A multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model

Abstract

The invention discloses a multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, comprising: establishing a temperature variance calculation model for discrete points in the radial direction of a polishing disc surface, and a water channel volume calculation model for the polishing disc; using the value ranges of the widths of the water channels of the polishing disc, the value ranges of the widths of the intervals between the water channels, the value ranges of the number of water channels, the value ranges of the widths of the intervals inside the cooling water channels, the value ranges of the widths of the intervals outside the cooling water channels, and the value ranges of the water channel depths as constraints; taking the minimum temperature variance for discrete points in the radial direction of the polishing disc surface, the maximum water channel volume for the polishing disc, and the maximum thickness for the polishing disc as optimization objectives; optimizing the water channel width, water channel depth, the widths of the intervals inside the cooling water channels, the widths of the intervals outside the cooling water channels, the widths of the intervals between the water channels, the thickness of the polishing disc, and the number of water channels; and using the optimal solution obtained by optimization as the structural parameters of the cooling water channels of the polishing disc.

Description

Technical Field

[0001] The invention belongs to the technical field of semiconductor ultra-precision machining, and in particular relates to a multi-objective optimization method for a polishing machine cooling structure based on a heat generation model. Background Art

[0002] Silicon carbide (SiC), a widely used semiconductor material, boasts a wide bandgap, high critical breakdown potential, and high-temperature resistance, making it widely used in new energy vehicles, aerospace, and electronic equipment. To ensure product quality and stability in practical applications, SiC substrates must possess an ultra-flat surface. However, SiC substrates are extremely difficult to process due to their high hardness, brittleness, and chemical stability, which have limited the development and application of SiC materials. Chemical mechanical polishing (CMP) is internationally recognized as the only effective method for achieving ultra-smooth, damage-free, and globally planarized nanoscale surfaces. The primary mechanism of this technique is the coupling of the chemical action of the polishing slurry with the frictional cutting action of the polishing pad and abrasive particles, resulting in both high material removal rates and low surface roughness.

[0003] Current research on polishing temperature fields primarily utilizes mathematical modeling and finite element analysis software. In contrast, limited research has focused on reducing temperature nonuniformity on the polishing surface during chemical mechanical polishing. Temperature uniformity has a significant impact on SiC workpiece polishing (nonuniform disk temperature can be transmitted to the SiC workpiece surface, causing warping, which in turn reduces workpiece precision and polishing machine yield, leading to increased production costs and reduced efficiency). This is directly related to polishing effectiveness and quality, polishing efficiency and stability, and process parameters and equipment requirements. Therefore, in-depth research on optimizing the polishing surface temperature field using a chemical mechanical polishing heat generation model is essential. Once this understanding is established, the heat generation model can be used to improve the existing polishing disk structure, thereby enhancing the precision and yield of SiC substrates. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, which can optimize the cooling water channel structure of the polishing machine and improve the temperature uniformity of the polishing disk surface.

[0005] The technical solution provided by the present invention is:

[0006] A multi-objective optimization method for a polishing machine cooling structure based on a heat generation model includes:

[0007] Establish a calculation model for the temperature variance of the temperature measurement points in the radial direction of the polishing disk surface:

[0008] as well as

[0009] Calculation model of water channel volume of polishing disc:

[0010]

[0011] Where Q i is the heat of any temperature measuring point i on the polishing disc surface, n is the number of temperature measuring points in the radial direction of the polishing disc; w si is the width of each waterway, w ji is the width of each waterway, ε is the number of waterways, w in is the interval width in the cooling water channel, w out is the width of the outer interval of the cooling water channel, d d is the depth of each cooling water channel;

[0012] The constraints are the range of the width of each water channel of the polishing plate, the range of the width of each water channel interval, the range of the number of water channels, the range of the width of the interval inside the cooling water channel, the range of the width of the interval outside the cooling water channel, and the range of the water channel depth.

[0013] Taking the minimum temperature variance of discrete points in the radial direction of the polishing disc surface, the maximum water channel volume of the polishing disc, and the maximum polishing disc thickness as the optimization objectives, the polishing disc water channel width, water channel depth, inner interval width of the cooling water channel, outer interval width of the cooling water channel, interval width of each water channel, polishing disc thickness, and number of water channels were optimized.

[0014] The optimal solution obtained by optimization is used as the structural parameters of the polishing disk cooling water channel.

[0015] Preferably, the calculation model of the heat at any temperature measuring point on the polishing disk surface is:

[0016]

[0017] Where r is the heat flux distribution coefficient; v is the relative speed between the silicon carbide workpiece and the polishing disc; μ P is the friction coefficient between the workpiece and the polishing pad and abrasive; F is the pressure exerted by the upper and lower polishing discs on the workpiece; h x is the convection heat transfer coefficient between the local silicon carbide workpiece and polishing disk and the air; t w is the surface temperature of silicon carbide workpiece; t f is the air temperature around the polishing machine, A is the surface area of ​​the air contact, A xis the area of ​​contact between the disk surface and the air; c is the specific heat capacity of the polishing liquid; m is the mass of the polishing liquid flowing into the polishing interface per unit time; t is the polishing time; ΔT1 is the temperature difference between the polishing liquid at the time of inflow and the temperature of the polishing liquid at the time of outflow; K is the proportional coefficient, ΔT2 is the temperature difference between the polishing disk surface and the coolant, λ is the thermal conductivity; l is the plate length, and Nu is the Nusselt number of the fluid.

[0018] Preferably, the relative speed between any point on the workpiece and the polishing disc is:

[0019]

[0020] Among them, ω P is the angular velocity of the polishing disc, ω w is the angular velocity of the workpiece; is the angle between the line connecting the center of the polishing disk and the center of the workpiece and the X-axis in the workpiece coordinate system, e is the ratio of the distance from a point on the workpiece to the center of the planetary gear to the radius of the outer ring gear, and (x, y) is the motion trajectory of the workpiece.

[0021] Preferably, the motion trajectory model of the workpiece is:

[0022]

[0023] Among them, k is the ratio of the radius of the center gear to the outer ring gear; m is the speed ratio of the outer ring gear to the center gear; ζ is the speed ratio of the polishing plate to the center gear, and R is the radius of the outer ring gear.

[0024] Preferably, the polishing plate water channel width, water channel depth, cooling water channel inner interval width, cooling water channel outer interval width, each water channel interval width, polishing plate thickness and water channel number are optimized by NSGA-II algorithm.

[0025] Preferably, the process of optimization by the NSGA-II algorithm includes the following steps:

[0026] Step 1: Randomly generate an initial population, which includes N pop Individuals; each of the individuals is a set consisting of the polishing plate water channel width, water channel depth, cooling water channel inner interval width, cooling water channel outer interval width, each water channel interval width, polishing plate thickness and water channel number;

[0027] Step 2: Update the current population using the crossover and mutation methods to obtain the crossover and mutation population;

[0028] Step 3: Merge the crossover and mutation populations with the current population, perform non-dominated sorting on the merged population to obtain the individual rank, and calculate the crowding distance of each individual. Sorting the population according to the order of individual rank in ascending order and crowding distance in descending order, retaining the top N popIndividuals as a new population;

[0029] Repeat steps 2-3 until the specified number of cycles is reached and the optimal solution set is obtained;

[0030] Step 4: Select a solution that can minimize the temperature variance of discrete points in the radial direction of the polishing disk surface from the optimal solution set as the final solution.

[0031] The beneficial effects of the present invention are:

[0032] The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model provided by the present invention can optimize the cooling water channel structure of the polishing machine, improve the temperature uniformity of the polishing disk surface, and thus improve the polishing quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of the double-sided high-precision grinding and polishing machine described in the present invention.

[0034] Figure 2 It is a structural schematic diagram of the lower polishing plate described in the present invention.

[0035] Figure 3 This is a diagram showing the position of the SiC workpiece according to the present invention after a certain time t.

[0036] Figure 4 This is a simplified diagram of the velocity model of the SiC workpiece relative to the polishing disk according to the present invention.

[0037] Figure 5 This is a simplified diagram of the motion boundary of the SiC workpiece described in the present invention.

[0038] Figure 6 Schematic diagram of the cooling water channel structure and design variables of the present invention.

[0039] Figure 7 This is the temperature distribution diagram of the polishing disk surface simulated by Ansys before optimization of the present invention.

[0040] Figure 8 This is the temperature distribution diagram of the polishing disk surface optimized by Ansys simulation of the present invention.

[0041] Figure 9 This is a comparison diagram of radial temperature before and after optimization of the present invention. DETAILED DESCRIPTION

[0042] The present invention will be described in further detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0043] like Figure 1-2As shown, the double-sided high-precision grinding and polishing machine includes at least one planetary wheel 300 for placing a SiC workpiece 400. The SiC workpiece 400 is supported in the planetary wheel 300, which meshes with the lower polishing plate 500 and the inner ring gear 200 through gears. The planetary wheel contains multiple SiC workpieces, which are distributed on the planetary wheel at equal angular intervals around the center of the planetary wheel. During polishing, the upper polishing plate 100 is driven downward by a cylinder (not shown) and applies pressure to the SiC workpiece. The planetary wheel 300 rotates around the inner ring gear 200 through gear meshing.

[0044] During the SiC workpiece polishing process, the primary temperature increase on the polishing contact surface is due to friction between the SiC workpiece and the abrasive, polishing pad, and polishing disc. In actual polishing, the polishing disc and SiC workpiece / plane wheel can be simplified as two planes in relative motion. Because the SiC workpiece is mounted within the planet wheel, and to simplify the mathematical model, the SiC workpiece and planet wheel can be considered as a single unit.

[0045] In view of the operating principle of the SiC workpiece 400 during polishing, the present invention provides a multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, such as Figure 3-6 The specific implementation process is as follows.

[0046] a. Obtain the operating parameters of the double-sided high-precision grinding and polishing equipment

[0047] b. Convert the obtained operating parameters into the planetary wheel motion parameters in the double-sided polishing machine

[0048] c. Establishing a SiC workpiece motion trajectory model based on the motion parameters

[0049] d. According to the SiC workpiece motion trajectory model, the SiC workpiece motion velocity model can be derived

[0050] e. Establish a SiC workpiece polishing heat generation model based on the SiC workpiece motion velocity model

[0051] f. Establish a multi-objective optimization model for water cooling structure based on the SiC polishing heat generation model

[0052] g. Verification using ANSYS software

[0053] Step a, specifically, obtain the operating parameters of the double-sided high-precision grinding and polishing equipment, the operating parameters including the inner ring gear 200 speed ω1, the outer ring gear 600 speed ω3, the inner ring gear 200 radius r and the outer ring gear 600 radius R.

[0054] Step b: converting the obtained operating parameters into the planetary gear motion parameters in the double-sided polishing machine.

[0055] Specifically, the linear velocities of the contact points between the planetary wheel 300 and the inner ring gear 200 and the contact points between the planetary wheel 300 and the outer ring gear 600 are the same, such as Figure 3 , the corresponding motion parameters can be calculated as follows:

[0056]

[0057] Among them, ω H is the orbital angular velocity of the planetary gear 300, ω2 is the rotational angular velocity of the planetary gear 300, ω1 is the angular velocity of the inner ring gear 200, and ω3 is the angular velocity of the outer ring gear 600.

[0058] Step c: establishing a motion trajectory model of the SiC workpiece 400 based on the motion parameters and simplifying the planetary wheel 300 and the SiC workpiece 400 as a whole.

[0059] like Figure 3 The figure shows the position of the SiC workpiece 400 after a certain time t. Based on the set double-sided high-precision grinding and polishing machine model, the movement time t of the planetary wheel 300 is set to obtain the revolution angle and rotation angle of the planetary wheel 300. The calculation method is as follows:

[0060] Since it is a compound motion of revolution and rotation, the vector method is used to analyze and solve the motion trajectory of any point on the workpiece relative to the polishing plate 500, and the coordinate system X is established with the center of the polishing plate as the origin, the horizontal right direction as the positive X direction, and the vertical upward direction as the positive Y direction. P -Y p (Polishing plate coordinate system); after time t, X P -Y p The coordinate system is rotated by angle α to obtain X' P -Y' p Coordinate system.

[0061] From the vector method we know that:

[0062] OP'=OO1'+O1'P'

[0063] Let |O1'P'| = l (0 ≤ L ≤ r), where L is the distance from a point P' on the planetary gear to the center of rotation of the planetary gear 300, which can be expressed in coordinates:

[0064]

[0065] OO1' can be expressed as:

[0066] OO'1=i(Rr)cos(θ-α)+j(Rr)sin(θ-α);

[0067] In the above formula, θ = ∠(i,OO'1); α=∠(X'P ,OX P )(angle of rotation of the polishing disk 500), where i is the unit vector in the x-direction; and j is the unit vector in the y-direction.

[0068] From the above formula we can get:

[0069]

[0070] Substituting the above formula into the equation, we can get:

[0071]

[0072] The three angles can be expressed as:

[0073]

[0074] Among them, ω P is the rotation speed of the polishing disc 500, θ=∠(i,OO'1); α=∠(X' P ,OX P )(angle of polishing disc rotation).

[0075] To simplify the parameters, extract the relationship between related variables:

[0076]

[0077] k represents the ratio of the radius of the inner ring gear 200 to the outer ring gear 600; m represents the speed ratio of the outer ring gear 600 to the inner ring gear 200; e represents the ratio of the distance from a point P on the workpiece to the center of the planetary wheel 300 to the radius of the outer ring gear 600; n represents the speed ratio of the polishing disk 500 to the inner ring gear 200.

[0078] According to the above-mentioned motion parameters of the planetary wheel 300, the motion trajectory model of the SiC workpiece 400 can be obtained:

[0079]

[0080] In step d, Figure 4 The figure is a simplified diagram of the velocity model of the SiC workpiece 400 relative to the polishing plate 500. According to the above motion trajectory equation of the SiC workpiece 400, the velocity of any point on the trajectory can be obtained:

[0081] (1) Taking the SiC workpiece 400 as a reference, the radial velocity and circumferential velocity at point P are:

[0082]

[0083] Where V ρ,w For SiC workpiece 400 radial velocity, V θ,wis the circumferential speed of the SiC workpiece 400.

[0084] (2) Taking the polishing disc 500 as a reference, the radial velocity and circumferential velocity at point P are:

[0085]

[0086] (3) The radial velocity and circumferential velocity of any point P on the SiC workpiece 400 relative to the polishing plate 500 are:

[0087]

[0088] Where V ρ is the radial velocity, V θ is the circumferential velocity, V θ,P The circumferential speed of the polishing disc is 500, V ρ,P is the radial speed of the polishing disk 500.

[0089] (4) With the center of the SiC workpiece 400 as the coordinate origin, the horizontal right direction is the positive direction of the x-axis, and the vertical upward direction is the positive direction of the y-axis, establish the X G -Y G Coordinate system (workpiece coordinate system), radial and circumferential speed in X G -Y G The direction components are:

[0090]

[0091] (5) Substituting the above equation into the equation, we can get the velocity of any point P on the workpiece relative to the polishing plate 500 in X G -Y G Directional component V x 、V y :

[0092]

[0093] (6) With the polishing disc 500 as the center, the horizontal right direction is the positive direction of the x-axis, and the vertical upward direction is the positive direction of the y-axis. P -Y P Coordinate system (polishing disc coordinate system), X G -Y G Any point in the coordinate system (workpiece coordinate system) is converted to X P -Y P The relationship in the coordinate system is:

[0094]

[0095] in For X P -Y P Coordinate origin and XG -Y G The line connecting the coordinate origin and X P -Y P The angle of the coordinate X axis.

[0096] (7) Convert the coordinates of any point P on the workpiece into X P -Y P The coordinates of the SiC workpiece 400 can be obtained by calculating the speed of any point P on the SiC workpiece 400 relative to the polishing plate 500:

[0097]

[0098] Specifically, during the operation of the double-sided polisher in step e, the majority of heat generated on the polishing plate 500 surface comes from friction between the abrasive, the SiC workpiece 400, and the polishing pad. From an energy conversion perspective, the SiC workpiece 400, under the pressure of the upper and lower polishing plates 500, rubs against the polishing pad and the abrasive in the grinding fluid, converting the mechanical energy of the polisher into heat. Therefore, the temperature rise on the working surface of the polishing plate is directly related to the pressure applied by the upper and lower polishing plates, the coefficient of friction between the workpiece and the polishing pad, the relative speed between the SiC workpiece 400 and the polishing plate 500, and the abrasive in the grinding fluid.

[0099] Using the finite element method, the mechanical energy consumed by friction in a very small area of ​​the polishing pad and the SiC workpiece 400 is calculated as follows:

[0100]

[0101] Wherein, f is the friction force generated in the extremely small area where the workpiece contacts the polishing pad and abrasive; v is the relative speed between the SiC workpiece 400 and the polishing plate 500 in the extremely small area where the workpiece contacts the polishing pad and abrasive; and t0 is the friction time between the workpiece and the abrasive and polishing pad in this extremely small area.

[0102] The friction force f generated in the extremely small area where the SiC workpiece 400 contacts the polishing pad and abrasive is calculated as follows:

[0103] f=μ P ×F

[0104] Where μ P is the friction coefficient between the SiC workpiece 400 and the polishing pad and abrasive; F is the pressure applied by the upper and lower polishing plates 500 to the workpiece.

[0105] During the polishing process of the double-sided polisher, the heat generated by friction is not completely transferred to the polishing plate 500, but is transferred to the SiC workpiece 400 and the polishing plate 500 in a certain proportion. The heat flow distribution coefficient is calculated as follows:

[0106]

[0107] Where r is the heat flow distribution coefficient; λ w is the thermal conductivity of the SiC workpiece 400; λ p is the thermal conductivity of the polishing pad; D is the thermal diffusivity of the polishing pad; v is the relative speed between the SiC workpiece 400 and the polishing plate 500; r g is the radius of the SiC workpiece 400 .

[0108] According to the above-mentioned velocity equation of the SiC workpiece 400, the heat generation at any point on the trajectory can be calculated as follows:

[0109]

[0110] Where r is the heat flux distribution coefficient; v is the relative speed between the SiC workpiece 400 and the polishing plate 500; μ P is the friction coefficient between the SiC workpiece 400 and the polishing pad and abrasive; F is the pressure applied by the upper and lower polishing plates 500 to the workpiece; and t is the polishing time.

[0111] In step f, specifically, according to the heat transfer law, a mathematical model is established by combining the heat generated by polishing in the radial direction of the polishing disc 500 and the cooling of the cooling water channel.

[0112] There are three factors that cause heat dissipation on the polishing disk: air convection heat dissipation, polishing liquid convection heat dissipation and cooling water flow heat dissipation.

[0113] (1) The air heat dissipation is solved as follows:

[0114] According to the local Newton cooling formula, the heat flux density on the surface can be expressed as:

[0115] Q x =h x ·(t w -t f )

[0116] Where h x is the convection heat transfer coefficient between the local silicon carbide workpiece and polishing disk and the air; t w is the surface temperature of silicon carbide workpiece; t f is the air temperature around the polishing machine. Since the polishing disc rotates at a constant speed during the polishing process, the air heat dissipation process is considered to be steady state, and the local surface heat transfer coefficient at each location is considered to be the same value, 10W (m 2 / ℃), the total heat dissipation of air can be obtained by integrating the local heat flux density over the entire heat transfer surface:

[0117]

[0118] Where A is the surface area in contact with air and t is the polishing time.

[0119] (2) According to heat transfer theory, the heat dissipation of polishing liquid is as follows:

[0120] Q slurry =K·c·m·t·ΔT1

[0121] Where c is the specific heat capacity of the polishing liquid; m is the mass of the polishing liquid flowing into the polishing interface per unit time; t is the polishing time; ΔT1 is the difference between the polishing liquid temperature at inflow and the polishing liquid temperature at outflow; K is the proportional coefficient, which is used as a correction formula (because not all polishing liquid will flow through the polishing interface, and the temperature rise is not the difference between the initial temperature of the polishing liquid and the temperature of the polishing disk surface). K×c×m is equivalent to the convective heat transfer coefficient between the polishing liquid and the polishing interface.

[0122] (3) The heat dissipation of the cooling water channel is as follows:

[0123] The heat exchange between the coolant and the polishing surface above is a convective heat transfer phenomenon caused by the forced flow of coolant under the action of external force, and it is a forced convective heat transfer without phase change. The convective heat transfer between the coolant and the top of the polishing plate belongs to the heat transfer of the constant fluid swept flat plate. The average surface heat transfer coefficient of the entire plate length is:

[0124]

[0125] Where h is the average surface heat transfer coefficient of the entire plate length; λ is the thermal conductivity; l is the plate length, which is taken as the centerline length of each water channel in this paper; Nu is the Nusselt number of the fluid, which is related to the flow state of the fluid and needs to be judged by the Reynolds number Re:

[0126]

[0127] Where ρ is the fluid density; υ is the characteristic velocity of the flow field; L is the characteristic length of the flow field; and μ is the dynamic viscosity coefficient of the fluid.

[0128] Under the condition of fluid sweeping the flat plate, the critical value of the laminar turbulent Reynolds number is Re=5×10 5

[0129] Since the workpiece is performing a composite friction rotation motion of rotation and revolution, the friction with the polishing disk surface is not uniform in area, which will cause the temperature in different places to be different. The temperature of the wall through which the coolant flows changes along the way. If the coolant is idealized to keep its temperature constant, then this heat transfer phenomenon is constant heat flow cooling the non-isothermal wall.

[0130] a) When cooling with constant heat flow along the entire length of the water channel, the average Nu number of laminar convection heat transfer is:

[0131] Nu=0.680Re 1 / 2 Pr1 / 3

[0132] b) When cooling with constant heat flow along the entire length of the water channel, the average Nu number of turbulent convection heat transfer is:

[0133] Nu=0.037Re 4 / 5 Pr 1 / 3

[0134] Where Re is the Reynolds number of the fluid; Pr is the Prandtl number of the fluid

[0135] The heat removed by the coolant in any cooling channel of the polishing disc is obtained from the above formula:

[0136]

[0137] Where Q fluid is the heat carried away by the coolant from the polishing disc that is parallel to the cooling water channel and has the same area; h is the average heat transfer coefficient of the heat transfer surface; A is the contact area between the polishing disc and the coolant; t is the polishing time; ΔT2 is the temperature difference between the polishing disc surface and the coolant.

[0138] According to the above analysis of heat dissipation factors, the heat generation model at any point on the polishing disk is:

[0139]

[0140] Where Q i is the heat at any point on the disk (i = 1, 2, ..., n); Q is the heat generated by friction per unit time at any point on the disk; Q slurry Q is the heat removed by the polishing fluid per unit time at any point on the disk; Air Q is the heat carried away by the air per unit time at any point on the disk; fluid It is the heat removed by the cooling water channel at any point within the influence range of the cooling water channel.

[0141] According to the heat generation model of the SiC workpiece 400, a multi-objective optimization model of the water cooling structure is established as follows:

[0142]

[0143] Among them, D is the thickness of the polishing disk 500, w si is the width of each waterway, w ji The width of each waterway, ε is the number of waterways, w in is the cooling water channel interval width (the distance from the inner ring of the polishing disc to the first cooling water channel on the left side), w out d is the outer spacing width of the cooling water channel (the distance from the right side of the outermost cooling water channel to the outer ring of the polishing disc), d is the depth of any water channel d.

[0144] The optimization objective function established is minF = {f1, -f2, -f3};

[0145] in:

[0146]

[0147] f3=D;

[0148] Where f1 represents objective function 1, i.e., the temperature variance of several points on the polishing disc in the radial direction; f2 represents objective function 2, i.e., the volume of the cooling channel; f3 represents objective function 3, i.e., the thickness of the polishing disc; D is the thickness of the polishing disc, w si is the width of each waterway, w ji The width of each waterway, ε is the number of waterways, w in Width of interval in cooling water channel, w out Cooling water channel outer interval width, d d Depth of waterway.

[0149] In this embodiment, based on the above objective function, the optimal thickness of the polishing disk, the optimal water channel structure parameters of the polishing disk, and the optimal water channel structure volume are designed using a multi-objective optimization algorithm based on NSGA-II.

[0150] The specific calculation process is as follows:

[0151] Input parameters are: population size (number of solutions) N pop , the maximum number of iterations t max , the number of cross elements is N corssover , the number of mutation elements is N mutate , mutation rate mu, objective function.

[0152] The output parameters are: Pareto optimal solution, corresponding parameters of the polishing disk water cooling structure, optimal disk thickness of the polishing disk and optimal water cooling structure volume.

[0153] The basic principle of the algorithm is: based on the crossover and mutation of the genetic algorithm, the non-dominated sorting and crowding distance are used to select the Pareto optimal solution.

[0154] The specific steps of the algorithm are:

[0155] (1) Initialize the solutions in the population. Each solution in the population contains multiple optimization design variables (water channel width of the water cooling structure, water channel depth of the water cooling structure, width of the inner and outer intervals of the water cooling structure, intervals between each water channel of the water cooling structure, and thickness of the polishing plate).

[0156] Each solution in the population contains a continuous part and a discrete part. The continuous solution in the population is initialized by a random generation method, namely the water channel width of the water cooling structure, the water channel depth of the water cooling structure, the width of the inner and outer intervals of the water cooling structure, the interval between each water channel of the water cooling structure, and the thickness of the polishing plate:

[0157] X p,q =lb q +(ub q -lb q )·rand

[0158] Where, X p,q represents the q-th dimensional solution of the p-th solution in the population, lb q represents the lower bound of the q-th dimension solution, ub q It represents the upper bound of the q-th dimensional solution, and rand is a random number generated by the system, with a value between 0 and 1.

[0159] Use random generation to initialize the discrete solution in the population, that is, the number of cooling channels:

[0160] S=Randbetween(a,b)

[0161] Where S represents the number of cooling water channels, and Randbetween is a function that randomly selects an integer from a to b, where a and b are the upper and lower limits of the number of cooling water channels, respectively.

[0162] (2). Calculate the objective function value based on the current solution.

[0163] (3) For each iteration:

[0164] a. Generate a cross population. The number of cross elements generated in each iteration is N. crossover , each time two elements in the population are selected for crossover, a total of N crossovers are required crossover / 2 times.

[0165] The following pair of formulas is used to realize the intersection of continuous solutions:

[0166]

[0167] Here, X1 and X2 are the continuous solutions from two solutions in the population, one row with m dimensions, where m represents the number of dimensions of the continuous solution. α is a one-row, m-dimensional array of random numbers. Y1 and Y2 represent the two continuous solutions after the crossover. The multiplication of the two arrays in the formula multiplies the elements at corresponding positions in the arrays.

[0168] The crossover of discrete solutions is achieved through partial matching crossover (PMX). The principle of PMX is to take the fragments at the same position of two solutions and exchange them.

[0169] b. Produce a mutant population.

[0170] The mutation method of continuous solutions is as follows: first, randomly select m·mu elements to be mutated from the m-dimensional continuous solution. Then, the mutation of the continuous solution in the elements is realized using the following formula:

[0171] Y(i)=X(i)+σ·randn

[0172] Among them, σ represents the variable step length of the i-th dimension element in the continuous solution, and randn is a random number generated by the system that obeys the normal distribution.

[0173] The variation method of the discrete solution is: randomly select two different numbers from the number of cooling water channels and swap the two values.

[0174] c. Combine the original population, cross population and mutation population to form a mixed population.

[0175] d. Perform non-dominated sorting on a mixed population.

[0176] e. Calculate the crowding distance of each particle in the mixed population.

[0177] f. Sort the mixed population according to the non-dominated sorting results and the crowding distance of the particles, and retain the top N pop The solution is used as the basis for the next iteration. The sorting rule is: first sort in ascending order according to the rank obtained by non-dominated sorting, and then sort the elements of each same rank in descending order according to the crowding distance.

[0178] (4) After reaching the set number of iterations, the final population (optimal solution set) is returned. (At this time, the population contains the optimal solution set for the radial temperature fluctuation of the polishing disk, the thickness of the polishing disk, and the volume of the water cooling structure.)

[0179] Afterwards, the solution that can achieve the minimum temperature fluctuation in the radial direction of the polishing disk in the optimal solution set is selected as the final solution. The final solution corresponds to the optimal disk thickness, optimal water channel structure parameters and optimal water channel structure volume of the polishing disk.

[0180] In step g, specifically, the double-sided high-precision grinding and polishing process is modeled and simulated using the Ansys / Workbench transient thermal module, as shown in FIG. Figure 5 The figure is a simplified diagram of the motion boundary of the SiC workpiece 400. The pressure applied normal to the surface of the SiC workpiece 400 is used to simulate the pressure exerted by the cylinder-driven upper polishing plate 100 on the SiC workpiece 400, and the rotational speed around each Z axis is applied to the SiC workpiece 400 and the lower polishing plate 500.

[0181] like Figures 7 to 9, which are Ansys simulation temperature before optimization, Ansys simulation temperature after optimization, and Ansys and Matlab radial simulation temperature before and after optimization. Figure 7-9 It can be seen that after optimization using the method provided by the present invention, the radial temperature fluctuation (variance) of the polishing disk was relatively optimized by 13.4%; the maximum disk surface temperature dropped from 61.0°C to 58.2°C, and the average temperature dropped from 43.5°C to 38.7°C; the maximum radial temperature dropped from 52.9°C to 50.7°C, and the average temperature dropped from 36.4°C to 34.8°C. This fully demonstrates that the optimization method provided by the present invention can improve the cooling effect of the polishing disk and improve the temperature uniformity of the polishing disk surface.

[0182] The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model provided by the present invention comprises the following steps: obtaining operating parameters of a polishing device in advance; obtaining motion parameters of a planetary wheel from the obtained operating parameters; deducing a motion trajectory model of a SiC workpiece from the motion parameters of the planetary wheel; deducing the motion speed of each point on the SiC trajectory from a simplified motion diagram of the SiC workpiece relative to a polishing disk; obtaining the total amount of heat generated at each point on the SiC trajectory based on the motion speed of each point on the SiC trajectory, thereby obtaining a heat generation model of the SiC workpiece; and deducing an objective function based on a multi-objective optimization algorithm, thereby obtaining parameters of the optimized water-cooling structure of the polishing disk; and finally performing a comparison and verification before and after the optimization using Ansys software.

[0183] Based on the motion trajectory model of the SiC workpiece, it is possible to predict where the polishing concentration area appears on the polishing disk surface, and targeted optimization can be performed to make the polishing contact area uniform; based on the heat generation model of the polishing disk surface, the temperature distribution during the polishing process can be predicted; based on the multi-objective optimization method of NSGA-Ⅱ, the water cooling structure can be optimized for the temperature change of the polishing disk in a more scientific and accurate manner.

[0184] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model, characterized in that: include: Establish a calculation model for the temperature variance of the temperature measurement points in the radial direction of the polishing disk surface: as well as Calculation model of water channel volume of polishing disc: f2=πd d [(w in +w s1 ) 2 -w in 2 +(w in +w s1 +w j1 +w s2 ) 2 -(w in +w s1 +w j1 ) 2 +...... +(in in +in s1 +in j1 +in s2 +in j2 +......+in s(ε-1) +in j(ε-1) +in si ) 2 -(In in +in s1 +in j1 +in s2 +in j2 +......+in s(ε-1) +in j(ε-1) ) 2 ]; Where Q i is the heat of any temperature measuring point i on the polishing disc surface, n is the number of temperature measuring points in the radial direction of the polishing disc; w si is the width of each waterway, w ji is the width of each waterway, ε is the number of waterways, w in is the interval width in the cooling water channel, w out is the width of the outer interval of the cooling water channel, d d is the depth of each cooling water channel; The constraints are the range of the width of each water channel of the polishing plate, the range of the width of each water channel interval, the range of the number of water channels, the range of the width of the interval inside the cooling water channel, the range of the width of the interval outside the cooling water channel, and the range of the water channel depth. Taking the minimum temperature variance of discrete points in the radial direction of the polishing disc surface, the maximum water channel volume of the polishing disc, and the maximum polishing disc thickness as the optimization objectives, the polishing disc water channel width, water channel depth, inner interval width of the cooling water channel, outer interval width of the cooling water channel, interval width of each water channel, polishing disc thickness, and number of water channels were optimized. The optimal solution obtained by optimization is used as the structural parameters of the polishing disk cooling water channel.

2. The multi-objective optimization method for the polishing machine cooling structure based on the heat generation model according to claim 1, characterized in that: The calculation model of the heat at any temperature measuring point on the polishing disk is: Where r is the heat flux distribution coefficient; v is the relative speed between the silicon carbide workpiece and the polishing disc; μ P is the friction coefficient between the workpiece and the polishing pad and abrasive; F is the pressure exerted by the upper and lower polishing discs on the workpiece; h x is the convection heat transfer coefficient between the local silicon carbide workpiece and polishing disk and the air; t w is the surface temperature of silicon carbide workpiece; t f is the air temperature around the polishing machine, A is the surface area of ​​the air contact, A x is the area of ​​contact between the disk surface and the air; c is the specific heat capacity of the polishing liquid; m is the mass of the polishing liquid flowing into the polishing interface per unit time; t is the polishing time; ΔT1 is the temperature difference between the polishing liquid at the time of inflow and the temperature of the polishing liquid at the time of outflow; K is the proportional coefficient, ΔT2 is the temperature difference between the polishing disk surface and the coolant, λ is the thermal conductivity; l is the plate length, and Nu is the Nusselt number of the fluid.

3. The multi-objective optimization method for the polishing machine cooling structure based on the heat generation model according to claim 2, wherein The relative speed between any point on the workpiece and the polishing disc is: Among them, ω P is the angular velocity of the polishing disc, ω w is the angular velocity of the workpiece; is the angle between the line connecting the center of the polishing disk and the center of the workpiece and the X-axis in the workpiece coordinate system, e is the ratio of the distance from a point on the workpiece to the center of the planetary gear to the radius of the outer ring gear, and (x, y) is the motion trajectory of the workpiece.

4. The multi-objective optimization method for the polishing machine cooling structure based on the heat generation model according to claim 3, characterized in that: The motion trajectory model of the workpiece is: Among them, k is the ratio of the radius of the center gear to the outer ring gear; m is the speed ratio of the outer ring gear to the center gear; ζ is the speed ratio of the polishing plate to the center gear, and R is the radius of the outer ring gear.

5. The multi-objective optimization method for the polishing machine cooling structure based on the heat generation model according to claim 3 or 4, characterized in that, The polishing plate water channel width, water channel depth, cooling channel inner interval width, cooling channel outer interval width, each channel interval width, polishing plate thickness and water channel number are optimized by NSGA-Ⅱ algorithm.

6. The multi-objective optimization method for the cooling structure of a polishing machine based on a heat generation model according to claim 5, wherein: The optimization process using the NSGA-Ⅱ algorithm includes the following steps: Step 1: Randomly generate an initial population, which includes N pop Individuals; each of the individuals is a set consisting of the polishing plate water channel width, water channel depth, cooling water channel inner interval width, cooling water channel outer interval width, each water channel interval width, polishing plate thickness and water channel number; Step 2: Update the current population using the crossover and mutation methods to obtain the crossover and mutation population; Step 3: Merge the crossover and mutation populations with the current population, perform non-dominated sorting on the merged population to obtain the individual rank, and calculate the crowding distance of each individual. Sorting the population according to the order of individual rank in ascending order and crowding distance in descending order, retaining the top N pop Individuals as a new population; Repeat steps 2-3 until the specified number of cycles is reached and the optimal solution set is obtained; Step 4: Select a solution that can minimize the temperature variance of discrete points in the radial direction of the polishing disk surface from the optimal solution set as the final solution.

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