A method, system and device for constructing a normal variation recovery coefficient model

Abstract

The application relates to a construction method, system and device of a novel normal variable restitution coefficient model, and the method comprises the following steps: establishing a physical model of a ball and a base contact collision, obtaining a functional relationship between a restitution coefficient and an equivalent strain in a plastic stage according to an energy equivalence principle under the condition that a volume of an effective deformation domain at a maximum compression moment is equal to a volume of an elastic effective deformation domain; establishing a numerical simulation model of a ball-base normal contact collision, performing numerical simulation of the contact collision under multiple working conditions based on the simulation model to obtain simulation results; introducing a dimensionless parameter and fitting a mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage by combining the simulation results; and obtaining the normal variable restitution coefficient model based on the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage and the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage. According to the application, high-precision prediction of contact collision dynamics response results can be realized without relying on complex contact collision theories.

Description

Technical Field

[0001] This invention relates to the field of multibody system dynamics and control technology, and in particular to a novel method, system and device for constructing a normal variable restitution coefficient model. Background Technology

[0002] Contact collisions frequently occur between mechanical systems and are an extremely complex mechanical phenomenon closely related to various factors such as the material properties, geometry, relative motion, and environmental medium of the colliding objects. With the rapid development of high-tech industries, mechanical systems are becoming increasingly precise and complex. The prevalence of contact collisions easily causes localized damage to mechanical systems and leads to a decline in their overall performance. Therefore, conducting research on dynamic modeling of complex systems is urgently needed.

[0003] The coefficient of restitution is a crucial parameter for assessing energy loss during contact collisions. In-depth research on it is beneficial for accurately predicting contact collision phenomena and further understanding the overall dynamic response of mechanical systems. Due to the extremely short duration and complex nature of contact collisions, conventional sensors struggle to capture the process precisely. Currently, most researchers rely on finite element numerical simulations to obtain data and use numerical fitting methods to establish models with varying coefficients of restitution. However, this approach is time-consuming, and the computational accuracy of the constructed models falls far short of current requirements. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a novel method, system and device for constructing a normal variable restitution coefficient model, which solves the technical problems that the analysis and processing time of the existing restitution coefficient model establishment scheme is too long and the calculation accuracy of the model cannot meet the required standards.

[0006] (II) Technical Solution

[0007] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0008] In a first aspect, embodiments of the present invention provide a method for constructing a novel normal variable restoring coefficient model based on the energy equivalence principle, comprising:

[0009] A physical model of the contact collision between the sphere and the substrate is established. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage is obtained by analyzing the contact collision model between the sphere and the substrate based on the principle of energy equivalence.

[0010] A numerical simulation model of sphere-base normal contact collision was established, and simulation results were obtained by performing multi-condition contact collision numerical simulation based on the simulation model.

[0011] A dimensionless parameter is introduced as an intermediate parameter, and the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage is fitted by combining the simulation results.

[0012] Based on the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage, as well as the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage, a normal strain restitution coefficient model is obtained.

[0013] Among them, the dimensionless parameters are mechanical property characterization parameters including the material's yield strength, sphere density, and the initial relative contact velocity between the sphere and the substrate.

[0014] Optionally, a physical model of the sphere-substrate contact collision is established. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the elastic effective deformation domain volume, the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage is obtained by analyzing the sphere-substrate contact collision model based on the energy equivalence principle.

[0015] By simulating the process of applying a vertically downward initial velocity field to a sphere and causing the sphere to collide with a base with its lower edge fixed, a physical model and constitutive model of the contact collision between the sphere and the base are established.

[0016] Based on the constitutive model, the folded constitutive model and related folded mechanical parameters are obtained;

[0017] The energy conversion during the contact collision process of the established physical model of the sphere and the substrate is analyzed, and the relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained.

[0018] Based on the principle of energy median equivalence, an energy median equivalent point is found in the contact collision model between the sphere and the substrate, and the expression for the strain energy density of the energy median equivalent point is obtained. The strain energy density of the energy median equivalent point can be equivalent to the average strain energy density of the system.

[0019] Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the functional relationship between the restitution coefficient and the equivalent plastic strain is obtained based on the relationship between the restitution coefficient and the strain energy of the contact collision model, the expression of the strain energy density at the energy median equivalent point, and the relevant reduced mechanical parameters.

[0020] in,

[0021] The constitutive model for the collision model of the sphere and the substrate is as follows:

[0022]

[0023] In equation (1), σ is stress, ε is strain, E is the elastic modulus of the material, and σ y and ε y These represent the yield strength and yield strain of an ideal elastoplastic material, respectively.

[0024] The relevant reduced mechanical parameters of the reduced constitutive model are:

[0025]

[0026]

[0027] In equations (2) and (3), E * To convert the elastic modulus, E1 and E2 represent the elastic modulus of the sphere and the substrate, respectively, and u1 and u2 are the Poisson's ratios of the sphere and the substrate, respectively. This is the equivalent yield strain.

[0028] Optionally, the energy conversion during the contact collision process of the established physical model of the sphere-substrate contact collision is analyzed, and the relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained, including:

[0029] By analyzing the process of the collision model between the sphere and the base, we obtained the kinetic energy expressions for the non-collision and the kinetic energy conversion expressions for the collision.

[0030] By rearranging the expressions for kinetic energy when no collision occurs and for kinetic energy conversion when a collision occurs, and combining the equivalent relationship between elastic strain energy and rebound kinetic energy at the moment of collision, the expression for kinetic energy at the end of the collision is obtained.

[0031] The coefficient of restitution for a sphere-substrate contact collision was calculated using the Newtonian coefficient of restitution model.

[0032] Based on the kinetic energy expression and the coefficient of restitution at the end of the collision, an initial relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained. Based on the initial relationship, and combined with the kinetic energy conversion expression of the collision, a relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained.

[0033] in,

[0034] The expression for the kinetic energy without a collision is:

[0035]

[0036] In equation (4), E k0 Let ρ be the initial kinetic energy of the sphere, which is also the total energy of the sphere and the base system at the initial moment, ρ be the density of the sphere, V1 be the volume of the sphere, and v be the initial kinetic energy of the sphere. nc The initial relative velocity between the sphere and the base;

[0037] The expression for the kinetic energy conversion during a collision is:

[0038] E k0 =E ε =E εe +E εp (5)

[0039] In equation (5), E ε For strain energy, E εe E is the elastic strain energy. εp It is the plastic strain energy;

[0040] The expression for the transposition process is:

[0041]

[0042] The expression for the kinetic energy at the moment the collision ends is:

[0043]

[0044] In equation (7), v r The rebound velocity of the sphere at the instant the collision ends;

[0045] The coefficient of restitution for a sphere-substrate contact collision is:

[0046]

[0047] In equation (8), Ce is the coefficient of restitution;

[0048] The initial relationship between the coefficient of restitution and the strain energy of the contact collision model is as follows:

[0049]

[0050] The relationship between the coefficient of restitution and the strain energy of the contact collision model is as follows:

[0051]

[0052] Optionally, based on the principle of median energy equivalence, an energy median equivalent point is found in the collision model between the sphere and the substrate, and the expression for the strain energy density at this energy median equivalent point is obtained, including:

[0053] Based on the principle of energy median equivalence, an energy median equivalent point M in the contact collision model between the sphere and the substrate is found, and the expression for the strain energy density of the energy median equivalent point is obtained.

[0054] The strain energy density at the median equivalent point under complex stress is equivalently transformed into the strain energy density under uniaxial stress.

[0055] When the contact collision model enters the plastic stage, the equivalent elastic strain energy density and equivalent plastic strain energy density of the plastic stage are obtained based on the strain energy density under uniaxial stress state, and then the strain energy density of the energy median equivalent point of the plastic stage is obtained.

[0056] in,

[0057] The expression for the system energy is:

[0058] U = υ M V (11)

[0059] In equation (11), U is the work done by the external force on the object, V is the volume of the effective deformation domain of the object, and υ M The strain energy density is the equivalent point of the energy median under complex stress conditions.

[0060] The strain energy density under uniaxial stress is:

[0061]

[0062] In equation (12), σ ij and ε ij Let σ be the stress and strain tensor components at point M under complex stress conditions. eq With ε eq These are the equivalent stress and equivalent strain at point M, respectively;

[0063] The equivalent elastic strain energy density is:

[0064]

[0065] The equivalent plastic strain energy density is:

[0066]

[0067] The strain energy density at the median equivalent point of the energy during the plastic stage is:

[0068] υ M =υ εe +υ εp (15).

[0069] Optionally, under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, based on the relationship between the coefficient of restitution and the strain energy of the contact collision model, the expression for the strain energy density at the energy median equivalent point, and relevant reduced mechanical parameters, the functional relationship between the coefficient of restitution and the equivalent plastic strain is obtained, including:

[0070] Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the elastic effective deformation domain volume, the relationship between the restitution coefficient and the strain energy of the contact collision model and the strain energy density expression of the energy median equivalent point are used to obtain the relationship between the restitution coefficient and the strain energy of the effective deformation domain.

[0071] Based on the relationship between the coefficient of restitution and the strain energy of the effective deformation domain, the relationship between the equivalent elastic strain energy density and the equivalent plastic strain energy density, the initial functional relationship between the coefficient of restitution and the equivalent plastic strain is obtained.

[0072] Based on relevant reduced mechanical parameters, the initial functional relationship between the coefficient of restitution and the equivalent plastic strain is decomposed to obtain the functional relationship between the coefficient of restitution and the equivalent plastic strain;

[0073] in,

[0074] The relationship between the coefficient of restitution and the strain energy of the effective deformation domain is as follows:

[0075]

[0076] In equation (16), V2 is the effective deformation domain volume at the moment of maximum compression, and V3 is the effective elastic deformation domain volume at the moment of maximum compression.

[0077] The initial functional relationship between the restitution coefficient and the equivalent plastic strain is as follows:

[0078]

[0079] The equivalent strain at point M in the initial functional relation can be decomposed into:

[0080]

[0081] In equation (18), ε p Equivalent plastic strain;

[0082] The functional relationship between the restitution coefficient and the equivalent plastic strain is as follows:

[0083]

[0084] Optionally, a numerical simulation model of sphere-base normal contact collision is established, and simulation results are obtained by performing multi-condition contact collision numerical simulations based on the simulation model, including:

[0085] Preprocessing is performed, including defining the simulation model as an axisymmetric model, refining the mesh of the contact area, and setting geometric parameters, so as to establish a sphere-base normal contact collision numerical simulation model using finite element method.

[0086] Based on the sphere-base normal contact collision numerical simulation model, multi-condition contact collision numerical simulations were performed using the finite element method to obtain the coefficient of restitution Ce and the equivalent plastic strain ε obtained through inverse calculation. p The simulation results.

[0087] Optionally, a dimensionless parameter is introduced as an intermediate parameter, and the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage is fitted based on the simulation results, including:

[0088] Use a dimensionless parameter as an intermediate parameter and logarithmize the dimensionless parameter;

[0089] Based on the logarithmically transformed dimensionless parameters and simulation results, the mapping relationship between dimensionless parameters and equivalent strain in the plastic stage is obtained;

[0090] in,

[0091] Dimensionless parameter is

[0092]

[0093] The mapping relationship between dimensionless parameters and equivalent strain in the plastic stage is as follows:

[0094]

[0095] In equation (21), e is the natural constant.

[0096] Optionally, the normal variable restoring coefficient model is:

[0097]

[0098] In equation (22), when v nc As v approaches 0, the coefficient of restitution approaches 1; as v... nc As v increases, the coefficient of recovery strictly decreases monotonically; when v nc As the value approaches infinity, the coefficient of restitution approaches 0.

[0099] Secondly, embodiments of the present invention provide a novel system for constructing a normal variable restoring coefficient model based on the principle of energy equivalence, comprising:

[0100] The model building and analysis module is used to build a physical model of the contact collision between the sphere and the substrate. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the model of the contact collision between the sphere and the substrate is analyzed based on the principle of energy equivalence to obtain the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage.

[0101] The finite element simulation module is used to establish a numerical simulation model of sphere-base normal contact collision, and to obtain simulation results by performing multi-condition contact collision numerical simulation based on the simulation model.

[0102] The parameter introduction and fitting module is used to introduce a dimensionless parameter as an intermediate parameter and fit the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage based on the simulation results.

[0103] The module for establishing the normal variable restitution coefficient model is used to obtain the normal variable restitution coefficient model based on the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage, as well as the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage.

[0104] Among them, the dimensionless parameters are mechanical property characterization parameters including the material's yield strength, sphere density, and the initial relative contact velocity between the sphere and the substrate.

[0105] Thirdly, an embodiment of the present invention provides a novel normal variable restoring coefficient model construction device based on the energy equivalence principle, comprising:

[0106] At least one database;

[0107] And a memory that is communicatively connected to the at least one database;

[0108] The memory stores instructions that can be executed by the at least one database. These instructions are executed by the at least one database to enable the at least one database to perform the construction method of the novel normal variable restitution coefficient model based on the energy equivalence principle as described above, so as to achieve high-precision prediction of the relative error of the contact collision dynamic response results within 5%.

[0109] (III) Beneficial Effects

[0110] The beneficial effects of this invention are: the construction process of the novel normal variable restitution coefficient model provided by this invention is simple and clear, without relying on complex contact collision theory or requiring a large amount of complicated processing and analysis. Regardless of the complexity and prevalence of contact collision processes, the variable restitution coefficient model established by this invention can achieve high-precision prediction of contact collision dynamic response results, and has corresponding prospects and practical application significance. Attached Figure Description

[0111] Figure 1 This is a flowchart illustrating a method for constructing a novel normal variable restoring coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0112] Figure 2 This is a schematic diagram of step S1 of a method for constructing a novel normal variable restoring coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0113] Figure 3This is a schematic diagram of the contact collision between a sphere and a substrate, illustrating a method for constructing a novel normal variable restitution coefficient model based on the principle of energy equivalence proposed in an embodiment of the present invention.

[0114] Figure 4 This is a schematic diagram of step S13 of the method for constructing a novel normal variable restoring coefficient model based on the principle of energy equivalence proposed in an embodiment of the present invention.

[0115] Figure 5 This is a schematic diagram of step S14 of the method for constructing a novel normal variable restoring coefficient model based on the principle of energy equivalence proposed in an embodiment of the present invention.

[0116] Figure 6 This is a schematic diagram of step S15 of the method for constructing a novel normal variable restitution coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0117] Figure 7 This is a schematic diagram of step S2 of the method for constructing a novel normal variable restitution coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0118] Figure 8 The figure shows a numerical simulation model of a sphere colliding with a substrate, which is a method for constructing a novel normal variable restitution coefficient model based on the principle of energy equivalence proposed in an embodiment of the present invention.

[0119] Figure 9 This is a schematic diagram of step S3 of a method for constructing a novel normal variable restoring coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0120] Figure 10 The figure shows the numerical fitting results of a novel normal variable restitution coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0121] Figure 11 The figure shows the piecewise fitting results of a method for constructing a novel normal variable restitution coefficient model based on the energy equivalence principle proposed in an embodiment of the present invention.

[0122] Figure 12 This is a comparison of the coefficient of restitution results of the contact collision process between an alumina sphere and an aluminum substrate, based on a novel normal variable restitution coefficient model constructed according to the principle of energy equivalence proposed in this invention.

[0123] Figure 13 This is a comparison of the coefficient of restitution results of the contact collision process between an alumina sphere and a steel substrate, based on a novel normal variable restitution coefficient model constructed according to the principle of energy equivalence proposed in this invention.

[0124] Figure 14 This is a schematic diagram of the overall process for constructing a novel normal variable restoring coefficient model based on the principle of energy equivalence, as proposed in an embodiment of the present invention. Detailed Implementation

[0125] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the figures and specific embodiments.

[0126] like Figure 1 As shown in the embodiment of the present invention, a method for constructing a novel normal variable restitution coefficient model based on the energy equivalence principle is proposed. The method includes: First, establishing a sphere-base contact collision model. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the elastic effective deformation domain volume, the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage is obtained by analyzing the sphere-base contact collision model according to the energy equivalence principle. Second, establishing a sphere-base normal contact collision numerical simulation model, and performing multi-condition contact collision numerical simulations based on the simulation model to obtain simulation results. Third, introducing a dimensionless parameter as an intermediate parameter, and fitting the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage based on the simulation results. Finally, based on the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage, and the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage, a normal variable restitution coefficient model is obtained.

[0127] The novel normal variable restitution coefficient model provided by this invention has a simple and clear construction process, requiring neither reliance on complex contact collision theory nor extensive and cumbersome processing and analysis. Regardless of the complexity and prevalence of contact collision processes, the variable restitution coefficient model established by this invention can achieve high-precision prediction of contact collision dynamic response results, demonstrating promising prospects and practical application significance.

[0128] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the figures. Although exemplary embodiments of the present invention are shown in the figures, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0129] Specifically, the present invention provides a method for constructing a novel normal variable restoring coefficient model based on the principle of energy equivalence, which includes:

[0130] S1. Establish a physical model of the contact collision between the sphere and the substrate. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, analyze the contact collision model between the sphere and the substrate based on the principle of energy equivalence to obtain the functional relationship between the recovery coefficient and the equivalent strain in the plastic stage.

[0131] This invention focuses on the normal contact collision process between a sphere and a substrate, analyzing the energy conversion throughout the entire collision process based on the principle of energy equivalence. It assumes that the effective deformation domain volume at the moment of maximum compression during the collision is equal to the effective elastic deformation domain volume, thereby obtaining the coefficient of restitution Ce and the equivalent strain ε during the plastic stage. p The functional relationship between them.

[0132] Furthermore, such as Figure 2 As shown, step S1 includes:

[0133] S11. By simulating the process of applying a vertically downward initial velocity field to the sphere and causing the sphere to collide with the fixed base at its lower edge, a contact collision model and its constitutive model between the sphere and the base are established.

[0134] The constitutive model for the collision between the sphere and the substrate is as follows:

[0135]

[0136] In equation (1), σ is stress, ε is strain, E is the elastic modulus of the material, and σ y and ε y These represent the yield strength and yield strain of an ideal elastoplastic material, respectively.

[0137] refer to Figure 3 The collision process between the sphere and the substrate is shown. The sphere is considered an ideal elastic material, and the substrate is an ideal elastoplastic material. Its constitutive model is shown in equation (1). An initial vertically downward velocity field v is applied to the sphere. nc This causes the sphere to come into contact with the fixed base at its lower edge. After the contact and collision, the sphere bounces back.

[0138] S12. Based on the constitutive model, the reduced constitutive model and related reduced mechanical parameters are obtained. For the sphere-base system, its reduced mechanical parameters (mainly including the reduced elastic modulus E) are... * and reduced yield strain )

[0139] The relevant reduced mechanical parameters of the reduced constitutive model are as follows:

[0140]

[0141]

[0142] In equations (2) and (3), E * To convert the elastic modulus, E1 and E2 represent the elastic modulus of the sphere and the substrate, respectively, and u1 and u2 are the Poisson's ratios of the sphere and the substrate, respectively. To account for the yield strain, σ y It represents the yield strength.

[0143] S13. Analyze the energy conversion of the established sphere-base contact collision model during the contact collision process to obtain the relationship between the restitution coefficient and the strain energy of the contact collision model.

[0144] Furthermore, such as Figure 4 As shown, step S13 includes:

[0145] S131. By analyzing the process of the collision model between the sphere and the base, the kinetic energy expressions for the non-collision and the kinetic energy conversion expressions for the collision are obtained.

[0146] S132. By rearranging the kinetic energy expressions for the non-collision and collision-related kinetic energy conversion expressions, and combining the equivalent relationship between the elastic strain energy and the rebound kinetic energy at the moment of collision, the kinetic energy expression at the end of the collision is obtained.

[0147] S133. The coefficient of restitution for a sphere-substrate contact collision is calculated using the Newtonian coefficient of restitution model.

[0148] S134. Based on the kinetic energy expression and the coefficient of restitution at the end of the collision, the initial relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained. Based on the initial relationship, the relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained by combining the kinetic energy conversion expression of the collision.

[0149] S14. Based on the principle of median energy equivalence, find a median energy equivalent point in the contact collision model between the sphere and the substrate, and derive the expression for the strain energy density at this median energy equivalent point. The strain energy density at this median energy equivalent point can be equivalent to the average strain energy density of the system, where the system is the contact collision system composed of the sphere and the plate.

[0150] In a specific embodiment, at the initial moment, an initial vertically downward velocity field is applied to the sphere, and the total energy of the system can be expressed by formula (4), that is, the kinetic energy expression for the system without collision is:

[0151]

[0152] In equation (4), E k0 Let ρ be the initial kinetic energy of the sphere, which is also the total energy of the sphere and the base system at the initial moment, ρ be the density of the sphere, V1 be the volume of the sphere, and v be the initial kinetic energy of the sphere. nc Let be the initial relative velocity between the sphere and the base.

[0153] Subsequently, the sphere collides with the base, causing localized compression deformation in the contact area. At the moment of maximum compression, the system's initial kinetic energy E... k0The strain energy E is completely converted into the system's stored energy. ε (including elastic strain energy E) εe and plastic strain energy E εp Therefore, the expression for the kinetic energy conversion during the collision is:

[0154] E k0 =E ε =E εe +E εp (5)

[0155] In equation (5), E ε For strain energy, E εe E is the elastic strain energy. εp It is the plastic strain energy;

[0156] After simple transposition, the expression for term processing is:

[0157]

[0158] At the end of the collision, the elastic strain energy E εe The energy is completely converted into the rebound kinetic energy of the system; therefore, the expression for the kinetic energy at the end of the collision is:

[0159]

[0160] In equation (7), v r The rebound velocity of the sphere at the instant the collision ends;

[0161] The coefficient of restitution for a sphere-substrate contact collision is calculated using the Newtonian variable coefficient of restitution model:

[0162]

[0163] In equation (8), Ce is the coefficient of restitution.

[0164] Combining equations (7) and (8), the initial relationship between the coefficient of restitution and the strain energy of the contact collision model can be obtained as follows:

[0165]

[0166] Observing the right side of equation (9), the denominator is the initial kinetic energy E of the system. k0 That is, the total strain energy E stored in the system at the moment of maximum compression. ε Therefore, the above equation can be further expressed as the relationship between the coefficient of restitution and the strain energy of the contact collision model:

[0167]

[0168] Furthermore, such as Figure 5 As shown, step S14 includes:

[0169] S141. Based on the principle of energy median equivalence, find an energy median equivalent point M in the contact collision model between the sphere and the substrate, and obtain the strain energy density expression of the energy median equivalent point.

[0170] S142. The strain energy density at the median equivalent point of energy under complex stress state is equivalently transformed into the strain energy density under uniaxial stress state.

[0171] S143. When the contact collision model enters the plastic stage, the equivalent elastic strain energy density and equivalent plastic strain energy density of the plastic stage are obtained based on the strain energy density under uniaxial stress. This leads to the strain energy density at the median equivalent point of the plastic stage. The plastic stage indicates that the stress state of the model has reached the yield limit.

[0172] in,

[0173] According to the principle of median energy equivalence, there exists at least one point M in the entire object where the product of the strain energy density obtained by the equivalent stress integral at that point and the effective deformation domain volume equals the work done by the external force on the object. This point is called the median energy equivalence point. The expression for the system energy is:

[0174] U = υ M V (11)

[0175] In equation (11), U is the work done by the external force on the object, V is the volume of the effective deformation domain of the object, and υ M The strain energy density is the equivalent point of the energy median under complex stress conditions.

[0176] Furthermore, the strain energy density at point M under complex stress conditions can be equivalently transformed into the strain energy density under uniaxial stress conditions, where the strain energy density under uniaxial stress conditions is:

[0177]

[0178] In equation (12), σ ij and ε ij Let σ be the stress and strain tensor components at point M under complex stress conditions. eq With ε eq The Von Mises equivalent stress and equivalent strain at point M are respectively;

[0179] At the moment of maximum compression, the system has entered the plastic stage, and the equivalent elastic strain energy density is:

[0180]

[0181] Similarly, the equivalent plastic strain energy density is:

[0182]

[0183] Adding equations (13) and (14) yields the strain energy density at the energy median equivalent point of the plastic stage:

[0184] υ M =υ εe +υ εp (15).

[0185] S15. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, based on the relationship between the coefficient of restitution and the strain energy of the contact collision model, the expression for the strain energy density at the energy median equivalent point, and the relevant reduced mechanical parameters, the functional relationship between the coefficient of restitution and the equivalent plastic strain is obtained.

[0186] Furthermore, such as Figure 6 As shown, step S15 includes:

[0187] S151. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the elastic effective deformation domain volume, the relationship between the restitution coefficient and the strain energy of the contact collision model, and the expression of the strain energy density at the energy median equivalent point, are used to obtain the relationship between the restitution coefficient and the strain energy of the effective deformation domain.

[0188] S152. Based on the relationship between the coefficient of restitution and the strain energy of the effective deformation domain, the equivalent elastic strain energy density, and the equivalent plastic strain energy density, the initial functional relationship between the coefficient of restitution and the equivalent plastic strain is obtained.

[0189] S153. Based on the relevant reduced mechanical parameters, the initial functional relationship between the coefficient of restitution and the equivalent plastic strain is decomposed to obtain the functional relationship between the coefficient of restitution and the equivalent plastic strain.

[0190] in,

[0191] Furthermore, assuming that the effective deformation domain volume V2 at the moment of maximum compression is equal to the effective elastic deformation domain volume V3, and combining equations (10), (11), and (15), the relationship between the restitution coefficient and the strain energy of the effective deformation domain is obtained as follows:

[0192]

[0193] In equation (16), V2 is the effective deformation domain volume at the moment of maximum compression, and V3 is the effective elastic deformation domain volume at the moment of maximum compression.

[0194] Substituting equations (13) and (14) into equation (16) and rearranging, we obtain the initial functional relationship between the restitution coefficient and the equivalent plastic strain as follows:

[0195]

[0196] It is worth mentioning that equation (17) only applies to ε eq Greater than or equal to When this condition is met, it indicates that the system has entered the plastic stage. Furthermore, ε... eq Divided into reduced yield strain With equivalent plastic strain ε p The sum of the initial functional relationship, the equivalent strain at point M is decomposed into:

[0197]

[0198] In equation (18), ε p This is the equivalent plastic strain.

[0199] Next, substituting equation (18) into equation (17), we obtain the functional relationship between the coefficient of restitution and the equivalent plastic strain as follows:

[0200]

[0201] Equation (19) above represents the functional relationship between the coefficient of restitution and the equivalent plastic strain. Next, we will further explore the expression of to establish the final variable coefficient of restitution model.

[0202] From equations (6) and (11), it can be seen that,

[0203]

[0204] Combining equations (13) and (14), we can obtain

[0205]

[0206] Divide both sides of the equation by σ. y Combining equation (18), we can simplify to obtain:

[0207]

[0208] Therefore, we consider introducing a dimensionless parameter S.

[0209]

[0210] Based on the above analysis, when the materials of the two objects in contact and collision are determined, It is determined that V1 / V2 is a dimensionless parameter. Since the change in the effective deformation domain volume V2 of the system is difficult to capture, the subsequent fitting only involves the dimensionless parameter S and the equivalent plastic strain ε of the system. p The mapping relationship can be determined.

[0211] S2. Establish a numerical simulation model of sphere-base normal contact collision, and perform multi-condition contact collision numerical simulation based on the simulation model to obtain simulation results.

[0212] Furthermore, such as Figure 7 As shown, step S2 includes:

[0213] S21. Perform preprocessing including defining the simulation model as an axisymmetric model, refining the mesh of the contact area, and setting geometric parameters, so as to establish a sphere-base normal contact collision numerical simulation model using finite element method.

[0214] S22. Based on the sphere-base normal contact collision numerical simulation model, multi-condition contact collision numerical simulations were performed using the finite element method to obtain the result including the coefficient of restitution C. e And the equivalent plastic strain ε is obtained by reverse calculation. p The simulation results.

[0215] Based on the above analysis, this invention aims to use the finite element multi-condition numerical calculation results to further fit and obtain the mapping relationship between the dimensionless parameter S and the equivalent plastic strain of the system. Figure 8 This is a numerical simulation model of normal contact collision between an elastic sphere and an elastoplastic substrate.

[0216] To improve computational simulation efficiency, an axisymmetric model was used for the study. To obtain high-precision simulation results, the mesh in the contact area was refined. To eliminate the energy loss caused by stress wave propagation, L = 2R = 70 mm was set, where the radius of the sphere is R, and the base size is L × L. The specific material parameters of the sphere and the base are shown in Table 1. The initial relative contact velocity for each working condition ranged from 0 to 70 m / s.

[0217] Table 1 Material Parameters

[0218]

[0219] Using the finite element software to output the coefficient of restitution Ce, the equivalent plastic strain ε is obtained by back-calculation using equation (19). p .

[0220] S3. Introduce a dimensionless parameter as an intermediate parameter, and combine the simulation results to fit the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage.

[0221] Furthermore, such as Figure 9 As shown, step S3 includes:

[0222] S31. Introduce a dimensionless parameter as an intermediate parameter and logarithmize the dimensionless parameter.

[0223] S32. Based on the logarithmically transformed dimensionless parameters and simulation results, the mapping relationship between dimensionless parameters and equivalent strain in the plastic stage is obtained.

[0224] Since the dimensionless parameter S varies over a large range, it is logarithmically transformed. Based on the numerical calculation results, the equivalent plastic strain ε is further plotted. p The functional relationship between the logarithmically transformed dimensionless parameter S and the parameter S is as follows: Figure 10 As shown.

[0225] observe Figure 10 It can be seen that the equivalent plastic strain ε P The mapping relationship with the logarithmically transformed dimensionless parameter S has a clear numerical boundary point, such as:

[0226] S = e 5 (e is the natural constant) (20-1)

[0227] The initial collision velocity corresponding to this dividing point can be expressed as:

[0228]

[0229] Piecewise fitting of the function yields the following results: Figure 11 As shown, the fitted formula is:

[0230]

[0231] Substituting the expression for the dimensionless parameter S, we can obtain the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage as follows:

[0232]

[0233] In equation (21), e is the natural constant.

[0234] S4. Based on the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage, as well as the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage, a new normal variable coefficient of restitution model is obtained.

[0235] Furthermore, the novel normal variable restoring coefficient model based on equations (21) and (19) is as follows:

[0236]

[0237] Thus, the new normal variable restoring coefficient model has been established. In the above variable restoring coefficient model, i.e., in equation (22), when v nc As v approaches 0, the coefficient of restitution approaches 1; as v... nc As v increases, the coefficient of recovery strictly decreases monotonically; when v nc As the value approaches infinity, the coefficient of restitution approaches 0.

[0238] It is worth mentioning that this invention is the first to apply the energy equivalence principle commonly used in material indentation experiments to the contact collision problem. Combined with the analysis of the energy conversion process in the contact collision process, a new variable restitution coefficient model is obtained. At the same time, it is proved that it has high-precision predictive performance for contact collision response. The obtained formula (22) has certain guiding significance for the study of contact collision problems.

[0239] In another specific embodiment, to further verify the effectiveness of the established variable restitution coefficient model, the prediction results of the established variable restitution coefficient model are compared with those of several widely used restitution coefficient models (Thornton model, Wu model, J-G1 model, and J-G2 model). Since the experiment can only provide data results at lower collision velocities, the results for high-speed collisions are based on finite element numerical simulation results.

[0240] Taking the following experiment as an example, the results of the coefficient of restitution during the contact and collision process between the alumina sphere and the aluminum substrate are compared. Figure 12 As shown in the figure. A comparison of the coefficient of restitution results for the contact collision process between alumina spheres and steel substrates is presented. Figure 13 As shown in Table 2.

[0241] Table 2 Finite Element Material Parameters

[0242]

[0243] Depend on Figure 12 and Figure 13 It can be seen that the prediction results of the variable restitution coefficient model established in this invention can all be in good agreement with the experimental results. For the contact collision process at high speed, the model can also be consistent with the finite element results.

[0244] In summary, the variable restitution coefficient model based on the energy equivalence principle established in this invention has good predictive performance. Using the numerical model established in this invention, high-precision predictions of contact collision dynamic responses can be made without relying on other complex contact collision theoretical models or other simulation software. The relative errors compared with finite element experiments are all within 10%, and most errors can be controlled within 5%.

[0245] Furthermore, the present invention also provides a novel normal variable restoring coefficient model construction system based on the energy equivalence principle, which includes:

[0246] The model building and analysis module is used to build a physical model of the contact collision between the sphere and the substrate. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the model of the contact collision between the sphere and the substrate is analyzed based on the principle of energy equivalence to obtain the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage.

[0247] The finite element simulation module is used to establish a numerical simulation model of sphere-base normal contact collision, and to obtain simulation results by performing multi-condition contact collision numerical simulation based on the simulation model.

[0248] The parameter introduction and fitting module is used to introduce a dimensionless parameter as an intermediate parameter and fit the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage based on the simulation results.

[0249] The module for establishing the normal variable restitution coefficient model is used to obtain the normal variable restitution coefficient model based on the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage, as well as the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage.

[0250] Furthermore, a novel normal variable restitution coefficient model construction device based on the energy equivalence principle is provided, comprising: at least one database; and a memory communicatively connected to the at least one database; wherein the memory stores instructions executable by the at least one database, the instructions being executed by the at least one database to enable the at least one database to execute a normal restitution coefficient construction method based on the energy equivalence principle as described above, thereby achieving high-precision prediction of contact collision dynamic response results.

[0251] In summary, given the limitations of existing variable restitution coefficient models in terms of computational accuracy, this invention provides a novel method, system, and device for constructing a normal variable restitution coefficient model based on the energy equivalence principle, considering material properties and initial collision velocity. This model can predict contact collision dynamics responses with high accuracy. (Reference) Figure 14 The implementation process of the invention mainly includes the following three steps: First, for the sphere-substrate contact collision process, the effective deformation domain volume at the moment of maximum compression is set to be equal to the effective elastic deformation domain volume. Based on the principle of energy equivalence, the recovery coefficient and the equivalent strain ε in the plastic stage are derived and obtained. p The functional relationship is determined; secondly, a sphere-base normal contact collision numerical simulation model is established, and multi-condition contact collision numerical simulation research is carried out; a dimensionless parameter S is introduced to further fit the equivalent strain ε in the plastic stage. p The mapping relationship between S and S is obtained; based on this, a new method for constructing a normal variable restitution coefficient model based on the energy equivalence principle can be obtained. The effectiveness of the model is verified by comparison with experimental and finite element results.

[0252] It is foreseeable that the variable restitution coefficient model based on the energy equivalence principle established in this invention will have good predictive performance for all kinds of complex and common contact and collision processes.

[0253] Since the systems / devices described in the above embodiments of the present invention are systems / devices used to implement the methods of the above embodiments of the present invention, those skilled in the art can understand the specific structure and modifications of the systems / devices based on the methods described in the above embodiments of the present invention, and therefore will not be repeated here. All systems / devices used in the methods of the above embodiments of the present invention fall within the scope of protection of the present invention.

[0254] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0255] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions.

[0256] It should be noted that any figure marks placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In claims that enumerate several means, several of these means may be embodied by the same hardware. The use of the terms first, second, third, etc., is merely for convenience of expression and does not indicate any order. These terms can be understood as part of the component names.

[0257] Furthermore, it should be noted that in the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0258] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the claims should be interpreted to include both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0259] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

Claims

1. A method for constructing a normal variable restoring coefficient model based on the energy equivalence principle, characterized in that, include: A physical model of the contact collision between the sphere and the substrate is established. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage is obtained by analyzing the contact collision model between the sphere and the substrate based on the principle of energy equivalence. Based on the principle of median energy equivalence, a median energy equivalent point is found in the collision model between the sphere and the substrate, and the expression for the strain energy density at this median energy equivalent point is obtained, including: Based on the principle of energy median equivalence, an energy median equivalent point M in the contact collision model between the sphere and the substrate is found, and the expression for the strain energy density of the energy median equivalent point is obtained. The strain energy density at the median equivalent point under complex stress is equivalently transformed into the strain energy density under uniaxial stress. When the contact collision model enters the plastic stage, the equivalent elastic strain energy density and equivalent plastic strain energy density of the plastic stage are obtained based on the strain energy density under uniaxial stress state, and then the strain energy density of the energy median equivalent point of the plastic stage is obtained. in, The expression for the system energy is: （11） In equation (11), U is the work done by the external force on the object, and V is the volume of the effective deformation domain of the object. The strain energy density is the equivalent point of the energy median under complex stress conditions. The strain energy density under uniaxial stress is: （12） In equation (12), and These are the stress and strain tensor components at point M under complex stress conditions. and These are the equivalent stress and equivalent strain at point M, respectively; The equivalent elastic strain energy density is: （13） In equation (13), To adjust for yield strain, To convert the elastic modulus, For stress, In response to the situation; The equivalent plastic strain energy density is: （14） The strain energy density at the median equivalent point of the energy during the plastic stage is: （15）； A numerical simulation model of sphere-base normal contact collision was established, and simulation results were obtained by performing multi-condition contact collision numerical simulation based on the simulation model. A dimensionless parameter is introduced as an intermediate parameter, and the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage is fitted by combining the simulation results. Based on the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage, as well as the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage, a normal strain restitution coefficient model is obtained. Among them, the dimensionless parameters are mechanical property characterization parameters including the yield strength of the substrate material, the density of the sphere, and the initial relative contact velocity between the sphere and the substrate.

2. The method for constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 1, characterized in that, A physical model of the collision between a sphere and a substrate is established. Under the condition that the effective deformation domain volume at the moment of maximum compression is equal to the effective elastic deformation domain volume, the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage is obtained by analyzing the collision model based on the principle of energy equivalence. This includes: By simulating the process of applying a vertically downward initial velocity field to a sphere and causing the sphere to collide with a base with its lower edge fixed, a physical model and constitutive model of the contact collision between the sphere and the base are established. Based on the constitutive model, the folded constitutive model and related folded mechanical parameters are obtained; The energy conversion during the contact collision process of the established physical model of the sphere and the substrate is analyzed, and the relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained. Based on the principle of energy median equivalence, an energy median equivalent point is found in the contact collision model between the sphere and the substrate, and the expression for the strain energy density of the energy median equivalent point is obtained. The strain energy density of the energy median equivalent point is equivalent to the average strain energy density of the system. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the functional relationship between the restitution coefficient and the equivalent plastic strain is obtained based on the relationship between the restitution coefficient and the strain energy of the contact collision model, the expression of the strain energy density at the energy median equivalent point, and the relevant reduced mechanical parameters. in, The constitutive model for the collision model of the sphere and the substrate is as follows: （1） In equation (1), For stress, Let E be the strain, and E be the elastic modulus of the material. and These represent the yield strength and yield strain of an ideal elastoplastic material, respectively. The relevant reduced mechanical parameters of the reduced constitutive model are: （2） （3） In equations (2) and (3), To convert the elastic modulus, and These represent the elastic moduli of the sphere and the substrate, respectively. and The Poisson's ratios for the sphere and the base, respectively. This is the equivalent yield strain.

3. The method for constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 2, characterized in that, The energy conversion during the contact collision process of the established physical model of the sphere-substrate contact collision is analyzed, and the relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained, including: By analyzing the process of the collision model between the sphere and the base, we obtained the kinetic energy expressions for the non-collision and the kinetic energy conversion expressions for the collision. By rearranging the expressions for kinetic energy when no collision occurs and for kinetic energy conversion when a collision occurs, and combining the equivalent relationship between elastic strain energy and rebound kinetic energy at the moment of collision, the expression for kinetic energy at the end of the collision is obtained. The coefficient of restitution for a sphere-substrate contact collision was calculated using the Newtonian coefficient of restitution model. Based on the kinetic energy expression and the coefficient of restitution at the end of the collision, an initial relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained. Based on the initial relationship, and combined with the kinetic energy conversion expression of the collision, a relationship between the coefficient of restitution and the strain energy of the contact collision model is obtained. in, The expression for the kinetic energy without a collision is: （4） In equation (4), This represents the initial kinetic energy of the sphere, which is also the total energy of the sphere and the base system at the initial moment. For the density of a sphere, Let the volume of the sphere be... The initial relative velocity between the sphere and the base; The expression for the kinetic energy conversion during a collision is: （5） In equation (5), For strain energy, It is the elastic strain energy. It is the plastic strain energy; The expression for the transposition process is: （6） The expression for the kinetic energy at the moment the collision ends is: （7） In equation (7), The rebound velocity of the sphere at the instant the collision ends; The coefficient of restitution for a sphere-substrate contact collision is: （8） In equation (8), Ce is the coefficient of restitution; The initial relationship between the coefficient of restitution and the strain energy of the contact collision model is as follows: （9） The relationship between the coefficient of restitution and the strain energy of the contact collision model is as follows: （10）。 4. The method for constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 1, characterized in that, Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, based on the relationship between the coefficient of restitution and the strain energy of the contact collision model, the expression for the strain energy density at the energy median equivalent point, and relevant reduced mechanical parameters, the functional relationship between the coefficient of restitution and the equivalent plastic strain is obtained as follows: Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the elastic effective deformation domain volume, the relationship between the restitution coefficient and the strain energy of the contact collision model and the strain energy density expression of the energy median equivalent point are used to obtain the relationship between the restitution coefficient and the strain energy of the effective deformation domain. Based on the relationship between the coefficient of restitution and the strain energy of the effective deformation domain, the relationship between the equivalent elastic strain energy density and the equivalent plastic strain energy density, the initial functional relationship between the coefficient of restitution and the equivalent plastic strain is obtained. Based on relevant reduced mechanical parameters, the initial functional relationship between the coefficient of restitution and the equivalent plastic strain is decomposed to obtain the functional relationship between the coefficient of restitution and the equivalent plastic strain; in, The relationship between the coefficient of restitution and the strain energy of the effective deformation domain is as follows: （16） In equation (16), To compress the effective deformation domain volume at the maximum moment, To compress the volume of the effective elastic deformation domain at the maximum moment; The initial functional relationship between the restitution coefficient and the equivalent plastic strain is as follows: （17） The equivalent strain at point M in the initial functional relation can be decomposed into: （18） In equation (18), Equivalent plastic strain; The functional relationship between the restitution coefficient and the equivalent plastic strain is as follows: （19）。 5. The method for constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 4, characterized in that, A numerical simulation model of sphere-base normal contact collision was established. Based on the simulation model, numerical simulations of contact collision under multiple working conditions were performed to obtain simulation results, including: Preprocessing is performed, including defining the simulation model as an axisymmetric model, refining the mesh of the contact area, and setting geometric parameters, so as to establish a sphere-base normal contact collision numerical simulation model using finite element method. Based on the sphere-base normal contact collision numerical simulation model, multi-condition contact collision numerical simulations were performed using the finite element method to obtain the coefficient of restitution Ce and the equivalent plastic strain obtained through inverse calculation. The simulation results.

6. The method for constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 5, characterized in that, Introducing a dimensionless parameter as an intermediate parameter, and fitting the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage based on simulation results, includes: Use a dimensionless parameter as an intermediate parameter and logarithmize the dimensionless parameter; Based on the logarithmically transformed dimensionless parameters and simulation results, the mapping relationship between dimensionless parameters and equivalent strain in the plastic stage is obtained; in, Dimensionless parameter is （20） The mapping relationship between dimensionless parameters and equivalent strain in the plastic stage is as follows: （21） In equation (21), e is the natural constant.

7. The method for constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 6, characterized in that, The normal variable restitution coefficient model is as follows: （22） In equation (22), when As the coefficient of restitution approaches 0, the coefficient of restitution approaches 1. along with As increases, the coefficient of recovery strictly decreases monotonically; when As the value approaches infinity, the coefficient of restitution approaches 0.

8. A system for implementing the method of constructing a normal variable restoring coefficient model based on the energy equivalence principle as described in claim 1, characterized in that, include; The model building and analysis module is used to build a physical model of the contact collision between the sphere and the substrate. Under the condition that the effective deformation domain volume at the maximum compression moment is equal to the effective elastic deformation domain volume, the model of the contact collision between the sphere and the substrate is analyzed based on the principle of energy equivalence to obtain the functional relationship between the coefficient of restitution and the equivalent strain in the plastic stage. The finite element simulation module is used to establish a numerical simulation model of sphere-base normal contact collision, and to obtain simulation results by performing multi-condition contact collision numerical simulation based on the simulation model. The parameter introduction and fitting module is used to introduce a dimensionless parameter as an intermediate parameter and fit the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage based on the simulation results. The module for establishing the normal variable restitution coefficient model is used to obtain the normal variable restitution coefficient model based on the functional relationship between the restitution coefficient and the equivalent strain in the plastic stage, as well as the mapping relationship between the dimensionless parameter and the equivalent strain in the plastic stage. Among them, the dimensionless parameters are mechanical property characterization parameters including the material's yield strength, sphere density, and the initial relative contact velocity between the sphere and the substrate.

9. A device for constructing a normal variable restoring coefficient model based on the principle of energy equivalence, characterized in that, include: At least one database; And a memory that is communicatively connected to the at least one database; The memory stores instructions that can be executed by the at least one database. These instructions are executed by the at least one database to enable the at least one database to perform the method for constructing a normal variable restitution coefficient model based on the energy equivalence principle as described in any one of claims 1-7, so as to achieve high-precision prediction of the relative error of the contact collision dynamic response results within 5%.

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