Iwan Model Research Articles

A quantitative characterization model for nonlinear dynamic parameters of O-rings

When the rubber O-ring follows the primary seal in the axial direction as a secondary seal, there is hysteresis behavior between the restoring force and displacement. However, the dynamic parameters of O-rings are mostly expressed as constants in dynamic analysis at present, which cannot accurately describe the dynamic behavior of sealing systems. In response to the problem of poor track performance of mechanical seals, based on the actual working conditions in nuclear reactor coolant pumps, vibration experiments with high pressure and water lubrication are carried out on ethylene-propylene-diene monomer (EPDM) rubber O-rings, which can reveal the laws in the actual situation. The experimental results confirm that there are nonlinear variations of O-ring dynamic parameters in vibration, which cannot be expressed by constants. In order to quantitatively characterize the nonlinear behavior, this study establishes a novel mathematical model and analyze the influence of working conditions. A method combining the nonlinear properties of both interfacial sliding and body viscoelasticity of O-rings is proposed. The nonlinear stiffness, damping and friction (NSDF) model is established based on the adjusted Iwan model and the trace method. The finite element analysis and vibration experiments are carried out to study the hysteretic behavior and determine the parameters of the model. Furthermore, the influence of medium pressure and vibration amplitude on interfacial stiffness and O-ring stiffness and damping are discussed. It is pointed out that O-ring stiffness and damping decrease with increasing amplitude and increase with increasing pressure. The comparative analysis of experiments and model shows that the proposed model can provide an accurate determination of the nonlinear behavior of O-rings in vibration. The results and the proposed model can provide a basis for the evaluation of the dynamic performance of mechanical seal systems.

Analysis of bolt bonding surfaces by the finite element method based on the equivalent Iwan model

This study establishes a finite element model based on the Iwan model to accurately characterize the force–displacement relationship and energy dissipation in bolted joints under small-amplitude tangential displacement. The force–displacement behavior of the Iwan model is transformed into a stress–strain relationship using a hybrid hardened intrinsic model. A subroutine developed with UMAT and UHARD is used to simulate the elastic–plastic behavior of the Iwan model during surface contact in the finite element model. Three-dimensional modeling and joint simulation are conducted using ABAQUS software. Experimental data verify the model's validity, and the effects of multiple factors on the bolted bonding surface are analyzed. The influence of friction coefficient, cyclic displacement amplitude, and preload on the force–displacement relationship of the bolted bonding surface is explored. Polynomial interpolation of the loading and unloading curves is applied to investigate the energy dissipation phenomenon. Results show that the finite element method can effectively reflect the hysteresis and energy dissipation behavior of the bonding surface. Increased friction coefficient and preload improve residual stiffness and energy dissipation capacity, while larger cyclic displacement amplitudes increase energy dissipation but have a minimal effect on residual stiffness.

Parameter Identification and Energy Dissipation Analysis of Premium Connections Based on the Iwan Model

The premium connection is an important section of the tubing column. Under intricate downhole conditions, axial vibration generates alternating loads that cause energy dissipation between the sealing surfaces of the premium connection, reducing sealing performance. To investigate this issue, the mutual conversion process of sticking, slipping, and macroscopic slipping stages between the sealing surfaces of the premium connection under axial loads must be assessed. In this study, a finite element analysis model of a taper–taper Φ88.9 mm × 6.45 mm P110 premium connection is developed based on the discrete Iwan model’s ontological relationship, and the sealing surface’s force–displacement hysteresis curve is obtained. The equivalent Iwan model for this particular premium connection is constructed by discretizing the hysteresis curve and identifying the model’s four sets of parameters. The correctness of the parameter identification method of the equivalent Iwan model is verified by comparing and analyzing the similarity of the two models. The energy dissipation in the sealing surfaces of the premium connection for different working conditions under dynamic loading is analyzed. This study reveals that the area similarity of the hysteresis curves of the two models is more than 92%, while the positional error is less than 2%. The sealing surface displacement amplitude of the premium connection is between 0.04 mm and 0.07 mm, while the sealing surface energy dissipation increases linearly, which may lead to a decline in sealing performance.

Influence of bolt preload degradation on nonlinear vibration responses of jointed structures

The clamping performance of bolted joints was gradually degrading under long-term vibration loads, which induced a great impact on the stick–slip friction contact behavior of bolted joint interfaces. In this paper, a time-varying Iwan model was developed to reproduce the tangential hysteresis behavior of bolted joint interfaces by considering preload degradation. A three-degree-of-freedom mass–spring-damper oscillator was numerically simulated to investigate the influence of preload degradation on nonlinear vibration responses, as well as the experimental investigations of a bolted joint structure. The comparison results showed that the proposed model could well describe the effects of preload degradation on the stick–slip friction contact behavior of bolted joint interfaces. The numerical results revealed the nonlinear effects of preload degradation on the frequency response functions (FRFs), which demonstrated good agreement with experimental results.

Rub-impact investigation of a bolted joint rotor-bearing system considering hysteresis behavior at mating interface

Hysteresis behavior at the mating interface can induce nonlinear stiffness and frictional dissipation, which may lead to a complex vibration character, self-excited vibration, and even the rubbing fault for the bolted joint rotor system. The present work aims to investigate the effect mechanism of hysteresis behavior on the rotor dynamics and the mechanism of bolted joint performance change induced by a rubbing fault. Firstly, the bolted joint model considering the hysteresis behavior at the mating interface is proposed based on the Iwan model. Then, a non-dimensional dynamic model of the bolted joint rotor system with rubbing fault is established by combining the lumped-mass method and fixed-point rub-impact force model. After that, the nonlinear response of the bolted joint rotor system considering the hysteresis behavior at the mating interface and the effect of rubbing fault on the dynamic performance of such a rotor system is explored. Finally, an experimental verification is carried out by adopting a rotor system test rig with a different stiffness rubbing device. The result shows that the rubbing fault will reduce the critical speed by changing the equivalent average stiffness of the bolted joint and aggravate the self-excited vibration of the system, leading to a stronger nonlinear performance of the rotor system. The outcome of the present work can provide valuable insights into vibration prediction, health detection, and rubbing fault diagnosis for a rotor system with a bolted joint.

Modeling of residual stiffness phenomenon in modified Iwan model of bolted joints and its application

Bolted joints have been widely used in various mechanical structures. Due to the presence of contact interfaces, the joints exhibit complex nonlinear behavior under dynamic loading. Effective prediction of the dynamic response of bolted structures requires the construction of appropriate dynamic models. This paper proposes a modified Iwan model which gives a more comprehensive description of joints than the previous Iwan models, especially for the phenomenon of residual stiffness in macro slip. The equations of the model's backbone curve, hysteresis curve, and energy dissipation are derived. The parameter identification procedure is also provided. Subsequently, connection elements based on the modified Iwan model are integrated into a single bolted joint and a thin-walled cylinder containing multiple bolted joints, the responses under quasi-static unidirectional loading, quasi-static cyclic loading and constant-frequency excitation are investigated. The physical interpretation of the parameters in the model is discussed, thus explaining the relationship between the bolted joint's physical parameters and some important variables. The results indicate that the model can effectively characterize the nonlinear mechanical behavior of the bolted joint for both micro and macro slip regime, with significant improvement in computational efficiency.

Tangential contact modeling to seal considering elastic-plastic for lubrication transition mechanism

Researches on the reciprocating seals lubrication under elastic-hydrodynamic lubrication (EHL) are mature, and leakage of failure criterion has been described with Couette flow for more than 30 years, which could not reflect to leakage mechanism in multiscale. Thus, it is necessary to explore seal leakage failure to focus on micro convex bodies of asperities model under contact pressure and cycle tangential friction stress in mixed lubrication. This is because convex bodies behaviors determine sealing effect and lubrication behaviors in microscale with subjecting to the dominant pressure. Interaction between convex bodies fatigue hysteresis curve and elastic-plastic strain are also calculated to explore sealing effect with leakage rate mechanism. We then design water seal at high pressure of 100 MPa with the speed of 0.1–1 m/s and medium temperature from 5 ℃ to 40 ℃. IWAN model of the convex bodies are calculated. Probability density function and Jenkin’s elements critical slip displacement are obtained. Convex bodies of radial and tangential deformation are also calculated through loading of contact pressure and friction stress with cycle strength coefficient to obtain seal fatigue lifespan. Ratio to seal stick and slip friction is calculated for evaluating the loading boundary. Seal leakage failure mechanism with fatigue characteristics is illustrated with macro lubrication parameters and micro convex bodies mechanics performance.

A Dynamic Iwan Model to Describe the Impact Failure of Bolted Joints

Due to the nonlinearity of the contact interface, as well as the material, jointed structures exhibit complex mechanical behaviors under impact loading. In order to accurately characterize the dynamic response of a joint, this work presents a nonlinear dynamic model (DICF model). First, the effects of loading velocity, preload and friction coefficient on the displacement–load curve are discussed based on a validated finite element model. Numerical simulation results show that the critical load and critical displacement are linearly related to the normalized logarithmic velocity and linearly related to the normalized preload and friction coefficient. Subsequently, a DICF model that consists of sliding, collision and failure is proposed. The constitutive relations of the model are derived, and dynamic correction functions are introduced to characterize the effects of velocity, preload and friction coefficient. A parameter identification method for the model is also provided. Finally, the DICF model is compared with the finite element simulation results, with an error of 0.43% for quasi-static conditions, a minimum error of 0.17% and a maximum error of −1.41% for impact conditions, in addition to significantly improved accuracy compared to the EC3 model, which indicates that it can effectively capture the behavior of bolted joints under impact loading conditions.

A novel iterative model updating for jointed structures using nonlinear FRFs

A novel iterative model updating method is developed to identify the local nonlinear joint properties using the frequency response functions (FRFs) of assembled structures. In this paper, the least-squares fitting method was used to transform the sensitivity matrix into a square iteration matrix to match the dimensions of the objective functions and nonlinear joint model parameters. Leveraging the Newton’s iteration, the adaptive successive over-relaxation (A-SOR) was used to ensure iteration convergence while the multi-scale parameter adjusting (MPA) strategy was developed to degrade the ill-condition of the iteration matrix. Two updating examples of phenomenological equivalence models were applied to demonstrate the effectiveness of the proposed method. The nonlinear FRFs of a lap-type bolted joint beam system with Iwan model were simulated as the objective functions to identify the local nonlinear joint properties, as well as experimental investigations of a metal rubber isolation system with a high-order polynomial model. The proposed method was validated by the good agreement of the comparison results, and it indicated a better model updating performance with a much smaller condition number of the iteration matrix.

Modeling and analyzing the influence of slip velocity on joint surface

Millions of joints are utilized in large-scale equipment to interconnect components. However, the intricate nonlinear mechanical behavior exhibited at joint interfaces poses challenges in accurately modeling equivalent joints. The Jenkins element with viscoelasticity is built upon the Iwan model, and a novel Iwan-Stribeck-RIPP (Reduced Iwan Plus Pinning) model is proposed to depict the slip velocity and pinning effects concurrently. Analytical expressions for force-displacement, energy dissipation-displacement, and force-energy dissipation under microslip and macroslip were derived. A joint interface experimental platform was constructed to reveal the influence of slip velocity on the joint interface. The results indicate strong alignment between the analytical solution of the Iwan-Stribeck-RIPP model and the experimental outcomes of the joint interface. Moreover, the model effectively captures both slip velocity and pinning effects. Introducing slip velocity into the new model promises to enhance the accuracy of force-displacement analysis at the joint interface. This enhancement is attributed to the inclusion of both frictional energy and kinetic energy dissipation resulting from the slip velocity in the analytical model of the joint structure.

Experimental analysis of structural nonlinear damping ratio induced by bolt joint friction

Friction is an important source of energy dissipation in structural damping. The effect of friction on the damping ratio, however, has not been fully investigated. This paper presents an experimental study of the nonlinear damping ratio induced by friction at bolted joints of a bridge model in the laboratory. The decay responses of the bridge were tested under various bolt configurations and pre-torques. The nonlinear characteristics of the damping ratio were analyzed, and the experimental results were interpreted through numerical simulations. The relationship between damping ratio and amplitude of the Iwan model was derived. The results show that friction induces a nonlinear damping ratio. The damping ratio exhibits two opposite nonlinear characteristics under the influence of bolt joints. The damping ratio may either decrease with decreasing amplitude or may increase, and both of these nonlinear patterns can be elucidated by the Iwan model. Numerical simulations successfully replicate these two nonlinear damping ratios. A case study of an actual steel truss bridge is used to discuss the possible effects of bolt joints on the damping ratio. The results of this paper reveal the nonlinear damping patterns induced by bolt joints and provide an optional model for such structures.

A novel physics-based modeling approach for tangential fretting contact behavior of jointed interface considering multi-scale effects

A novel physics-based constitutive model has been developed to map the tangential fretting behavior of joint surfaces. The model integrates the fractal normal contact model, which considers multi-scale effects, and the Iwan model through the Coulomb friction law. In this model, a new distribution of yield force is proposed for Jenkins elements, which is determined by fractal topography and material parameters and related to the scale of asperity. The effects of fractal topography, material parameters, and the normal load applied to the joint surface on the tangential responses such as tangential force, tangential stiffness, energy dissipation, and the distribution of yield force have been discussed. It has been found that the fractal parameters D and G have opposite effects on the tangential responses and yield force distribution.

Periodic foundation piles for the seismic protection of structures

This study introduces a novel solution for seismic protection of structures based on resonant metamaterials, named Periodic Foundation Piles, which can be integrated with deformable soil deposits in order to filter shear waves in a specific frequency range. A Periodic Foundation Pile consists of an array of vertical periodic structural elements containing internal resonators suitably tuned to one or more natural frequencies of the soil deposit. The proposed system is equivalent to a discontinuous foundation pile and can be installed in the ground with approximately the same procedure for piles, thus making it suitable also for applications in existing structures. The performance of the Periodic Foundation Piles in reducing the amplitude of a seismic motion has been shown through non-linear site response analyses carried out using real acceleration records as input motion. A soil deposit with an increasing shear wave velocity profile has been considered; the nonlinear behaviour of the soil has been modelled through the Iwan model, calibrated using a normalized secant shear modulus curve accounting for the influence of the confining pressure on the stress-strain relationship. Numerical results, presented in terms of peak acceleration, horizontal displacement and shear deformation profiles, as well as in terms of Fourier amplitude and response spectra, indicate that Periodic Foundation Piles may noticeably reduce the amplitudes of seismic motion in a suitable frequency range, hence potentially representing an innovative strategy to mitigate the effects of earthquakes on structures.

Simulation of Preload Relaxation of Bolted Joint Structures under Transverse Loading

In this study, based on the Iwan model, the connection interface of the bolted joint structure subjected to lateral loads was simulated and comparatively analyzed. Commercial finite element software was used to model the bolted joint structure. Monotonic lateral loads and cyclic displacement loads were applied to the model. The changes in the preload force of the bolted connection structure, as well as the changes in the sticking zone and stress state of the connection interface, were analyzed, and the loading results of monotonic load and cyclic displacement load were compared. The results show that the contact interface stress decreases with the increase in displacement load, and this increase is also a nonlinear relationship, which is approximately in phase with the trend of the contact surface slip curve. The amount of contact surface stress loss and the amount of preload loss are not directly related to the magnitude of the initial preload, regardless of the loading conditions. The contact surface is also circular under any form of displacement loading, whether it is stressed or slipped. The amount of preload loss is proportional to the amount of bolt compression for that variable.

Modeling for Hysteresis Contact Behavior of Bolted Joint Interfaces with Memory Effect Penalty Constitution

A novel penalty contact constitution was developed to replicate the hysteresis memory effect observed in contact interfaces. On this basis, a refined finite element analysis (FEA) was performed to study the stick–slip friction contact behavior of bolted joint interfaces. The analysis was validated by comparing it with the experimental hysteresis loops in the literature. The simulated hysteresis loops were subsequently used to identify four parameters of the Iwan model. Additionally, the effects of bolt clamping, friction coefficient, and excitation amplitude were individually examined. It was found that the deterioration in bolt clamping performance resulted in a decrease in both the equivalent joint stiffness and energy dissipation. Similarly, the reduction in the friction coefficient yielded a comparable impact. Furthermore, the identified model parameters of critical stick–slip force and displacement exhibited a quasi-linear relationship to the bolt preload and friction coefficient.

Tangential contact modeling of joint interface considering elastic-plastic state based on IWAN model

A tangential contact model is proposed to describe the tangential response of the joint interface. Firstly, a normal contact model considering elastic-plastic state is established. Secondly, the tangential contact behavior of asperities subjected to normal load is analogously represented through the configuration of parallel Jenkins elements within the IWAN model. A continuous function with well-defined physical significance is formulated to delineate the distribution of critical slip displacements among asperities. Finally, the precision of the tangential model is affirmed through a comparison with previously published experimental data. Through an investigation of the influences of normal load and surface topography parameters on the slip rate at the joint interface, an in-depth analysis of the contact state of the joint interface is conducted.

Modelling and experimental parameter identification for fasteners in composite–aluminium bolted structures

Deformation of composite–aluminium bolted joints subjected to uniaxial quasistatic tension load is modelled using an Iwan model for each fastener. Experimental data obtained with the digital image correlation technique are used to identify a suitable Iwan model distribution function and parameters to represent the bolts in single-shear and double-shear bolted lap joints. It is seen that the model, with parameters identified from the experiments, represents the displacements of the joint correctly, and an implementation in a commercial finite element software is demonstrated. The proposed model is intended as a computationally efficient structural element for modelling structures containing multiple fasteners.

A novel bolted joint model with stick-slip hysteresis properties considering pressure-dependent stiffness: Theoretical and experimental investigations

Considering the influence of normal pressure on tangential stiffness, in this paper, an improved Iwan model with pressure-dependent stiffness is proposed to better describe tangential stick-slip hysteresis behaviors of bolted fiber-reinforced composite joints. In the model, the expression of the force-displacement relationship is derived from the evolution of the slip area. The parameters of the model are obtained based on multi-scale fractal contact theory, which avoids the inconvenience of parameter estimation methods requiring special quasi-static experiments. Meanwhile, the tangential behavior experiment of bolted fiber-reinforced composite joints is carried out. By comparing the hysteresis curve results and the stiffness softening law, the accuracy of the model and the necessity of considering the pressure dependence of the tangential stiffness are proved.

Modelling tangential friction considering contact pressure distribution of rough surfaces

Frictional interfaces play an important role on the dynamic response of jointed structures. To accurately predict the dynamics of jointed structures, the phenomenological Iwan-type models, which consist of many spring-slider elements in parallel or series, are often used to describe interface frictional behavior. In this paper, a novel tangential friction modelling approach based on the framework of Iwan model is proposed. Specifically, the density function of slider critical slip force, which is vital to deduce the final form of Iwan model, is determined by a new method. The method is based on the real rough surface and contact pressure results due to rough contact are introduced to derive the form of Iwan model. This provides a physical method to derive the density function of slider critical slip force, while in the past the density function is usually assumed artificially without a clear physical meaning. In the proposed method, twofold Weibull mixture model is used to represent the contact pressure distribution of actual rough surfaces. Following this, the corresponding Iwan density function is derived based on the local Coulomb friction. Then substituting Iwan density function into Iwan model, the explicit relationship between the tangential force and the relative displacement is deduced. The proposed modelling approach is applied to sphere-on-sphere contact and the comparison between the simulation and theoretical results shows perfect agreement. Then, the proposed modelling approach is validated against published experimental results for a flat-on-flat contact and a bolted joint. Compared to the classic Iwan model, the proposed model can better match the experimental results at the transition from microslip to macroslip. This study considers the influence of real rough contact characteristics on tangential friction behavior and provides a new tangential friction model deriving method.

An approach of micro-slip modeling based on asymmetric contact pressure distribution and its application in nonlinear boundary beam system

A novel micro-slip friction modeling approach based on the Iwan model is presented here. The normal load and tangential stiffness are reassigned reasonably to obtain the tangential force–displacement expression, and the relationship between the asymmetry of contact pressure distribution and the Iwan density function is established. The micro-slip model depends on the distribution of contact pressure, and has the ability to degenerate into a macro-slip model. Based on the model, a simplified non-linear dynamics model of a rotating blade with a dovetail joint is developed, and its effectiveness is verified by comparing it with a relevant reference. The first-order bending vibration of the blade under distributed excitation is analyzed. The results indicate that the pressure distribution of the contact interface has a significant effect on the amplitude–frequency response of the blade and the contact behavior on the joint interface. Compared with the proposed micro-slip model, the single point contact model overestimates the response amplitude. The amplitude–frequency curve obtained by this model is obviously different from the macro-slip model. It is proved that the micro-slip model can more accurately simulate the nonlinear vibration characteristics of tenoned blades, which provides new insights for the study of the vibration characteristics of tenoned blades.