objective, resulting in poor optimization effects.

[0005] In view of this, the applicant hereby submits this application after studying the existing technology. Summary of the Invention

[0006] The present invention provides a multi-objective optimization method, apparatus, equipment and medium for double-sided grinding and polishing process to improve at least one of the above-mentioned technical problems.

[0007] In a first aspect, embodiments of the present invention provide a multi-objective optimization method for a double-sided grinding and polishing process, which includes steps S1 to S4.

[0008] S1. Obtain the equipment parameters of the double-sided grinding and polishing equipment. These parameters include: upper and lower grinding disc dimensions, center wheel dimensions, carrier disc dimensions, number of teeth on the upper and lower grinding discs, number of teeth on the center wheel, number of teeth on the outer gear ring, grinding disc rotation speed range, and rotation speed ranges for the center wheel and outer gear ring.

[0009] S2. Based on the equipment parameters and the initial optimization model pre-constructed based on the kinematic model of the double-sided grinding and polishing equipment, construct a multi-objective optimization model for the double-sided grinding and polishing equipment. The multi-objective optimization model uses the grinding disc rotation speed n as the criterion.p Center wheel speed n s The workpiece eccentricity d is used as the optimization variable. The multi-objective optimization model uses surface quality uniformity (VCSD) and grinding disc wear uniformity (VCSD) as optimization variables. w Material removal rate VCSD v Processing stability V range Consistency V in removing double-sided materials D To optimize the objective.

[0010] S3. Using the particle swarm optimization algorithm, with the grinding disc rotation speed n p Center wheel speed n s The workpiece eccentricity d is used as the coordinate of the iterative particle to solve for multiple sets of solutions for the optimization variables.

[0011] S4. Based on the multiple solutions of the optimization variables, select the preferred solutions for each optimization objective, as well as the global optimal solution that satisfies all optimization objectives.

[0012] Secondly, embodiments of the present invention provide a multi-objective optimization method and apparatus for a double-sided grinding and polishing process, which includes a parameter acquisition module, a modeling module, a solution module, and a screening module.

[0013] The parameter acquisition module is used to acquire the equipment parameters of the double-sided grinding and polishing equipment. These parameters include: upper and lower grinding disc dimensions, center wheel dimensions, carrier disc dimensions, number of teeth on the upper and lower grinding discs, number of teeth on the center wheel, number of teeth on the outer gear ring, grinding disc rotation speed range, and rotation speed ranges for the center wheel and outer gear ring.

[0014] The modeling module is used to construct a multi-objective optimization model for the double-sided grinding and polishing equipment based on the equipment parameters and an initial optimization model pre-built based on the kinematic model of the double-sided grinding and polishing equipment. The multi-objective optimization model uses the grinding disc rotation speed n as a reference. p Center wheel speed n s The workpiece eccentricity d is used as the optimization variable. The multi-objective optimization model uses surface quality uniformity (VCSD) and grinding disc wear uniformity (VCSD) as optimization variables. w Material removal rate VCSD v Processing stability V range Consistency V in removing double-sided materials D To optimize the objective.

[0015] The solver module is used to solve the problem using a particle swarm optimization algorithm, with the millstone rotation speed n. p Center wheel speed n s The workpiece eccentricity d is used as the coordinate of the iterative particle to solve for multiple sets of solutions for the optimization variables.

[0016] The filtering module is used to filter out the preferred solutions for each optimization objective and the global optimal solution that meets all optimization objectives based on multiple sets of solutions for the optimization variables.

[0017] Thirdly, embodiments of the present invention provide a multi-objective optimization method and apparatus for a double-sided grinding and polishing process, comprising a processor, a memory, and a computer program stored in the memory. The computer program can be executed by the processor to implement a multi-objective optimization method for a double-sided grinding and polishing process as described in any paragraph of the first aspect.

[0018] Fourthly, embodiments of the present invention provide a computer-readable storage medium. The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform a multi-objective optimization method for a double-sided grinding and polishing process as described in any paragraph of the first aspect.

[0019] By adopting the above technical solution, the present invention can achieve the following technical effects:

[0020] The multi-objective optimization method for a double-sided grinding and polishing process disclosed in this invention can effectively improve the trajectory uniformity on the workpiece, thus facilitating the acquisition of a more uniform workpiece surface quality. Furthermore, it significantly reduces the range of motion speeds in the double-sided grinding and polishing process, resulting in smoother processing and a reduction in the risk of scrap. Simultaneously, the difference in material removal between the upper and lower surfaces of the workpiece is reduced by an order of magnitude. This multi-objective optimization method helps improve processing quality, reduce scrap rates, and achieve higher processing efficiency. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a logical flowchart of a multi-objective optimization method.

[0023] Figure 2 This is a flowchart illustrating a multi-objective optimization method.

[0024] Figure 3 This is a schematic diagram of the substrate and the grinding disc.

[0025] Figure 4 This is a schematic diagram of the trajectory distribution on the substrate surface.

[0026] Figure 5 This is a schematic diagram showing the division of the grinding disc surface into regions.

[0027] Figure 6 This is a comparison diagram of the trajectory distribution on the surface of the grinding disc before and after optimization.

[0028] Figure 7 It is a trajectory distribution map of the substrate surface before optimization.

[0029] Figure 8 It is a trajectory distribution diagram on the optimized substrate surface.

[0030] Figure 9 This is a comparison diagram of the velocity distribution on the substrate surface before and after optimization.

[0031] Figure 10 This is a comparison diagram of the velocity distribution on the optimized substrate surface. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0033] Example 1, please refer to Figures 1 to 10 The first embodiment of the present invention provides a multi-objective optimization method for a double-sided grinding and polishing process, which can be executed by a multi-objective optimization device for a double-sided grinding and polishing process (hereinafter referred to as: multi-objective optimization device). In particular, it is executed by one or more processors in the multi-objective optimization device to realize the method comprising steps S1 to S4.

[0034] S1. Obtain the equipment parameters of the double-sided grinding and polishing equipment. These parameters include: upper and lower grinding disc dimensions, center wheel dimensions, carrier disc dimensions, number of teeth on the upper and lower grinding discs, number of teeth on the center wheel, number of teeth on the outer gear ring, grinding disc rotation speed range, and rotation speed ranges for the center wheel and outer gear ring.

[0035] It is understood that the multi-objective optimization device can be the control device of a double-sided grinding and polishing equipment, a portable laptop computer, a desktop computer, a server, a smartphone, or a tablet computer, or other electronic devices with computing power.

[0036] S2. Based on the equipment parameters and the initial optimization model, construct a multi-objective optimization model for the double-sided grinding and polishing equipment. The initial optimization model is pre-constructed based on the kinematic model of the double-sided grinding and polishing equipment.

[0037] The multi-objective optimization model uses the grinding wheel rotation speed n as an example. p Center wheel speed n s And the workpiece eccentricity d is the optimization variable.

[0038] The multi-objective optimization model uses surface quality uniformity VCSD and grinding disc wear uniformity VCSD as its objectives. w Material removal rate VCSD v Processing stability V range Consistency V in removing double-sided materials D To optimize the objective.

[0039] S3. Using the particle swarm optimization algorithm, with the grinding disc rotation speed n p Center wheel speed n s The workpiece eccentricity d is used as the coordinate of the iterative particle to solve for multiple sets of solutions for the optimization variables.

[0040] S4. Based on the multiple solutions of the optimization variables, select the preferred solutions for each optimization objective, as well as the global optimal solution that satisfies all optimization objectives.

[0041] Existing technologies for double-sided grinding only optimize parameters for a single objective, resulting in unsatisfactory optimization results. Therefore, the inventors, through extensive creative work, coupled and optimized multiple objectives, thus inventing the embodiments of this invention.

[0042] This invention provides a multi-objective optimization method for double-sided grinding and polishing processes, which solves the multi-objective optimization problem under the coupling of multiple process parameters in the double-sided grinding and polishing of thin-film parts such as semiconductor substrates, ceramic substrates, and glass panels. It can quickly obtain the optimal grinding and polishing process parameters and predict the grinding and polishing results. This effectively improves the stability of the grinding and polishing process and enhances processing quality.

[0043] The optimal grinding and polishing process parameters obtained through the multi-objective optimization method in this invention can improve the trajectory uniformity on the workpiece, which is more conducive to obtaining a uniform workpiece surface quality. Furthermore, it can significantly reduce the motion speed range of the double-sided grinding and polishing process, making processing smoother and reducing the risk of scrap to some extent. Simultaneously, the difference in material removal between the upper and lower surfaces of the workpiece is reduced by an order of magnitude. The multi-objective optimization method helps to improve processing quality, reduce scrap rate, and achieve higher processing efficiency.

[0044] like Figure 1 As shown, based on the above embodiments, in an optional embodiment of the present invention, the fitness function (i.e., the objective function) of the multi-objective optimization model is:

[0045] f = k1 × (VCSD) upper +VCSD lower )

[0046] +k2×(VCSD w_upper +VCSDw_lower )

[0047] -k3×(VCSD v-upper +VCSD v_lower )

[0048] +k4×(V range_upper +V range_lower )

[0049] +k5×V D

[0050] In the formula, k1 is the weighting coefficient for substrate surface quality uniformity, and VCSD is the weighting coefficient for substrate surface quality uniformity. upper and VCSD lower These are the evaluation indicators for the uniformity of the substrate's upper and lower surface quality, k2 is the weighting coefficient for the uniformity of grinding disc wear, and VCSD. w_upper and VCSD w_lower These are the evaluation indicators for the wear uniformity of the upper and lower grinding disc surfaces, k3 is the weighting coefficient for the stability of the substrate surface processing, and VCSD. v-upper and VCSD v_lower These are the evaluation indicators for the stability of the processing on the upper and lower surfaces of the substrate, respectively; k4 is the weighting coefficient for velocity fluctuation; and V... range_upper and V range_lower These represent the range of relative velocity fluctuations on the upper and lower surfaces of the substrate, k5 is the weighting coefficient for the consistency of material removal rates on both sides of the substrate, and V... D This represents the difference in material removal rates between the upper and lower surfaces of the substrate.

[0051] Preferably, the constraint St of the multi-objective optimization model is:

[0052]

[0053] In the formula, n u-pmin and n u-pmax The rotational speed n of the upper grinding disc are respectively u-p Minimum and maximum values, n l-pmin and n l-pmax The rotational speed n of the lower grinding disc are respectively l-p Minimum and maximum values, n smin and n smax The rotational speeds of the central wheel are n and n respectively. s Minimum and maximum values, d min and d max These are the minimum and maximum values ​​of the workpiece eccentricity d, respectively.

[0054] Specifically, the weighting coefficients are set according to actual needs. Those skilled in the art can set a larger weight value for whichever optimization objective is more prominent; this invention does not impose specific limitations on the specific values ​​of the weighting coefficients.

[0055] Based on the above embodiments, in an optional embodiment of the present invention, the kinematic model of the double-sided polishing equipment includes a wafer surface trajectory model for double-sided polishing, a polishing disc surface trajectory model for double-sided polishing, a relative velocity model between the wafer and the polishing disc, and a material removal rate calculation model for the substrate surface.

[0056] The surface trajectory model of a wafer after double-sided grinding and polishing is as follows:

[0057]

[0058] In the formula, x and y are the coordinates of the wafer, e is the distance between the center of the sun gear and the carrier disk, t is the processing time, and n is the distance between the center of the sun gear and the carrier disk. w For the workpiece's rotation speed, z s For the number of teeth of the sun gear, z p For the number of teeth on the planetary gear disk, z f For the number of teeth on the external gear ring, n s d is the rotational speed of the center wheel, d is the workpiece eccentricity, L is the position of the abrasive grain on the grinding disc, and n is the position of the abrasive grain on the grinding disc. p α is the grinding disc rotation speed, and α is the initial phase angle of the abrasive grains.

[0059] Preferably, the calculation model for the substrate surface quality uniformity index VCSD is as follows:

[0060]

[0061] In the formula, n is the number of grids divided on the substrate, and L is the number of grids divided on the substrate. i For the trajectory length within each grid of the substrate, This represents the average length of the trajectory within each grid on the substrate.

[0062] Specifically, the surface trajectory distribution of the double-sided polished wafer is calculated based on the double-sided polished wafer surface trajectory model, and the trajectory length on the substrate surface is also calculated.

[0063] Let the time step be t. p When t p When the value is sufficiently small, the trajectory can be approximated as a straight line, and the calculation equation is:

[0064]

[0065] The substrate surface is then divided into grids, and the trajectory distribution difference coefficient in each grid is calculated and denoted as the wafer trajectory distribution uniformity coefficient. This coefficient is used as the evaluation index of substrate surface quality uniformity (VCSD).

[0066] The surface trajectory model of the grinding disc in double-sided polishing is as follows:

[0067]

[0068] In the formula, R is the distance from the abrasive grain point to the center of the grinding disc, and ω is the distance from the abrasive grain point to the center of the grinding disc. h ω is the angular velocity of the carrier disk's revolution. w ω is the angular velocity of the grinding wheel, t is the processing time, α is the initial phase angle of the abrasive grains, r is the distance from the center of the carrier plate to the center of the grinding wheel, ω2 is the angular velocity of the sun gear, and φ is the initial phase angle of the workpiece.

[0069] Preferably, the evaluation index for the uniformity of wear on the grinding disc surface is VCSD. w The calculation model is as follows:

[0070]

[0071] In the formula, M is the number of rings divided by the grinding disc, and ρ u For the density of each ring trajectory on the surface of the grinding disc, This represents the average length of each ring trajectory on the surface of the grinding disc.

[0072] Specifically, the grinding disc is divided into annular regions, and the standard deviation of the trajectory density in each annular region is calculated and denoted as the uniformity coefficient of trajectory distribution on the grinding disc surface. This coefficient is then used as the evaluation index for the wear uniformity of the grinding disc surface (VCSD). w .

[0073] The relative velocity model between the wafer and the grinding disc is as follows:

[0074]

[0075] In the formula, v w c is the relative velocity between the wafer and the grinding disc, n crev The rotational speed of the planetary wheel, R crev Let n be the radius of the planetary wheel. crot For the orbital speed of the planetary wheel, L h The distance between the centers of the planetary wheel and the sun wheel, θ h The angle through which the workpiece rotates, n w For the workpiece's rotation speed, R w Let α be the workpiece radius and α be the initial phase angle of the abrasive grains.

[0076] Preferably, the evaluation index for the stability of the substrate surface processing is VCSD. v The calculation model is as follows:

[0077]

[0078] In the formula, H is the number of grids divided in the substrate, and v q The relative velocities of each grid on the substrate surface with the grinding disc, This represents the average relative velocity between the substrate surface and the grinding disc.

[0079] More preferably, the range of relative velocity fluctuations on the substrate surface, V rangeThe calculation model is as follows:

[0080] V eange =v max -v min

[0081] In the formula, v max The maximum value of the relative velocity between the substrate surface and the grinding disk, v min This represents the minimum relative velocity between the substrate surface and the grinding disc.

[0082] Specifically, the substrate surface is divided into a grid, and the average velocity in each grid is calculated. The difference coefficient of the average velocity is then calculated and denoted as the fitness coefficient of the uniformity of the velocity distribution on the wafer surface. This coefficient is used as an evaluation index for the stability of the substrate surface processing. v Currently, optimization of double-sided grinding and polishing processes, both domestically and internationally, mainly focuses on improving workpiece surface uniformity, grinding disc wear uniformity, or material removal rate by optimizing processing parameters. Research on process stability is limited, but the stability requirements are extremely high for processing ultra-thin, large-sized parts. Therefore, the inventors, through extensive creative work, have developed the technical solution of this invention.

[0083] Furthermore, the maximum relative velocity v is obtained based on the relative velocity model between the wafer and the grinding disc. max and minimum value v min Thus, the range V of the relative velocity fluctuation on the substrate surface is obtained. range .

[0084] A model for calculating the material removal rate on the substrate surface is established based on the motion trajectory model of double-sided grinding and polishing.

[0085] The material removal rate (MRR) calculation model for the substrate surface is:

[0086]

[0087] In the formula, V T Remove volume from material, S w The surface area of ​​the workpiece is given by t, and the processing time is given by S. ABC For the cross-sectional area of ​​the abrasive trajectory, N T The number of meshes for the workpiece, L i This represents the length of the abrasive grain trajectory.

[0088] Preferably, the uniformity of substrate double-sided material removal rate V D The calculation model is as follows:

[0089] V D =|MRR upper -MRR lower |

[0090] In the formula, MRRupper Material removal rate and MRR on the substrate surface lower The material removal rate is the material removal rate of the lower surface of the substrate.

[0091] Specifically, during double-sided polishing, because the upper surface of the substrate rotates at a higher speed relative to the polishing disc than the lower surface, a difference in material removal rates occurs between the upper and lower surfaces, affecting the wafer's surface accuracy. Therefore, the consistency of material removal rates on both sides of the substrate can be used to evaluate the quality of double-sided polishing.

[0092] Based on the above embodiments, in an optional embodiment of the present invention, step S3 specifically includes steps S31 to S35.

[0093] S31. Set the algorithm parameters for the particle swarm optimization algorithm. These parameters include: initial population size, maximum number of iterations, individual learning factor, swarm learning factor, inertia weight, iteration step size range, and weight coefficients for each optimization objective.

[0094] S32. Initialize the particle population, calculate the fitness of each particle, and find the optimal fitness.

[0095] S33. Subsequently, the particle swarm proceeds to the next iteration according to the velocity and displacement directions calculated by the iterative equation.

[0096] S34. Determine if the iteration count has reached the maximum iteration count. If it does, proceed to step S35. If it does not, return to step S32, set the iteration count to 1, and continue the iteration calculation.

[0097] S35. Output multiple solutions for the optimization variables, and the algorithm terminates.

[0098] Based on the above embodiments, in an optional embodiment of the present invention, step S4 specifically includes steps S41 to S43.

[0099] S41. Based on the multiple solutions of the optimization variables, calculate the values ​​of each evaluation index corresponding to each solution.

[0100] S42. Based on the values ​​of each evaluation index corresponding to each set of solutions, select the set of solutions that makes each evaluation index reach its optimal value, and use it as the priority solution for the optimization objective corresponding to that evaluation index.

[0101] S43. Based on the values ​​of each evaluation index corresponding to each set of solutions, perform weighted calculations according to the multi-objective optimization model to select the global optimal solution that meets all optimization objectives.

[0102] In this embodiment, the lower the value of the evaluation index, the better the characteristic effect corresponding to the evaluation index. Step S42 compares the evaluation index values ​​(i.e., the values ​​of each evaluation index) of the five optimization objectives corresponding to each group of solutions. The optimization solution with the smallest value of a certain evaluation index is the preferred solution for that optimization objective. The minimum value of the weighted calculation of the five evaluation indices corresponding to each group of solutions is the global optimal solution that satisfies all optimization objectives.

[0103] The multi-objective optimization method for double-sided grinding and polishing processes in this invention is applicable to the optimization of double-sided grinding and polishing processes for thin-film parts made of semiconductor substrates such as sapphire, single-crystal silicon, and silicon carbide, as well as other materials. By establishing the double-sided grinding and polishing motion trajectory, it establishes the intrinsic relationships between multiple process parameters and surface quality uniformity, grinding disc wear uniformity, material removal rate, processing stability, and consistency of material removal on both sides, providing a computational model (i.e., a fitness function) for subsequent multi-objective optimization of double-sided grinding and polishing process parameters.

[0104] The embodiments of the present invention utilize the particle swarm optimization algorithm to calculate the optimal solution set of the fitness function. Based on this optimal solution set, different weights can be set for different optimization objectives to solve the different requirements of each optimization objective in the actual processing process.

[0105] The optimization results obtained by applying the particle swarm optimization algorithm using the above fitness function are as follows:

[0106] Table 1 Comparison of original process parameters and process parameters after multi-objective optimization

[0107]

[0108] From a kinematic perspective, the process parameters obtained by the multi-objective optimization method in this embodiment of the invention, compared with the original kinematic process parameters, improve the trajectory uniformity on the workpiece, which is more conducive to obtaining a uniform workpiece surface quality. Although the trajectory uniformity of the grinding wheel deteriorates slightly, the degree of deterioration is very small and within an acceptable range. The average speed of the optimized motion is greatly increased, mainly due to the increase in the rotational speed of the upper wheel. The optimized motion speed range is significantly reduced, resulting in smoother processing and reducing the risk of scrap to some extent. At the same time, the difference in material removal between the upper and lower surfaces of the workpiece is reduced by an order of magnitude.

[0109] In summary, the optimized process parameters help improve processing quality, reduce scrap rate, and achieve higher processing efficiency.

[0110] Example 2: This embodiment of the invention provides a multi-objective optimization method and apparatus for a double-sided grinding and polishing process, which includes a parameter acquisition module, a modeling module, a solution module, and a screening module.

[0111] The parameter acquisition module is used to acquire the equipment parameters of the double-sided grinding and polishing equipment. These parameters include: upper and lower grinding disc dimensions, center wheel dimensions, carrier disc dimensions, number of teeth on the upper and lower grinding discs, number of teeth on the center wheel, number of teeth on the outer gear ring, grinding disc rotation speed range, and rotation speed ranges for the center wheel and outer gear ring.

[0112] The modeling module is used to construct a multi-objective optimization model for the double-sided grinding and polishing equipment based on the equipment parameters and an initial optimization model pre-built based on the kinematic model of the double-sided grinding and polishing equipment. The multi-objective optimization model uses the grinding disc rotation speed n as a reference. p Center wheel speed n s The workpiece eccentricity d is used as the optimization variable. The multi-objective optimization model uses surface quality uniformity (VCSD) and grinding disc wear uniformity (VCSD) as optimization variables. w Material removal rate VCSD v Processing stability V range Consistency V in removing double-sided materials D To optimize the objective.

[0113] The solver module is used to solve the problem using a particle swarm optimization algorithm, with the millstone rotation speed n. p Center wheel speed n s The workpiece eccentricity d is used as the coordinate of the iterative particle to solve for multiple sets of solutions for the optimization variables.

[0114] The filtering module is used to filter out the preferred solutions for each optimization objective and the global optimal solution that meets all optimization objectives based on multiple sets of solutions for the optimization variables.

[0115] Based on the above embodiments, in an optional embodiment of the present invention, the solving module specifically includes a parameter setting unit, an initialization unit, an iteration unit, a judgment unit, and an output unit.

[0116] The parameter setting unit is used to set the algorithm parameters of the particle swarm optimization algorithm. These parameters include: initial population size, maximum number of iterations, individual learning factor, swarm learning factor, inertia weight, iteration step size range, and weight coefficients for each optimization objective.

[0117] The initialization unit is used to initialize the particle population, calculate the fitness of each particle, and find the optimal fitness.

[0118] The iteration unit is used for the subsequent iteration of the particle swarm according to the velocity and displacement directions calculated by the iteration equation.

[0119] The judgment unit is used to determine whether the number of iterations has reached the maximum number of iterations. If it does, proceed to step S35; otherwise, return to step S32, set the number of iterations to 1, and continue the iterative calculation.

[0120] The output unit is used to output multiple solutions for the optimization variables, at which point the algorithm terminates.

[0121] Based on the above embodiments, in an optional embodiment of the present invention, the screening module specifically includes an index calculation unit, a first screening unit, and a second screening unit.

[0122] The index calculation unit is used to calculate the values ​​of each evaluation index corresponding to each set of solutions based on the multiple sets of solutions of the optimization variables.

[0123] The first screening unit is used to select the set of solutions that makes each evaluation index reach its optimal value based on the values ​​of each set of solutions, and use it as the priority solution for the optimization objective corresponding to that evaluation index.

[0124] The second screening unit is used to perform weighted calculations based on the values ​​of each evaluation index corresponding to each group of solutions, according to the multi-objective optimization model, to screen out the global optimal solution that meets all optimization objectives.

[0125] Example 3: This embodiment of the invention provides a multi-objective optimization method and apparatus for a double-sided grinding and polishing process, comprising a processor, a memory, and a computer program stored in the memory. The computer program can be executed by the processor to implement a multi-objective optimization method for a double-sided grinding and polishing process as described in any paragraph of Example 1.

[0126] Example 4: This embodiment of the invention provides a computer-readable storage medium. The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform a multi-objective optimization method for a double-sided grinding and polishing process as described in any paragraph of Example 1.

[0127] In the several embodiments provided in this invention, it should be understood that the disclosed apparatus and methods can also be implemented in other ways. The apparatus and method embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0128] In addition, the functional modules in the various embodiments of the present invention can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0129] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, electronic device, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. In the absence of further restrictions, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0130] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0131] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0132] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0133] The use of "first" and "second" in the embodiments is merely to distinguish similar objects and does not represent a specific ordering of objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0134] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for a double-sided grinding and polishing process, characterized in that, Comprising: Obtaining equipment parameters of the double-sided polishing equipment; wherein the equipment parameters comprise: sizes of upper and lower grinding discs, size of a center wheel, size of a carrier disc, number of teeth of the upper and lower grinding discs, number of teeth of the center wheel, number of teeth of an outer gear ring, rotation speed range of the grinding discs, rotation speed range of the center wheel and the outer gear ring; According to the device parameters, and based on an initial optimization model pre-constructed based on a kinematics model of the double-sided grinding and polishing device, a multi-objective optimization model of the double-sided grinding and polishing device is constructed; wherein the multi-objective optimization model takes the grinding disc rotating speed , the center wheel rotating speed , and the workpiece eccentricity as optimization variables; the multi-objective optimization model takes the surface quality uniformity , the grinding disc wear uniformity , the material removal rate , the machining process stability , and the double-sided material removal consistency as optimization objectives; The particle swarm optimization algorithm is used to solve the coordinates of the iteration particles by taking the grinding disc rotating speed , the center wheel rotating speed , and the workpiece eccentricity as the optimization variables, so as to obtain multiple sets of solutions of the optimization variables. According to the multiple sets of solutions of the optimization variables, a priority solution of each optimization target and a global optimal solution meeting all the optimization targets are screened out; The fitness function of the multi-objective optimization model is: In the formula, is a weight coefficient of the uniformity of the substrate surface quality, are evaluation indexes of the uniformity of the upper and lower substrate surface quality, respectively, are evaluation indexes of the uniformity of the upper and lower grinding disc surface wear, respectively, is a weight coefficient of the stability of the substrate surface processing, are evaluation indexes of the stability of the upper and lower substrate surface processing, respectively, is a weight coefficient of the consistency of the material removal rate of the substrate double side, is a difference value of the material removal rate of the upper and lower substrate surface.​​​​​​​ The constraint condition of the multi-objective optimization model is: In the formula, and The rotation speed of the upper grinding disc is respectively Minimum and maximum values and The rotation speeds of the lower grinding discs are respectively Minimum and maximum values and The rotational speeds of the center wheel are respectively Minimum and maximum values and These are the workpiece eccentricity. The minimum and maximum values; Evaluation index of substrate surface quality uniformity The calculation model is: wherein is the number of grids divided for the substrate, is the length of the trajectory within each grid of the substrate, is the average value of the length of the trajectory within each grid of the substrate; Evaluation index of uniformity of surface wear of grinding plate The calculation model of the evaluation index of uniformity of surface wear of grinding plate is: In the formula, the number of rings divided by the millstone, the average length of the track of each ring on the surface of the millstone, the average length of the track of each ring on the surface of the millstone, Evaluation index of substrate surface processing process stability The calculation model for: wherein the number of grid divided for the substrate, the relative velocity of each grid of the substrate surface to the grinding disc, the average of the relative velocity of the substrate surface to the grinding disc; Range of substrate surface relative speed fluctuations The computational model is: wherein is the maximum value of the relative velocity of the substrate surface to the grinding disk, is the minimum value of the relative velocity of the substrate surface to the grinding disk; Substrate double-sided material removal rate uniformity The computational model is: wherein is the material removal rate of the upper surface of the substrate, is the material removal rate of the lower surface of the substrate; The kinematic model of the double-sided polishing equipment comprises: The wafer surface trajectory model of the double-sided polishing is: wherein, and are coordinates of the wafer, is the center distance of the sun gear and the carrier plate, is the processing time, is the rotation speed of the workpiece, is the number of teeth of the sun gear, is the number of teeth of the planet carrier, is the number of teeth of the outer ring gear, is the rotation speed of the center wheel, is the eccentricity of the workpiece, is the position of the abrasive particles on the grinding disc, is the rotation speed of the grinding disc, is the initial phase angle of the abrasive particles; The grinding disc surface trajectory model of the double-sided polishing is: wherein is the distance of the abrasive particle from the center of the grinding disk, is the angular velocity of the carrier disk, is the angular velocity of the grinding disk, is the processing time, is the initial phase angle of the abrasive particle, is the distance of the center of the carrier disk from the center of the grinding disk, is the angular velocity of the sun gear, is the initial phase angle of the workpiece; The wafer and grinding disc relative speed model is: wherein is the wafer and plate relative speed, is the planetary wheel rotational speed, is the planetary wheel radius, is the planetary wheel orbital speed, is the planetary wheel and sun wheel center distance, is the workpiece angle turned, is the workpiece rotational speed, is the workpiece radius, is the abrasive particle initial phase angle; Material removal rate calculation model for substrate surface is: wherein is the material removal volume, is the workpiece surface area, is the machining time, is the abrasive grain track cross-sectional area, is the number of grid divisions of the workpiece, is the abrasive grain track length.

2. The multi-objective optimization method of a double-sided polishing process according to claim 1, wherein, The particle swarm optimization algorithm is used to solve the coordinates of the iteration particles by taking the grinding disc rotating speed , the center wheel rotating speed , and the workpiece eccentricity as the optimization variables, and a plurality of sets of solutions of the optimization variables are obtained, specifically including: S31, setting algorithm parameters of the particle swarm optimization algorithm; wherein the algorithm parameters comprise: initial population size, maximum iteration number, individual learning factor, group learning factor, inertia weight, iteration step range, and weight coefficients of each optimization target; S32, initializing a particle population, calculating the fitness of each particle, and finding the optimal fitness; S33, then the particle swarm performs the next iteration in the direction of the speed displacement calculated according to the iteration equation; S34, judging whether the iteration number reaches the maximum iteration number, if yes, entering step S35, if not, returning to step S32, setting the iteration number to 1 and continuing iteration calculation; S35, outputting the multiple sets of solutions of the optimization variables, and terminating the algorithm.

3. The multi-objective optimization method of a two-side polishing process according to claim 1, wherein, According to the multiple sets of solutions of the optimization variables, a priority solution of each optimization target and a global optimal solution meeting all the optimization targets are screened out, specifically comprising: According to the multiple sets of solutions of the optimization variables, the numerical values of each evaluation index corresponding to each set of solutions are calculated; According to the numerical values of each evaluation index corresponding to each set of solutions, a set of solutions that optimizes each evaluation index is screened out as the priority solution of the optimization target corresponding to the evaluation index; According to the numerical values of each evaluation index corresponding to each set of solutions, a global optimal solution meeting all the optimization targets is screened out through weighted calculation according to the multi-objective optimization model.

4. A multi-objective optimization method device of a double-sided grinding and polishing process, characterized in that, A multi-objective optimization method suitable for performing a double-sided polishing process according to any one of claims 1 to 3, The multi-objective optimization method device comprises: A parameter acquisition module is configured to obtain equipment parameters of the double-sided polishing equipment; wherein the equipment parameters comprise: sizes of upper and lower grinding discs, size of a center wheel, size of a carrier disc, number of teeth of the upper and lower grinding discs, number of teeth of the center wheel, number of teeth of an outer gear ring, rotation speed range of the grinding discs, rotation speed range of the center wheel and the outer gear ring; The modeling module is configured to construct a multi-objective optimization model of the double-sided polishing equipment according to the equipment parameters and an initial optimization model pre-constructed based on a kinematics model of the double-sided polishing equipment, wherein the multi-objective optimization model takes the grinding disc rotating speed ω, the center wheel rotating speed ωc and the workpiece eccentricity e as optimization variables, and takes the surface quality uniformity, the grinding disc wear uniformity, the material removal rate, the machining process stability and the double-sided material removal consistency as optimization objectives. ​​​​​​​​ a solving module configured to solve the coordinates of the iteration particles by using a particle swarm optimization algorithm to obtain a plurality of sets of solutions of the optimization variables, wherein the optimization variables include a rotational speed of the grinding disc , a rotational speed of the center wheel , and an eccentricity of the workpiece . A screening module is configured to screen out a priority solution of each optimization target and a global optimal solution meeting all the optimization targets according to the multiple sets of solutions of the optimization variables.

5. A multi-objective optimization method device of a double-sided polishing process, characterized in that, The computer readable storage medium comprises a stored computer program, wherein the computer readable storage medium controls the device where the computer readable storage medium is located to perform the multi-objective optimization method of the double-sided polishing process according to any one of claims 1 to 3 when the computer program runs.

6. A computer-readable storage medium, characterized in that, ​

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