A design method for fractal heat conduction channel of machine tool spindle

Abstract

The present invention relates to the technical field of high-speed, high-precision CNC machine tools, and discloses a method for designing a fractal heat conduction channel for a machine tool spindle. By simulating and experimentally comparing the maximum temperature and overall temperature distribution of the fractal heat conduction channel with those of a straight heat conduction channel and a structure without a heat conduction channel, it was found that the method of the present invention makes the temperature field distribution in the spindle region more uniform and reduces the maximum temperature. The method is capable of rapidly dissipating the heat generated by the machine tool's main heat source under steady-state conditions, wherein the temperature stabilizes after an initial rapid rise, indicating that the test model has reached thermal equilibrium. Using 95% of the maximum temperature as the criterion, the fractal heat conduction path model and the straight heat conduction path model require approximately 33 minutes and 51 minutes, respectively, to reach steady state. Under the same experimental conditions, the fractal heat conduction path model achieves thermal equilibrium more quickly. Compared with the straight heat conduction path model, the temperature measurement points of the fractal heat conduction path model have lower temperatures at the same locations.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed and high-precision CNC machine tools, and in particular to a design method for a fractal heat conduction channel of a machine tool spindle. Background Art

[0002] High-speed, high-precision CNC machine tools are the primary development direction of the modern machine tool manufacturing industry and serve as the "mother machines" of manufacturing in numerous fields. To ensure high precision in machined workpieces, the machine tools themselves require high machining and assembly accuracy. However, in actual operation, machine tool accuracy can be affected by many factors, such as thermal deformation, a key issue. According to statistics, errors caused by heat account for 40%-70% of total machine tool errors. Temperature rise is the fundamental cause of thermal deformation. As heat is conducted from the heat source to the outside, due to the varying structural and material thermal conductivity of various components, large CNC machine tool components are subject to the combined influence of internal and external heat sources, resulting in uncontrollable temperature rise and temperature field distribution.

[0003] During high-speed operation, a large amount of heat is generated by internal heat sources such as the bearings and motors inside the machine tool spindle. If this heat is not quickly removed, it will continue to accumulate in the machine tool spindle. This heat propagates in different directions and at different speeds within the machine tool, resulting in an unevenly distributed temperature field inside the machine tool. To reduce temperature rise and shorten thermal equilibrium time, researchers have taken two approaches to quickly remove internal heat: structural design and enhanced heat exchange.

[0004] With the goal of quickly dissipating the heat generated by the main heat source of the machine tool under steady-state conditions, it is necessary to optimize and design a simple, effective and cost-effective heat conduction channel structure and its generation scheme.

[0005] When designing a heat transfer channel, it's important to explore the appropriate distribution and shape to ensure it can efficiently transfer heat from the heat source. Currently, there are numerous approaches to designing heat transfer channels, but a simple, effective, and cost-effective heat transfer channel structure and generation solution has yet to be established. Summary of the Invention

[0006] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to provide a design method for a fractal heat conduction channel of a machine tool spindle to solve the technical problem that the main heat source of the machine tool cannot quickly dissipate the heat generated under steady-state conditions.

[0007] The present invention is achieved through the following technical solutions:

[0008] A method for designing a fractal heat conduction channel for a machine tool spindle comprises the following steps:

[0009] Step 1: Select the machine tool spindle design domain and heat source, establish a simplified model based on the size parameters of the machine tool spindle design domain, set thermal boundary conditions based on the parameters of the heat source, and establish the temperature field of the heat conduction channel;

[0010] Step 2: Select the fractal dimension and bifurcation angle within the design domain of the heat conduction channel, determine the number of branches and the length and width ratios of each branch, and determine the length and width of each branch channel based on the volume fraction of the heat conduction channel in the total design domain;

[0011] Step 3: Determine whether the distribution of branch channels is reasonable. If not, redetermine the number of branches and fractal dimension, calculate the length ratio and width ratio, and then determine the width and length of each branch of the fractal heat conduction channel based on the volume fraction, and generate the heat conduction channel.

[0012] Step 4: Use Solidworks to perform modeling, import the heat conduction channel model into COMSOL software, perform thermal steady-state thermal conductivity performance analysis, obtain the maximum temperature and overall temperature distribution of the model, and compare it with the no-channel and straight-channel heat conduction channel models to obtain a comparison of the heat conduction channel performance before and after fractal optimization design.

[0013] Preferably, in step 1, the heat source includes a spindle motor and a spindle bearing.

[0014] Preferably, in step 1, the thermal boundary condition is simplified as follows: one side of the rectangular area is a heat source, the side opposite the heat source is a cooling water jacket, and both sides are thermal insulation.

[0015] Preferably, in step 1, the temperature field of the heat conduction channel is established by combining the thermal boundary conditions and the two-dimensional steady-state Fourier law.

[0016] Preferably, in step 2, the bifurcation angle is selected as 90 degrees, the fractal dimension is selected as an empirical value of 3, and the length L0 of the main channel is determined according to the length and width of the design domain.

[0017] Preferably, in step 2, the length of the fractal heat conduction channel satisfies the following conditions:

[0018]

[0019]

[0020] Where W represents the design domain width, which can be calculated by the difference between the inner and outer diameters of the main shaft heat conduction channel; L represents the design domain width; L0 represents the main channel length. The sum of the even-numbered branches is related to the design domain width, and the sum of the odd-numbered branches is related to the design domain length.

[0021] Preferably, in step 2, the length and width of each branch meet the following conditions:

[0022]

[0023] Where α represents the length ratio and β represents the width ratio.

[0024] Preferably, in step 2, the length ratio and width ratio are determined according to the fractal dimension, and the specific formula is as follows:

[0025]

[0026] Where ΔL represents the length fractal dimension, ΔW represents the width fractal dimension, and the empirical value is 3.

[0027] Preferably, in step 2, the width of each branch is determined according to the length, volume fraction and width ratio of each branch. The specific formula is as follows:

[0028]

[0029] Where W k represents the width of each branch, S represents the total area of ​​the fractal channel, S k Indicates the total area of ​​branch channels at all levels.

[0030] Preferably, in step 2, the total area S of the fractal channel is equal to the product of the total area of ​​the design domain and the volume fraction:

[0031] S=W×L×λ

[0032] Where λ represents the volume percentage parameter.

[0033] Compared with the prior art, the present invention has the following beneficial technical effects:

[0034] The present invention provides a design method for a fractal heat conduction channel for a machine tool spindle. By simulating and experimentally comparing the maximum temperature and overall temperature distribution of a fractal heat conduction channel with that of a straight heat conduction channel and a structure without a heat conduction channel, it is found that the method of the present invention makes the temperature field distribution in the spindle area more uniform and reduces the maximum temperature. The method is able to quickly remove the heat generated by the main heat source of the machine tool under steady-state conditions, wherein the temperature tends to stabilize after an initial rapid rise, indicating that the test model has reached thermal equilibrium. Taking 95% of the maximum temperature as the criterion, the fractal heat conduction path and the straight heat conduction path models require approximately 33 minutes and 51 minutes, respectively, to reach steady state. Under the same experimental conditions, the fractal heat conduction path model achieves thermal equilibrium faster. Compared with the straight heat conduction path model, the temperature measurement points of the fractal heat conduction path model have lower temperatures at the same location. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of the design method of the fractal heat conduction channel of the machine tool spindle in the present invention;

[0036] Figure 2This is a simplified process diagram of the two-dimensional heat conduction channel of the machine tool spindle in the present invention. Figure (a) is a schematic diagram of the thermal boundary; Figure (b) is a simplified two-dimensional schematic diagram.

[0037] Figure 3 This is a simplified schematic diagram of the boundary conditions of the two-dimensional rectangular cross-section heat conduction channel in the present invention;

[0038] Figure 4 This is a schematic diagram of the dimensions of the spindle heat conduction channel design area in the present invention;

[0039] Figure 5 It is a fractal network structure with a bifurcation angle of 90° in the present invention;

[0040] Figure 6 Figure 2 is a diagram of the heat conduction channel model in the present invention. Figure (a) is a fractal heat conduction channel model; Figure (b) is a straight heat conduction channel model.

[0041] Figure 7 Figure 2 is the simulation result of the fractal heat conduction channel model in the present invention. Figure (a) is the temperature trend of the fractal heat conduction channel, and Figure (b) is the isotherm.

[0042] Figure 8 This is the maximum temperature comparison of the simulation of the rectangular cross-section fractal heat conduction channel, the straight heat conduction channel, and the structure without heat conduction channel in the present invention. DETAILED DESCRIPTION

[0043] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0044] The present invention is described in further detail below with reference to the accompanying drawings:

[0045] The present invention provides a fractal structure optimization design method for machine tool heat conduction channels. Taking a certain model of CNC machine tool spindle as an example, under steady-state working conditions, the optimal heat conduction path from the inside to the outside of the main heat source heat conduction channel is designed, thereby achieving highly efficient heat conduction. This is of great significance for improving the temperature field distribution of precision machine tools, enhancing the working performance of machine tools and the processing accuracy of machine tools.

[0046] Specifically, according to Figure 1 As shown, the design method of the fractal heat conduction channel of the machine tool spindle includes the following steps:

[0047] Step 1: Select the machine tool spindle design domain and heat source parameters, establish a simplified model based on the size parameters of the machine tool spindle design domain, set thermal boundary conditions based on the heat source parameters, and establish the temperature field of the heat conduction channel;

[0048] Step 2: Select the fractal dimension and bifurcation angle within the design domain of the heat conduction channel, determine the number of branches and the length and width ratios of each branch, and determine the length and width of each branch channel based on the volume fraction of the heat conduction channel in the total design domain;

[0049] Step 3: Determine whether the distribution of branch channels is reasonable. If not, redetermine the number of branches and fractal dimension, calculate the length ratio and width ratio, and then determine the width and length of each branch of the fractal heat conduction channel based on the volume fraction, and generate the heat conduction channel.

[0050] Step 4: Use Solidworks to build a model, import the model into COMSOL software, perform thermal steady-state thermal conductivity performance analysis, obtain the maximum temperature and overall temperature distribution of the model, and compare it with the channel-free and straight channel thermal conduction channel models to obtain a comparison of the thermal conduction channel performance before and after fractal optimization design.

[0051] Specifically, in step 1, the heat source includes a spindle motor and a spindle bearing.

[0052] Specifically, in step 1, the thermal boundary condition is simplified to a rectangular region in which one side is a heat source, the side opposite the heat source is a cooling water jacket, and both sides are thermal insulation.

[0053] Specifically, in step 1, the temperature field of the heat conduction channel is established by combining the thermal boundary conditions and the two-dimensional steady-state Fourier law.

[0054] Specifically, in step 2, the bifurcation angle is selected as 90 degrees, the fractal dimension is selected as the empirical value 3, and the length L0 of the main channel is determined according to the length and width of the design domain.

[0055] Specifically, in step 2, the length of the fractal heat conduction channel satisfies the following conditions:

[0056]

[0057]

[0058] Where W represents the design domain width, which can be calculated by the difference between the inner and outer diameters of the main shaft heat conduction channel; L represents the design domain width; L0 represents the main channel length. The sum of the even-numbered branches is related to the design domain width, and the sum of the odd-numbered branches is related to the design domain length.

[0059] Specifically, in step 2, the length and width of each branch meet the following conditions:

[0060]

[0061] Where α represents the length ratio and β represents the width ratio.

[0062] Specifically, in step 2, the length ratio and width ratio are determined according to the fractal dimension. The specific formula is as follows:

[0063]

[0064] Where ΔL represents the length fractal dimension, ΔW represents the width fractal dimension, and the empirical value is 3.

[0065] Specifically, in step 2, the selection of the number of classifications k should be the maximum value that ensures that the fractal channel does not exceed the design domain.

[0066] Specifically, in step 2, the width of each branch is determined according to the length, volume fraction and width ratio of each branch. The specific formula is as follows:

[0067]

[0068] Where W k represents the width of each branch, S represents the total area of ​​the fractal channel, S k Indicates the total area of ​​branch channels at all levels.

[0069] Specifically, in step 2, the total area S of the fractal channel is equal to the product of the total area of ​​the design domain and the volume fraction:

[0070] S=W×L×λ

[0071] Where λ represents the volume percentage parameter.

[0072] Specifically, in step 3, whether the distribution is reasonable is determined by determining whether the fractal heat conduction channel exceeds the design domain and whether there is interference between the branches.

[0073] Example

[0074] according to Figure 1 The flow chart of the method for designing the layout of the fractal heat conduction channel of a machine tool is shown. The technical solution of the present invention specifically includes the following steps:

[0075] Step 1: Select the machine tool design area and main heat source, and select the bearing support area of ​​a certain type of CNC machine tool spindle as the design domain, such as Figure 2 As shown. Figure 2 Figure (a) shows the process of abstracting a 3D model from a solid model, and Figure (b) shows the process of abstracting a 2D model from a 3D model. The design domain length L is 210 mm, and the design domain width W is 140 mm. Figure 4 As shown. The equivalent heat flux density of the bearing heat source is 4×10 4 W / m 2 , other boundary conditions such as Figure 3 shown.

[0076] Specifically, according to Fourier's law, the heat transfer control equation under two-dimensional steady state is as shown in Equation 1:

[0077]

[0078] In the above formula, δ represents the thermal conductivity, T is the temperature state variable, and Q is the total calorific value.

[0079] Step 2: Select the fractal dimension and bifurcation angle within the design domain of the heat conduction channel, determine the number of branches and the length and width ratios of each branch, and determine the length and width of each branch channel based on the volume fraction of the heat conduction channel in the total design domain.

[0080] Specifically, the structural parameters describing the fractal heat conduction channel are to ensure the similarity between the local and the whole. Therefore, the length ratio and diameter ratio in a fractal heat conduction channel should remain constant and independent of the number of branches. For a fractal heat conduction channel network, its branch number k, length ratio α and width ratio β determine the overall structure:

[0081]

[0082] In the formula, the fractal dimensions ΔL and ΔW are set to an empirical value of 3 and can be adjusted later; the previous branch is divided into two at the next level, so N = 2; the length ratio α and width ratio β are preliminarily determined to be 0.7937.

[0083] Specifically, the main channel length of the fractal heat conduction channel is shown in Formula 3:

[0084]

[0085] Specifically, the length of each branch can be calculated by combining the length ratio and the main channel length, as shown in Formula 4:

[0086]

[0087] Specifically, the bifurcation angle of the fractal channel is 90 degrees, and the length of each level is limited by the length and width of the design domain, such as Figure 5 And as shown in formula 5:

[0088]

[0089] Specifically, due to the limitation of the design domain width, the maximum value of the branch number k is 4, otherwise the terminal branch will exceed the design domain.

[0090] Specifically, according to the length L of each branch k , volume fraction λ and width ratio β, the width of each branch W can be determined k , as shown in Equation 6:

[0091]

[0092] Step 3: Determine whether the distribution is reasonable by checking whether the fractal heat conduction channel exceeds the design domain and whether there is interference between the branches.

[0093] Specifically, such as Figure 6 As shown, Figure 6 Figure (a) shows a schematic diagram of the structure of a fractal heat conduction channel model, while Figure (b) shows a schematic diagram of the structure of a straight heat conduction channel model with the same volume fraction. Based on fractal theory, a rectangular cross-section fractal heat conduction channel model (210 mm long and 140 mm wide) was designed for the heat conduction channel region of a certain machine tool spindle bearing, assuming a volume fraction of 30%. Its structural parameters are shown in Table 1.

[0094] Table 1 Geometric parameters of the main axis two-dimensional fractal heat conduction channel

[0095]

[0096]

[0097] Specifically, through structural verification, there is no interference between the branches, and the fractal heat conduction channel is within the overall design domain.

[0098] Step 4: Thermal Steady-State Analysis. Use Solidworks to build the model, then import it into COMSOL software for thermal steady-state analysis. Obtain the model's maximum temperature and overall temperature distribution, and compare it with models with no channel and straight channel heat conduction channels to compare the heat conduction channel performance before and after fractal optimization design.

[0099] Specifically, the following steps are included:

[0100] 1. Set the initial conditions. This includes setting the heat source, room temperature, heat conduction channel material, and convective heat transfer coefficient. A geometric model of the fractal heat conduction channel was created in the SolidWorks modeling software. The model consisted of a flat plate embedded in a tree-shaped fractal heat conduction channel. The planar dimensions were set to 210 mm × 140 mm, and the plate thickness was 10 mm. The fractal parameters were calculated as follows: length ratio, width ratio 0.7937; bifurcation angle 90°; number of branching levels 4; and other branching parameters are shown in Table 1.

[0101] ② Meshing: Use the automatic generation method to mesh the 3D model. The mesh size of key areas should be finer, such as the heat source location and the location of high thermal conductivity materials.

[0102] ③Simulation solution. Calculate the final temperature field distribution and heat flow direction, import the model into COMSOL software, perform thermal steady-state thermal performance analysis, obtain the model's maximum temperature and overall temperature distribution, and compare them with the no-channel and straight-channel thermal conduction channel models to obtain a comparison of the thermal conduction channel performance before and after fractal optimization design, as shown in the figure below. Figure 7 and Figure 8 As shown, Figure 7 The middle figure (a) shows the simulated temperature field distribution of the fractal heat conduction channel, and the middle figure (b) shows the simulated isotherm distribution of the fractal heat conduction channel.

[0103] This method evaluates design performance based on temperature performance. Simulation and experimental results show that fractal heat conduction channels offer superior temperature performance, resulting in lower maximum temperatures after reaching thermal stability. The maximum temperature of the model with heat conduction channels was reduced by over 50% compared to that without them, and by 8°C compared to traditional straight heat conduction channels.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A design method for a fractal heat conduction channel of a machine tool spindle, characterized in that: The steps include: Step 1: Select the machine tool spindle design domain and heat source, establish a simplified model based on the size parameters of the machine tool spindle design domain, set thermal boundary conditions based on the parameters of the heat source, and establish the temperature field of the heat conduction channel; Step 2: Select the fractal dimension and bifurcation angle within the design domain of the heat conduction channel, determine the number of branches and the length and width ratios of each branch, and determine the length and width of each branch channel based on the volume fraction of the heat conduction channel in the total design domain; According to the fractal dimension, the length ratio and width ratio are determined. The specific formula is as follows: ， Where, represents the length ratio, Indicates width ratio; Represents the length fractal dimension, Indicates the width fractal dimension, the empirical value is 3; The width of each branch is determined according to the length, volume fraction and width ratio of each branch. The specific formula is as follows: Where, Indicates the width of each branch, represents the total area of ​​the fractal channel, Indicates the total area of ​​branch channels at all levels; Step 3: Determine whether the distribution of branch channels is reasonable. If not, redetermine the number of branches and fractal dimension, calculate the length ratio and width ratio, and then determine the width and length of each branch of the fractal heat conduction channel based on the volume fraction, and generate the heat conduction channel. Step 4: Use Solidworks to perform modeling, import the heat conduction channel model into COMSOL software, perform thermal steady-state thermal conductivity performance analysis, obtain the maximum temperature and overall temperature distribution of the model, and compare it with the no-channel and straight-channel heat conduction channel models to obtain a comparison of the heat conduction channel performance before and after fractal optimization design.

2. The design method of a fractal heat conduction channel for a machine tool spindle according to claim 1, characterized in that: In step 1, the heat source includes the spindle motor and the spindle bearing.

3. The design method of a fractal heat conduction channel for a machine tool spindle according to claim 1, characterized in that: In step 1, the thermal boundary conditions are simplified to a rectangular area with a heat source on one side, a cooling water jacket on the opposite side of the heat source, and thermal insulation on both sides.

4. The method for designing a fractal heat conduction channel for a machine tool spindle according to claim 1, characterized in that: In step 1, the temperature field of the heat conduction channel is established by combining the thermal boundary conditions and the two-dimensional steady-state Fourier law.

5. The method for designing a fractal heat conduction channel for a machine tool spindle according to claim 1, characterized in that: In step 2, the bifurcation angle is set to 90 degrees and the fractal dimension is set to the empirical value of 3. The length of the main channel is determined according to the length and width of the design domain. .

6. The method for designing a fractal heat conduction channel for a machine tool spindle according to claim 1, characterized in that: In step 2, the length of the fractal heat conduction channel meets the following conditions: Where, It represents the width of the design domain and can be calculated by the difference between the inner and outer diameters of the heat conduction channel of the spindle; represents the design domain width; Represents the length of the main channel. The sum of the even-numbered branches is related to the width of the design domain, and the sum of the odd-numbered branches is related to the length of the design domain.

7. The method for designing a fractal heat conduction channel for a machine tool spindle according to claim 1, wherein: In step 2, the length and width of each branch meet the following conditions: ， Where, represents the length ratio, Indicates the width ratio.

8. The method for designing a fractal heat conduction channel for a machine tool spindle according to claim 1, characterized in that: In step 2, the total area of ​​the fractal channel It is equal to the product of the total area of ​​the design domain and the volume fraction: Where, Indicates volume percentage parameter.

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