Multi-stage rocket sled whole trajectory dynamics modeling method

Abstract

The invention discloses a multi-stage rocket sled full ballistic dynamics modeling method, which fully considers the mass time-varying characteristic, the rigidity time-varying characteristic and the nonlinear contact characteristic between a rocket sled and a sliding rail in a rocket sled full ballistic motion process, simplifies the sliding rail into a one-dimensional beam unit for modeling, and enables a fastener to be equivalent to a vertical spring. A rocket sled is simplified into a beam-mass point unit for modeling, and an engine propellant is equivalent to non-structural mass. A sliding rail is regarded as a linear time-invariant system, a rocket sled is regarded as a linear time-varying system, and a nonlinear contact model is adopted between a sliding shoe of the rocket sled and the sliding rail. According to the invention, researchers can conveniently obtain more optimized and more reliable rocket sled test equipment, so that the development period and cost of the system are reduced, and the development risk is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of shooting range testing, and in particular relates to a method for modeling the full trajectory dynamics of a multi-stage rocket sled. Background Art

[0002] A high-speed rocket sled is a ground test platform that connects the earth and the sky between laboratory tests and flight tests. Rocket sled tests generally use rocket engines to provide power, pushing the rocket sled forward at high speed to obtain test data. The rocket sled can be used to conduct full-scale, high-fidelity ground dynamic environmental tests on aircraft components, subsystems or systems. It is an important ground test device for solving key aircraft technologies. For example, the finalization test of the US ramjet engine and the final ground environmental assessment of the inertial platform are both completed using rocket sled tests.

[0003] With the development of high-speed aircraft, in order to meet the test requirements, more rocket sled tests under complex working conditions need to be carried out, so various forms of rocket sled structures need to be designed. If an appropriate rocket sled system model can be established, and appropriate methods can be used to accurately and quickly analyze its dynamic characteristics and vibration loads, it can provide a design basis for the development of rocket sled test equipment that meets the requirements and has good performance when designing rocket sled test equipment, so that researchers can obtain more optimized and more reliable rocket sled test equipment, thereby reducing the system's development cycle and cost, and reducing development risks. In addition, due to the harsh full-ballistic dynamics environment conditions of the high-speed rocket sled system, when establishing the rocket sled system model for dynamics analysis, the on-orbit stability and safety assessment of the rocket sled cannot be limited to the dynamics and kinematics analysis under quasi-static conditions of certain specific point speeds, but needs to focus on the full-ballistic design of the entire system. Therefore, the study of the full-process simulation analysis and calculation method of the rocket sled system has important engineering application significance.

[0004] The mechanical model of the rocket sled system can essentially be simplified to the problem of a mobile structure moving on a fixed beam. This study calls it the "mobile structure-fixed beam problem". Since the 19th century, researchers from various countries have published a large number of papers on this problem. From simple to complex, they have proposed many models that can meet their respective research needs. Due to its unique working mode, the full-process dynamic model of the rocket sled is very complex. The models currently used in the literature are not yet suitable for the rocket sled system. The complexity of the full-process simulation of the rocket sled system is mainly reflected in the following aspects: (1) The characteristics of the time-varying problem are more complex. The rocket sled system contains multiple solid rocket engines. After each stage of the engine is completed, it will separate, which will cause the rocket sled system to exhibit fast time-varying stiffness characteristics. (2) The nonlinear problem caused by the collision between the shoe and the rail. Due to the gap between the rail and the shoe, under the action of complex mechanical loads, the collision between the shoe and the rail will inevitably make the mechanical model of the rocket sled system strongly nonlinear. (3) Calculation time cost. The solution to nonlinear time-varying problems cannot be solved by the modal superposition method, and the direct integration method must be used. In addition, the existence of nonlinear factors will greatly increase the solution time. In addition, the rocket sled runs at a very high speed, and the model that needs to be established has a large degree of freedom. The solution of large-scale nonlinear time-varying problems also places high demands on the level of computer hardware.

[0005] In summary, the study of the full-process dynamic simulation analysis and calculation method of the rocket sled system can further enrich the "moving structure-fixed beam problem", and at the same time provide a fast calculation method for the structural design and response prediction of the rocket sled system, which has important engineering application value. Summary of the invention

[0006] In order to overcome the shortcomings of the prior art, the present invention provides a method for modeling the full trajectory dynamics of a multi-stage rocket sled, which fully considers the time-varying characteristics of mass and stiffness during the full trajectory motion of the rocket sled, as well as the nonlinear contact characteristics between the rocket sled and the slide rail, simplifies the slide rail into a one-dimensional beam unit model, and the fasteners are equivalent to vertical springs. The rocket sled is simplified into a beam-mass point unit model, and the engine propellant is equivalent to a non-structural mass. The slide rail is regarded as a linear time-invariant system, and the rocket sled is regarded as a linear time-varying system. A nonlinear contact model is adopted between the rocket sled slide shoe and the slide rail. The present invention facilitates researchers to obtain more optimized and more reliable rocket sled test equipment, thereby reducing the system's development cycle and cost, and reducing development risks.

[0007] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0008] Step 1: Establish the stiffness matrix and mass matrix of the beam element; only consider the vertical translation and rotation in the vertical plane. The beam elements are all Euler beams, and the shear of the beam is not considered.

[0009] Step 2: Establish the stiffness matrix of the lightweight spring element;

[0010] The spring model is established using a single-degree-of-freedom two-node spring unit, and the stiffness matrix of the spring unit is a 2×2 matrix;

[0011] Step 3: Establish the mass matrix of the concentrated mass unit;

[0012] The concentrated mass unit is a single-node unit, and its moment of inertia is 0, so its mass matrix is ​​in the form of a 2×2 matrix;

[0013] Step 4: Calculate the damping of the slide rail structure;

[0014] Rayleigh damping is used to simulate the damping of the slide structure, and the damping matrix C is expressed as:

[0015] C=αM+βK (1)

[0016] Where C is the Rayleigh damping matrix of the structure, α and β are the corresponding Rayleigh damping coefficients;

[0017] Step 5: Establish the thrust sled beam unit model;

[0018] The thrust sled is modeled using two-degree-of-freedom Euler beam elements and concentrated mass elements. The thrust sled is filled with fuel and the mass is evenly distributed, so the length of the beam element is determined.

[0019] Step 6: Calculate the mass matrix and stiffness matrix of the thrust sled;

[0020] According to the thrust sled geometry and material parameters and the length of the beam unit, the mass matrix and stiffness matrix of the thrust sled beam unit and the concentrated mass unit are calculated according to the establishment method of the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1; the overall mass matrix and stiffness matrix of the thrust sled are obtained by using the matrix splicing method;

[0021] Step 7: Thrust sled model verification;

[0022] The eigenvalue decomposition method is used to calculate the vertical forward three-order modal natural frequencies and vibration shapes of the thrust sled, and the calculated results are compared with the modal test results;

[0023] Step 8: Modeling of product skid beam unit;

[0024] Obtain the total mass and center of mass position of the product sled in the 3D modeling software; split the product sled according to different geometric shapes and parameters, and the length of each beam unit is different; set the elastic modulus according to the material properties of each part of the product sled; set the beam unit to be lightweight and concentrate the mass at the concentrated mass point; modify the established finite element model using the measured mass and center of mass position;

[0025] Step 9: Calculate the mass matrix and stiffness matrix of the product skid;

[0026] According to the geometric and material parameters of the product skid and the length of the beam unit, the mass matrix and stiffness matrix of the beam unit and the concentrated mass unit of the product skid are calculated according to the establishment method of the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1; the overall mass matrix and stiffness matrix of the product skid are obtained by using the matrix splicing method;

[0027] Step 10: Product skid model verification;

[0028] The eigenvalue decomposition method is used to calculate the vertical forward three-order modal natural frequencies and vibration modes of the product skid, and the calculated results are compared with the modal test results;

[0029] Step 11: Establish the slide rail beam unit model;

[0030] The main body of the slide rail is modeled as an Euler beam with two degrees of freedom, and the slide rail fastener is modeled as a spring damping system. The node connected to the buckle has only one degree of freedom of vertical motion.

[0031] Step 12: Determine the stiffness matrix and mass matrix of the slide model;

[0032] Splice the overall matrix of the slide rail, determine the geometry, material parameters and modeling method of the slide rail, and write a simulation calculation program to calculate the mass matrix and stiffness matrix of the slide rail;

[0033] Step 13: Verification of the finite element modeling method of the slide rail;

[0034] Substitute the calculated mass matrix and stiffness matrix of the slide rail into the eigenvalue decomposition method program to calculate the vertical forward fourth-order natural frequency and vibration mode of the slide rail finite element model, and compare the calculated results with the modal test results;

[0035] Step 14: Determine the connection mode of the rocket sled-slideway coupling system;

[0036] The connection between the rocket sled and the slide shoe is modeled as a nonlinear spring unit; the spring unit is respectively connected to the slide shoe node and the slide rail node that coincides with the slide shoe node, the stiffness matrix and mass matrix of the whole system are spliced ​​to obtain the overall stiffness matrix and overall mass matrix of the whole system, and the damping of the whole system is represented by Rayleigh damping to obtain the damping matrix of the whole system;

[0037] Step 15: Verification of the finite element model of the sled-rail coupling system in a static state;

[0038] The eigenvalue decomposition method is used to calculate the vertical first six-order natural frequencies and vibration modes of the overall system, and the calculation results of the program are compared with those of commercial software.

[0039] Preferably, when the slide rail body is modeled as an Euler beam with two degrees of freedom, a Timoshenko beam is used to simulate the main part of the slide rail, and the slide rail buckle is simplified into a spring-damper system, one end of the spring is fixedly connected to the slide rail, and a fixed constraint is applied to the other end, that is, the support beam and the foundation part are regarded as a rigid body with infinite mass; the mass matrix, damping matrix and stiffness matrix of the slide rail structure are corrected through the modal test data of the slide rail structure to ensure that the dynamic model of the slide rail structure is consistent with the actual physical model.

[0040] Preferably, the upper left corner of the unit mass matrix and the lower right corner of the stiffness matrix of the Euler beam respectively represent the coupling relationship between the two degrees of freedom of the beam node itself; when two adjacent beam units are spliced, the values ​​at the common nodes are directly added, and the values ​​at other positions remain unchanged.

[0041] Preferably, the sliding shoe and the sliding rail are connected by a nonlinear spring, and a segmented linear spring is set according to the distance between the sliding shoe node and the sliding rail node. When the distance between the two is within the shoe-rail gap range, the spring stiffness is smaller than the spring stiffness when the distance between the two is outside the shoe-rail gap range;

[0042] set up is the displacement at the jth sliding shoe node, is the displacement of the i-th node of the rail, and the position of the i-th node of the rail is close to the position of the j-th shoe. Then at time k, the nonlinear stiffness of the shoe-rail contact is described as:

[0043]

[0044] In the formula, represents the contact stiffness between the jth sliding shoe and the i-th node of the sliding rail; τ represents the gap between the shoe and the rail; and represents the vibration displacement of the i-th node of the rail and the j-th node of the sliding shoe at time k; k a Indicates the stiffness when the shoe rail is not in contact; represents the contact stiffness between the jth node of the sliding shoe and the ith node of the sliding rail,

[0045] Preferably, when the sliding shoe and the sliding rail are in contact, the shoe-rail connection stiffness comes entirely from the stiffness of the sliding rail, and the stiffness of the sliding rail varies with the distance between the deformation point and the nearest buckle; when the two are not in contact, the contact stiffness between the shoe and the rail is 0.

[0046] A computer program, which enables a computer to execute the above-mentioned kinetic modeling method.

[0047] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the above-mentioned dynamic modeling method.

[0048] A computer-readable storage medium stores a computer program, which implements the above-mentioned dynamic modeling method when executed by a processor.

[0049] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned dynamic modeling method.

[0050] A computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and the above-mentioned dynamic modeling method is implemented when the instructions are executed by the at least one processor.

[0051] The beneficial effects of the present invention are as follows:

[0052] 1. The present invention proposes a method for establishing a full ballistic dynamics model of a multi-stage rocket sled-slideway coupling system by using a beam-mass point. This method changes the current situation in which the on-orbit stability and safety assessment of the rocket sled is limited to the dynamics analysis of the speed of certain specific points, and realizes the full-process dynamics modeling of the rocket sled operation.

[0053] 2. The present invention adopts modal test to correct the low-frequency characteristics of the established rocket sled model and slide rail model, thereby improving the model accuracy.

[0054] 3. The sled-rail coupling dynamic model established by the present invention fully considers the time-varying characteristics of mass, time-varying characteristics of stiffness and nonlinear contact characteristics of the shoe-rail during the full ballistic motion of the rocket sled.

[0055] 4. The present invention considers the unevenness of the slide rail surface as the displacement load applied to the connection between the slide rail and the slide shoe, thereby realizing the rapid loading of the key external load of the rocket sled.

[0056] 5. The present invention provides a design basis for developing a rocket sled system that meets the requirements and has good performance, making it easier for researchers to obtain more optimized and more reliable rocket sled test equipment, thereby reducing the system's development cycle and cost and reducing development risks. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flowchart of the method of the present invention.

[0058] Figure 2 It is a schematic diagram of the finite element model of the product skid of the present invention.

[0059] Figure 3 It is a schematic diagram of the finite element model of the thrust sled of the present invention.

[0060] Figure 4 It is a schematic diagram of the track finite element model of the present invention.

[0061] Figure 5 It is a schematic diagram of the nonlinear contact relationship of the shoe rail of the present invention.

[0062] Figure 6 It is a schematic diagram of the finite element model of the sled-rail coupling system of the present invention. DETAILED DESCRIPTION

[0063] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0064] The purpose of the present invention is to propose a full-process simulation analysis and calculation method for a multi-stage rocket sled system under high-speed conditions, in view of the fact that the evaluation of the stability and safety of the on-orbit operation of the rocket sled is currently limited to the dynamics and kinematic analysis of the speed of certain specific points. The time-varying mass characteristics, the time-varying stiffness characteristics and the nonlinear contact characteristics between the rocket sled and the slide rail in the whole ballistic motion process of the rocket sled are fully considered, the slide rail is simplified to a one-dimensional beam unit model, the fastener is equivalent to a vertical spring, the rocket sled is simplified to a beam-mass point unit model, and the engine propellant is equivalent to a non-structural mass. The slide rail is regarded as a linear time-invariant system, and the rocket sled is regarded as a linear time-varying system. A nonlinear contact model is adopted between the rocket sled slide shoe and the slide rail.

[0065] The technical solution adopted by the present invention to solve the technical problem comprises the following steps:

[0066] Step 1: Establish the stiffness matrix and mass matrix of the beam element. Considering the large amount of calculation required for the entire calculation, in order to reduce the model's degrees of freedom, only the vertical translation and rotation in the vertical plane are considered. The beam elements are all Euler beams, and the shear of the beam is not considered.

[0067] Step 2: Establish the stiffness matrix of the lightweight spring unit. The spring model is established using a single-degree-of-freedom two-node spring unit, so the stiffness matrix of the spring unit is a 2×2 matrix.

[0068] Step 3: Establish the mass matrix of the concentrated mass unit. The concentrated mass unit involved in the present invention is a single-node unit, and its moment of inertia is considered to be 0, so its mass matrix is ​​in the form of a 2×2 matrix.

[0069] Step 4: Calculate the damping of the slide rail structure. Use Rayleigh damping to simulate the damping of the slide rail structure. The damping matrix C can be expressed as:

[0070] C=αM+βK(1)

[0071] Where C is the Rayleigh damping matrix of the structure, and α and β are the corresponding Rayleigh damping coefficients.

[0072] Step 5: Establish the thrust sled beam unit model. Considering the large amount of simulation calculations for the entire ballistic process, in order to reduce the system's degrees of freedom, the thrust sled is modeled using two-degree-of-freedom Euler beam units and concentrated mass units. The thrust sled is filled with fuel and the mass is evenly distributed, so the length of the beam unit is determined.

[0073] Step 6: Calculate the mass and stiffness matrix of the thrust sled. According to the thrust sled geometry and material parameters and the length of the beam unit, and the method of establishing the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1, write a program to calculate the mass matrix and stiffness matrix of the thrust sled beam unit and the concentrated mass unit. After obtaining the stiffness matrix and mass matrix of the unit, use the matrix splicing method to obtain the overall mass matrix and stiffness matrix of the thrust sled.

[0074] Step 7: Thrust sled model verification. In order to verify the correctness of the finite element modeling method of the thrust sled, the vertical forward three-order modal natural frequencies and vibration shapes of the thrust sled are calculated using the eigenvalue decomposition method according to the thrust sled overall stiffness matrix and overall mass matrix calculated previously, and the calculated results are compared with the modal test results.

[0075] Step 8: Modeling the beam unit of the product sled. Obtain the total mass and center of mass position of the product sled in the 3D modeling software, or measure it based on the solid model. During modeling, the product sled is split according to different geometric shapes and parameters, and the length of each beam unit is different. Set the elastic modulus according to the material properties of each part of the product sled. In order to facilitate the matching of the center of gravity position, assume that the beam unit is lightweight and concentrate the mass at the concentrated mass point. Use the measured mass and center of mass position to modify the established finite element model.

[0076] Step 9: Calculate the mass and stiffness matrix of the product skid. According to the geometric and material parameters of the product skid and the length of the beam unit, and the method of establishing the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1, write a program to calculate the mass matrix and stiffness matrix of the beam unit and the concentrated mass unit of the product skid. After obtaining the stiffness matrix and mass matrix of the unit, use the matrix splicing method to obtain the overall mass matrix and stiffness matrix of the product skid.

[0077] Step 10: Product skid model verification. In order to verify the correctness of the finite element modeling method of the product skid, the vertical forward three-order modal natural frequencies and vibration modes of the product skid are calculated using the eigenvalue decomposition method based on the product skid overall stiffness matrix and overall mass matrix calculated previously, and the calculated results are compared with the modal test results.

[0078] Step 11: Establish the rail beam unit model. The rail is made of I-beam, and the rail body is modeled as a two-degree-of-freedom Euler beam. The rail fastener is modeled as a spring damping system. Due to the constraint of the buckle, the node connected to the buckle has only one degree of freedom of vertical movement.

[0079] Step 12: Determine the stiffness matrix and mass matrix of the slide model. Splice the overall matrix of the slide, determine the geometry, material parameters and modeling method of the slide, and write a simulation calculation program to calculate the mass matrix and stiffness matrix of the slide.

[0080] Step 13: Verification of the finite element modeling method of the slide rail. Substitute the calculated mass matrix and stiffness matrix of the slide rail into the eigenvalue decomposition method program, calculate the vertical forward fourth-order natural frequency and vibration mode of the finite element model of the slide rail, and compare the calculated results with the modal test results.

[0081] Step 14: Determine the connection mode of the rocket sled-slideway coupling system. The connection relationship between the rocket sled and the slide shoe is modeled as a nonlinear spring unit. The spring unit is connected to the slide shoe node and the slide rail node that coincides with the slide shoe node. The stiffness matrix and mass matrix of the whole system are spliced ​​to obtain the overall stiffness matrix and overall mass matrix of the whole system. Rayleigh damping is used to represent the damping of the whole system, and the damping matrix of the whole system can be obtained.

[0082] Step 15: Verification of the finite element model of the sled-rail coupling system in a static state. Establish a rocket sled-rail system model, write a program to calculate the overall stiffness matrix, mass matrix and damping matrix of the whole system, and use the eigenvalue decomposition method to calculate the vertical forward six-order natural frequencies and vibration modes of the whole system through the calculated overall stiffness matrix and mass matrix, and compare the program calculation results with those of commercial software.

[0083] In the rail modeling method, the Timoshenko beam is used to simulate the main part of the rail, and the rail buckle is simplified to a spring-damper system. One end of the spring is fixed to the rail, and the other end is subject to a fixed constraint, that is, the rail beam, foundation and other parts are regarded as rigid bodies with infinite mass. The rocket sled is fixed during the movement, that is, the rail structure is a time-invariant system. The mass matrix, damping matrix and stiffness matrix of the rail structure are corrected through the modal test data of the rail structure to ensure that the dynamic model of the rail structure is consistent with the actual physical model.

[0084] The upper left corner of the mass matrix and the lower right corner of the stiffness matrix of the Euler beam element represent the coupling relationship between the two degrees of freedom of the beam node. When two adjacent beam elements are spliced, the values ​​at the shared nodes are directly added, and the values ​​at other locations remain unchanged.

[0085] The engine propellant is equivalent to non-structural mass and simplified into a series of concentrated mass points fixed on the rocket sled beam model, and the mass varies according to a certain function. During the operation of each stage of the engine, the consumption of propellant makes the rocket sled present a time-varying mass, and the effect of the consumption of propellant on the stiffness of the rocket sled is negligible; the corresponding engine is thrown away immediately after the propellant is consumed, so that the rocket sled presents the characteristics of rapid time-varying mass and stiffness, and it is assumed that the change of stiffness is instantaneous.

[0086] The mass matrix, damping matrix and stiffness matrix of the rocket sled structure are corrected through the modal test data of the rocket sled structure at a specific time t=t* to ensure that the dynamic model of the rocket sled structure is consistent with the actual physical model.

[0087] The shoe and the rail are connected by a nonlinear spring. The piecewise linear spring is set by the distance between the shoe node and the rail node. When the distance between the two is within the shoe-rail gap range, the spring stiffness is small; when the distance between the two is outside the shoe-rail gap range, the spring stiffness is large. Assume is the displacement at the jth sliding shoe node, is the displacement of the i-th node of the slide rail (the position of the i-th node of the slide rail is close to the position of the j-th slide shoe), then at time k, the nonlinear stiffness of the shoe-rail contact can be described as:

[0088]

[0089] In the formula, represents the contact stiffness between the jth sliding shoe and the ith node of the sliding rail. T represents the gap between the shoe and the rail. and represents the vibration displacement of the i-th node of the rail and the j-th node of the shoe at time k. ka represents the stiffness when the shoe and rail are not in contact. represents the contact stiffness between the jth node of the sliding shoe and the oth node of the sliding rail,

[0090] The connection stiffness between the shoe rails is related to the contact relationship between the shoe rails. When the two are in contact, the connection stiffness of the shoe rails comes entirely from the stiffness of the rails, and the stiffness of the rails changes with the distance between the deformation point and the nearest buckle; when the two are not in contact, the contact stiffness between the shoe rails is 0.

[0091] It should be noted that due to the existence of the buckle boundary condition, the contact stiffness of the shoe and the rail at different positions is different. Equivalent calculation can be performed using the finite element model of the slide rail.

[0092] During the assembly process of the rail model and the rocket sled model, the speed change of the rocket sled causes the node positions of the shoe to not coincide with the node positions of the rail. Therefore, the rail structure needs to be discretized again in each calculation step to obtain a new mass matrix, damping matrix, stiffness matrix, etc. This approach consumes a lot of calculation time. Considering the calculation cost, the nodes of the rail structure are not changed during the entire calculation process, and the nodes of the shoe rail and the rail at the adjacent position are matched.

[0093] Example:

[0094] The present invention is a kinematic and dynamic analysis method for a supersonic rocket sled-track coupling system. The method comprises the following steps. Figure 1 :

[0095] Step 1: Establish the stiffness matrix and mass matrix of the beam element. The beam element consisting of two nodes has a total of four degrees of freedom, including a lateral displacement v at each node. i and a small angle φ i , the stiffness matrix of the beam element is as follows:

[0096]

[0097] Where E and I are the elastic modulus and section moment of inertia of the beam, respectively, and l is the length of the beam element.

[0098] Use the consistent mass matrix as the mass matrix of the rocket sled and rail finite element model:

[0099]

[0100] where ρ, A, and I are the density, cross-sectional area, and moment of inertia of the beam, respectively, and 1 is the length of the beam element.

[0101] Step 2: Establish the stiffness matrix of the lightweight spring unit. Use a single-degree-of-freedom two-node spring unit to establish the spring model. The stiffness of the spring unit is k, and the deformation displacement and internal force at the two nodes i and j are u respectively. i 、f i 、u j 、f j The right direction is the positive direction, and the matrix form of the light spring is shown in formula (5).

[0102]

[0103] Step 3: Establish the mass matrix of the concentrated mass unit. For a concentrated mass unit with a mass of m, its 2×2 mass matrix is ​​calculated as shown in the following formula (6).

[0104]

[0105] Step 4: Calculate the damping of the slide rail structure. Determine the reference damping coefficients α and β using a method based on the system's sensitive frequency range.

[0106]

[0107] Where: ξ is the damping ratio corresponding to the upper and lower limits of the sensitive frequency, ω a Take the fundamental frequency of the multi-degree-of-freedom system, ω b Select from the high-order vibration mode frequencies that contribute significantly to the dynamic response. Select appropriate ξ, ω a With ω b After that, the overall damping matrix of the slide rail can be obtained by bringing it into numerical calculation through the overall mass matrix and the overall stiffness matrix.

[0108] Step 5: Establish the thrust sled beam unit model. The thrust sled is a hollow cylinder with an outer diameter of 0.3m, an inner diameter of 0.288m, a wall thickness of 0.006m, and a total length of 4.385m. There are four slides on the thrust sled, and the mass of the slides is 28kg. When performing finite element modeling, the following assumptions are made: the thrust sled is filled with fuel, and the mass is evenly distributed, and the density is taken as 1.6kg / m 3 The thrust sled body is modeled as a two-degree-of-freedom Euler beam element with a unit length of 108.5752 mm, a total of 40 beam elements and 41 nodes. The slide shoe is modeled as a concentrated mass unit at the 2nd, 15th, 28th and 41st nodes. In addition, concentrated mass units are used to simulate the fuel in the thrust sled. The mass of each concentrated mass unit is 11.4 kg, and there are a total of 41 uniformly distributed concentrated mass units. The established finite element model is attached. Figure 2 shown.

[0109] Step 6: Calculate the mass and stiffness matrix of the thrust sled. According to the thrust sled geometry and material parameters and the length of the beam unit, and the method of establishing the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1, write a program to calculate the mass matrix and stiffness matrix of the thrust sled beam unit and the concentrated mass unit. After obtaining the stiffness matrix and mass matrix of the unit, use the matrix splicing method to obtain the overall mass matrix and stiffness matrix of the thrust sled.

[0110] Step 7: Thrust sled model verification. In order to verify the correctness of the finite element modeling method of the thrust sled, this section uses the eigenvalue decomposition method to calculate the vertical forward three-order modal natural frequencies and vibration shapes of the thrust sled based on the thrust sled overall stiffness matrix and overall mass matrix calculated previously, and compares the calculated results with the modal test results, as shown in Table 1.

[0111] Table 1 Comparison of simulation results and modal test results

[0112] Degree Simulation results / Hz Experimental results / Hz error 1 46.11 47.09 2.08％ 2 125.68 122.97 2.20％ 3 266.82 225.08 18.54％

[0113] Step 8: Modeling of product sled beam units. The product sled adopts an integrated arrow sled design, which is mainly composed of a test piece and a sliding shoe. The total length of the test piece is 2.951m. It is an empty cabin with an overall wall thickness of 6mm and an outer diameter of 300mm. It is divided into 4 sections. Sections 1 and 2 are combined together to form a hollow cone, and sections 3 and 4 are hollow cylinders. The mass of the product sled is about 229kg, and its center of mass is located about 1m away from the tail. The material is 45 steel, and the elastic modulus of 45 steel is 210Gpa. The cone structure with constantly changing inner and outer diameters at the front end of the product sled is simplified into a group of 11 stepped beam units with increasing inner and outer diameters for simulation. In order to facilitate the matching of the center of gravity position, see the attached figure. Figure 3 Assuming that the beam element is lightweight, the mass is concentrated at the concentrated mass point, and it is assumed that the internal mass of the front tapered part of the product skid changes linearly with the change of the outer diameter, and the mass inside each part of the other two parts is evenly distributed.

[0114] Step 9: Calculate the mass and stiffness matrix of the product skid. According to the geometric and material parameters of the product skid and the length of the beam unit, and the method of establishing the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1, write a program to calculate the mass matrix and stiffness matrix of the beam unit and the concentrated mass unit of the product skid. After obtaining the stiffness matrix and mass matrix of the unit, use the matrix splicing method to obtain the overall mass matrix and stiffness matrix of the product skid.

[0115] Step 10: Product skid model verification. In order to verify the correctness of the finite element modeling method of the product skid, this section uses the eigenvalue decomposition method to calculate the vertical forward three-order modal natural frequencies and vibration shapes of the product skid based on the product skid overall stiffness matrix and overall mass matrix calculated previously, and compares the calculated results with the modal test results, as shown in Table 2.

[0116] Table 2 Comparison of simulation results and modal tests

[0117] Mass / kg Center of mass position / m First order / Hz Second order / hz Third order / Hz simulation 229.02 1.03 187.05 426.46 688.22 test 229.00 1.00 190.315 429.683 686.590 error 0.01％ 0.01％ 1.72％ 0.75％ 0.24％

[0118] Step 11: Establish the rail beam unit model. Establish the rail beam unit model. The rail is made of I-beam, with a height of 0.144m, a cross-sectional area of ​​9.714×10^(-3)m^2, a horizontal axis section moment of inertia of 2.372×10^(-5)m^4, and a vertical axis section moment of inertia of 7.108×10^(-6)m^4. The rail material density is 7.85×10^3kg / m^3, the Young's modulus is 210Gpa, the shear modulus is 80.77Gpa, and the Poisson's ratio is 0.3. The rail fastener is modeled as a spring damping system, and the support stiffness is 8.1×10^8N / m. The rail fastener is modeled as a spring damping system. Due to the constraint of the buckle at the buckle, the node connected to the buckle has only one degree of freedom of vertical motion. The length of the beam unit is selected as 0.1m, the distance between adjacent buckles of the slide rail is 1m, and considering the length of the slide rail in the slide rail modal test, the total length of the slide rail model is determined to be 10m. The finite element model of the slide rail is shown in the attached Figure 4 .

[0119] Step 12: Determine the stiffness matrix and mass matrix of the slide model. According to the method introduced in step 2, perform the overall matrix splicing method on the slide, determine the geometry, material parameters and modeling method of the slide, and write a simulation calculation program to calculate the mass matrix and stiffness matrix of the slide.

[0120] Step 13: Verification of the finite element modeling method of the slide rail. Substitute the calculated mass matrix and stiffness matrix of the slide rail into the eigenvalue decomposition method program, calculate the vertical forward fourth-order natural frequency and vibration mode of the slide rail finite element model, and compare the calculated results with the modal test results, as shown in Table 3.

[0121] Table 3 Comparison of simulation and experimental natural frequencies

[0122] Simulation results / Hz Modal test results / Hz error 1 468.31 461.10 1.56％ 2 478.59 477.19 0.29％ 3 495.76 491.39 0.89％ 4 519.85 512.11 1.51％

[0123] Step 14: Determine the connection mode of the rocket sled-slide rail system. The connection relationship between the rocket sled and the slide shoe is modeled as a nonlinear spring unit. The spring unit is connected to the slide shoe node and the slide rail node that coincides with the slide shoe node, see the attached Figure 5 The unit stiffness matrix of the spring unit is as follows (8). At the same time, since the spring unit is lightweight, its mass matrix is ​​a zero matrix.

[0124]

[0125] where [k s (d)] represents the spring unit stiffness matrix, k(d) represents the spring unit stiffness. d represents the distance between the sliding shoe and the nearest buckle,

[0126] Step 15: Verification of the finite element model of the sled-rail coupling system in a static state. The rocket sled-rail system model is established. The rail length is 10m. The rocket sled includes a first-stage product sled and a third-stage thrust sled. Each product sled has two slides, and each thrust sled has four slides. The entire rocket sled system is connected to the rail through a total of 14 springs simulating the slides. The finite element model of the sled-rail coupling system is attached. Figure 6 . A program was written to calculate the overall stiffness matrix, mass matrix and damping matrix of the whole system. The vertical first six-order natural frequencies and vibration modes of the whole system were calculated using the eigenvalue decomposition method based on the calculated overall stiffness matrix and mass matrix. The calculation results of the program were compared with those of commercial software.

[0127] Table 4 Comparison of calculation results between simulation program and commercial software

[0128] First order / Hz Second order / Hz Third order / Hz Fourth order / Hz Fifth order / Hz Sixth order / Hz Simulation Program 142.67 177.34 180.31 185.48 193.50 205.61 Nastran 150.41 199.33 180.31 185.48 193.50 205.61 error 5.15％ 0.01％ 0 0 0 0

Claims

1. A method for modeling the full trajectory dynamics of a multi-stage rocket sled, characterized in that: The steps include: Step 1: Establish the stiffness matrix and mass matrix of the beam element; only consider the vertical translation and rotation in the vertical plane. The beam elements are all Euler beams, and the shear of the beam is not considered. Step 2: Establish the stiffness matrix of the lightweight spring element; The spring model is established using a single-degree-of-freedom two-node spring unit, and the stiffness matrix of the spring unit is a 2×2 matrix; Step 3: Establish the mass matrix of the concentrated mass unit; The concentrated mass unit is a single-node unit, and its moment of inertia is 0, so its mass matrix is ​​in the form of a 2×2 matrix; Step 4: Calculate the damping of the slide rail structure; Rayleigh damping is used to simulate the damping of the slide structure, and the damping matrix C is expressed as: C=αM+βK(1) Where C is the Rayleigh damping matrix of the structure, α and β are the corresponding Rayleigh damping coefficients; Step 5: Establish the thrust sled beam unit model; The thrust sled is modeled using two-degree-of-freedom Euler beam elements and concentrated mass elements. The thrust sled is filled with fuel and the mass is evenly distributed, so the length of the beam element is determined. Step 6: Calculate the mass matrix and stiffness matrix of the thrust sled; According to the thrust sled geometry and material parameters and the length of the beam unit, the mass matrix and stiffness matrix of the thrust sled beam unit and the concentrated mass unit are calculated according to the establishment method of the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1; the overall mass matrix and stiffness matrix of the thrust sled are obtained by using the matrix splicing method; Step 7: Thrust sled model verification; The eigenvalue decomposition method is used to calculate the vertical forward three-order modal natural frequencies and vibration shapes of the thrust sled, and the calculated results are compared with the modal test results; Step 8: Modeling of product skid beam unit; Obtain the total mass and center of mass position of the product skid in the 3D modeling software; split the product skid according to different geometric shapes and parameters, and the length of each beam unit is different; Set the elastic modulus according to the material properties of each part of the product skid; set the beam unit to be lightweight and concentrate the mass at the concentrated mass point; modify the established finite element model using the measured mass and center of mass position; Step 9: Calculate the mass matrix and stiffness matrix of the product skid; According to the geometric and material parameters of the product skid and the length of the beam unit, the mass matrix and stiffness matrix of the beam unit and the concentrated mass unit of the product skid are calculated according to the establishment method of the stiffness matrix and mass matrix of the beam unit and the concentrated mass unit in step 1; the overall mass matrix and stiffness matrix of the product skid are obtained by using the matrix splicing method; Step 10: Product skid model verification; The eigenvalue decomposition method is used to calculate the vertical forward three-order modal natural frequencies and vibration modes of the product skid, and the calculated results are compared with the modal test results; Step 11: Establish the slide rail beam unit model; The main body of the slide rail is modeled as an Euler beam with two degrees of freedom, and the slide rail fastener is modeled as a spring damping system. The node connected to the buckle has only one degree of freedom of vertical motion. Step 12: Determine the stiffness matrix and mass matrix of the slide model; Splice the overall matrix of the slide rail, determine the geometry, material parameters and modeling method of the slide rail, and write a simulation calculation program to calculate the mass matrix and stiffness matrix of the slide rail; Step 13: Verification of the finite element modeling method of the slide rail; Substitute the calculated mass matrix and stiffness matrix of the slide rail into the eigenvalue decomposition method program to calculate the vertical forward fourth-order natural frequency and vibration mode of the slide rail finite element model, and compare the calculated results with the modal test results; Step 14: Determine the connection mode of the rocket sled-slideway coupling system; The connection between the rocket sled and the slide shoe is modeled as a nonlinear spring unit; the spring unit is respectively connected to the slide shoe node and the slide rail node that coincides with the slide shoe node, the stiffness matrix and mass matrix of the whole system are spliced ​​to obtain the overall stiffness matrix and overall mass matrix of the whole system, and the damping of the whole system is represented by Rayleigh damping to obtain the damping matrix of the whole system; Step 15: Verification of the finite element model of the sled-rail coupling system in a static state; The eigenvalue decomposition method is used to calculate the vertical first six-order natural frequencies and vibration modes of the overall system, and the calculation results of the program are compared with those of commercial software.

2. A multi-stage rocket sled full trajectory dynamics modeling method according to claim 1, characterized in that: When the slide rail body is modeled as an Euler beam with two degrees of freedom, a Timoshenko beam is used to simulate the main part of the slide rail, and the slide rail buckle is simplified into a spring-damper system. One end of the spring is fixedly connected to the slide rail, and a fixed constraint is applied to the other end, that is, the support beam and the foundation part are regarded as a rigid body with infinite mass; the mass matrix, damping matrix and stiffness matrix of the slide rail structure are corrected through the modal test data of the slide rail structure to ensure that the dynamic model of the slide rail structure is consistent with the actual physical model.

3. A multi-stage rocket sled full trajectory dynamics modeling method according to claim 1, characterized in that: The two areas at the upper left corner of the unit mass matrix and the lower right corner of the stiffness matrix of the Euler beam respectively represent the coupling relationship between the two degrees of freedom of the beam node itself; when two adjacent beam units are spliced, the values ​​at the common nodes are directly added, and the values ​​at other positions remain unchanged.

4. A method for modeling the full trajectory dynamics of a multi-stage rocket sled according to claim 1, characterized in that: The sliding shoe and the sliding rail are connected by a nonlinear spring, and a segmented linear spring is set according to the distance between the sliding shoe node and the sliding rail node. When the distance between the two is within the shoe-rail gap range, the spring stiffness is smaller than the spring stiffness when the distance between the two is outside the shoe-rail gap range; set up is the displacement at the jth sliding shoe node, is the displacement of the i-th node of the rail, and the position of the i-th node of the rail is close to the position of the j-th shoe. Then at time k, the nonlinear stiffness of the shoe-rail contact is described as: In the formula, represents the contact stiffness between the jth sliding shoe and the i-th node of the sliding rail; τ represents the gap between the shoe and the rail; and represents the vibration displacement of the i-th node of the rail and the j-th node of the sliding shoe at time k; k a Indicates the stiffness when the shoe rail is not in contact; represents the contact stiffness between the jth node of the sliding shoe and the ith node of the sliding rail, 5. The method for modeling the full trajectory dynamics of a multi-stage rocket sled according to claim 1, characterized in that: When the sliding shoe and the sliding rail are in contact, the shoe-rail connection stiffness comes entirely from the stiffness of the sliding rail, and the stiffness of the sliding rail changes with the distance between the deformation point and the nearest buckle; when the two are not in contact, the contact stiffness between the shoe and the rail is 0.

6. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 5.

7. An electronic device, characterized in that: include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method as claimed in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

9. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes a method as claimed in any one of claims 1 to 5.

10. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 5 is implemented.

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