A rocket sled chiseling effect analysis method based on sled-track relationship coupling

Abstract

The present invention discloses a method for analyzing the gouging effect of a rocket sled coupled with a sled-rail relationship. The method comprises: performing three-dimensional modeling of the rocket sled body and rail, determining the positional relationship between the sled body and rail, simplifying the sled body, and obtaining a simplified sled-rail coupled three-dimensional model. The sled-rail coupled three-dimensional model is then imported into finite element software, meshing the sled body and rail separately, and extracting the model's node and unit information. The simplified sled body and rail three-dimensional models are discretized into a series of material points with mass. An updated Lagrangian format motion description method is used to establish the control equations for the rocket sled gouging calculation. The background grid is updated using a display time integral method, and information mapping between the material points of the discrete simplified sled body model and rail model and the background grid nodes is achieved through shape functions. The rocket sled gouging phenomenon is analyzed using MPM3D software. The present invention overcomes the mesh distortion problem of traditional finite element methods and accurately analyzes the rocket sled gouging effect.

Description

Technical Field

[0001] The invention belongs to the technical field of shooting range testing, and in particular relates to a method for analyzing the chiseling effect of a rocket sled. Background Art

[0002] Rocket sled testing is a large-scale, high-precision ground-based dynamic simulation test method developed in the mid-to-late 20th century. It is primarily used to measure a range of performance indicators throughout the entire trajectory of weapons and equipment, including launch, flight, and impact. With the rapid development of hypersonic weapons and equipment, there is an urgent need to increase the speed of rocket sled testing. However, when the sled's operating speed approaches hypersonic speed, the high-speed impact of the shoe on the rail can sometimes cause "raindrop-shaped" or "spindle-shaped" gouging damage on the contact surface of the shoe and rail. This can cause a sharp deterioration in the rocket sled's operating mechanical environment and, in severe cases, even lead to rail breakage, resulting in test failure. Therefore, gouging significantly limits the increase in rocket sled testing speed and has become a key issue that needs to be addressed in the development of hypersonic rocket sled testing technology. Hypersonic rocket sled testing is extremely expensive, making it unrealistic to study the gouging problem entirely through rocket sled testing. Numerical analysis of hypersonic rocket sled gouging is an effective approach to provide technical support for the integration of hypersonic rocket sled test solutions.

[0003] After searching the existing technical literature, it was found that the Chinese invention patent application number is 202011120848.X, and the invention name is: A method for studying the gouging effect of a rocket sled shoe rail. The patent states: "The invention discloses a method for studying the gouging effect of a rocket sled shoe rail. By simplifying the sled body portion above the slide shoe of the rocket sled system, an equivalent plane strain analysis model is established. The Stefani Parker semi-empirical formula is then used to determine the matching standard of the slide shoe and slide rail materials used in the analysis model. The appropriate constitutive model and state equation are selected based on the behavior of the material when gouging occurs. Finally, a corresponding model is designed based on actual working conditions to study the critical conditions for the generation of the gouging effect and the influence of different factors on the critical conditions. The establishment, calculation and analysis of the above model are completed based on the material point method theory combined with NairnMPM software." The patent equates the rocket sled model to a two-dimensional plane strain analysis model and analyzes the gouging phenomenon of the rocket sled test. Through the analysis of the gouging phenomenon, it is known that most of the gouging occurs on the sides and corners of the track. The two-dimensional equivalent model proposed by this method cannot restore the actual working conditions where gouging occurs. Moreover, two-dimensional numerical simulation ignores the influence of the third dimension on the structure during the structural mechanics analysis, which leads to the neglect of some characteristics in the three-dimensional space. Summary of the Invention

[0004] To overcome the shortcomings of the existing technology, the present invention provides a method for analyzing the gouging effect of a rocket sled coupled with a sled-rail relationship. The method comprises three-dimensionally modeling the rocket sled body and rail, determining the positional relationship between the sled body and rail, simplifying the sled body, and obtaining a simplified sled-rail coupled three-dimensional model. The sled-rail coupled three-dimensional model is then imported into finite element software, meshing the sled body and rail separately, and extracting the model's node and unit information. The simplified sled body and rail three-dimensional models are discretized into a series of material points with mass. The updated Lagrangian format motion description method is used to establish the control equations for the rocket sled gouging calculation. The background mesh is updated using the display time integral method, and shape functions are used to achieve information mapping between the material points of the discrete simplified sled body model and rail model and the background mesh nodes. The rocket sled gouging phenomenon is then analyzed using MPM3D software. The present invention overcomes the mesh distortion problem of traditional finite element methods and accurately analyzes the rocket sled gouging effect.

[0005] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0006] Step 1: 3D model the rocket sled and the slide rails, determine the positional relationship between the sled and the slide rails, simplify the sled, and obtain a simplified sled-slide rail coupled 3D model, as follows:

[0007] The rocket sled body and rails were modeled using 3D design software. The constructed sled body model was symmetrically placed on the rail model, with the free surface of the upper slider of the shoe in close contact with the upper surface of the rail. The rotation angles of the sled body along the x, y, and z axes during actual operation were calculated based on the shoe-rail clearance, aerodynamic forces, and track irregularities. The sled body was rotated according to the calculated results, resulting in three different motion postures: roll, pitch, and yaw. The positional relationship between the sled body and the rails remained unchanged, and the sled body crossbeam, engine, retaining ring, stiffening beam, and bolt components were deleted, leaving only the shoe and longitudinal beam structure. This resulted in a simplified sled-rail coupling 3D model.

[0008] Step 2: Import the simplified skid-rail coupling 3D model created in step 1 into the finite element software. Mesh the skid and rail separately using eight-node hexahedral elements. Extract the model's node numbers and coordinates, element numbers, and corresponding node numbers.

[0009] Step 3: Discretize the simplified skid-rail coupled 3D model into a series of material points with mass;

[0010] The simplified skid-rail coupling 3D model is divided into several regions using eight-node hexahedral elements. Each region is discretized using the nodes of each element as material points. The material point information of the model is obtained based on the node information and element information of the model.

[0011] The spatial coordinates of the material point I M =(x M ,y M ,z M ) is equal to the spatial coordinate of the unit node I N =(x N ,y N ,z N );

[0012] The material point mass is equal to the unit node mass, and the unit coordination mass matrix M is converted to e Convert to element lumped mass matrix

[0013]

[0014] Where n e is the number of element nodes; the element coordination mass matrix Where V e is the unit volume, ρ is the mass density, and N is the interpolation function;

[0015] After obtaining the mass of each material point, the Dirac Delta function is used to represent the density of the continuum after the material point is discretized:

[0016]

[0017] Where δ is the Dirac Delta function;

[0018] Step 4: Use the updated Lagrangian format motion description method to establish the control equations for the rocket sled chiseling calculation;

[0019] When the updated Lagrangian format is used for rocket sled chiseling calculations, heat exchange is not considered. The governing equations include the mass conservation equation, momentum equation, energy equation, constitutive relations, geometric equations, boundary conditions, and initial conditions. The mass conservation equation is:

[0020]

[0021] The momentum equation is:

[0022]

[0023] Where, σ ij is the Cauchy stress; b i is the force per unit mass of the object, is the acceleration;

[0024] The energy equation is:

[0025]

[0026] Where, ε ij is the strain tensor;

[0027] The constitutive relationship is:

[0028]

[0029] The geometric equation is:

[0030]

[0031] Boundary conditions:

[0032]

[0033] Where, Γ t and Γ u are given traction boundary and given displacement boundary respectively, n j is the unit vector of the outer normal of the boundary;

[0034] Step 5: Use the display time integration method to update the background grid. The background grid is an 8-node grid. Shape functions are used to implement information mapping between the material points of the discrete simplified sled-rail coupled 3D model and the background grid nodes. The MPM3D software imports the model material point information from step 3 and uses the control equations from step 4 to complete the analysis of the rocket sled chiseling phenomenon.

[0035] The beneficial effects of the present invention are as follows:

[0036] The present invention overcomes the grid distortion problem of the traditional finite element method and accurately analyzes the chiseling effect of the rocket sled. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the test system of the present invention, where (a) is a schematic diagram of the actual rocket sled test system, and (b) is a schematic diagram of the simplified sled-slide rail coupling three-dimensional model.

[0038] Figure 2 These are partial enlarged views of the chiseling at different positions of the slide rail of the present invention, wherein (a) shows the chiseling on the side surface of the rail; and (b) shows the chiseling at the corners of the side of the rail. DETAILED DESCRIPTION

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

[0040] This invention addresses the shortcomings of two-dimensional plane strain analysis models by providing a method for analyzing the gouging effect of a rocket sled coupled to the sled-track relationship. This method establishes a three-dimensional model of the sled-track coupling by determining the positional relationship between the sled and the track. Using the material point method, it overcomes the mesh distortion issues inherent in traditional finite element methods, enabling accurate analysis of the rocket sled gouging effect.

[0041] A method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship comprises the following steps:

[0042] Step 1: 3D model the rocket sled and the slide rails, determine the positional relationship between the sled and the slide rails, simplify the sled, and obtain a simplified sled-slide rail coupled 3D model, as follows:

[0043] The rocket sled body and rails were modeled using 3D design software. The constructed sled body model was symmetrically placed on the rail model, with the free surface of the upper slider of the shoe in close contact with the upper surface of the rail. The rotation angles of the sled body along the x, y, and z axes during actual operation were calculated based on the shoe-rail clearance, aerodynamic forces, and track irregularities. The sled body was rotated according to the calculated results, resulting in three different motion postures: roll, pitch, and yaw. The positional relationship between the sled body and the rails remained unchanged, and the sled body crossbeam, engine, retaining ring, stiffening beam, and bolt components were deleted, leaving only the shoe and longitudinal beam structure. This resulted in a simplified sled-rail coupling 3D model.

[0044] Step 2: Import the simplified skid-rail coupling 3D model created in step 1 into the finite element software. Mesh the skid and rail separately using eight-node hexahedral elements. Extract the model's node numbers and coordinates, element numbers, and corresponding node numbers.

[0045] Step 3: Discretize the simplified skid-rail coupled 3D model into a series of material points with mass;

[0046] The simplified skid-rail coupling 3D model is divided into several regions using eight-node hexahedral elements. Each region is discretized using the nodes of each element as material points. The material point information of the model is obtained based on the node information and element information of the model.

[0047] The spatial coordinates of the material point I M =(x M ,y M ,z M ) is equal to the spatial coordinate of the unit node I N =(x N ,y N ,z N );

[0048] The material point mass is equal to the unit node mass, and the unit coordination mass matrix M is converted to e Convert to element lumped mass matrix

[0049]

[0050] Where n e is the number of element nodes; the element coordination mass matrix Where V e is the unit volume, ρ is the mass density, and N is the interpolation function;

[0051] After obtaining the mass of each material point, the Dirac Delta function is used to represent the density of the continuum after the material point is discretized:

[0052]

[0053] Where δ is the Dirac Delta function;

[0054] Step 4: Use the updated Lagrangian format motion description method to establish the control equations for the rocket sled chiseling calculation;

[0055] When the updated Lagrangian format is used for rocket sled chiseling calculations, heat exchange is not considered. The governing equations include the mass conservation equation, momentum equation, energy equation, constitutive relations, geometric equations, boundary conditions, and initial conditions. The mass conservation equation is:

[0056]

[0057] The momentum equation is:

[0058]

[0059] Where, σ ij is the Cauchy stress; b i is the force per unit mass of the object, is the acceleration;

[0060] The energy equation is:

[0061]

[0062] Where, ε ij is the strain tensor;

[0063] The constitutive relationship is:

[0064]

[0065] The geometric equation is:

[0066]

[0067] Boundary conditions:

[0068]

[0069] Where, Γ t and Γ u are given traction boundary and given displacement boundary respectively, n j is the unit vector of the outer normal of the boundary;

[0070] Step 5: Use the display time integration method to update the background grid. The background grid is an 8-node grid. Shape functions are used to implement information mapping between the material points of the discrete simplified sled-rail coupled 3D model and the background grid nodes. The MPM3D software imports the model material point information from step 3 and uses the control equations from step 4 to complete the analysis of the rocket sled chiseling phenomenon. Specific embodiment:

[0072] S1. Perform three-dimensional modeling of the rocket sled body and the slide rail, determine the positional relationship between the sled body and the slide rail, simplify the sled body, and obtain a simplified sled body-slide rail coupled three-dimensional model;

[0073] S2. Importing the skid-rail coupled three-dimensional model established in step S1 into finite element software, meshing the skid and rail, respectively, and extracting node and unit information of the model;

[0074] S3, discretizing the simplified skid body 3D model and the slide rail 3D model into a series of material points with mass;

[0075] S4. Use the updated Lagrangian format motion description method to establish the control equations for the rocket sled chiseling calculation;

[0076] S5. Use the display time integration method to update the background grid, realize the information mapping between the material points of the discrete simplified sled model and the slide rail model and the background grid nodes through the shape function, and complete the analysis of the rocket sled chiseling phenomenon based on the MPM3D software.

[0077] Specifically, in step S1, the rocket sled body and the slide rail are modeled using three-dimensional design software according to the design plan, and the constructed sled body model is symmetrically placed on the slide rail model, with the free surface of the upper slider of the slide shoe close to the upper surface of the slide rail. Then, according to conditions such as the shoe-rail gap, aerodynamic force, and track irregularity, the rotation angles of the sled body along the x, y, and z axes during actual operation are calculated, and the sled body is rotated according to the calculation results so that the sled body exhibits three different motion postures of roll, pitch, and yaw; the positional relationship between the sled body and the slide rail remains unchanged, and the sled body crossbeam, engine, retaining ring, stiffening beam, bolts and other components are deleted, leaving only the slide shoe and longitudinal beam structure, to obtain a simplified sled body-slide rail coupling three-dimensional model.

[0078] Specifically, in step S2, the simplified skid model and the track model are meshed in the finite element software. The corresponding mesh form in the three-dimensional material point method is an eight-node hexahedral unit. After discretizing the simplified skid model using the eight-node hexahedral unit, the node numbers and node coordinates of the model, the unit numbers, and the node numbers corresponding to the units are extracted.

[0079] Specifically, in step S3, the model is divided into several regions by eight-node hexahedral elements, each region is discretized with the nodes of each element as material points, and the material point information of the model is obtained according to the node information and element information of the model.

[0080] The spatial coordinates of the material point I M =(x M ,y M ,z M ) is equal to the spatial coordinate of the unit node I N =(x N ,y N ,z N ).

[0081] The material point mass is equal to the unit node mass, and the unit coordination mass matrix M is converted to e Convert to element lumped mass matrix

[0082]

[0083] Where n e is the number of element nodes; the element coordination mass matrix Where V e is the unit volume, ρ is the mass density, and N is the interpolation function.

[0084] Furthermore, after obtaining the mass of each material point, the Dirac Delta function is used to represent the density of the continuum after the material point is discretized:

[0085]

[0086] Where δ is the Dirac Delta function.

[0087] Specifically, in step S4, when the rocket sled chiseling calculation adopts the updated Lagrangian format, heat exchange is not considered, and the control equations include the mass conservation equation, momentum equation, energy equation, constitutive relationship, geometric equation, boundary conditions and initial conditions, where the mass conservation equation is:

[0088]

[0089] The momentum equation is:

[0090]

[0091] Where, σ ij is the Cauchy stress; b i is the force per unit mass of the object, is the acceleration.

[0092] The energy equation is:

[0093]

[0094] Where, ε ij is the strain tensor;

[0095] The constitutive relationship is:

[0096]

[0097] The geometric equation is:

[0098]

[0099] Boundary conditions:

[0100]

[0101] Where, Г t and Γ u are given traction boundary and given displacement boundary respectively, n j is the unit vector of the outer normal of the boundary.

[0102] Specifically, in step S5, the background grid for analyzing the chiseling problem based on the three-dimensional model is an 8-node grid, and the information mapping between the material points and the background grid nodes is realized through shape functions; the MPM3D software imports the model material point information in step S3 and uses the control equations in S4 to complete the analysis of the rocket sled chiseling phenomenon.

Claims

1. A method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship, characterized in that: The following steps are involved: Step 1: 3D model the rocket sled and the slide rails, determine the positional relationship between the sled and the slide rails, simplify the sled, and obtain a simplified sled-slide rail coupled 3D model, as follows: The rocket sled body and rails were modeled using 3D design software. The constructed sled body model was symmetrically placed on the rail model, with the free surface of the upper slider of the shoe in close contact with the upper surface of the rail. The rotation angles of the sled body along the x, y, and z axes during actual operation were calculated based on the shoe-rail clearance, aerodynamic forces, and track irregularities. The sled body was rotated according to the calculated results, resulting in three different motion postures: roll, pitch, and yaw. The positional relationship between the sled body and the rails remained unchanged, and the sled body crossbeam, engine, retaining ring, stiffening beam, and bolt components were deleted, leaving only the shoe and longitudinal beam structure. This resulted in a simplified sled-rail coupling 3D model. Step 2: Import the simplified skid-rail coupling 3D model created in step 1 into the finite element software. Mesh the skid and rail separately using eight-node hexahedral elements. Extract the model's node numbers and coordinates, element numbers, and corresponding node numbers. Step 3: Discretize the simplified skid-rail coupled 3D model into a series of material points with mass; The simplified skid-rail coupling 3D model is divided into several regions using eight-node hexahedral elements. Each region is discretized using the nodes of each element as material points. The material point information of the model is obtained based on the node information and element information of the model. The spatial coordinates of the material point I M =(x M ,y M ,z M ) is equal to the spatial coordinate of the unit node I N =(x N ,y N ,z N ); The mass of the material point is equal to the mass of the unit node. The unit coordination mass matrix M is converted to e Convert to element lumped mass matrix Where n e is the number of element nodes; the element coordination mass matrix Where V e is the unit volume, ρ is the mass density, and N is the interpolation function; After obtaining the mass of each material point, the Dirac Delta function is used to represent the density of the continuum after the material point is discretized: Where δ is the Dirac Delta function; Step 4: Use the updated Lagrangian format motion description method to establish the control equations for the rocket sled chiseling calculation; When the updated Lagrangian format is used for rocket sled chiseling calculations, heat exchange is not considered, and the governing equations include the mass conservation equation, momentum equation, energy equation, constitutive relations, geometric equations, boundary conditions, and initial conditions; Step 5: Use the display time integration method to update the background grid. The background grid is an 8-node grid. Shape functions are used to implement information mapping between the material points of the discrete simplified sled-rail coupled 3D model and the background grid nodes. The MPM3D software imports the model material point information from step 3 and uses the control equations from step 4 to complete the analysis of the rocket sled chiseling phenomenon.

2. The method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship according to claim 1, characterized in that: The mass conservation equation is:

3. The method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship according to claim 1, characterized in that: The momentum equation is: Where σ ij is the Cauchy stress; b i is the force per unit mass of the object, is the acceleration.

4. The method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship according to claim 1, characterized in that: The energy equation is: Where, ε ij is the strain tensor.

5. The method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship according to claim 1, characterized in that: The constitutive relationship is:

6. The method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship according to claim 1, characterized in that: The geometric equation is:

7. The method for analyzing the chiseling effect of a rocket sled coupled with a sled-track relationship according to claim 1, characterized in that: The boundary conditions are: Where, Γ t and Γ u are given traction boundary and given displacement boundary respectively, n j is the unit vector of the outer normal of the boundary.

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