Simulation method of flow-heat-solid coupling characteristics of high-speed electric spindle based on rotating heat pipe

Abstract

The present invention discloses a method for simulating the flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotary heat pipe, comprising the following steps: Step 1: designing the structural parameters of the rotary heat pipe according to the heating and heat dissipation conditions and geometric constraints of the high-speed electric spindle, and placing the designed rotary heat pipe into the high-speed electric spindle; Step 2: establishing a gas-liquid phase change model of the rotary heat pipe, and performing fluid simulation analysis on the rotary heat pipe to reveal the influence of the evaporation section mechanism and filling rate of the rotary heat pipe on the heat dissipation performance of the rotary heat pipe under the complex working conditions of the high-speed electric spindle; Step 3: establishing a flow-heat-solid coupling characteristic model of a high-speed electric spindle with a rotary heat pipe, performing transient heat transfer analysis on the high-speed electric spindle and obtaining the temperature field, and performing transient deformation analysis on the high-speed electric spindle and obtaining the deformation field. The method can reveal the mechanism of action of the rotary heat pipe on the fluid-heat-solid interaction characteristics of the high-speed electric spindle.

Description

Technical Field

[0001] The invention belongs to the technical field of simulation analysis, and specifically relates to a method for simulating flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe. Background Art

[0002] The working conditions of high-speed precision machine tools (HSPMTs) are extremely extreme. Their main working conditions are: high spindle speeds of 20,000-40,000 r / min, fast feed speeds of 40-90 m / min, and a maximum processing speed of 150 m / min. The machining errors of HSPMTs significantly affect the geometric accuracy of machined parts. The above extreme working conditions cause HSPMTs to generate a large amount of heat, and the heat load intensity of the heat source is extremely high. The heat generated by the heat source flows into the key parts of the HSPMT in the form of conduction, resulting in uneven temperature distribution, and then thermally induced errors (TIE) are generated. The machining accuracy of HSPMT is very sensitive to TIE, and the machining errors caused by TIE account for 50%-70% of the total machining errors of HSPMT. Therefore, TIE control is an effective means to improve the geometric accuracy of machining complex parts. The high-speed motorized spindle (HSMS) is one of the most important functional components. Its closed and compact structure makes it difficult to dissipate internal heat, which makes the HSMS have a significant temperature gradient, an extremely long thermal equilibrium time (TET) and a significant thermal elongation (TE). The TE of the HSMS contributes significantly to the machining error, so HSMS cooling and TIE control are essential.

[0003] At present, there are two main control methods for TIE, namely, compensation of TIE and reducing errors by controlling temperature rise. The compensation method mainly offsets the current original error by artificially creating new errors, which can improve machining accuracy and reduce machining costs within a certain range. However, as a passive post-compensation method, the TIE compensation method has certain limitations in its compensation range and effectiveness. Moreover, when the thermal characteristics of the machine tool are relatively poor, the passive TIE compensation cannot meet the requirements of machining accuracy. Uneven temperature distribution is the main reason for the existence of TIE, and the root cause is the weak heat dissipation performance (HDP) of the HSMS. The circulating cooling system (CCS) is usually used to dissipate excessive electric heat and friction heat to reduce the uneven distribution of the temperature field and control the TIE of the HSMS. However, the HDP of the CCS based on the principle of forced convection of the coolant is limited, and there are key problems such as poor temperature control stability, complex control algorithm, and easy leakage of coolant.

[0004] It is concluded that the compensation accuracy of the existing TIE compensation method depends on complex mathematical modeling theory. As a post-compensation method, the compensation delay is serious, and it is difficult to achieve effective control of TIE caused by heat under complex working conditions. For the method of reducing errors by controlling temperature rise, CCS is used to control the temperature of CWJ and coolant to dissipate most of the heat generated by the stator. However, the fundamental problems of uneven temperature field distribution and large temperature gradient cannot be avoided. In addition, CCS often needs to be equipped with peripheral cooling equipment, including circulating coolers, cold sources, etc. The use of peripheral cooling equipment is expensive and takes up space, and coolant leakage can easily pollute the environment. Obviously, neither of the two existing TIE control methods can fully meet the requirements of TIE control.

[0005] Heat pipes exhibit excellent HDP, and their heat exchange efficiency is much higher than that of conventional CCS. The reason is that conventional CCS uses forced convection to achieve heat dissipation, while heat pipes use the latent heat of fluid phase change for heat output and exchange. The HDP of heat pipes with latent heat of phase change is much higher than that of conventional forced convection CCS. At present, no RHP design method for HSMS cooling and TIE control has been proposed, and the RHP gas-liquid phase change simulation method applied to this scenario has not been studied. That is, RHP design and HDP analysis methods for HSMS cooling and TIE control have not been reported, and the mechanism of the action of RHP on the fluid-thermal-solid interaction characteristics (FTSIC) of HSMS has not yet been revealed. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a simulation method for the flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe, so as to reveal the action mechanism of the rotating heat pipe on the flow-heat-solid interaction characteristics of the high-speed electric spindle.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for simulating flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe comprises the following steps:

[0009] Step 1: Design the structural parameters of the rotary heat pipe according to the heating and heat dissipation conditions and geometric constraints of the high-speed electric spindle, and place the designed rotary heat pipe into the high-speed electric spindle;

[0010] Step 2: Establish a gas-liquid two-phase flow phase change model of the rotary heat pipe and perform fluid simulation analysis on the rotary heat pipe to reveal the influence of the evaporation section mechanism and filling rate on the heat dissipation performance of the rotary heat pipe under the complex working conditions of the high-speed electric spindle;

[0011] Step 3: Establish a fluid-heat-solid coupling characteristic model of the high-speed electric spindle with a rotating heat pipe, perform transient heat transfer analysis on the high-speed electric spindle and obtain the temperature field, perform transient deformation analysis on the high-speed electric spindle and obtain the deformation field. Furthermore, in step 1, the high-speed electric spindle is mainly powered by two heat sources when working, namely the built-in motor and the front and rear bearings;

[0012] The power loss of the motor is:

[0013] P s =P e (1-η)

[0014] Among them, P s Indicates power loss; P e represents the rated power; η represents the motor efficiency;

[0015] At high speed, one third of the heat is distributed on the rotor and two thirds of the heat is distributed on the stator, then:

[0016]

[0017] Among them, q rotor represents the heat distributed on the rotor; q stator Represents the heat on the stator; V rotor Indicates the volume of the rotor; V stator represents the volume of the rotor;

[0018] The friction torque generated by the rolling bearing causes friction heat Q, which is:

[0019] Q = 1.047 × 10 -4 ×Mn

[0020] Where M represents the bearing friction torque; n Indicates the bearing speed;

[0021] The friction torque M is:

[0022]

[0023] Where M1 represents the torque of the external load; M0 represents the torque of the viscous friction of the lubricant; f1 represents the coefficient related to the bearing structure and load; F β Indicates the magnitude and direction of force; d m represents the average diameter of the bearing; v represents the dynamic viscosity; f0 represents the coefficient related to the bearing and lubrication method.

[0024] Furthermore, in step 1, the internal space of the high-speed electric spindle is compact, the heat dissipation condition is poor, and the spindle housing and the air are in a natural convection heat transfer mode; according to the Nusselt number criterion, the convection heat transfer coefficient is:

[0025] h=(Nu·λ) / L

[0026] Wherein, h represents the convective heat transfer coefficient; Nu represents the Nusselt number; L represents the characteristic size; and λ represents the thermal conductivity.

[0027] Further, in step 1, the centrifugal acceleration of the rotating heat pipe is:

[0028] a=ω 2 rsinα

[0029] The reflux acceleration of the fluid in a rotating heat pipe a Equal to the acceleration due to gravity, that is, a / g = 1;

[0030] Wherein, ω represents the angular velocity of rotation; r represents the minimum inner radius of the rotating heat pipe; α represents the taper of the inner surface of the rotating heat pipe;

[0031] The length of the rotating heat pipe is determined according to the geometric constraints of the high-speed electric spindle and the distribution position of the heat source, and the evaporation section of the rotating heat pipe should cover the motor rotor and the front and rear bearings.

[0032] Furthermore, in step 2, a gas-liquid phase change model of a rotating heat pipe is constructed using ANSYS FLUENT, a VOF model is used to simulate the mass conversion and energy conversion process during the gas-liquid phase change, and a Lee model is used to simulate the mechanism of gas-liquid two-phase evaporation, boiling and condensation.

[0033] Furthermore, the method of using the VOF model to simulate the mass conversion and energy conversion process during the gas-liquid phase change process is as follows:

[0034] The volume fractions of the gas phase and liquid phase in the rotating heat pipe are defined as α V and α L , in each grid cell in the computational domain, the following continuity equation is satisfied:

[0035]

[0036] Among them, ρ L represents the density of the liquid phase; ρ V represents the density of the gas phase; u Indicates dynamic viscosity; S m ,L and S m , V represent the mass source terms of liquid phase and gas phase respectively; represents the gradient operator;

[0037] The momentum equation is:

[0038]

[0039] Among them, I represents a unit tensor; FCSF represents the source phase of the volume force generated by the continuous surface tension; ρ represents the gas phase density; p represents the pressure inside the tube; u T represents the velocity vector; g represents the acceleration due to gravity;

[0040] The energy equation is:

[0041]

[0042] Where ρ represents the density of the mixed phase; e represents internal energy; k represents thermal conductivity; T represents temperature; S E represents the energy conversion source term;

[0043] Density ρ, thermal conductivity k and dynamic viscosity u The internal energy is solved by averaging the volume of the mixed phase and using the average mass e :

[0044]

[0045] In a rotating heat pipe, surface tension affects the dynamic evolution of bubble generation, growth, merging and rupture, and is also an important factor affecting bubble flow and wall wettability. Therefore, a continuous medium surface force model is introduced under the action of surface tension, and the interface pressure difference is added to the momentum equation in the form of body force. In the two-phase flow model, k j =-k i , but:

[0046]

[0047] Among them, σ ij Represents the surface tension coefficient; α i represents the volume fraction of one phase; ρ represents the volume average density; ρ i represents the density of one of the phases; ρ j represents the density of the other phase; k i represents the surface curvature;

[0048] The contact angle of the air-liquid interface is θ w , then the unit normal gradient near the wall interface is It is expressed as:

[0049]

[0050] in, and denote the unit normal gradient and tangential gradient near the wall, respectively.

[0051] Furthermore, the method of using the Lee model to simulate the mechanism of gas-liquid two-phase evaporation, boiling and condensation is as follows:

[0052] During the evaporation process:

[0053]

[0054] During the condensation process:

[0055]

[0056] The energy during evaporation and condensation is converted into:

[0057]

[0058] Among them, m LV and m VL represent the mass of liquid-gas and gas-liquid transitions respectively; T represents the temperature of the mixed phase; T sat Indicates the saturation temperature when the working fluid undergoes phase change; D Sm represents the Sauter mean diameter; ΔH represents the saturation enthalpy difference; β e and β c Respectively represent the evaporation and condensation coefficients; α V and α L Represent the volume fractions of gas phase and liquid phase respectively; ρ V and ρ L denote the volume fractions of gas and liquid phases, respectively;

[0059] T sat represents saturation temperature; M′ represents molar mass; ΔH represents saturation enthalpy difference; D Sm represents the Sauter mean diameter; R represents the ideal gas constant; S E represents the energy conversion source term.

[0060] The beneficial effects of the present invention are:

[0061] The present invention provides a simulation method for the fluid-heat-solid coupling characteristics of a high-speed electric spindle based on a rotary heat pipe. Firstly, the geometric structure of the rotary heat pipe is designed according to the working principle, working conditions and geometric constraints of the high-speed electric spindle, and the designed rotary heat pipe is embedded in the high-speed electric spindle to increase the heat dissipation performance of the high-speed electric spindle; then, a gas-liquid phase change model of the rotary heat pipe is established, and the influence of the evaporation mechanism and filling rate of the rotary heat pipe at different speeds on the heat dissipation performance of the rotary heat pipe is studied; finally, a fluid-heat-solid coupling characteristic model of the high-speed electric spindle with a rotary heat pipe is established to reveal the action mechanism of the rotary heat pipe on the fluid-heat-solid interaction characteristics of the high-speed electric spindle. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0063] Figure 1 The schematic diagram of the method for simulating the flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe of the present invention;

[0064] Figure 2 It is the relationship curve diagram between taper and speed;

[0065] Figure 3 The structural parameters of the rotary heat pipe designed in this embodiment;

[0066] Figure 4 The geometric model diagram of the high-speed electric spindle with a rotating heat pipe;

[0067] Figure 5 This is a schematic diagram of the interface between 2D UDF and FLUENT;

[0068] Figure 6 are the boundary conditions for the rotating heat pipe phase change model;

[0069] Figure 7 This is the curve diagram of the effect of rotation acceleration on EHTC of evaporation section;

[0070] Figure 8 To design the phase change mechanism of RHP at different speeds;

[0071] Fig. 9 is the RHP gas volume fraction distribution diagram when the filling rate (FR) is 50%;

[0072] Fig.10 is the RHP temperature field distribution diagram when FR is 50%;

[0073] Fig.11 is a RHP (rotating heat pipe) with three different FRs;

[0074] Fig.12 is the HTP (heat transfer performance) of RHP with different FR;

[0075] Fig.13 It is the simulation accuracy diagram;

[0076] Fig.14 Comparison diagram of the geometric model of the high-speed electric spindle; (a) without RHP; (b) with RHP;

[0077] Fig.15 Meshing for the fluid-thermal-solid interaction model;

[0078] Fig.16Comparative analysis of transient temperature field: (a) overall temperature distribution of a conventional liquid-cooled high-speed electric spindle (FCHSMS) without RHP; (b) overall temperature distribution of a HSMS with RHP; (c) shaft temperature distribution of a conventional FCHSMS without RHP; (d) shaft temperature distribution of a HSMS cloud diagram with RHP;

[0079] Fig.17 Temperature comparison analysis; (a) overall temperature; (b) shaft temperature;

[0080] Fig.18 Comparative analysis of transient thermal deformation; (a) overall axial elongation of traditional FCHSMS without RHP; (b) overall axial elongation of HSMS with RHP; (c) axial elongation of the shaft core in traditional FCHSMS without RHP; (d) axial elongation of the shaft core in HSMS with RHP;

[0081] Fig.19 Comparative analysis of thermal deformation; (a) overall thermal elongation; (b) core thermal elongation.

[0082] Symbol Table

[0083]

[0084] DETAILED DESCRIPTION

[0085] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0086] like Figure 1 As shown, the simulation method of the flow-heat-solid coupling characteristics of the high-speed electric spindle of the rotating heat pipe in this embodiment includes the following steps:

[0087] Step 1: Design the structural parameters of the rotary heat pipe according to the heating and heat dissipation conditions and geometric constraints of the high-speed electric spindle, and place the designed rotary heat pipe into the high-speed electric spindle;

[0088] Step 2: Establish a gas-liquid two-phase flow phase change model of the rotary heat pipe and perform fluid simulation analysis on the rotary heat pipe to reveal the influence of the evaporation section mechanism and filling rate on the heat dissipation performance of the rotary heat pipe under the complex working conditions of the high-speed electric spindle;

[0089] Step 3: Establish a fluid-heat-solid coupling characteristic model of the high-speed electric spindle with a rotating heat pipe, perform transient heat transfer analysis on the high-speed electric spindle and obtain the temperature field, perform transient deformation analysis on the high-speed electric spindle and obtain the deformation field.

[0090] 1. Design of Rotating Heat Pipe (RHP)

[0091] 1.1 Heat generation and dissipation of HSMS

[0092] The speed range of the high-speed motorized spindle (HSMS) is 0-40000r / min. During the use of the HSMS, the friction heat of the bearing ring / ball interface and the Joule heat of the motor also increase with the increase of the speed. Therefore, the RHP design for HSMS cooling and thermally induced error (TIE) control should consider the heating and heat dissipation of the HSMS. Then the electric heat of the built-in motor and the friction heat of the bearing are calculated.

[0093] 1.1.1 Heating of HSMS

[0094] HSMS is generally composed of a shaft core, front and rear bearing groups, motor, cooling water jacket, housing, cooling chamber, etc. When HSMS is working, there are two main heat sources inside, namely the front and rear bearings and the built-in motor.

[0095] For electric motors, the loss of rated power is usually converted into electrical heating of the stator and rotor. s The approximate calculation is:

[0096] P s =P e (1-η)

[0097] Among them, P s Indicates power loss; P e represents the rated power; η represents the motor efficiency. Under the HSMS high-speed condition, η is taken as 0.75.

[0098] In addition, one third of the heat is distributed on the rotor, and the remaining two thirds of the heat is distributed on the stator. Then the heat generation rate is:

[0099]

[0100] Among them, q rotor represents the heat distributed on the rotor; q stator Represents the heat on the stator; V rotor Indicates the volume of the rotor; V stator represents the volume of the rotor;

[0101] The friction torque generated by the rolling bearing causes friction heat Q, which is:

[0102] Q = 1.047 × 10 -4 ×Mn

[0103] Where M represents the bearing friction torque; n Indicates the bearing speed;

[0104] The friction torque M is:

[0105]

[0106] Where M1 represents the torque of the external load; M0 represents the torque of the viscous friction of the lubricant; f1 represents the coefficient related to the bearing structure and load; F β Indicates the magnitude and direction of force; d m Indicates the average diameter of the bearing; v represents dynamic viscosity; f0 represents the coefficient related to the bearing and lubrication method.

[0107] 1.1.2 Heat dissipation of HSMS

[0108] The internal space of HSMS is compact and the heat dissipation condition is poor. The spindle housing and air are in natural convection heat transfer mode. According to the Nusselt number criterion, the convection heat transfer coefficient (CHC) is:

[0109] h=(Nu·λ) / L

[0110] Wherein, h represents the convective heat transfer coefficient; Nu represents the Nusselt number; L represents the characteristic size; and λ represents the thermal conductivity.

[0111] 1.2 RHP design method for HSMS cooling and TIE control

[0112] The internal components of HSMS are tightly assembled in a closed and compact space. Existing cooling methods are difficult to effectively remove the internal heat of HSMS in a closed and compact space. RHP is a heat transfer device that relies on the phase change of its internal working fluid. When RHP is embedded in the shaft core of HSMS, its rotation is inevitable. Therefore, the design of RHP is based on the working principle and heat transfer characteristics of HSMS.

[0113] 1.2.1 RHP taper design

[0114] The taper is an important parameter of RHP, which determines its normal start-up, smooth operation and HTP. So the taper is designed according to the speed of HSMS. The centrifugal acceleration of the rotating heat pipe is:

[0115] a=ω 2 rsinα

[0116] Wherein, ω represents the angular velocity of rotation; r represents the minimum inner radius of the rotating heat pipe; α represents the taper of the inner surface of the rotating heat pipe;

[0117] On the one hand, the larger the taper α, the greater the axial component of the centrifugal force of the RHP on the liquid. The axial component of the centrifugal force is conducive to the return of the coolant from the condensation section to the evaporation section. On the other hand, the larger the taper, the thicker the wall of the condensation section, and the more difficult it is to condense in the condensation section. Therefore, the taper of the RHP should be neither too large nor too small.

[0118] The taper design is based on the smooth return of the working fluid at low speed, which can satisfy the smooth return of the working fluid at high speed. Figure 2 As shown in (a), when the minimum speed is 100r / min, the backflow acceleration is equivalent to the gravity acceleration, that is, a / g=1, and then the taper is approximately 1.6°. When the minimum speed is 200r / min, according to Figure 2 (b), the taper is about 0.25°. In order to coordinate the condensate return and wall thickness, the taper is designed to be 0.6°.

[0119] 1.2.2 Geometric design of RHP

[0120] In this embodiment, the RHP is designed according to the heat source distribution position, geometric constraints and the working conditions of the HSMS, such as Figure 3 As shown. According to the support span, the total length of the RHP is 335mm. The evaporation section should cover the front and rear bearings and the rotor. The length of the evaporation section is 161mm, the length of the insulation section is 13mm, and the length of the condensation section is 161mm. The outer diameter is 17mm based on the inner diameter of the shaft core, and the minimum wall thickness is 1mm to ensure that the RHP has sufficient strength. The taper is 0.6°. In order to simulate and analyze the heat dissipation performance (HDP) of the RHP, 9 monitoring points are set to monitor the temperature changes, as shown in Figure 3 Among them, Te1~Te4 are used to monitor the temperature of the evaporation section, Ta is used to monitor the temperature change of the adiabatic section, and Tc1~Tc4 are used to monitor the temperature of the condensation section.

[0121] The RHP of this embodiment is embedded in the shaft core of the HSMS through a flange connection, and then the installation and removal process is realized, such as Figure 4 The main material parameters of the designed RHP and HSMS are listed in Table 1. The materials of the shaft core, bearings and motor of HSMS are 41CrAlMo74, AISI E52100 and copper, respectively, and the materials of other parts in HSMS are HT350 and #20 steel. The material of RHP is copper, and the working fluid is R134a.

[0122] Table 1 Main material parameters of HSMS and RHP

[0123]

[0124]

[0125] 1.3 Phase transition model of RHP

[0126] 1.3.1 VOF model

[0127] Establishing the gas-liquid phase transition model of RHP cannot avoid the phase interface problem. There are many solution models in the Euler-Eulerian method, and the VOF model can determine the multiphase interface, so it is one of the most widely used solution methods. This embodiment uses the VOF model for numerical solution. The volume fractions of the gas phase and the liquid phase in RHP are defined as α V and α L In each mesh element in the computational domain, the following continuity equation is satisfied.

[0128]

[0129] Among them, ρ L represents the density of the liquid phase; ρ V represents the density of the gas phase; u Indicates dynamic viscosity; S m ,L and S m , V represent the mass source terms of liquid phase and gas phase respectively; represents the gradient operator;

[0130] For a grid cell, when the grid cell does not contain a gas phase fluid, α V = 0. When the grid cell is completely filled with gas phase fluid, α V =1. When 0<α V <1, the grid cell is located at the phase boundary. In this way, the phase interface can be determined and the changes of the gas-liquid interface can be tracked.

[0131] The momentum equation is:

[0132]

[0133] Among them, I represents a unit tensor; F CSF represents the source phase of the volume force generated by the continuous surface tension; ρ represents the gas phase density; p represents the pressure inside the tube; u T represents the velocity vector; g represents the acceleration due to gravity;

[0134] The energy equation is:

[0135]

[0136] Where ρ represents the density of the mixed phase; e represents internal energy; k represents thermal conductivity; T represents temperature; S E represents the energy conversion source term; density ρ, thermal conductivity k and dynamic viscosity u The internal energy is solved by averaging the volume of the mixed phase and using the average mass e :

[0137]

[0138] The continuity equation only calculates the volume fraction of the second phase, and the velocity field and temperature field are solved by the momentum equation, and the energy equation is solved to obtain the result of the gas-liquid mixed phase. In RHP, surface tension affects the dynamic evolution of bubble generation, growth, merging and rupture, and is also an important factor affecting bubble flow and wall wettability. Therefore, the continuum surface force (CSF) model is introduced under the action of surface tension, and the interface pressure difference is added to the momentum equation in the form of body force.

[0139]

[0140] Among them, σ ij Represents the surface tension coefficient; α i represents the volume fraction of one phase; ρ i represents the density of one of the phases; ρ j represents the density of the other phase; k i represents the surface curvature;

[0141] In the two-phase flow model, k j =-k i , Simplify the above formula to:

[0142]

[0143] Where ρ represents the volume average density;

[0144] The contact angle of the air-liquid interface is θ w , then the unit normal gradient near the wall interface is Expressed as

[0145]

[0146] in, and denote the unit normal gradient and tangential gradient near the wall, respectively.

[0147] Contact angle θ w The smaller the contact angle, the better the wettability and the easier it is to form a condensation film on the condensation wall. w is the angle between the walls of the second phase contact (1-α L ) and the tangent line of the gas-liquid interface, its value is 20°.

[0148] 1.3.2 Lee model

[0149] There are typical phase change processes in RHP, including evaporation, boiling and condensation. The Lee model can describe the heat and mass transfer of each phase, and the Lee model is easy to apply. Therefore, this embodiment uses the Lee model to simulate the mechanism of gas-liquid two-phase evaporation, boiling and condensation.

[0150] During the evaporation process:

[0151]

[0152] During the condensation process:

[0153]

[0154] The energy during evaporation and condensation is converted into:

[0155]

[0156] Among them, m LV and m VL represent the mass of liquid-gas and gas-liquid transitions respectively; T represents the temperature of the mixed phase; T sat Indicates the saturation temperature when the working fluid undergoes phase change; D Sm represents the Sauter mean diameter; ΔH represents the saturation enthalpy difference; β e and β c Respectively represent the evaporation and condensation coefficients; α V and α L Represent the volume fractions of gas phase and liquid phase respectively; ρ V and ρ L Represent the volume fraction of gas phase and liquid phase respectively; M′ represents the molar mass; ΔH represents the saturation enthalpy difference; R represents the ideal gas constant; S E represents the energy conversion source term.

[0157] β e and β c The values ​​of are the relaxation factors of the evaporation and condensation processes, which control the evaporation and condensation rates. For the numerical solutions of different working conditions, β e and β c There are different values. e and β c The value range is [0.1, 10 7 ], if β e and β c If the value of is reasonable, the best simulation result is obtained when the phase interface temperature is as close to the saturation temperature as possible, and then β e and β c The optimal value of β e = 0.1 and β c =0.1.

[0158] 1.3.3 Solution process

[0159] ANSYS FLUENT 2022R1 is used to build a gas-liquid phase change model. According to the Lee model shown in Section 2.3.2, the UDF is expressed as C++ language to define the mass source term and energy source term, and then the mass conversion and energy conversion process in the gas-liquid phase change process are simulated through FLUENT VOF. The internal connection between ANSYS FLUENT and the program is achieved by compiling UDF. Set the parameters and initialize them in Table 2, and then load the UDF source program using the fluent compilation interface. The energy source phase is hung in the mixed phase area of ​​the cellzone, the mass transfer source phase of the liquid phase is hung in the liquid phase area of ​​the fluid domain, and the mass transfer source phase of the gas phase is hung in the gas phase area of ​​the fluid domain. The schematic diagram of the two-dimensional (2D) UDF and FLUENT interface solution is shown in the figure. Figure 5 shown.

[0160] Table 2 Transient solver settings

[0161]

[0162]

[0163] 2 Heat transfer characteristics of RHP

[0164] 2.1 Basic assumptions and boundary conditions

[0165] 2.1.1 Basic assumptions

[0166] In order to reasonably simplify the mathematical model, the following basic assumptions are made when simulating evaporation and condensation phenomena:

[0167] (1) In RHP, the saturation pressure is a constant and the saturation temperature is a fixed value.

[0168] (2) Except for liquid density and surface tension coefficient, other physical parameters, including viscosity, specific heat capacity, thermal conductivity, etc., are constant.

[0169] (3) Since the pressure difference in RHP is very small, the gas phase is considered to be an incompressible fluid.

[0170] (4) The effect of shear force on the gas-liquid interface is ignored.

[0171] 3.1.2 Boundary conditions

[0172] When the speed of HSMS was 3000 / min, the HDP of RHP was simulated at three different FRs of 30%, 50% and 70%, and then the effect of FR on HDP was studied. During the simulation, the boundary condition of the evaporation section was set to a constant heat flux q, and the condensation section was in a state of convective heat transfer of cooling water. The boundary condition of the condensation section was the cooling water temperature T ∞ and the convective heat transfer coefficient h c, the heat flux density of the adiabatic section is set to zero. In order to compare the differences in the working performance of R134a working fluid under different filling rates, the heating power W and the cooling water temperature T in the simulation ∞ The boundary conditions are consistent.

[0173] The heat flux density of the evaporation section is:

[0174]

[0175] Where q is the heat flux density of the evaporation section; d is the outer diameter of the RHP; l e is the length of the heating section; W represents the heating power.

[0176] The convective heat transfer coefficient (CHTC) of the condensation section is:

[0177]

[0178] Where Q c is the heat output of the condensing section; is the average temperature of the condensing part; T ∞ is the temperature of the cooling water.

[0179] In order to save calculation time, the liquid density and surface tension of the R134a working fluid are set as variables that change with temperature, and other physical parameters are set as constants. In the Lee model, the pressure in the flow field is assumed to be constant, and the gas phase is regarded as an incompressible fluid, so the gas density of the R134a working fluid is set to a constant. To improve the stability of the simulation process, the density of the R134a working fluid ρ L and the surface tension parameter σ LV The piecewise polynomial interpolation function is used.

[0180] ρ L =15985.46 -141.2287T+0.46059T 2 -0.00051383T 3

[0181] σ LV =0.01271+2.804×10 -4 T-1.5859×10 -6 T 2 +1.991×10 -9 T 3

[0182] The boundary conditions of the simulation model are set as follows Figure 6 As shown. A constant heat flux is applied to the evaporation section. According to formula (17), the thermal power is 30W and the equivalent heat flux q is 3490W / m 2 The adiabatic section is the boundary condition for convective heat transfer, hc 700Wm -2 k -1 , zero heat flux is applied to the left and right end faces and adiabatic section of the RHP as boundary conditions.

[0183] 2.1.3 Heat transfer performance

[0184] The HTP of RHP is evaluated by the equivalent heat transfer coefficient (EHTC),

[0185]

[0186] in, is the average temperature of Te1~Te4, is the average temperature of Tc1 to Tc4,

[0187] 2.2 Analysis of simulation results

[0188] 2.2.1 Evaporation stage mechanism

[0189] Figure 7 The curve diagram of the influence of rotation acceleration on the EHTC of the evaporation section, ΔT sat for

[0190] ΔT sat =T local -T sat

[0191] Among them, T local Represents the local temperature; T sat Represents the saturation temperature; ΔT sat Indicates the saturation temperature difference.

[0192] Figure 7 It shows that the transition stage and nucleate boiling stage continue to move backward with the increase of acceleration, and the required ΔT sat The above conclusion means that more heat needs to be input to realize the transformation of the heat transfer mode inside the evaporation section from the natural convection stage to the nucleate boiling stage.

[0193] Input thermal power 30W, running time 0.1s, Figure 8 The phase change mechanism of the evaporation section of the designed RHP at speeds of 1000r / min, 2000r / min, 6000r / min and 15000r / min is given. When the speed is lower than 2000r / min, several obvious bubbles are generated inside the evaporation section, and the boiling mode is mainly nucleate boiling. When the speed increases to above 2000r / min, the nucleate boiling heat transfer mode in the evaporation section is suppressed, and the bubbles gradually disappear. Figure 7 and Figure 8 , when ΔT satWhen the ratio of a / g is the same, the greater the ratio, the earlier the heat transfer mode. This phenomenon is ultimately caused by the acceleration when the speed increases. The local saturation temperature increases with the increase in speed, and the phase change mode gradually changes from nucleate boiling heat transfer to natural convection heat transfer.

[0194] Fig. 9 This is the gas phase distribution of RHP with FR of 50%. The evaporation mechanism of the designed RHP for HSMS cooling and TIE control is different from that of ordinary heat pipes. For the built-in RHP, at 3000r / min, the bubbles in the evaporation section are small and dense. This indicates that the heat transfer method is natural convection heat transfer, which verifies the effectiveness of the gas phase distribution of the designed RHP.

[0195] like Fig. 9 As shown in the figure, RHP mainly relies on centrifugal force to drive the working fluid to reflux. In the evaporation section, the fluid is close to the RHP wall. Moreover, bubbles are gradually generated along the wall under the action of heat, and then the steam gathers in the condensation section. When the fluid cools, the fluid flows back to the evaporation point along the RHP wall under the action of centrifugal force, thereby realizing heat output from the evaporation section to the condensation section.

[0196] Fig.10 is the temperature field of the designed RHP, and the FR is 50%. The results show that it takes about 0.1s for heat to be transferred from the wall of the evaporation section to the inside, and then the temperature continues to rise to a new stage in about 1s. Since the FR of the designed RHP is relatively large and the condensation section is long, the liquid film in the evaporation section occupies a large part of the space, and the temperature distribution in the evaporation section is relatively uniform. At about 5 to 10s, it was found that the liquid vapor carried the internal heat of the HSMS, and under the action of the internal pressure difference, it began to move to the condensation section at the junction of the adiabatic section and the condensation section, indicating that the vapor of the working liquid escaped from the gas-liquid interface and moved to the condensation section. Under the action of convective heat transfer, the temperature of the wall began to drop from the wall to the inside, and the temperature inside the condensation section decreased slightly. The temperature difference between the highest temperature and the lowest temperature in the condensation part did not exceed 2°C. Moreover, after 10s, it gradually reached a stable state, and then the temperature of the condensation section remained unchanged. The results show that the temperature of the phase change interface is about 298K, which is close to the saturation temperature of R134a. This proves that β in Section 2.3.2 e = 0.1 and β c =The rationality of the value of 0.1.

[0197] 2.2.2 Effect of FR on heat transfer performance

[0198] FR is an important parameter affecting RHP HTP. Fig.11 As shown, according to the working conditions of HSMS, this example studies the HTP of RHP with different FRs. The boundary conditions are calculated using no-load conditions and a speed of 3000 r / min.

[0199] HTPs with RHPs of different FRs such as Fig.12 As shown. For each boundary condition, the EHTC of the RHP increases first and then decreases with FR. When the FR is 50%, the maximum heat transfer coefficient (MHTC) is reached, and the average temperature difference between the evaporation section and the condensation section is also smaller than that when the FRs are 30% and 70%. For different FRs, when the FR is 30%, the internal temperature difference of the RHP is the largest, and the EHTC of the RHP is the lowest. The EHTC of the RHP with a FR of 30% is about 20.58% lower than that of the RHP with a FR of 50%. This is because most of the working fluid in the RHP is concentrated in the adiabatic section or concentrated in the area with a larger inner diameter under the action of centrifugal force. When the FR of the RHP is small, the liquid film at the evaporation end becomes thinner in the area with a larger inner diameter. The thin liquid film is conducive to reducing the internal pressure of the fluid, thereby reducing the boiling point. Then the working fluid in the RHP starts quickly under a smaller heat flux density. However, due to the small thickness of the liquid film, the dry-up failure of the liquid film may occur in the process of the RHP inner cavity changing with its diameter. Once the condensed water is not replenished in time, the temperature of the RHP will be too high, and then the RHP will fail, affecting the HTP of the RHP. When the FR reaches 70%, the EHTC of the RHP is also reduced by about 16.2% compared with the RHP with FR of 50%. This is because the thickness of the liquid film in the evaporation section increases when the FR amount is large. In particular, the internal pressure of the working fluid near the wall surface increases, resulting in a high boiling point of the working fluid. Finally, it affects the smooth reflux of the working liquid.

[0200] 2.2.3 Model Accuracy Verification

[0201] In order to verify the RHP gas-liquid phase change simulation model, the average Nusselt number and Rayleigh number of the 20s evaporation section were calculated with a FR of 50%. The Nusselt number Nu was calculated according to the empirical formula, namely:

[0202] Nu=0.776Ra 0.246 (2) Where Ra is the Rayleigh number, which is used to determine whether the flow state is laminar, turbulent, or transitional. Its value is:

[0203]

[0204] Where g is the acceleration due to gravity; β is the volume expansion coefficient of the fluid; L is the characteristic length of the evaporation section; ΔT is the temperature difference between the top and bottom of the fluid; α is the thermal diffusivity of the liquid; μ is the dynamic viscosity; Pr represents the Prandtl number; and Gr represents the Grashof number.

[0205] The Nusselt numbers are listed in Table 3 and compared with the results obtained by the current model. Fig.13 As shown. Then the Nusselt number is calculated according to the current model. The Rayleigh number Ra is 10 in the current model. 5 .

[0206] Table 3 RHP model accuracy analysis

[0207]

[0208] Fluid-heat-solid interaction characteristics of 3HSMS and RHP

[0209] 3.1 Thermal boundary conditions

[0210] According to the actual working conditions of HSMS, the ambient temperature is 15 °C and the spindle speed is 3000 r / min. According to the classical heat transfer theory, the heat generation, CHTC of cooling water and air, EHTC of RHP and thermal contact resistance (TCR) are calculated, and then the boundary conditions acting on the FTSIC model of HSMS with RHP are obtained, as listed in Table 4.

[0211] Table 4 Thermal boundary conditions of HSMS at a speed of 3000 r / min

[0212]

[0213] 3.2 Model construction and meshing

[0214] The FTSIC of HSMS is simulated and analyzed to simplify its complex structure, reduce the amount of calculation and improve the calculation efficiency. The HSMS is axially symmetrically distributed, and then half of the original HSMS is used as a simulation model to reduce the amount of calculation. In addition, the effects of all water holes, screws, keyways, chamfers, bevels, fillets and other small structures on the transient FTSIC of HSMS are ignored. In addition, in order to verify the effectiveness of the proposed HSMS model with RHP, the FTSIC model of the traditional FCHSMS without RHP is constructed as a comparison model. Fig.14 (a) is a simplified model of the traditional FCHSMS without RHP. Fig.14 (b) is a simplified model of HSMS with RHP.

[0215] The simplified three-dimensional (3D) solid model was imported into ANSYS, and the 3D solid model was meshed using regular tetrahedron units. The principle of meshing is that the mesh of the solid part with a larger temperature gradient is denser. There are 96,765 units and 289,995 nodes in total. Fig.15 As shown in the figure, the mesh division is reasonable. The single simulation time is about 90 minutes.

[0216] 3.3 Simulation results

[0217] 3.3.1 Transient temperature field analysis

[0218] according to Fig.12The results show that the HTP of the RHP with FR of 50% is stronger than that of the RHP with FR of 30% and 70%. Therefore, the RHP with FR of 50% is embedded in the shaft core in the axial direction of the HSMS for FTSIC simulation, and the thermal boundary conditions are listed in the table. The boundary conditions in Table 4 are applied to the FTSIC model of the traditional FCHSMS without RHP and the HSMS with RHP, thereby verifying the effectiveness of the designed RHP on HSMS cooling and TIE control.

[0219] Fig.16 Figure 2 shows the transient temperature fields of the traditional FCHSMS without RHP and the HSMS with RHP. Fig.16 (a) shows the transient temperature field distribution of the traditional FCHSMS without RHP, and the rotor temperature is obviously as high as 75°C. Fig.16 (c) is the transient temperature distribution of the shaft core in the traditional FCHSMS without RHP, and the rotor is in contact with the shaft core through the rotor bushing. As a result, the shaft core temperature is as high as 76.8°C. The heat entering the shaft core is transferred along its axial ends, and its temperature distribution decreases along the axial direction. In the traditional FCHSMS without RHP, the bearings are another important heat source. The heat dissipation conditions of the bearings and rotors are poor, resulting in obvious heat accumulation in the traditional FCHSMS without RHP, that is, the internal electrical heat and friction heat cannot be effectively discharged through CCS. Compared with the traditional FCHSMS without RHP, in the HSMS, RHP with a FR of 50% is embedded in the shaft core, and the evaporation section of the RHP is placed horizontally near the rotor and bearings. The designed cooling chamber continuously cools the condensation section to ensure the smooth reflux of the working fluid in the RHP, thereby effectively dissipating the internal heat of the HSMS. The transient temperature field distribution of the HSMS and RHP is shown in Figure 2. Fig.16 (b) shows that compared with the conventional FCHSMS without RHP, the internal temperature of the HSMS with RHP is more uniform. For the HSMS with RHP, the temperature of the rotor is about 35°C. Fig.16 (a) and 16(b), the temperature of the HSMS with RHP is reduced by 54.5% compared with the conventional FCHSMS because the designed RHP can output the internal heat of the HSMS. In addition, the EHTC of the RHP designed according to Section 3.2.2 is 821.18 W / (m 2 ℃), RHP can dissipate the heat generated by the rotor and front and rear bearings. Therefore, the shaft core temperature is greatly reduced and the shaft core temperature field is uniform, such as Fig.16 (d) as shown.

[0220] Fig.17(a) is the overall temperature distribution of the conventional FCHSMS without RHP and the HSMS with RHP. When the maximum, minimum and average temperatures no longer change with the use time, it means that the conventional FCHSMS without RHP and the HSMS with RHP have reached a thermal equilibrium state. Fig.17 (a), the TETs of the conventional FCHSMS without RHP and the HSMS with RHP are about 1900s and 1200s, respectively. Fig.17 (b), in the conventional FCHSMS without RHP and HSMS with RHP, the TET of the shaft core is about 2000s and 800s. In summary, TET is a key factor to measure the thermal stability of HSMS, and the designed RHP can reduce the TET of HSMS, that is, the TET of HSMS with RHP is shortened by 58.33% compared with that without conventional FCHSMS. Therefore, the designed RHP can improve the thermal stability of HSMS.

[0221] 3.3.2 Transient deformation field analysis

[0222] The transient temperature distribution of the conventional FCHSMS without RHP and the HSMS with RHP in Section 4.3.1 is imported as thermal load into the transient thermal deformation field simulation, and the thermal deformation is magnified 480 times, as shown in Fig.18 as shown in .

[0223] Fig.18 (a) shows the overall axial TE of the conventional FCHSMS without RHP. The results show that there are obvious TE and bending deformations. The maximum overall axial TE of the conventional FCHSMS without RHP appears at the leftmost end of the shaft, with a value of about -19 μm. In addition, in the conventional FCHSMS without RHP, the maximum axial TE of the shaft core is about -33 μm, as shown in Figure 2. Fig.18 (c) Fig.18 As shown in (b), under the same thermal boundary conditions, the maximum overall axial TE of the HSMS with RHP is about -9.8 μm. Fig.18 As shown in (d), the maximum axial TE of the core is about -9.8 μm. In addition, for the HSMS with RHP, compared with the traditional FCHSMS without RHP, the maximum overall axial TE of the HSMS and the core is reduced by 48% and 70%, respectively. That is, the designed RHP can effectively reduce the TIE of the HSMS.

[0224] Fig.19(a) and 19(b) show the TE of the conventional FCHSMS without RHP and the HSMS with RHP. The thermal deformation range of the HSMS with RHP is [-10μm, +10μm], and the thermal deformation range of the conventional FCHSMS without RHP is [-35μm, +30μm]. It is concluded that the thermal deformation fluctuation range of the HSMS with RHP is significantly smaller than that of the conventional FCHSMS without RHP. Moreover, the thermal deformation of the HSMS with RHP is more symmetrical and stable than that of the conventional FCHSMS without RHP, which is extremely important for improving the thermal stability of the HSMS.

[0225] 4 Conclusion

[0226] Aiming at the problem that the TIE of HSMS significantly affects the geometric accuracy of complex machined parts under extreme manufacturing conditions, a RHP design method for HSMS cooling and TIE control is proposed, and a new RHP is designed according to the working principle of RHP, working conditions and geometric constraints of HSMS. Then RHP is embedded into HSMS to increase the HDP of HSMS. Then a gas-liquid two-phase flow model is established, and the evaporation mechanism of RHP at different speeds is studied. In addition, the HTP of 30%, 50% and 70% RHP is compared and analyzed. Finally, the FTSIC model of HSMS with RHP is established, and the action mechanism of the designed RHP gas-liquid two-phase flow on the FTSIC of HSMS is studied. In addition, the FTSIC simulation results of HSMS with RHP are compared with those of traditional FCHSMS without RHP, which verifies the proposed RHP design method for HSMS cooling and TIE control. The main conclusions are summarized as follows:

[0227] (1) According to the working principle, working conditions and geometric constraints of RHP, a new RHP design method for HSMS cooling and TIE control is proposed. Then the size, working fluid and FR of RHP are determined according to the heat generation, heat dissipation conditions, working conditions and geometric constraints of HSMS. The designed RHP can effectively derive the electrical heat and friction heat of HSMS, reduce the temperature and axial TE, and improve the thermal stability of HSMS. Then the designed RHP is embedded in the shaft core of HSMS.

[0228] (2) The HDP of high-speed RHP was studied, and the evaporation mechanism of gas-liquid two-phase flow of RHP was studied under the conditions of 1000r / min, 2000r / min, 6000r / min, and 15000r / min. The results show that when the speed is lower than 2000r / min, obvious bubbles are generated in the evaporation section, and the boiling mode is mainly nucleate boiling. When it is higher than 2000r / min, the nucleate boiling heat transfer mode in the evaporation section is suppressed, the bubbles gradually disappear, and the boiling mode changes from nucleate boiling to natural convection heat transfer.

[0229] (3) The effect of FR on the HDP of the designed RHP was studied. The HDP of the RHP with FR of 50% was higher than that of the RHP with FRs of 30% and 70%, and its value was 821.18W / (m 2 ℃). The internal temperature difference of the RHP at FR 30% and 70% is larger than that of the RHP at FR 50%. When FR is 30%, EHTC is about 20.58% lower than that at FR 50%. When FR is 70%, EHTC is also reduced by 16.2% compared with that at FR 50%.

[0230] (4) The FTSIC model of the HSMS with RHP and the conventional FCHSMS without RHP was established. The results show that the design of RHP reduces the maximum overall temperature (MOT) of the HSMS from 74.8℃ to 35℃, and the design of RHP reduces the TET from 1900s to 1200s. In other words, compared with the FCHSMS without RHP, the MOT and TET of the HSMS with RHP are reduced by 53.2% and 36.8%, respectively. More importantly, the TE of the HSMS with RHP is in the range of [-10μm, +10μm], while the TE of the conventional FCHSMS without RHP is in the range of [-35μm, +30μm].

[0231] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for simulating the flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe, characterized in that: The steps include: Step 1: Design the structural parameters of the rotary heat pipe according to the heating and heat dissipation conditions and geometric constraints of the high-speed electric spindle, and place the designed rotary heat pipe into the high-speed electric spindle; Step 2: Establish a gas-liquid two-phase flow phase change model of the rotating heat pipe and perform fluid simulation analysis on the rotating heat pipe; Step 3: Establish a fluid-heat-solid coupling characteristic model of the high-speed electric spindle with a rotating heat pipe, perform transient heat transfer analysis on the high-speed electric spindle and obtain the temperature field, perform transient deformation analysis on the high-speed electric spindle and obtain the deformation field; In the step 2, a gas-liquid phase change model of a rotating heat pipe is constructed using ANSYS FLUENT, a VOF model is used to simulate the mass conversion and energy conversion process during the gas-liquid phase change, and a Lee model is used to simulate the mechanism of gas-liquid two-phase evaporation, boiling and condensation; The method of using the VOF model to simulate the mass conversion and energy conversion process during the gas-liquid phase change is: The volume fractions of the gas phase and liquid phase in the rotating heat pipe are defined as α V and α L , in each grid cell in the computational domain, the following continuity equation is satisfied: Among them, ρ L represents the density of the liquid phase; ρ V represents the density of the gas phase; u Indicates dynamic viscosity; S m ,L and S m , V represent the mass source terms of liquid phase and gas phase respectively; represents the gradient operator; The momentum equation is: Among them, I represents a unit tensor; F CSF represents the source phase of the volume force generated by the continuous surface tension; ρ represents the density of the mixed phase; p represents the pressure inside the tube; u T The velocity vector g represents the acceleration due to gravity; The energy equation is: Where e represents internal energy; k represents thermal conductivity; T represents temperature; S E represents the energy conversion source term; Density ρ, thermal conductivity k and dynamic viscosity u The internal energy e is solved by averaging the volume of the mixed phase and using the average mass: Under the action of surface tension, the continuous medium surface tension model is introduced, and the interface pressure difference is added to the momentum equation in the form of volume force; in the two-phase flow model, k j =-k i , but: Among them, σ ij Represents the surface tension coefficient; α i represents the volume fraction of one phase; ρ represents the volume average density; ρ i represents the density of one of the phases; ρ j Indicates the density of the other phase; k i represents the surface curvature; The contact angle of the air-liquid interface is θ w , then the unit normal gradient near the wall interface is It is expressed as: in, and denote the unit normal gradient and tangential gradient near the wall, respectively; The method of using Lee model to simulate the mechanism of gas-liquid two-phase evaporation, boiling and condensation is: During the evaporation process: During the condensation process: The energy during evaporation and condensation is converted into: Among them, m LV and m VL represent the mass transitions of liquid-gas and gas-liquid, respectively; T represents the temperature of the mixed phase; T sat Indicates the saturation temperature when the working fluid undergoes phase change; D Sm represents the Sauter mean diameter; ΔH represents the saturation enthalpy difference; β e and β c Respectively represent the evaporation and condensation coefficients; α V and α L represent the volume fractions of gas phase and liquid phase respectively; ρ V and ρ L denote the density of gas phase and liquid phase respectively; M' represents molar mass; R represents ideal gas constant; S E represents the energy conversion source term.

2. The method for simulating flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe according to claim 1, characterized in that: In the step 1, the high-speed electric spindle is mainly provided with two heat sources when working, namely the built-in motor and the front and rear bearing groups; The power loss of the motor is: P.S s JP e (1-η) Among them, P s Indicates power loss; P e represents the rated power; η represents the motor efficiency; Under high-speed conditions, one-third of the heat is distributed on the rotor and two-thirds of the heat is distributed on the stator, then: Among them, q rotor represents the heat distributed on the rotor; q stator Represents the heat on the stator; V rotor Indicates the volume of the rotor; V stator represents the volume of the rotor; The friction torque generated by the rolling bearing causes friction heat Q, which is: Q=1.047×10 -4 ×Mn Wherein, M represents the bearing friction torque; n represents the bearing speed; The friction torque M is: Where M1 represents the torque of the external load; M0 represents the torque of the viscous friction of the lubricant; f1 represents the coefficient related to the bearing structure and load; F β Indicates the magnitude and direction of force; d m represents the average diameter of the bearing; v represents the dynamic viscosity; f0 represents the coefficient related to the bearing and lubrication method.

3. The method for simulating flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe according to claim 1, characterized in that: In the step 1, the internal space of the high-speed electric spindle is compact, the heat dissipation condition is poor, and the spindle housing and the air are in a natural convection heat transfer mode; according to the Nusselt number criterion, the convection heat transfer coefficient is: h=(Nu·λ) / L Wherein, h represents the convective heat transfer coefficient; Nu represents the Nusselt number; L represents the characteristic size; and λ represents the thermal conductivity.

4. The method for simulating flow-heat-solid coupling characteristics of a high-speed electric spindle based on a rotating heat pipe according to claim 1, characterized in that: In step 1, the centrifugal acceleration of the rotating heat pipe is: a = ω 2 rsina In a rotating heat pipe, the reflux acceleration a of the fluid is equal to the acceleration of gravity, that is, a / g=1; Wherein, ω represents the angular velocity of rotation; r represents the minimum inner radius of the rotating heat pipe; α represents the taper of the inner surface of the rotating heat pipe; The length of the rotating heat pipe is determined according to the geometric constraints of the high-speed electric spindle and the distribution position of the heat source, and the evaporation section of the rotating heat pipe should cover the motor rotor and the front and rear bearings.

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