Pre-sliding Regime Research Articles

A new quasi-static friction model for the spherical hinge bearing in structural engineering

For most frictional issues in structural engineering, the classical friction law named after Coulomb is a reliable and convenient tool, but it cannot be used to predict a slippage-related quasi-static process due to the lack of relevant items. In this paper, based on some commonly used dynamic friction models, a new rate-independent friction model is proposed to describe a quasi-static frictional process in structural field, e.g., the motion of a spherical hinge bearing in a pedestrian bridge under reciprocal pedestrian and temperature loads. Most quasi-static processes happen at the pre-sliding regime when a friction contact tends to slide slightly before the Coulomb friction is reached. The well-known Dahl model, LuGre model, and other test-based dynamic models are surveyed, and their shortcomings in engineering use are summarized subsequently. The new model, the same as the Dahl model, is rate-independent, but adopts a more engineering-oriented form. On the basis, it can be easily applied on a finite element analysis by adjusting a built-in ideal elastoplastic model. Meanwhile, the accuracy has no obvious decrease according to a test-based comparison between the Dahl model and the new. The coefficient of stiffness deviation, defined as the deviation of the pre-sliding friction stiffness from the initial friction stiffness, is introduced into the new model, which makes the model possible to predict the energy dissipation at the pre-sliding regime and can be well explained by the asperity-based theory at microscopic level. The impacts from the curvature and the coverage of a contact on the coefficient of static friction are assessed by the finite element method. It is shown that the curvature has very few impacts while the coverage is highly positively related to the observed coefficient of friction. A friction test of a spherical hinge is then carried out to verify the new model. By data regression, the coefficient of stiffness deviation for the proposed model and the exponent for the Dahl model are identified as 0.492 and 2.272, respectively. A comparison of friction torque-slippage hysteresis loops shows both the Dahl model and the proposed model have good predication as the normal force is large enough and the proposed one is even better in some load cases. Finally, a brief application on a pedestrian bridge of the new model is introduced. It indicates that there will be some mechanical residuals when a spherical hinge is applied with a reciprocating load, but the residuals tend to be limited.

A force controlled tribometer for pre-sliding measurements at the nanometer scale

In the pre-sliding friction regime, interfaces partially stick and partially slip. The pre-slip is thought to be locally initiated at regions of the interface where the ratio of shear stress to normal stress exceeds a critical value. The displacements involved in pre-slip can be limited to the nanoscale, especially for stiff interfaces. Furthermore, little is known experimentally about the interplay between surface topography, pre-sliding behavior and wear. In this work, we introduce a pre-sliding tribometer that enables the study of how the pre-sliding friction at various types of ball-on-flat interfaces evolves as a function of wear. Polytetrafluoroethylene-on-silicon (PTFE-on-Si) pre-sliding measurements covering interfacial displacements up to 50 nm, conducted with the new instrument, show good agreement with Mindlin theory predictions, without adjustable parameters.

An asperity-based statistical model for the adhesive friction of elastic nominally flat rough contact interfaces

Contact mechanics-based models for the friction of nominally flat rough surfaces have not been able to adequately capture certain key experimentally observed phenomena, such as the transition from a static friction peak to a lower level of sliding friction and the shear-induced contact area reduction that has been observed in the pre-sliding regime especially for soft materials. Here, we propose a statistical model based on physically-rooted contact mechanics laws describing the micromechanics of individual junctions. The model considers the quasi-static tangential loading, up to full sliding, of the contact between a smooth rigid flat surface and a nominally flat linear elastic rough surface comprising random independent spherical asperities, and accounts for the coupling between adhesion and friction at the micro-junction level. The model qualitatively reproduces both the macroscopic shear-induced contact area reduction and, remarkably, the static friction peak without the need to explicitly introduce two different friction levels. It also demonstrates how the static friction peak and contact area evolution depend on the normal load and certain key microscale interface properties such as surface energy, mode mixity and frictional shear strength. “Tougher” interfaces (i.e. with larger surface energy and smaller mode mixity parameter) are shown to result in a larger real contact area and a more pronounced static friction peak. Overall, this work provides important insights about how key microscale properties operating at the asperity level can combine with the surface statistics to reproduce important macroscopic responses observed in rough frictional soft contact experiments.

Modelling and identification of the asymmetric hysteresis in the viscoelastic response of the fingertip under indentation: A multistate friction model with switching parameters

This paper presents a dynamic model for the identification of asymmetric hysteresis in the force response of the fingertip under cyclic local deformation of the fingertip soft tissues. Viscoelastic effects, marked anisotropy and nonlinearity contribute to the hysteretic behaviour of the force of the fingertip undergoing indentation. The fingertip force in response to an indentation stimulus varies along the loading and unloading cycles; the resulting hysteresis loops are asymmetric. The asymmetry arises from the simultaneous convexity of the branches of the hysteresis loop. The proposed model belongs to the class of multistate friction models that can effectively describe the hysteresis in the presliding regime of motion of general mechanisms with friction, by exploiting a mechanical analogy obtained through the concatenation of multiple elasto-plastic elements. The multistate model, which provides the mechanical representation of the fingertip response through a set of newly-conceived switching elements and viscoelastic blocks, can reproduce the convex and asymmetric hysteresis loops of the fingertip mechanical response, including the viscoelastic effects of stress relaxation and the influence of time interval between consecutive cycles of indentation.The model has been validated through the experimental identification of fingertip indentation tests performed on an optomechanical test-rig. This model potentially opens the way for efficient model-based control strategies of servomechanisms involved in tactile and haptic displays and interfaces.

Evaluation of Pre-Sliding Behavior at a Rough Interface: Modeling and Experiment

AbstractOne of the main issues in precision engineering is the lack of deep understanding of the pre-sliding behavior at the interface of mating surfaces of positioning mechanisms. In addition to the mechanical properties of the contacting bodies, their surface topography plays a key role in the pre-sliding regime and has a great impact on the frictional stiffness. This paper experimentally evaluates a boundary element method (BEM) model for the pre-sliding behavior at the interface of a smooth silicon wafer and a rough polymeric ball. The polymeric ball is either high-density polyethylene (HDPE) or polyoxymethylene (POM). The experiments are conducted at three different normal loads on five different spots on the wafer. The sliding stroke and coefficient of friction are extracted from experiments to be implemented as inputs to the numerical model. The roughness of the balls is also another input. The numerical and experimental friction hysteresis loops are compared. There is a small difference in the predicted pre-sliding distance from the experiments. The lateral stiffness, calculated at three different points on the pre-sliding regime of friction hysteresis loops, is compared with the Mindlin’s solution and experimental values for both contact interfaces and normal loads.

Pre-compensation of servo tracking errors through data-based reference trajectory modification

This paper presents a new dynamic error compensation approach with novel data-based closed-loop tuning scheme to enhance tracking accuracy of machine tool feed-drives. Both servo dynamics and friction disturbance induced positioning errors are pre-compensated by modifying the reference trajectory. Velocity and acceleration profiles of reference trajectory are modulated to achieve perfect tracking. Reference position profile is modified based on the pre-sliding friction regime to eliminate quadrant glitches. Optimal error compensation is achieved by a digital trajectory pre-filter whose parameters are tuned automatically by making on-the-fly iterative adjustments. Effectiveness of proposed compensation approach is validated experimentally in multi-axis feed-drive systems.

Friction microdynamics in the time and frequency domains: Tutorial on frictional hysteresis and resonance in precision motion systems

This paper provides an overview and tutorial on the key behaviors of mechanical friction in both the time and frequency domains to understand friction effects on precision motion control systems, and presents implications of this behavior for high-precision applications. Friction behaves differently depending on the operating regime. In the steady sliding regime, friction is a function of the relative velocity of two objects sliding against each other, and characterized by static, Coulomb and viscous terms. We observe more complex frictional behaviors as the velocity and displacement are near zero, which is the pre-sliding regime. Friction in this regime depends on the displacement of objects in contact, acting as a nonlinear hysteretic spring. In this paper, we focus on the time- and frequency-domain phenomena caused by the nonlinear hysteretic elasticity of such pre-sliding friction. Frictional microdynamic behaviors in each domain are experimentally studied with a servomotor system testbed and using the Generalized Maxwell-Slip (GMS) friction model. Friction model identification methods based on experimental observations are also discussed in both the time- and frequency-domains. We also present structures for accurate time-domain simulation of friction.

Issues in validation of pre-sliding friction models for ultra-high precision positioning

Friction is one of the main disturbances in nanometric positioning. Recently, it was shown that ultra-high precision positioning typically happens in the pre-sliding motion regime where friction is characterized by an elasto-plastic nonlinear hysteretic behavior with a marked stochastic variability. With the aim of providing the tools for the development of robust control typologies for ultra-high precision mechatronics devices, different pre-sliding friction models are thus considered in this work. The most relevant ones are hence experimentally validated, as well as compared in terms of the complexity of identifying their characteristic parameters and of simulating the factual dynamic response. It is hence shown that the generalized Maxwell-slip model can account for all the important pre-sliding frictional effects in nanometric positioning applications. A thorough sensitivity analysis of the parameters of the generalized Maxwell-slip model model is therefore performed allowing to establish that three Maxwell-slip blocks are the minimum needed to approximate the behavior of the real precision positioning systems, six blocks allow representing excellently the real behavior, while the slower dynamics, which induces a difficult real-time implementation, with a very limited gain in terms of model accuracy, does not justify the usage of a larger number of elements.

Relationship between the real contact area and contact force in pre-sliding regime**Project supported by the National Natural Science Foundation of China (Grant No. 11272171), the Natural Science Foundation of Beijing City, China (Contract No. 3172017), and the Education Ministry Doctoral Fund of China (Grant No. 20120002110070).

The pre-sliding regime is typically neglected in the dynamic modelling of mechanical systems. However, the change in contact state caused by static friction may decrease positional accuracy and control precision. To investigate the relationship between contact status and contact force in pre-sliding friction, an optical experimental method is presented in this paper. With this method, the real contact state at the interface of a transparent material can be observed based on the total reflection principle of light by using an image processing technique. A novel setup, which includes a pair of rectangular trapezoidal blocks, is proposed to solve the challenging issue of accurately applying different tangential and normal forces to the contact interface. The improved Otsu’s method is used for measurement. Through an experimental study performed on polymethyl methacrylate (PMMA), the quantity of contact asperities is proven to be the dominant factor that affects the real contact area. The relationship between the real contact area and the contact force in the pre-sliding regime is studied, and the distribution of static friction at the contact interface is qualitatively discussed. New phenomena in which the real contact area expands along with increasing static friction are identified. The aforementioned relationship is approximately linear at the contact interface under a constant normal pressure, and the distribution of friction stress decreases from the leading edge to the trailing edge.

DYNAMIC FRICTION BEHAVIOR IN PRE-SLIDING REGIME OF PNEUMATIC ACTUATORS

This paper focuses on investigating friction behavior in pre-sliding regime and developing a new mathematical model of friction for fluid power actuators. Using pneumatic cylinders with different sizes, an experimental setup is built to measure friction force-displacement characteristics in presliding regime under various conditions of pressures in the cylinder chambers. A new mathematical model of friction for the pneumatic cylinders is proposed by incorporating a hysteresis function into the new modified LuGre model. The experimental results show that when the pressures are varied, friction of the pneumatic cylinders in pre-sliding regime is represented by behavior of a nonlinear spring. In addition, hysteresis behavior with nonlocal memory is obtained in the friction forcedisplacement characteristics and that the size of the hysteresis loop is increased with increasing pressures in the cylinder chambers. The simulation results show that the new friction model can accurately simulate the friction behavior of the pneumatic cylinders in pre-sliding regime as well as sliding regime.

Contouring control for three-axis machine tools based on nonlinear friction compensation for lead screws

Friction is the main disturbance in mechanical systems especially in computerized numerical control machine tools with high precision, speed, and performance requirements. Much recent research have proven that a controller with friction compensation provides better performance. Some classical friction models such as the Coulomb–viscous–Stribeck friction model, the Lugre model, and the Generalized Maxwell Slip (GMS) model have been proposed to compensate for frictional effects to reduce the contour error and to improve the surface quality. However, most of the conventional friction models focus on frictional properties in pre-sliding regime and low velocity sliding regime. These models do not fully describe and compensate for friction in machine tool systems in case of high speed motion or insufficient lubrication. This paper presents a new friction model that combines the conventional Coulomb-viscous friction model and a nonlinear sinusoidal component for fully describing the friction behaviour of feed drive systems. In addition, this study presents controller design with feed forward compensation based on the proposed friction model. Experiments were conducted to compare the control performance between the proposed and the conventional friction models. Experimental results indicate that the mean contour error has been significantly reduced by 26% after applying the proposed controller.

Characterization of friction force and nature of bifurcation from experiments on a single-degree-of-freedom system with friction-induced vibrations

Experimental investigation is performed on a test set-up representing a single-degree-of-freedom friction-induced system. The experimental set-up consists of a rigid mass (oscillator) connected to a fixed support through a spring and the mass in frictional contact with a moving belt. The major objectives of the experiments are to characterize (i) the nature of friction-induced oscillations, (ii) the nature of bifurcation associated with frictional instability in the system, and (iii) the nature of friction force that is responsible for the oscillations observed from the experiment. The phase portrait of the system shows significant overshoot of the oscillator velocity above the belt velocity indicating the existence of hysteretic loop around zero relative velocity (pre-sliding regime). The bifurcation diagram clearly demonstrates the subcriticality of the Hopf bifurcation associated with the system negating all empirical friction models which yield supercritical Hopf bifurcation. The friction force-relative velocity curve shows significant hysteretic behavior, both in the pre-sliding as well as in the pure sliding domains. This observation hints towards a dynamic or an acceleration-dependent friction model as an appropriate choice for representing the friction force obtained from our experimental set-up.

Experimental investigation of friction behavior in pre-sliding regime for pneumatic cylinder

Friction always presents in pneumatic cylinders and causes difficulties in controlling position and velocity of pneumatic systems. In order to improve the control performance of the pneumatic systems, it is necessary to fully understand behavior of friction in the pneumatic cylinders. So far, dynamic friction behavior of pneumatic cylinders has been investigated but mainly focused on the friction behavior in sliding regime. In pre-sliding regime, friction behavior has not been investigated. In this paper, experimental investigations of friction behavior of a pneumatic cylinder in pre-sliding regime are made. The friction force is calculated from the equation of motion of the piston using the measured values of pressures in the two cylinder chambers and the piston displacement. The pressures are controlled by using two proportional pressure control valve. The friction force versus piston displacement characteristics are measured and analysed under various operating conditions of the applied force and the pressures. Experimental results show that: i) the piston motion in pre-sliding regime exhibits a nonlinear spring behavior; ii) hysteretic behavior with nonlocal memory is verified; iii) the pressures have influence only on the size of the hysteretic loop. These experimental results can be applied to develop a friction model for pneumatic cylinders.

Friction modeling, identification, and compensation based on friction hysteresis and Dahl resonance

This paper studies effects of friction on control systems and utilizes the observed frictional behavior to develop a parameter identification method for a friction model using frequency domain measurements. Friction exists in a wide range of drive systems due to physical contacts in bearing elements, transmissions, or motion guides. Friction in a control system can deteriorate performance by causing limit cycles or stick–slip, as well as larger tracking errors. Friction compensation can help to reduce following errors, but requires physical understanding and a reliable model of friction in both the gross- and the pre-sliding regimes. In this paper, we adopt the Generalized Maxwell-Slip (GMS) model and develop a frequency-domain method to identify the model parameters based on the frictional resonances, which occur due to the elastic behavior of friction at small amplitudes. With the experimentally identified parameters, the friction model is utilized to compensate the friction effects in a motion control system. The resulting system performance of a compensated and uncompensated control system is then compared in both the frequency and time domains to demonstrate the Dahl resonance identification method for a GMS model.

Dahl and LuGre dynamic friction models — The analysis of selected properties

The paper presents a method of determination of parameters for LuGre and Dahl dynamic friction models. The method involves the use of numeric optimisation, in which the objective function is a minimisation of the sum of squares of relative errors between the actual and modelled friction hysteresis courses. It was specified that the limiting value of the cycle time of the signal, forcing the relative motion, above which the simulation of friction hysteresis in the presliding regime is not dependent on the velocity of displacement. The analyses of numerical results indicated that the parameters of dynamic models have limited the scope of application in relation to the normal forces exerted on the kinematic friction pairs, as opposed to the static friction models.

Prestiction friction compensation in direct-drive mechatronics systems

LuGre model has been widely used in friction modeling and compensation. However, the new friction regime, named prestiction regime, cannot be accurately characterized by LuGre model in the latest research. With the extensive experimental observations of friction behaviors in the prestiction, some variables were abstracted to depict the rules in the prestiction regime. Based upon the knowledge of friction modeling, a novel friction model including the presliding regime, the gross sliding regime and the prestiction regime was then presented to overcome the shortcomings of the LuGre model. The reason that LuGre model cannot estimate the prestiction friction was analyzed in theory. Feasibility analysis of the proposed model in modeling the prestiction friction was also addressed. A parameter identification method for the proposed model based on multilevel coordinate search algorithm was presented. The proposed friction compensation strategy was composed of a nonlinear friction observer and a feedforward mechanism. The friction observer was designed to estimate the friction force in the presliding and the gross sliding regimes. And the friction force was estimated based on the model in the prestiction regime. The comparative trajectory tracking experiments were conducted on a simulator of inertially stabilization platforms among three control schemes: the single proportional-derivative (PD) control, the PD with LuGre model-based compensation and the PD with compensator based on the presented model. The experimental results reveal that the control scheme based on the proposed model has the best tracking performance. It reduces the peak-to-peak value (PPV) of tracking error to 0.2 mrad, which is improved almost 50% compared with the PD with LuGre model-based compensation. Compared to the single PD control, it reduces the PPV of error by 66.7%.

A Comparison of Contact Stiffness Measurements Obtained by the Digital Image Correlation and Ultrasound Techniques

The digital image correlation (DIC) and ultrasound techniques have both previously been employed to measure the contact stiffness of real engineering interfaces, but a comprehensive comparison of these techniques has not previously been carried out. Such a comparison is addressed in the present paper. The principal novelty in this work is that DIC and ultrasound are used to simultaneously measure contact stiffness in the same tests and on the same contact interface. The results show that ultrasound measures somewhat higher contact stiffness magnitudes than DIC: at an average normal contact pressure of 70 MPa, ultrasound was around three times stiffer. Given that the techniques are vastly different in their measurement approach (DIC measures micron-scale relative displacements from external side-on images of the interface, while ultrasound uses the reflection of an Angstrom scale ultrasonic perturbation from the interior of the interface itself), this level of agreement is thought to be encouraging. The difference in results can partly be explained by consideration of inherent physical differences between the techniques which have previously received little attention. Ultrasound measurement will always give the local elastic ‘unloading stiffness’ (even at a plastically deforming contact); whereas, a load-deflection technique like DIC, will give the ‘loading stiffness’. The reason for this difference is discussed in the paper and tests carried out under increasing tangential load in the pre-sliding regime illustrate this difference experimentally. Under normal loading, the increase in real contact area obscures the effect to some extent as both DIC and ultrasound stiffnesses increase with normal load. The results suggest that rough interfaces may be satisfactorily modelled as a variable stiffness spring whose stiffness increases with contact pressure as the smooth contact case is approached.

Identification of Friction Models for Precise Positioning System in Machine Tools

Abstract This paper focuses on friction identification and numerical validation on ball-screw driven XY milling table. Two friction models namely; static friction model and Generalized Maxwell-slip (GMS) model are identified and validated numerically. Static friction model is identified by measuring the control command signals of various constant velocities while friction-position behavior during sliding and pre-sliding regimes is determined to identify GMS model. Parameters of static friction model are estimated using heuristic approach while application of piecewise linear functions and theory of superposition in virgin curve are used in approximating the parameters of GMS model. Based on obtained parameters, the models are generated in simulation using MATLAB/Simulink to verify the friction models and glitches formed during motion of low velocity. Simulation results showed that GMS model produced clearer and larger glitches compared to static friction model during low velocity motion. GMS model is capable of characterizing the friction behavior during pre-sliding.

Theoretical analysis of the dynamic behavior of presliding rolling friction via skeleton technique

Depending on the application, friction in mechanical systems can be a desirable or an undesirable thing. In order to optimally utilize or compensate for the frictional effect in the system, characterization of the frictional behavior is a crucial task. Unfortunately, friction force exhibits strong (hysteretic) nonlinear relationship with sliding velocity, displacement and time, which makes the characterization to become a difficult task to fulfill. The classical Coulomb friction has been widely used, especially in the field of control engineering to compensate for the static force in a system. However, despite its simplicity, the effectiveness of the Coulomb model in capturing the frictional behavior of friction in the presliding regime is very low.This paper deals with the derivation of equivalent modal parameters, namely the stiffness and damping elements, to represent the hysteresis friction element on mechanical systems. The analysis is carried out using the skeleton technique, which employs the instantaneous amplitude and frequency of the excitation input and the response of the system. Subsequently, the dynamic analysis is performed on the equivalent system and the result is compared to that of the original system. The results show good agreement between the equivalent system and the original system for wide range of excitation.

On the relationship between normal load and friction force in pre-sliding frictional contacts. Part 2: Experimental investigation

When a tangential force is exerted on one of a pair of contacting bodies, the pre-sliding regime is traversed, before an object grossly slides. This paper is dedicated to the experimental investigation of the relation between the normal load and the friction force during the pre-sliding regime up to the point of sliding. For this purpose, a previously developed linear tribometer is used. A parametric model equation is constructed to fit adequately the measured hysteresis data. Thereafter, a parameter study is conducted to identify the influence of the normal load on the equation’s parameters. The results confirm the theoretical trend (presented in Part 1) that the coefficient of friction decreases, and the pre-sliding distances increases with increasing normal load, for a variety of contacting surfaces.