Optimization design and thermal error suppression method for liquid cooling bionic flow channel of electric spindle of numerical control machine tool

Abstract

The invention discloses a numerical control machine tool motorized spindle liquid cooling bionic flow channel optimization design and thermal error suppression method, which comprises the following specific steps: S1, carrying out topological optimization on a water-cooled jacket to obtain a topological optimization water-cooled jacket; s2, improving the topological optimization water-cooled jacket by using a sharkskin rib structure and combining an NSGA-II algorithm to obtain a secondary optimization water-cooled jacket; and S3, performing heat-fluid-solid simulation and experimental research on the motorized spindle system adopting the secondary optimization water-cooled jacket to obtain a rotating speed adaptive cooling scheme. The method has the advantages that a'topological optimization-bionic structure 'progressive design process is constructed, sharkskin is embedded into the wall surface of a topological optimization water-cooled jacket channel, the size is optimized through an orthogonal test, and the error of the motorized spindle is maximally reduced by 1 / 5; through multiple groups of rotating speed-flow matching tests, optimal flow databases corresponding to different rotating speed intervals are established, a rotating speed adaptive cooling scheme which can be directly applied to engineering practice is formed, and the temperature and thermal deformation of key components are reduced.

Description

Technical Field

[0001] This invention belongs to the field of thermal error suppression technology for CNC machine tool electric spindles, and in particular relates to an optimized design of liquid-cooled bionic flow channel and a method for thermal error suppression for CNC machine tool electric spindles. Background Technology

[0002] In the high-end manufacturing sector, the development of precision machining technology has placed higher demands on the machining accuracy, stability, and reliability of CNC machine tools. Electric spindle systems for CNC machine tools are widely used in various high-precision machining scenarios due to their high stability, high control accuracy, and rapid response capabilities. However, in electric spindle systems, the built-in motor, as one of the components that generates the most heat, has poor heat dissipation performance. Furthermore, bearing frictional heat further leads to uneven temperature distribution within the system, causing severe thermal deformation and ultimately significantly affecting the machining accuracy of the machine tool. Therefore, improving the heat dissipation performance of the electric spindle system and controlling thermal errors has become a key challenge in improving the machining accuracy of CNC machine tools.

[0003] Electric spindle thermal management systems can be categorized by heat dissipation method into air cooling, phase change material cooling, heat pipe cooling, and liquid cooling. Liquid cooling, using water as the medium, is currently the mainstream method. Its core is the traditional water-cooled jacket employing spiral or serpentine channels. However, this method suffers from drawbacks such as high flow resistance and uneven cooling. Furthermore, its design relies on experience or biomimetic references, lacking systematic optimization and failing to adapt to different operating conditions, thus limiting improvements in heat dissipation efficiency. To address this situation, scholars have conducted relevant research: Zhang et al. established a heat-fluid-structure interaction model, optimized the U-shaped channel, and explored its parameter effects, confirming that this channel can reduce system temperature and radial thermal deformation; Tang et al. proposed a novel rectangular channel with added cylindrical protrusions to enhance heat dissipation performance through enhanced eddy currents. Currently, research on water-cooled jacket design largely focuses on optimizing the shape and size of existing structures, and heat dissipation performance still relies on designer experience and biomimetic references.

[0004] Topology optimization, as a highly flexible conceptual design method, has demonstrated significant advantages in fields such as structural design and heat transfer optimization. In recent years, topology optimization considering fluid-structure interaction has become a research hotspot. Researchers have focused on improving heat transfer performance by modifying the cross-sectional shape of channels, designing fractal channel structures, adopting biomimetic channels, and using multi-inlet and multi-outlet arrangements. Zhang et al. constructed a pseudo-three-dimensional water-cooled radiator structure based on a two-dimensional double-layer model with the goal of minimizing power consumption and thermal resistance; Navah et al. established a three-dimensional thermofluid topology optimization model for laminar flow, using the density method and taking the regional average temperature and surface average temperature as objective functions; Palumbo et al. applied topology optimization methods in radiator design to achieve minimization of temperature fluctuations and maximization of heat transfer efficiency; Pan et al. proposed a two-step adaptive mesh refinement strategy from coarse to fine in the topology optimization framework based on the density method of OpenFOAM, and verified that the strategy can sharpen the fluid-solid interface while controlling costs; Li et al. used a multi-objective topology optimization method to provide a convergent and effective solution for the design of water-cooled jackets and freely mounted cooling plates for machine tool electric spindles; Gilmore et al. obtained a novel manifold microchannel radiator structure through three-dimensional multi-objective topology optimization, which reduced pressure drop loss by 17% and thermal resistance by 22.4% compared with rectangular manifold microchannels; all of the above topology optimization studies added Brinkman drag terms related to flow velocity to the fluid momentum equation. However, topology optimization of water-cooled jackets for electric spindle systems still faces two major bottlenecks: First, the three-dimensional structure and turbulent flow lead to high computational complexity and poor convergence, making it difficult for traditional Reynolds-averaged Navier-Stokes models to balance computational efficiency and accuracy; second, existing research is mostly limited to the two-dimensional design domain, and the optimization of three-dimensional flow channel cross-sectional shapes lacks systematic theoretical guidance. There is an urgent need to develop a liquid-cooled biomimetic flow channel optimization design and thermal error suppression method suitable for CNC machine tool electric spindle systems. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an optimized design of the liquid-cooled bionic flow channel and a method for suppressing thermal errors in the electric spindle of CNC machine tools, so that the designed water-cooling jacket can significantly reduce the electric spindle error and generate a speed-adaptive cooling scheme that can effectively suppress thermal errors.

[0006] The technical solution adopted by this invention to solve the above problems is: a method for optimizing the design of liquid-cooled bionic flow channels and suppressing thermal errors in CNC machine tool electric spindles, comprising the following specific steps: S1 performs topology optimization on the design domain of the water-cooled jacket geometric model of the electric spindle under a density field with uniform initial density distribution. The optimal heat dissipation capacity and minimum power dissipation are the multiple objective functions, and the topology-optimized water-cooled jacket is obtained. S2 draws inspiration from the sharkskin rib structure and analyzes the main rib height, main rib width, and main and secondary rib height ratio and related parameters through orthogonal experiments. Combined with the NSGA-II algorithm, the topology optimization water cooling jacket is improved to obtain a secondary optimized water cooling jacket with a sharkskin biomimetic structure. S3 conducts thermal-fluid-solid simulation and experimental research on an electric spindle system using a secondary optimized water-cooling jacket. Through multiple sets of speed-flow matching tests, it establishes an optimal flow database corresponding to different speed ranges. Linear regression is used to construct the correlation function between speed and optimal flow to obtain a speed-adaptive cooling scheme.

[0007] Compared with existing technologies, the advantages of this invention are as follows: It constructs a progressive design process of "topology optimization - bionic structure," embedding shark skin into the topology-optimized water-cooling jacket channel wall. Dimensions are optimized through orthogonal experiments, resulting in a bionic radiator with superior heat dissipation performance compared to traditional water-cooling jackets, and a maximum reduction in electric spindle error of 1 / 5. Through multiple sets of speed-flow matching experiments, an optimal flow database corresponding to different speed ranges is established, forming a speed-adaptive cooling solution that can be directly applied to engineering practice. Compared with traditional fixed flow solutions, precise matching of speed and flow reduces the temperature and thermal deformation of key components.

[0008] As a preferred option, the topology optimization method in step S1 is as follows: using the best heat dissipation capacity and the minimum power dissipation as multiple objective functions, perform two-dimensional topology optimization on the half-size water cooling jacket to obtain a three-dimensional half-size water cooling jacket; roll up the full-size water cooling jacket formed by the symmetrically designed three-dimensional half-size water cooling jacket to obtain a complete cylindrical topology-optimized water cooling jacket.

[0009] As a preferred approach, the two-dimensional topology optimization is as follows: Within the design domain of a half-size water-cooled jacket, the inflow and outflow of the water-cooled jacket are arranged on the same parallel edge. A uniform heat load Q* is applied to the design domain, the volumetric flow rate at the inlet is set to fully developed flow conditions, the inlet temperature is set to T*=293K, and the outlet pressure is set to p*=0Pa. The optimization objective is defined as heat transfer and fluid dissipation power. A fluid-structure heat transfer topology optimization model is constructed, with the following expression: ; ; in, J h Let Ω be the heat transfer objective function, representing maximizing the heat exchange efficiency between the cooling component and the fluid; Ω is the design domain. These are the design variables before filtering. T* The temperature is dimensionless. J f Let be the fluid dissipation loss function, representing the pumping power required to minimize fluid flow on the cooling component; Here, u* is the gradient operator, α* is the velocity, and α* is the dimensionless permeability. After normalizing the average temperature and fluid dissipation power, the objective function can be expressed as: ; In the formula, ω These are the weighting coefficients; J min and J max These correspond to the minimum and maximum values ​​obtained in their respective single-objective topology optimizations; the topology optimization problem of the multi-objective function of the water-cooled jacket can be expressed as: In the formula, Da For Darcy's number, q As a penalty factor, Pr For Prandtl numbers, Re Let Reynolds number be 1. h * The heat transfer coefficient is... For design variables.

[0010] Preferably, the sharkskin rib structure consists of 3 to 5 ribs.

[0011] Preferably, the orthogonal experimental analysis specifically includes: Focusing on three factors—the height h of the main rib, the width b of the main rib, and the height ratio w of the main and secondary ribs—a three-factor, four-level orthogonal experiment was designed. Range analysis was performed on the orthogonal experimental results, using the highest temperature T as the starting point. max Pressure drop ΔPa and temperature standard deviation T α To evaluate the performance, we analyzed the impact of various factors on the heat dissipation performance and pressure drop of the water-cooled jacket, and obtained the optimal parameter matching.

[0012] Preferably, the order of influence on temperature T is b>w>h, with the main rib width b having the greatest impact on the highest temperature T. max The main rib width *b* has the greatest impact, and the larger the main rib width *b*, the lower the temperature *T*. The order of impact on pressure drop *ΔPa* is h>w>b. The main rib size has the greatest impact on pressure drop *ΔPa*, and the larger the main rib height *h*, the higher the pressure drop *ΔPa*. Regarding *T*... α The order of influence is h>b>w, with the main rib height h affecting T. α The effect is greatest; changing the height h of the main rib can alter the uniformity of temperature distribution in the water-cooled jacket.

[0013] Preferably, the height h of the main rib is 2.4 mm, the width b of the main rib is 0.8 mm, and the height ratio w of the main and secondary ribs is 1.8.

[0014] As a preferred approach, the steps for thermal-fluid-solid modeling are as follows: establish a thermal-fluid-solid finite element model; define the physical field type and apply boundary conditions; solve for the temperature field, fluid pressure, velocity field, and thermal deformation field under steady-state conditions; and perform post-processing and analysis.

[0015] As a preferred option, the correlation function between rotational speed and optimal flow rate is: ; Where y is the optimal flow rate and x is the rotational speed. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the design process of the water-cooling jacket for the electric spindle of this invention.

[0017] Figure 2 This is a geometric model diagram of the water-cooling jacket of the electric spindle of the present invention.

[0018] Figure 3 This is a semi-topology optimization water-cooling diagram under different weighting factors according to the present invention.

[0019] Figure 4 This is a graph showing the average temperature of the water-cooled jacket under different weighting factors according to the present invention.

[0020] Figure 5 This is a diagram showing the pressure difference of the water-cooled jacket under different weighting factors according to the present invention.

[0021] Figure 6 Temperature diagrams of the water-cooled jacket under different Reynolds numbers according to the present invention.

[0022] Figure 7 Diagrams showing different sharks and their corresponding bar structures and microchannel flow layouts.

[0023] Figure 8 This is a Pareto solution set diagram for the present invention.

[0024] Figure 9 This is a graph showing the proportion of each variable in the three factors of the orthogonal experimental design of this invention.

[0025] Figure 10 This is a comparison diagram of the three-dimensional models of the semi-S-shaped water jacket (SCP) and the semi-secondary optimized water jacket (BTCP) of the present invention.

[0026] Figure 11 This is a graph showing the variation trend of three parameters of the three water-cooled jackets of the present invention with Reynolds number.

[0027] Figure 12 This is a pressure drop diagram of the three water-cooled jackets of the present invention as a function of Reynolds number.

[0028] Figure 13 This is a temperature diagram of the three-dimensional rectangular water-cooled plate and the cylindrical water-cooled jacket of the present invention.

[0029] Figure 14 This is a graph showing the average temperature variation trend of the three-dimensional rectangular water-cooled plate and cylindrical water-cooled jacket of the present invention with Reynolds number.

[0030] Figure 15 This is a diagram of the experimental setup for the water-cooled jacket of this invention.

[0031] Figure 16 A partial sectional view of the complete cooling circuit and electric spindle system for the topology-optimized water-cooled jacket and the secondary-optimized water-cooled jacket.

[0032] Figure 17 This is a finite element mesh model of the electric spindle system of the present invention.

[0033] Figure 18 This is a temperature field comparison diagram of the electric spindle system equipped with an S-type water cooling jacket and a secondary optimized water cooling jacket according to the present invention.

[0034] Figure 19 This is a comparison diagram of the temperature field of the stator of the electric spindle system equipped with an S-type water cooling jacket and a secondary optimized water cooling jacket according to the present invention.

[0035] Figure 20 This is a streamline distribution diagram of the complete cooling circuit of the S-type water-cooling jacket and the secondary optimized water-cooling jacket of the present invention.

[0036] Figure 21 This is a pressure distribution diagram of the complete cooling circuit of the S-type water-cooling jacket and the secondary optimized water-cooling jacket of the present invention.

[0037] Figure 22 This is a prototype drawing of the secondary optimized water cooling jacket and the S-shaped water cooling jacket of the present invention.

[0038] Figure 23 This is a diagram of the experimental platform for the electric spindle system of the present invention.

[0039] Figure 24 This is a cross-sectional view of the electric spindle system of the present invention.

[0040] Figure 25 The diagram shows the average temperature and steady-state thermal elongation of key components of the electric spindle system under different rotational speeds and flow rates according to the present invention.

[0041] Figure 26 Temperature diagram of the electric spindle housing with the secondary optimized water cooling jacket of this invention.

[0042] Figure 27 This diagram shows the optimal flow rate and rotational speed of the electric spindle system equipped with an S-type water cooling jacket and a secondary optimized water cooling jacket according to the present invention.

[0043] Figure 28 This is a thermal deformation diagram of the electric spindle system of the present invention, which is equipped with an S-type water cooling jacket and a secondary optimized water cooling jacket.

[0044] Figure 29 This is an error diagram of the electric spindle at different speeds according to the present invention. Detailed Implementation

[0045] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of the present invention, including various details of these embodiments to aid understanding, and should be considered merely exemplary.

[0046] This invention proposes an optimized design and thermal error suppression method for the liquid-cooled biomimetic flow channel of a CNC machine tool electric spindle, the steps of which are as follows: S1 performs topology optimization on the geometric model of the water-cooling jacket of the electric spindle under a density field with a uniform initial density distribution. The optimal heat dissipation capacity and minimum power dissipation are used as multiple objective functions to obtain the topology-optimized water-cooling jacket.

[0047] Construction of the geometric model of the water-cooling jacket of the S11 electric spindle Considering manufacturing costs, computational costs, and model convergence, the overall design concept of the water-cooled jacket is as follows: Figure 1 As shown, the three-dimensional topology optimization problem of the water-cooled jacket is transformed into a two-dimensional topology optimization problem. The design of a half-size water-cooled jacket is used to replace the full-size water-cooled jacket. The optimal heat dissipation capacity and minimum power dissipation are taken as the multiple objective functions. Then, the two half-size water-cooled jackets are combined together and rolled into a cylindrical water-cooled jacket, which is finally applied to the electric spindle to achieve error compensation.

[0048] S12 Topology Optimization Within the fluid-structure topology optimization domain, the design domain is theorized as a porous material. It is assumed that the fluid resistance F is linearly related to the flow velocity u, expressed as F = -αu, where α is the permeability. The design domain is divided into a finite number of cells, each assigned a design variable γ, with a value between 0 and 1. Black areas represent solids, γ = 0, α → ∞, F → ∞. Gray areas represent fluids, γ = 0, α → 0, F → 0. The solid and fluid materials are shown in Table 1.

[0049] Table 1 Material List S121 governing equation For incompressible laminar flow, the dimensionless continuity equation and momentum conservation equation are expressed by dimensionless physical quantities, including velocity u*, pressure p*, Reynolds number Re, and gradient operator. The dimensionless physical quantities mentioned above are defined as follows: (1) in U and L These are characteristic velocity and length, respectively. For density, This refers to dynamic viscosity.

[0050] For incompressible laminar flow, the continuity equation is as follows: (2) The momentum conservation equation is expressed as: (3) According to Darcy's law, volume forces F* It is proportional to the velocity u*. Dimensionless permeability is denoted as... α* It is determined by subsequent penalty function interpolation.

[0051] (4) (5) (6) In equations (5) and (6), It is used for adjustment The penalty factor for the shape of the function, and It is related to the Darcy number Da and the Reynolds number Re. Therefore, the momentum equation can be expressed as: (7) S122 conjugate heat transfer: The dimensionless energy conservation equation is derived from dimensionless temperature. T* And Prandtl Pr The definition is given as follows: (8) in, T B and T W These are the average temperature and the wall temperature, respectively. The thermophysical properties of a fluid are determined by its specific specific heat capacity. C P and fluid thermal conductivity k f Characterization is a key parameter in heat transfer analysis.

[0052] Therefore, the dimensionless heat transfer equation is expressed as: (9) in Q* This represents the dimensionless rate of heat generation, while k s This represents the thermal conductivity of a solid.

[0053] Equation (10) can be obtained from equation (9). When γ When 0 and 1 are taken, equation (10) represents the simplified form of the solid domain and fluid domain of equation (9), respectively.

[0054] (10) in, Q* This represents the dimensionless thermal emissivity and is related to temperature. T* Proportional, and expressed in the form of Newton's law of cooling. (11) Because the heat source is related to the topology, the term This indicates that the fluid domain does not generate heat. Therefore, when the thermal conductivity of the solid material increases significantly, the solid domain can effectively dissipate the generated heat, thus forming a relatively simple channel layout. To increase the effective heat exchange surface area, a bifurcated channel structure is preferred. Therefore, assuming... Design variables Taking this into account, and substituting equation (11) into equation (10), we get: (12) S123 Density Filtering and Projection To avoid the checkerboard pattern in the design domain, a density filtering method using the Holmtz partial differential form is employed. (13) in, R min The filter radius is the unit size. These are the design variables before filtering; These are the design variables after filtering.

[0055] The density filtering method described above improves the stability of the numerical solution. However, it also leads to an increase in gray cells. To address the gray cell problem, hyperbolic tangent projection is employed: (14) in, These are the projected output design variables. and These are the projection point and the slope, respectively. In this paper, =0.5 and =8.

[0056] The penalty factor q is 10 -2 The Darcy number Da is 10. -4 The Prandtl number Pr is 6.78. Under the same thermal boundary conditions, the temperature of the water-cooled jacket decreases with increasing Reynolds number Re. The Reynolds number Re is taken as 100, and the heat transfer coefficient h* is taken as 100.

[0057] S13 electric spindle water-cooling jacket topology optimization Cross-section of the electric spindle cooling channel is as follows Figure 2As shown in (a), the inner diameter Φ1 is 95 mm and the outer diameter Φ2 is 101 mm. To simplify the topology optimization model and reduce computation, the three-dimensional design domain is unfolded into a rectangle, and multi-objective topology optimization is performed on the two-dimensional rectangular design domain. To further improve the stability and convergence of the topology optimization model, the two-dimensional rectangular design domain is divided into two halves, and topology optimization is performed only on one half, as shown in (a). Figure 2 As shown in (b), the characteristic length L is 10 mm. Furthermore, within this design domain, the inflow and outflow of the water-cooled jacket are arranged on the same parallel edge. A uniform heat load Q* is applied to the design domain. The inlet volumetric flow rate is set to fully developed flow conditions, the inlet temperature is set to T* = 293 K, and the outlet pressure is set to p* = 0 Pa.

[0058] To improve cooling performance and reduce flow resistance, the optimization objective is defined as heat transfer and fluid dissipation power, and a fluid-structure heat transfer topology optimization model is constructed, the expression of which is as follows: (15) (16) in, J h The objective function for heat transfer is to maximize the heat exchange efficiency between the cooling component and the fluid. J f Ω is the fluid dissipation loss function, representing the pumping power required to minimize fluid flow on the cooling component; Ω is the design domain.

[0059] After normalizing the average temperature and fluid dissipation power, the objective function can be expressed as: (17) In the formula, ω is the weighting coefficient; J min and J max These correspond to the minimum and maximum values ​​obtained in their respective single-objective topology optimizations. Ultimately, the multi-objective topology optimization problem for the water-cooled jacket can be formulated as: (18) S14 Topology Optimization Results and Numerical Simulation S141 Topology Optimization Results Topology optimization was performed using COMSOL Multiphysics 6.2. The weighting coefficients ω were set to 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9, respectively. These weighting coefficients directly affect the flow channel structure parameters. Figure 3As can be seen, with the increase of the weighting coefficient, the width of the internal flow channels of the water-cooled jacket becomes narrower and the number of flow channels increases. The heat dissipation performance of the water-cooled jackets corresponding to different weighting coefficients varies significantly. To verify the effectiveness of the topology optimization results, thermal characteristics analysis was performed on topology-optimized water-cooled jackets (TCPs) with different design Reynolds numbers under different weighting coefficients.

[0060] The Reynolds numbers at the water-cooled jacket inlet are 1000, 5000, 10000, 15000, and 20000, respectively, and the heat flux applied throughout the design domain is 15330 W / m². 2 The average temperature distribution of the design domain at different Reynolds numbers is as follows: Figure 4 As shown in (a), it can be observed that the average temperature of TCP decreases as the Reynolds number increases. When the Reynolds number changes from 1000 to 10000, the average temperature of TCP shows a rapid decreasing trend. When the Reynolds number changes from 10000 to 20000, the rate of decrease in average temperature begins to slow down, and the heat dissipation effect does not improve significantly. Figure 4 (b) shows the variation of TCP's maximum temperature with Reynolds number, and the trend is consistent with the average temperature. The maximum temperature decreases slowly after the Reynolds number exceeds 10000. It can be assumed that TCP reaches a steady state at a Reynolds number of 10000.

[0061] Figure 5 This demonstrates how TCP pressure varies with the Reynolds number, for all... ω The pressure difference curve shows that the pressure difference increases with the increase of the Reynolds number. As the Reynolds number increases, the disturbances and friction effects of fluid flow intensify, leading to a rise in pressure loss. When the Reynolds number Re is less than 5000, the pressure difference curves corresponding to different weights almost overlap, indicating that Re has little effect on the pressure difference at this point. As the Reynolds number further increases, exceeding 5000, the curves for different Re values ​​gradually separate, and the larger the Re value, the faster the pressure difference increases and the higher the final pressure difference value. ω The curve with a value of 0.9, in the high Reynolds number region near Re=20000, indicates a pressure difference much higher than... ω The curve with a weight of 0.2 indicates that under high Reynolds number flow conditions, the weight... ω The effect on the pressure difference becomes very obvious. ω An increase in pressure may strengthen the fluid's resistance mechanism, thereby significantly increasing pressure loss.

[0062] Table 2 and Figure 6 These represent the steady-state temperature distribution and temperature variance of TCP at a Reynolds number Re=10000. ω When the coefficient of performance is 0.9, both the average temperature and the temperature standard deviation are minimized. However, the pressure drop loss is much greater than other pressure drop losses, which will hinder the normal flow of fluid in the cooling channel. In addition, the three cases with the lowest temperature standard deviation correspond to different weighting coefficients. ω =0.4, 0.5, and 0.6. However, as the weighting coefficient increases, the more branching the flow channel, the higher the processing cost. Considering economic efficiency, the final weighting coefficient was selected. ω TCP = 0.4 was used as the initial water cooling jacket in this paper.

[0063] Table 2. Average temperature and temperature variance of liquid cooling plates with different weights S2 draws inspiration from the sharkskin rib structure and analyzes relevant parameters such as the height and width of the main ribs and the ratio of the height of the main and secondary ribs through orthogonal experiments. Combined with the NSGA-II algorithm, the topology optimization water jacket is improved twice to obtain a secondary optimized water jacket with a sharkskin biomimetic structure.

[0064] The internal structure of microchannel heat sinks is improved by employing a biomimetic sharkskin rib structure to enhance heat transfer performance and reduce pressure drop. Different sharkskin rib structures are shown below. Figure 7 As shown in (a), it consists of 3 to 5 ribs. The scales of the rib structure corresponding to the Caribbean reef shark are regular semi-elliptical peaks, and their specific structure is as follows: Figure 7 As shown in (b), it consists of one main rib and two secondary ribs, with a semi-elliptical geometry chosen as the basic pattern. This rib structure simulates the leading peak of the ribs and is arranged on the inner surface of the flow channel, as shown in [example image]. Figure 7 As shown in (c).

[0065] S21 Bionic Shark Skin Rib Structure Design S211 Orthogonal Experimental Design Orthogonal experimental design is a research method for solving multi-factor, multi-level problems. By selecting a small number of representative experiments, it helps researchers analyze experimental results more accurately. The thermal performance of water-cooled jackets is affected by multiple factors. Focusing on three factors—the height (h) of the main ribs (sharkskin), the width (b) of the main ribs, and the ratio of the heights of the main and secondary ribs (w)—a three-factor, four-level orthogonal experiment was designed. The factor levels are shown in Table 3. The results of 16 orthogonal experiments are shown in Table 4. The evaluation index includes the highest temperature T. max Pressure drop ΔPa and temperature standard deviation T α .

[0066] Table 3. Factor Level Table for Orthogonal Experiment Table 4. Orthogonal experimental design and results S212 Orthogonal Analysis Range analysis has the advantages of being simple, fast, accurate, and intuitive. Range analysis was performed on 16 sets of orthogonal experimental results. To obtain the best parameter matching, the range (R) of each factor was used to evaluate its influence on the heat dissipation performance and pressure drop of the water-cooled jacket. The R value was calculated using equation (19). The larger the R value, the more significant the influence of the corresponding factor. (19) As shown in Table 5, the order of influence of each factor on T is b>w>h, and the main rib width has the following effect on T. max The main rib width has the greatest impact. The larger the main rib width, the lower the temperature. The order of influence of each factor on ΔPa is h>w>b, with the main rib size having the greatest impact on ΔPa. The larger the main rib height h, the higher the corresponding ΔPa. Regarding T... α The order of influence is h>b>w, and the width of the main rib affects T. α The main rib width has the greatest impact, and changing the width of the main rib can improve the uniformity of temperature distribution in the water-cooled plate.

[0067] Table 5. Range Analysis Results S22 optimizes sharkskin rib dimensions based on NSGA-II. To ensure fast and accurate fitting, the least squares method is used to fit the objective function. T is selected. max The evaluation metrics ΔPa and S are used as objective functions. The accuracy of the model is determined by R². The final fitted function is shown in the following equation: (20) (twenty one) T was calculated max , △Pa and T α coefficient of determination R 2 The values ​​of 0.995, 0.997, and 0.994, respectively, indicate that the fitted objective function can replace numerical simulation, further verifying the accuracy and reliability.

[0068] Based on the above fitting function, the optimization constraint function of NSGA-II is established, as shown in equation (23): (twenty two) Using NSGA-II to obtain the Pareto optimal solution set, such as Figure 8 As shown. The parameter settings are as follows: population size 80, maximum number of generations 300, optimal individual coefficient 0.8, fitness function bias 1×10⁻⁶. -6 .Depend on Figure 8 It can be seen that the Pareto solution sets are mutually constrained, i.e., T max When T increases, σ It also increases accordingly, while ΔPa decreases.

[0069] Figure 8 By analyzing the optimization results, the proportions of three variables—main rib height (h), main rib width (b), and the ratio of main to secondary rib height (w)—in each interval were obtained, such as... Figure 9 As shown. A has the highest proportion (97%) in the interval [2, 2.4]; B has the highest proportion (39%) in the interval [2, 2.4]; C has the highest proportion (68%) in the interval [2, 2.4]. Based on the above analysis, the final structural parameters are determined to be: h = 2.4 mm, b = 0.8 mm, w = 1.8. The final biomimetic water-cooled jacket (BTCP) is shown below. Figure 10 As shown in (a), an S-type water-cooled jacket (SCP) is introduced for comparison, and the corresponding 3D model is as follows. Figure 10 As shown in (b).

[0070] Analysis of heat dissipation and flow characteristics of S23 water-cooled jacket S231 heat dissipation performance analysis Figure 11 (a) is the water-cooled jacket T max The trend of Reynolds number (Re) changes. When Re increases from 2000 to 10000, the maximum temperatures of BTCP, TCP, and SCP decrease by 21.4K, 24.5K, and 31.5K, respectively. However, when Re increases from 10000 to 20000, the temperature difference between the three flow channel cooling plates gradually decreases, with the maximum temperatures decreasing by only 2.8K, 3.8K, and 2.7K, respectively. Overall, BTCP shows the most significant advantage in maximum temperature control, while SCP and TCP show similar results.

[0071] Figure 11 (b) shows the trend of the average temperature of the water cooling jacket as a function of Re. It is roughly the same as the trend of the highest temperature. BTCP has the best performance, while TCP and SCP have similar heat dissipation capabilities.

[0072] Figure 11 (c) is the water-cooled jacket T α As Re changes, BTCP clearly outperforms SCP and TCP in achieving thermal uniformity. When Re increases from 2000 to 10000, the S values ​​of BTCP, TCP, and SCP decrease by 77.8%, 74.1%, and 67.7%, respectively; however, when Re increases from 10000 to 20000, the S values ​​of the three models only decrease by 20.0%, 14.1%, and 25.4%, respectively, indicating that thermal uniformity tends to stabilize.

[0073] S232 Flow Characteristics Analysis Pressure drop loss is an important indicator of the flow characteristics of cooling channels. The greater the pressure drop loss, the higher the energy consumption required for fluid flow. Figure 12The pressure distribution inside the cooling channels is shown for different inlet Reynolds numbers: the maximum pressure in all three channels is located near the inlet, and the pressure drop loss increases with increasing inlet Reynolds number Re. However, the increasing trend of pressure drop loss in BTCP and TCP is much smaller than that in SCP. When the inlet Reynolds number Re < 8000, the pressure drop loss increases relatively slowly, while when Re > 8000, the pressure drop loss increases rapidly. The maximum pressures of the cooling fluid in BTCP, TCP, and SCP are 4893 Pa, 9893 Pa, and 36768 Pa, respectively.

[0074] At the same inlet Reynolds number, the pressure drop loss of BTCP is slightly less than that of TCP channel. When Re is 10000, the pressure drop loss of BTCP is reduced by 81.48% and 75.07% compared with SCP and TCP, respectively. Therefore, the energy consumption of cooling fluid flow in BTCP channel is significantly reduced, greatly reducing the required pump power and the risk of cooling fluid leakage.

[0075] S24 Equivalence Analysis The thickness of the 3D design domain is relatively small compared to its perimeter and length. Thickness has a relatively small impact on heat transfer performance. The simplification process of the topology optimization model considers maintaining the proportional relationship between the design domain area and the heat transfer surface area; therefore, it is assumed that the simplified 2D model has similar heat transfer performance to the original 3D model. However, replacing the actual 3D toroidal model with a 3D planar model may neglect some 3D effects such as edge effects or corner effects, which may affect the heat transfer performance of the actual 3D model. To address this issue, the heat transfer performance of a 3D rectangular model and a 3D cylindrical model are compared.

[0076] Figure 13 The average temperature and isotherm plots of the three-dimensional rectangular model and the three-dimensional cylindrical model are displayed. Figure 14 The average and maximum temperatures of the 3D rectangular and 3D cylindrical models are presented for Reynolds numbers [1000, 20000]. It can be seen that at the same Reynolds number, the temperature distributions of the two models are almost identical, with the average surface temperature of the 3D cylindrical model consistently slightly lower than that of the 3D rectangular model. Although there are slight differences in the temperature distributions and average surface temperatures of the 3D cylindrical and 3D rectangular models, their heat transfer performance is essentially the same. Therefore, overall, the heat transfer performance of the two models before and after simplification is almost identical, making the choice of a straight liquid-cooled plate for heat transfer performance verification reasonable.

[0077] S25 Experimental Verification To verify the multi-objective topology optimization method for cooling plates in precision machine tools, experiments were conducted to measure the heat dissipation and flow performance of the liquid cooling plate in the topology-optimized channel. The cooling plate was fabricated using 3D printing technology, with Aisi10Mg cast aluminum alloy as the metal material. This alloy has a density of 2721 kg / m³ and a thermal conductivity of 170 W / (m²). K), specific heat capacity at constant pressure is 900 J / (kg) K). The heating power is maintained at 500W, and the inlet Reynolds number Re is [2000, 20000]. A copper plate is used to uniformly heat the bottom of the cooling plate, and the remaining boundaries are heated by natural convection.

[0078] Experimental setup such as Figure 15 As shown: The bottom of the water-cooled jacket is heated by a uniformly heated copper plate. The industrial cooler controls the inlet liquid temperature at 293K, which serves as the reference temperature for the entire fluid circulation process. The liquid actuator drives the coolant to circulate within the cooling channel, maintaining a constant Reynolds number. Flow rate is continuously collected using a precision flow meter and a liquid reservoir. Simultaneously, temperature sensors are placed at the inlet and outlet of the cooling plate to collect the temperature difference. In addition, a differential pressure sensor is used to measure the pressure change between the inlet and outlet of the cooling plate. The collected data is transmitted in real time to a paperless recorder for subsequent processing.

[0079] The experimental data are shown in Table 6. The average temperature gradually decreases with increasing Reynolds number (Re). The difference between the measured temperature data and the simulation results is not significant and decreases with increasing inlet Reynolds number (Re). This difference is due to the actual contact state between the heating plate and the cooling plate and the actual surface quality of the machined material. Incomplete contact between the heating plate and the cooling plate, and insufficient contact between the coolant and the flow channel surface, lead to reduced heat transfer efficiency. Furthermore, heat dissipation to the surrounding air during the experiment further reduces the experimental data. Therefore, the measured average temperature is lower than the simulation prediction. The pressure drop of the water-cooled jacket increases with increasing Re. The experimentally measured pressure drop is greater than the simulation result because of frictional losses during the cycle. The maximum error between the experiment and the simulation is 8%, which is within an acceptable range.

[0080] Table 6 Temperature of Experimental and Simulated BTCP In summary, compared to SCP and TCP, BTCP offers significant advantages, specifically in two key performance indicators: pressure loss and average surface temperature. Lower pressure loss means reduced energy consumption during fluid circulation, thus improving energy efficiency; lower average temperature indicates superior heat dissipation performance, which is crucial for the overall efficiency of the cooling plate. Therefore, BTCP not only saves energy but also boasts excellent cooling performance, making it a promising candidate for applications in cooling systems.

[0081] S3 conducts thermal-fluid-solid simulation and experimental research on an electric spindle system using a secondary optimized water-cooling jacket. Through multiple sets of speed-flow matching tests, it establishes an optimal flow database corresponding to different speed ranges. Linear regression is used to construct the correlation function between speed and optimal flow to obtain a speed-adaptive cooling scheme.

[0082] S31 water-cooled jacket arrangement The BTCP was integrated into the electric spindle system for multiphysics simulation analysis, and its cooling performance was compared with that of SCP. The flow channels were combined to form a complete cooling loop to cover the motor stator. Figure 16 (a) and (b) illustrate two complete cooling loops. Figure 16 (c) shows a simplified structure of an electric spindle equipped with a water-cooled jacket.

[0083] S32 Finite Element Model and Boundary Conditions A secondary optimized water-cooling jacket is embedded in the high-speed electric spindle to replace the traditional water-cooling jacket with an S-shaped cooling channel. A thermo-thermal-fluid-structure interaction (T / S) simulation model of the high-speed electric spindle system using the novel water-cooling jacket is constructed. The steps of the T / S simulation of the high-speed electric spindle system are as follows: a1. Establish a thermo-fluid-structure interaction finite element model; a2. Define the physical field types and apply boundary conditions; a3. Solve for the steady-state temperature field, fluid pressure, velocity field, and thermal deformation field; a4. Perform post-processing and analysis.

[0084] To facilitate subsequent thermo-fluid-structure interaction analysis, some small chamfers, fillets, screws, retaining rings, stators, and thin gaskets were simplified, and the bearings were simplified to hollow cylinders. The simplified high-speed electric spindle-bearing system model was imported into COMSOL Multiphysics 6.2 software. Tetrahedral elements were used to mesh the entire high-speed electric spindle-bearing system, and the mesh was refined in areas with large temperature gradients, such as the novel water-cooling jacket, stator, rotor, and shaft. The entire model has 1,435,856 elements and 275,369 nodes. Figure 17 As shown.

[0085] The rear bearing of the electric spindle employs a spring-loaded constant-pressure preload method, and the rear bearing housing is equipped with a bearing housing guide sleeve with balls, allowing the bearing housing and the outer ring of the bearing to move axially. To ensure the relative movement of the bearing assembly during thermal deformation, the contact between the inner and outer rings of the bearing and the balls is set to a non-separated state; the contact between other components is set to a fixed state to ensure model convergence.

[0086] The expression for the governing equations in steady-state thermal simulation is as follows: (twenty three) Where T is the temperature of each unit, λ x , λ y , λ z These are the thermal conductivity of the material in the x, y, and z directions, respectively.

[0087] The thermal deformation of the high-speed electric spindle-bearing system can be solved using Hooke's Law: (twenty four) Where ε is the strain vector, α is the coefficient of thermal expansion, and ΔT is the temperature rise vector.

[0088] First, set the ambient temperature, i.e., both the air temperature and the initial cooling water temperature are 20℃. The expression for the inlet flow rate is: (25) Where A is the cross-sectional area, v in The inlet velocity is calculated using equation (25), and the maximum inlet velocity under actual operating conditions is 2.06 m / s. The simulation was conducted under no-load conditions, with the high-speed electric spindle-bearing system rotating at 10000 r / min. The heat source intensity and heat dissipation of the high-speed electric spindle-bearing system were calculated using the experimental iterative method, as shown in Table 7.

[0089] Table 7 Thermal boundary conditions at a rotational speed of 12000 r / min S33 heat transfer capacity and system efficiency S331 Temperature Field Distribution Figure 18 The temperature field of the middle cross section of a high-speed electric spindle-bearing system using SCP and BTCP is shown under two inlet boundary conditions. When the inlet flow rate is 1.64 × 10⁻⁶... -5 m 3 At a flow rate of 1.23 × 10⁻⁶ K / s, the average temperature of the SCP is slightly higher than that of the BTCP. The highest temperature using the SCP is 349 K, while the highest temperature using the BTCP is 337 K, occurring at the rotor. This is because the motor is enclosed within a high-speed electric spindle-bearing system. The bearings, stator, and rotor generate a large amount of heat. The water-cooled jacket is in contact with the stator, while the bearings and rotor are not in direct contact with the water-cooled jacket. Therefore, the stator temperature decreases significantly, while the bearing and rotor temperatures decrease less noticeably. -4 m 3 At / s, the heat transfer capacity of both water cooling jackets is improved. At this time, the highest temperature using BTCP is 323K, which is 15K lower than the highest temperature of 338K using SCP.

[0090] Figure 19 The import flow rate is 1.23 × 10⁻⁶. -4 At a flow rate of m³ / s, the highest stator temperatures using BTCP and SCP are 317 K and 319 K, respectively, occurring in the inner ring of the stator. For SCP, the temperature is particularly high in areas without cooling channels; while for BTCP, the overall temperature distribution on the outer surface of the stator is more uniform.

[0091] Table 8 lists the import flow rate of 1.23 × 10⁻⁶. -4The average temperature of each major component is measured in m³ / s. In the high-speed electric spindle-bearing system using BTCP, the temperatures of BTCP and SCP are 305.31 K and 288.37 K, respectively; the housing temperatures of the high-speed electric spindle-bearing systems using BTCP and SCP are 309.13 K and 301.73 K, respectively; more importantly, the spindle core temperatures of the high-speed electric spindle-bearing systems using BTCP and SCP are 315.37 K and 309.20 K, respectively. Compared with the spindle core temperature of the high-speed electric spindle-bearing system using SCP, the spindle core temperature of the system using BTCP is significantly lower, which helps to reduce thermal deformation. In addition, more heat is transferred from the bearing to the spindle core in the high-speed electric spindle-bearing system using BTCP than in the system using SCP. Therefore, the bearing temperature before and after using the BTCP system is lower than that in the system using SCP, indicating that BTCP has superior cooling performance.

[0092] Table 8 Average Temperature of Major Components Pressure drop of S332 cooling system Figure 20 The import flow rate is 1.23 × 10⁻⁶. -4 At a flow rate of m³ / s, the velocity streamline distribution inside the cooling channel shows that the velocity field of the cooling water inside the BTCP is more uniform than that inside the SCP, and the velocity of the cooling water inside the BTCP is also lower. The maximum velocities of the cooling water inside the SCP and BTCP are 2.4 m / s and 2.3 m / s, respectively, occurring at the inlet. For the BTCP, after the cooling water is diverted at the inlet, the fluid is evenly distributed around the water jacket, making the overall flow velocity more uniform than that of the SCP, which is also the reason for the uniform heat transfer capacity of the BTCP.

[0093] Figure 21 The import flow rate is 1.23 × 10⁻⁶. -4 The pressure distribution inside the water-cooled jacket at a flow rate of m³ / s shows that the maximum pressures of both SCP and BTCP occur near the cooling channel inlet, at 2.38 × 10⁻⁶ m³ / s. 4 and 5.15×10 3 Pa. For SCP, the pressure inside the cooling channel decreases as the fluid flow path increases; conversely, the pressure field of BTCP is uniformly distributed throughout the entire cooling channel, and the total pressure drop of BTCP is much smaller than that of SCP, thus significantly reducing the power consumption of external pumps.

[0094] S34 Experimental Apparatus and Measuring Instruments To evaluate the improvement in heat dissipation performance, experimental measurement data was compared with numerical simulation results to verify the accuracy and reliability of the simulation model. 3D printing was used for fabrication, and the prototypes of the original water-cooling jacket SCP and the secondary optimized water-cooling jacket BTCP are shown below. Figure 22As shown. The experimental setup for the thermal characteristics of the electric spindle is as follows. Figure 23 As shown. A precision magnetic PT100 temperature sensor is used to measure the surface temperature of the electric spindle system. The sensor's measurement range is -50~200℃ (±0.15℃). The sensor's installation location is as follows. Figure 24 As shown, specifically, T1 corresponds to the surface temperature of the inclined surface of the front housing of the electric spindle, T2 corresponds to the housing temperature of the front bearing, T3 corresponds to the temperature of the electric spindle flange, T4 corresponds to the housing temperature of the electric spindle clamp, T5 corresponds to the housing temperature of the electric spindle cooling area, T6 corresponds to the temperature of the rear bearing, and T7 corresponds to the temperature of the stator. The temperatures of the internal components of the electric spindle are obtained through built-in temperature sensors embedded in the windings, reflecting the temperature changes in the core heat source area. Furthermore, to comprehensively evaluate the overall temperature distribution of the electric spindle system, an infrared thermal imaging measurement is performed using a FLUKE Ti480U infrared thermal imager; to achieve dynamic monitoring of thermal deformation, a laser displacement sensor is used to measure the thermal elongation of the electric spindle in real time. This laser displacement sensor has a measurement range of 0.5 mm and an accuracy of 0.5 μm. The cooling system uses an FLTZ-003 variable frequency chiller, which supports variable frequency control of the compressor and water pump. It can adapt to the real-time heat load and has a maximum cooling capacity of 10kW. The temperature control range is 4-40℃, the temperature control accuracy is ±0.1℃, and the maximum pump pressure is 7bar.

[0095] S35 Measurement Results and Comparative Verification S351 Experimental Conditions The electric spindle was run at a constant speed of 8000 r / min for 3000 s, with an inlet temperature of 21℃ and an ambient temperature maintained at 20±1℃. Under no-load conditions, the thermal characteristics of electric spindles equipped with different water-cooling jackets were measured. The data acquisition system recorded temperature data once per second, and each test was conducted after the electric spindle had cooled to room temperature.

[0096] The measured results show that the radial error of the electric spindle is approximately 10% of the axial error, which is within an acceptable range and has a limited impact on the overall accuracy. However, the axial error becomes the dominant factor restricting the working accuracy of the electric spindle. Therefore, future research will focus on the analysis and control of the axial error.

[0097] The Influence of S352 Flow Rate on Thermal Characteristics and Thermal Error Figure 25Table 9 shows the relationship between flow rate and the temperature and thermal error of key components in electric spindle systems equipped with SCP and BTCP (hereinafter referred to as SCP system and BTCP system, respectively). Increasing the flow rate has a significant effect on reducing the temperature of the front bearing, rear bearing, and stator, as well as reducing thermal error. Moreover, the temperature reduction gradient gradually decreases with increasing flow rate. Taking the 12000 r / min operating condition as an example, when the flow rate of the BTCP system is increased from 8 L / min to 20 L / min, the front bearing temperature decreases from 318.2 K to 310.8 K (a decrease of 7.4 K), and the stator temperature decreases from 309.1 K to 305.7 K (a decrease of 3.4 K). When the flow rate of the SCP system is increased from 8 L / min to 22 L / min, the front bearing temperature decreases from 322.2 K to 316.8 K (a decrease of 5.4 K), and the stator temperature decreases from 310.6 K to 307.1 K (a decrease of 3.5 K). Increasing the flow rate can improve the convective heat transfer coefficient between the cooling medium and the component surface, accelerating heat transfer. However, when the flow rate exceeds a certain value, the convective heat transfer coefficient tends to saturate, and heat exchange enters a "dynamic equilibrium state," with the component temperature drop less than 0.5K. The cooling gain of the core component due to the flow rate is significantly weakened. Unlike the core component, the shell temperature has a lower sensitivity to cooling flow rate: within the full flow rate test range, the shell temperature fluctuation is very small. The core reason is that the shell is in direct contact with the cooling circuit, and the heat from the core component is indirectly transferred to the shell through the water-cooled jacket. The temperature gradient is small, and the transfer path is stable, so it is less affected by changes in flow rate. This phenomenon can also be observed using an infrared thermal imager such as... Figure 26 Observed.

[0098] Thermal error is negatively correlated with cooling flow rate and exhibits a significant "threshold effect." At lower flow rates, thermal error decreases rapidly with increasing flow rate. For example, at a working rate of 12,000 r / min, when the flow rate of the BTCP system increases from 8 L / min to 20 L / min, the thermal error decreases from 47.2 μm to 37.9 μm (a decrease of 19.7%); when the flow rate of the SCP system increases from 8 L / min to 22 L / min, the thermal error decreases from 58.6 μm to 46.7 μm (a decrease of 20.3%). During this stage, the increased flow rate directly suppresses thermal deformation of the electric spindle by reducing the temperature rise gradient of the core components. When the flow rate exceeds a certain value, the thermal errors of both the BTCP and SCP systems tend to stabilize. For example, under the condition of 16000 r / min, when the flow rate of the BTCP system increases from 20 L / min to 23 L / min, the thermal error decreases from 43.1 μm to 42.2 μm, a decrease of only 2.1%. At this point, the temperature of the core components is close to the thermal equilibrium state, and the increase in thermal deformation of the electric spindle is negligible. Continuing to increase the flow rate has no practical optimization value.

[0099] Table 9. Average temperature and steady-state thermal expansion of key components at different rotational speeds. As described above, the optimal flow rate of the electric spindle under several different operating conditions when the steady-state thermal error is achieved is quickly obtained across the entire speed range. A correlation function between the electric spindle speed change and the flow rate is established through linear regression. Mathematical modeling and regression analysis are performed using the least squares method. The final fitting result is shown in equation (26), and the fitted image is as follows. Figure 27 As shown, both systems exhibit a significant linear positive correlation between rotational speed and optimal flow rate, with the optimal flow rate steadily increasing with increasing rotational speed. Across the entire rotational speed range, the optimal flow rate of the SCP system is consistently higher than that of the BTCP system. At 8000 r / min, the optimal flow rate of the SCP system is 17 L / min, exceeding that of the BTCP system by 1 L / min. At 18000 r / min, the optimal flow rate of the SCP system is 31 L / min, exceeding that of the BTCP system by 6 L / min. This indicates that the BTCP system has better thermal management efficiency, and its flow rate advantage over the SCP system becomes more pronounced as rotational speed increases.

[0100] (26) Analysis of Thermal Deformation Field and Thermal Equilibrium Time of S353 Electric Spindle Figure 28 The thermal deformation field of the electric spindle system under SCP and BTCP at a rotational speed of 12000 r / min and an inlet flow rate of 15 L / min is shown. The maximum deformation of the electric spindle system occurs at its rightmost end because the left-end bearing is subject to axial and radial fixed constraints, while the right-end bearing is only subject to radial fixed constraints.

[0101] Figure 29The thermal elongation and thermal equilibrium time of electric spindle systems equipped with two types of water-cooled jackets at different speeds were demonstrated. Due to environmental influences and mechanical vibrations, the experimentally measured thermal elongation fluctuated. However, the simulation did not consider ambient temperature fluctuations, so the simulated thermal elongation remained highly stable after the electric spindle reached thermal equilibrium. The final comparison results of thermal elongation are shown in Table 10. At a speed of 8000 r / min, in the SCP system, the experimentally measured maximum axial thermal elongation of the electric spindle was 42.3 μm, while the simulated value was 37.5 μm, with a maximum deviation of 4.8 μm. In the BTCP system, the experimentally measured maximum axial thermal elongation of the electric spindle was 34.6 μm, while the simulated value was 30.4 μm. BTCP reduced the maximum thermal deformation of the electric spindle by approximately 18.2%. The thermal equilibrium times of BTCP and SCP were 672 s and 1254 s, respectively, a reduction of 46.4%. When the speed increased to 16000 r / min, the thermal elongation of both cooling structures increased. The simulation error for thermal deformation was within 12.1%, indicating good consistency between the simulation and experimental results. At higher speeds, the heat generation of the electric spindle increased, further highlighting the advantages of BTCP, with a 19.9% ​​reduction in maximum thermal elongation and a 62.5% reduction in thermal equilibrium time.

[0102] Table 10 Comparison of Experimental and Numerical Simulation Results To reduce thermal errors, a novel, efficient topology optimization and biomimetic design method for the heat-fluid flow problem of cooling components in high-speed electric spindle systems is proposed. The heat transfer performance of biomimetic sharkskin water jackets of different sizes was investigated, and the optimal flow rate required for high-speed electric spindles under different operating conditions was determined. Finally, the effectiveness of the topology optimization method was verified through thermo-fluid-structure interaction simulations and experimental studies.

[0103] The following conclusions can be drawn: (1) A progressive design method of "topology optimization-bionic structure" was proposed and implemented. Based on this design method, a bionic topology secondary optimization water cooling jacket was embedded into the electric spindle, which significantly improved the machining accuracy of the electric spindle.

[0104] (2) The heat transfer performance and pressure drop of shark skin of different sizes were obtained through orthogonal experiments and the Pareto front of the cooling channel design was generated. The optimal parameters were obtained by NSGA-II genetic algorithm to provide support for balancing pumping power and heat dissipation requirements in practical applications.

[0105] (3) The biomimetic topology optimization and traditional water cooling jacket were applied to the high-speed electric spindle system and thermal-fluid-solid coupling simulation and experimental research were carried out. The heat transfer performance of the two water cooling jackets was compared: the heat transfer performance of the two water cooling jackets was similar at low flow rate, while the heat dissipation performance of the biomimetic topology secondary optimization water cooling jacket was far superior to that of the traditional water cooling jacket at high flow rate.

[0106] (4) Under the same pumping flow rate, the pressure drop of the biomimetic topology secondary optimization water jacket is much higher than that of the traditional water jacket. The larger the inlet flow rate, the more significant the advantage. The optimal flow rate under different operating conditions was found, which further reduced the pressure drop.

[0107] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can occur depending on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for optimizing the design of liquid-cooled biomimetic flow channels and suppressing thermal errors in CNC machine tool electric spindles, characterized in that, The specific steps include the following: S1 performs topology optimization on the design domain of the water-cooled jacket geometric model of the electric spindle under a density field with uniform initial density distribution. The optimal heat dissipation capacity and minimum power dissipation are the multiple objective functions, and the topology-optimized water-cooled jacket is obtained. S2 draws inspiration from the sharkskin rib structure and analyzes the main rib height, main rib width, and main and secondary rib height ratio and related parameters through orthogonal experiments. Combined with the NSGA-II algorithm, the topology optimization water cooling jacket is improved to obtain a secondary optimized water cooling jacket with a sharkskin biomimetic structure. S3 conducts thermal-fluid-solid simulation and experimental research on an electric spindle system using a secondary optimized water-cooling jacket. Through multiple sets of speed-flow matching tests, it establishes an optimal flow database corresponding to different speed ranges. Linear regression is used to construct the correlation function between speed and optimal flow to obtain a speed-adaptive cooling scheme.

2. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 1, characterized in that, The method for topology optimization in step S1 is as follows: Using optimal heat dissipation capacity and minimum power dissipation as multiple objective functions, a two-dimensional topology optimization is performed on a half-size water cooling jacket to obtain a three-dimensional half-size water cooling jacket; the full-size water cooling jacket formed by the symmetrically designed three-dimensional half-size water cooling jacket is rolled up to obtain a complete cylindrical topology-optimized water cooling jacket.

3. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 2, characterized in that, Two-dimensional topology optimization specifically involves: Within the design domain of a half-size water-cooled jacket, the inflow and outflow of the water-cooled jacket are arranged on the same parallel edge. A uniform heat load Q* is applied to the design domain, the volumetric flow rate at the inlet is set to fully developed flow conditions, the inlet temperature is set to T*=293K, and the outlet pressure is set to p*=0Pa. The optimization objective is defined as heat transfer and fluid dissipation power. A fluid-structure heat transfer topology optimization model is constructed, with the following expression: ； ； in, J h Let Ω be the heat transfer objective function, representing maximizing the heat exchange efficiency between the cooling component and the fluid; Ω is the design domain. These are the design variables before filtering. T* The temperature is dimensionless. J f Let be the fluid dissipation loss function, representing the pumping power required to minimize fluid flow on the cooling component; Here, u* is the gradient operator, α* is the velocity, and α* is the dimensionless permeability. After normalizing the average temperature and fluid dissipation power, the objective function can be expressed as: ； In the formula, ω These are the weighting coefficients; J min and J max These correspond to the minimum and maximum values ​​obtained in their respective single-objective topology optimizations; the topology optimization problem of the multi-objective function of the water-cooled jacket can be expressed as: In the formula, Da For Darcy's number, q As a penalty factor, Pr For Prandtl numbers, Re Let Reynolds number be 1. h * The heat transfer coefficient is... For design variables.

4. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 1, characterized in that, The sharkskin-like rib structure consists of 3 to 5 ribs.

5. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 4, characterized in that, The orthogonal experimental analysis specifically includes: Focusing on three factors—the height h of the main rib, the width b of the main rib, and the height ratio w of the main and secondary ribs—a three-factor, four-level orthogonal experiment was designed. Range analysis was performed on the orthogonal experimental results, using the highest temperature T as the starting point. max Pressure drop ΔPa and temperature standard deviation T α To evaluate the performance, we analyzed the impact of various factors on the heat dissipation performance and pressure drop of the water-cooled jacket, and obtained the optimal parameter matching.

6. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 5, characterized in that, The order of influence on temperature T is b>w>h, and the main rib width b affects the highest temperature T. max The greater the width b of the main rib, the lower the temperature T. The order of influence on pressure drop ΔPa is h>w>b. The size of the main sharkskin has the greatest impact on pressure drop ΔPa; the larger the main rib height h, the higher the corresponding pressure drop ΔPa. The effect on temperature standard deviation T... α The order of influence is h>b>w, and the effect of the main rib height h on the temperature standard deviation T is... α The effect is greatest; changing the height h of the main rib can alter the uniformity of temperature distribution in the water-cooled jacket.

7. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 6, characterized in that, The height h of the main rib is 2.4 mm, the width b of the main rib is 0.8 mm, and the height ratio w of the main and secondary ribs is 1.

8.

8. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 1, characterized in that, The steps of the thermal-fluid-solid simulation are as follows: a1. Establish a thermal-fluid-solid finite element model; a2. Define the physical field type and apply boundary conditions; a3. Solve for the temperature field, fluid pressure, velocity field and thermal deformation field under steady state; a4. Perform post-processing and analysis.

9. The method for optimizing the liquid-cooled bionic flow channel and suppressing thermal errors of CNC machine tool electric spindles according to claim 1, characterized in that, The correlation function between rotational speed and optimal flow rate is: ； Where y is the optimal flow rate and x is the rotational speed.

Images