Equivalent Spring Research Articles

Modeling and comfort analysis of arrayed air cushion mattress for pressure ulcer prevention and assisted repositioning

Assisting immobile individuals with regular repositioning to adjust pressure distribution on key prominences such as the back and buttocks is the most effective measure for preventing pressure ulcers. However, compared to active self-repositioning, passive assisted repositioning results in distinct variations in force distribution on different body parts. This incongruity can affect the comfort of repositioning and potentially lead to a risk of secondary injury, for certain trauma or critically ill patients. Therefore, it is of considerable practical importance to study the passive turning comfort and the optimal turning strategy. Initially, in this study, the load-bearing characteristics of various joints during passive repositioning were examined, and a wedge-shaped airbag configuration was proposed. The airbags coupled layout on the mattress was equivalently represented as a spring-damping system, with essential model parameters determined using experimental techniques. Subsequently, different assisted repositioning strategies were devised by adjusting force application positions and sequences. A human-mattress force-coupled simulation model was developed based on rigid human body structure and equivalent flexible springs. This model provided the force distribution across the primary pressure points on the human body. Finally, assisted repositioning experiments were conducted with 15 participants. The passive repositioning effectiveness and pressure redistribution was validated based on the simulation results, experimental data, and questionnaire responses. Furthermore, the mechanical factors influencing comfort during passive assisted repositioning were elucidated, providing a theoretical foundation for subsequent mattress design and optimization of repositioning strategies.

An analytical model for dynamic analysis of inhomogeneous sandwich plate

Sandwich plates are widely used in the engineering domain and are extensively studied by researchers for their special performances. Among them, the sandwich plate with coordinate-dependent material parameters has excellent vibration isolation performance. However, there are few effective and convenient analytical methods for solving the dynamic response of this type of sandwich plate. To solve this problem, an equivalent spring-based model for the dynamic analysis of the sandwich plate is proposed in this paper. Assuming that the sandwich plate is a linear elastic structure, and considering the core plate as equivalent springs, whose stiffness coefficients are derived based on the classical elasticity theory and Kirchhoff hypothesis. Besides, displacement solutions of base and constrained plates of the sandwich plate in the x, y and z directions are expressed as a two-dimensional Fourier series supplemented with several one-dimensional Fourier series, respectively. Then, according to the orthogonality of trigonometric functions and selectivity of Dirac functions, the displacements of the sandwich plate are solved accurately. By comparing with available analytical and numerical results, the proposed method is proven to have excellent performance in dealing with the sandwich plate with coordinate-dependent material parameters. Finally, the dynamic characteristics and vibration isolation performance of the inhomogeneous sandwich plate are discussed. The results show that the proposed method can be used to design the inhomogeneous sandwich plate and improve their vibration isolation performance significantly.

The Behaviour of Building Frames on Raft Foundation using Dynamic Analysis

When designing building frames for seismic reasons, the effect of soil flexibility is typically disregarded, and the design is executed using the outcomes of dynamic analysis with a fixed base condition. Because the overall lateral stiffness of the structure decreases as a result of soil flexibility, the lateral natural period lengthens. The building frames situated on the Raft foundation may experience a significant change in seismic response due to this extension of the lateral natural period (T). Therefore, it is imperative to consider the soil's flexibility, also known as soil structure interaction, when doing analysis on the foundation's supporting layer.
 This paper examines how asymmetric building frames with raft footings behave dynamically when subjected to seismic forces that involve soil-structure interaction. The analysis is performed with SAP 2000*V21 FEM software. The structure is idealized as a three-dimensional space frame, with slabs modeled as a thin shell with four noded plate elements and six degrees of freedom at each node, and beams and columns modeled as two noded line elements. The soil is represented as equivalent springs with one (Winkler) and six (Modified Winkler) degrees of freedom; the stiffness of these springs varies depending on the type of soil and is determined by its dynamic shear modulus and poissons ratio. The Modified Winkler and Winkler raft foundations are modeled as thin shells with four noded plate elements, each with six degrees of freedom, and are criticized so that the element aspect ratios are equal to one.
 
 To assess the impact of soil structure interaction on building frames, the response is compared for a range of building frames with and without consideration of soil flexibility in terms of fundamental Natural Period, Seismic Base Shear, and Max. Lateral Displacement. The parametric study for Zone V takes into account the influence of various parameters, including the number of bays, stories, span lengths, and soil types (i.e., soft, medium, and stiff).
 
 It is discovered that the fundamental lateral natural period and seismic base shear of the system are significantly altered by the influence of soil flexibility on building frames. As soil stiffness decreases, the lateral natural period and seismic base shear increase as a result of soil flexibility. Additionally, it has been noted that as the number of bays increases, so do the building's base shear and lateral period. As the number of bays and stories increases, so does the maximum lateral displacement. 

Site Specific Non-Linear Ground Response Analysis and Soil Structure Interaction Study of Newly Constructed Dharahara Tower

This study investigates the seismic performance of the recently reconstructed Dharahara tower, a historically significant monument in Nepal that has experienced damage in past earthquakes and was completely destroyed in the recent Gorkha earthquake. Ground Response Analysis (GRA) and Soil-Structure Interaction (SSI) investigations are conducted to assess its structural behavior. GRA includes free field and structure-influenced analyses, with subsequent comparative assessment. Additionally, 3D non-linear finite element analysis is employed to derive equivalent spring constants representing soil and foundation characteristics, which are incorporated into the SSI analysis. These computed spring constants are used to model support conditions, allowing for an evaluation of the super-structural response. The study also employs non-linear dynamic analysis to compare structural responses between fix-based and spring-based models. The results indicate that the presence of the structure significantly influences surface wave motion amplification in GRA, resulting in peak ground accelerations (PGAs) that exhibit de-amplification in the free field and amplification in the presence of the structure. Furthermore, the introduction of an equivalent spring system in the soil-structure model changes the system's vibration period and damping characteristics, leading to enhanced dynamic response compared to the fixed-base model.

Fatigue crack driving force of railway bogie frames using rigid-flexible coupled dynamics: A case for beam model

The stress intensity factor is essential to determine the residual fatigue lifetime of cracked components. However, the traditional method used to determine the stress intensity factor is very difficult to characterize the dynamic behaviors of structure arising from the fatigue crack. This paper proposed a methodology to determine the dynamic stress intensity factor (DSIF) of a crack incorporating with the rigid-flexible coupled dynamics. Firstly, a rigid-flexible coupled dynamic model of cantilever beam representing the typical structure of bogie frame with a straight crack was developed based on SIMPACK platform. In the model, the equivalent spring - contact element was employed to model the contact behaviors of crack interface. Subsequently, the DSIF considering the crack closure effect was calculated by the node displacement extrapolation. The validity of proposed method was demonstrated through comparing the DSIF with those obtained by other analytical methods. The results suggest that the proposed methodology can characterize the closure effect of crack, and yield more accurate estimation for the DSIF. This method establishes a link between the multibody system dynamics and the fracture mechanics, which enable us to calculate the DSIF of crack under the operating condition using a rigid-flexible coupled dynamic model.

A two-dimensional friction-decoupling method based on numerical integration method and momentum theorem

This article introduces a simplified Two-Dimensional Friction-Coupling Model (TDFC) designed for typical surface-to-surface contact friction systems in engineering structures. With the assumption of a constant friction force magnitude within each calculation time step, the alteration of the friction direction of TDFC within each calculation time step can be visualized as the rotation of a circular radius under horizontal bidirectional dynamic loads. This dynamic force analysis approach is referred to as the “Circular making”. It is noteworthy that the friction direction change in each calculation time step demonstrates unidirectional rotatability. Leveraging this rotatability and assuming uniform rotation, the momentum theorem accurately determines the direction of the plane friction acting on the TDFC model at the end of each calculation time step. This allows for the decoupled calculation of plane friction and precise response calculation of the TDFC model. The study verifies the reliability of theoretical assumptions, such as constant friction force magnitude and uniform rotation, with a time step of 0.01 s. Additionally, by introducing an equivalent spring effect to modify the TDFC model, it is observed that the modified TDFC effectively simulates the behavior of the Friction Pendulum Bearing (FPB) under horizontal bidirectional seismic loads. Compared to the ABAQUS finite element model of FPB, the modified TDFC model provides a more efficient approach for rapidly and accurately calculating the response of various FPB types under horizontal bidirectional seismic loads by adjusting parameter values of the modified TDFC model.

An equivalent spring model for seam-clip connections of high-vertical standing seam metal cladding systems

The mechanical behavior of the seam-clip connections plays a pivotal role in the effective wind resistance design of the extensively used high vertical standing seam metal cladding system (SSMCS). An equivalent spring model is developed to represent the mechanical behavior of these connections to simplify the contact problems in the general finite element model, which is time-consuming due to the highly nonlinear contact boundary conditions. The developed model is composed of continuous horizontal and rotational springs as well as dispersed vertical rigid connections. A series of tensile experiments are first conducted to investigate the mechanical behavior of seam-clip connections to calibrate the spring parameters in the developed model. Subsequently, the equivalent spring model is validated by the structural response of a double-span sheet module (DSSM) using experimental investigation and finite element analyses. It is found that the shell finite element model incorporating the developed equivalent spring model can achieve an acceptable structural response while remarkably reducing memory requirements and computational time to about 0.3 % and 0.4 ‰, correspondingly, compared to the contact boundary condition analysis. It highlights the advancement in evaluating the structural response of high-vertical SSMCS in practical engineering applications using this developed model. Furthermore, the developed equivalent spring model has proved to be effective in predicting wind-induced seam-clip pullout failures according to the established failure criteria derived from the structural response of the system.

Nonlinear analysis model and seismic resilience assessment of LEM-filled CFS residence

Lightweight EPS materials (LEM)-filled cold-formed steel (CFS) shear wall structure is a new type of green, low-carbon and prefabricated rural residence, which has drawn in expanding consideration due to the promotion of the rural revitalization strategy. However, most of the existing research on this type of residence has focused on its behaviours of components, with little attention was paid to its overall response to resist earthquake disasters. During the past two decades, significant advancements have been made in effectively mitigating building collapses and reducing casualties resulting from earthquakes. Thus, the concept of seismic resilience is proposed, and the seismic performance requirements of structural design have been elevated from “safety” to “resilience”. To analyze the seismic resilience of LEM-filled CFS residence, this paper proposed a strut and tie- equivalent spring model to establish the simplified analysis model of a single composite wall, and the precision of the model was confirmed by test results, in which the nonlinear characteristic and the supporting effect of fillers was considered. Subsequently, three LEM-filled CFS residences are designed using the direct displacement-based design method. Then the three-D models are established for nonlinear analysis, and the inter-drift ratio (IDR) and residual inter-drift ratio (RIDR) are adopted to estimate the seismic response of the three archetypes. The seismic resilience of the three archetypes are assessed based on FEMA P58. This paper would provide a guidance for the nonlinear analysis and seismic resilience assessment of this type of residences, and promote the application and popularization of this kind of residence.

Assessing the Equivalent Spring Method for Modelling of Lightweight-concrete Encased Cold-formed Steel Elements in Compression

Using concrete for filling and bracing is one of the most crucial ways to improve cold-formed steel (CFS) elements' stability behavior and performance. An example is the novel building system made up by CFS encased in ultra-lightweight concrete. The numerical analysis of such structural members using solid finite elements is time-consuming, thus the need for an easy-to-use modelling technique has arisen. As a result, a simple time-efficient equivalent spring model (ESM) has been introduced as a viable method for properly analyzing complex structural behavior in numerous cases, replacing the concrete solid with one-directional springs applying the Winkler foundation. This study aims to examine the validity and limitations of the ESM by comparing it to 3D solid model (SMOD) results for internal plate elements. The analysis results indicate that the ESM could provide accurate results in the b/t range of 100 or less for a wide range of PAC modulus (50–250 MPa) with an error of less than 5%; hence, using spring in modelling PAC within these limits is deemed acceptable. Nevertheless, for larger b/t values up to 175, doubled the calculated spring stiffness is highly recommended. In addition, the results reveal that the applicability of ESM is limited for b/t above 175; the model fails to predict the ultimate failure load, and the failure mode. Finally, this study ends by recommending one equation for calculating equivalent foundation spring stiffness for internal components that ensure optimal performance of the ESM analysis.

Effect of steel grid on enhancing seismic performance of bridge pier with low reinforcement ratio: Shaking table test and numerical simulation

The railway bridge piers with large cross section and low reinforcement ratio are easy to damage under earthquakes in China. The steel grid has been proved to be an effective strengthening method to improve the cyclic behavior using quasi-static test. In this study, shaking table tests were conducted to investigate the seismic response of three pier specimens. Experimental results indicated that the steel grid delayed the crack development and occurrence of uplifting-rocking phenomenon for the railway pier. For strengthened piers, about 7.5%-51.4% reduction, 9.1%-21.9% and 7.6%-27.4% enhancement is measured for displacement of pier top, acceleration of pier top and energy dissipation. To obtain the effect of design parameter variation of steel grid on seismic damage (i.e., the horizontal distance between steel grid and the surface of pier specimen, steel grid area and vertical spacing of steel grid), the numerical analysis mode of strengthened pier was established. The mechanical model of steel grid obtained by deriving the equivalent spring calculation method is used in the numerical simulation model. The results show that the horizontal distance variety between steel grid and surface of pier specimen has the most obvious impact to strengthening effect, while the vertical spacing of steel grid is the least. The smaller horizontal distance between steel grid and the surface of pier specimen, the higher steel grid area and shorter vertical spacing of steel grid are the most significant to reduce the different damage probability of the bridge pier.

Laser-Welded Corrugated-Core Sandwich Composition—Numerical Modelling Strategy for Structural Analysis

Laser-welding technology has recently enabled the production of corrugated-core steel sandwich panels (CCSSPs) as an innovative large-scale, lightweight structural solution in maritime and infrastructure applications. Detailed numerical analyses, specifically weld-region stress prediction in the presence of transverse patch loading and supports, are computationally challenging and time-consuming for their optimal design. This paper introduces an efficient, simplified combined sub-modelling approach for accurately predicting the detailed structural response of welded corrugated-core steel panels. The approach rests on the homogenisation of the three-dimensional (3D) panel into a two-dimensional equivalent orthotropic single layer (EOSL), where the effect of transverse compressive loads and local support conditions are captured separately via different 2D and 3D sub-modelling techniques, together with a model introduced for calculation of the weld region’s equivalent spring stiffnesses. A laser-welded corrugated-core steel sandwich panel (CCSSP), as a future generation of the steel bridge deck, was examined using different modelling approaches. It was shown that the proposed combined sub-modelling approach can accurately predict stresses and displacements in all the constituent members of the cross-section, including the welds, in a reasonable calculation time when compared with a 3D reference model, unlike the conventional homogenisation approaches.

Dynamic Bending Model Describing the Generation of Negative Stiffness by Buckled Beams: Qualitative Analysis and Experimental Verification

This work addresses the dynamic modeling of a negative stiffness absorber consisting of an assembly of curved beams. Design rules are derived from the orders of magnitude of stiffness and elastic energy stored by the negative stiffness elements. Although static and dynamic performances are widely documented using equivalent spring–mass system equations of motion, this paper presents a modeling approach based on beam dynamics to predict the behavior by incorporating the generation of negative stiffness with prestressed Euler beams. The static behavior is first recalled to feed the dynamic beam model with realistic orders of magnitude. The latter is derived from the beam balance instead of the spring–mass system and aims at solving the beam problem, which encompasses more realistic phenomena compared to introducing the equivalent stiffness in the spring–mass equation of motion. The consistency of the beam modeling is confirmed by comparison with available models in the literature and finite element simulations. A mock-up is built in which beam-type components are 3D-printed. Axial loading is introduced on the curved beams to evaluate its influence on the response of the isolator, and the observed softening trend complies with the theoretical predictions.

Prediction of post-fire seismic performance of reinforced concrete frames

Due to the importance of evaluating the seismic behavior of structures after a fire, a numerical study was conducted on RC frames using the detailed finite element method. The simulation process consists of two separate steps. The first step is heat transfer analysis to estimate heat distribution in the various elements of RC frames, and the second step is evaluating the post-fire seismic performance of the frames using thermal–mechanical analysis. The test specimens used to verify the proposed FE model include two RC frames with different beam-column bending capacity ratios, which are in two different conditions, including the specimens at ambient temperature as control specimens and fired specimens inside of the furnace chamber. In the heat transfer analysis step, the sensitivity of responses to two effective parameters, including the moisture content and the emissivity of the concrete surface has been investigated. In the post-fire analysis, among the various models presented for the post-fire behavior of concrete, three stress–strain models were selected for cyclic analysis of RC frames and the results were compared with the test data. Also, the bond-slip behavior of the concrete-steel interface has been simulated using the equivalent springs technique. It was seen from the comparison of the numerical results with the test data, that the proposed model accurately estimates the resistance and the dissipated energy of frames in each cycle. In addition, parametric studies showed that every 30 min increase in the fire duration based on the ISO 834 standard curve causes a 10% decrease in post-fire seismic resistance compared to the control specimen.

Low-Frequency Ultrawide Band Gap Study of Symmetric Conical Scatterer Phononic Crystal

PurposeOne of the key challenges in the research of phononic crystals is achieving small-size control of large wavelengths, which means obtaining low-frequency band gaps with relatively small lattice dimensions. Previous studies have mostly been unsatisfactory in this regard. To obtain lower starting frequencies and more satisfactory band gap widths, this work presents a novel design for a phononic crystal structure.Design ApproachThe proposed phononic crystal consists of a silicon rubber connecting plate, an epoxy resin substrate, and tungsten metal cone scatterers. Through finite element method (FEM) calculations and analysis, we have successfully achieved an ultrawide band gap. To delve further into the origin of the ultra-wideband gap in a newly conceived phononic crystal, the vibrational modes of this crystal were carefully studied.FindingsThis work has successfully achieved an ultrawide band gap with a width ranging from 122.47 to 4360.2 in the case of a lattice constant of a = 8.5 mm. It was found that the low-frequency ultra-wideband gap cannot be obtained without the presence of silicone rubber. Furthermore, an equivalent spring model was developed, and the accuracy of this model was successfully validated through meticulous calculations. At last, It is found that d1, d4, h1, and h3 have the most pronounced effect on the ultrawide bandgap, and the intrinsic reason is the fact that they determine the geometric structure of the silicone rubber connection plate.Research Limitations/implicationsDue to the chosen research method of finite element analysis, the study results may vary depending on the different mesh discretizations, but this type of error is small and can be ignored.Practical ImplicationsThis work provides a new design solution for phononic crystal miniaturization.Originality/valueCompared with previous reports, the new phonon crystals designed in this paper have smaller size, lower starting frequency, and wider band gap.

Current Hydrological Conditions Research of the Chaika lake System in the Territory of the Volga-Akhtuba Floodland

The nature protection measures performed within the national project "Ecology" on the lake system "Chaika" were analysed, the flooding status of the floodland before and after the measures implementation was compared with the equivalent special spring release. A positive effect in increasing the floodland area was confirmed. The chemical analysis results of water and composition of bottom sediments were presented. The bottom sediment was found fertile to be classified as calc-sapropel.

A spiral slotted transducer with high longitudinal-torsional conversion rate

The longitudinal-torsional (L-T) composite piezoelectric transducer has wide applications in material processing, welding, and other fields due to its exceptional machining efficiency. This study introduces a spiral slotted L-T transducer, which is designed to achieve a high L-T conversion rate at low operating frequency. The equivalent spring concept is employed to derive the equivalent circuit of the L-T transducer, which provides a convenient study for the frequency characteristics of the transducer. A finite element model is developed to analyze the performance of the transducer and investigate the effect of the spiral slot parameters on the resonance frequency, amplitude, and the L-T conversion rate of it. Two prototype transducers are constructed and measured experimentally. Theoretical computation results, finite element simulation results, and experimental results are compared to each other. The comparison results demonstrate that the proposed computation model provides accurate prediction of the L-T coupling resonance frequency of the transducer. By adjusting the spiral slot parameters of the transducer, a higher L-T conversion rate can be achieved, which may have more applications in practical engineering.

Mechanically Coupled Single-Crystal Silicon MEMS Resonators for TCF Manipulation

This paper presents mechanically coupled single-crystal silicon (SCS) microelectromechanical system (MEMS) resonators for temperature coefficient of frequency (TCF) manipulation. The reported mechanically coupled square extensional (SE) mode resonator consists of two square plates coupled with a beam or a third square plate purposely vibrating in another bulk mode. The SE mode resonators and the coupled structure can be considered as two kinds of individual resonators with different TCFs. Within the specific dimensions of the coupled resonator, the resonant frequencies of the two components are assumed to be equal. Hence, the TCF of the mechanically coupled resonator could be manipulated by adjusting the sizes of the coupling parts. The design and fabrication of coupled resonators have been completed in a degenerate-doped (100) SCS wafer. Measurement results illustrate that the TCFs of the coupled resonators can be purposely manipulated by adjusting the volume and equivalent spring constant ratios of the individual resonators. The minimal measured frequency shift is roughly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 10 ppm for an 18 MHz coupled SE mode resonator, over the entire industrial temperature range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 40 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C to 85 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C. This work highlights a novel and effective way to manipulate the TCFs of MEMS resonators via mechanical coupling. 2022-0197

Design optimization of offshore wind jacket piles by assessing support structure orientation relative to metocean conditions

Abstract. The orientation of a three-legged offshore wind jacket structure in 60 m water depth, supporting the IEA 15 MW reference turbine, has been assessed for optimizing the jacket pile design. A reference site off the coast of Massachusetts was considered, including site-specific metocean conditions and realistically plausible geotechnical conditions. Soil–structure interaction was modeled using three-dimensional finite-element (FE) ground–structure simulations to obtain equivalent mudline springs, which were subsequently used in nonlinear elastic simulations, considering aerodynamic and hydrodynamic loading of extreme sea states in the time domain. Jacket pile loads were found to be sensitive to the maximum 50-year wave direction, as opposed to the wind direction, indicating that the jacket orientation should be considered relative to the dominant wave direction. The results further demonstrated that the jacket orientation has a substantial impact on the overall jacket pile mass and maximum pile embedment depth and therefore represents an important opportunity for project cost and risk reductions. Finally, this research highlights the importance of detailed knowledge of the full global model behavior (both turbine and foundation) for capturing this optimization potential, particularly due to the influence of wind–wave misalignment on pile loads. Close collaboration between the turbine supplier and foundation designer, at the appropriate design stages, is essential.

Deployment analysis of membranes with creases using a nonlinear torsion spring model

Membranes have been widely applied in spacecrafts, such as solar sails and deployable antenna structures, due to their light weight and high compact ratio. The geometric profile of deployed membranes has an important impact on the performance of a membrane-based spacecraft, which should be accurately predicted during the deployment process. However, some observable dynamic deployment characteristics of membranes are difficult to be simulated accurately. In this paper, an equivalent torsion spring model for the membrane crease is proposed and derived to accurately describe the complex deployment process of the membrane. The elastic and plastic phases of the equivalent spring are both considered and derived in this model. Based on this method, the experimentally-observed spring-back position and the corresponding torque of the membrane can be quantitatively predicted. Combining the equivalent torsion spring model with the finite element software, the deployment processes of a single-fold and a Miura-fold are simulated and compared with the experimental results, showing a good agreement. Finally, the deployment process of a 3-axis stabilized solar sail is simulated using this method.

Calculation Model of Contact Load and Axial Stiffness of Planetary Thread Roller Bearing Based on Direct Stiffness Method

AbstractPlanetary Threaded Roller Bearing (PTRB) is a new bearing suitable for the heavy load linear drive mechanism. The load is transferred internally through annular threads, affecting the bearing capacity of the thread's contact load distribution characteristics. The structure of PTRB is discretized to study the contact load distribution of PTRB. The axial stiffness of the thread's teeth, its axial stiffness, and the contact stiffness of contact points are calculated. Moreover, a 1D equivalent spring network model is proposed based on discretized structure and stiffness. The PTRB contact load calculation model is proposed using the direct stiffness method and a 1D equivalent spring network model. Finally, the accuracy of the model proposed in this paper for calculating the contact load distribution of threaded teeth is verified by comparing the results obtained from theoretical model calculations, finite element methods, and experiments. The theoretical model proposed in this paper can provide theoretical guidance for PTRB parameters.