Precise worm grinding wheel gear grinding machine tool cooling element and multi-target heat-flow topological design optimization method thereof

Abstract

The invention discloses a multi-objective heat-flow topology design optimization method for a cooling element of a precise gear grinding machine tool, which comprises the following steps of: 1, defining a design domain: unfolding the cooling element into a plane, defining a two-dimensional design domain representing the geometric structure of the cooling element, and discretizing by adopting a finite element method; step 2, numerical modeling: modeling the cooling element into a porous medium; under the condition that laminar flow cannot be compressed, the fluid dynamics is controlled by a dimensionless form of a continuity equation and a momentum equation; the fluid-solid coupling heat transfer model is controlled by a dimensionless energy conservation equation; 3, constructing an objective function, wherein an optimization objective is defined as a weighting function of heat transfer and fluid dissipation power, and a fluid-solid heat transfer topological optimization model is constructed; 4, solving the objective function; and 5, recovering the shape structure of the cooling element. The invention further discloses a precise gear grinding machine tool and a cooling element.

Description

Technical Field

[0001] The invention belongs to the technical field of optimization design, and specifically relates to a cooling element of a precision worm wheel gear grinding machine tool and a multi-objective thermal-fluid topology design optimization method thereof. Background Art

[0002] The significance of precision worm gear grinding machines (GGMTs) lies in their ability to achieve tight tolerances and improve the overall quality and performance of machining high-performance gears, making them indispensable in industries that require high precision, such as aerospace, automotive, and engineering. Thermal errors in GGMTs are mainly caused by uneven temperature rise of machine tool components and are a key factor affecting machining accuracy. In particular, the moving heat source in the GGMT, represented by the moving nut, causes uneven temperature distribution throughout the GGMT, resulting in significant thermal errors and reduced grinding accuracy. Therefore, the temperature rise and thermal errors caused by the moving heat source should be reduced.

[0003] The prior art believes that temperature rise is the root cause of thermal errors in GGMT. Therefore, a closed-loop circulating cooling system is used to effectively control the thermal errors caused by the heat generated by the heat source. The coolant is supplied to the hollow screw shaft (SS) in the ball screw feed drive system (BSFDS) through the circulating cooling system, thereby achieving temperature control of the SS. With the existing cooling system, although the temperature rise of the BSFDS is reduced, the closed-loop cooling system currently used often leads to problems such as insufficient rigidity of stainless steel, uneven axial temperature distribution, and coolant leakage in rotating parts. Then the positioning accuracy and repeatability of the BSFDS, as well as the gear grinding accuracy of the entire machine tool will not be significantly improved.

[0004] In the prior art, CEs with serpentine and spiral channels are used to improve heat transfer efficiency and capacity. These designs are widely used in various industrial applications due to their ability to provide excellent thermal control capabilities. Serpentine cooling channels are characterized by their winding paths that promote turbulence, enhance convective heat transfer, and ensure more uniform cooling. The geometry of these channels, including the curvature and pitch of the bends, is optimized to maximize heat dissipation capacity while minimizing pressure drop. Spiral cooling channels and their spiral paths offer a different approach to improving heat transfer capacity. The spiral channels achieve continuous movement of the fluid and increase turbulence, significantly improving heat transfer capacity. The pitch, diameter, and helix angle of the spiral channels are optimized to improve thermal and fluid dynamics. Both serpentine and spiral cooling channels have shown excellent performance in terms of thermal control. Although serpentine and spiral cooling channels have significant advantages in improving heat transfer efficiency and capacity, they also have significant disadvantages. Serpentine channels have high pressure drops, and spiral channels face complexities in design optimization and potential uneven heat transfer capacity.

[0005] In summary, the prior art has the following deficiencies:

[0006] (1) The hollow stainless steel circulating cooling system effectively controls the temperature and thermal error of the GGMT. However, the non-uniform temperature gradient in the axial direction of the hollow SS of the GGMT causes the dynamic changes of the positioning error (PE) and repeatability error (RPE) of the BSFDS.

[0007] (2) Although CE effectively reduces thermal errors, in the existing technology, CE is mostly designed based on experience and still has limitations in terms of heat transfer and thermal error control efficiency and ability. Summary of the invention

[0008] In order to reduce the temperature rise of the moving heat source of the precision worm wheel gear grinding machine and the thermal error of the BSFDS to improve the machining accuracy of the entire GGMT, the hollow SS can no longer be used as a cooling element (CE). Instead, solid stainless steel should be used to improve the rigidity of the stainless steel. In addition, in order to ensure uniform axial temperature distribution and avoid coolant leakage in the rotating parts, as well as to reduce the temperature of the moving nut (MN), an additional CE should be designed, and the CE is in contact with the MN. Due to the changes in CE, a more systematic and scientific cooling strategy and CE design method are urgently needed.

[0009] In view of this, the object of the present invention is to provide a cooling element for a precision gear grinding machine and a multi-objective thermal-fluid topology design optimization method thereof. By applying the designed cooling element to the moving nuts (MN) of the X, Y and Z axes of the GGMT, the heat transfer capacity and efficiency can be significantly improved, thereby improving the machining accuracy of the GGMT.

[0010] In order to achieve the above object, the present invention provides the following technical solutions:

[0011] The present invention first proposes a multi-objective thermal-fluid topological design optimization method for a cooling element of a precision worm wheel gear grinding machine tool, comprising the following steps:

[0012] Step 1: Define the design domain

[0013] The cooling element is unfolded into a plane, a two-dimensional design domain representing the geometric structure of the cooling element is defined, and a finite element method is used for discretization;

[0014] Step 2: Numerical modeling

[0015] The cooling element is modeled as a porous medium; under the condition of laminar incompressible flow, the fluid dynamics are governed by the dimensionless forms of the continuity equation and the momentum equation; the fluid-solid coupled heat transfer model is governed by the dimensionless energy conservation equation;

[0016] Step 3: Construct the objective function

[0017] In order to improve cooling performance and reduce flow resistance, the optimization objective is defined as a weighted function of heat transfer and fluid dissipation power, and a fluid-solid heat transfer topology optimization model is constructed:

[0018]

[0019] Where: J is the optimization target; J th is the heat transfer term; J f is the fluid dissipation work term; w1 and w2 are J th and J f is the weight factor; Ω is the design domain; V f is the volume fraction occupied by the fluid flow path; Vol is the total volume contained in the design domain; γ is the design variable; h * is the dimensionless heat transfer coefficient; T * is the dimensionless temperature; is the dimensionless gradient operator; u * is the dimensionless flow velocity; α * is the dimensionless permeability; Vol Ω is the total volume contained in the design domain; Q is the heat load applied by the design domain; is the dimensionless inlet pressure; Γ is the flow channel; Γ in is the flow channel entrance;

[0020] Step 4: Solve the objective function

[0021] The sensitivity is solved by the adjoint method, and the gradient calculated by the adjoint method is used to form a quadratic subproblem of the sequential quadratic programming method. The design variable γ is updated by solving the quadratic subproblem to ensure that the solution moves toward the optimal configuration until the set iterative convergence condition is met. The topological design channel is designed in the cooling element.

[0022] Step 5: Restore the shape and structure of the cooling element.

[0023] Furthermore, in step 2, the method of modeling the cooling element as a porous medium is as follows: within the fluid-solid topology design domain, the design domain is theorized as a porous material, assuming that the fluid resistance F is linearly related to the flow velocity u:

[0024] F=-αu

[0025] Where: α is the permeability;

[0026] The domain of the design domain is divided into a finite number of elements, each of which has a design variable γ, which takes values ​​between 0 and 1; when representing a solid: γ = 0, α → ∞ and F → ∞; when representing a fluid: γ = 1, α → 0 and F → 0.

[0027] Furthermore, in step 3, the fluid dynamics is represented by the continuity equation and the momentum equation by the velocity u*, pressure p*, Reynolds number Re and gradient operator To express it dimensionlessly:

[0028]

[0029] in: is the gradient operator; U and L are characteristic velocity and length, respectively; ρ is the density; μ is the dynamic viscosity;

[0030] For incompressible laminar flow, the continuity equation is:

[0031]

[0032] The momentum conservation equation is:

[0033]

[0034] Among them: F * It is the volume force;

[0035] According to Darcy's law, the body force F* is proportional to the velocity u*, given by α * The dimensionless permeability represented by is then determined by subsequent penalty function interpolation:

[0036] F * =-α * u *

[0037]

[0038]

[0039] The penalty factor q is related to the Darcy number Da and the Reynolds number Re, resulting in the momentum equation:

[0040]

[0041] Where: q is the penalty factor; Da is the Darcy number.

[0042] Furthermore, the dimensionless energy conservation equation is given by the dimensionless temperature T * and the Prandtl number Pr, defined as follows:

[0043]

[0044] Where: T B and T w The average temperature and the wall temperature are respectively; the thermophysical properties of the fluid are characterized by its specific heat capacity C p and thermal conductivity k fis a characteristic and is a key parameter in heat transfer analysis; μ is the fluid viscosity;

[0045] The dimensionless energy conservation equation is expressed as:

[0046]

[0047] Where: u * Indicates speed; is the gradient operator; Q * represents the dimensionless rate of heat generation, and the dimensionless temperature T * Proportional to:

[0048]

[0049] By introducing the design variable γ, we get:

[0050]

[0051] Furthermore, in order to avoid the checkerboard phenomenon in the design domain, density filtering in the form of Holmz partial differential equation is adopted:

[0052]

[0053] Where: R min is the filter radius, taking the cooling element size; θ is the design variable before filtering; is the filtered design variable; represents the gradient operator;

[0054] In order to solve the problem of gray elements, the hyperbolic tangent projection technique is used:

[0055]

[0056] in: is the output design variable after projection, η and β are the projection point and slope, respectively.

[0057] Furthermore, in the step one, the cooling element is symmetrically divided into two equal halves, and the two-dimensional design domain is defined as a geometric structure representing one half of the cooling element; in the step five, the two cooling elements are symmetrically combined into one.

[0058] The present invention also proposes a cooling element for a precision worm wheel gear grinding machine, which is designed using the multi-objective thermal-fluid topology design optimization method as described above.

[0059] The present invention also proposes a precision worm wheel gear grinding machine, comprising an X-axis, a Y-axis and a Z-axis, wherein the X-axis, the Y-axis and the Z-axis are each provided with a ball screw feed drive system, wherein the ball screw feed drive system comprises a screw shaft and a movable nut cooperating with the screw shaft, wherein the movable nut comprises a nut and a nut housing, wherein a cooling element as described above is provided between the nut and the nut housing.

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

[0061] Thermal error significantly reduces the machining accuracy of precision worm wheel gear grinding machines, so it is imperative to effectively control the thermal error of precision worm wheel gear grinding machines. In order to control the thermal error, an innovative idea of ​​directly cooling the moving heat source of the gear grinding machine is proposed to replace the existing hollow screw cooling method. A precision worm wheel gear grinding machine cooling element and its multi-objective thermal-fluid topological design optimization method are proposed to design the cooling element of the precision worm wheel gear grinding machine. The designed cooling element is applied to the moving nut (MN) of the X, Y and Z axes of the GGMT. The axial thermal expansion of the screw shaft is reduced by the cooling strategy and multi-objective topological design optimization method. The results show that the heat transfer capacity of the topologically optimized shape channel is more prominent than that of the traditional serpentine cooling channel, and the pressure drop is 2-3 times lower than that of the traditional serpentine channel. The cooling element is embedded in the ball screw feed drive system of the precision gear grinding machine, which reduces the temperature rise of the moving nut by more than 3K and the thermal elongation of the screw shaft by 10%. By using the designed cooling element with a topologically optimized shape channel, the improvement rate of repeat positioning accuracy is in the range of [29.03%, 92.59%]. The cylindrical gears were processed using a gear grinding machine with a designed cooling element. The results showed that the grinding accuracy of the precision worm wheel gear grinding machine was improved by about 65%. In summary, the cooling element of the precision worm wheel gear grinding machine and its multi-objective thermal-fluid topological design optimization method of the present invention can significantly improve the heat transfer capacity and efficiency by applying the designed cooling element to the moving nuts (MN) of the X, Y and Z axes of the GGMT, thereby improving the processing accuracy of the GGMT. 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 Cooling strategy for GGMT;

[0064] Figure 2 A schematic diagram of the design method;

[0065] Figure 3 Solid domain and fluid domain in topology optimization;

[0066] Figure 4 It is the TO model;

[0067] Figure 5 is the mesh division result;

[0068] Figure 6 Simulate data for cooling plates;

[0069] Figure 7 is the structural dimensions and boundary conditions;

[0070] Figure 8 For CP with TOC;

[0071] Fig. 9 Provide experimental platform setup and procedures;

[0072] Fig.10 is the surface temperature of the cooling plate;

[0073] Fig.11 is the average surface temperature;

[0074] Fig.12 It is a curve diagram of pressure drop data;

[0075] Fig.13 is the CE embedding process and boundary conditions;

[0076] Fig.14 is the temperature field;

[0077] Fig.15 For the experimental device;

[0078] Fig.16 To measure the position;

[0079] Fig.17 It is the temperature curve of the moving nut;

[0080] Fig.18 Thermal expansion of the end face of the screw shaft support;

[0081] Fig.19 is the repeat positioning error;

[0082] Fig. 20 A gear grinding device;

[0083] Fig.21 For the measurement results. DETAILED DESCRIPTION

[0084] 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.

[0085] 1. Precision gear grinding machine

[0086] GGMT consists of several key components, including three BSFDS axes (X, Y, and Z) and three rotation axes (A, B, and C), such as Figure 1 As shown. The X-axis is used to adjust the lateral position between the grinding wheel and the workpiece. The Y-axis is used to adjust the height between the grinding wheel and the workpiece. The Z-axis is used to adjust the front-to-back position between the grinding wheel and the workpiece. The A-axis is a rotary axis used to tilt the grinding wheel, allowing different gear tooth profiles to be accommodated. The B-axis is a rotary axis used to adjust the angle of the grinding wheel. The C-axis is the rotary axis of the workpiece, which allows continuous grinding as the workpiece rotates. The grinding principle is as follows. Gear grinding is achieved by controlling the spatial position of the linear axis and the rotary axis. The workpiece rotates with the C-axis, and the angle of the grinding wheel is adjusted using the A-axis and B-axis to match the tooth profile of the gear. The X, Y, and Z axes are used to control the relative position between the grinding wheel and the workpiece to ensure grinding accuracy. The cooling system plays a vital role in maintaining the proper temperature of the X, Y, and Z axes. The cooling system consists of an industrial chiller, a liquid flow control system, a cooling element (CE) located on the moving nut (MN), a data acquisition system, and a data processing system. The cooling system is used to control the temperature of the BSFDS in the GGMT and reduce thermal errors in the X, Y, and Z axes. The data acquisition system and data processing system are used to continuously monitor and collect temperature rise, pressure drop, etc.

[0087] GGMT's cooling strategy is as follows Figure 1 As shown. This embodiment focuses on the cooling element topology design of the X, Y and Z axis MN. Here, the Y axis is taken as an example to demonstrate the idea of ​​directly cooling the mobile heat source of the GGMT. The goal is to improve the heat dissipation efficiency by embedding the TO-based CE into the GGMT. The TO method is used to design the CE of the GGMT. Specifically, the CE with a TO-shaped channel (TOC) is designed to fit tightly and be embedded in the nut housing and used to wrap the MN. Based on the dimensionless control equation, the MTO model of fluid-solid heat transfer is proposed. The cooling system consists of an industrial-grade cooler and a liquid flow meter, which together provide a constant coolant inlet velocity. The heat transfer performance of the designed CE with TOC is evaluated through a comprehensive analysis of the temperature variation, pressure drop and thermal elongation of the screw shaft. In addition, the PE and RPE of the BSFDS and the overall machining accuracy of the entire GGMT are used to demonstrate the effectiveness of the MTO method for precision GGMTCE. These indicators jointly determine the efficacy of the MTO applied to the CE inside the GGMT.

[0088] 2. Topology optimization design

[0089] The overall design concept is as follows: The process begins with the design of a half-size free-mount cooling plate (CP). This half-size CP has a TOC designed for optimal fluid flow and heat dissipation. Two half-size CPs are then combined into a full-size CP. The full-size plate effectively doubles the cooling capacity and the surface area available for heat transfer. Subsequently, the full-size CP is formed and assembled into a cylindrical CE. The overall design concept is as follows Figure 2 shown.

[0090] 2.1. Fluid-Solid Heat Transfer Topology Optimization Problem

[0091] In the fluid-solid TO domain, the design domain is theorized as a porous material, assuming that the fluid resistance F is linearly related to the flow velocity u:

[0092] F=-αu

[0093] Where: α is the permeability.

[0094] The domain of the design domain is divided into a finite number of elements, each of which has a design variable γ, which takes a value between 0 and 1; Figure 3 As shown, the black area represents a solid and the white area represents a fluid. When representing a solid: γ=0, α→∞ and F→∞; when representing a fluid: γ=1, α→0 and F→0.

[0095] 2.1.1 Incompressible laminar flow

[0096] For incompressible laminar flow, the dimensionless continuity equation and momentum conservation equation are expressed by dimensionless physical quantities. The dimensionless physical quantities include velocity u*, pressure p*, Reynolds number Re, and gradient operator The above dimensionless physical quantity is defined as:

[0097]

[0098] in: is the gradient operator; U and L are the characteristic velocity and length, respectively; ρ is the density; μ is the dynamic viscosity.

[0099] For incompressible laminar flow, the continuity equation is:

[0100]

[0101] The momentum conservation equation is:

[0102]

[0103] Among them: F * It is the volume force.

[0104] According to Darcy's law, the body force F* is proportional to the velocity u*, given by α *The dimensionless permeability represented by is then determined by subsequent penalty function interpolation:

[0105] F * =-α * u *

[0106]

[0107]

[0108] The penalty factor q is related to the Darcy number Da and the Reynolds number Re, resulting in the momentum equation:

[0109]

[0110] Where: q is the penalty factor; Da is the Darcy number.

[0111] 2.1.2 Conjugate heat transfer

[0112] The dimensionless energy conservation equation is given by the dimensionless temperature T * and the Prandtl number Pr, defined as follows:

[0113]

[0114]

[0115] Where: T B and T w The average temperature and the wall temperature are respectively; the thermophysical properties of the fluid are characterized by its specific heat capacity C p and thermal conductivity k f is a characteristic and is a key parameter in heat transfer analysis; μ is the fluid viscosity.

[0116] The dimensionless energy conservation equation is expressed as:

[0117]

[0118] Where: u * Indicates speed; Q * represents the dimensionless rate of heat generation, and the dimensionless temperature T * Proportional to:

[0119]

[0120] By introducing the design variable γ, we get:

[0121]

[0122] 2.1.3 Density filtering and projection

[0123] In order to avoid the checkerboard phenomenon in the design domain, density filtering in the form of Holmz partial differential equation is used:

[0124]

[0125] Where: R min is the filter radius, taking the cooling element size; θ is the design variable before filtering; is the filtered design variable; Represents the gradient operator.

[0126] The above density filtering method enhances the stability of the numerical solution. However, it also leads to a surge in gray elements. In order to solve the problem of gray elements, the hyperbolic tangent projection technique is used:

[0127]

[0128] in: is the output design variable after projection, η and β are the projection point and slope, respectively.

[0129] In this embodiment, η = 0.5, β = 8. The penalty factor q is 10 -2 , the Darcy number is 10 -4 , Pr is taken as 6.78. Under the same thermal boundary conditions, the temperature of CP decreases with the increase of Reynolds number Re. The Reynolds number Re is taken as 200, and the heat transfer coefficient h* is taken as 100.

[0130] 2.2 Topology Design Optimization Method

[0131] Existing nut housing such as Figure 4 (a). In order to accommodate CE, the structure of the nut housing was modified, as shown in Figure 4 (b), where the hollow space for accommodating the CE is specified. Then the size of the TO design domain is determined. Specifically, according to Figure 4 (c), the outer diameter Φ1 is 96 mm, the inner diameter Φ2 is 80 mm, the length and thickness of CE are 81 mm and 8 mm respectively. The cross-sectional distance is 40 mm. In order to simplify the TO model, the three-dimensional design domain is expanded, as shown in Figure 4 (d) As shown. The effect of thickness on CE heat transfer efficiency is not significant, so the thickness degree of freedom is not considered to reduce the computational load. Multi-objective topology optimization (MTO) is performed on a two-dimensional rectangular design domain. The design domain dimensions are as follows: width is 243mm and length is 220πmm. In order to further improve the stability and convergence of the TO model, the two-dimensional rectangular design domain is divided in half from the middle, and symmetric boundary conditions are set. Therefore, the final design domain is a rectangle of 243aL×110πaL, as shown in Figure 4(e) is shown. L and a represent the characteristic length and the scale factor, respectively. The scale factor a is specified as 1 / 60 to reduce the computational scale. Considering the inconvenience of arranging CE due to the movement of MN in the axial direction of SS, an embedded CE is designed. In addition, the inflow and outflow of CP are arranged on the same parallel side in the design domain. The two-dimensional design domain and boundary conditions are shown in Figure 4 (f) A uniform heat load Q* is applied to the design domain. The volume flow rate at the inlet is set to fully developed flow conditions, the inlet temperature is set to T* = 0 K, and the outlet pressure is set to P* = 0 Pa.

[0132] Specifically, the cooling element of the precision gear grinding machine tool and the multi-objective thermal-fluid topology design optimization method thereof in this embodiment include the following steps:

[0133] Step 1: Define the design domain

[0134] The cooling element is unfolded into a plane, a two-dimensional design domain representing the geometric structure of the cooling element is defined, and the finite element method is used for discretization. In this embodiment, the cooling element is symmetrically divided into two halves, and the two-dimensional design domain is defined as the geometric structure representing one half of the cooling element, that is, in this embodiment, only one half of the cooling element needs to be designed.

[0135] Step 2: Numerical modeling

[0136] The cooling element is modeled as a porous medium; under the condition of laminar incompressible flow, the fluid dynamics are governed by the dimensionless forms of the continuity equation and the momentum equation; the fluid-solid coupled heat transfer model is governed by the dimensionless energy conservation equation;

[0137] Step 3: Construct the objective function

[0138] In order to improve cooling performance and reduce flow resistance, the optimization objective is defined as a weighted function of heat transfer and fluid dissipation power, and a fluid-solid heat transfer topology optimization model is constructed:

[0139]

[0140] Where: J is the optimization target; J th is the heat transfer term; J f is the fluid dissipation work term; w1 and w2 are J th and J f is the weight factor; Ω is the design domain; V f is the volume fraction occupied by the fluid flow path; Vol is the total volume contained in the design domain; γ is the design variable; h * is the dimensionless heat transfer coefficient; T * is the dimensionless temperature; is the dimensionless gradient operator; u * is the dimensionless flow velocity; α* is the dimensionless permeability; Vol Ω is the total volume contained in the design domain; Q is the heat load applied by the design domain; is the dimensionless inlet pressure; Γ is the flow channel; Γ in is the flow channel entrance;

[0141] Step 4: Solve the objective function

[0142] The sensitivity is solved by the adjoint method, and the gradient calculated by the adjoint method is used to form a quadratic subproblem of the sequential quadratic programming method. The design variable γ is updated by solving the quadratic subproblem to ensure that the solution moves toward the optimal configuration until the set iterative convergence condition is met. The topological design channel (TOC) is designed in the cooling element.

[0143] Step 5: Restoring the shape and structure of the cooling element. In this embodiment, the two cooling elements are symmetrically combined into one, and then restored to an arc shape.

[0144] In this embodiment, the iterative convergence condition is:

[0145]

[0146] Where: k represents the number of iterations; Represents the value of the objective function after the kth iteration.

[0147] In order to meet the mesh density and basic uniformity criteria of the TO, a free triangular mesh was used during the construction process. A direct correlation between the mesh size and the filter length used in the TO is given. When the number of elements is 18087, the effect of the additional element number increment on the objective function becomes negligible while maintaining a high level of computational efficiency. When the number of elements is 18087, the size of the elements ranges from 1.15×10 -4 m to 0.0576m. Therefore, the total number of components in the entire design domain of TO is 18087. Figure 5 The meshing results are depicted.

[0148] This embodiment also proposes a cooling element for a precision gear grinding machine, which is designed using the multi-objective thermal-fluid topology design optimization method described above in this embodiment.

[0149] The present embodiment also proposes a precision gear grinding machine tool, comprising an X-axis, a Y-axis and a Z-axis, wherein the X-axis, the Y-axis and the Z-axis are each provided with a ball screw feed drive system, the ball screw feed drive system comprising a screw shaft and a movable nut cooperating with the screw shaft, the movable nut comprising a nut and a nut housing, and a cooling element as described above in the present embodiment is provided between the nut and the nut housing.

[0150] 2.3 Topological results and experimental verification

[0151] 2.3.1 TO Results

[0152] Table 1 shows the TO design results when the Reynolds number Re is 200. Volume fraction V f is set to 0.50, 0.55, and 0.60. The weight factor w1 is set to 0.6, 0.7, 0.8, 0.85, and 0.9. The TO results show that with the increase of volume fraction, the branches of TOC become thinner and more numerous, while the incidence of disconnected channels also increases, which indicates that the convergence of the TO model decreases. In addition, at the same volume fraction, increasing the weight factor w1 leads to subtle changes in the channel structure. The difference in TO results directly affects the heat transfer performance.

[0153] Table 1TO design results

[0154]

[0155]

[0156] In order to verify the validity of the TO results, thermal characteristics of different TOCs at different Reynolds numbers were analyzed. The specific boundary settings are as follows: Re is set to 200, 500, 1000, 1500 and 2000. The initial temperature of the inlet is 293.15K, and the outlet pressure is maintained at 0Pa. The remaining boundaries are under adiabatic anti-slip conditions, and 8000W / m 3 The material properties are shown in Table 2.

[0157] Table 2 Material properties of solids and liquids

[0158]

[0159] When the Reynolds number Re is 500, the surface temperature distribution in the design domain is shown in Table 3. Volume fraction V f The weight ratio w1 has an effect on the surface temperature distribution and temperature uniformity. When Re is 200, 1000 and 2000, the surface temperature distribution is shown in Table A. f The temperature field distribution of TOC obtained at different volume fractions V f and temperature field distribution of TOC obtained under weight ratio w1.

[0160] Table 3 Surface temperature distribution

[0161]

[0162]

[0163] Table 4 lists the steady-state temperature distribution of the cooling fluid when the Reynolds number Re is 500. f , the three instances with the lowest average temperature appear at w1 values ​​of 0.6, 0.8, and 0.9, respectively. When w1 is 0.9, the pressure drop loss is much more significant than the pressure drop loss at other w1 values, thereby hindering the normal flow of the fluid in the cooling channel. Therefore, the TO results when w1 is 0.9 will not be considered in the later discussion. According to the temperature data listed in Table 4, when V f When V is set to 0.55 and w1 is set to 0.8, the optimal conditions of the lowest maximum fluid temperature of only 317K and the most uniform temperature distribution are achieved. Therefore, it can be concluded that when Re is 500, when V f When w1 and w2 are 0.55 and 0.8 respectively, the TO cooling channel obtains the best heat dissipation performance. In addition, according to Table A, the same pattern is observed under different Reynolds numbers.

[0164] Table 4 Average surface temperature (K)

[0165]

[0166] 2.3.2 Simulation and experimental verification

[0167] This example uses the average surface temperature, outlet temperature and pressure drop as evaluation indicators. Then the heat transfer performance of CP containing TOC and CP containing SC is compared. These evaluation indicators show similar trends. The independent variable is Re, which is set to 200, 500, 750, 1000, 1500 and 2000. Figure 6 As shown in (a), the average surface temperature of the full-size CP and the half-size CP are compared. The average surface temperature of the full-size CP drops from about 350K to about 300K. For the half-size CP, the average surface temperature drops from about 320K to about 296K. The simulated average surface temperatures of the full-size CP and the half-size CP are the same, so it is reasonable to simplify the full-size CP to the half-size CP for the design of to. Figure 6 (b) shows the pressure drop of the two CPs. The drop in outlet temperature reflects the trend of the average temperature. In terms of pressure drop, the pressure drop of the full-size CP with TOC is about one-quarter to one-third of the pressure drop of the CP with SC. Similarly, the pressure drop of the half-size CP with TOC is about one-third to one-half of the pressure drop of the CP with SC, showing a consistent proportional relationship. In addition, Figure 6 The simulated outlet temperature in (b) shows the same Figure 6 The simulated surface average temperature shows a similar trend as shown in (a). Therefore, it is reasonable to replace the full-size CP with TOC and the half-size CP with TOC. In addition, the heat transfer capacity and efficiency of the full-size and half-size CP with TOC are stronger than those of the CP with SC.

[0168] Considering the practical application of the designed CE, a half-size CP was used in the actual application. This choice aims to maintain the consistency of the result trend while reducing the experimental cost as much as possible. Therefore, the two-dimensional TO results were expanded to obtain the three-dimensional CP, such as Figure 7 In order to study the cooling performance of the designed CP with TOC, the designed CP with TOC was manufactured using 3D printing technology, as shown in Figure 8 The experimental conditions are as follows: the inlet fluid flow rate is vin. The outlet pressure is kept at 0 Pa. The bottom of the CP is uniformly heated by a copper plate with a fixed heating power of 200 W. In addition to these conditions, the remaining boundaries are characterized by natural convection with a heat transfer coefficient of 9.7 W / (m2·K).

[0169] The purpose of the experimental study is to verify the heat transfer capacity and efficiency of the designed CP with TOC. The heat transfer capacity and efficiency of the designed CP with TOC are compared with that of the CP with SC. The experimental study was conducted to verify the heat dissipation performance of cathodic protection with TOC. The experimental setup is as follows Fig. 9 (a). The bottom of the CP is heated by a uniformly heated copper plate, and the distilled water circulation in the cooling channel is driven by an industrial-grade chiller, and Re is kept constant. The flow rate is regulated by a two-stage control, namely preliminary adjustment by a ball valve and fine-tuning by a needle valve. In addition, the flow rate is continuously collected using a precision flow meter and an accumulator. At the same time, temperature probes are strategically placed at the inlet and outlet of the CP to collect the temperature difference. In addition, a differential pressure sensor is installed to quantify the pressure change between the inlet and outlet of the CP. The collected data is immediately transmitted to the data logger for subsequent processing. In order to capture the thermal distribution on the upper surface of the CP, an infrared thermal imager was used. Fig. 9 (b) shows the experimental flow chart.

[0170] The heating power is maintained at 200 W. The inlet Re is 500. The inlet diameter represented by d is set to 9.7 mm. The inlet Re is defined as:

[0171]

[0172] In this way, the flow velocity v can be obtained, so the flow velocity q is determined using q = Av. The cross-sectional area A of the inlet is expressed as A = πd 2 / 4. Then, the corresponding flow rate q under different Reynolds numbers Re is determined, as shown in Table 5.

[0173] Table 5 Flow rate

[0174]

[0175] The inlet temperature is controlled by an industrial chiller at 20°C, which is the baseline temperature of the entire fluid circulation process. The temperature sensor located at the CP inlet is responsible for monitoring and recording the average temperature of the inflow flow, which is represented by T in When cooling water is introduced into the industrial chiller, the cooling cycle process begins, ensuring that the tin is kept at around 20°C. Once the fluid completely fills the cooling channel and the measurement data displayed on the recorder stabilizes, experimental data collection begins.

[0176] During the experiment, experimental data of CP containing SC and TOC were collected. In order to capture the temperature field on the CP surface, an infrared thermal imager was used. The temperature of the CP surface is shown in Fig.10 In order to accurately represent the temperature field of the CP with SC and TOC, three experiments were carried out under each working condition, and the surface temperature was taken as the average of the three experimental data.

[0177] by Fig.10 The experimental data shown are used as input to calculate the average surface temperature, and then the simulation value is compared with the experimental data, as shown in Fig.11 As shown. With the increase of Reynolds number Re, the surface average temperature gradually decreases. In the computational simulation, the initial surface average temperature of the CP containing TOC is slightly higher than that of the CP containing SC. However, with the increase of Re, the temperature difference between the CP containing SC and TOC gradually decreases and finally reaches an equilibrium state. The initial temperature difference is recorded as 2.8K, and as Re increases, the initial temperature difference decreases to 0.3K. In contrast, the experimental data show an opposite trend to the simulation results. Throughout the experiment, the surface average temperature of the CP containing TOC is always lower than that of the CP containing SC. Initially, for the simulation results, when the inlet Re is 2000, the CP temperature of TOC is lower than that of SC by 5K, and the temperature gap narrows to 0.1K. The difference between the measured data and the simulation results is not obvious and decreases with the increase of inlet Re. This difference is attributed to the actual contact state between the heating plate and the CP. Specifically, the contact between the heating plate and the CP is not perfect, resulting in a decrease in heat transfer efficiency. In addition, there will be heat loss to the surrounding air in the experiment, which may further reduce the experimental data. Therefore, the measured surface average temperature is lower than the simulation prediction results.

[0178] The pressure drop between the input and output measured by the differential pressure sensor does not fully reflect the actual pressure loss of the CP due to friction loss during the circulation process. In order to more accurately evaluate this parameter, an empty pipe is first used, and then the pressure drop Pe between the input and output is measured. The empty pipe is then replaced with a CP, and the pressure drop Pc between the input and output is measured. The pressure drop Pe is then subtracted from the pressure drop Pc to determine the actual pressure loss of the CP with SC and TOC. For both the simulation results and the experimental data, the CP with SC exhibits a higher pressure loss compared to the CP with TOC. Specifically, as Fig.12 As shown, the experimental data show that under the same Reynolds number Re, the pressure loss of CP with TOC is only 1 / 3 to 1 / 2 of that of CP with SC, which indicates that cathodic protection with TOC has significant advantages in saving cycle energy and improving heat transfer efficiency.

[0179] The results show that CPs with TOC have significant advantages over CPs with SC. Specifically, CPs with TOC excel in two key performance indicators: pressure loss and surface average temperature. Lower pressure loss indicates reduced energy consumption during fluid circulation, thereby improving energy efficiency. In addition, lower surface average temperature shows excellent heat dissipation, which is crucial to the overall efficacy of CPs. Therefore, CPs with TOC are not only energy-saving but also have excellent cooling performance, making them promising for application in cooling systems.

[0180] 3. Experimental verification

[0181] 3.1 Heat source load and thermal boundary conditions

[0182] 3.1.1 Heat source load

[0183] In GGMT, the main heat sources of BSFDS include motor, bearing pair and nut pair. Considering the distance between motor and other components and the insulation effect of silicon steel coupling, it is difficult for the heat of motor to enter BSFDS of GGMT. Since the temperature rise is not obvious, heat radiation is not considered. The motor runs at a speed of 1000r / min. The lead L of SS f is 20mm. When the nut reaches the limit position, it decelerates and then accelerates to a constant speed to complete the reverse motion. Since the duration of deceleration and acceleration is significantly shorter than that of constant speed motion, the heat generated in the constant speed stage is mainly considered. The heat generation of the bearing and nut pair is calculated using the existing method. The heat generation rate of the bearing and nut pair is calculated according to Q = 1.047 × 10 -4 nM determined.

[0184] 3.1.2 Convection coefficient

[0185] This embodiment takes into account the natural convection coefficient of the stationary surface / air and the forced convection coefficient of the moving surface / air. In addition, the designed CE is in contact with the MN, and this embodiment also takes into account the forced convection coefficient between the CE and the MN. The specific information of the BSFDS of GGMT is shown in Table 6. The BSFDS of GGMT consists of several key components, such as the nut pair with model FSC32-20K3. The rolling guide pair model is HGH-30CA. The movement is driven by the SMMA-312G67BDK stepper motor. The motor is supported by the support block ZS25-130 to ensure stable and safe installation. The fixed support seat BK25 is used to fix one end of the nut pair. The servo driver is SD20-452T3M3F0D51B1.

[0186] Table 6 Experimental device models

[0187]

[0188] When the speed is 1000r / min, the heating power and boundary conditions are: the heating power of the fixed bearing, the supporting bearing and the nut pair are 13.1W, 13.1W and 45.65W respectively. The convection coefficient of the rotating surface / air and the stationary surface / air is 26.93W / (m 2 ·K), the convection coefficients of the linear motion surface / air and CE / MN are 10.63W / (m 2 ·K)、28.4W / (m 2 K) and 1826.4W / (m 2 ·K).

[0189] 3.2 Thermal Fluid-Solid Behavior Simulation

[0190] Fig.13 A modified MN with an embedded CE is shown. The nut pair is the main heat-generating component with a heating boundary on its inner wall and a specified heating power of 43.65 W. The inlet and outlet of the designed CE are facilitated by M6-sized threaded holes. During the simulation, the Reynolds number Re at the inlet is precisely adjusted to 1000 and the outlet pressure is maintained at 0 Pa. In addition, the convection coefficient of the outer surface of the MN (excluding the area in contact with the CE) is 9.7 W / (m 2 ·K). The thermal fluid-solid simulation was carried out for 5 hours.

[0191] When the BSFDS of GGMT runs continuously for 5 hours, the temperature distribution in the MN not affected by CE is as follows Fig.14 As shown in (a), the temperature distribution in the MN affected by CE and with TOC and SC is shown in Fig.14(b) and (c). It is noteworthy that the CE containing TOC and SC significantly reduced the temperature of MNs, resulting in a temperature decrease of about 10 °C. Under the action of CE with SC and TOC, the temperature difference between MNs was not obvious, verifying the effectiveness of CP with TOC, that is, verifying the effectiveness of the MTO-based CE design.

[0192] 3.3 Experimental Verification

[0193] 3.3.1 Experimental setup

[0194] The designed CE was manufactured using 3D printing technology and embedded in the BSFDS of GGMT. Fig.15 As shown. To ensure that the environmental conditions do not introduce measurement errors to the measurement results, the ambient temperature is controlled at 293.15K. The temperature rise, the thermal expansion of the stainless steel end face and the positioning accuracy of the BSFDS are used as evaluation indicators. To measure the temperature rise, several PT100 temperature sensors are used. The temperatures of the front and rear bearing housings and the MN are collected by PT100 sensors. The eddy current displacement sensor is used to measure the thermal expansion of the stainless steel end face, with special attention to the support end.

[0195] In order to accurately assess the positioning accuracy, a Renishaw XL-80 laser interferometer was used. The MN with the interferometer was traversed on a precisely defined path ranging from 0 to 1200 mm. The measurement range was divided by seven different points, positioned at 200 mm intervals, to assess the positioning accuracy, such as Fig.16 As shown. The MN with the interferometer pauses at each point for 5 seconds. The servo motor is calibrated to run at 1000r / min.

[0196] Fig.17 The detailed temperature changes of MNs within the GGMT BSFDS during about 5 hours of continuous operation are shown. The temperature of MNs without CE effect is much higher than that of MNs with CE effect with SC and TOC. Specifically, the temperature of MNs with CE and TOC effect is 3K lower than that of MNs without CE effect, and the temperature of MNs with CE effect and SC effect is 2.5K lower than that of MNs without CE effect. That is, the heat transfer ability of CE with TOC is stronger than that of CE with SC. In addition, the temperature of MNs with TOC CE is lower than that of MNs with SC CE. The designed CE with TOC is able to reduce the temperature of MNs. CE with TOC has a stronger heat dissipation ability than CE with TOC.

[0197] The axial thermal expansion of the stainless steel support end surface (SES) is as follows Fig.18As shown. For the GGMT BSFDS without CE influence, the SS undergoes rapid thermal expansion in the initial stage of operation. Over time, especially in the first 2 hours, the temperature increase causes the SES to gradually stabilize. After 2 hours, the rate of change of thermal elongation of the SS becomes more gentle. However, the thermal expansion process continues, eventually resulting in an axial thermal expansion of about 42μm. In contrast, when the BSFDS of GGMT is affected by the embedded CE, the axial thermal expansion of the SES is reduced compared with the SES without CE influence. The SES with CE plus TOC is slightly lower than that with CE plus SC. Compared with the screw shaft support end face not affected by CE, the axial thermal expansion of the SES of SS under the action of CE plus TOC and SC shows a similar change law, and the final expansion is reduced from the initial 42μm to 32μm. When the BSFDS of GGMT runs for 2 hours, in the subsequent 2 to 5 hours, the average axial thermal expansion of the SS SES under the influence of CE and TOC is reduced by about 10% compared with the SS SES without CE influence. When the SS's SES undergoes axial thermal expansion, the positioning accuracy and repeatability will decrease. As the axial thermal elongation of the SS's SES increases, the pitch of the SS also increases, resulting in an increase in the axial movement distance of the MN and the table driven by the SS with the same number of rotations, thereby introducing more significant PE and RPE.

[0198] RPE was measured as Fig.19As shown. Under the combined effect of CE and TOC, the PE of the BSFDS of GGMT is significantly reduced compared with the GGMT BSFDS not affected by CE. Then, the effectiveness of the CE design of the GGMT BSFDS based on MTO is fully verified. The results show that the application of the designed CE with TOC on MN can significantly improve the repeatability accuracy, and the positioning accuracy is improved by 31.00% to 92.59% compared with the case without cooling. When the running time T = 0.5h, the RPE range is [14.4μm, 36.2μm] when the BSFDS of GGMT is not affected by CE, and then when the BSFDS of GGMT is affected by CE and SC, the RPE range is reduced to [1.6μm, 22.0μm], and when GGMT is affected by CE and TOC, the RPE range is reduced to [11.1μm, 18.4μm]. At T = 1 hour, when the BSFDS of GGMT was not affected by CE, the range of RPE was [31.0 μm, 60.0 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [4.5 μm, 33.7 μm], and when GGMT BSFDS was affected by CE and TOC, the range of RPE decreased to [3.7 μm, 30.1 μm]. At T = 1.5 hours, when the BSFDS of GGMT was not affected by CE, the range of RPE was [52.2 μm, 86.5 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [10.6 μm, 42.6 μm], and when GGMT BSFDS was affected by CE and TOC, the range of RPE decreased to [9.8 μm, 39.2 μm]. At T = 2 h, when the BSFDS of GGMT was not affected by CE, the range of RPE was [71.4 μm, 110.2 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [23.6 μm, 72.0 μm], and when GGMT BSFDS was affected by CE and TOC, the range of RP-E decreased to [23.3 μm, 68.1 μm]. At T = 2.5 h, when the BSFDS of GGMT was not affected by CE, the range of RPE was [95.9 μm, 139.6 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [21.1 μm, 82.9 μm], and when GGMT BSFDS was affected by CE and TOC. At T = 3 h, when the BSFDS of GGMT was not affected by CE, the range of RPE was [108.5 μm, 159.8 μm], which was reduced to [48.0 μm, 102.6 μm] when the BSFDS of GGMT was affected by CE and SC, and to [48.0 μm, 102.6 μm] when the BSFDS of GGMT was affected by CE and TOC.At T = 3.5 hours, when the BSFDS of GGMT was not affected by CE, the range of RPE was [120.6 μm, 174.9 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [72.7 μm, 127.9 μm], and when GGMT BSFDS was affected by CE and TOC. At T = 4 hours, when the BSFDS of GGMT was not affected by CE, the range of RPE was [133.5 μm, 187.0 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [79.2 μm, 135.9 μm], and when GGMT BSFDS was affected by CE and TOC. At T = 4.5 hours, when the BSFDS of GGMT was not affected by CE, the range of RPE was [138.6 μm, 208.0 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [90.6 μm, 146.6 μm], and when GGMT BSFDS was affected by CE and TOC. At T = 5 hours, when the BSFDS of GGMT was not affected by CE, the range of RPE was [154.5 μm, 215.4 μm], when GGMTBSFDS was affected by CE and SC, the range of RPE decreased to [83.9 μm, 151.1 μm], and when GGMT BSFDS was affected by CE and TOC, the range of RP-E decreased to [83.1 μm, 147.9 μm]. At T=0.5 hour, T=1 hour, T=1.5 hours, T=2 hours, T=2.5 hours, T=3 hours, T:3.5 hours, T=4 hours, T=4.5 hours and T=5 hours, the average reduction rates of RPE were 65.79%, 65.95%, 65.99%, 51.02%, 59.83%, 45.96%, 33.46%, 34.11%, 32.47% and 38.03%, respectively.

[0199] Compared with the BSFDS without CE, the RPE reduction rate of BSFDS under the influence of CE and TOC was evaluated, as shown in Table 7. From 0.5 h to 3.5 h, under the influence of CE and TOC, the repetitive positioning accuracy of BSFDS was improved by 29.03% to 92.59% compared with the BSFDS without CE. From 4 h to 5 h, the repetitive positioning accuracy under the influence of CE with TOC was improved by 29.17% to 46.22% compared with the case without CE, which significantly improved the repetitive positioning accuracy. In addition, under the influence of CE with TOC, the RPE of BSFDS was much smaller than that of BSFDS without CE. The reduction rate in the time range [0.5h, 3.5h] was lower than that in the time range [4h, 5h] because the thermal equilibrium state was reached in the time range [4h, 5h]. When the thermal equilibrium state was reached, the temperature and thermal error of BSFDS in GGMT did not change significantly, so the RPE also remained stable.

[0200] Table 7 Repeat positioning error reduction rate

[0201]

[0202] The RPE reduction rate of BSFDS under CE plus TOC was evaluated compared with that under CE plus SC, as shown in Table 8. From 0.5 h to 3.5 h, the repetitive positioning accuracy of BSFDS under CE plus TOC was improved by 9.82% to 79.44% compared with that of BSFDS under CE plus SC. From 4 h to 5 h, the repetitive positioning accuracy of BSFDS under CE plus TOC was improved by 7.64% to 18.09% compared with that of BSFD under CE plus SC.

[0203] Table 8 Repeat positioning accuracy improvement rate

[0204]

[0205] From the above analysis, it can be concluded that the temperature of MN is significantly reduced by more than 3K under the influence of CE and TOC compared with MN without CE. The axial thermal expansion of SS SES is reduced by nearly 10%. More importantly, the results show that the CE with TOC designed on MN significantly improves the repeatability accuracy compared with the case without CE and the case with CE and SC. When the BSFDS of GGMT is affected by CE and TOC, the improvement rate of repeatability accuracy is in the range of [29.03%, 92.59%], while the BSSDS of GGMT is not affected by CE. Compared with the BSFDS of GGMT under the influence of CE and SC, the improvement rate of repeatability accuracy of GGMT's BSSDS under the influence of CE and TOC is in the range of [7.28%, 79.44%].

[0206] 3.3.3 Actual processing verification

[0207] To verify the effectiveness of the proposed MTO for CE in BSFDS, CE with TOC was embedded into the X, Y, and Z axes of precision GGMT by modifying the nut housings of X, Y, and Z axes. Then, high-performance gears were machined by GGMT with and without performing CE, as shown in Fig. 20 As shown. Specific information about the processed gear is as follows. The number of teeth is 50, the gear module is 5mm, the pressure angle is 20°, the addendum coefficient and the root coefficient are 1.0 and 1.25 respectively. The profile angle is equal to the pressure angle, the face width is 100mm, the helix angle is 15°, and the pitch circle diameter is 250mm. The process parameters are as follows. The rotation speed of the silicon carbide-based grinding wheel is 2000r / min. The rotation speed of the processed gear is 100r / min. The radial feed speed is 2mm / min and the axial feed speed is 1mm / min. The grinding depth is 0.002mm / min. The abrasive grain size of the grinding wheel is #120. The frequency of grinding wheel correction is as follows, and the grinding wheel is dressed after every 10-20 workpieces to maintain its shape and sharpness. A diamond dressing table is used. Oil-based coolant is used for the grinding process. To ensure effective cooling and lubrication, the coolant flow rate is 40L / min and the pressure is 6bar.

[0208] The geometric accuracy of the machined gears is as follows: Fig.21As shown. By implementing CE with TOC, it was observed that the maximum errors of the left and right tooth surfaces were reduced from 18.5μm to 6.3μm and from 16.7μm to 5.4μm, respectively. The implementation of CE and TOC improved the grinding accuracy of GGMT by more than about 65%. The combination of CE and SC improved the grinding accuracy of GGMT by about 53%. More importantly, the maximum errors of the left and right tooth surfaces were within the tolerance requirements outlined in ISO1328-1:2013. It is worth noting that CE with TOC was proven to be more effective than CE with SC in improving grinding accuracy. The effectiveness of the proposed CE MTO was fully verified in the BSFDS of precise GGMT.

[0209] 4. Conclusion

[0210] In order to reduce thermal errors, the MTO method of CE in precision GGMT BSFDS is proposed. The concept of MN direct temperature control is proposed, and the MTO model is established to maximize heat transfer and minimize fluid power dissipation. The main conclusions of this example are summarized as follows:

[0211] (1) A direct cooling strategy for MN in GGMT BSFDS was proposed and implemented. Based on the cooling strategy, CE was designed using the MTO method and then embedded in the nut shell, which significantly improved the machining accuracy of the entire GGMT.

[0212] (2) A fluid-solid heat transfer TO model was established to design the CE. Using the dimensionless equation, its convergence was effectively enhanced, the pressure drop was greatly reduced, and the cooling channel was optimized to achieve energy saving and improve heat dissipation performance. The designed CE has a volume fraction V f The best cooling performance is achieved when the weighting factor w1 is 0.8.

[0213] (3) The effectiveness of direct cooling of MN and TO model in GGMT BSFDS was confirmed through empirical tests. The results show that the overall temperature of MN is significantly reduced by more than 3K when CE is used. The axial thermal expansion of SS SES is reduced by about 10%. The results show that the repeated positioning accuracy can be significantly improved by using the designed CE with TOC in GGMT for repeated positioning of MN compared with the influence of no CE and the influence of CE with SC. When the BSFDS of GGMT is affected by CE with TOC, the improvement rate of repeated positioning accuracy is in the range of [29.03%, 92.59%]. The implementation of CE and TOC improves the grinding accuracy of GGMT by more than about 65%. The cooling and thermal error reduction effect of CE with TOC is much more significant than the reduction effect of CE with SC.

[0214] In conclusion, MTO of CE in precision GGMT provides a new solution to the thermal error control problem. Future research may further explore the application of more complex geometric designs and novel materials to further improve the cooling efficiency and thermal control performance of the system.

[0215] Table A

[0216]

[0217]

[0218]

[0219] 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 multi-objective thermal-fluid topological design optimization method for cooling elements of precision worm wheel gear grinding machine tools, characterized by: The steps include: Step 1: Define the design domain The cooling element is unfolded into a plane, a two-dimensional design domain representing the geometric structure of the cooling element is defined, and a finite element method is used for discretization; Step 2: Numerical modeling The cooling element is modeled as a porous medium; under the condition of laminar incompressible flow, the fluid dynamics are governed by the dimensionless forms of the continuity equation and the momentum equation; the fluid-solid coupled heat transfer model is governed by the dimensionless energy conservation equation; Step 3: Construct the objective function In order to improve cooling performance and reduce flow resistance, the optimization objective is defined as a weighted function of heat transfer and fluid dissipation power, and a fluid-solid heat transfer topology optimization model is constructed: Minimize γ∈[0,1] J-w1J th +w2J f w1+w2=1 J th =∫ Ω (1-γ)h * (1-T * )dΩ s.t.∫ Ω γdQ≤V f ·Vol Ω Where: J is the optimization target; J th is the heat transfer term; J f is the fluid dissipation work term; w1 and w2 are J th and J f is the weight factor; Ω is the design domain; V f is the volume fraction occupied by the fluid flow path; Vol is the total volume contained in the design domain; γ is the design variable; h * is the dimensionless heat transfer coefficient; T * is the dimensionless temperature; is the dimensionless gradient operator; u * is the dimensionless flow velocity; α * is the dimensionless permeability; Vol Ω is the total volume contained in the design domain; Q is the heat load applied by the design domain; is the dimensionless inlet pressure; Γ is the flow channel; Γ in is the flow channel entrance; Step 4: Solve the objective function The sensitivity is solved by the adjoint method, and the gradient calculated by the adjoint method is used to form a quadratic subproblem of the sequential quadratic programming method. The design variable γ is updated by solving the quadratic subproblem to ensure that the solution moves toward the optimal configuration until the set iterative convergence condition is met, and a topological design channel is designed in the cooling element. Step 5: Restore the shape and structure of the cooling element.

2. The multi-objective thermal-fluid topological design optimization method for the cooling element of the precision worm wheel gear grinding machine tool according to claim 1, characterized in that: In step 2, the method of modeling the cooling element as a porous medium is as follows: within the fluid-solid topology design domain, the design domain is theorized as a porous material, assuming that the fluid resistance F is linearly related to the flow velocity u: F=-αu Where: α is the permeability; The domain of the design domain is divided into a finite number of elements, each of which has a design variable γ, which takes values ​​between 0 and 1; when representing a solid: γ = 0, α → ∞ and F → ∞; when representing a fluid: γ = 1, α → 0 and F → 0.

3. The multi-objective thermal-fluid topological design optimization method for the cooling element of the precision worm wheel gear grinding machine tool according to claim 1, characterized in that: In step 3, fluid dynamics is determined by the continuity equation and momentum equation, which are the velocity u*, pressure p*, Reynolds number Re and gradient operator. To express it dimensionlessly: in: is the gradient operator; U and L are characteristic velocity and length, respectively; ρ is the density; μ is the dynamic viscosity; For incompressible laminar flow, the continuity equation is: The momentum conservation equation is: Among them: F * It is the volume force; According to Darcy's law, the body force F* is proportional to the velocity u*, given by α * The dimensionless permeability represented by is then determined by subsequent penalty function interpolation: F * =-a * you * The penalty factor q is related to the Darcy number Da and the Reynolds number Re, resulting in the momentum equation: Where: q is the penalty factor; Da is the Darcy number.

4. The multi-objective thermal-fluid topological design optimization method for the cooling element of a precision worm wheel gear grinding machine tool according to claim 1, characterized in that: The dimensionless energy conservation equation is given by the dimensionless temperature T* and the Prandtl number Pr and is defined as follows: Where: T B and T w The average temperature and the wall temperature are respectively; the thermophysical properties of the fluid are characterized by its specific heat capacity C p and thermal conductivity k f is a characteristic and is a key parameter in heat transfer analysis; μ is the fluid viscosity; The dimensionless energy conservation equation is expressed as: Where: u * Indicates speed; is the gradient operator; Q * represents the dimensionless rate of heat generation, and the dimensionless temperature T * Proportional to: Q * =h * (1-T * ) By introducing the design variable γ, we get:

5. The multi-objective thermal-fluid topological design optimization method for the cooling element of a precision worm wheel gear grinding machine tool according to claim 1, characterized in that: In order to avoid the checkerboard phenomenon in the design domain, density filtering in the form of Holmz partial differential equation is used: Where: R min is the filter radius, taking the cooling element size; θ is the design variable before filtering; is the filtered design variable; represents the gradient operator; In order to solve the problem of gray elements, the hyperbolic tangent projection technique is used: in: is the output design variable after projection, η and β are the projection point and slope, respectively.

6. The multi-objective thermal-fluid topological design optimization method for the cooling element of a precision worm wheel gear grinding machine tool according to claim 1, characterized in that: In the step 1, the cooling element is symmetrically divided into two halves, and the two-dimensional design domain is defined as the geometric structure representing one half of the cooling element; in the step 5, the two cooling elements are symmetrically combined into one.

7. A cooling element for a precision worm wheel gear grinding machine, characterized in that: The design is obtained by using the multi-objective thermal-fluid topology design optimization method as described in any one of claims 1 to 6.

8. A precision worm wheel gear grinding machine, characterized in that: It includes an X-axis, a Y-axis and a Z-axis, each of which is provided with a ball screw feed drive system, the ball screw feed drive system includes a screw shaft and a movable nut matched with the screw shaft, the movable nut includes a nut and a nut housing, and a cooling element as claimed in claim 7 is provided between the nut and the nut housing.

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