Tangential Damping Research Articles

Modelling and stability analysis of a high-speed train braking system

The stability of a braking system is crucial for the steady and safe operation of trains. To investigate the dynamic behaviors and stability of a train braking system as influenced by key parameters, a numerical model integrating mode-coupling, negative friction–velocity slope (NFVS), and stick–slip theories was established. Additionally, the wheelset connected with the braking system was contained in the model considering that mode-coupling and stick–slip characteristics were affected by system structures. Based on this model, the influence and mechanism of stiffness, damping, and NFVS characteristics on mode-coupling of the braking system were revealed. The results showed that when the tangential and normal contact stiffness values of the pad were close, the system experienced mode-coupling instability and vibrations in these two directions were coupled. When the tangential and normal damping values of the pad were unequal, the energy dissipation in the two directions became different and the system instability was enhanced. Additionally, the system complex eigenvalues always had positive real parts and the dynamic behaviors were more complicated by considering NFVS at relatively low speeds. This is because NFVS characteristics can be equivalent to negative damping values, which cause the difference in tangential and normal damping values and continuously input energy into the braking system, then weakening the system stability.

Theoretical Model of Tangential Contact Stiffness and Damping of Solid-Liquid Interface in Macroscopic Relative Motion

Theoretical Model of Tangential Contact Stiffness and Damping of Solid-Liquid Interface in Macroscopic Relative Motion

Dynamic Friction-Slip Model Based on Contact Theory

In ultra-precision positioning equipment, the positioning accuracy is affected by the friction characteristics, especially the pre-slip stage. At present, the research on friction mainly includes contact theory and the dynamic friction process. There is no time variable in contact theory models, so they only apply to the stage of static contact, while the establishment of a friction dynamics model depends on parameter identification and cannot reflect the influence of a rough morphology and load. Therefore, neither theory can elucidate the ultra-precise slip mechanism. In this paper, maximum static friction force, tangential stiffness, and tangential damping models of contact surfaces were deduced through fractal contact theory. By substituting the contact parameters into the modified LuGre model, a dynamic slip model of the mask was established. Finally, the above model was verified by a reticle dynamic slip measurement system. The experimental results showed that in the pre-slip stage of the reticle, with an increase in the normal external load, the slippage of the reticle decreased. The theoretical value calculated by the model was basically consistent with the experimental value, and the slippage of the reticle mainly originated from the tangential deformation and relative sliding of the contact surface. With the increase in the normal external load, the proportion of the tangential deformation in the sliding of the entire contact surface was larger. For the change in slippage during different motion stages, the theoretical value was close to the experimental value after eliminating system errors such as vibration and fiber bending, which proved the correctness of the model in this paper.

Dynamic Tangential Contact Stiffness and Damping Model of the Solid–Liquid Interface

In order to establish the tangential contact stiffness and damping model of the solid–liquid interface by tangential exciting vibration force under mixed lubrication, the finite difference method was firstly used to solve the average flow equation considering the effect of roughness on the lubrication effect, and the bearing capacity, shear force, and friction coefficient of the oil film were obtained, and thereby the dynamic tangential contact stiffness and damping of the oil film under tangential harmonic excitation were calculated. Then, according to the relationship between the normal deformation and the load of the solid contact microconvex body in the elastic/elastic–plastic/plastic deformation stage, integrating the tangential stick–slip theory, considering the effect of fluid lubrication on the solid contact friction coefficient, and tangential dynamic excitation, the tangential contact stiffness and damping of the microconvex body in three deformation stages were calculated. Furthermore, the dynamic tangential contact stiffness and damping of the solid–liquid interface were obtained by summing the solid surface contact part and the solid–liquid contact part in parallel according to the assumption of microconvex Gaussian distribution. Finally, through simulation analysis and experiments, the variation of the tangential dynamic contact stiffness and damping of the solid–liquid interface with normal load, tangential exciting frequency, and displacement amplitude was revealed and verified.

Contact Characteristics and Tribological Properties of the Weaving Surface of Mn-Cu and Fe-Zn Damping Alloys.

In this paper, laser texturing is performed on the surface of Mn-Cu and Fe-Zn damping alloys and the tribological properties of the samples with various surface weaves under dry-sliding conditions are investigated. The results show that the surface weave parameters affect the size of the contact surface and change the number of micro-convex bodies at the contact interface. This leads to changes in the tangential damping of the contact and further affects the magnitude of the friction coefficient. Additionally, the damping properties significantly affect the wear mechanism and make it more prone to adhesive wear.

An improved fractal model for tangential contact damping of high contact ratio gear considering friction effect

On the basis of the M-B fractal theory, a geometric model and contact mechanical model of the tooth surface contact mode were analyzed. According to the energy dissipation mechanism of tangential contact damping, a tangential contact damping model of tooth surface considering variable friction under dry friction condition was established by introducing the correction coefficient of tooth surface. First, obtained the load and tangential damping of a micro-convex body, and then the contact load and tangential contact damping of the tooth surface are obtained by integrating on the tooth surface. It was shown that the tangential contact damping of tooth surface is affected by various parameters including roughness amplitude, fractal dimension, curvature radius of tooth surface, normal contact load and tangential normal load ratio. The simulation results show that the tangential contact damping gradually increases when the normal contact load, friction coefficient, curvature radius of driving wheel and roughness amplitude increase. The tangential contact damping on the tooth surface increased with the increase in the tangential normal load ratio. When the tangential normal load ratio is 0.09, the tangential contact damping of the tooth surface reached a maximum, and then decreased with the increase of the tangential normal load ratio. The change in the tooth surface tangential contact damping with the fractal dimension is similar to the change in the tangential normal load ratio, which also increased and then decreased. When the fractal dimension is approximately 1.64, the tangential contact damping of the tooth surface reached the maximum. The tangential contact damping of tooth surface increases with the increase of modulus, transmission ratio and the number of teeth of the driving gear, and the number of teeth and modulus have a great influence on it, while the influence of transmission ratio is relatively weak.

Tangential Damping Model of Bolted Joint with the Physics-Based Friction Coefficient

The stiffness and damping modeling of joint surfaces are important for analyzing the dynamic characteristics of bolted joints, which has a great influence on the working precision of the machine tool. In this paper, a damping model is presented to predict the tangential damping of the joint accurately. The fractal theory is introduced to characterize the rough contact surface by using fractal dimension D and fractal roughness parameter G. For each micro-contact, the contact region can be divided into stick section and slip one. The energy dissipation of the micro-contact, which can be described as the tangential damping of bolted joint, emerges in the slip section. The physics-based friction coefficient is introduced to define the energy dissipation function based on the relationship between the deformation of micro-contact and the normal pressure. The energy dissipation factor and the proportional damping of the micro-contact can be obtained. The total tangential damping of bolted joint can be obtained by integrating the whole contact surfaces. Experimental set-up is designed to verify the proposed model. Compared with the constant friction coefficient damping model, the results show that the proposed model can more accurately describe the tangential damping of bolted joint.

МЕХАНИЗМ ОБРАЗОВАНИЯ ТРЕЩИН В КЛАДКЕ ЛИЦЕВОГО СЛОЯ НАРУЖНЫХ СТЕН ПРИ ТЕМПЕРАТУРНЫХ ВОЗДЕЙСТВИЯХ

On the basis of the carried out experimental and numerical studies, the mechanism of crack formation in the masonry of the face layer with flexible ties under temperature influences has been established. Experimental studies were carried out for five years on a floor-high fragment of a building formed by external three-layer walls resting on a monolithic reinforced concrete slab. Numerical studies were carried out using the author's specialized program for calculating masonry structures, which implements the finite element method, taking into account structural nonlinearity. The program was verified by comparing the calculation results with the experimental data, as well as at the stage before the formation of cracks using the LIRA-SAPR program. It is shown that, depending on the ratio of the tensile strength of the masonry along the vertical joints and the cut along the horizontal mortar joints, different variants of crack development are possible. Vertical cracks, like expansion joints, reduce tensile and shear stresses. Cutting the masonry along the horizontal mortar joint at the base of the wall leads to a reduction in the length of the area of influence of the floor slab. Together, this leads to a decrease in the level of tensile and tangential stresses and damping of the crack propagation process. At the top of the wall, the effect of the floor slab on the stress-strain state of the masonry is relatively small and the temperature deformations there are close to free. This made it possible to apply a simplified methodology for assessing the crack opening width. A method is proposed for calculating the facing layer masonry for temperature effects and for assigning distances between vertical expansion joints.

In Situ Investigation of Load-Dependent Nonlinearities in Tangential Stiffness and Damping of Spherical Contacts

Abstract Seemingly stationary (pre-sliding) interfaces between different materials, parts, and components are major sources of compliance and damping in structures. Classical pre-sliding contact models assume smooth elastic contact and predict that frictional slip leads to a well-defined set of stiffness and damping nonlinearities. However, reported data deviate from those predictions, and literature lacks a conclusive evidence leading to those deviations. In this work, the authors measure tangential stiffness and damping capacities inside a scanning electron microscope (SEM) while monitoring contacts between a rigid spherical probe and two materials (high-density polyethylene (HDPE) and polyurethane elastomer). Measured force, displacement, contact area, stiffness, and damping are then compared with predictions of classical models. In situ SEM images synchronized to the tangential force–displacement responses are utilized to relate the degree of plasticity and geometric alterations to stiffness and damping nonlinearities. In agreement with the classical models, increasing tangential loads cause softening in contacts under light normal preloads. In contrast, stiffness for HDPE increases with increasing tangential loads at heavy normal preloads due to plasticity and pileups over the contact. Material damping is prevalent for all loading cases in polyurethane samples thanks to nearly fully adhered contact, whereas for only light tangential loads in HDPE. With increasing tangential loading, specific damping capacity of HDPE contacts increases tenfold. This nonlinear increase is due to plastic shearing and frictional losses induced by tangential loading. Those findings suggest that predictive interface models should include geometric alterations of contact, plasticity, and material damping.

Investigation of Tangential Contact Damping of Rough Surfaces From the Perspective of Viscous Damping Mechanism

AbstractThe contact damping between rough surfaces has an important influence on the wear, vibration, contact fatigue, and energy dissipation between interfaces. In this paper, based on contact theory, a tangential damping mathematical model of rough surfaces is established from the point of view of viscous contact damping energy dissipation mechanism of asperities and considering the fractal characteristics of three-dimensional topography of rough surfaces. Through the combination of micro-contact modeling and macro dynamic testing of composite beams, the analysis results show that there are important evolution rules between tangential damping and surface fractal parameters and material parameters. The nonlinear relations between them are as follows: tangential contact damping is positively correlated with normal load, load ratio, and maximum contact area of asperity, and negatively correlated with fractal roughness; tangential contact damping increases first and then decreases with the increase of three-dimensional fractal dimension. The results of computational and experimental modal analysis show that the established mathematical model is feasible for predicting tangential damping. The study of tangential contact damping between surfaces can lay a foundation for improving the performance of assembly interfaces.

Investigation on stiffness and damping of transient non-Newtonian thermal elastohydrodynamic point contact for crowned herringbone gears

Abstract The stiffness and damping models of elastohydrodynamic point contact for herringbone gears with crown modification both in normal and tangential directions are developed. The lubrication performance of crowned herringbone gears in transient non-Newtonian thermal elastohydrodynamic point contacts are investigated to validate the developed models. The effects of operating and geometric parameters of crowned herringbone gear on stiffness and damping of elastohydrodynamic point contact are analyzed. The results show that in herringbone gear transmission, crown modification significantly affects oil film stiffness and damping. Low rotation speed substantially increases the damping. Helix angle contributes to the tangential stiffness and damping. This indicates that rationally selecting parameters can obtain appropriate oil film stiffness and damping to alleviate impact and vibration of herringbone gears.

A Model of Tangential Contact Damping Considering Asperity Interaction and Lateral Contact

A precise tangential contact damping model is proposed, which includes the lateral contact of the upper–lower asperities and the interaction of adjacent asperities. The effects of the normal static preload, frequency, and amplitude of tangential displacement on the tangential contact damping were analyzed by simulation, respectively. Furthermore, the results of simulation are verified by experiment. The tangential contact damping of considering the interaction and lateral contact of asperity is very close to the experimental results.

Comprehensive multivariate sensitivity analysis of CFD-DEM simulations: Critical model parameters and their impact on fluidization hydrodynamics

The development of CFD-DEM is critical for investigating particle phenomena and their coupling with reactor transport. However, there continues to be considerable uncertainty in the selection of model parameters because of limitations in: (a) experimental measurements of multi-particle interactions, and (b) computational resources which have restricted most numerical studies to 2D simulations, in very small-scale systems (<50k particles) and/or to local sensitivity analysis. The focus of this study is to identify critical model parameters in 3D CFD-DEM simulations of fluidized beds through multivariate sensitivity analysis and quantify their impact on hydrodynamics. Towards this end, thirteen model parameters are considered and the sampling design matrix is constructed using the Morris-One-At-a-Time (MOAT) screening method. 3D CFD-DEM simulations with almost 170,000 glass bead particles (0.4 mm diameter) are conducted in a small rectangular pulsating fluidized bed, selected because of its repeatable bubbling patterns. Detailed bubble and particle dynamics data from 250+ simulations show that: (a) choosing exceedingly low normal spring stiffness has strong implications on particle velocities; (b) the impact of all contact dissipation parameters (normal restitution, friction and tangential damping) is tightly coupled and sensitivity to any one hinges on the choices of others; and (c) the stability of bubble patterns is contingent on their choices and almost-ideal as well as extremely dissipative systems exhibit no patterns. In addition, by investigating particle dynamics inside and around bubbles, we derive a working expression for the optimal choice of spring stiffness. Overall, this first-of-its-kind analysis provides important guidelines for CFD-DEM model parameter selection and the statistical framework developed here provides a robust strategy for the fundamental investigation of other particle-scale phenomena and simulation-based reactor design and optimization.CFD-DEM, gas-solid fluidization, pulsating reactor, multivariate sensitivity, linear spring-dashpot model, spring stiffness

Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive

• New stiffness and damping models are developed for oil film in normal and tangential directions. • Smaller lubricant stiffness is beneficial for alleviating gear meshing impact and shear vibration. • Meshing impact and friction heat is suppressed by either larger normal lubricant damping or smaller tangential lubricant damping. • Better combined stiffness and damping can be achieved by optimizing gear geometric parameters and operating conditions. Innovative stiffness and damping models for oil films are developed to account for the impacts in both normal and tangential directions. Given that these models are applied to a gear drive in line contact elastohydrodynamic lubrication (EHL), the combined stiffness is derived from the stiffness of both the oil film and gear tooth while the combined damping is established from the damping of these parts. The effects of three fundamental parameters (contact force, rotation speed, and tooth numbers) of the gear drive in line contact EHL on the combined stiffness and damping are then investigated. The results reveal that the small normal and tangential stiffness of the lubricant can alleviate meshing impact and shear vibration, while the impact and friction heat can be reduced by using an oil film with either a large normal damping or small tangential damping. Given that its amplitude and fluctuation are closely related to shear rate, effective viscosity, entrainment velocity, and curvature radii, the improved combined stiffness and damping can be obtained by rationally matching the geometric and operating parameters.

A piezoelectric active sensing method for quantitative monitoring of bolt loosening using energy dissipation caused by tangential damping based on the fractal contact theory

Monitoring of bolt looseness is essential for ensuring the safety and reliability of equipment and structures with bolted connections. It is well known that tangential damping has an important influence on energy dissipation during wave propagation across the bolted joints, which require different levels of preload. In this paper, the energy dissipation generated by tangential damping of the bolted joints under different bolt preloads was modeled analytically based on fractal contact theory, which took the imperfect interface into account. A saturation value exists with the increase of the bolt preload, and the center frequency of emitted signal is demonstrated to affect the received energy significantly. Compared with previous similar studies based on experimental techniques and numerical method, the investigation presented in this paper explains the phenomenon from the inherent mechanism, and achieves the accurate quantitative monitoring of bolt looseness directly, rather than an indirect failure index. Finally, the validity of the proposed method in this paper was demonstrated with an experimental study of a bolted joint with different preload levels.

A generic wear prediction procedure based on the discrete element method for ball mill liners in the cement industry

A generic procedure to predict the wear evolution of lining surfaces, namely the spatial distribution of wear and the progressive modification of the geometry due to wear, is introduced in the context of shell liners in ball mills. The wear data is accumulated on the surface of the liner by 3D discrete element method (DEM) simulations of the ball charge in an axial slice of the mill, which is either closed by a periodic boundary condition or by frictionless end walls. The calibration of this wear data with the measured wear profiles of the shell liner in a 5.8m diameter industrial cement tube mill shows that the tangential damping energy defined by the linear spring-slider-damper DEM contact law is the best fitting wear model of 6 different models. The gradual update of the liner shape delivers adequate results for liners without an axial height variation, while the accuracy of fully variable geometrical modifications is limited by the computation time. Nevertheless, detailed phenomena, like the creation of grooves in the liner, were for the first time numerically modeled.

Study on tangential stiffness and friction damping of rough contacts

Study on tangential stiffness and friction damping of rough contacts

Stiffness and Damping Properties of a Swing Clamp: Model and Experiment

The dynamics of a workpiece, and hence its behaviour in a machining process, is significantly influenced by the fixture system. In such assembled systems, contacts between the parts have great impact on the vibration characteristics of the complete structure. Prediction of the dynamic behaviour of a workpiece-fixture-system can help to avoid undesirable results like poor workpiece surface quality and thus a reduction of rejects can be achieved. This paper introduces experimental studies and a model for describing the tangential stiffness and damping properties of a swing clamp. A modification of an existing material model was used to represent the transfer function, in terms of force and relative displacement, between the contact surfaces. An experimental setup for assessing the model parameters was established. An approach for parameter extraction is also provided. The proposed model can be adapted for other clamping mechanisms.

Seismic behavior of soil–pile–structure interaction with a modified Desai thin-layer interface element

The Desai thin-layer interface element is widely utilized in the simulation of interaction between piles and soil under seismic load. Conventional seismic analysis using the interface element cannot simulate the process of energy dissipation because tangential damping is disregarded. In this study, Rayleigh damping is added to the interface element to simulate energy dissipation in a strong nonlinear contact behavior. A user-defined element program based on a modified Desai interface element is developed. A hyperbolic model is adopted to simulate normal and tangential interaction behaviors. Certain behavior pattern rules of the modified Desai element, such as bonding, slipping, gapping, and reclosing, are defined. A three-dimensional pile–soil–structure model with a modified Desai interface element is established to investigate the effect of contact patterns on the inner force responses of a superstructure and pile foundation to an earthquake. Numerical results show that the contact patterns significantly influence the shear force, bending moment, and torque of the superstructure, while axial force is unaffected. With regard to the pile foundation, shear force and bending moment are also significantly influenced.

Stiffness and Damping Model of Bolted Joints with Uneven Surface Contact Pressure Distribution

Bolted connections are widely employed to fix the structural components, in which the bolted joint is one of the weakest parts and can significantly affect the dynamic characteristics of the machine tool. In this research, a stiffness and damping model based on the uneven surface contact pressure is presented for the bolted joint to accurately predict the dynamic characteristic of a bolted assembly. The normal and tangential stiffness and damping of the contact surface can be deduced based on the fractal contact theory. However, the contact surface pressure of bolted joint is unevenly distributed due to the influence of the concentrated force of multi-bolts. Therefore, the pressure of the contact surface is introduced to define the stiffness and damping of bolted joint. The assumption is that the contact surface is flat in the macro-scale. Then, we can obtain the pressure distribution of contact surface through the finite element (FE) method. The nonlinear relationship of stiffness, the damping of the bolted joint, and the pressure of contact surface can be obtained and assigned to the FE model based on the pressure distribution of the contact surface. An experimental set-up with a box-shaped specimen is designed for validating the proposed model. The equal pre-tightening force and bending moment effect case studies are provided to demonstrate the effectiveness of the model. The results show that the proposed model can be used to accurately predict the dynamic characteristic of the machine tool.