A design method of shell-imitated rubber bushing based on micro-contact mechanics model

Abstract

The application discloses a shell-imitating rubber bushing design method based on a micro-contact mechanics model and belongs to the technical field of rubber bushings. The shell-imitating rubber bushing design method comprises the following steps: a shell-imitating rubber joint bearing with a "steel-rubber-steel" interface cooperative structure is designed; a uniaxial tensile test is conducted on a rubber bushing material to obtain stress-strain data, a fitting tool is used to process the test data, a rubber constitutive model is selected according to the deviation value of a fitting curve and a test curve; contact stress analysis and static stiffness calculation of the bionic rubber bushing are conducted; the radial contact area of the rubber bushing is calculated, the steel-rubber interface contact area is optimized by controlling the geometric angle and the radius of the steel layer; and the single stress-strain result obtained through finite element analysis is introduced into fatigue analysis software to predict the fatigue life of the rubber bushing. The application applies a shell bionic structure to a heavy-load truck chassis rubber bushing, and solves the technical problems of insufficient stiffness and fatigue failure of the existing heavy-load truck rubber bushing under high-strength dynamic load.

Description

Technical Field

[0001] This invention relates to a design method for shell-like rubber bushings based on a microscopic contact mechanics model, belonging to the field of rubber bushing technology. Background Technology

[0002] With the rapid growth of global logistics and transportation demand, the heavy-duty truck industry, as a core support of the long-haul logistics system, is facing multiple challenges in terms of vehicle reliability, durability, and ride comfort under complex operating conditions. The chassis suspension system of heavy-duty trucks needs to continuously withstand high-intensity dynamic loads, alternating impacts, and multi-directional vibration excitations.

[0003] To mitigate the damage to vehicle structures caused by such extreme operating conditions, rubber bushings have been increasingly applied to the suspension connection points of heavy-duty truck chassis. Through elastic deformation, they absorb vibration energy and disperse stress concentration, thereby protecting critical components such as the chassis and engine mounts from premature failure due to fatigue damage. However, in actual service, rubber bushings must withstand complex loads from multiple directions: radial impacts when driving on rough roads, and torsional and axial excitations during emergency braking or cornering. Under such high-frequency impacts, large temperature differences, and long-term alternating loads, rubber bushings are prone to material aging, creep, and stiffness degradation, leading to decreased vibration isolation performance and even structural cracking, severely impacting vehicle safety and service life.

[0004] Bionics offers new insights into engineering materials and structural design. In nature, the nacreous layer of seashells achieves a perfect balance between high strength and high toughness through a multi-scale hierarchical structure resembling "brick-mud-brick," utilizing the layered arrangement of aragonite (inorganic material) and biopolymers (organic material). The inorganic material provides structural strength, while the organic material dissipates energy and transfers loads. Based on the strengthening mechanism of the nacreous layer—"aragonite-biopolymer-aragonite"—a novel rubber bushing with stress dispersion and crack inhibition properties can be constructed through the synergistic design of organic / inorganic materials. Summary of the Invention

[0005] The purpose of this invention is to provide a design method for shell-like rubber bushings based on a microscopic contact mechanics model, in order to solve the technical problems of insufficient stiffness and easy fatigue failure of existing heavy-duty truck rubber bushings under high-intensity dynamic loads, and to significantly improve the load-bearing capacity and service life of rubber bushings.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A design method for a shell-like rubber bushing based on a microscopic contact mechanics model, characterized by the following steps:

[0008] (1) Bionic rubber bushing design

[0009] Based on the toughening mechanism of the "brick-mud-brick" multi-scale hierarchical structure of the nacreous layer of seashells, a shell-like rubber joint bearing with a "steel-rubber-steel" interface synergistic structure is designed.

[0010] The shell-like rubber spherical bearing comprises six core components: an upper cover plate, a lower cover plate, a sleeve, a central shaft, a rubber bushing, and a bushing. The rubber bushing is integrally formed with the upper cover plate, lower cover plate, central shaft, and bushing through a vulcanization injection molding process, thus constructing a composite structure with stress dispersion and crack suppression characteristics.

[0011] The structural parameters of the imitation seashell rubber spherical bearing include: the outer diameter of the rubber bushing is 53.8 mm, the inner diameter is 22.3 mm, the radius of the central shaft ball is 40 mm, and the bushing thickness is 5 mm.

[0012] (2) Finite element preprocessing

[0013] Stress-strain data were obtained by conducting uniaxial tensile tests on the rubber bushing material. The test data were then processed using a fitting tool, and a rubber constitutive model was selected based on the deviation between the fitted curve and the test curve.

[0014] Specifically, dumbbell-shaped specimens were prepared according to GB / T 528 standard. The two ends of the specimens were tightened and stretched using a universal testing machine. High-precision strain gauges and force sensors were used to collect stress-strain data in real time. The test data were processed using the Abaqus fitting tool. Based on the deviation between the material mechanics fitting curve and the experimental mechanics curve, the final selected rubber constitutive model was the Ogden third-order constitutive model with the following parameters: Mu1=13.55, Mu2=-2.34, Mu3=0.09, Alpha1=1.51, Alpha2=2.21, Alpha3=-2.47.

[0015] The upper cover plate, lower cover plate, central shaft, and bushing are simplified as analytical rigid bodies. The reference points of the central shaft and bushing are defined at their respective geometric centers. The upper and lower cover plates are considered as a whole, and their reference points are set at their geometric centers. Specifically:

[0016] Because the elastic modulus of metal components is much higher than that of rubber materials, and the system boundary conditions are set so that the metal components are completely fixed, the elastic deformation of the metal surface during contact is typically less than 0.01%, which is negligible compared to the macroscopic deformation of the rubber components. This characteristic allows the metal components to be simplified as analytical rigid bodies during finite element modeling, avoiding the waste of computational resources caused by meshing the metal components and effectively improving the convergence of contact iterations. In Abaqus, setting up a rigid body requires defining a reference point. The rigid body does not deform during the analysis; its motion is entirely determined by the motion of the reference point. The reference point is equivalent to the "master control point" of the rigid body, and the motion of all nodes (or geometric points) on the rigid body is completely consistent with the motion of the reference point. In the metal components of this rubber spherical bearing, the reference points of the central shaft and bushing are defined at their respective geometric centers, and the upper and lower cover plates are considered as a whole, with their reference points also set at their geometric centers.

[0017] (3) Finite element modeling and calculation

[0018] (3-1) Based on the determined rubber constitutive model and parameters, in the finite element model, the following steps are performed in sequence: setting the binding constraints between each component, setting the load and boundary conditions, and mesh generation;

[0019] The binding constraint settings include: binding a portion of the central shaft area to the inner surface of the rubber bushing, binding the outer surface of the bushing to the inner surface of the rubber bushing, and binding the outer surface of the rubber bushing to the upper and lower cover plates.

[0020] The load and boundary condition settings include: setting the six degrees of freedom of each node of the outer ring of the shell-like rubber spherical bearing to be completely fixed, and applying loads of six degrees of freedom motion with the central axis reference point as the force application point. The six degrees of freedom motion includes radial displacement, axial deflection, radial deflection and axial rotation.

[0021] The meshing includes: using a hexahedral mesh, with C3D8R elements used for the rigid metal part and C3D8RH elements used for the rubber bushing part.

[0022] (3-2) Based on the finite element model and load settings, perform contact stress analysis and static stiffness calculation of the biomimetic rubber bushing;

[0023] The radial displacement load is a concentrated force of F=53300N applied in the X direction within 1 second; the axial deflection load is a concentrated force of F=26700N applied in the Y direction within 1 second; the radial deflection load is a torsion of Angle=0.1Rad applied around the X axis within 1 second; the axial rotation load is a torsion of Angle=0.1Rad applied around the Y axis within 1 second.

[0024] A specific stage of the loading process is selected as the interval for static stiffness calculation:

[0025] In the calculation of radial and axial stiffness, the loaded force and loaded displacement are used as the basic calculation parameters. The radial stiffness and axial stiffness are calculated according to the formulas K1=ΔF / ΔX and K2=ΔF / ΔX respectively. K1 is the radial stiffness, K2 is the axial stiffness, ΔF is the change of load, and ΔX is the change of radial or axial displacement.

[0026] In the calculation of torsional stiffness, torque and deflection angle are used as the basic calculation parameters. The torsional stiffness is calculated according to the formula K3=ΔM / Δθ, where K3 is the torsional stiffness, ΔM is the change in torque, and Δθ is the change in deflection angle.

[0027] (4) Micromechanical property analysis

[0028] Based on simulation results, the radial contact area of ​​the rubber bushing is calculated, and the contact area of ​​the steel-rubber interface is optimized by controlling the geometric angle and radius of the steel layer. The radial load acting on the rubber bushing is decomposed into normal force and tangential force. The normal force is borne by the high strength characteristics of the steel component, and the tangential force is absorbed and dissipated by the high elasticity and viscoelasticity characteristics of the rubber bushing, so as to achieve uniform stress distribution and crack suppression.

[0029] The format for calculating the radial contact area is as follows:

[0030]

[0031] Where r is the radius of the cylindrical section of the central shaft, l2 is the contact length between the rubber bushing and the cylindrical section of the central shaft, R1 is the outer diameter of the central shaft sphere, H is half the height of the rubber bushing, R2 is the outer contour radius of the rubber bushing, and θ2 is the contact half angle between the central shaft journal and the rubber bushing.

[0032] (5) Fatigue load calculation

[0033] The single stress-strain results obtained from the finite element analysis are imported into fatigue analysis software, fatigue algorithms and material properties are set, cyclic loading simulation is performed, and the fatigue life of the rubber bushing is predicted.

[0034] The fatigue load calculation software used is Fe-Safe. First, the designed shell-like rubber spherical bearing is imported into Abaqus to acquire single-cycle stress-strain data. Then, the acquired stress-strain results are imported into Fe-Safe for cyclic loading. The corresponding fatigue algorithm is set, and the material properties are defined. The number of cycles under the corresponding load is output. The shell-like rubber spherical bearing can withstand a greater force under the same number of fatigue cycles, and when the loading force is around 75,000 N, the logarithmic life of the shell-like rubber spherical bearing exceeds 14, approaching infinite life, which meets the design requirements.

[0035] The beneficial effects of this invention are:

[0036] 1. This invention addresses the problem of insufficient stiffness and easy fatigue failure in existing spherical bearings used in heavy-duty trucks by proposing a biomimetic design for spherical bearings, specifically a biomimetic seashell structure spherical bearing. Based on the strengthening mechanism of the "brick-mud" multi-scale hierarchical structure of the nacreous layer of seashells, a novel composite bearing structure with stress dispersion and crack suppression characteristics is constructed through the synergistic design of organic / inorganic materials and the optimization of interlayer interfaces.

[0037] 2. This invention employs the finite element method to construct a high-precision simulation model of a shell-like rubber joint bearing. The rubber is defined using the Odgen constitutive equation. The model is assembled and established through assembly, setting analysis steps, defining interactions and boundary conditions, and setting loads. Furthermore, the influence of different mesh types and mesh sizes on the simulation results of the shell-like rubber joint bearing is analyzed. Experimental results show that the simulation model parameters for the rubber sleeve are hexahedral element mesh type and 18,000 mesh elements.

[0038] 3. Based on the constructed shell-like rubber spherical plain bearing, this invention establishes a simulation analysis process for the static stiffness, stress deformation, and fatigue life of the rubber spherical plain bearing under six different service conditions (axial motion, vertical radial motion, horizontal radial motion, torsional motion, horizontal deflection motion, and vertical deflection motion). After calculation, the spatial distribution of stress field, strain field, and displacement field is extracted through a visualization module, and quantitative analysis is performed in conjunction with cloud maps and path extraction tools. The results show that the shell-like heavy-duty truck spherical plain bearing has higher stiffness and stronger load-bearing capacity.

[0039] 4. For the fatigue life simulation prediction of the imitation shell rubber spherical plain bearing, this invention subjected the imitation shell rubber spherical plain bearing and commercially available spherical plain bearing to cyclic loading with equal force and angle. The results show that fatigue failure of the rubber spherical plain bearing first occurs in the rubber solid part, especially at the boundary between the rubber material and the metal material. Under a peak radial load of ±53.3kN and bidirectional symmetrical loading conditions, the imitation shell heavy-duty truck spherical plain bearing has a vibration frequency of 0.5-3Hz, approximately sinusoidal, and a cycle life greater than or equal to 300,000 cycles.

[0040] This invention innovatively proposes the application of a seashell-inspired bionic structure to the rubber bushing of a heavy-duty truck chassis, providing a new approach to the design of the rubber bushing and extending the fatigue life of the rubber joint bearing. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the shell-like rubber joint bearing structure of the present invention;

[0042] Figure 2 This is a cross-sectional view of the shell-like rubber joint bearing of the present invention;

[0043] Figure 3 This is a flowchart illustrating the design process of the biomimetic seashell rubber bushing of this invention.

[0044] Figure 4 This is a schematic diagram of the load setting in this invention;

[0045] Figure 5 In the middle: (a) Apply loads to different mesh types, (a-1) radial loading, (a-2) axial loading, (a-3) deflection loading, (a-4) torsional loading; (b) Apply loads to models with different mesh numbers, (b-1) radial loading, (b-2) axial loading, (b-3) deflection loading, (b-4) torsional loading;

[0046] Figure 6 A schematic diagram of a six-degree-of-freedom load application on a shell-like rubber bushing.

[0047] Figure 7 The stress comparison is shown between a general rubber bushing and a biomimetic rubber bushing. Among them, (a) is the radial loading of the general rubber bushing, (b) is the radial loading of the biomimetic rubber bushing, (c) is the axial loading of the general rubber bushing, (d) is the axial loading of the biomimetic rubber bushing, (e) is the deflection loading of the general rubber bushing, and (f) is the deflection loading of the biomimetic rubber bushing.

[0048] Figure 8 The figures show a comparison of the stiffness of a shell-like rubber spherical plain bearing and a regular rubber spherical plain bearing. (a) compares the radial stiffness, (b) compares the axial stiffness, (c) compares the deflection stiffness, and (d) compares the torsional stiffness.

[0049] Figure 9 The diagram shows a comparison of the fatigue life of the biomimetic rubber bushing and the traditional rubber bushing. (a) shows the fatigue verification process of the rubber bushing, (b-1) shows the failure point of the general rubber bushing, (b-2) shows the failure point of the biomimetic rubber bushing, (c) shows the comparison of the life of the rubber bushing under different pressures, and (d) shows the comparison of the life of the rubber bushing under different stresses.

[0050] Figure 10 Figure showing the stress analysis of the rubber bushing structure and micro-interface;

[0051] Figure 11 for Figure 10 Enlarged view of a portion of the image;

[0052] In the diagram: 1. Central shaft, 2. Shaft sleeve, 3. Rubber bushing, 4. Upper cover, 5. Lower cover. Detailed Implementation

[0053] A design method for biomimetic shell rubber bushings based on a microscopic contact mechanics model includes: biomimetic rubber bushing design, finite element preprocessing, finite element modeling and calculation, fatigue load calculation, and microscopic mechanical property analysis.

[0054] 1. Bionic rubber bushing design

[0055] This embodiment focuses on the biomimetic design of a rubber bushing for a certain heavy-duty truck. The shell-inspired rubber bushing is based on the strengthening mechanism of the "brick-mud-brick" multi-scale hierarchical structure of the nacreous layer of a shell. Through the synergistic design of organic / inorganic materials and the optimization of interlayer interfaces, a novel composite rubber bushing with stress dispersion and crack suppression characteristics is constructed.

[0056] The imitation seashell rubber spherical bearing consists of six core components: an upper cover plate, a lower cover plate, a sleeve, a central shaft, rubber, and a bushing. Its three-dimensional structure and sectional views are shown below. Figure 1 , Figure 2 As shown, the imitation shell rubber spherical bearing is a key component of automotive shock absorption. The rubber bushing is integrated with the upper and lower cover plates, central shaft, and bushing components through a vulcanization injection molding process, achieving the connection between the various components.

[0057] Table 1 Basic parameters of rubber spherical plain bearings

[0058] parameter Dimensions (mm) Bionic rubber bushing outer diameter 53.8 Bionic rubber bushing inner diameter 22.3 Central axis sphere radius 40 bushing thickness 5

[0059] After completing the design of the rubber bushing, this embodiment designed a set of biomimetic rubber bushing performance verification procedures; such as... Figure 3 As shown, the designed model was imported into HyperMesh to generate a mesh. At the same time, the basic experimental data of the rubber material exported from the universal testing machine was processed using the fitting function of Abaqus to select the most suitable rubber constitutive model. After completing the above preparations, the interaction, boundary conditions, and loads were set in Abaqus. The mechanical properties of traditional rubber bushings and shell-like rubber bushings were compared. Finally, the results file in Abaqus was imported into Fe-Safe to explore the fatigue life advantage of shell-like rubber bushings.

[0060] 2. Finite element preprocessing

[0061] In this embodiment, natural rubber is used as the material. As a hyperelastic material, its nonlinear characteristics stem from the viscoelastic nature of the polymer itself and are closely related to preparation parameters such as vulcanization process, filler ratio (e.g., carbon black content), and crosslinking density. Therefore, accurately describing the material parameters of rubber components is a very challenging task in simulation. To accurately simulate the mechanical parameters of the shell-like rubber bushing, this embodiment selects several hyperelastic constitutive models to fit the material parameters in Abaqus. Based on the constitutive parameters of various existing constitutive models, and considering the deviation between the material mechanics fitting curve and the experimental mechanics curve, the constitutive model result that best matches the rubber parameters is selected as the constitutive model for the rubber material.

[0062] The specific operation is as follows: dumbbell-shaped specimens were prepared according to GB / T 528 standard. The two ends of the specimens were tightened and stretched using a universal testing machine. Then, high-precision strain gauges and force sensors were used to collect stress-strain data in real time. Based on the data collected by the universal testing machine, the uniaxial tensile stress-strain curve of the rubber material studied in this study was obtained. Then, the fitting tool in Abaqus was used to fit the curve, and finally, the third-order Ogden equation was determined as the constitutive equation for this study. The relevant parameters are shown in Table 2 below:

[0063] Table 2 Parameters of Ogden's third-order constitutive model

[0064] Mu1 Mu2 Mu3 Alpha1 Alpha2 Alpha3 13.55 -2.34 0.09 1.51 2.21 -2.47

[0065] Because the elastic modulus of metal components is much higher than that of rubber materials, and the system boundary conditions are set so that the metal components are completely fixed, the elastic deformation of the metal surface during contact is typically less than 0.01%, which is negligible compared to the macroscopic deformation of the rubber components. This characteristic allows the metal components to be simplified as analytical rigid bodies during finite element modeling, avoiding the waste of computational resources caused by meshing the metal components and effectively improving the convergence of contact iterations. In Abaqus, setting up a rigid body requires defining a reference point. The rigid body does not deform during the analysis; its motion is entirely determined by the motion of the reference point. The reference point is equivalent to the "master control point" of the rigid body, and the motion of all nodes (or geometric points) on the rigid body is completely consistent with the motion of the reference point. In the metal components of this rubber spherical bearing, the reference points of the central shaft and bushing are defined at their respective geometric centers, and the upper and lower cover plates are considered as a whole, with their reference points also set at their geometric centers.

[0066] 3. Finite element modeling and calculation

[0067] 3-1 After setting the material parameters of the shell-like rubber bushing, it is necessary to set the mechanical properties, boundary conditions, and loads of the rubber bushing, and then mesh it.

[0068] 1) Binding settings

[0069] In Abaqus, binding constraints "glue" different components into a unified whole by forcing the displacement coordination of two contact surfaces or boundaries, eliminating numerical problems caused by mesh mismatch or complex contact definitions. Binding constraints ensure the effective transfer of loads within the structure and prevent stress distribution distortion due to connection failures. To accurately simulate the real-world working conditions of shell-like rubber joint bearings and avoid simulation errors caused by issues such as model clipping, the relevant bindings are as follows:

[0070] ① Bind the central shaft area to the rubber sleeve area;

[0071] ② Bind the central shaft portion to the inner surface of the bushing;

[0072] ③ Bind the outer surface of the bushing to the inner surface of the rubber sleeve;

[0073] ④ Bind the outer surface of the rubber sleeve to the upper and lower cover plates.

[0074] 2) Load and boundary condition settings

[0075] To accurately simulate the real working conditions of the shell-like rubber spherical plain bearing, in terms of boundary condition settings, to ensure that the outer ring chassis of the shell-like rubber spherical plain bearing is fixed, the six degrees of freedom of each node of the outer ring of the rubber spherical plain bearing are set to be completely fixed.

[0076] Regarding load settings, such as Figure 4 As shown, the central axis is determined as the object applying the force. Since the central axis is set as a rigid body, all reference points of the central axis are selected as the points of application of concentrated forces. This embodiment will analyze the various motion states of the shell-like rubber joint bearing, so it is necessary to simulate the motion of each of the six degrees of freedom, namely radial displacement (concentrated force applied in the X direction), radial deflection (torque applied in the X direction), axial deflection (concentrated force applied in the Y direction), and axial rotation (torque applied in the Y direction). This rubber joint bearing is a symmetrical geometry, so the concentrated force and torque applied in the Z direction are consistent with those in the X direction, and therefore can be omitted from calculation.

[0077] 3) Grid generation

[0078] HyperMesh was used to generate tetrahedral and hexahedral meshes for the shell-like rubber bushing, respectively. Figure 5 As shown, after weighing the relationship between computational accuracy and computational cost, a hexahedral mesh was ultimately adopted. The rigid body was constructed using C3D8R, while the rubber part, due to its large deformation characteristics, was meshed using C3D8RH. After determining the mesh type, the influence of mesh size on computational accuracy was further investigated. The study showed that mesh size had little impact on the results, with an error within 2%, which was negligible. Finally, a rubber bushing with a mesh size of 18,000 was selected.

[0079] 3-2, Bionic rubber bushing load setting

[0080] Regarding load settings, the central axis is determined as the object applying the force. Since the central axis is set as a rigid body, the reference point of the central axis is selected as the point of application of the concentrated force. This study will analyze the various motion states of the shell-like rubber spherical bearing, so it is necessary to simulate the motion of each of the six degrees of freedom: radial displacement (concentrated force applied in the X direction), radial deflection (torque applied in the X direction), axial deflection (concentrated force applied in the Y direction), and axial rotation (torque applied in the Y direction). This rubber spherical bearing is a symmetrical geometry, so the concentrated force and torque applied in the Z direction are consistent with those in the X direction, and therefore can be omitted from calculation.

[0081] The magnitude of the applied concentrated force and torque, and the application speed are as follows:

[0082] (1) A concentrated force of F = 53300 N is applied in the X direction within 1 second.

[0083] (2) A concentrated force of F = 26700 N is applied in the Y direction within 1 second.

[0084] (3) Torsion in the X direction within 1 second with an angle = 0.1 Rad

[0085] (4) Torsion in the Y direction within 1 second with an angle = 0.1 Rad

[0086] Simulation methods were established for the above four loading conditions, and the simulation loading process for various motions is as follows: Figure 6 As shown.

[0087] 3-3, Contact Stress Analysis of Bionic Rubber Bushing

[0088] As shown in Figures 7(a) and 7(b), when the same radial load is applied to the traditional rubber bushing and the shell-like rubber bushing, the maximum stress of the shell-like rubber bushing is significantly reduced from 4.887 MPa in the traditional bushing to 1.242 MPa, with a stress level reduction of 74.6%. At the same time, the maximum stress concentration area is shifted and dispersed from the edge of the traditional bushing, effectively avoiding the risk of microcrack initiation and propagation caused by local stress overload, further reducing the probability of fatigue failure of the bushing due to stress concentration, and significantly improving the structural service safety.

[0089] As shown in Figures 7(c) and 7(d), when the same axial load is applied to the traditional rubber bushing and the shell-like rubber bushing, the maximum stress of the shell-like rubber bushing decreases from 4.119 MPa in the traditional bushing to 1.427 MPa, a reduction of 65.4%, and the stress distribution becomes more uniform. This performance optimization stems from the significant increase in axial contact area brought about by the shell-like structural design—the larger contact interface provides a wider carrier for load transfer, allowing the axial force to be evenly diffused throughout the bushing, effectively avoiding localized stress overload problems. This fundamentally delays early failure of the rubber layer caused by stress concentration, further ensuring the structural stability and long-term service reliability of the bushing under axial stress conditions.

[0090] As shown in Figures 7(e) and 7(f), when the same radial deflection load is applied to both the traditional rubber bushing and the shell-like rubber bushing, the location of maximum stress concentration remains consistent, but the maximum stress value of the shell-like rubber bushing is significantly reduced. Under radial deflection conditions, the stress in the traditional bushing tends to be confined to the two ends of the rubber layer, resulting in significant local stress accumulation. In contrast, the shell-like structure, through topological optimization of the interface between the steel and rubber layers, allows some of the stress originally concentrated at the two ends of the rubber layer to be uniformly transferred to the middle region along the steel-rubber interface, effectively widening the stress distribution range and alleviating the local stress concentration effect. This optimized stress transfer mode not only reduces the risk of stress overload in local areas of the rubber layer but also delays problems such as rubber molecular chain damage, cross-linking fracture, and microcrack initiation caused by long-term stress concentration, thereby significantly improving the fatigue resistance and long-term service life of the rubber bushing.

[0091] 3.4 Static Stiffness Analysis of Bionic Rubber Bushing

[0092] In the three types of axial and radial motions of translational motion, the loading force and loading displacement are used as the basic calculation parameters, and a certain stage of the loading process is taken as the static stiffness calculation interval. In the radial stiffness calculation, based on the exported data points, the 0.3s-0.8s loading process is selected as the calculation interval, that is, the interval of the cyclic loading force value of 15990N-42640N is taken as the calculation interval, and the calculation method is as follows (1); In the axial stiffness calculation, based on the exported data points, the 0.3s-0.8s loading process is selected as the calculation interval, that is, the interval of the cyclic loading force value of 8010N-21360N is taken as the calculation interval, and the calculation method is as follows (2).

[0093] In the three types of torsional deflection motions of rotational motion, the deflection in the X direction is the same as that in the Z direction, while the torsion in the Y direction is a different working condition. With torque and deflection angle as the basic calculation parameters, the calculation methods for the three types of rotational motions are consistent: the interval of 0.03Rad-0.08Rad in the cycle segment is taken as the calculation interval, and the calculation method is as follows (3).

[0094] (1)

[0095] (2)

[0096] (3)

[0097] By studying the mechanical properties of shell-like rubber spherical plain bearings and general rubber spherical plain bearings, the static stiffness of the two types of bearings is as follows: Figure 8 As shown, the results indicate that the imitation shell rubber spherical plain bearing has higher stiffness than ordinary rubber spherical plain bearings. Therefore, the imitation shell rubber spherical plain bearing is better able to cope with high-intensity dynamic loads and severe vibration impacts on bumpy roads, and its performance is superior.

[0098] 3-5, Fatigue life analysis of shell-like rubber bushings

[0099] Fe-Safe, as a fatigue analysis software, has the following specific analysis process: Figure 9 As shown:

[0100] First, the designed shell-like rubber spherical bearing is imported into Abaqus to acquire single-cycle stress-strain data. Then, the acquired stress-strain results are imported into Fe-Safe for cyclic loading. The corresponding fatigue algorithm is set and the material properties are defined. The number of cycles under the corresponding load is output.

[0101] Comparing traditional rubber bushings and shell-like rubber bushings, it can be found that under the same radial load, traditional rubber spherical plain bearings are prone to fatigue failure at both ends. This may cause the rubber bushings to gradually loosen and lose their load-bearing capacity during the operation of heavy-duty trucks. In contrast, the shell-like rubber bushings only suffer a small amount of fatigue failure at the interface between the rubber bushing and the bushing, which undoubtedly has better durability.

[0102] Furthermore, to compare the advantages of shell-like rubber bushings, this study compared the fatigue life of traditional rubber bushings and shell-like rubber bushings, and produced comparative analysis charts of loading force versus cycle number and rubber bushing stress versus cycle number. As shown in the figure, this embodiment analyzed the relationship between loading force and the fatigue cycle number of rubber spherical bearings. The results show that shell-like rubber spherical bearings can withstand a greater force under the same fatigue cycle number, and when the loading force is around 75,000 N, the logarithmic life of shell-like rubber spherical bearings exceeds 14, approaching infinite life, which meets the design requirements.

[0103] like Figure 9As shown in the figure, this embodiment analyzes the relationship between maximum stress and the number of cycles of the rubber joint bearing. The results show that the stress of the imitation shell rubber joint bearing is significantly reduced compared with that of the general rubber joint bearing, which makes the imitation shell rubber joint bearing have a longer fatigue life.

[0104] 3-6, Mechanical Properties Analysis of Imitation Shell Rubber Bushing

[0105] This embodiment will systematically analyze the performance advantages of shell-like rubber bushings compared to ordinary rubber bushings from the dual perspectives of macroscopic structural features and microscopic mechanical mechanisms: at the macroscopic level, it focuses on optimizing global performance parameters such as the overall load-bearing area and structural stiffness of the bushing, while at the microscopic level, it delves into the transmission path of internal forces under load, stress distribution laws, and material interface synergistic mechanisms.

[0106] For both general rubber bushings and shell-like rubber bushings, under the same applied pressure, shell-like rubber bushings have a larger stress-bearing area, according to the formula... It can be concluded that the biomimetic rubber bushing has less stress under pressure, and therefore has a longer fatigue life.

[0107] (1) Calculation of the bearing area of ​​general rubber bushing

[0108] like Figure 10 As shown, the contact surface between a typical rubber bushing and the central shaft (1 / 4 model) mainly includes: the contact surface S1 with the small diameter section of the central shaft and the contact surface S2 with the large diameter section of the central shaft.

[0109] When a typical rubber bushing is subjected to a radial load, the contact area is as follows: Figure 10 As shown in (a):

[0110]

[0111] Solving Substituting the relevant parameters into the calculation yields S. a =7573.65mm 2 Where r is the radius of the cylindrical section of the central axis, l2 is the contact length between the rubber bushing and the minor diameter section of the central axis, and H is half the height of the rubber bushing.

[0112] (2) Calculation of the bearing area of ​​the imitation seashell rubber bushing

[0113] like Figure 10 As shown, the contact surfaces (1 / 4 model) between the shell-like rubber bushing and the central shaft mainly include: the contact surface S3 with the cylindrical section of the central shaft, the contact surface S4 with the neck of the central shaft, and the contact surface S5 with the sphere of the central shaft.

[0114] When the rubber bushing is subjected to a radial load, the contact area is as follows: Figure 10 As shown in (d):

[0115]

[0116] Solving Where r is the radius of the cylindrical section of the central shaft, l2 is the contact length between the rubber bushing and the cylindrical section of the central shaft, R1 is the outer diameter of the central shaft sphere, H is half the height of the rubber bushing, R2 is the outer contour radius of the rubber bushing, and θ2 is the contact half angle between the central shaft journal and the rubber bushing.

[0117] By analyzing the radial contact area of ​​general rubber bushings and imitation seashell rubber bushings, it can be seen that as... Figure 10 As Ɵ2 changes, the radial contact area of ​​the shell-like rubber bushing changes. However, due to the manufacturing process and to ensure the structural strength and fatigue life of the rubber body, the angle change is controlled between 52° and 90°. During this process, as the angle Ɵ2 decreases, the radial contact area S... b Gradually increase, when R2 remains constant at 45mm (maximum value), S b From 10064.63mm 2 Increased to 11708.67 mm 2 The contact area increased by 16.33%, and the growth trend of the contact area conformed to the change of the cosine function (the change trend gradually decreased). The increase in contact area caused the contact pressure Pmax to gradually decrease, and the fatigue life of the rubber bushing was further improved.

[0118] At the same time, changes in the size of R2 will also affect the contact area. Figure 10 As the radius R2 changes, the radial contact area of ​​the shell-like rubber bushing changes. However, due to the manufacturing process and to ensure the structural strength and fatigue life of the rubber body, the radius change is controlled between 40mm and 45mm. During this process, as the radius R2 increases, the radial contact area S... b As S gradually increases, when Ɵ2 remains constant at 52°, b From 10064.63mm 2 Increased to 11708.67 mm 2 The contact area increased by 16.33%, and the growth trend of the contact area conforms to an exponential function (the trend gradually decreases). The increase in contact area leads to an increase in contact pressure P. max As the fatigue rate gradually decreases, the fatigue life of the rubber bushing is further improved.

[0119] Therefore, by Figure 10 It can be known that S bmax =11708.67 mm 2 Compared to ordinary rubber bushings S a =7573.65mm 2The contact area increased by 58.78%, which to some extent resulted in a more uniform stress distribution in the rubber bushing. bmin =10064.63mm 2 Compared to ordinary rubber bushings S a =7573.65mm 2 The contact area increased by 36.49%, which to some extent resulted in a more uniform stress distribution in the rubber bushing.

[0120] like Figure 10 (b) and Figure 10 As shown in (e), the microscopic interface of traditional rubber bushings is mostly a simple contact between a single rubber and metal component, with a uniform interface structure and a lack of force diversion design. When radial loads are applied, the force transmission path is singular, and the load is directly concentrated in a local area of ​​the rubber-metal interface, resulting in a significant stress gradient at the microscopic level—local stress peaks easily appear inside the rubber, and the edge of the rubber-metal interface becomes the core area of ​​stress concentration. This concentrated stress continuously compresses the rubber molecular chains, destroying their cross-linked structure, and simultaneously triggering shear stress overload at the interface, leading to the initiation and propagation of microcracks in the rubber material, ultimately causing interface delamination or fatigue failure of the rubber itself, limiting the load-bearing capacity and service life of the bushing.

[0121] Compared to traditional rubber bushings, the shell-like rubber bushing is based on the multi-scale hierarchical mechanism of the nacreous layer of a shell, known as "brick-mud-brick." It constructs a layered collaborative structure of "steel-rubber-steel" at the microscopic interface. Through interface topology optimization and material property matching, a unique force decomposition and transmission mechanism is formed. When the rubber layer of the shell-like rubber bushing is subjected to a radial load, when the radial force (F...) x When applied to the bushing, the rubber layer, constrained by the steel layer, cannot undergo unidirectional compressive deformation alone. Instead, it achieves this deformation through the synergistic effect of the micro-interfaces. x It is decomposed into a normal force (F) pointing along the geometric center of the bushing. n ) and the tangential force (F) parallel to the steel-rubber interface t This shell-like structure, to a certain extent, disperses the stress on the rubber bushing, avoids stress concentration, and improves the fatigue life of the rubber bushing.

[0122] Normal force (F) n Perpendicular to the steel-rubber interface, it is mainly supported by the high strength of the steel layer, and the excellent compressive strength of the steel material is used to distribute the load, avoiding excessive compression damage to the rubber layer due to unidirectional high pressure.

[0123] Tangential force (F) t The energy is transferred parallel to the interface and absorbed by the high elasticity and viscoelasticity of the rubber layer. Energy dissipation is achieved through the stretching and slippage of the rubber molecular chains, thus avoiding the local accumulation of tangential stress at the interface.

[0124] like Figure 10 (c) and 10(f) show the performance enhancement effect of the micro-interface stress decomposition of the shell-like rubber bushing:

[0125] (1) Stress homogenization and peak value reduction

[0126] The force decomposition at the microscopic level prevents the load from being concentrated in a single interface region. Instead, it achieves a uniform stress distribution across the entire interface through a synergistic mechanism of "normal force borne by the steel layer + tangential force dissipated by the rubber layer." On the one hand, the normal force diffuses across the entire interface through the rigid support of the steel layer, preventing excessive local compressive stress on the rubber. On the other hand, the tangential force is uniformly absorbed by the elastic deformation of the rubber layer, transforming the stress on the rubber molecular chains from "local compression" to "global tension-slip." This significantly reduces the peak microscopic stress, effectively mitigating molecular chain damage and cross-linking fracture in the rubber material.

[0127] (2) Interface synergistic suppression of crack initiation and propagation

[0128] Traditional bushings, with their single interface, are prone to "peeling" microcracks at the rubber-metal interface due to stress concentration. In contrast, the layered interface structure of the shell-like bushing forms a crack-inhibiting barrier through force decomposition.

[0129] The dispersion and transmission of normal force avoids local tensile stress overload at the interface between the rubber layer and the steel layer, and reduces the initiation of interface peeling cracks.

[0130] The energy dissipation of tangential force through the rubber layer reduces the driving force for crack propagation. Even if a tiny crack appears inside the rubber, the global distribution of tangential force will cause the stress at the crack tip to gradually decrease, preventing the formation of concentrated stress that could drive the crack to propagate further.

[0131] In summary, the shell-like rubber bushing decomposes a single radial load into a dual-path transmission of normal load and tangential energy dissipation, fundamentally solving the core problems of micro-stress concentration and interface load imbalance in traditional bushings, and ultimately achieving a significant enhancement in load-bearing capacity, stiffness stability, and fatigue life.

Claims

1. A design method for a shell-like rubber bushing based on a microscopic contact mechanics model, characterized in that, Includes the following steps: (1) Bionic rubber bushing design Based on the toughening mechanism of the "brick-mud-brick" multi-scale hierarchical structure of the nacreous layer of seashells, a shell-like rubber joint bearing with a "steel-rubber-steel" interface synergistic structure is designed. The imitation seashell rubber spherical bearing includes an upper cover plate, a lower cover plate, a sleeve, a central shaft, a rubber bushing, and a bushing. The rubber bushing is integrally formed with the upper cover plate, the lower cover plate, the central shaft, and the bushing through a vulcanization injection molding process. (2) Finite element preprocessing Stress-strain data were obtained by conducting uniaxial tensile tests on the rubber bushing material. The test data were then processed using a fitting tool, and a rubber constitutive model was selected based on the deviation between the fitted curve and the test curve. (3) Finite element modeling and calculation (3-1) Based on the determined rubber constitutive model and parameters, in the finite element model, the following steps are performed in sequence: setting the binding constraints between each component, setting the load and boundary conditions, and mesh generation; The binding constraint settings include: binding a portion of the central shaft to the inner surface of the rubber bushing, binding the outer surface of the bushing to the inner surface of the rubber bushing, and binding the outer surface of the rubber bushing to the upper and lower cover plates; (3-2) Based on the finite element model and load settings, perform contact stress analysis and static stiffness calculation of the biomimetic rubber bushing; (4) Micromechanical property analysis Based on simulation results, the radial contact area of ​​the rubber bushing is calculated, and the contact area of ​​the steel-rubber interface is optimized by controlling the geometric angle and radius of the steel layer. The radial load acting on the rubber bushing is decomposed into normal force and tangential force. The normal force is borne by the high strength characteristics of the steel component, and the tangential force is absorbed and dissipated by the high elasticity and viscoelasticity characteristics of the rubber bushing, so as to achieve uniform stress distribution and crack suppression. The format for calculating the radial contact area is as follows: Where r is the radius of the cylindrical section of the central axis, l2 is the contact length between the rubber bushing and the cylindrical section of the central axis, R1 is the radius of the sphere of the central axis, H is half the height of the rubber bushing, R2 is the outer contour radius of the rubber bushing, and θ2 is the contact half angle between the journal of the central axis and the rubber bushing. (5) Fatigue load calculation The single stress-strain results obtained from finite element analysis are imported into fatigue analysis software. Fatigue algorithms and material properties are set, and cyclic loading simulation is performed to predict the fatigue life of the rubber bushing.

2. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 1, characterized in that, In step (2), the rubber constitutive model is the Ogden third-order constitutive model with the following parameters: Mu1=13.55, Mu2=-2.34, Mu3=0.09, Alpha1=1.51, Alpha2=2.21, Alpha3=-2.

47.

3. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 1, characterized in that, Step (2) further includes: simplifying the upper cover plate, lower cover plate, central shaft and bushing into analytical rigid bodies, defining the reference points of the central shaft and bushing at their respective geometric centers, and treating the upper and lower cover plates as a whole and setting their reference points at the geometric center.

4. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 1, characterized in that, In step (3-1), the load and boundary condition settings include: setting the six degrees of freedom of each node of the outer ring of the shell-like rubber spherical bearing to be completely fixed, and applying loads of six degrees of freedom motion respectively with the central axis reference point as the force application point. The six degrees of freedom motion includes radial displacement, axial deflection, radial deflection and axial rotation.

5. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 1, characterized in that, In step (3-1), the mesh division includes: using a hexahedral mesh, using C3D8R elements for the rigid metal part, and using C3D8RH elements for the rubber bushing part.

6. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 4, characterized in that, The load for radial displacement is a concentrated force of F=53300N applied in the X direction within 1 second; the load for axial deflection is a concentrated force of F=26700N applied in the Y direction within 1 second; the load for radial deflection is a torsion of Angle=0.1Rad applied around the X axis within 1 second; the load for axial rotation is a torsion of Angle=0.1Rad applied around the Y axis within 1 second.

7. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 1, characterized in that, In step (3-2), a certain stage of the loading process is taken as the static stiffness calculation interval: In the calculation of radial and axial stiffness, the loaded force and loaded displacement are used as the basic calculation parameters. The radial stiffness and axial stiffness are calculated according to the formulas K1=ΔF / ΔX and K2=ΔF / ΔX respectively. K1 is the radial stiffness, K2 is the axial stiffness, ΔF is the change of load, and ΔX is the change of radial or axial displacement. In the calculation of torsional stiffness, torque and deflection angle are used as the basic calculation parameters. The torsional stiffness is calculated according to the formula K3=ΔM / Δθ, where K3 is the torsional stiffness, ΔM is the change in torque, and Δθ is the change in deflection angle.

8. The design method for a shell-like rubber bushing based on a microscopic contact mechanics model according to claim 1, characterized in that, In step (5), the fatigue load calculation software is Fe-Safe software.

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