Method for determining compression characteristic of MgO powder in mineral insulated cable in finite element simulation

Abstract

The invention discloses a method for determining the compression characteristic of MgO powder in a mineral insulated cable. First, a simplified experimental scheme is employed to determine mesoscopic parameters required for particle flow discrete element method (PFC) simulation. Then, the constitutive parameters of a DPC (Ducker-Prager / Cap) model are obtained by utilizing a PFC (Power Factor Correction) simulation technology; then, a user-defined material subprogram (VUSDFLD) is developed, a DPC model is integrated into finite element analysis software ABAQUS, and accurate simulation of the MgO powder pressing process is achieved. Finally, based on the steps, the compression characteristic of the MgO powder is successfully determined.

Description

Technical Field

[0001] This invention belongs to the technical field of mineral-insulated cable rolling forming, and in particular relates to a method for determining the compression characteristics of MgO powder in mineral-insulated cables in finite element simulation. Background Technology

[0002] Mineral-insulated cables, as high-performance fire-resistant cables, are widely used in various complex working conditions. Because mineral-insulated cables are composite structures consisting of copper conductors, insulating powder, and copper tubing, the forming process involves the simultaneous deformation of the copper material and insulating powder, as well as the density of the magnesium oxide filling. Currently, research on the compression characteristics of MgO powder in mineral-insulated cables using finite element simulations mainly relies on trial and error methods, which are not only costly and inefficient but also lack accuracy. This undoubtedly limits the calculation of relevant mechanical parameters of the cable under complex working conditions and reduces the production capacity of new mineral-insulated cable products for enterprises. Summary of the Invention

[0003] The purpose of this invention is to provide a method for determining the compressibility characteristics of MgO powder in mineral insulation in finite element simulation by combining PFC particle flow, DPC model and Abaqus software, in order to address the shortcomings of existing technologies.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for determining the compressibility of MgO powder in mineral-insulated cables in finite element simulation includes:

[0006] 1. Experimental method to determine the microscopic parameters of PFC particle flow.

[0007] 2. The DPC constitutive parameters of MgO powder with different relative densities were obtained through PFC particle flow simulation molding experiments and triaxial compression experiments.

[0008] 3. Write the subroutine VUSDFLD and combine it with the DPC model to simulate the molding experiment of MgO powder in Abaqus and compare it with the actual experiment.

[0009] Compared with existing technologies, this method offers the following advantages: It avoids the complexity and errors associated with calibrating multiple parameters in traditional methods by employing a simplified experimental scheme to determine the microscopic parameters required for the Particle Flow Procedure (PFC). Directly obtaining the constitutive parameters of the DPC model using PFC simulation significantly improves efficiency and saves time and cost. Developing a user-defined material subroutine (VUSDFLD) allows for dynamic adjustment of the DPC constitutive parameters applied to MgO powder compression analysis during compression, resulting in a more realistic representation. Determining the compression characteristics of MgO powder through molding experiments not only provides benchmark data for the microscopic parameters of PFC but also validates the results through simulations in Abaqus software, ensuring the effectiveness of the PFC particle flow and DPC models. Compared to traditional rolling experiments, this method is simpler and more efficient, making it particularly suitable for rapidly evaluating and validating the performance of MgO powder in mineral-insulated cables. Attached Figure Description

[0010] Figure 1 Flowchart for determining the compressibility properties of MgO powder in finite element simulation

[0011] Figure 2 Schematic diagram of the inclined plane experiment Detailed Implementation

[0012] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for determining the compressibility characteristics of MgO powder in mineral-insulated cables in finite element simulation by combining PFC particle flow, DPC model, and finite element software Abaqus.

[0013] To make the objectives, features and advantages of this invention more apparent and understandable, the invention will now be described in further detail with reference to the accompanying drawings.

[0014] Experimental methods were used to determine the microscopic parameters of PFC particle flow, including:

[0015] Step 101: Observe the shape and size of MgO particles using an optical microscope;

[0016] Step 102: Determine the coefficient of friction between MgO powder particles using an inclined plane experiment;

[0017] Step 103: Determine the macroscopic modulus and stiffness parameters of MgO powder through molding experiments.

[0018] Step 101 specifically includes:

[0019] Observation under an optical microscope revealed that the MgO powder particles were relatively regular in shape, basically spherical, and about 200 mesh in size.

[0020] Step 102 specifically includes:

[0021] First, apply double-sided tape to one side of both the wooden plank and the metal block. Next, evenly sprinkle MgO powder onto the tape. Construct a ramp made of the wooden plank and place the metal block on it. Slowly increase the angle of the ramp by pushing the supporting planks until the metal block just begins to slide, as shown. Figure 2 At this point, record the angle between the wooden board and the horizontal plane, and use the tangent of this angle to calculate the friction angle.

[0022] Step 103 specifically includes:

[0023] First, a blind hole with a radius of 10 mm and a depth of 45 mm was machined into an alloy steel bar with a radius of 15 mm and a length of 50 mm to create the upper mold. Next, a cylinder with a length of 10 mm and a radius of 9.9 mm was machined into one end of an alloy steel bar with a length of 15 mm and a radius of 20 mm to create the lower mold. After filling the lower mold with MgO powder to a height of 40 mm, the upper mold was placed on top of the powder. The powder was compressed to a height of 30 mm using a universal testing machine, and the axial stress-strain curve was recorded during this process. Subsequently, this compression process was simulated in PFC software. Based on experience, the stiffness ratio Kratio was set to 1.5, and the macromodulus Emod was adjusted. By comparing the experimentally and simulated axial stress-strain curves, the macromodulus Emod was finally determined to be 1.5e9 Pa.

[0024] The DPC constitutive parameters of MgO powder were obtained through PFC particle flow, including:

[0025] Step 201: Generate the model components required for the PFC simulation experiment;

[0026] Step 202: Obtain the shear surface parameters (d and β) of MgO at different relative densities;

[0027] Step 203: Obtain the cap yield surface parameters (p) of MgO at different relative densities. a ,R,p b );

[0028] Step 204: Obtain the elastic parameters (E and υ) of MgO at different relative densities.

[0029] Step 201 specifically includes:

[0030] Enter the microscopic parameters of MgO powder into the PFC program to create a simulation assembly that includes sidewalls, top and bottom walls, and spherical particles.

[0031] Step 202 specifically includes:

[0032] First, compression molding experiments were conducted at the minimum relative density. When the axial strain was 0.25, the maximum radial stress was 63 MPa. Based on this, the confining pressure ϭ3 for the triaxial tests was set to 10 MPa, 30 MPa, and 50 MPa. Subsequently, triaxial tests were performed under these three confining pressure conditions at different relative densities, and the maximum axial stress ϭ1 when the axial strain reached 0.2 was recorded. Through these experiments, the shear surface parameters β and d under different relative densities were fitted.

[0033] Fitted coordinates (p, q):

[0034]

[0035] Step 203 specifically includes:

[0036] PFC molding experiments were conducted, starting with a relative density of MgO of 0.56 and unloading at 0.6, 0.64, 0.68, 0.72, and 0.745. The maximum axial stress p0 and radial stress q0 corresponding to different relative densities were recorded. Using the known shear surface parameters β and d, the Cap yield surface parameters for MgO were calculated. Furthermore, based on the hardening criterion of the DPC model, the hardening parameter p0 was calculated. b The relevant plastic volumetric strain εpl v.

[0037] The p-value corresponding to the intersection of the hat surface and the transition surface:

[0038]

[0039] Eccentricity parameter R:

[0040]

[0041] The average compressive yield stress p b :

[0042]

[0043] Plastic volumetric strain:

[0044]

[0045] RD0—Initial relative density of MgO, RD—Current relative density of MgO

[0046] Step 204 specifically includes:

[0047] Calculate E and υ corresponding to different relative densities using the unloading stage data from the PFC molding test in step 203.

[0048] Poisson's ratio υ of MgO powder:

[0049]

[0050] dϭ z —Axial stress increment during the unloading phase; dϭ r —Radial stress increment during unloading phase

[0051] Elastic modulus E of MgO powder:

[0052]

[0053] dε z —Axial strain increment during unloading phase

[0054] Simulate molding experiments in Abaqus and compare them with actual experiments, including:

[0055] Step 301: Write the field redefinition subroutine VUSDFLD;

[0056] Step 302: Complete the molding experiment in Abaqus;

[0057] Step 303: Compare the axial stress-strain curves of the Abaqus simulated molding experiment with those of the actual experiment;

[0058] Step 304: Compare the relative density curves of the Abaqus simulated molding experiment with those of the actual experiment.

[0059] Step 301 specifically includes:

[0060] In Abaqus, the compressive yield mean stress p of the DPC model b There is a direct relationship between PEEQ (plastic volumetric strain) and the field variable. Therefore, PEEQ can be extracted as the field output, and the relationship between it and RD can be used to write a subroutine VUSDFLD to dynamically adjust the DPC constitutive parameters of MgO powder during Abaqus simulation of molding experiments.

[0061] Step 302 specifically includes:

[0062] Molding experiments are axisymmetric problems. After establishing an axisymmetric model in Abaqus, the simulation experiment can be completed by combining the subroutine written in step 301 and setting boundary conditions consistent with the actual experiment.

[0063] Steps 303 and 304 specifically include:

[0064] In the post-processing step 302, the contact stress variation curves of all nodes in the contact area between MgO and the upper mold during compression are extracted, and their average values ​​are obtained. These average values ​​are then compared with the axial stress-strain curves from the actual experiment and the PFC simulation experiment. Simultaneously, the relative density variation curves of all integration points of the MgO portion during compression are extracted, and their average values ​​are obtained. These average values ​​are then compared with the relative density curves from the actual experiment.

Claims

1. A method for determining the compressibility characteristics of MgO powder in mineral-insulated cables, characterized in that, include: First, a simplified experimental scheme was adopted to determine the microscopic parameters required for particle flow discrete element method (PFC) simulation. Next, the constitutive parameters of the DPC (Drucker-Prager / Cap) model were obtained using PFC simulation technology. Then, by developing a user-defined material subroutine (VUSDFLD) and integrating the DPC model into the finite element analysis software ABAQUS, an accurate simulation of the MgO powder compression process was achieved. Finally, based on the above steps, the compression characteristics of MgO powder were successfully determined.

2. The method for determining the compressibility characteristics of MgO powder in mineral-insulated cables according to claim 1, characterized in that, By employing a simplified experimental scheme to determine the microscopic parameters required for the Particle Flow Program (PFC), the complexity and errors associated with calibrating multiple parameters in traditional methods are avoided. The constitutive parameters of the DPC model are directly obtained using PFC simulation technology, significantly improving efficiency and saving time and cost. A user-defined material subroutine (VUSDFLD) was developed, enabling the DPC constitutive parameters applied to MgO powder compression analysis to be dynamically adjusted during compression, better reflecting actual conditions. The compression characteristics of MgO powder were determined through molding experiments, providing benchmark data for the microscopic parameters of PFC and verifying them through simulation in Abaqus software, ensuring the effectiveness of the PFC particle flow and DPC models. Compared to traditional rolling experiments, this method is simpler and more efficient, particularly suitable for rapidly evaluating and verifying the performance of MgO powder in mineral-insulated cables.

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