Nonlinear Friction Behavior Research Articles

Numerical modeling and experimental validation for suspended ceiling system with free boundary condition

As one type of commonly used non-structural component in public buildings, suspended ceilings (SCs) may suffer severe damage or even collapse under earthquakes. However, convincing numerical simulation on the SC is scarce due to its strongly nonlinear behavior. A refined numerical model for SC with free boundary condition is developed based on a full-scale shaking table test in this study. Grid connections, between main tees, main tee and cross tee, and cross tee and sub cross tee, are the main source of strong nonlinearity in SC. Their hysteretic models are built according to the cyclic loading tests first. The nonlinear impact and friction behavior at the ceiling perimeter are also considered. By conducting time history analysis of SC, the simulated responses of acceleration, displacement, and axial force of grid members are analyzed and compared with shaking table test results. The comparison results demonstrate that the proposed model is capable of predicting the seismic responses of the SC. Lastly, parametric analysis is conducted to investigate the influence of the width of peripheral gap, the length and diameter of threaded rods, and the thickness of panels on the seismic performance of SC. Outcome of this study is beneficial for modeling and seismic design of SC system.

Mathematical modeling for nonlinear dynamic mixed friction behaviors of novel coupled bearing lubricated with low-viscosity fluid

This paper aims to develop a mathematical model for investigating the nonlinear dynamic mixed friction behaviors, including hydrodynamic force, contact force, deformation, and displacements, of the novel coupled bearing lubricated with low-viscosity fluid. The model fully couples the five-degrees-of-freedom rotor dynamic model with the mixed elastohydrodynamic lubrication model of the novel coupled bearing, considering the unbalance and exciting forces/comments caused by the propeller rotor. A comparative analysis is carried out to validate the effectiveness of the present model. Through the numerical simulation, the dynamic nonlinear mixed friction behaviors of the novel coupled bearing under low-viscosity lubricant are revealed. Based on the established mathematical model, a series of parametric studies are conducted to explore the effect of the structural parameters on the nonlinear mixed friction behavior of the novel coupled bearing. Numerical results demonstrate that the exciting moments increase the range of the journal orbit, thereby generating the edge asperity contact for both the journal and thrust bearings. The angular displacement along the y axis improves the transient mixed friction performances of the thrust bearing. Furthermore, numerical results reveal that the increasing length–diameter ratio of the journal bearing (the specific pressure remains constant) improves the nonlinear dynamic mixed friction behaviors of the thrust bearing. In addition, the nonlinear dynamic mixed friction performance of the journal bearing becomes better with the increase in the thrust bearing radius.

Experimental study on nonlinear friction behavior of granular flow lubrication

Solid granules have good lubrication performance and load-bearing capacity, which has been concerned by researchers. However, the correlation mechanism between lubrication performance and granular medium dynamics is hardly focused on. In this study, the characteristics of two parallel friction pairs lubricated by the granular medium are experimentally investigated to study the nonlinear friction behavior during this process. The experimental results showed that the fluctuation behavior of friction force and friction coefficient with time shows a more flat nonlinear trend with the increase of the shear velocity and the pressure load. The discrete element simulation results corresponding to the experiment revealed that the change of nonlinear behavior of measured friction and friction coefficient is closely related to the evolution of force chains and dynamic characteristics of this granular flow lubrication system. The shear dilatancy amplitude of this granular flow lubrication system decreases obviously with the increase of the shear velocity and the pressure load. The flow states of granular medium is the main reason influencing the nonlinearity of shear gap. This study reveals the key factors affecting the friction nonlinearity and provides an evidence for the formation of granular shear dilatancy between two friction pairs lubricated by granular medium.

Measurement and Modelling of a Cycloidal Gearbox in Actuator with Permanent Magnet Synchronous Machine

Compact geared servo drives are a common part of modern industrial automation; thus, their proper modelling is a necessary part for the application and control design. The presented paper focuses on the mathematical model of the cycloidal gearbox, which is used in the compact actuator with a permanent magnet synchronous motor. A measurement procedure to obtain the necessary gearbox parameters is presented along with its mathematical model. A new approach was used to model the stiction and nonlinear gearbox friction behaviour in all four quadrants. A simulation of the actuator with the modelled gearbox is described and its results are compared with the real system measurement. Obtained results show a high match between simulation and experimental results and confirm the correctness of the simulation model.

An extended LuGre model for estimating nonlinear frictions in feed drive systems of machine tools

Nonlinear frictions in feed drive axes affect the control accuracy and dynamic of the machine tools. Conventional dynamic friction models neglect the position-dependent friction, caused by manufacturing errors and misalignment as well as the environment. This paper proposes an extended LuGre friction model for estimating the dynamic and position-dependent friction effects. The conventional LuGre model is modified by a position-dependent term, which describes the nonlinear friction behavior of machine axes with long travel distance. An online data-driven identification approach is developed to fast parametrize and update the model. The suggested method is validated on a real machine tool.

Nonlinear analysis of the ballast influence on the train-bridge resonance of a simply supported railway bridge

In the present work, the influence of the ballast-deck interface on the dynamic response of single ballasted track, simply supported high speed railway bridges is investigated. The ballasted track railway bridge is modelled by a composite Euler-Bernoulli beam with two layers connected between them through longitudinal springs and dampers representing the nonlinear friction behavior occurring at their interface. A constant moving load model termed (HSLM-A) is utilized to simulate the moving trains. The governing nonlinear transverse vibration equation of the system has been derived by using the Hamilton’s principle. By applying the Galerkin method and using the Differential Quadrature Method (DQM) and the Integral Quadrature Method (IQM), the time history of the studied beam is numerically solved by the Runge-Kutta scheme. Considering two railway bridges having different lengths, the obtained results have shown that the dynamics of the system is governed essentially by a Duffing like oscillator, where the ballast superstructure contributes through both additional nonlinear stiffness and damping. The ballast-bridge interface was found to affect largely the dynamic response at resonance of short-span bridge than that of lengthier structures. In this last case the ballast influence can be reduced to just an additional mass.

Strain-Induced Nonlinear Frictional Behavior of Graphene Nanowall Films.

Graphene nanowall (GNW) films, a representation of three-dimensional (3D) carbon nanomaterial films, are emerging as promising candidates for applications in electric devices and composites, on account of their 3D structures and exceptional properties of graphene sheets. However, the frictional responses of GNW films, which exhibit significant influence on their performances, have seldom been reported. Herein, we reported a growth process of a GNW film by the chemical vapor deposition method and studied the frictional behavior of the GNW film for the first time. The results demonstrated the nonlinearity between the frictional force of the GNW film and normal load. Based on the structural evolution of the GNW film with normal load and frictional tests on precompressed GNW films, the influence of the strain property of the GNW film, namely, the strengthening effect, could be confirmed. The results of molecular dynamics simulations show that the bending force of GNWs in front of the tip plays a determinate role in the frictional force of the GNW film. Furthermore, the bending force is proportional to the bending contact area, which increases nonlinearly with the normal load due to the strengthening effect of the GNW film. The result suggests that the nonlinear increase of the bending contact area induced by the strengthening effect of the GNW film is the key factor that leads to its nonlinear frictional force. This study provides a novel insight into the frictional responses of GNW films, which would be beneficial for the design and application of electric devices and composites made of GNW and other 3D carbon nanomaterial films.

Nonlinear friction behavior in ultrasonic welding of aluminum alloy to carbon fiber reinforced PA6 composite

Accurate prediction of the friction-mediated interaction between workpieces in ultrasonic welding requires nonlinear multi-physical models. Local contact points that are in slip receive a heat flux from friction, which raises the local temperature and therefore, changes the local material stiffness and local stresses. These local changes affect the contact status and the overall dynamics. The effects of vibration amplitude and clamping force on the nonlinear friction behavior in ultrasonic welding of aluminum alloy to carbon fiber reinforced thermoplastic (CFRTP) are particularly important process parameters that can be controlled. Their effect is investigated through a multiphysics coupled model with consideration of the nonlinear contact, nonlinear structural dynamics, and the transient heat conduction. Solutions are obtained by combining the harmonic balance method with the finite element method. Intuitively, large amplitudes promote sliding and higher heating, while large clamping forces can promote sticking and lower heating. Unexpectedly however, results show that the amplitude has a limited influence on the process, while the clamping force has a significant influence. That is because optimal heating results from a balanced manifestation of sticking, sliding and temperature at the interface. In particular, results suggest that a low clamping force with a high vibration amplitude is desirable for the ultrasonic welding of aluminum alloys to CFRTP composites.

Nonlinear frictional contact behavior of porous polymer hydrogels for soft robot

Focusing on the oblique frictional contact problem of hydrogel for soft robot, a numerical contact model is developed to analyze the nonlinear behaviors including local contact large deformation and friction effect of hydrogel soft material during oblique contact. Based on the constitutive relation of hyperelastic material, the updated free energy function of hydrogel is derived. The contact algorithm is given to compute the contact responses of both collinear contact example and oblique contact example. The applicability of classical Hertz contact theory is discussed. The influence of coefficient of friction on the stress distribution of contact zone and the contact states of contact surface are also investigated. The numerical results show that the material nonlinearity and the geometric nonlinearity (i.e. large deformation) of hydrogel lead to the invalidation of classical Hertz contact theory. For the oblique contact, the internal stress grads of hydrogel will be redistributed as the coefficient of friction increases. Meanwhile, the maximum stress position moves from underside to the contact surface. Two high stress zones occur inside and on the contact surface at the same time, respectively. Besides, when the coefficient of friction is smaller (i.e. <i>μ</i> < 0.05), for the collinear contact all contact points on the contact surface are in critical state from static friction to dynamic friction. But for the oblique contact, some contact points are always in stable static friction state.

Validation of a Coupled Simulation for Machine Tool Dynamics Using a Linear Drive Actuator

In order to ensure high productivity capabilities of machine tools at a low cost but at increased geometric accuracy, modeling of their static and dynamic behavior is a crucial task in structure optimization. The drive control and the frictional forces acting in feed axes significantly determine the machine’s response in the frequency domain. The aim of this study was the accurate modeling and the experimental investigation of dynamic damping effects using a machine tool test rig with three-axis kinematics. For this purpose, an order-reduced finite element model of the mechanical structure was coupled with models of the drive control and of the non-linear friction behavior. In order to validate the individual models, a new actuator system based on a tubular linear drive was used for frequency response measurements during uniaxial carriage movements. A comparison of the dynamic measurements with the simulation results revealed a good match of amplitudes in the frequency domain by considering dynamic damping. Accordingly, the overall dynamic behavior of machine tool structures can be predicted and thus optimized by a coupled simulation at higher level of detail and by considering the damping effects of friction. Dynamic testing with the newly designed actuator is a prerequisite for model validation and control drive parameterization.

Experimental and computational investigations of nonlinear frictional behavior in threaded fasteners

The conventional engineering design of threaded fasteners applies a linear model determining axial force from fastening torque and was found to be applicable only for vanishing inelastic deformations. Applications of the linear formula can result in a significant over-estimate of the axial force. Detailed experiments reveal that plasticity and wear damage in contact surfaces change frictional behavior and cause an over-proportional increment in tightening torque. A modified friction model was proposed based on the frictional dissipation energy and verified experimentally and computationally. The corresponding force-torque model shows good consistency with experiments and can be applied to predict plastic fastening processes.

Study of the identification model of tribological interaction of friction couples

In this paper identification of dynamic systems under conditions of unlubricated friction is analyzed and problems related to the dynamics of materials frictional interaction are considered. Algorithms of automatic control and catastrophe theory were used to study frictional properties of materials. The authors developed a special device to study tribotechnical characteristics of materials. A mathematical algorithm for studying the tribological contact in the form of a tribological system based on the input-output models is presented. The scope of application, requirements for input and output data, use of the algorithm in case of contact surface evolution are determined. The results obtained indicate the nonlinear friction behavior for friction couples PTFE-Copper, PTFE-Steel and PTFE-Titanium. The relationship between the stability of the system and changes occurring in the tribocontact was found. Processing of obtained dynamic characteristics of tribological interaction of friction couples shows periods of material wear and energy consumption for the formation of a new surface in terms of time

Semi-analytic modelling of cutting forces in micro ball-end milling of NAK80 steel with wear-varying cutting edge and associated nonlinear process characteristics

Cutting edge of miniature ball-end mill is one of decisive importance for the machining performance by affecting the thermal and mechanical load in cutting process. In this paper, a semi-analytic model is proposed to estimate the cutting forces in micro ball-end milling of NAK80 steel considering wear-varying cutting edge and the associated nonlinear process characteristics. The wear-varying cutting edge geometry under the different wear stage is obtained by 3D optical profilometer. The measured results indicate that cutting edge of miniature ball-end mill under the different wear stage includes not only the enlarged cutting edge radius but also the extended flank wear land, which can be described by a combination of edge radius and flank wear land width. The influence laws of the edge radius and flank wear land width on tangential and feed force coefficients are investigated, and the enlarged edge radius and extended flank wear land under different wear stage could be separated from each other by utilizing the cutting force coefficients data based on their different sensitivity on cutting forces. A semi-analytic method is developed to predict the shearing/plowing/friction forces in primary and tertiary shear zones based on classical oblique cutting and slip-line field model. The nonlinear tool-chip friction behavior with the phenomenon that the ratio of tool-chip contact length to uncut chip thickness and friction factor nonlinearly change with the ratio of uncut chip thickness to edge radius are investigated and employed to estimate rake/shear/friction angles, and the nonlinear strain gradient plasticity effect with the fact that effective strain gradient is affected by not only rake angle and shear angle, but also primary shear zone thickness that obviously increases with reduce of the ratio of uncut chip thickness to edge radius are considered to estimate the shear flow stress. The nonlinear behavior derived from the tool-chip/workpiece friction and material constitutive affects the contribution level of size effect on cutting forces in micro ball-end milling. Finally, to calibrate and validate the effectiveness of the proposed cutting forces model, a set of micro ball-end milling of NAK80 steel experiments are performed on a three axis ultra-precision machine by using same solid carbide tool with wear-varying cutting edge under different wear stage. The comparisons between the predicted and measured results show that the proposed model can provide higher accuracy and better understanding for micro ball-end milling of NAK80 steel.

Probing the Self-Assembly and Nonlinear Friction Behavior of Confined Gold Nano-Particles.

For the wide application of nanoparticles (NPs) (e.g., in nanotribology), it is of fundamental and practical importance to understand the self-assembly and lubrication behavior of confined NPs. In this work, a systematic study was conducted to probe the assembly and associated surface forces of spherical gold nanoparticles (Au NPs, diameter ∼5 nm) confined between pairs of mica (negatively charged) and (3-aminopropyl)triethoxysilane modified mica (APTES-mica, positively charged) surfaces using a surface forces apparatus (SFA) under aqueous conditions. It is observed that Au NPs were squeezed out of the confined gap between two mica surfaces during the loading process, resulting from the repulsive electric-double layer force. In contrast, multilayers of Au NPs were confined between two APTES-mica surfaces because of the attractive double-layer force between oppositely charged Au NPs and APTES-mica. Interestingly, the interaction between Au NPs and APTES-mica is stronger than the interactions between Au NPs, resulting in the rearrangement of the confined Au NPs under shearing. Importantly, a large friction coefficient (μ > 0.7) with unexpected nonlinear stick-slip friction was observed when sliding two APTES-mica surfaces with thin layers of Au NPs (∼20 nm) confined in between. The observed stick-slip motion could be explained by the velocity-dependent friction model where a critical shear velocity was required for transiting from stick-slip to smooth sliding. Our study provides useful information on the assembly and interaction forces of confined nanoparticles on charged surfaces, with implications for predicting the behaviors of NPs under confinement in various engineering applications.

Assessment of Friction Behavior with Surface Location Error Analysis in Milling Process

Accurate roundness or circularity measurement is essential to obtain correct functioning of assemblies, making roundness an important quality control parameter in manufacturing industry. Since circular motion while milling a circular work piece leads to quadrant glitches, a phenomenon familiar with existence of highly nonlinear friction behavior, roundness measurement was conducted to investigate this surface location error due to feed rate of the moving work table. This paper presents friction behavior on a milling process circular work piece in line resulted from identified surface error location (SLE).

Adaptive point-to-point control system design using friction-based optimal state feedback

Abstract This paper presents an adaptive control system design for high-precision positioning of a point-to-point (PTP) servo actuator. These mechanisms are characterized by nonlinear friction behaviour, vibrational modes, and dead times which are limitations to precise motion. In the proposed strategy, adaptation of a primary controller (PID) efforts is obtained depending on an optimal state feedback. As a new methodology, estimating the states of a PTP servo actuator was carried out based on the observed friction forces besides the control signal. Performances of the proposed control systems were verified using numerical simulations and compared with that of the primary controller. The results demonstrate that, the proposed scheme achieved high-precision positioning of the PTP servo actuator regardless of the presence of its dynamics problems. Moreover, the simplicity of the proposed control technique and its effectiveness for getting high-precision motion support its applicability to variety of applications.

An improved nonlinear modelling and identification methodology of a servo-pneumatic actuating system with complex internal design for high-accuracy motion control applications

Precise and smooth motion control of servo-pneumatic actuating systems can be improved only by using appropriate mathematical models and identification procedures. In this paper, an improved modelling and parameter identification methodology of a servo-pneumatic linear drive unit with complex internal design that takes into account the influence of dead volume in terms of system dynamics has been developed. The proposed modelling methodology considers the nonlinear mass flow characteristic, dead zone of the valve, polytropic temperature model, heat transfer and nonlinear friction behavior. Experimental results indicates that a proper identification of the dead volume improves model accuracy in terms of pressure dynamics, piston velocity and piston position and therefore the proposed modelling methodology can be a good starting point to design better motion controllers in the field of servo-pneumatic actuating systems.

Constraint ability of superposed woven fabrics wound on capstan

Existing capstan equations cannot describe engineering applications where an external pressure is applied. This paper aims at improving available formulations for predicting the constraint ability of woven fabrics wound on capstans. A rigorous and comprehensive model for the capstan effect is proposed taking into account local external pressure and non-linear frictional behavior. In this model, a modified version of Howell's equation in terms of stress is used in combination with the existence of local external pressure. Non-dimensional analytical solutions for tension transmission as well as the maximum tension force held by woven fabric are derived. A model for the constraint ability of an original woven fabric overlapped by another one is also developed and solution is numerically obtained. It is clear that some parameters such as frictional coefficient, tension force applied on initial position, localization and magnitude of external pressure play important roles on achieving optimum constraint ability. Among those parameters, the interaction of initial tension force and external pressure as well as the frictional coefficient dominate the constraint ability effectiveness. The constraint ability is shown to be maximized when local external pressure is applied close to the initial position.

Numerical simulation and experimental investigation on densification, shape deformation, and stress distribution of Ti6Al4V compacts during hot isostatic pressing

Hot isostatic pressing of metal powders involves a complex thermal and mechanical coupling process. A constitutive model based on Perzyna’s elastic-viscoplasticity equation was proposed, and a Lagrangian finite element method was applied to analyze the large deformation, nonlinear friction, powder flow, and densification behavior during hot isostatic pressing. The mechanical behavior of the powders was analyzed in terms of stress distribution. For comparison to the simulation results, the density, shape deformation, and residual stress of the specimens were evaluated using Archimedes’ principle, 3D measuring technology, and Empyrean X-ray diffractometer.

Dynamic Friction Parameter Identification Method with LuGre Model for Direct-Drive Rotary Torque Motor

Attainment of high-performance motion/velocity control objectives for the Direct-Drive Rotary (DDR) torque motor should fully consider practical nonlinearities in controller design, such as dynamic friction. The LuGre model has been widely utilized to describe nonlinear friction behavior; however, parameter identification for the LuGre model remains a challenge. A new dynamic friction parameter identification method for LuGre model is proposed in this study. Static parameters are identified through a series of constant velocity experiments, while dynamic parameters are obtained through a presliding process. Novel evolutionary algorithm (NEA) is utilized to increase identification accuracy. Experimental results gathered from the identification experiments conducted in the study for a practical DDR torque motor control system validate the effectiveness of the proposed method.