Vertical machining center main shaft bearing system, closed-loop two-phase pulsating heat pipe and design method thereof

Abstract

The invention discloses a design method of a closed-loop two-phase pulsating heat pipe, which comprises the following steps of: 1, determining geometric parameters: determining the inner diameter size of the closed-loop two-phase pulsating heat pipe according to a selected working fluid; 2, multi-phase flow behavior simulation, wherein the gas-liquid phase change behavior and the temperature field of the closed-loop two-phase pulsating heat pipe are obtained through simulation; thirdly, experimental research is conducted, wherein the starting performance and the steady-state heat transfer characteristic of the closed-loop two-phase pulsating heat pipe are obtained through experimental analysis; and 4, establishing a response surface model: establishing the correlation between the heat transfer performance and the design and operation parameters of the closed-loop two-phase pulsating heat pipe through the response surface model, and obtaining the influence of the working fluid, the number of turns, the cooling air flow and the heat flux density on the effective heat transfer coefficient of the closed-loop two-phase pulsating heat pipe. And determining design parameters of the closed-loop two-phase pulsating heat pipe including the number of turns, the cooling air flow and the heat flux density. The invention further discloses a closed-loop two-phase pulsating heat pipe and a vertical machining center spindle bearing system.

Description

Technical Field

[0001] The invention belongs to the technical field of thermal error control, and specifically relates to a spindle bearing system of a vertical machining center, a closed-loop two-phase pulsating heat pipe and a design method thereof. Background Art

[0002] High machining accuracy of vertical machining center (VMC) is essential to ensure the geometric accuracy of machined parts. As one of the core functional components of VMC, the spindle bearing system (SBS) is an important heat source in VMC, resulting in significant thermal error (TE). The TE of SBS is a key factor affecting the machining accuracy and efficiency of the entire VMC. Specifically, during high-speed machining, the heat generated by the friction between the motor and the bearing is transferred to the SBS through heat conduction, resulting in uneven temperature distribution and TE. Due to this TE, the relative spatial position error between the tool and the workpiece changes, which has an adverse effect on the machining accuracy of the entire VMC. Therefore, in order to improve the machining accuracy of VMC, the TE of SBS in VMC should be reduced.

[0003] At present, error compensation and temperature rise reduction are two common methods for controlling TE. Error compensation strategies mainly rely on machine learning and deep learning techniques, using artificial neural networks to predict spindle TE. The prediction results are then fed back to the computer numerical control system for real-time TE compensation. However, as a post-compensation method, error compensation has a significant delay, especially in the case of poor thermal stability, which makes it difficult to meet high-precision machining requirements. Direct temperature rise reduction is a more effective TE control strategy. Reducing temperature rise usually involves using a circulating cooling system to dissipate excess internal heat inside the VMC. However, while cooling water jackets can effectively reduce spindle temperature and TE, they also have limitations. Due to single-phase heat transfer, their heat transfer capacity is limited, often resulting in uneven temperature distribution and excessive temperature gradients. In addition, circulating cooling systems are prone to coolant leakage. For the SBS of VMC, the bearing pair and motor are the main heat sources, and they are usually enclosed in a relatively closed space. Existing cooling methods do not dissipate heat well in such a compact space. Therefore, it is necessary to study efficient heat dissipation methods for enclosed compact spaces.

[0004] The heat transfer performance of a two-phase heat transfer device is much higher than that of a single-phase heat transfer device because the absorption and release of latent heat during the phase change process significantly improves the heat transfer efficiency. As a promising two-phase passive heat transfer device, the two-phase pulsating heat pipe (TPPHP) has attracted widespread attention due to its unique working mechanism and excellent heat transfer performance. The TPPHP consists of a repeatedly bent capillary filled with a working fluid. In the evaporation section, the heat source causes the fluid to evaporate to form bubbles. In the condensation section, the heat source causes the vapor to condense into liquid. Through the self-excited oscillating flow of the liquid part and the vapor part, heat is transferred from the evaporation part to the condensation part. Based on the phase change and circulation mechanism of the pulsating heat pipe, its heat transfer efficiency is much higher than that of other heat pipes. In addition, compared with other types of heat pipes (such as sintered core heat pipes and loop heat pipes), the TPPHP has the advantages of simple structure, light weight, good flexibility, and no need for an internal capillary wick structure. The pulsating heat pipe (PHP) can use low-cost commercial pipes and does not require special processing, so its manufacturing cost is lower than that of other two-phase heat transfer devices. Therefore, the application of TPPHP to SBS in VMC is expected to achieve more uniform temperature distribution, reduce thermal deformation (TD) of SBS, and provide a promising solution for practical applications. Closed-loop TPPHPs (CLTPPHPs) exhibit significant HTP due to strong fluid circulation. CLTPPHP exhibits excellent heat transfer capability with a simple and compact structure, making it a promising solution to address the heat dissipation challenges of VMC SBS. Summary of the invention

[0005] In view of this, an object of the present invention is to provide a vertical machining center spindle bearing system, a closed-loop two-phase pulsating heat pipe and a design method thereof.

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

[0007] The present invention first proposes a design method for a closed-loop two-phase pulsating heat pipe, comprising the following steps:

[0008] Step 1: Determine the geometric parameters

[0009] According to the cooling jacket size of the main shaft bearing system, the geometric size of the closed-loop two-phase pulsating heat pipe is determined; according to the selected working fluid, the inner diameter size of the closed-loop two-phase pulsating heat pipe is determined;

[0010] Step 2: Multiphase flow behavior simulation

[0011] The multiphase flow behavior of the closed-loop two-phase pulsating heat pipe is simulated to obtain the gas-liquid phase change behavior and temperature field of the closed-loop two-phase pulsating heat pipe;

[0012] Step 3: Experimental research

[0013] The startup performance and steady-state heat transfer characteristics of the closed-loop two-phase pulsating heat pipe were obtained through experimental analysis.

[0014] Step 4: Build a response surface model

[0015] The correlation between the heat transfer performance and the design and operating parameters of the closed-loop two-phase pulsating heat pipe was established through the response surface model. The influence of working fluid, number of turns N, cooling air flow CAFR and heat flux density q on the effective heat transfer coefficient of the closed-loop two-phase pulsating heat pipe was obtained, and the design parameters of the closed-loop two-phase pulsating heat pipe including the number of turns N, cooling air flow CAFR and heat flux density q were determined.

[0016] Furthermore, in step 1, the method for determining the inner diameter size of the closed-loop two-phase pulsating heat pipe according to the working fluid is:

[0017]

[0018] Where: d in is the inner diameter of the closed-loop two-phase pulsating heat pipe; ρ L and ρ V are the liquid density and gas phase density respectively; g is the gravitational acceleration; σ is the surface tension.

[0019] Furthermore, in step 2, the method steps for simulating the multiphase flow behavior of the closed-loop two-phase pulsating heat pipe are as follows:

[0020] 21) Construct the control equations: Use the fluid volume model to simulate the phase change in the two-phase pulsating heat pipe. The fluid volume model is used to track the gas-liquid interface through the phase volume fraction in the element and determine the flow changes of the gas and liquid phases in each element; Use the Lee model to define the phase change process and simulate the energy and mass transfer during the phase change process inside the two-phase pulsating heat pipe;

[0021] 22) Solution settings and boundary conditions

[0022] Set the working angle and filling rate of the two-phase pulsating heat pipe; set the gravity acceleration; set the pipe wall material; set the liquid relative heat capacity and surface tension coefficient of the working liquid; set the gas relative heat capacity of the working liquid; set the target saturation temperature and saturation pressure of the working liquid;

[0023] The adiabatic section is regarded as an adiabatic wall. During the simulation, the boundary conditions of the heat flux density of the evaporation section and the convection coefficient of the condensation section are kept consistent.

[0024] 23) Grid division

[0025] Adopt unstructured grids to closely align the unstructured grids with the changes of the working fluid, provide high interface resolution, and accurately capture dynamic processes such as bubble generation, growth, movement, and liquid reflux; add boundary layer grids near the tube wall to accurately capture the formation of thin liquid films near the tube wall and the generation and evolution of small bubbles;

[0026] 24) Simulation

[0027] The multiphase flow behavior of the closed-loop two-phase pulsating heat pipe is simulated, and the influence of the number of turns of the closed-loop two-phase pulsating heat pipe on the start-up time and heat transfer performance is obtained.

[0028] Furthermore, in step 21), the method of simulating the phase change in the two-phase pulsating heat pipe using the fluid volume model is as follows: in the closed-loop two-phase pulsating heat pipe, each element in the calculation domain satisfies the condition:

[0029] α V +α L =1

[0030] Where: α L and α V are the volume fractions of liquid and gas phase, respectively;

[0031] The continuity equation is:

[0032]

[0033] Where: S m,L represents the mass source term of the liquid phase; S m,V represents the gas phase mass source term; represents the gradient operator;

[0034] The momentum equation is:

[0035]

[0036] Where: ρ is the density of the mixed phase; u is the kinetic viscosity coefficient; for……; is...; I is the equivalent tensor; F CSF is the volume force source term generated by surface tension;

[0037] The energy equation is:

[0038]

[0039] Where: e is internal energy; k is thermal conductivity; is the maximum temperature difference; S E As a source of energy;

[0040] The volume average method is used to solve the thermophysical properties of the mixed phase and we get:

[0041] ρ=α L ρ L +(1-α L )ρ V

[0042] μ=α Lμ L +(1-α L )μ V

[0043] k=α L k L +(1-α L ) V

[0044] Where: ρ is the density of the mixed phase; ρ L and ρ V are the liquid phase density and the gas phase density respectively;

[0045] μ is the dynamic viscosity of the mixed phase; μ L and μ V are the liquid phase dynamic viscosity and the gas phase dynamic viscosity respectively;

[0046] k is the thermal conductivity of the mixed phase; k L and k V are the liquid phase thermal conductivity and the gas phase thermal conductivity respectively;

[0047] Solving for the internal energy using the mass average method yields:

[0048]

[0049] Where: e is internal energy; e L and e V are the internal energies of the liquid phase and the gas phase, respectively.

[0050] Furthermore, in step 21), the method of simulating the energy and mass transfer in the phase change process inside the two-phase pulsating heat pipe using the Lee model is:

[0051] During the evaporation process:

[0052]

[0053] Where: m L represents the mass conversion from liquid phase to gas phase; β e is the evaporation coefficient; α L Liquid volume fraction; ρ L and ρ V are the liquid phase density and gas phase density respectively; T is the temperature of the mixed phase; T sat is the saturation temperature; D Sm is the Sauter mean diameter; M is the molar mass; R is the ideal gas constant; ΔH is the saturation temperature difference;

[0054] During the condensation process:

[0055]

[0056] Where: mV Indicates the mass conversion from gas phase to liquid phase; β c is the condensation coefficient; α V is the gas phase volume fraction;

[0057] Ensure dynamic balance of mass transfer rate during phase change:

[0058]

[0059] Where: l and ρ v are the liquid phase density and gas phase density, respectively.

[0060] Further, in step 22), the heat flux density of the evaporation section is:

[0061]

[0062] Where: q is the heat flux density; P is the heating power of the evaporation section; d is the diameter of the pulsating heat pipe; l e is the length of the evaporation section;

[0063] The convection heat transfer coefficient is:

[0064]

[0065] Where: h is the convective heat transfer coefficient; h eff is the effective heat transfer coefficient; and are the temperature differences between the evaporator and condenser parts respectively.

[0066] Furthermore, in step 4, a polynomial with an explicit expression is constructed to approximate the complex implicit relationship between the design parameters and the target variable:

[0067]

[0068] Where: Y is the predicted response value; x i and x j are the i-th and j-th influencing factors respectively; k is the number of influencing factors; β0 is the intercept coefficient; β i is the linear coefficient; β ij is the interaction coefficient; β ii is the quadratic coefficient; ε is the error term.

[0069] Furthermore, in step 4, the Prandtl number Pr is selected to convert the type of working fluid into a quantifiable value:

[0070]

[0071] Where: Pr is the Prandtl number; c pis the specific heat capacity; μ is the dynamic viscosity; k is the thermal conductivity.

[0072] The present invention also proposes a closed-loop two-phase pulsating heat pipe, which is designed using the design method of the closed-loop two-phase pulsating heat pipe as described above.

[0073] The present invention also proposes a spindle bearing system for a vertical machining center, including a spindle and a cooling water jacket mounted outside the spindle, a front bearing and a rear bearing are respectively provided between the two ends of the cooling water jacket and the spindle, a sleeve is provided between the front bearing and the rear shaft layer, and the closed-loop two-phase pulsating heat pipe as described above is installed on the inner wall of the cooling water jacket.

[0074] The beneficial effects of the present invention are:

[0075] The spindle bearing system of a vertical machining center undergoes significant thermal expansion due to insufficient heat dissipation, resulting in machining errors and workpiece geometry deviations. Conventional cooling methods cannot effectively dissipate heat and control thermal errors. In order to solve this problem, the present invention proposes a design method for a closed-loop two-phase pulsating heat pipe, and the designed closed-loop two-phase pulsating heat pipe is used to dissipate internal heat and adjust the thermal deformation of the spindle bearing system of a vertical machining center. In the design process of the closed-loop two-phase pulsating heat pipe, a gas-liquid phase change model is established to verify the heat dissipation performance and phase change behavior of heat pipes with different turning configurations. The effects of design and operating parameters on the performance of the heat pipe are experimentally studied. In addition, response surface analysis is used to reveal the relationship between the convective heat transfer coefficient and the design and operating parameters, and the design parameters of the closed-loop two-phase pulsating heat pipe including the number of turns N, the cooling air flow CAFR and the heat flux density q are determined. The closed-loop two-phase pulsating heat pipe designed by the present invention is embedded in the spindle bearing system of a vertical machining center. The application of the closed-loop two-phase pulsating heat pipe in the heat dissipation and thermal deformation control of the spindle of the vertical machining center significantly improves the machining accuracy, providing a new solution for precision machining. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] 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:

[0077] Figure 1 It is the main flow field framework diagram of the design method of the closed-loop two-phase pulsating heat pipe of the present invention; Figure 2 for the CLTPPHP structure and measurement points;

[0078] Figure 3 Schematic diagram of CLTPPHP boundary condition mesh division; Figure 4 is the initial water distribution of each CLTPPHP; Figure 5 is the gas-liquid volume fraction contour;

[0079] Figure 6 is the temperature distribution; Figure 7This is a schematic diagram of the CLTPPHP experimental platform; Figure 8 is the startup characteristic of CLTPPHP in the experiment;

[0080] Fig. 9 The simulated pressure distribution contours at 21s, 23.5s and 25s; Fig.10 is the thermal resistance of CLTPPHP in the experiment;

[0081] Fig.11 is the thermal resistance of CLTPPHP in the experiment; Fig.12 Schematic diagram of temperature measurement points in simulation and experiment;

[0082] Fig.13 is the response surface model; (a) h eff =(N,Pr); (b)h eff =(q,Pr); (c)h eff =(N,q) response surface model;

[0083] Fig.14 SBS for the vertical machining center VTM260; Fig.15 For thermal behavior measurements; Fig.16 To simulate the transient temperature field; Fig.17 To simulate the temperature field;

[0084] Fig.18 are the experimental and simulated temperatures of the front and rear bearings; Fig.19 To simulate the transient thermal deformation field; Fig. 20 To simulate the transient thermal deformation curve;

[0085] Fig.21 The experimental and simulated axial thermal elongation of SC; Fig. 22 This is the actual processing drawing; Fig.23 To process workpieces;

[0086] Fig.24 is the saturated vapor pressure curve; Fig.25 is the wavelet power spectrum; Fig.26 is the physical schematic diagram of the experimental setup; Fig. 27 It is the CLTPPHP prototype; Fig.28 Schematic diagram of CAFR measurement points.

[0087] Parameter Description:

[0088] DETAILED DESCRIPTION

[0089] 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.

[0090] like Figure 1 As shown, the design method of the closed-loop two-phase pulsating heat pipe in this embodiment includes the following steps:

[0091] Step 1: Determine the geometric parameters

[0092] The geometrical dimensions of the closed-loop two-phase pulsating heat pipe are determined according to the cooling jacket dimensions of the main shaft bearing system; the inner diameter dimensions of the closed-loop two-phase pulsating heat pipe are determined according to the selected working fluid.

[0093] Step 2: Multiphase flow behavior simulation

[0094] The multiphase flow behavior of the closed-loop two-phase pulsating heat pipe is simulated to obtain the gas-liquid phase change behavior and temperature field of the closed-loop two-phase pulsating heat pipe.

[0095] The method steps for simulating the multiphase flow behavior of a closed-loop two-phase pulsating heat pipe are as follows:

[0096] 21) Construct the control equations: Use the fluid volume model to simulate the phase change in the two-phase pulsating heat pipe. The fluid volume model is used to track the gas-liquid interface through the phase volume fraction in the element and determine the flow changes of the gas and liquid phases in each element; Use the Lee model to define the phase change process and simulate the energy and mass transfer during the phase change process inside the two-phase pulsating heat pipe;

[0097] 22) Solution settings and boundary conditions

[0098] Set the working angle and filling rate of the two-phase pulsating heat pipe; set the gravity acceleration; set the pipe wall material; set the liquid relative heat capacity and surface tension coefficient of the working liquid; set the gas relative heat capacity of the working liquid; set the target saturation temperature and saturation pressure of the working liquid;

[0099] The adiabatic section is regarded as an adiabatic wall. During the simulation, the boundary conditions of the heat flux density of the evaporation section and the convection coefficient of the condensation section are kept consistent.

[0100] 23) Grid division

[0101] Adopt unstructured grids to closely align the unstructured grids with the changes of the working fluid, provide high interface resolution, and accurately capture dynamic processes such as bubble generation, growth, movement, and liquid reflux; add boundary layer grids near the tube wall to accurately capture the formation of thin liquid films near the tube wall and the generation and evolution of small bubbles;

[0102] 24) Simulation

[0103] The multiphase flow behavior of the closed-loop two-phase pulsating heat pipe is simulated, and the influence of the number of turns of the closed-loop two-phase pulsating heat pipe on the start-up time and heat transfer performance is obtained.

[0104] Step 3: Experimental research

[0105] The startup performance and steady-state heat transfer characteristics of a closed-loop two-phase pulsating heat pipe were obtained through experimental analysis

[0106] Step 4: Build a response surface model

[0107] The correlation between the heat transfer performance and the design and operating parameters of the closed-loop two-phase pulsating heat pipe was established through the response surface model. The influence of working fluid, number of turns N, cooling air flow CAFR and heat flux density q on the effective heat transfer coefficient of the closed-loop two-phase pulsating heat pipe was obtained, and the design parameters of the closed-loop two-phase pulsating heat pipe including the number of turns N, cooling air flow CAFR and heat flux density q were determined.

[0108] This design example also proposes a closed-loop two-phase pulsating heat pipe, which is designed using the design method of the closed-loop two-phase pulsating heat pipe as described above.

[0109] This embodiment also proposes a spindle bearing system for a vertical machining center, including a spindle and a cooling water jacket mounted outside the spindle, a front bearing and a rear bearing are respectively provided between the two ends of the cooling water jacket and the spindle, a sleeve is provided between the front bearing and the rear shaft layer, and a closed-loop two-phase pulsating heat pipe as described above is installed on the inner wall of the cooling water jacket.

[0110] The specific implementation methods and technical effects of the present invention are described in detail below with reference to specific examples.

[0111] 1. CLTPPHP design and multi-phase flow behavior

[0112] 1.1 Geometric parameters of CLTPPHP

[0113] This embodiment aims to explore the application of CLTPPHP in the VMC VTM260 vertical SBS to output internal heat and reduce temperature rise and TD. Through the phase change and pulsation of the internal working fluid, CLTPPHP can achieve efficient heat transfer. In order to study the effects of different working fluids on CLTPPHP HTP, the following typical working fluids were selected in this embodiment, including methanol, anhydrous ethanol and distilled water. These liquids have excellent thermophysical properties, including low viscosity, high latent heat of vaporization and high specific heat capacity, and ensure safety, thermal stability and cost-effectiveness, making them ideal for evaluating CLTPPHP HTP. In CLTPPHP, the working fluid flows mainly in the form of steam and liquid. Therefore, the pipe diameter directly determines whether CLTPPHP can establish a self-excited oscillating flow. If the diameter of CLTPPHP is too large, the working fluid cannot form an effective gas-liquid distribution. However, if the inner diameter is too small, the frictional resistance to the flow of steam and liquid will increase, thereby hindering the normal startup of CLTPPHP. Many experimental studies have found that PHP can operate normally when the pipe diameter is within the following range. In this embodiment, the method for determining the inner diameter size of the closed-loop two-phase pulsating heat pipe according to the working fluid is:

[0114]

[0115] Where: d in is the inner diameter of the closed-loop two-phase pulsating heat pipe; ρ L and ρ V are the liquid density and gas phase density respectively; g is the gravitational acceleration; σ is the surface tension.

[0116] According to the above formula, the maximum diameters of the CLTPPHP for methanol, distilled water, and anhydrous ethanol are calculated to be 4 mm, 5.4 mm, and 3.4 mm, respectively. Therefore, in this embodiment, the inner diameter of the CLTPPHP is selected to be 3 mm, the wall thickness is 0.5 mm, and the sample is made of a round copper tube. The number of turns (N) in the CLTPPHP will produce a pressure difference, affecting the internal fluid flow, and thus affecting its HTP and operating performance. Therefore, it is crucial to study how the number of turns affects the HTP of the designed CLTPPHP. Considering that most PHPs used in processing applications usually adopt a single-loop design, the number of turns in this embodiment is selected to start from 1 to ensure consistency with actual applications. Taking into account the experimental and economic costs, a large number of turns increases the complexity of the experimental study. Therefore, in order to simplify the experimental design, the number of turns of 1, 2, and 3 were finally selected to study the HTP and operating performance. In this embodiment, the filling rate of the CLTPPHP is determined to be 60%. The final structure of the designed CLTPPHP is as shown Figure 2 The outer radius of the bend is 12.5 mm and the inner radius is 7.5 mm.

[0117] 1.2. CLTPPHP multiphase flow behavior simulation

[0118] 1.2.1 Control equations

[0119] The phase changes in CLTPPHP are studied by numerical solution using the volume of fluid (VOF) model. The VOF model is used to track the vapor-liquid interface through the phase volume fraction within the element and determine the flow changes associated with the vapor and liquid phases in each element. In CLTPPHP, in a closed-loop two-phase pulsating heat pipe, each element in the computational domain satisfies the condition:

[0120] α V +α L =1

[0121] Where: α L and α V are the volume fractions of liquid and gas phase, respectively.

[0122] The continuity equation is:

[0123]

[0124] Where: S m,L represents the mass source term of the liquid phase; S m,V represents the gas phase mass source term; Represents the gradient operator.

[0125] In any given element, if α L = 0, the element does not contain liquid fluid. L =1, the element is completely occupied by the liquid phase. If 0<α L <1, the element is at a phase interface. This allows the phase interface to be determined and the evolution of the gas-liquid interface to be tracked over time.

[0126] The momentum equation is:

[0127]

[0128] Where: ρ is the density of the mixed phase; u is the kinetic viscosity coefficient; is the gradient of the pressure field; is the velocity field gradient; I is the equivalent tensor; F CSF is the volume force source term generated by surface tension;

[0129] The energy equation is:

[0130]

[0131] Where: e is internal energy; k is thermal conductivity; is the maximum temperature difference; S E As a source of energy;

[0132] The volume average method is used to solve the thermophysical properties of the mixed phase and we get:

[0133] ρ=α L ρ L +(1-α L )ρ V

[0134] μ=α L μ L +(1-α L )μ V

[0135] k=α L k L +(1-α L ) V

[0136] Where: ρ is the density of the mixed phase; ρ L and ρ v are the liquid phase density and gas phase density respectively; μ is the dynamic viscosity of the mixed phase; μ L and μ V are the liquid viscosity and gas viscosity respectively; k is the thermal conductivity of the mixed phase; k L and k V are the liquid phase thermal conductivity and the gas phase thermal conductivity, respectively.

[0137] Solving for the internal energy using the mass average method yields:

[0138]

[0139] Where: e is internal energy; e L and e V are the internal energies of the liquid phase and the gas phase, respectively.

[0140] The continuity equation provides the volume fraction of the second phase, while the volume fraction of the first phase is given by α L =1-α V The velocity field and temperature field are obtained by solving the momentum and energy equations. The Lee model represents the heat and mass exchange that can occur at the phase interface and in each phase, which allows comprehensive simulation of fluid dynamics and heat transfer phenomena in PHP while considering the interaction between liquid and gas phases. Therefore, the Lee model is used to simulate the energy and mass transfer during the phase change process inside the designed CLTPPHP by:

[0141] During the evaporation process:

[0142]

[0143] Where: m L represents the mass conversion from liquid phase to gas phase; βe is the evaporation coefficient; α L Liquid volume fraction; ρ v is the gas phase density; T is the temperature of the mixed phase; T sat is the saturation temperature; D Sm is the Sauter mean diameter; M is the molar mass; R is the ideal gas constant; ΔH is the saturation temperature difference; ρ L and ρ V are the liquid phase density and the gas phase density respectively;

[0144] During the condensation process:

[0145]

[0146] Where: m V Indicates the mass conversion from gas phase to liquid phase; β c is the condensation coefficient; α V is the gas phase volume fraction;

[0147] In fact, β e and β c Represent the evaporation coefficient and condensation coefficient respectively. e and β c The larger the value of , the faster the evaporation and condensation rates. e and β c If the value of is too low, the liquid-vapor interface temperature will deviate from the saturation temperature, thus reducing the accuracy of the numerical simulation. e and β c Too high a value of will lead to difficulty in converging the control equation. In the prior art, β e and β c They are usually chosen in the range of [0.1, 100], and their values ​​are usually set equal. However, since evaporation and condensation in the PHP thermal equilibrium process are transient processes, a fixed value may lead to an imbalance in the mass transfer rate during the phase change process. In this example, β e Set to 0.1, which is a suitable evaporation rate for this example and a classic value for water evaporation. c is calculated as the density of the liquid in the element ρ l and steam density ρ v The ratio of β c The value of changes dynamically according to the following formula to ensure the dynamic balance of mass transfer rate during phase change:

[0148]

[0149] Where: l and ρ v are the liquid phase density and gas phase density, respectively.

[0150] 1.2.2 Solution settings and boundary conditions

[0151] For the established physical model, computational fluid dynamics (CFD) method is used for unsteady state solution. Considering that the designed CLTPPHP is vertically oriented, the gravity effect is taken into account, and the gravity acceleration in the Y direction is set to -9.81m / s 2 The wall of the designed CLTPPHP is set to copper, liquid is defined as the primary phase, and vapor is defined as the secondary phase. The specific heat and saturation temperature of the liquid and vapor phases are defined by using user defined functions (UDFs). Based on the Lee model theory shown in Section 1.2.1, the phase change process is defined, and the energy and mass source terms are specified through UDFs. The surface tension coefficient is set to a constant of 0.072N / m. The calculation time step is set to 10 -4 s, the convergence criterion of the residual is set to 10 -4 .

[0152] according to Figure 3 Set the boundary conditions of the simulation model. The adiabatic section is regarded as an ideal adiabatic wall because the heat transfer between the air and this section is negligible compared to the internal phase change heat transfer, so a zero heat flux density boundary condition is applied. In order to study the performance difference of CLTPPHP under different turns, the boundary conditions of the heat flux density of the evaporation section and the convection coefficient of the condensation section are kept consistent throughout the simulation. The heat flux density of the evaporation section is:

[0153]

[0154] Where: q is the heat flux density; P is the heating power applied to the evaporation section, which is 15W, 30W and 45W when N=1, N=2 and N=3 respectively; d is the diameter of the pulsating heat pipe; the heat flux density of the evaporation section during the entire simulation process is 7528W / m2.

[0155] The condensation section is cooled by low temperature cooling air, the boundary condition is convection heat transfer, and the convection heat transfer coefficient is:

[0156]

[0157] Where: q is the heat flux density, calculated as 7528W / m 2 ; h is the convection heat transfer coefficient; h eff is the effective heat transfer coefficient; and are the temperature differences between the evaporator and condenser, respectively. For the simulation setup, h is 465W / (m 2 ·K).

[0158] The target saturation temperature is set to 308.15K. Fig.24As shown in the figure, at the saturation temperature of 308.15K, the corresponding saturation pressures of water, anhydrous ethanol and methanol are P sat-D , P sat-A and P sat-M .P sat-D , P sat-A and P sat-M The calculated values ​​are 5.60 kPa, 14.20 kPa, and 26.93 kPa, respectively. Therefore, in the simulation, when the working fluid is water, anhydrous ethanol, and methanol, the working pressure of the heat pipe is set to 5.60 kPa, 14.20 kPa, and 26.93 kPa, respectively. This ensures that the working fluid can be transformed from liquid to vapor in the evaporation section and condensed in the condensation section, such as Figure 4 The figure shows the initial water distribution diagram. 1.2.4 Analysis of simulation results

[0159] (1) Gas-liquid phase transition behavior of CLTPPHP

[0160] Figure 5 Shown at 7528W / m 2Phase change distribution of CLTPPHPs with different numbers of turns over time under heat flux density of . Specifically, the red area indicates that the gas phase volume fraction is 1, which means that the area is completely vapor. The blue area indicates that the gas phase volume fraction is 0, which means that the area contains only liquid. Other color areas represent gas-liquid mixed phases, with gas-liquid phase volume fractions between 0 and 1. Shades close to red indicate higher vapor volume in the area, and shades close to blue indicate higher liquid volume. Moments A to E represent the start-up of the pulsating heat pipe, and moments F to G represent the vapor-liquid phase distribution during its stable operation. It is obvious that the phase change behavior of CLTPPHP follows the same pattern regardless of the number of turns. As the heating power is applied, the temperature in the evaporation section reaches a superheated state, resulting in liquid evaporation and bubble formation on the evaporation section wall. These bubbles gradually coalesce and expand, pushing the working fluid on both sides of the tube wall to move upward. With the continuous heat input, the gas plug in the pipe expands, increasing the overall internal pressure. As the volume of the gas plug in the evaporation section increases, the liquid plug decreases, inducing short-range motion. At this stage, the evaporation section is mainly composed of long gas plugs, while the condensation section mainly contains long liquid plugs. With further input of heat, the pressure difference between the evaporation and condensation sections increases, causing the gas plug in the evaporation section to further expand, pushing the adjacent liquid plug to move significantly, thereby starting the CLTPPHP. In this stage, the temperature of the evaporation section continues to increase with the heat input. In contrast, under low-temperature boundary conditions, the temperature in the condensation section decreases, resulting in a decrease in pressure. The huge pressure difference generated by the increase in pressure in the evaporation section and the decrease in condensation pressure overcomes the resistance required for the design of the CLTPPHP, causing the working fluid to begin to flow in a directional manner and form a closed-loop circulation. The long gas plugs generated in the evaporation section gradually shrink and condense into liquid plugs as they move toward the condensation section. These liquid plugs then move down to the evaporation section, where continued heating leads to a superheated state, triggering liquid evaporation and the formation of a large number of bubbles. As these bubbles merge into long and thin gas plugs, the pressure in the evaporation section increases, which drives the flow of liquid plugs and bubbles. This cyclic process causes the working fluid to flow in a directional manner within the designed CLTPPHP. This directional flow is determined to be a random process that may be different even under similar boundary and operating conditions. In addition, the distribution of bubbles and liquid plugs is uneven due to surface tension, flow direction, and friction. In addition, the startup time and running time of CLTPPHP are shortened as the number of turns increases.

[0161] (2) Temperature field

[0162] Figure 6 Demonstrated at 7528W / m 2Temperature variation of CLTPPHPs with different numbers of turns over time under heat flux density of . It is obvious that the temperature variation behavior of CLTPPHP follows the same pattern regardless of the number of turns. With the continuous application of a constant heat flux to the evaporation section, the heat is transferred to the liquid pool in the evaporation section through the outer wall, causing the internal working fluid to continue to evaporate and condense in the condensation section until a steady state is reached. At time B, bubbles begin to form on the inner wall of the designed CLTPPHP and local evaporation occurs in the evaporation section. At this stage, the temperature distribution in the system is relatively uniform and the overall temperature level is low. As time passes (time CD), the temperature of the evaporation section gradually increases, significantly enhancing the evaporation process. This leads to the generation of more bubbles, which expand rapidly and drive the flow of the working fluid in the pipe. At this stage, pulsating flow is gradually established and the temperature distribution in the system begins to show obvious non-uniformity. At time E, the liquid returns to the condenser section, where the enhanced turbulence causes the temperature to gradually decrease. In the stable operation stage (time FG), the flow of the working fluid becomes stable. Periodic evaporation and condensation processes occur in the pipe, resulting in a more uniform temperature distribution. The flow imbalance caused by heating and cooling generates dynamic pressure fluctuations between the liquid and gas phases in the pipe, which drives periodic oscillations and heat exchange. The oscillation of the working fluid causes the temperature signal to fluctuate periodically over time. This pulsating behavior reflects the unstable operation of the CLTPPHP. Therefore, analyzing the pulsation frequency is crucial to understand the dynamic behavior and heat transfer efficiency, providing crucial guidance for further design optimization.

[0163] Frequency analysis of temperature data has proven to be a promising tool for characterizing this unstable behavior, especially for detecting the dominant frequency in the flow motion through wavelet transform. When q = 7528 W / m2, the simulated temperature data of the stable operation of the condensation section were extracted, the data were filtered, and then wavelet analysis was performed to extract the dominant frequency value. The results of the wavelet analysis are shown in Figure 2. Fig.25 As shown. When the heat flux q = 7528W / m2, the maximum main frequency values ​​of the temperature signals of N = 1, N = 2 and N = 3 are 0.025Hz, 0.032Hz and 0.054Hz respectively. In addition, with the increase of the number of turns, the main frequency of CLTPPHP also increases, indicating that the oscillation frequency of the working fluid in the heat pipe is accelerated. This shows that increasing the number of bends can help improve the heat transfer performance of CLTPPHP during stable operation and promote more efficient heat exchange.

[0164] 1.3 Experimental study

[0165] This example studies the effects of operating and design parameters on the operating performance of HTP and CLTPPHP to ensure that the operating parameters match the design parameters, optimizes the HTP and operating performance of the designed CLTPPHP, and demonstrates the applicability of CLTPPHP in VMC SBS.

[0166] 1.3.1 Experimental Design

[0167] like Figure 7 As shown, this embodiment creates an experimental device to test the HTP of the designed CLTPPHP. The experimental device mainly consists of four parts: the designed CLTPPHP, the data acquisition and analysis system, the heating system, and the cooling system. The CLTPPHP is bent by a copper tube with an inner diameter of 3 mm and a wall thickness of 0.5 mm, and its dimensions are described in Section 1.1. The CLTPPHP is divided into three parts: an evaporation section with a length of 100 mm, an adiabatic section of 200 mm, and a condensation section of 100 mm.

[0168] The heating system consists of a heating resistor wire that can withstand high temperatures and a direct current (DC) regulated power supply. The heating resistor wire is uniformly wrapped with high temperature resistant glass fiber to prevent conductivity between the heating wire and the metal tube wall, thereby avoiding short circuits that may damage the DC power supply. Powered by the DC power supply, the heating resistor wire indirectly heats the wall of the designed CLTPPHP evaporation section. The evaporation section and the insulation section of the CLTPPHP are covered with insulation cotton to minimize heat dissipation to the external environment, thereby reducing experimental errors.

[0169] The cooling system uses forced convection air cooling, and electric fans help in heat exchange in the condensing section. An anemometer is used to record the actual cooling air flow rate (CAFR). For data acquisition and monitoring of CAFR, the anemometer is connected to the computer through a universal serial bus (USB) interface. The hardware and software modules constitute the data acquisition and analysis system. K-type thermocouples and LR8510-30 multi-channel data acquisition cards are used in the hardware module to obtain the surface temperature of the designed CLTPPHP. Figure 2 As shown in the figure, the locations and sizes of the measurement points on the designed CLTPPHP are marked. In order to collect data and visualize them in real time during the experimental study, the LabVIEW computer monitoring platform was used in the software module. The physical diagram and specific types of the experimental device are shown in Appendix A.

[0170] Experiments were conducted to investigate the effects of design and operating conditions on the HTP of the designed CLTPPHP HTP, based on the parameters listed in Table 1. Appendix B provides the measurement methods for the power and CAFR corresponding to each heat flux density.

[0171] Table 1. Setup and operating conditions.

[0172]

[0173] To ensure smooth experimentation, the operation of each system was thoroughly checked beforehand. Insulation material was wrapped around the insulation section to guarantee thermal performance.

[0174] 1.3.3 Startup performance

[0175] The startup performance is mainly reflected in the startup time and temperature. The startup time and temperature reflect the rapidity and sensitivity of CLTPPHP respectively. The sign of startup is that after a steady rise in the initial stage of the experiment, the temperature curve has the first large peak-to-valley oscillation. Shorter startup time and lower startup temperature indicate that CLTPPHP is easier to start. Figure 8 (a) to (c) show the heat flux density when 7528W / m 2 The temperature curves of the designed CLTPPHP during the startup phase under different working fluids and different turns. The results show that the designed CLTPPHP shows similar patterns when using ethanol, methanol and water as working fluids. As the number of turns increases, the required startup time and temperature decrease.

[0176] An increase in the number of turns results in a greater imbalance between the pipes inside the CLTPPHP. At the turns, the flow path of the liquid changes, resulting in a significant increase in local pressure fluctuations. This exacerbates the level of disturbance inside the CLTPPHP, promotes directional flow of the internal working mass, and promotes the start-up of the designed CLTPPHP. Fig. 9 As shown, the pressure non-uniformity in the CLTPPHP increases with the increase in the number of turns. The pressure distribution at t = 21s, t = 23.5s, and t = 25s shows that the pressure distribution becomes more asymmetric with the increase in the number of turns. This asymmetry creates a significant pressure difference between adjacent pipes and aggravates the internal disturbance. At the turns, local pressure fluctuations are observed, which changes the flow path of the working fluid and enhances the internal circulation. The intensification of pressure fluctuations promotes the transportation of high-temperature working fluid from the evaporation section to the condensation section. In the condensation section, additional heat is released to complete the heat transfer process. With the increase in the number of turns, the internal circulation of the working fluid is accelerated, resulting in a decrease in the startup temperature and a shortened startup time of the designed CLTPPHP.

[0177] 1.3.4 Steady-state heat transfer characteristics

[0178] When the number of turns is 1, i.e., N=1, the thermal resistance (TR) of the designed CLTPPHP decreases as the heating power increases, e.g. Fig.10(a) is shown. In descending order, the TR of the CLTPPHP using three different working fluids are anhydrous ethanol, distilled water and methanol. When anhydrous ethanol, distilled water and methanol are used as working fluids, the average TR of the designed CLTPPHP in the steady state is 1.34K / W, 1.74K / W and 2.15K / W, respectively. When methanol is used as the working fluid, the designed CLTPPHP has the lowest TR because the saturation temperature and latent heat of vaporization of methanol are lower than those of the other two fluids, which enables the designed CLTPPHP with methanol as the working fluid to quickly form a vapor core in the evaporation section and condense in the condensation section. The gas-liquid mixture promotes the internal flow quality, making the temperature distribution of the designed CLTPPHP more uniform and the temperature difference smaller. Among the above three fluids, anhydrous ethanol has the highest viscosity, and then anhydrous ethanol has a greater flow resistance, including intermolecular forces and viscous forces between the fluid and the tube wall. This affects the growth of bubbles and creates resistance to the liquid flow within the designed CLTPPHP in the steady-state stage, and then the heat is absorbed by the vapor plug and the temperature difference increases. Therefore, under the same heat input conditions, the designed ethanol-containing CLTPPHP exhibited the highest TR in the steady-state stage.

[0179] When N=2 and N=3, TR changes as follows: Fig.10 (b) and (c). When the heating power increases, the overall TR decreases. In the designed CLTPPHPs at steady state, the TRs of the above three working fluids are arranged in descending order as anhydrous ethanol, methanol and distilled water. When N = 2, the average TRs of the designed CLTPPHPs with anhydrous ethanol, methanol and distilled water as working fluids are 0.77 K / W, 0.52 K / W and 0.41 K / W, respectively. When N = 3, the average TRs of the designed CLTPPHPs with anhydrous ethanol, methanol and distilled water as working fluids are 0.30 K / W, 0.24 K / W and 0.19 K / W, respectively. The TR of the designed CLTPPHP with the same working fluid decreases with increasing speed. More heat is output from the evaporation section to the condensation section because the volume of the working fluid in the specified CLTPPHP increases with increasing speed at the same filling rate. In addition, the pressure difference at the turn promotes the oscillation of the gas-liquid mixture in the designed CLTPPHP, enhancing its thermal conductivity and reducing the TR.

[0180] When q=10037W / m 2 When the cooling air speed is 1m / s, 2m / s, 3m / s, 4m / s and 5m / s, the TR of the designed CLTPPHP under different working fluids and speeds is as follows Fig.11As shown. The TR of the designed CLTPPHP generally increases with increasing CAFR. As CAFR increases, more heat is discharged from the condensation section by forced convection, accelerating the condensation of steam inside the designed CLTPPHP. This increases the temperature difference between the evaporation and condensation sections, ultimately leading to an increase in TR. This indicates that the maximum heat transfer capacity increases with increasing CAFR. A higher CAFR can accelerate the condensation of internal steam and reduce the possibility of local drying in the designed CLTPPHP. Therefore, the heat transfer limit and HTP of the designed CLTPPHP are improved. It is also obvious that TR increases with increasing CAFR. Since ethanol has the highest viscosity among the three working fluids mentioned above, the enhancing effect of ethanol on the heat transfer limit of the designed CLTPPHP is most significant among methanol, ethanol and water. When ethanol is used as the working fluid, the condensation process is accelerated, resulting in an increase in the fluid volume inside the designed CLTPPHP. In contrast, this increases the resistance to the circulation of the gas-liquid mixture inside the designed CLTPPHP, resulting in heat accumulation and a larger temperature difference. Finally, the TR of the designed CLTPPHP is improved.

[0181] 1.3.6. Correlation of thermal properties

[0182] This example uses RSM to establish the correlation between HTP and design and operating parameters. RSM is fitted to approximate the true limit state surface. This method is a statistical experimental technique used to study the impact of multiple variables on a system. This example approximates the complex implicit relationship between design parameters and target variables by constructing a polynomial with an explicit expression:

[0183]

[0184] Where: Y is the predicted response value; x i and x j are the i-th and j-th influencing factors respectively; k is the number of influencing factors; β0 is the intercept coefficient; β i is the linear coefficient; β ij is the interaction coefficient; β ii is the quadratic coefficient; ε is the error term. According to the values ​​of intercept, linear coefficient, interaction coefficient and quadratic coefficient, RSM can be divided into linear, interaction and quadratic types.

[0185] Combined with the experimental results in Section 1.3.4, Design Expert was used as the analysis software to study the effects of working fluid, number of turns N, CAFR and heat density q on the EHTC of the designed CLTPPHP. The multivariate quadratic equation was used to fit the relationship between EHTC and influencing factors, and the EHTC approximate function of the designed CLTPPHP was derived based on these variables. This relationship was used to predict the EHTC of various CLTPPHPs and determine the sensitivity of the thermal performance of the designed CLTPPHP to the design and operating parameters.

[0186] In this embodiment, the Prandtl number Pr is selected to convert the type of working fluid into a quantifiable value. In the heat transfer process of the designed CLTPPHP, most of the heat is transferred through phase change and internal fluid convection. Therefore, it is appropriate to select the Prandtl number Pr to represent the thermophysical properties of the working fluid. Specifically, the Prandtl number Pr is selected to convert the type of working fluid into a quantifiable value:

[0187]

[0188] Where: Pr is the Prandtl number; c p is the specific heat capacity; μ is the dynamic viscosity; k is the thermal conductivity.

[0189] By using the Prandtl number, the effects of different working fluids on the designed CLTPPHP HTP were quantitatively analyzed. As shown in Table 2, by using the sequential probability value coefficient (Sequential p-value), the lack of fit probability value (Lack of Fitp-value), the predicted determination coefficient (predicted R 2 ) and the adjusted coefficient of determination (adjusted R 2 ), and compared the fitting results of multiple polynomial models. The results show that the fitting performance of the quadratic polynomial model is the best choice.

[0190] Table 2 Variance analysis and comparison of various models

[0191]

[0192] According to the definition of ANOVA, the p-value is a key parameter. When p < 0.05, the term has a significant effect on the latent variable. On the contrary, when p > 0.05, the term has an insignificant effect on the latent variable. In order to further optimize the RSM and reduce the interference of insignificant or mismatched terms, the terms with p-values ​​greater than 0.05 were deleted. The RSM was then reanalyzed. Table 3 lists the final results of the RSM with the selected parameters as input and their interactive effects on EHTC. The sequential p-value of the RSM is less than 0.0001, which verifies the accuracy of the experimental results and the reliability of the RSM. Therefore, within the given range of experimental data, the fitted RSM can be used to predict the EHTC of the designed CLTPPHP.

[0193] Table 3 Results of variance analysis

[0194]

[0195] Based on the above analysis, the final regression equation of RSM is:

[0196] h eff =-11884.74077+2342.08013×Pr+109.21243×N+0.654459×CAFR+0.146378×q-15.75025×Pr×N-0.003371×Pr×q+0.008755×N×q-101.67877×Pr 2 +51.74492×N 2 -5.14167E-06×q 2

[0197] In order to comprehensively analyze the effects of Pr, N, CAFR, and q on the designed CLTPPHP HTP, the three-dimensional RSM of EHTC was Fig.12 As shown. Fig.13 (a), EHTC increases first and then decreases with the number of turns. Increasing the number of turns within a specific range can improve EHTC. However, after exceeding a certain critical value, EHTC decreases when the number of turns N increases further. EHTC increases with the increase of Prandtl number Pr because the working fluid with higher Pr has higher viscosity and thermal diffusivity, which is beneficial to the heat transfer process. There is a significant interaction between the number of turns N and Prandtl number Pr. When the number of turns N is small, the effect of Prandtl number Pr on EHTC is small. However, when the number of turns N is high, EHTC is significantly enhanced with the increase of Prandtl number Pr.

[0198] according to Fig.13(b), EHTC increases significantly with increasing heat flux density because the fluid velocity and turbulence increase with increasing heat flux density, thereby enhancing HTP. The interaction between heat flux density and Prandtl number Pr is very complex. In the low power range, the effect of Prandtl number Pr on EHTC is not significant. In the high power range, the effect of Prandtl number Pr on EHTC increases significantly. The above results indicate that under high power conditions, Prandtl number Pr plays a more prominent role in improving HTP. From Fig.13 (c) It can be seen that the interaction between the number of turns N and the heat flux density is significant. When the number of turns N is small, the EHTC increases significantly with the increase of the heat flux density. However, under the condition of a large number of N turns, the EHTC does not increase significantly with the increase of the heat flux density. This indicates a balance between the number of turns N and the heat flux density.

[0199] In addition, the parameter estimation method can be used to optimize the key parameters in RSM so that it can better fit the experimental data. According to the above analysis, the maximum HTP of CLTPPHP is achieved when the number of turns, working fluid and CAFR are 3, water and 3m / s respectively. The maximum EHTC of the designed CLTPPHP is obtained by the final regression equation of RSM.

[0200] 2. Verification of CLTPPHP of vertical machining center spindle

[0201] In this example, a thermal-fluid-solid interaction analysis of the SBS in the VMC was performed by finite element simulation to verify the effectiveness of the designed CLTPPHP. The key is to determine the heat source and heat dissipation conditions. Friction heat from the front and rear bearings is the main source of SBS in the VTM260. The heat transfer mode mainly includes forced convection heat transfer of cooling oil / stator and rotating parts / surrounding air.

[0202] Heat generation rate Q of rolling bearing rb :Q rb =0.105×10 -6 Mn

[0203] Torque M of bearing friction:

[0204] M=M0+M1;M0=f0×10 -7 (γ·n) 2 / 3 d m 3 ; M1=f1P1d m

[0205] Where: M0 is the friction torque related to lubrication; M1 is the friction torque related to load; f0 is the bearing type and lubrication coefficient; γ is the kinematic viscosity of the lubricant; n is the bearing speed; f1 is the bearing type and load coefficient; P1 is the calculated load for determining the bearing friction torque; dm is the average bearing diameter.

[0206] The convection coefficients of shaft core / air, static surface / air, end face / air and water jacket / contact parts are calculated to be 64.44 W / m 2 K, 9.7W / m 2 K, 64.44W / m 2 h and 873.5W / m 2 According to the above formula, the heating rates of the front and rear bearings are 3.461×106 and 1.625×106 W / m 3 According to Section 1.3.5, when the number of turns, working fluid and CAFR are 3, water and 3m / s respectively, the maximum EHTC of the designed CLTPPHP is 2738.64W / m 2 · K. The final heating rate and boundary conditions are calculated and are shown in Table 4.

[0207] Table 4 Heat source load and convection coefficient

[0208]

[0209] 2.2 Simulation and experimental verification

[0210] This embodiment establishes a thermal fluid-solid iterative behavior model of the SBS in the VMC VTM260. The main heat sources include the front and rear bearings. To mitigate TE, the designed CLTPPHP is embedded in the SBS in the VTM260 to improve the heat dissipation capacity and efficiency and eliminate the heat generated by the front and rear bearings. The embedded CLTPPHP is used to export the internal heat of the SBS in the VTM260 to achieve uniform temperature distribution and reduce axial elongation (AE). The SBS model is simplified by the structure that has the least impact on the thermal fluid-solid behavior, including threaded holes, chamfers, fillets, etc. Fig.14 (a) The designed CLTPPHP is embedded in the cooling jacket of the SBS in the VMC VTM260. Fig.14 (b). Fig.14 As shown in (c), some holes are drilled in the cooling water jacket. The heat pipes are inserted into these holes to ensure that the heat pipes can be firmly fixed on the cooling water jacket. During the implementation, the original cooling water jacket was replaced by a machined cooling water jacket. The effectiveness of the designed CLTPPHP on the heat output and TE control of the VMC SBS was verified by comparing the thermal-fluid-structure interaction behaviors of the SBS with and without the designed CLTPPHP.

[0211] 2.2.1 Experimental setup

[0212] The SBS of VMC VTM260 was taken as the research object, and the temperature field and TD of SBS were measured. A temperature and thermal deformation synchronous acquisition system based on the American NI SCXI architecture was used. The temperature sensor is a precision magnetic PT100, which is installed in different locations such as the motor, the outer ring of the bearing and the environment. The TD of SBS is measured by a high-precision eddy current sensor, such as Fig.15 shown.

[0213] 2.2.2 Analysis of thermal-fluid-solid interaction behavior

[0214] (1) Temperature field distribution

[0215] This example uses the heat generation rate and heat dissipation conditions as input to establish a closed-loop iterative model of thermal fluid-solid interaction behavior. Fig.16 As shown in (a), the maximum temperature of the entire SBS without CLTPPHP embedded is 85.921, and the maximum temperature of the spindle core (SC) is about 83.566. Compared with the maximum temperatures of the vertical SBS and spindle core without CLTPPHP embedded, the maximum temperatures of the vertical SBS and spindle core embedded with CLTPPHP are reduced by 36.784 and 36.425, respectively.

[0216] When the thermal equilibrium state is reached, the temperature of the vertical SBS in the VMC stops fluctuating over time. At this point, the multiphase flow behavior of the embedded CLTPPHP and the thermal fluid-solid interaction behavior of the vertical SBS reach a stable state. In addition, the thermal equilibrium time is a key parameter for evaluating the transient thermal behavior of the SBS with and without embedded CLTPPHP. The strong thermal stability leads to a short thermal equilibrium time. The strong thermal stability of the vertical SBS is conducive to the high-precision machining of the entire VMC. The vertical SBS is considered to have reached a thermal equilibrium state when the temperature reaches 95% of the maximum temperature, which is defined as the thermal equilibrium time. Fig.17 The temperatures of the main components in the vertical SBS with and without embedded CLTPPHP are shown. The thermal equilibrium times of the vertical SBS without and with embedded CLTPPHP are approximately 3400 and 560 seconds, respectively. These results indicate that by embedding CLTPPHP in the vertical SBS, internal heat dissipation is enhanced, which greatly shortens the thermal equilibrium time. Ultimately, the thermal stability of the vertical SBS is enhanced.

[0217] like Fig.18As shown, the simulated temperature values ​​are compared with the experimental temperature values, and the results show that the thermal fluid-solid interaction model can accurately simulate the spindle temperature. The simulation results and experimental data show that the temperature variation trends at different time points are similar, and the error range is relatively small, which proves the reliability and accuracy of the thermal fluid-solid interaction model. The simulated temperature of the front bearing without embedded CLTPPHP reaches about 77°C after 8000 seconds, while the experimental data is about 76°C. The simulated temperature of the rear bearing without embedded CLTPPHP reaches about 55°C, and the experimental data is about 54.5°C. The simulated temperature of the front bearing with embedded CLTPPHP remains at 25°C, which is very close to the experimental value, indicating that the error is negligible. Similarly, the rear bearing with embedded CLTPPHP shows a temperature close to 22°C, which is consistent with the experimental results with minimal deviation. Embedded CLTPPHP achieves a significant reduction in the temperature of the front and rear bearings. These quantitative comparisons further verify the effectiveness of the model in accurately predicting temperature under different conditions.

[0218] (2) Thermal deformation field

[0219] Under thermal load, vertical SBS will undergo AE, resulting in reduced machining accuracy of the entire VMC. Fig.19 As shown in (a) and (c), the maximum deformation of the vertical SBS and SC without embedded CLTPPHP is about 369.87 μm. Fig.19 (b) and (d) show that the maximum TD of the vertical SBS and SC with embedded CLTPPHP is about 141.83 μm. The embedded CLTPPHP significantly reduces the TD of the entire SBS and SC.

[0220] By comparing the simulated TD values ​​of SBS and SC, it can be seen that the embedded CLTPPHP can effectively reduce the TD in the vertical SBS and SC, as Fig. 20 As shown. The maximum TD of the vertical SBS without CLTPPHP embedded reaches about 360μm after 8000 seconds. The average TD after 8000 seconds is about 170μm. The maximum TD of the SC without CLTPPHP embedded is about 360μm, and the average TD deformation decreases to about 165μm after 8000 seconds. The maximum TD of the SBS embedded with CLTPPHP reaches about 153μm, and the average TD of the SBS embedded with CLTPPHP is about 30μm. The average TD of the SC with embedded CLTPPHP is about 40μm, while the maximum TD is about 150μm. Compared with the vertical SBS without CLTPPHP embedded, the maximum TD of the vertical SBS and SC embedded with CLTPPHP is reduced by 61.7%. These results verify the effectiveness of the designed CLTPPHP on the heat output and TE control of VMC SBS.

[0221] like Fig.21As shown, the simulated and experimental AE values ​​are compared, and the results show that the thermal fluid-solid interaction model is able to accurately simulate TD. According to the simulation results, the AE of the SC without CLTPPHP reaches about 150μm at 8000 seconds. The experimental AE of the SC without CLTPPHP also shows a similar trend, with an axial AE of about 150μm at 8000 seconds, and the AE simulation results of the SC with CLTPPHP show a maximum value of about 20μm. The experimental data of the AE of the SC using CLTPPHP are in good agreement with the simulation results, and the AE is also around 20μm, with negligible deviations. These quantitative comparisons further verify the effectiveness of the thermal fluid-solid interaction model in accurately predicting TD under different conditions.

[0222] 2.2.3 Actual processing

[0223] like Fig. 22 As shown, VMC VTM260 is used to machine the workpiece. The main machining process parameters are as follows: The rotation speed of SBS in VMC is 3000r / min. The cutting speed is 50m / min. The feed speeds of X, Y and Z axes are 100mm / min, 150mm / min and 120mm / min, respectively. The cutting depth is 0.1mm. The machined workpiece was placed in a measuring chamber at a constant temperature of 20℃ for 8 hours, and its geometric accuracy was measured using a coordinate measuring machine. In particular, the height of the machined workpiece was used as an evaluation index to show the reduction effect of the designed CLTPPHP on the SBS AE in VMC VTM260.

[0224] according to Fig.23 , the ideal sizes of size 1 and size 2 are 10 mm and 20 mm, respectively. Due to the existence of TE, the actual sizes of size 1 and size 2 will deviate from their ideal sizes. Table 5 lists the geometric errors of size 1 and size 2. It is obvious that embedded CLTPPHP significantly improves the machining accuracy of VMC VTM260. When the SBS of VMC VTM260 is not embedded with CLTPPHP, the actual size of size 1 is 9.981 mm, with a deviation of 0.019 mm. For VMC VTM260 with embedded CLTPPHP, the actual size of size 1 is 9.992 mm, with a deviation of 0.008 mm. Compared with VMC VTC260 without embedded CLTPPHP, the reduction rate of TE is 57.89%. For VMC VTM260 without embedded CLTPPHP, the actual size of size 2 is 19.980 mm, with a deviation of 0.020 mm. For VMC VMM260 with embedded CLTPPHP, the actual size of size 2 is 19.991 mm, with a deviation of 0.009 mm. Compared with the VMC VTC260 without embedded CLTPDPH, the reduction rate of TE is 55.00%.

[0225] Table 5 Geometric errors of size 1 and size 2

[0226]

[0227] 3. Conclusion

[0228] This embodiment proposes a two-phase closed-loop pulsating heat pipe for the spindle bearing system of a vertical machining center, aiming to achieve efficient heat transfer and thermal error control. The heat transfer performance of the pulsating heat pipe is explored through numerical simulation and experimental research. The designed heat pipe is then embedded in the cooling jacket of the spindle bearing system of the vertical machining center, and its effectiveness is verified by experiments. The main conclusions are as follows:

[0229] (1) A closed-loop two-phase pulsating heat pipe was designed to dissipate heat and regulate the thermal deformation of a spindle bearing system in a vertical machining center. This example studies the effects of heating power, working fluid, number of turns, and cooling air flow rate on the heat transfer performance of a closed-loop two-phase pulsating heat pipe. Methanol provides the best performance with a single-turn thermal resistance of 0.61 K / W, while distilled water performs best with two-turn and three-turn thermal resistances of 0.41 K / W and 0.19 K / W, respectively. The heat transfer performance improves with the increase in the number of turns and cooling air flow rate, but decreases when the heating power exceeds the optimal threshold.

[0230] (2) A response surface model was established to illustrate the nonlinear relationship between the effective heat transfer coefficient and key variables. The interaction between the number of turns, heating power, and cooling air flow rate significantly affects the heat transfer performance and helps to optimize the design of closed-loop two-phase pulsating heat pipes. The optimization range of the response surface model is as follows: the number of turns is between 1 and 3, the Prandtl number (Pr) is between 6.9 and 16, the cooling air flow rate is between 1 and 5 m / s, and the heat flux density is between 5018 and 17565 W / m 2 between.

[0231] (3) Parameter optimization was performed through response surface model, and the peak value of equivalent heat transfer coefficient of pulsating heat pipe reached 2738.64W / m 2 ·K, which greatly exceeds the traditional cooling water jacket. The closed-loop two-phase pulsating heat pipe is embedded in the cooling water jacket of the vertical machining center, effectively reducing the maximum temperature, thermal equilibrium time and thermal deformation. As a result, the geometric errors of size 1 and size 2 are reduced by 57.89% and 55.00%, respectively, compared with the system without heat pipes. This proves the effectiveness of closed-loop two-phase pulsating heat pipes in improving productivity and providing new solutions for heat dissipation in precision machining.

[0232] Appendix A

[0233] The physical diagram of the CLTPPHP experimental device is shown in Fig.26 The designed CLTPPHP prototype is shown in Fig. 27Table 9 lists the types of DC power supplies and other equipment.

[0234] Table 9 Specific types of experimental equipment

[0235]

[0236] Appendix B

[0237] The experiments were conducted in a controlled environment equipped with central air conditioning, and the laboratory temperature was kept stable. Before each experiment, the air conditioning system was started and the indoor temperature was stabilized at 24±1℃. The experiment started only when the room temperature reached and remained at this value. The air temperature distribution in the laboratory was almost uniform due to the uniform cooling effect provided by the air conditioning system. Therefore, it was assumed that the cooling air temperature remained consistent in all experiments. Given the preset cooling temperature, the condensing section temperature was adjusted by adjusting the cooling air flow rate (CAFR). CAFR was measured using an anemometer, and due to the influence of its position on the measurement results, the anemometer was placed as close as possible to the condensing section of the designed CLTPPHP. In order to minimize the measurement error in CAFR, the average value of multiple measurements was used. In the experimental study, as Fig.28 As shown, four CAFR monitoring points were selected and five measurements were taken. The final CAFR was determined as the average of these measurements.

[0238]

[0239] Where: V C1i 、V C2i 、V C3i and V C4i Respectively represent the measuring point V C1 、V C2 、V C3 and V C4 The CAFR at

[0240] Table 10 lists the heat load for each heat flux density.

[0241] Table 10 Heating power (P) corresponding to each heat flux density (q)

[0242]

[0243] 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 design method for a closed-loop two-phase pulsating heat pipe, characterized in that: The steps include: Step 1: Determine the geometric parameters According to the cooling jacket size of the main shaft bearing system, the geometric size of the closed-loop two-phase pulsating heat pipe is determined; according to the selected working fluid, the inner diameter size of the closed-loop two-phase pulsating heat pipe is determined; Step 2: Multiphase flow behavior simulation The multiphase flow behavior of the closed-loop two-phase pulsating heat pipe is simulated to obtain the gas-liquid phase change behavior and temperature field of the closed-loop two-phase pulsating heat pipe; Step 3: Experimental research The startup performance and steady-state heat transfer characteristics of the closed-loop two-phase pulsating heat pipe were obtained through experimental analysis. Step 4: Build a response surface model The correlation between the heat transfer performance and the design and operating parameters of the closed-loop two-phase pulsating heat pipe was established through the response surface model. The influence of working fluid, number of turns N, cooling air flow CAFR and heat flux density q on the effective heat transfer coefficient of the closed-loop two-phase pulsating heat pipe was obtained, and the design parameters of the closed-loop two-phase pulsating heat pipe including the number of turns N, cooling air flow CAFR and heat flux density q were determined.

2. The design method of a closed-loop two-phase pulsating heat pipe according to claim 1, characterized in that: In step 1, the method for determining the inner diameter size of the closed-loop two-phase pulsating heat pipe according to the working fluid is: Where: d in is the inner diameter of the closed-loop two-phase pulsating heat pipe; ρ L and ρ V are the liquid phase density and gas phase density of the working liquid respectively; g is the gravitational acceleration; σ is the surface tension.

3. The design method of a closed-loop two-phase pulsating heat pipe according to claim 1, characterized in that: In step 2, the method steps for simulating the multiphase flow behavior of the closed-loop two-phase pulsating heat pipe are: 21) Construct the control equations: Use the fluid volume model to simulate the phase change in the two-phase pulsating heat pipe. The fluid volume model is used to track the gas-liquid interface through the phase volume fraction in the element and determine the flow changes of the gas and liquid phases in each element; Use the Lee model to define the phase change process and simulate the energy and mass transfer during the phase change process inside the two-phase pulsating heat pipe; 22) Solution settings and boundary conditions Set the working angle and filling rate of the two-phase pulsating heat pipe; set the gravity acceleration; set the pipe wall material; set the liquid relative heat capacity and surface tension coefficient of the working liquid; set the gas relative heat capacity of the working liquid; set the target saturation temperature and saturation pressure of the working liquid; The adiabatic section is regarded as an adiabatic wall. During the simulation, the boundary conditions of the heat flux density of the evaporation section and the convection coefficient of the condensation section are kept consistent. 23) Grid division Adopt unstructured grids to closely align the unstructured grids with the changes of the working fluid, providing high interface resolution to accurately capture dynamic processes such as bubble generation, growth, movement, and liquid reflux; Add boundary layer mesh near the tube wall to accurately capture the formation of thin liquid film near the tube wall and the generation and evolution of small bubbles; 24) Simulation The multiphase flow behavior of the closed-loop two-phase pulsating heat pipe is simulated, and the influence of the number of turns of the closed-loop two-phase pulsating heat pipe on the start-up time and heat transfer performance is obtained.

4. The design method of a closed-loop two-phase pulsating heat pipe according to claim 3, characterized in that: In step 21), the method of simulating the phase change in the two-phase pulsating heat pipe using the fluid volume model is as follows: in the closed-loop two-phase pulsating heat pipe, each element in the calculation domain satisfies the condition: α V +α L ＝1 Where: α L and α V are the volume fractions of liquid and gas phase, respectively; The continuity equation is: Where: S m,L represents the mass source term of the liquid phase; S m,V represents the gas phase mass source term; represents the gradient operator; The momentum equation is: Where: ρ is the density of the mixed phase; u is the kinetic viscosity coefficient; is the pressure difference; is the velocity field gradient; I is the equivalent tensor; F CSF is the volume force source term generated by surface tension; The energy equation is: Where: e is internal energy; k is thermal conductivity; is the maximum temperature difference; S E is the energy source term; The volume average method is used to solve the thermophysical properties of the mixed phase and we get: p=a L r L +(1-a L )r V μ = a L m L +(1-a L )m V k=a L k L +(1-a L )k V Where: ρ is the density of the mixed phase; ρ L and ρ V are the liquid phase density and the gas phase density respectively; μ is the dynamic viscosity of the mixed phase; μ L and μ V are the liquid phase viscosity and the gas phase viscosity respectively; k is the thermal conductivity of the mixed phase; k L and k V are the liquid phase thermal conductivity and the gas phase thermal conductivity respectively; Solving for the internal energy using the mass average method yields: Where: e is internal energy; e L and e V are the internal energies of the liquid phase and the gas phase, respectively.

5. The design method of a closed-loop two-phase pulsating heat pipe according to claim 3, characterized in that: In step 21), the method of simulating the energy and mass transfer in the phase change process inside the two-phase pulsating heat pipe using the Lee model is: During the evaporation process: Where: m L represents the mass conversion from liquid phase to gas phase; β e is the evaporation coefficient; α L Liquid volume fraction; ρ L and ρ V are the liquid phase density and gas phase density respectively; T is the temperature of the mixed phase; T sat is the saturation temperature; D Sm is the Sauter mean diameter; M is the molar mass; R is the ideal gas constant; ΔH is the saturation temperature difference; During the condensation process: Where: m V Indicates the mass conversion from gas phase to liquid phase; β c is the condensation coefficient; α V is the gas phase volume fraction; Ensure dynamic balance of mass transfer rate during phase change: Where: l and ρ v are the liquid phase density and gas phase density, respectively.

6. The design method of a closed-loop two-phase pulsating heat pipe according to claim 3, characterized in that: In the step 22), the heat flux density of the evaporation section is: Where: q is the heat flux density; P is the heating power of the evaporation section; d is the diameter of the pulsating heat pipe; l e is the length of the evaporation section; The convection heat transfer coefficient is: Where: h is the convective heat transfer coefficient; h eff is the effective heat transfer coefficient; and are the temperature differences between the evaporator and condenser parts respectively.

7. The design method of a closed-loop two-phase pulsating heat pipe according to claim 1, characterized in that: In step 4, the complex implicit relationship between the design parameters and the target variable is approximated by constructing a polynomial with an explicit expression: Where: Y is the predicted response value; x i and x j are the i-th and j-th influencing factors respectively; k is the number of influencing factors; β0 is the intercept coefficient; β i is the linear coefficient; β ij is the interaction coefficient; β ii is the quadratic coefficient; ε is the error term.

8. The design method of a closed-loop two-phase pulsating heat pipe according to claim 1, characterized in that: In step 4, the Prandtl number Pr is selected to convert the type of working fluid into a quantifiable value: Where: Pr is the Prandtl number; c p Specific heat; μ is dynamic viscosity; k is thermal conductivity.

9. A closed-loop two-phase pulsating heat pipe, characterized in that: The heat pipe is designed by using the design method of the closed-loop two-phase pulsating heat pipe as described in any one of claims 1 to 7.

10. A spindle bearing system for a vertical machining center, comprising a spindle and a cooling water jacket sleeved outside the spindle, a front bearing and a rear bearing being respectively arranged between the two ends of the cooling water jacket and the spindle, characterized in that: The closed-loop two-phase pulsating heat pipe according to claim 8 is installed on the inner wall of the cooling water jacket.

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