Topology Optimization Method for the Cooling Jacket Structure of the Electric Spindle

Abstract

The present invention discloses a topology optimization method for the cooling water jacket structure of an electric spindle, comprising the following steps: Step 1: establishing an equivalent model of the cooling water jacket; 11) importing the three-dimensional geometric model of the cooling water jacket and the boundary conditions of the equivalent model into a RANS model and a Darcy model respectively; 12) performing numerical simulation and calculating P-error; 13) judging whether the value of P-error is less than or equal to a set threshold; 14) calculating V av ‑error, T av ‑error and T max ‑error; 15) Determine whether the values ​​in the half-inlet length vector and the Reynolds number Re vector are traversed: If so, obtain the equivalent model of the cooling water jacket; Step 2: Perform topology optimization on the cooling water jacket structure: 21) Import the obtained equivalent model of the cooling water jacket into the parameter interpolation model to construct the objective function and constraints; 22) Perform topology optimization on the spindle cooling water jacket structure; 23) Determine whether the topology calculation converges: If so, output the topology optimized flow channel of the cooling water jacket.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric spindle design, and specifically relates to a topology optimization method for a cooling water jacket structure of an electric spindle. Background Art

[0002] The continuous emergence and rapid development of high-precision machining technologies have placed high demands on the accuracy, stability, and reliability of precision machine tools. Motorized spindle systems (MSSs), with their superior performance, including high stability, high control accuracy, and fast response speed, are widely used in precision machine tools to achieve high-precision machining of complex parts. Numerous studies have shown that machining errors caused by thermal error (TE) account for 70% of total errors. In motorized spindle systems, the internal motor is one of the components that generates the most heat and has poor heat dissipation performance (HDP). Furthermore, frictional heat from the bearings leads to uneven temperature distribution within the motorized spindle system, ultimately causing severe thermal deformation and severely impacting the machining accuracy of the machine tool. Therefore, improving the heat dissipation performance (HDP) of the motorized spindle system is crucial. Currently, a commonly used cooling method is to deploy a cooling system with a high-efficiency cooling water jacket (CWJ) to remove the large amount of heat generated by the internal motor. Conventional cooling channels used in high-efficiency cooling water jackets (CWJs) include spiral and serpentine channels. However, spiral and serpentine cooling channels have some obvious disadvantages, including uneven temperature distribution and large pressure drop (PDL) between the inlet and outlet.

[0003] At present, most of the research on cooling water jackets is to optimize the existing spiral and serpentine cooling channel structures and sizes. The design ideas of cooling water jackets rely on the experience of designers and are designed with reference to bionic structures in nature. There is a lack of exploration of new channel structures, and the guiding effect on cooling channel design is limited. For the design requirements of different actual working conditions, these empirical designs are often difficult to work directly because the heat transfer performance of spiral and serpentine cooling channels is limited. The topology optimization method is a new conceptual design optimization method that is not limited to changing the shape and size and has a high degree of freedom. The topology optimization method uses a characteristic function that represents the existence of material domains in a fixed design domain as design variables, and derives the optimal configuration through mathematical methods. At present, the topology optimization method has been widely used in structural design, heat conduction and fluid optimization design problems. In recent years, the topology optimization method of conjugate heat transfer of fluid-solid coupling has been a research hotspot.

[0004] Topology optimization methods add a velocity-dependent Brinkman penalty term to the fluid momentum equation. When the drag term is zero, the fluid can flow smoothly, and the region is considered a fluid domain. When the drag term is so large that the fluid cannot flow through, the region is treated as a solid domain, and this model is called the Brinkman model. However, in real-world models, especially 3D design spaces, the large design domain size and complex fluid flow conditions make topology optimization very time-consuming and often fail to converge. Summary of the Invention

[0005] In view of this, an object of the present invention is to provide a method for topological optimization of the cooling water jacket structure of an electric spindle, which can improve the heat dissipation performance and reduce the pressure drop loss.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for topological optimization of a cooling water jacket structure of an electric spindle comprises the following steps:

[0008] Step 1: Establish an equivalent model of the cooling water jacket

[0009] 11) Import the three-dimensional geometric model of the cooling water jacket and the boundary conditions of the equivalent model into the RANS model and the Darcy model respectively;

[0010] 12) Use the RANS model and Darcy model to perform numerical simulations and calculate the pressure error:

[0011] P-error=|(P Darcy -P RANS ) / P RANS |

[0012] Among them, P-error represents the pressure error; P Darcy represents the inlet and outlet pressure difference obtained by the Darcy model, P RANS represents the inlet and outlet pressure difference obtained by the RANS model;

[0013] 13) Determine whether the value of P-error is less than or equal to a set threshold: if so, execute step 14); if not, adjust the equivalent solid-liquid permeability used in the Darcy model and execute step 12);

[0014] 14) Calculate the speed error, average temperature error and maximum temperature error;

[0015] V av -error=|(V av-Darcy -V av-RANS ) / V av-RANS |

[0016] T av-error=|(T av-Darcy -T av-RANS ) / T av-RANS |

[0017] T max -error=|(T max-Darcy -T max-RANS ) / T max-RANS |

[0018] Among them, V av -error indicates speed error; V av-Darcy represents the fluid velocity obtained by the Darcy model; V av-RANS represents the fluid velocity obtained by the RANS model; T av -error indicates the average temperature error; T av-Darcy represents the average temperature obtained by the Darcy model; T av-RANS represents the average temperature obtained by the RANS model; T max -error indicates the maximum temperature error; T max-Darcy represents the maximum temperature obtained by the Darcy model; T max-RANS represents the maximum temperature obtained by the RANS model;

[0019] 15) Determine whether the values ​​in the half vector of the cooling water jacket inlet length L and the Reynolds number Re vector are traversed: if so, construct an equivalent model of the cooling water jacket and obtain expressions for the permeability ratio and the fluid permeability; if not, update the inlet length L and the Reynolds number Re and execute step 12);

[0020] Step 2: Topology optimization of the cooling water jacket structure

[0021] 21) Importing the obtained expressions of permeability ratio and fluid permeability into the parameter interpolation model, and constructing the objective function and constraints of topology optimization;

[0022] 22) Perform topological optimization on the spindle cooling water jacket structure to obtain the topologically optimized cooling channel of the cooling water jacket;

[0023] 23) Determine whether the topology calculation has converged: if so, output the topology optimized cooling channel of the cooling water jacket; if not, update the filter radius and weight factor and execute step 22).

[0024] Furthermore, in step 22), the fluid flow equation of the Darcy model includes:

[0025] Fluid continuity equation:

[0026]

[0027] Momentum equation:

[0028]

[0029]

[0030]

[0031]

[0032] The velocity field of the Darcy model is expressed as:

[0033]

[0034] in, represents the gradient; ρ and μ represent the fluid density and dynamic viscosity respectively; P represents the fluid pressure; P k represents the fluid pressure level; f represents the external force term; k represents the turbulent kinetic energy; κ represents the permeability; ω represents the specific dissipation rate; μ T represents the eddy viscosity; represents the fluid velocity in the Darcy model; α, β0, and All represent constants;

[0035] The heat transfer equation of the Darcy model is:

[0036]

[0037] C p represents the specific heat of the fluid; T represents the temperature of the solution domain; Q represents the heat source; k represents the thermal conductivity. When the design domain is solid, k = k f , when the design domain is fluid, k = k s , k s and k f denote the thermal conductivity of solid and fluid respectively;

[0038] Furthermore, in step 15), κ f / κ s The expression is:

[0039] κ f / κ s =10 7

[0040] Fluid permeability κ f The expression is:

[0041]

[0042] Among them, κ s represents the solid permeability; κ frepresents the fluid permeability; μ represents the dynamic viscosity; L represents the inlet length of the cooling water jacket; R represents the inlet width; and P represents the inlet and outlet pressure difference.

[0043] Furthermore, in step 21), the parameter interpolation model is:

[0044] Helmholtz-type partial differential equations are used for filtering. Density filtering can effectively avoid grid dependence and control the minimum size of the topological result. The density filtering expression is:

[0045]

[0046] Among them, R min represents the filter radius, Represents the filtered variable, represents the unfiltered design variable;

[0047] Density filtering will result in a large number of grayscale units. Hyperbolic tangent projection is used to obtain a clear topological flow channel. The projection expression is:

[0048]

[0049] Among them, β and η are divided into projection slope and projection point;

[0050] Using γ to interpolate the porous material domain, the functional relationship between the material properties and the design variables is:

[0051]

[0052]

[0053]

[0054]

[0055] Where, κ represents the permeability; s and κ f represent the permeability of solid and fluid respectively; k represents thermal conductivity; k s and k f denote the thermal conductivity of solid and fluid respectively; ρ denotes density; ρ s and ρ f Denote the density of solid and fluid respectively; C p represents specific heat; C ps and C pf represent the specific heat of solid and fluid respectively; P κ 、P k 、P ρ and Both are penalty parameters;

[0056] γ is a variable representing the solid and liquid phases of the material, and: when γ=0, it indicates that the material is a fluid; when γ=1, it indicates that the material is a solid; when 0<γ<1, it indicates that the material is a porous material.

[0057] Furthermore, in step 21), a weighted multi-objective method is used to minimize the average temperature of the design domain and the inlet and outlet pressure difference. The objective function is as follows:

[0058]

[0059] Where w is the weight factor, and its value range is [0,1]; T0 and P0 are the reference temperature and pressure respectively; T av represents the average temperature of the design domain; P in Indicates the inlet pressure.

[0060] Furthermore, in step 21), in the Darcy model, the pressure drop constraint has a great influence on the topological result. If no pressure drop constraint is imposed or an excessively large pressure drop constraint is imposed, the flow channel will be disconnected. Therefore, the pressure constraint is:

[0061] P in ≤P *

[0062] Among them, P * represents the pressure constraint threshold;

[0063] The cooling channel ratio constraint is:

[0064] ∫ Ω (1-γ)dΩ≤V w Vol Ω

[0065] Where Ω represents the design area; V w Indicates the volume ratio of the cooling channel; Vol Ω is the total volume of the design domain.

[0066] Furthermore, the method further includes step three: constructing a finite element model of the cooling water jacket using the obtained topologically optimized flow channel of the cooling water jacket, setting simulation boundary conditions, and performing simulation analysis on the electric spindle.

[0067] The beneficial effects of the present invention are:

[0068] The topology optimization method for the electric spindle cooling water jacket structure of the present invention establishes an equivalent model of the cooling water jacket based on the Darcy model under the geometric model and working conditions of the actual electric spindle, and determines the permeability ratio and the fluid permeability expression. During the topology optimization process, the fluid permeability can be calculated through the expression, and the optimal topology optimization flow channel of the cooling water jacket is obtained with the average temperature and pressure drop as the objective function. The topology optimization flow channel is arranged in the cooling water jacket, and an electric spindle cooling water jacket structure that can improve heat dissipation performance and reduce pressure drop loss can be obtained.

[0069] Fluid and solid permeability are important parameters in the Darcy model. However, currently, the consistency between the Darcy model and the turbulence model is ensured by manual adjustment of the permeability parameters. In actual topology optimization, permeability is affected by parameters such as the geometric dimensions of the design domain and the operating conditions of the cooling fluid. Changing any of these parameters requires corresponding adjustment of the permeability. This paper determines the permeability ratio of the Darcy model and the functional expression of fluid permeability with respect to design requirements and actual operating conditions based on the geometric dimensions and actual operating conditions of the electric spindle cooling system. This method can automatically adjust the equivalent solid-liquid permeabilities used in the Darcy model. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0071] Figure 1 This is a flow chart of an embodiment of a method for topological optimization of a cooling water jacket structure of an electric spindle according to the present invention;

[0072] Figure 2 Construct a flow chart for the cooling water jacket equivalent model;

[0073] Figure 3 is the turbulent velocity profile;

[0074] Figure 4 is the flow velocity profile of the Darcy model;

[0075] Figure 5 It is a traditional serpentine flow channel geometry model;

[0076] Figure 6 The graph of the effect of permeability ratio on average velocity and maximum temperature;

[0077] Figure 7 is the effect diagram of permeability on temperature field;

[0078] Figure 8 is the influence diagram of permeability ratio on velocity field;

[0079] Figure 9 This is the effect of permeability on velocity error and maximum temperature error;

[0080] Figure 10 This is the effect of inlet Reynolds number on the velocity error and average temperature error of the two models;

[0081] Figure 11 Velocity streamline diagrams for Darcy model and RANS model;

[0082] Figure 12 The running time diagrams of Darcy model and RANS model are shown;

[0083] Figure 13 The cooling channel topology results with different weight factors;

[0084] Figure 14 This is a three-dimensional model diagram of the cooling channel;

[0085] Figure 15 Velocity fields calculated for the Darcy model and the RANS model;

[0086] Figure 16 Temperature fields calculated for Darcy and RANS models;

[0087] Figure 17 It is a structural diagram of the electric spindle system;

[0088] Figure 18 is the finite element model of MSS;

[0089] Figure 19 Schematic diagram of traditional spiral flow channel and serpentine flow channel;

[0090] Figure 20 is the temperature field of the electric spindle;

[0091] Figure 21 is the temperature field of the stator outer surface;

[0092] Figure 22 is a graph of maximum and minimum temperatures;

[0093] Figure 23 is the temperature gradient of the stator outer surface under different inlet Reynolds numbers;

[0094] Figure 24 is the velocity streamline distribution of the cooling channel;

[0095] Figure 25 is the pressure field of the cooling channel;

[0096] Figure 26 is the pressure drop loss under different inlet Reynolds numbers;

[0097] Figure 27 is the thermal deformation distribution of MSS;

[0098] Figure 28 is the thermal deformation under different inlet Reynolds numbers. DETAILED DESCRIPTION

[0099] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0100] like Figure 1 The figure is a principle block diagram of an embodiment of the method for topological optimization of the electric spindle cooling water jacket structure of the present invention. The method for topological optimization of the electric spindle cooling water jacket structure of this embodiment includes the following steps:

[0101] Step 1: Establish an equivalent model of the cooling water jacket

[0102] 11) Import the three-dimensional geometric model of the cooling water jacket and the boundary conditions of the equivalent model into the RANS model and the Darcy model respectively;

[0103] 12) Use the RANS model and Darcy model to perform numerical simulations and calculate the pressure error:

[0104] P-error=|(P Darcy -P RANS ) / P RANS |

[0105] Among them, P-error represents the pressure error; P Darcy represents the inlet and outlet pressure difference obtained by the Darcy model, P RANS represents the inlet and outlet pressure difference obtained by the RANS model;

[0106] 13) Determine whether the value of P-error is less than or equal to a set threshold: if so, execute step 14); if not, adjust the equivalent solid-liquid permeability used in the Darcy model and execute step 12);

[0107] 14) Calculate the speed error, average temperature error and maximum temperature error;

[0108] V av -error=|(V av-Darcy -V av-RANS ) / V av-RANS |

[0109] T av -error=|(T av-Darcy -T av-RANS ) / T av-RANS |

[0110] T max -error=|(T max-Darcy-T max-RANS ) / T max-RANS |

[0111] Among them, V av -error indicates speed error; V av-Darcy represents the fluid velocity obtained by the Darcy model; V av-RANS represents the fluid velocity obtained by the RANS model; T av -error indicates the average temperature error; T av-Darcy represents the average temperature obtained by the Darcy model; T av-RANS represents the average temperature obtained by the RANS model; T max -error indicates the maximum temperature error; T max-Darcy represents the maximum temperature obtained by the Darcy model; T max-RANS represents the maximum temperature obtained by the RANS model;

[0112] 15) Determine whether the values ​​in the half vector of the cooling water jacket inlet length L and the Reynolds number Re vector are traversed: if so, construct an equivalent model of the cooling water jacket and obtain expressions for the permeability ratio and the fluid permeability; if not, update the inlet length L and the Reynolds number Re and execute step 12);

[0113] Step 2: Topology optimization of the cooling water jacket structure

[0114] 21) Importing the obtained expressions of permeability ratio and fluid permeability into the parameter interpolation model, and constructing the objective function and constraints of topology optimization;

[0115] 22) Perform topological optimization on the spindle cooling water jacket structure to obtain the topologically optimized flow channel of the cooling water jacket;

[0116] 23) Determine whether the topology calculation has converged: if so, output the topology optimized flow channel of the cooling water jacket; if not, update the filter radius and weight factor and execute step 22);

[0117] Step 3: Construct a finite element model of the cooling water jacket using the obtained topologically optimized flow channel of the cooling water jacket, set simulation boundary conditions, and perform simulation analysis on the electric spindle.

[0118] 1. Cooling water jacket equivalent model

[0119] like Figure 2 As shown in the figure, the 3D geometric model of the cooling water jacket (CWJ) is imported and the boundary conditions of the equivalent model are set. The RANS model and Darcy model are established for numerical simulation, and the pressure error P-error is defined as P-error=|(P Darcy -P RANS ) / P RANS |, where PDarcy is the fluid pressure obtained by Darcy model, P RANS is the fluid pressure obtained by the RANS model. In this embodiment, the threshold of the pressure error P-error is set to 0.01. If the condition of P-error≤0.01 is not met, the equivalent solid-liquid permeability used in the Darcy model is automatically adjusted until P-error≤0.01. Then the velocity error V is calculated. av -error, average temperature error T av -error, maximum temperature error T max -error, that is:

[0120] V av -error=|(V av-Darcy -V av-RANS ) / V av-RANS |

[0121] T av -error=|(T av-Darcy -T av-RANS ) / T av-RANS |

[0122] T max -error=|(T max-Darcy -T max-RANS ) / T max-RANS |

[0123] Update the inlet length L and Reynolds number Re and perform a new iteration until the values ​​in the half vector of the inlet length L and the Reynolds number Re vector are traversed. Finally, the fluid permeability κ is obtained. f Relationship with density, Reynolds number, design parameters and PDL.

[0124] 1.1 Convective heat transfer model based on Darcy model

[0125] 1.1.1 Fluid Flow Equations

[0126] Due to the large Reynolds number, the fluid in the cooling system of the motorized spindle system (MSS) is usually in a turbulent state. The flow velocity of the turbulent model produces pressure changes due to the friction of the boundary layer, forming a velocity gradient, such as Figure 3 In practical engineering applications, a RANS model is often used for simulation, followed by a turbulence model to simulate the flow in the cooling channel. The eddy viscosity coefficient of the turbulence model represents the Reynolds stress in terms of turbulent kinetic energy k and dissipation rate ω.

[0127] The internal flow of the fluid is represented by the incompressible NS equations, and the continuity equation is:

[0128]

[0129] Momentum equation:

[0130]

[0131]

[0132]

[0133]

[0134] in, represents the gradient; ρ and μ represent the fluid density and dynamic viscosity respectively; P represents the fluid pressure; P k represents the fluid pressure level; f represents the external force term; k represents the turbulent kinetic energy; ω represents the specific dissipation rate; μ T represents the eddy viscosity; represents the fluid velocity in the Darcy model; α, β0, and All represent constants.

[0135] On the one hand, the solution process of the RANS model is a nonlinear process, which takes up a lot of computing resources in the process of solving the actual 3D topological model. On the other hand, the RANS model is sensitive to the model settings, and its convergence performance is weak due to the complex 3D structure and working conditions of CWJ. When the RANS model is applied to topological problems, the convergence performance is difficult to guarantee and the computational efficiency is generally low. Therefore, a lightweight equivalent model that can guarantee good simulation accuracy and excellent convergence performance is a necessary condition to replace the RANS model. Figure 4 As shown in the figure, the Darcy model ignores the inertia term in the fluid NS equation and assumes that the weakening process of the flow velocity on the wall can be ignored in the absence of boundary effects. The velocity field of the Darcy model is expressed as:

[0136]

[0137] in, represents the fluid velocity in the Darcy model; κ represents the permeability.

[0138] 1.1.2 Heat transfer governing equations

[0139] Solve the heat transfer equation based on the velocity field of the RANS model. The heat transfer equation for solids is:

[0140]

[0141] The heat transfer equation for the fluid is:

[0142]

[0143] Among them, k s and k f Represent the thermal conductivity of solid and fluid respectively; C p is the specific heat of the fluid; T is the temperature of the solution domain; Q is the heat source; ρ represents the fluid density; u represents the fluid velocity;

[0144] There are solids and liquids in the Darcy model, but only fluids exist in the Darcy model. The Darcy model is represented by fluids, and the fluid thermal conductivity k f Solid permeability κ s and fluid permeability κ f Controlled at different locations. Therefore, for the Darcy model, the heat transfer equation of the Darcy model is:

[0145]

[0146] Among them, C p represents the specific heat of the fluid; T represents the temperature of the solution domain; Q represents the heat source; k represents the thermal conductivity. When the design domain is solid, k = k f , when the design domain is fluid, k = k s , k s and k f denote the thermal conductivity of solid and fluid respectively;

[0147] 1.2. Cooling water jacket physical model

[0148] use Figure 5 The conventional serpentine flow channel shown here tests the validity of the equivalent model. The flow channel model is a cylindrical structure with an inner diameter of 83 mm, an outer diameter of 92 mm, and a length of 86 mm. The coolant flows in from the left and exits from the right through the serpentine flow channel. V is the inlet velocity, V = v_in. T is the inlet temperature, T = T_in = 20°C. P is the outlet pressure, P = 1 atm. Because the inner surface of the CWJ contacts the outer surface of the stator, the heat source Q is evenly distributed on the inner surface of the CWJ, with a power of Q = 60 W. The cross section shows the mid-flow section of the serpentine flow channel. Ω s and Ω f are solid domain and fluid domain respectively. The material properties of solid and fluid are listed in Table 1. The inlet velocity is expressed as:

[0149] v_in=u av =(Reμ) / L in ρ=[Reμ(2L+R)] / (4LRρ)

[0150] Among them, v_in represents the inlet velocity; u av Indicates average speed; L in represents the characteristic length of the entrance; R represents the entrance width.

[0151] Table 1 Material properties of solids and fluids

[0152]

[0153]

[0154] 1.3 Fluid Permeability and Validity of Equivalent Models

[0155] The effectiveness of the equivalent model is evaluated by comparing the velocity field, temperature field and pressure field of the above two models. The velocity field is the average velocity of the middle section of the traditional serpentine flow channel. The temperature field is the average temperature T av and the maximum temperature T max The pressure field evaluation index is the pressure drop loss (PDL) between the inlet and outlet of the serpentine flow channel.

[0156] 1.3.1 Permeability ratio κ f / κ s Determination of

[0157] The inlet Reynolds number is 5000, and half of the inlet length L is L = 5 mm. Figure 6 The effect of permeability on flow rate and maximum temperature is shown. The difference between the average velocity of RANS and Darcy models decreases with the increase of permeability ratio. f / κ s ≥10 6 The maximum temperatures of the above two models also have similar trends.

[0158] Figure 7 The effect of permeability on the temperature field is shown. f / κ s = 10, the distribution areas of solid and liquid cannot be clearly distinguished in the temperature contour. As the permeability increases, the distribution of cooling channels becomes clearer. The temperature of the fluid distribution area is significantly lower than that of the solid area. f / κ s =10 7 and κ f / κ s =10 10 When , the temperature field distribution of the cooling channel is basically consistent, which is in good agreement with the results obtained by the RANS model. The solid permeability κ used in the Darcy model s is small and non-zero. Although the flow is suppressed, a small amount of fluid is still distributed in the solid domain. In contrast, the fluid in the RANS model flows only in the designed fluid domain, so the distribution of the cooling channels is clear.

[0159] The effect of permeability ratio on velocity field is as follows Figure 8 As shown. When κ f / κ s= 10, the solid domain cannot suppress the fluid. The flow pattern shows that the fluid is basically uniformly distributed in the geometric model. f / κ s =10 3 When , the fluid tends to flow along the serpentine channel. Due to the lack of inhibition of the fluid in the solid region, there is still a large amount of fluid distributed in the solid region. The fluid distribution in the solid domain increases with the permeability κ f / κ s Gradually decreases. When κ f / κ s ≥10 7 When , the fluid is mainly concentrated inside the cooling channel.

[0160] Effect of the permeability ratio on the velocity and temperature fields when the inlet length 2L varies. Figure 9 Shows the permeability versus velocity error V for different inlet lengths av -error and maximum temperature error T max -error effect. At different inlet lengths. Velocity error V av -error and maximum temperature error T max -error decreases with the increase of permeability, and f / κ s ≥10 6 Moreover, the smaller the length, the smaller the speed error V av -error and maximum temperature error T max -error is smaller. The validity of the constructed equivalent model is verified. When L = 3mm, V av -error=0.26% and T max -error=12.02%. When L=7mm, V av -error=5.89% and T max -error=14.15%. For all cases, the velocity error V av -error and maximum temperature error T max -error is within the acceptable error range. The conclusion is that when κ f / κ s ≥10 7 When κ is used, the solid domain can fully suppress the effect of the fluid, and then the continuous increase in permeability has little effect on velocity and temperature. f / κ s =10 7 permeability ratio.

[0161] 1.3.2 Derivation of fluid permeability

[0162] For a given inlet velocity, the pressure drop decreases as the fluid permeability decreases. Therefore, there is a specific κ f value to ensure that the Darcy and RANS models have the same PDL.

[0163] ΔP Darcy ≈ΔP RANS

[0164]

[0165] Among them, ΔP represents the pressure drop loss; ΔP Darcy and ΔP RANS denote the PDL between the inlet and outlet of Darcy and RANS models respectively; Γ in and Γ out represent the inlet boundary and outlet boundary respectively.

[0166] ΔP Darcy and ΔP RANS The PDL varies with the inlet length 2L and the Reynolds number. Therefore, the fluid permeability κ f It is related to the geometric dimensions of the topological domain and the flow state of the fluid, and its expression is established for subsequent topological design. The flow velocity on the circular cross section of the cooling channel is expressed as:

[0167]

[0168] Where u′ represents the flow velocity on the circular cross section; r represents the radial distance from the center line; R represents the radius of the circular cross section; n represents a constant, and n is approximately a constant for the actual flow rate; u av is the average velocity, calculated using the Reynolds number, which is:

[0169] u av =(Reμ) / (L in ρ)

[0170] Among them, L in is the characteristic length, L in =4S / C=(4LR) / 2L+R, S represents the cross-sectional area, and C represents the cross-sectional perimeter. Referring to the flow velocity on the circular cross-section, the flow velocity on the rectangular cross-section of the cooling channel is designed for turbulent flow, that is:

[0171]

[0172] Here, α represents a constant.

[0173] According to the law of mass conservation, the velocity vectors of the above two models are integrated within the cross-sectional area of ​​the cooling channel, that is:

[0174]

[0175] but:

[0176]

[0177] but:

[0178]

[0179] In order to further determine the applicability of the equivalent model, the effect of the inlet Reynolds number on the velocity error V was studied. av -error and average temperature error T av -error effect. Fluid permeability κ f Adjust the offspring into the Darcy model. Then get the calculation results, such as Figure 10 As shown. The velocity obtained by the RANS model is used as the benchmark. When L = 3mm, L = 4mm, L = 5mm, the inlet Reynolds number has an effect on the velocity error V av -error has little effect, the speed error V av -error is within 1%. The velocity error increases sharply with the entrance length. Specifically, Figure 11 As shown in (a), when L = 3mm, the streamline trajectories in the cooling channel obtained by the Darcy model and the RANS model are basically the same. The RANS model has a boundary layer effect, and due to the wall function, there is a hysteresis phenomenon at the corners of the cooling channel. In contrast, the Darcy model has no boundary layer, and the fluid is evenly distributed on the cross section of the cooling channel. However, under the condition of equal Reynolds number inlet, as the channel length increases, the flow velocity calculated by the Darcy model decreases but remains uniformly distributed. The RANS model generates more local vortices at the corners of the channel, and the irregular movement of the fluid forms a turbulent turbulent flow field, which increases the difference between the velocity fields predicted by the two models. Average temperature error T av -error decreases gradually with the inlet Reynolds number. Taking the temperature obtained by RANS model as the benchmark, when the inlet length L = 3mm and L = 7mm, the minimum average temperature error T of Darcy model is av -error are 2.71% and 1.29% respectively. The average temperature error T av -error is extremely small, which proves the applicability of the established equivalent diffusion coefficient and the validity of the equivalent model.

[0180] Fluid permeability κ f By fitting with different Reynolds numbers and inlet lengths, we get n = 6 and α = -0.1221, and the fluid permeability κ f Expressed as:

[0181]

[0182] 1.4 Efficiency of the Equivalent Model

[0183] The simulations were performed on a Dell workstation using an 11th Gen Core i7-11700K, using COMSOL as the multiphysics simulation software. The RANS model simulates fluid flow using the k-ω turbulence model, solving the conjugate heat transfer problem in two steps. The first step is to solve the turbulent flow, and the second step is to solve the solid and fluid heat transfer problem with a non-isothermal flow interaction interface. The direct solver is MUMPS, and the segregated solver is GMRES, with a tolerance of 0.0001. The Darcy model simulates fluid flow using the Darcy's law module, and the Darcy velocity and pressure fields are simulated in the solid and fluid heat transfer modules. The direct solver is MUMPS, and the segregated solver is PARDISO, with a tolerance of 0.00001. The same mesh is used to solve the above models.

[0184] Figure 12 The run times of the Darcy and RANS models for different inlet lengths, L, are shown, with an inlet Reynolds number of 5000. Because the flow complexity within the fluid increases with increasing inlet length, the computational time of the RANS model increases. The Darcy model solves the flow state linearly. Therefore, inlet length has little effect on the run time. When the inlet lengths are 3 mm, 4 mm, 5 mm, 6 mm, and 7 mm, the run times of the RANS model are 28.2, 23.5, 20.8, 78.1, and 66.6 times that of the Darcy model, respectively. The results show that using the Darcy model instead of the RANS model to simulate fluid flow can significantly reduce the run time. Therefore, the Darcy model is an efficient and lightweight equivalent conjugate heat transfer model. The 3D topology optimization model of the RANS model is extremely complex, and its convergence performance is poor due to the turbulent cooling conditions and the 3D structure of the CWJ. Furthermore, the 3D topology optimization model with the Darcy equivalent model converges more easily, thereby improving the convergence performance of the 3D topology optimization model.

[0185] 2. Cooling water jacket topology optimization

[0186] Fluid permeability κ of the equivalent model f Substitute the fluid permeability κ from the geometry and working conditions of the CWJ in the topology f In this case, the topological model selects inlet length L = 5 mm and inlet Reynolds number Re = 5000.

[0187] 3.1 Parameter Interpolation Model

[0188] The topological model optimizes fluid-solid materials in the design domain based on the SIMP method. The fluid and solid domains in the design domain are considered as porous material domains. The design variable γ is used to represent the solid-liquid phase of the unit material. γ is expressed in actual physical meaning by setting density filters and projections. When γ = 0, it represents fluid. When γ = 1, it represents solid. When 0 < γ < 1, it indicates that the domain is porous material. Helmholtz-type partial differential equations are used for filtering. Density filtering can effectively avoid mesh dependence and control the minimum size of the topological result to a certain extent. The density filtering expression is:

[0189]

[0190] Among them, R min represents the filter radius, Represents the filtered variable, represents the unfiltered design variable;

[0191] Density filtering will result in a large number of grayscale units. Hyperbolic tangent projection is used to obtain a clear topological flow channel. The projection expression is:

[0192]

[0193] Among them, β and η are divided into projection slope and projection point;

[0194] After density filtering and projection are obtained, the porous material domain is interpolated using γ, and the functional relationship between material properties and design variables is:

[0195]

[0196]

[0197]

[0198]

[0199] Where, κ represents the permeability; s and κ f represent the permeability of solid and fluid respectively; k represents thermal conductivity; k s and k f denote the thermal conductivity of solid and fluid respectively; ρ denotes density; ρ s and ρ f Denote the density of solid and fluid respectively; C p represents specific heat; C ps and C pf represent the specific heat of solid and fluid respectively; P κ 、P k 、P ρ and are penalty parameters, set to 3, 1, 1, and 1 respectively.

[0200] 2.2 Objective Function and Constraints

[0201] For a cooling channel, high heat dissipation performance (HDP) and low pressure drop (PDL) are essential. A weighted multi-objective approach is used to minimize the average temperature of the design domain and the inlet and outlet pressure difference. The objective function is as follows:

[0202]

[0203] Where w is the weight factor, and its value range is [0,1]; T0 and P0 are the reference temperature and pressure respectively; T av represents the average temperature of the design domain; P in Indicates the inlet pressure.

[0204] Constraints have a significant impact on the topology optimization results of the Darcy model. If there is no pressure drop constraint or the pressure drop loss (PDL) constraint is too large, the flow channel will be disconnected. Therefore, it is necessary to select an appropriate pressure constraint P * , the pressure constraint is obtained as:

[0205] P in ≤P *

[0206] Among them, P * Represents the pressure constraint threshold. In this embodiment, the pressure constraint threshold P * is 1000 Pa. The fluid permeability κ used in the topology f Calculated to be 7.94×10 -8 The cooling channel ratio constraint is:

[0207] ∫ Ω (1-γ)dΩ≤V w Vol Ω

[0208] Where Ω represents the design area; V w Indicates the volume ratio of the cooling channel; Vol Ω is the total volume of the design domain.

[0209] The final mathematical model of the cooling channel topology optimization problem is:

[0210] findγ

[0211]

[0212] 2.3 Analysis of topology optimization results

[0213] Figure 13The topology optimization results of the cooling channel under different weight coefficients are shown. Table 2 lists the heat dissipation performance (HDP) of the cooling water jacket (CWJ) with different topological structures. When w is small, the pressure drop loss (PDL) between the inlet and outlet dominates, and the generated cooling channel branches are not widely distributed. When w = 0.1, the average temperature of the design domain is 43.77 ° C, and the pressure drop loss (PDL) between the inlet and outlet is 450.81 Pa, which is less than half of the pressure constraint. In particular, the temperature variance is 514.13 ° C 2 . As the weight coefficient gradually increases, the contribution of the minimum average temperature to the objective function is reflected. The cooling channel branches are distributed in the design domain, the number of cooling channel branches increases, and there are a large number of cross-connections between different cooling channel branches, which reduces the overall temperature of the cooling channel and improves the heat dissipation performance (HDP). When w = 0.9, the average temperature of the design domain is reduced to only 24.49 ° C, the pressure drop loss (PDL) between the inlet and outlet is 979.93 Pa, and the temperature variance is significantly reduced to 8.551 ° C 2 A uniform temperature distribution was obtained. When w = 0.98, the topology results were similar to those when w = 0.9, but the average temperature and temperature variance were further reduced. Furthermore, the topology results with w = 0.9 demarcated small, unclear non-channel regions. Therefore, the topology results with w = 0.9 were selected as the topology optimization flow channel for the cooling water jacket.

[0214] Table 2 HDP of cooling channels with different topologies

[0215]

[0216] 2.4 Verification using RANS model

[0217] The 3D topology result is irregular in the circumferential direction, which brings certain difficulties to subsequent processing and manufacturing. In order to facilitate post-processing and manufacturing, the topology optimization flow channel is simplified. The cooling flow channel contour map of the inner surface of the design domain is exported, and then the wrap and stretch functions in the SOLIDWORKS modeling software are used to create a regular 3D model of the cooling flow channel, such as Figure 14 shown.

[0218] In order to verify the reliability of the optimization results, the selected topology optimized channel (TOC) was calculated in the RANS model, and the temperature field and velocity field were obtained. Figure 15The velocity fields calculated for the Darcy and RANS models are nearly identical. For the RANS model, the flow is primarily concentrated in the main cooling channel at the inlet. The flow distribution above and below the design domain is much less turbulent than that in the main channel at the inlet. The flow velocity in the main cooling channel is higher than that in the branch cooling channel. The flow distribution at the inlet of the Darcy model is more uniform than that of the RANS model, with streamlines distributed regularly along the cooling channel and no eddies. Figure 16 The surface temperature field in the design domain calculated for the above two models shows that the overall distribution trends of the two models are basically the same. The difference is that the temperature field calculated by the RANS model is clearer than that calculated by the Darcy model. The reason is that the RANS model takes into account the no-slip effect of the fluid wall, while the Darcy model does not take into account the no-slip effect of the fluid wall. Therefore, the heat dissipation performance (HDP) of the RANS model at the boundary of the cooling channel is worse than that of the Darcy model at the boundary of the cooling channel. For the RANS model, the temperature gradient at the boundary of the cooling channel is greater than the temperature gradient in other areas. The Darcy model overestimates the heat dissipation performance (HDP) of the fluid. The temperature obtained by the RANS model is used as a benchmark. The average temperatures of the design domain calculated by the Darcy and RANS models are 20.78℃ and 21.66℃, respectively, and the average temperature error T of the Darcy model is 0. av -error is 4.06%. The maximum temperatures of the design domain calculated by Darcy and RANS models are 23.23℃ and 25.09℃ respectively. The maximum temperature error T of Darcy model is av The error is 7.41%. Furthermore, for the topology optimized channel (TOC), the Darcy model has a lower temperature error than the serpentine channel because the overall temperature distribution of the TOC is more uniform. The temperatures calculated by both models are lower than those of the serpentine channel, thus reducing the temperature error. Although simulation errors exist, the errors in the velocity and temperature fields are within acceptable ranges. Therefore, the TOC calculated by the equivalent model can meet the needs of practical cases.

[0219] 3. Multi-physics simulation of electric spindle system

[0220] To verify the effectiveness of the topological model, the designed cooling water jacket structure was integrated into the motorized spindle system (MSS) for multi-physics simulation. The steps for multi-physics simulation of the motorized spindle system (MSS) are as follows: (1) Establish a thermal-fluid-solid coupling model. (2) Define the physical field type of the model and add boundary conditions to the finite element model. (3) Solve the temperature field, fluid pressure field, velocity field, and thermal deformation field under steady state. (4) Perform post-processing and analysis.

[0221] 3.1 Finite element model and boundary conditions

[0222] The model of the MSS is RT-C145-3 / 20000-GNE. The speed range of the MSS is 0-15000 r / min. The power loss is 800 W within the constant power range. The inlet temperature is 20°C. In order to facilitate the subsequent thermal-fluid-solid analysis, some small chamfers, fillets, screws, fillets, screw holes, eddy current sensors, thin washers, etc. are simplified. At the same time, the bearing is simplified as a hollow cylinder, and its internal structure is ignored, such as Figure 17 The simplified model is imported into COMSOL Multiphysics, and the cooling water jacket (CWJ) with spiral flow channels is integrated into the motorized spindle system (MSS). The motorized spindle system (MSS) is meshed using tetrahedral elements. The mesh is refined in areas with large temperature gradients, including the cooling water jacket, stator, rotor, and shaft core. There are a total of 1,090,490 elements and 195,886 mesh nodes, as shown in the figure. Figure 18 shown.

[0223] The governing equation for steady-state thermal analysis is expressed as:

[0224]

[0225] Where T = T(x,y,z) is the temperature of each element; λ x ,λ y and λ z are the thermal conductivities of the material in the X, Y, and Z directions, respectively.

[0226] Thermal deformation of the motorized spindle system (MSS) is calculated using Hooke's law

[0227] ε=α′·ΔT

[0228] Where α′ represents the thermal expansion coefficient of the material, ε represents the strain vector, and ΔT is the temperature rise vector.

[0229] The heat transfer governing equations are combined to perform thermal-fluid-solid coupling simulation analysis. To reduce the complexity of the simulation, the following assumptions are made: the fluid is incompressible; the fluid flow and heat transfer are stable; the channel walls are no-slip walls; the physical properties of the fluid and solid do not change with temperature; and gravity can be ignored.

[0230] First, set the ambient temperature, that is, the spindle air temperature and the initial cooling water temperature to 20 °C, and the maximum inlet flow rate to 1.85×10 -4 m 3 / s, the ingress traffic is expressed as:

[0231] Q in =v_in·A

[0232] where Qin represents the inlet flow rate; A represents the cross-sectional area; and v_in represents the inlet velocity. The maximum inlet Reynolds number under actual operating conditions was found to be 25517 Pa. In subsequent simulations, the inlet Reynolds number range was considered to be [5000 Pa, 25000 Pa]. The simulations were performed under no-load conditions with the motorized spindle system (MSS) rotating at 10000 rpm. The thermal boundary conditions of the MSS were calculated, as shown in Table 3.

[0233] Table 3 Thermal boundary conditions at a speed of 10000 r / min

[0234]

[0235] 3.2 Geometric Model of Traditional Channels

[0236] In order to verify the heat dissipation performance (HDP) of the cooling water jacket (CWJ), traditional flow channels with the same convective heat transfer area and the same inlet hydraulic diameter were designed for comparison, such as Figure 19 shown. Figure 19 (a) is a spiral flow channel with a spacing of 15 mm, a groove width of 10 mm, and a groove depth of 4.5 mm. Figure 19 (b) shows the serpentine flow channel, which uses a dual-inlet and outlet semi-heat dissipation structure to ensure equal inlet flow. The channel has a groove width of 12.5 mm, a groove depth of 4.5 mm, and a radial length of 72 mm.

[0237] 4.3 Comparison and Discussion

[0238] 4.3.1 Analysis of heat dissipation performance

[0239] When the inlet Reynolds number is 15000, Figure 20The temperature distribution in the middle section of the motorized spindle system (MSS) is shown for three different cooling water jackets (CWJs) with different cooling channels. Under the influence of the three different CWJs, the highest temperature of the MSS is located at the rotor. The rotor generates a large amount of heat and is enclosed within the motorized spindle, resulting in poor heat dissipation. The temperatures at the ends of the MSS and within the cooling channels are lower than those in other areas. Forced convection between the counterweights at both ends and the air accelerates the heat dissipation process. The cooling water inlet temperature is 20°C, and the cooling channels remove the heat generated by the stator. Free convection exists between the housing and the air. Consequently, heat dissipation efficiency is low, resulting in relatively high housing temperatures. The temperature distributions of the MSS under the influence of the two different CWJs with spiral and serpentine channels are similar. The temperature of the MSS under the CWJ with topology-optimized channels (TOC) is significantly lower than that of the MSS under the different CWJs. Cooling water jackets with traditional spiral and serpentine channels are shown. The maximum temperatures of the electric spindle system (MSS) under the influence of three different cooling water jackets (CWJs)—spiral, serpentine, and topology-optimized (TOC)—were 57.01°C, 58.38°C, and 55.56°C, respectively. The average temperatures of the MSS under the influence of three different cooling water jackets (CWJs)—spiral, serpentine, and TOC—were 40.73°C, 40.31°C, and 34.74°C, respectively. The average temperature of the MSS under the influence of the TOC CWJ was 14.7% and 13.8% lower than that under the influence of the spiral and serpentine CWJs, respectively.

[0240] When the inlet Reynolds number is 15000, Figure 21 The temperature distribution of the stator outer surface under three different cooling channel configurations is shown. For the spiral channel, the maximum and minimum temperatures on the stator outer surface are 46.1°C and 23.8°C, respectively. The temperature in areas without channel configuration is significantly higher than in areas with channel configuration. Furthermore, for the spiral channel, the stator outer surface temperature increases with the number of turns around the stator. The axial and radial temperature distributions are uneven. For the serpentine channel, the maximum and minimum temperatures on the stator outer surface are 47.1°C and 25.4°C, respectively. The overall temperature distribution of the stator outer surface with the serpentine channel is similar to that of the stator outer surface with the spiral channel. For the topology-optimized channel (TOC), the maximum and minimum temperatures on the stator outer surface are 37.4°C and 24.5°C, respectively. The maximum temperature of the stator outer surface with the TOC channel is significantly lower than that of the spiral and serpentine channels. Due to the diffuse distribution of the TOC channel, the temperature field is uniformly distributed across the stator outer surface, with no particularly high local temperatures.

[0241] Figure 22 The figure shows the relationship between the stator outer surface temperature and the inlet Reynolds number. The spiral and serpentine channels are unevenly distributed on the stator outer surface, resulting in higher temperatures in locations not covered by cooling channels. Consequently, the maximum stator outer surface temperature for the spiral and serpentine channels is much higher than that for the topology-optimized (TOC) channels. The stator outer surface temperature is lowest at the cooling channel inlet, where it is the same as the cooling water inlet temperature. Therefore, the minimum temperature difference among the three channels is not significant.

[0242] Figure 23 The temperature gradient of the stator outer surface under different inlet Reynolds numbers is shown. As the Reynolds number increases, the temperature gradient of the stator outer surface of the three cooling channels decreases. When the inlet Reynolds number is 5000, the temperature gradient of the spiral channel, serpentine channel and topology optimized channel (TOC) is 58.74℃ respectively. 2 ,46.47℃ 2 and 13.52℃ 2 When the inlet Reynolds number is 25000, the temperature gradients of the spiral channel, serpentine channel and topology optimized channel (TOC) are 34.43℃ respectively. 2 ,30.6℃ 2 and 6.84℃ 2 Therefore, the temperature field uniformity of the stator outer surface of TOC is significantly better than that of the stator outer surface of spiral and serpentine flow channels.

[0243] When the inlet Reynolds number is 15000, the velocity streamline distribution vector diagram inside the cooling channel is as follows Figure 24 As shown. For the spiral flow channel, the maximum internal flow velocity is 3.56m / s, and the velocity at the inlet and outlet is slightly higher than that in other areas. The streamlines in the spiral flow channel are concentrated in the narrow cross-section of the cooling channel, and the velocity does not change much. For the serpentine flow channel, the maximum internal flow velocity is 2.49m / s. Since the serpentine flow channel dissipates heat in a double-inlet and double-outlet manner, the single inlet flow rate is half of that of the spiral flow channel. Then the maximum velocity of the serpentine flow channel is less than the maximum velocity of the spiral flow channel. As shown Figure 24 As shown in (b), the velocity of the streamline is highest at the bend, and the turbulence intensity is more significant than that of the spiral flow channel. There are local vortices, and the overall streamlines are concentrated. For the topology optimized flow channel (TOC), the maximum internal flow velocity is 1.57m / s. It is also a dual-inlet and dual-outlet heat dissipation method. The flow velocity is higher in the middle section of the inlet, and then diffuses to both sides. The flow velocity slows down when the fluid enters the branch. It can be concluded that the heat dissipation performance (HDP) of the topology optimized flow channel (TOC) is higher than that of the spiral and serpentine flow channels. In addition, the topology optimized flow channel (TOC) can achieve more uniform cooling, while the spiral and serpentine flow channels cannot achieve uniform cooling.

[0244] 3.3.2 Pressure Drop Analysis

[0245] Pressure drop loss (PDL) is one of the important indicators to characterize the flow characteristics of cooling channels. The greater the pressure drop loss (PDL), the greater the energy consumption required for fluid flow. When the inlet Reynolds number is 15000, Figure 25 The internal pressure distribution in the cooling channel is shown. The maximum pressure is located near the inlet, reaching 14816 Pa for the spiral channel, 6178 Pa for the serpentine channel, and 2517 Pa for the topology-optimized channel (TOC). The internal pressure of the spiral and serpentine channels decreases as the cooling fluid flows. The pressure field in the topology-optimized channel (TOC) is evenly distributed throughout the cooling channel, and the overall PDL is much smaller than the previous two.

[0246] The pressure drop loss (PDL) at different inlet Reynolds numbers is as follows: Figure 26 As shown. Since the serpentine flow channel and the topology optimized flow channel (TOC) dissipate heat in a dual-inlet and dual-outlet mode, the total pressure drop loss (PDL) of the serpentine flow channel and the topology optimized flow channel (TOC) is the sum of the two calculated pressure drop losses (PDL). The pressure drop loss (PDL) of the above three cooling channels increases with the increase of the inlet Reynolds number, and the increasing trend of the pressure drop loss (PDL) of the topology optimized flow channel (TOC) is smaller than the PDLs of the other two traditional flow channels. For the same inlet Reynolds number, the pressure drop loss (PDL) of the serpentine flow channel is slightly smaller than that of the spiral flow channel, while the pressure drop loss (PDL) of the topology optimized flow channel (TOC) is the smallest. When the inlet Reynolds number is 25000, the pressure drop losses (PDL) of the spiral flow channel, serpentine flow channel and topology optimized flow channel (TOC) are 28850Pa, 27097Pa and 8929Pa, respectively. Compared with spiral and serpentine flow channels, the pressure drop loss (PDL) of the topology optimized flow channel (TOC) is reduced by 69.05% and 67.04%, respectively. Therefore, the energy dissipated by the topology optimized flow channel (TOC) is significantly reduced, thereby greatly reducing the required pump power.

[0247] 3.3.3 Thermal deformation analysis

[0248] Figure 27The thermal deformation distribution of an electric spindle system (MSS) under the influence of three different cooling water jackets (CWJs) with different cooling channels is shown in Table 4. When the inlet Reynolds number is 15,000, the maximum thermal deformation of the MSS in different directions under the influence of the three different cooling water jackets (CWJs) is listed. The maximum deformation of the MSS in the X, Y, and Z directions for the MSS with a spiral cooling water jacket is 119.47 μm, 26.66 μm, and 21.87 μm, respectively. The thermal deformation in the X direction is approximately 4.48 times and 5.46 times that in the Y and Z directions, respectively. The deformation of the MSS is primarily in the axial direction. Furthermore, the MSS with the spiral and serpentine cooling water jackets (CWJs) exhibit similar thermal deformation distributions. Under the influence of the cooling water jacket (CWJ) and topology-optimized cooling channels (TOC), the maximum deformations of the motorized spindle system (MSS) in the X, Y, and Z directions were 89.99 μm, 17.25 μm, and 17.17 μm, respectively. Under the influence of three different cooling water jacket (CWJ) configurations—spiral, serpentine, and topology-optimized cooling channels (TOC)—the total thermal deformation (TTD) of the motorized spindle system (MSS) was 124.35 μm, 121.1 μm, and 93.22 μm, respectively. The maximum thermal deformation occurred at the far right end of the motorized spindle system (MSS) because the left-end bearing was subject to axial and radial fixed constraints, while the right-end bearing was subject to radial fixed constraints.

[0249] Table 4 Maximum thermal deformation

[0250]

[0251] The relationship between thermal deformation and inlet Reynolds number is as follows: Figure 28As shown in the figure, with increasing inlet Reynolds number, the thermal deformation of the electric spindle system (MSS) under the three different cooling water jackets (CWJs) with spiral, serpentine, and helical channels decreases in sequence. The decreasing trend slows down with increasing inlet Reynolds number. Therefore, the thermal deformation of the electric spindle system (MSS) cannot be reduced by increasing the inlet Reynolds number. When the inlet Reynolds number is 5000, the total thermal deformation (TTD) of the electric spindle system (MSS) under the three different cooling water jackets (CWJs) with spiral, serpentine, and topology optimized (TOC) channels is 149.94μm, 144.54μm, and 119.74μm, respectively. Compared with the electric spindle system (MSS) under the two different cooling water jackets (CWJs) with spiral and serpentine channels, the thermal deformation of the electric spindle system (MSS) under the cooling water jacket (CWJ) with TOC is reduced by 20.14% and 17.15%. When the inlet Reynolds number is 25,000, the total thermal deformation (TTD) of the electrospindle system (MSS) with three different cooling water jackets (CWJs)—spiral, serpentine, and topology optimized flow channels (TOC)—is 110.63 μm, 106.37 μm, and 81.13 μm, respectively. Compared with the MSS with the two different CWJs with spiral and serpentine flow channels, the thermal deformation of the MSS with the CWJ with topology optimized flow channels (TOC) is reduced by 26.67% and 23.73%. Therefore, the higher the Reynolds number, the more significant the advantage of TOC.

[0252] 4. Conclusion

[0253] This embodiment proposes an efficient and highly convergent topological model for the structural design of the cooling water jacket (CWJ) of the electric spindle system (MSS). The Darcy model is used to simulate fluid flow, and a lightweight conjugate heat transfer equivalent model is established based on the actual size and working conditions of the cooling channel of the electric spindle system (MSS). The functional expression of the fluid permeability parameter is obtained. Then, the turbulence model is replaced by the equivalent model, and the combination of average temperature and pressure drop loss (PDL) is used as the optimization objective function of the topology, and the selected topology structure is verified by the RANS model. Finally, the topology optimized channel (TOC) structure is integrated into the cooling water jacket (CWJ) of the electric spindle system (MSS) for multi-physics field simulation. The conclusions are as follows:

[0254] (1) By analyzing the temperature and velocity fields obtained by Darcy and RANS models, the ratio of fluid permeability to fluid-solid permeability is determined to be κ f / κ s =10 7The average temperature error of the equivalent model decreases with the increase of the inlet Reynolds number. Compared with the RANS model, the maximum and minimum average temperature errors of the design domain calculated by the Darcy model are 11.61% and 1.29%, respectively. That is, they are within the acceptable range. The fluid permeability κ is further constructed. f The mapping relationship between the design dimensions of the cooling water jacket (CWJ) and the actual working conditions is shown. Compared with the RANS model, the running time of this equivalent model is reduced by up to 78.1 times, and the convergence performance of the 3D topology model is significantly improved.

[0255] (2) A lightweight Darcy equivalent model was established to replace the RANS model for the topology design of the cooling water jacket (CWJ) structure, and the SIMP method was used to interpolate the material properties. The average temperature and pressure drop loss (PDL) were used as the optimization objective functions of the topology. The topology results with a weighting factor w = 0.9 were selected and verified using the RANS model. The results show that the velocity field and temperature field calculated by the Darcy equivalent model and the RANS model are in good agreement. Compared with the RANS model, the average temperature error and maximum temperature error of the design domain calculated by the Darcy model are 4.06% and 7.41%, respectively. The feasibility and applicability of the established topology equivalent model are demonstrated.

[0256] (3) The proposed topological method is used to study the structural design method of the cooling water jacket (CWJ) and improve the HDP of the electric spindle system (MSS). A cooling water jacket (CWJ) with a topology optimized flow channel (TOC) is designed and integrated into the electric spindle system (MSS). Then, a thermal-fluid-solid numerical simulation model of the electric spindle system (MSS) is established, and the heat dissipation performance (HDP) of different cooling water jackets (CWJ) with spiral flow channels, serpentine flow channels and topology optimized flow channels (TOC) is compared. The results show that when the inlet Reynolds number is 15000, the average temperature of the electric spindle system (MSS) under the action of the cooling water jacket (CWJ) with TOC is reduced by 14.7% and 13.8% compared with the average temperature of the electric spindle system (MSS) under the action of two different cooling water jackets (CWJ). Spiral and serpentine flow channels. For the topology optimized flow channel (TOC), the pressure drop loss (PDL) is reduced by 83.01% and 59.26% compared with the spiral and serpentine flow channels, respectively. Compared with two different cooling water jackets (CWJs) with traditional spiral and serpentine flow channels, the total thermal deformation (TTD) of the MSS with the topology optimized flow channel (TOC) CWJ was reduced by 34.57% and 32.95%. The heat dissipation performance (HDP) of the topology optimized flow channel (TOC) was significantly stronger than that of the other two traditional spiral and serpentine flow channels.

[0257] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A method for topological optimization of the cooling water jacket structure of an electric spindle, characterized by: The steps include: Step 1: Establish an equivalent model of the cooling water jacket 11) Import the 3D geometric model of the cooling water jacket and the boundary conditions of the equivalent model into the RANS model and Darcy model respectively; 12) Use the RANS model and Darcy model to perform numerical simulations and calculate the pressure error: in, Indicates pressure error; represents the inlet and outlet pressure difference obtained by the Darcy model, represents the inlet and outlet fluid pressure difference obtained by the RANS model; 13) Judgment Is the value of less than or equal to the set threshold: if so, execute step 14); if not, adjust the equivalent solid-liquid permeability used in the Darcy model and execute step 12); 14) Calculate the speed error, average temperature error and maximum temperature error; in, Indicates speed error; represents the fluid velocity obtained by the Darcy model; represents the fluid velocity obtained by the RANS model; represents the average temperature error; represents the average temperature obtained by the Darcy model; represents the average temperature obtained by the RANS model; Indicates the maximum temperature error; represents the maximum temperature obtained by the Darcy model; represents the maximum temperature obtained by the RANS model; 15) Determine whether the values ​​in the half vector of the cooling water jacket inlet length L and the Reynolds number Re vector are traversed: if so, construct an equivalent model of the cooling water jacket and obtain expressions for the permeability ratio and fluid permeability; if not, update the inlet length L and Reynolds number Re and execute step 12); Permeability ratio The expression is: Fluid permeability The expression is: in, represents the solid permeability; represents the fluid permeability; represents dynamic viscosity; Indicates the inlet length of the cooling water jacket; Indicates the entrance width; Indicates fluid pressure; represents the fluid density; Step 2: Topology optimization of the cooling water jacket structure 21) Import the obtained expressions of permeability ratio and fluid permeability into the parameter interpolation model, and construct the objective function and constraints of topology optimization; 22) Perform topological optimization on the spindle cooling water jacket structure to obtain the topological optimized flow channel of the cooling water jacket; 23) Determine whether the topology calculation has converged: if so, output the topology optimized flow channel of the cooling water jacket; if not, update the filter radius and weight factor and execute step 22).

2. The method for topological optimization of the electric spindle cooling water jacket structure according to claim 1, characterized in that: In step 22), the fluid flow equation of the Darcy model includes: Fluid continuity equation: Momentum equation: The velocity field of the Darcy model is expressed as: in, represents the gradient; and represent the fluid density and dynamic viscosity respectively; Indicates fluid pressure; Indicates fluid pressure level; represents the external force term; represents turbulent kinetic energy; represents the permeability; represents the specific dissipation rate; represents the eddy viscosity; represents the fluid velocity in the Darcy model; 、 、 、 and All represent constants; The heat transfer equation of the Darcy model is: represents the specific heat of the fluid; represents the temperature of the solution domain; Indicates a heat source; represents the thermal conductivity. When the design domain is solid, , when the design domain is fluid, , and denote the thermal conductivities of solid and fluid, respectively.

3. The method for topological optimization of the electric spindle cooling water jacket structure according to claim 1, characterized in that: In step 21), the parameter interpolation model is: Helmholtz-type partial differential equations are used for filtering. Density filtering can effectively avoid grid dependence and control the minimum size of the topological result. The density filtering expression is: in, represents the filter radius, Represents the filtered variable, represents the unfiltered design variable; Density filtering will result in a large number of grayscale units. Hyperbolic tangent projection is used to obtain a clear topological flow channel. The projection expression is: in, and Divided into projection slope and projection point; use Interpolating the porous material domain, the functional relationship between the material properties and the design variables is: in, represents the permeability; and denote the permeabilities of solid and fluid, respectively; represents thermal conductivity; and denote the thermal conductivity of solid and fluid respectively; Indicates density; and denote the density of solid and fluid respectively; represents specific heat; and denote the specific heat of solid and fluid respectively; 、 、 and Both are penalty parameters; is represented as a variable representing the solid and liquid phases of the material, and: When , it indicates that the material is fluid; when When , it means the material is solid; when , it indicates that the material is porous.

4. The method for topological optimization of the electric spindle cooling water jacket structure according to claim 1, characterized in that: In step 21), a weighted multi-objective approach is used to minimize the average temperature of the design domain and the inlet and outlet pressure difference. The objective function is as follows: in, is the weight factor, and its value range is [0, 1]; and are the reference temperature and pressure, respectively; represents the average temperature of the design domain; Indicates the inlet pressure.

5. The method for topological optimization of the electric spindle cooling water jacket structure according to claim 1, characterized in that: In step 21), in the Darcy model, the pressure drop constraint has a significant impact on the topological results. If no pressure drop constraint is imposed or an excessively large pressure drop constraint is imposed, the flow channel will be disconnected. Therefore, the pressure constraint is: in, represents the pressure constraint threshold; Indicates the inlet pressure; The cooling channel ratio constraint is: in, Indicates the design area; Indicates the volume ratio of the cooling channel; is the total volume of the design domain; is a variable representing the solid and liquid phases of the material.

6. The method for topological optimization of the electric spindle cooling water jacket structure according to any one of claims 1 to 5, characterized in that: The method further includes step three: constructing a finite element model of the cooling water jacket using the obtained topologically optimized flow channel of the cooling water jacket, setting simulation boundary conditions, and performing simulation analysis on the electric spindle.

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