Heat dissipation optimization design method for large-size direct-drive rotary table

Through thermal-structural coupling simulation analysis, a large-size direct-drive turntable model was constructed, and the cooling pipe design was optimized, solving the problems of large heat dissipation design deviation and long cycle in the existing technology, and achieving efficient heat dissipation and improved stability.

CN121787124APending Publication Date: 2026-04-03CHONGQING UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-02-02
Publication Date
2026-04-03

AI Technical Summary

Technical Problem

Existing technologies for large-size direct-drive turntables lack accurate simulation analysis for heat dissipation design, resulting in uneven cooling medium flow, dead zones in heat dissipation, and failure to effectively combine thermal-structural coupling, leading to large design deviations, long cycles, and high consumption.

Method used

A thermal-structural coupled simulation analysis was adopted to construct a simplified overall model of the turntable, perform mesh generation, set the motor heat generation rate and contact heat transfer coefficient, simulate the convective heat transfer of the coolant, and screen the optimal cooling pipe design.

Benefits of technology

It enables the coordinated evaluation of the turntable temperature field and structural stress, quickly selects the optimal heat dissipation design, improves heat dissipation efficiency and operational stability, and shortens the design cycle.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a large-size direct-drive rotary table heat dissipation optimization design method which comprises the following steps: constructing a rotary table overall simplified model, and performing mesh generation on the rotary table overall simplified model to obtain a rotary table overall mesh model; determining the heat generation rate of the motor, setting the heat generation rate of the motor to the overall grid model of the rotary table, and simulating a transient heat conduction process; determining a contact heat transfer coefficient, setting the contact heat transfer coefficient to the overall grid model of the rotary table, and simulating actual contact between the parts; and designing a plurality of cooling pipelines, and carrying out the following operations on each cooling pipeline: arranging the cooling pipeline to the turntable overall grid model, and simulating forced convection heat exchange between the cooling liquid and the contact surface. And performing comparative analysis on the thermal-structural coupling transient simulation analysis results corresponding to the plurality of cooling pipelines, and screening out the cooling pipelines meeting the target requirements. Thermal-structure coupling can be combined, simulation analysis of efficient heat dissipation of the rotary table is achieved, and then the shape of the motor cooling pipeline is accurately optimized.
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Description

Technical Field

[0001] This invention relates to the field of thermal analysis of direct-drive turntables, and more specifically to a heat dissipation optimization design method for large-size direct-drive turntables. Background Technology

[0002] Large-size direct-drive rotary tables are widely used in aerospace, precision manufacturing, and heavy machinery industries. Their core advantages lie in zero transmission backlash, high positioning accuracy, and fast response speed. However, due to the high power and large size of the motors in large-size direct-drive rotary tables, and the significant heat generated by the stator windings during operation, as well as electromagnetic losses between the rotor and stator and bearing friction losses, additional heat can accumulate. If this heat cannot be dissipated in time, it can cause the internal temperature of the rotary table to rise, leading to thermal deformation, compromising the positioning accuracy and motion stability of the rotary table, and in severe cases, damaging critical components such as motor windings and bearings, affecting the service life and operational reliability of the rotary table.

[0003] Currently, the heat dissipation design for large-size direct-drive turntables often relies on empirical methods, referencing the cooling structures of similar equipment, and lacking precise simulation analysis. This design approach has the following drawbacks: First, the shape and layout of the cooling pipes lack optimization, resulting in uneven flow of the cooling medium within the pipes, low heat exchange efficiency, and dead zones in some areas. Second, it fails to fully consider the thermal-structural coupling effect during turntable operation; simple thermal simulation cannot accurately reflect the impact of the temperature field on the turntable's structural deformation and mechanical properties, leading to significant deviations between the actual heat dissipation effect and expectations. Third, traditional simulation techniques have not established a quantitative correlation between cooling pipe parameters and the turntable's temperature and stress fields, making it impossible to quickly select the optimal heat dissipation solution, resulting in long design cycles and high costs.

[0004] Therefore, there is an urgent need for a new heat dissipation design method for large-size direct-drive turntables that can combine thermal-structural coupling to achieve simulation analysis of efficient heat dissipation of the turntable, and then accurately optimize the shape of the motor cooling pipes. Summary of the Invention

[0005] In view of this, the purpose of this invention is to overcome the defects in the prior art and provide a heat dissipation optimization design method for large-size direct-drive turntables. This method can combine thermal-structural coupling to achieve simulation analysis of efficient heat dissipation of the turntable, thereby accurately optimizing the shape of the motor cooling pipes.

[0006] The large-size direct-drive turntable heat dissipation optimization design method of the present invention includes:

[0007] Construct a simplified overall model of the turntable, and then perform mesh generation on the simplified overall model of the turntable to obtain the overall mesh model of the turntable;

[0008] Determine the motor heat generation rate and set it in the overall mesh model of the turntable to simulate the transient heat conduction process;

[0009] Determine the contact heat transfer coefficient and set it in the overall mesh model of the turntable to simulate the actual contact between parts;

[0010] Design several types of cooling pipes, and perform the following operations for each type of cooling pipe: set the cooling pipe to the overall mesh model of the turntable to simulate the forced convection heat transfer between the coolant and the contact surface;

[0011] The results of thermal-structural coupling transient simulation analysis of several types of cooling pipes were compared and analyzed to select the cooling pipes that meet the target requirements.

[0012] Furthermore, the simplified model of the turntable is meshed, specifically including:

[0013] Mesh generation is performed on the simplified model of the turntable:

[0014] The grid size gradually transitions from the inside to the outside of the turntable, from... mm increases smoothly to mm, while controlling the grid aspect ratio at Within; generate surface meshes for each component of the turntable in sequence. At the connection surfaces of the components, ensure that adjacent components share the same surface mesh by using unified surface mesh parameters, and ensure that subsequent nodes can be glued one by one. Finally, generate a turntable mesh model including several hexahedral elements and several pentahedral transition elements.

[0015] Mesh the simplified model of the base:

[0016] The base is divided into sections. Each part is set to a separate PID, where the first part is... Each PID corresponds to a regular geometric region, and a hexahedral mesh is generated using the MAP command; the remaining... Each PID controller covers a complex transition region, employing adaptive tetrahedral mesh filling to adapt to complex boundaries; ultimately achieving... The nodes of each PID are continuously glued together to form a system including... A hybrid mesh model consisting of a hexahedral dominant subdomain and a tetrahedral transition subdomain is generated, ultimately producing a base mesh model comprising several hexahedral elements, several pentahedral elements, and several tetrahedral transition elements.

[0017] Furthermore, the motor heat generation rate includes the motor bearing heat generation rate, the motor stator heat generation rate, and the motor rotor heat generation rate;

[0018] The heat generation rate of motor bearings is determined according to the following formula. :

[0019] ;

[0020] in, Heat generated by bearing friction; ; This represents the total frictional torque of the bearing. This refers to the bearing speed; ; This refers to the rolling friction torque generated by elastic hysteresis. This refers to the sliding friction torque between the roller raceways; The frictional torque is caused by the viscosity of the lubricant. This refers to the bearing volume;

[0021] The stator heat generation rate of the motor is determined according to the following formula. :

[0022] ;

[0023] in, This is for the heat loss of the motor; Stator volume;

[0024] The rotor heat generation rate of the motor is determined according to the following formula. :

[0025] ;

[0026] in, This is for the heat loss of the motor; This refers to the rotor volume.

[0027] Furthermore, the contact heat transfer coefficient is determined according to the following formula. :

[0028] ;

[0029] in, The heat flow rate includes the actual contact heat flow rate and the heat flow rate transferred through the gap; Contact area; This refers to the temperature difference generated between the contact surfaces.

[0030] Furthermore, the forced convection heat transfer coefficient between the coolant and the contact surface is determined according to the following formula. :

[0031] ;

[0032] in, For Nuschelt numbers;

[0033] ; Friction factor; It is the Reynolds number; It is a Prandtl number;

[0034] The thermal conductivity of the fluid; It is the hydraulic diameter.

[0035] Furthermore, a comparative analysis of the thermal-structural coupling transient simulation results for several types of cooling pipes is conducted, specifically including:

[0036] For each type of cooling pipe, the following operations are performed: Extract the transient temperature field cloud map and transient deformation field cloud map of the turntable from the simulation analysis results; Using the central region of the turntable's upper surface as the target region, select within the target region... Each feature node; for The average deformation and average temperature rise of each node are analyzed to obtain the average deformation and average temperature rise of the nodes.

[0037] The cooling pipes with the smallest average node deformation and / or the lowest average node temperature rise are selected.

[0038] The beneficial effects of this invention are as follows: The large-size direct-drive turntable heat dissipation optimization design method disclosed in this invention adopts direct thermal-structural coupling simulation, which combines the temperature field with structural stress and deformation to comprehensively evaluate the impact of heat dissipation design on the turntable's operating accuracy and structural reliability. By comparing multiple design simulations, the optimal heat dissipation design can be quickly selected, avoiding design deviations caused by simple thermal simulation. This ensures that the final heat dissipation design not only meets the cooling requirements but also effectively controls thermal deformation, thereby providing technical support for improving the turntable's heat dissipation efficiency and operational stability. Attached Figure Description

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0040] Figure 1 This is a flowchart of the heat dissipation optimization design method of the present invention;

[0041] Figure 2 This is a simplified model of the turntable of the present invention;

[0042] Figure 3 This is a simplified model of the base of the present invention;

[0043] Figure 4 This is the turntable mesh generation model of the present invention;

[0044] Figure 5 This is the base mesh division model of the present invention;

[0045] Figure 6 This is a cross-sectional view of the overall grid division of the turntable according to the present invention;

[0046] Figure 7 This is a simplified triangular cross-section spiral cooling pipe model for the present invention;

[0047] Figure 8 This is a simplified rectangular cross-section spiral cooling pipe model for the present invention;

[0048] Figure 9 This is a simplified circular cross-section spiral cooling pipe model for the present invention;

[0049] Figure 10 295 feature nodes were selected from the upper surface of the turntable;

[0050] Figure 11 The total deformation curve of 295 feature nodes on the upper surface of the triangular cross-section turntable;

[0051] Figure 12 Temperature profiles of 295 characteristic nodes on the upper surface of the triangular cross-section turntable;

[0052] Figure 13 The total deformation curve of 295 feature nodes on the upper surface of the rectangular cross-section turntable;

[0053] Figure 14 Temperature profiles of 295 characteristic nodes on the upper surface of a rectangular cross-section turntable;

[0054] Figure 15 The total deformation curve of 295 feature nodes on the upper surface of the circular cross-section turntable;

[0055] Figure 16 Temperature profiles of 295 characteristic nodes on the upper surface of a circular cross-section turntable. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings, as shown in the figures:

[0057] This embodiment discloses a heat dissipation optimization design method for large-size direct-drive turntables, including the following steps:

[0058] Construct a simplified overall model of the turntable, and then perform mesh generation on the simplified overall model of the turntable to obtain the overall mesh model of the turntable;

[0059] Determine the motor heat generation rate and set it in the overall mesh model of the turntable to simulate the transient heat conduction process;

[0060] Determine the contact heat transfer coefficient and set it in the overall mesh model of the turntable to simulate the actual contact between parts;

[0061] Design several types of cooling pipes, and perform the following operations for each type of cooling pipe: set the cooling pipe to the overall mesh model of the turntable to simulate the forced convection heat transfer between the coolant and the contact surface;

[0062] The results of thermal-structural coupling transient simulation analysis of several types of cooling pipes were compared and analyzed to select the cooling pipes that meet the target requirements.

[0063] This invention constructs an overall mesh model of the turntable and incorporates key parameters such as motor heat generation rate, contact heat transfer coefficient, and forced convection of coolant to conduct transient simulation analysis involving thermal-structural coupling. This enables a coordinated evaluation of the turntable's temperature field, stress field, and thermal deformation behavior. Compared to traditional heat dissipation design methods that rely on experience, this method can quantitatively analyze the impact of different cooling pipe shapes on heat dissipation performance and structural deformation.

[0064] Finally, by comparing various cooling pipe schemes through simulation, the optimal design scheme that meets the reliability requirements can be quickly selected, effectively shortening the design cycle and reducing trial and error costs. This provides technical support for the refined design of cooling structures for large-size direct-drive turntables, which is conducive to improving the turntable's operational stability, positioning accuracy, and overall service life.

[0065] In this embodiment, the software LS-prepost can be used to simplify the modeling of the turntable, base, etc. All screws, vent holes, oil holes, and other small structures are ignored and treated as solids. Fillets, chamfers, and small holes that do not significantly affect the analysis results are omitted. Grooves, threaded holes, etc., are treated as solids, thus obtaining a simplified overall model of the turntable. This simplified overall model of the turntable includes the simplified turntable model (…). Figure 2 (as shown) and a simplified model of the base ( Figure 3 (As shown).

[0066] Furthermore, the simplified overall model of the turntable can be meshed using the software LS-prepost, specifically including:

[0067] The simplified model of the turntable was meshed using a layered transition strategy:

[0068] The grid size gradually transitions from the inside to the outside of the turntable, from... mm increases smoothly to mm, while controlling the grid aspect ratio at Within this range, to avoid affecting calculation accuracy due to poor mesh morphology, surface meshes were generated sequentially for each component of the turntable. At the connection surfaces of components, uniform surface mesh parameters were used to ensure that adjacent components shared a consistent surface mesh, ensuring that subsequent nodes could be glued together one by one. The final generated turntable mesh model included 141,678 hexahedral elements and 1,937 pentahedral transition elements (a total of 143,615 individual elements). Figure 4 (as shown)

[0069] Mesh the simplified model of the base:

[0070] The base is divided into sections. Each part is set to a separate PID, where the first part is... Each PID corresponds to a regular geometric region (such as a rib, cylindrical surface, etc.), and a hexahedral mesh is generated using the MAP command; the remaining PIDs... Each PID covers complex transition regions (such as irregular contours and multiple feature intersections), employing adaptive tetrahedral mesh filling to adapt to complex boundaries; ultimately achieving... The nodes of each PID are continuously glued together to form a system including... A hybrid mesh model consisting of one hexahedral dominant subdomain and one tetrahedral transition subdomain ultimately generates a base mesh model comprising 21,892 hexahedral elements, 413 pentahedral elements, and 152,756 tetrahedral transition elements (a total of 175,061 elements). Figure 5 (As shown).

[0071] The software LS-prepost can also be used to generate hexahedral meshes for simple models such as the stator, rotor, bearings, and motor connectors, which will not be elaborated here. The final complete mesh model is shown below. Figure 6 As shown.

[0072] In this embodiment, the motor heat generation rate includes the motor bearing heat generation rate, the motor stator heat generation rate, and the motor rotor heat generation rate; the heat generation rates of the motor stator, motor rotor, and motor bearings are calculated based on the motor and bearing model parameters. Among them, the bearing heat generation mainly originates from the frictional loss between the rolling elements and the inner and outer rings, and its heat generation is closely related to the rotational speed, load, lubrication conditions, and bearing type.

[0073] The heat generation rate of motor bearings is determined according to the following formula. :

[0074] ;

[0075] in, Heat generated by bearing friction; ; This represents the total frictional torque of the bearing. This refers to the bearing speed; ; This refers to the rolling friction torque generated by elastic hysteresis. This refers to the sliding friction torque between the roller raceways; The frictional torque is caused by the viscosity of the lubricant. This refers to the bearing volume;

[0076] Of the motor losses, stator iron losses and copper losses account for approximately 2 / 3 of the total losses, while rotor losses account for 1 / 3. The heat generation rate is calculated using the following formula:

[0077] The stator heat generation rate of the motor is determined according to the following formula. :

[0078] ;

[0079] in, This is for the heat loss of the motor; Stator volume;

[0080] The rotor heat generation rate of the motor is determined according to the following formula. :

[0081] ;

[0082] in, This is for the heat loss of the motor; This refers to the rotor volume.

[0083] In the software LS-prepost, the keyword *LOAD_HEAT_GENERATION_SET_SOLID is used to convert the electromagnetic loss of the motor stator coil, the rotor iron loss, and the frictional power consumption of the bearing into the volumetric heat generation rate, and apply it to the corresponding component entity set, thereby driving the transient heat conduction process inside the model.

[0084] In this embodiment, the thermal parameters (thermal conductivity, specific heat capacity, coefficient of thermal expansion), physical property parameters (elastic modulus, Poisson's ratio, density), and boundary conditions of the turntable are set in the software LS-prepost. Because there is contact interface thermal resistance between the turntable, bearings, and motor connectors, an additional contact heat transfer coefficient needs to be set to simulate the actual contact between the parts. The contact heat transfer coefficient is determined according to the following formula. :

[0085] ;

[0086] in, The heat flow rate includes the actual contact heat flow rate and the heat flow rate transferred through the gap; Contact area; This refers to the temperature difference generated between the contact surfaces.

[0087] Keywords used in the software LS-prepost:

[0088] *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE, enable the Thermal option, select the two contact surfaces, and input the calculated contact heat transfer coefficients into HTC to complete the model thermal contact settings.

[0089] In this embodiment, three types of cooling pipes are designed, as follows: Figure 7 , 8As shown in Figure 9, calculate the forced convection heat transfer coefficient between the coolant and the contact surface in the cooling pipe for three different cooling pipe schemes. This contact surface includes the motor stator and the base. The forced convection heat transfer coefficient between the coolant and the contact surface is determined using the following formula. :

[0090] ;

[0091] in, For Nuschelt numbers;

[0092] ; Friction factor; It is the Reynolds number; It is a Prandtl number;

[0093] The thermal conductivity of the fluid; It is the hydraulic diameter.

[0094] In the software LS-prepost, keywords are used to define convection boundary conditions:

[0095] *BOUNDARY_CONVECTION_SET: Select the base and stator surfaces that are in direct contact with the coolant, set the convection heat transfer coefficient in HMULT, and set the coolant temperature in TMULT to complete the forced convection heat transfer settings between the coolant and the contact surface.

[0096] In this embodiment, the following solver keywords are set in the LS-prepost software: *Termination time, *Solution method, *Thermal time step, *Thermo-structural coupled solver, *Nonlinear solver, etc.; the result output is set to global data output to ensure complete acquisition of simulation data for each region of the turntable; the solver software APDL is started to perform the solution calculation, and the thermo-structural coupled transient simulation analysis result files (d3plot format) corresponding to the three cooling pipe layout schemes are obtained; the d3plot result files are opened in the LS-prepost software to view and extract the transient temperature field cloud map and transient deformation field cloud map of the large-size direct-drive turntable;

[0097] Open the d3plot result files of the spiral cooling pipes with three cross-sections (equilateral triangle, rectangle, and circle) in the software; then extract the nodal temperature and deformation curves of the central region of the turntable surface for each scheme in the "History" module; to reduce data errors, 295 feature nodes were selected for analysis for each scheme (see...). Figure 10 Simulation results of the turntable operating under rated conditions for 20,000 seconds show:

[0098] The maximum deformation of the node corresponding to the equilateral triangular cross-section pipe is 64.2. m, average deformation is 63.7 m, the maximum temperature rise was 31.7℃, and the average temperature rise was 31.5℃ (see...). Figure 11 , 12 );

[0099] The maximum deformation of the rectangular cross-section is 64.9. m, average deformation is 64.4 m, the maximum temperature rise was 32.2℃, and the average temperature rise was 31.9℃ (see...). Figure 13 , 14 );

[0100] The maximum deformation of the circular cross-section is 66.8. m, average deformation is 66.5 m, the maximum temperature rise was 33.2℃, and the average temperature rise was 32.9℃ (see...). Figure 15 , 16 );

[0101] The results show that the average deformation difference between the equilateral triangle and the rectangular cross-section is only 0.7. The average deformation of a circular cross-section is approximately 2.8 m, while the average deformation of a circular cross-section is 2.8 m higher than that of a triangular cross-section. The temperature rise is also significantly higher, indicating that non-circular cross-sections (triangular and rectangular) have better cooling temperature control and deformation suppression effects, and the performance of both is similar. Furthermore, since the triangular cross-section has the smallest average deformation and the lowest average temperature rise, the spiral cooling pipe with a triangular cross-section is preferred as the optimal cooling pipe.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A heat dissipation optimization design method for a large-size direct-drive turntable, characterized in that: Includes the following steps: Construct a simplified overall model of the turntable, and then perform mesh generation on the simplified overall model of the turntable to obtain the overall mesh model of the turntable; Determine the motor heat generation rate and set it in the overall mesh model of the turntable to simulate the transient heat conduction process; Determine the contact heat transfer coefficient and set it in the overall mesh model of the turntable to simulate the actual contact between parts; Design several types of cooling pipes, and perform the following operations for each type of cooling pipe: set the cooling pipe to the overall mesh model of the turntable to simulate the forced convection heat transfer between the coolant and the contact surface; The results of thermal-structural coupling transient simulation analysis of several types of cooling pipes were compared and analyzed to select the cooling pipes that meet the target requirements.

2. The heat dissipation optimization design method for large-size direct-drive turntables according to claim 1, characterized in that: The simplified model of the turntable is meshed, specifically including: Mesh generation is performed on the simplified model of the turntable: The grid size gradually transitions from the inside to the outside of the turntable, from... mm increases smoothly to mm, while controlling the grid aspect ratio at Within; generate surface meshes for each component of the turntable in sequence. At the connection surfaces of the components, ensure that adjacent components share the same surface mesh by using unified surface mesh parameters, and ensure that subsequent nodes can be glued one by one. Finally, generate a turntable mesh model including several hexahedral elements and several pentahedral transition elements. Mesh the simplified model of the base: The base is divided into sections. Each part is set to a separate PID, where the first part is... Each PID corresponds to a regular geometric region, and a hexahedral mesh is generated using the MAP command; the remaining... Each PID controller covers a complex transition region, employing adaptive tetrahedral mesh filling to adapt to complex boundaries; ultimately achieving... The nodes of each PID are continuously glued together to form a system including... A hybrid mesh model consisting of a hexahedral dominant subdomain and a tetrahedral transition subdomain is generated, ultimately producing a base mesh model comprising several hexahedral elements, several pentahedral elements, and several tetrahedral transition elements.

3. The heat dissipation optimization design method for large-size direct-drive turntables according to claim 1, characterized in that: The heat generation rate of the motor includes the heat generation rate of the motor bearings, the heat generation rate of the motor stator, and the heat generation rate of the motor rotor; The heat generation rate of motor bearings is determined according to the following formula. : ; in, Heat generated by bearing friction; ; This represents the total frictional torque of the bearing. This refers to the bearing speed; ; This refers to the rolling friction torque generated by elastic hysteresis. This refers to the sliding friction torque between the roller raceways; The frictional torque is caused by the viscosity of the lubricant. This refers to the bearing volume; The stator heat generation rate of the motor is determined according to the following formula. : ; in, This is for the heat loss of the motor; Stator volume; The rotor heat generation rate of the motor is determined according to the following formula. : ; in, This is for the heat loss of the motor; This refers to the rotor volume.

4. The heat dissipation optimization design method for large-size direct-drive turntables according to claim 1, characterized in that: The contact heat transfer coefficient is determined according to the following formula. : ; in, The heat flow rate includes the actual contact heat flow rate and the heat flow rate transferred through the gap; Contact area; This refers to the temperature difference generated between the contact surfaces.

5. The heat dissipation optimization design method for large-size direct-drive turntables according to claim 1, characterized in that: The forced convection heat transfer coefficient between the coolant and the contact surface is determined using the following formula. : ; in, For Nuschelt numbers; ; Friction factor; It is the Reynolds number; It is a Prandtl number; The thermal conductivity of the fluid; It is the hydraulic diameter.

6. The heat dissipation optimization design method for large-size direct-drive turntables according to claim 1, characterized in that: A comparative analysis of the thermal-structural coupling transient simulation results for several types of cooling pipes is conducted, specifically including: For each type of cooling pipe, the following operations are performed: Extract the transient temperature field cloud map and transient deformation field cloud map of the turntable from the simulation analysis results; Using the central region of the turntable's upper surface as the target region, select within the target region... Each feature node; for The average deformation and average temperature rise of each node are analyzed to obtain the average deformation and average temperature rise of the nodes. The cooling pipes with the smallest average node deformation and / or the lowest average node temperature rise are selected.