Effect Of Coulomb Friction Research Articles

Effect of Lubricant on Surface Rolling Contact Fatigue Cracks

This study performed the finite element analysis of the cycle of stress intensity factors at the surface initiated rolling contact fatigue crack tip under Hertzian contact stress including an accurate model of friction between the faces of the crack and the effect of fluid inside the crack. A two-dimensional model of a rolling contact fatigue crack has been developed with FRANC-2D software. The model includes the effect of Coulomb friction between the faces of the crack. The fluid in the crack was assumed not only to lubricate the crack faces and reduce the crack face friction coefficient but also to generate a pressure.

Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.

The effect of Coulomb friction on the static performance of foil journal bearings

In foil bearings, the friction between bumps and their mating surfaces is the major factor which exerts great influence on the bearing performance. From this point of view, many efforts have been made to improve the understanding of the influence of the friction on the foil bearing performance by developing a number of analytical models. However, most of them did not consider the hysteretic behavior of the foil structure resulting from the friction. The present work developed the static structural model in which hysteretic behavior of the friction was considered. The foil structure was modeled using finite element method and the algorithm which determines the conditions of the contact nodes and the directions of the friction forces was used to take into account the friction. The developed model was integrated into the foil bearing prediction code to investigate the effects of the friction on the static performance of the bearing. The results of analysis show that multiple static equilibrium positions are presented for the one static load due to the friction, inferring its great effects on the dynamic performance. However, the effect of friction on the minimum film thickness which determines the load capacity of the bearing is negligible.

Multibody dynamics analysis of the driveshaft coupling of the ball and tripod types of constant velocity joints

The paper proposes a multibody dynamic simulation to numerically evaluate the generated axial force (GAF) and plunging resistant force (PRF) practically related to the shudder and idling vibration of an automobile. A numerical analysis of the drive shaft coupling of a ball joint (BJ) and two plunging type joints, a tripod joint (TJ), and a very low axial force tripod joint (VTJ), are conducted using the commercial program DAFUL. User-defined subroutines of a friction model illustrating the contacted parts of the outboard and inboard joint are subsequently developed to overcome the numerical instability and improve the solution performance. The Coulomb friction effect is applied to describe the contact models of the lubricated parts in the rolling and sliding mechanisms. The numerical results, in accordance with the joint articulation angle variation, are validated with experimentation. The offset between spider and housing is demonstrated to be the critical role in producing the third order component of the axial force that potentially causes the noise and vibration in the vehicle. The VTJ shows an excellent behavior for the shudder when compared with the TJ. In addition, a flexible nonlinear contact analysis coupled with multibody dynamics is also performed to show the dynamic strength characteristics of the rollers, housing, and spider.

Analysis of the van der Pol System With Coulomb Friction Using the Method of Multiple Scales

The effect of Coulomb friction on the nonlinear dynamics of a van der Pol oscillator is presented. A map from the magnitude of a peak to that of the succeeding valley in the time history is analytically described by considering both the exponential growth due to negative viscous damping and the switching condition due to Coulomb friction, which is a function of the sign of the velocity of the system. The steady states and their stability are clarified and the difference from those in the case without Coulomb friction is revealed. The addition of Coulomb friction makes the trivial equilibrium, which is an unstable focus in the system without friction, into a locally asymptotically stable equilibrium set. The branch of stable nontrivial steady states is not bifurcated from the trivial steady state by the effect of Coulomb friction and is different from the branch in the case without Coulomb friction, which is bifurcated from the trivial steady state through Hopf bifurcation. Furthermore, experiments are conducted and the theoretically predicted dynamics due to Coulomb friction is confirmed.

Nonlinear friction compensation of a 2-DOF planar parallel manipulator

The friction compensation method based on a nonlinear friction model is developed for a 2-DOF planar parallel manipulator. This nonlinear friction model enables reconstruction of viscous, Coulomb, and Stribeck friction effects of the parallel manipulator. Identification experiments are carried out, and parameters in the nonlinear friction model are estimated by nonlinear optimization. The dynamic control experiments are designed for the trajectory tracking of the parallel manipulator to study the friction compensation. The friction compensation performances are compared between the Coulomb + viscous friction model and the nonlinear friction model, also, the control performances without the friction compensation are given. Experiment results demonstrate that the tracking accuracy of the parallel manipulator can be improved obviously with the nonlinear friction compensation.

The coupled thermo-mechanical analysis in the upsetting process by the dynamic FEM

The effect of temperature is significant on both the die and the workpiece in metal forming processes. But, the applications of coupling mechanical work and thermal effect are somewhat complicated. In this study we apply the dynamic finite element method coupled with thermal effect to analyze the upsetting process with different models. The proposed models, either being drawn for industry necessity or designing for research study, are simulated and compared. At first, the numerical models for the upset forming of steel billet are setup. The models consider the different types of material constitutive equations, different thermal conditions, and Coulomb friction effect. The predicted relationship between the punch load and stroke, the temperature distribution of billet, and the full history of temperature variation are discussed. The influence and usage of the material constitutive equation for the thermal analysis is also assessed. Besides, the developed models of upsetting process are validated by comparison with the published paper. Finally, the proper techniques are implemented to solve the upsetting process with aluminum material. And the temperature distribution on the surface of the billet in experiment is measured by an infrared camera. A good agreement between the numerical result and experiment data shows the availability of the proposed model.

Precision Motion Control Methodology for Complex Contours

A general precision motion control methodology for complex contours is proposed in this paper. Each motion servomechanism dynamic model is divided into a linear portion and a portion containing nonlinear friction, unmodeled dynamics, and unknown disturbances. A full state feedback controller, based on a state space error system model, is developed to track general reference trajectories. The lumped static, Coulomb, and Stribeck friction effects are described using the Tustin friction model. Unmodeled dynamics and unknown disturbances are estimated using a Kalman filter that employs a first-order stochastic model. The nonlinear friction, unmodeled dynamics, and unknown disturbances are directly canceled by the controller. In the proposed motion control methodology, complex contours (i.e., contours whose radii of curvature constantly change along the contour) do not need to be decomposed into line segments and arcs and the reference signals do not need to be prefiltered. Also, the controller structure does not need to be adjusted to track different types of contours. Experiments are conducted on a two-axis laboratory grade machine tool for elliptical, limacon, and free-form contours. The results demonstrate the excellent tracking performance of the proposed motion control methodology. They also demonstrate that the performance is independent of the contours’ complexity.

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lame formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis.

Efficient stress evaluation of stationary viscoelastic rolling contact problems using the boundary element method: Application to viscoelastic coatings

The present work is a contribution towards the development of a new and novel technique to evaluate the contact stresses between linear-viscoelastic cylinders under stationary rolling contact loading. A two-dimensional numerical model is considered using a reference system fixed to the contact zone and including the effects of Coulomb friction between the rolling cylinders. The contact stresses are determined by solving a non-linear system of equations coming from the combination of the discretized boundary element viscoelastic equations and the fulfillment of the contact conditions, expressed using projection functions. The results obtained for viscoelastic rollers are compared with those from other authors for different rolling velocities, showing good agreement and consistency. Finally, some results for viscoelastic coatings are presented and commented.

1P1-D34 非線形ばね特性を持つ送り駆動系の動的挙動

This paper concerns dynamic characteristics of a feed drive system with the nonlinear spring behavior. The dynamic characteristics during the microscopic motion can be represented with a mixed term by combining Coulomb friction and the nonlinear spring behavior. Comparing experiment results with simulation results, it can be found that the dynamic characteristics are dominated by the Coulomb friction term in the range of 1OOμm and over, and described by the mixed term in the range of 5〜100μm. It is clarified that the effect of Coulomb friction on the mixed term is excessively strengthened when the Coulomb frictional coefficient is used in the range of 1OOμm and over.

TABULAR PULSE-WIDTH CONTROL OF A TWO DEGREE-OF-FREEDOM MANIPULATOR

Pulse-width control, when applied to single degree-of-freedom systems, is very effective in overcoming the deleterious effects of Coulomb friction and stiction. This paper applies pulse-width control to a multi-degree-of-freedom mechanism. Results are presented based both on simulations and on the performance of a two degree-of-freedom experimental manipulator developed at Bucknell University. A unique aspect of this research is the use of a table of pulse-width gain values rather than simply a single gain for each axis of motion. Results indicate that tabular pulse-width control produces responses that converge rapidly and achieve positioning accuracies equal to the precision of measurement sensors.

Boundary Element Analysis of Effects of Crack Face Friction and Trapped Fluid on Rolling Contact Fatigue Cracks

Boundary element analysis has been performed on the cycle of stress intensity factors at a surface initiated rolling contact fatigue crack tip under a Hertzian contact pressure distribution. The model includes the effects of Coulomb friction between the faces of the crack and the possible effect of fluid penetrating into the crack. Three possible models to show the influence of fluid on crack propagation have been investigated, namely, (a) a fluid lubrication model; (b) a hydraulic pressure model; and (c) a fluid entrapment model. The analysis results indicate that when the fluid entrapment model was used, the values of generated mode I and II stress intensities were reasonable and the results were consistent with the behavior of the crack. Therefore, the fluid entrapment model is considered to be the most promising for explaining the behavior of the rolling contact fatigue cracks.

Theory and application of a combined self-tuning adaptive control and cross-coupling control in a retrofit milling machine

In this paper, the control plant is a ball screw actuated milling machine table which has been retrofit with DC servo motor control. The retrofit milling machine has nonlinear time-varying behaviors because of the effect of irregular Coulomb friction of the sliding surface and obvious backlash. Thus, it is difficult for a conventional digital controller to provide a high contouring accuracy as well as adequate disturbance rejection and parameter variation robustness. To improve contouring performance of the retrofitted milling machine, a self-tuning adaptive control strategy, combined with cross-coupled control of axial motion is proposed. The proposed control scheme has been verified as being internally stable. Experimental results show that this control method achieves satisfactory contouring accuracy, transient response, tracking and robustness under the influence of backlash on each axis and irregular Coulomb friction. This performance verifies the applicability of this economic approach to automation of traditional milling machines.

Stabilization Control of a Simply Supported Buckled Beam

A stabilization control scheme for a simply supported buckled beam subjected to a compressive force is proposed theoretically and experimentally. It is easily predicted that the application of a control force based on P-control (control force is proportional to the deflection) increases the stiffness of the beam as well as the critical compressive force for the buckling. However, P-control cannot stabilize the buckled beam into the trivial steady state (straight position) for the following reason. Because the simply supported point is composed of rotatingequipment such as radial bearing, there is Coulomb friction in the circumferential direction around the rotatingaxis at that point and this friction causes the bendingmoment at the supporting point. As theoretically and experimentally clarified in our former study, in the neighborhood of the critical point, this effect of Coulomb friction produces an infinite number of fixed points for a compressive force. Then because the sum of the equivalent destabilization force in the lateral direction owing to the compressive force, originally existing stiffness of the beam, and the control force is spontaneously balanced with the effect of the bendingmoment due to the Coulomb friction, the beam cannot be stabilized to the trivial steady state by using the P-control. Also, in the same manner, the beam cannot be stabilized to the trivial steady state even by proportional derivative (PD) control. In this paper, we regard the effect of the Coulomb friction as a disturbance, and by estimating the disturbance with the aid of a disturbance observer, we stabilize the simply supported buckled beam to the trivial steady state. Furthermore, we conduct experiments using simple apparatus and we confirm the validity of the theoretically proposed control method.

Modeling and cancellation of pivot nonlinearity in hard disk drives

This paper considers the issue of modeling the pivot nonlinearity in a typical hard disk drive, taking into account viscous friction, Coulomb friction and hysteresis effects. It presents a nonlinear compensator design, based on a proposed model, to make the compensated system behave like a double integrator regardless of the magnitude of the input current. It describes extensive experiments, carried out in both time domain and frequency domain, to show the effects of pivot nonlinearity and the effectiveness of the compensator.

Boundary element analysis of surface initiated rolling contact fatigue cracks in wheel/rail contact systems

This study performed the boundary element analysis of the cycle of stress intensity factors at the surface initiated rolling contact fatigue crack tip under Hertzian contact stress including an accurate model of friction between the faces of the crack and the effect of fluid inside the crack. A two-dimensional model of a rolling contact fatigue crack has been developed. The model includes the effect of Coulomb friction between the faces of the crack. The fluid in the crack was assumed not only to lubricate the crack faces and reduce the crack face friction coefficient but also to generate a pressure. The obtained results are compared with those of other researchers showing good consistency.

INPUT SHAPING FOR A PD POSITION CONTROLLER UNDER COULOMB FRICTION

A proportional plus derivative controller is used on a system with coulomb friction. The proportional control decreases steady state error, while the derivative control reduces system oscillations. However, the derivative control also makes the system response more sluggish. As an alternative, input shaping can be used to reduce the system oscillations. Traditional input shapers are not designed to include the effects of coulomb friction so they may not work well in all cases. A new method of developing an input shaper to include the effects of coulomb friction is discussed. Simulation and experimentation show the effectiveness of the new shaper.

Effects of surface waves and marine soil parameters on seabed stability

Based on the Yamamoto's soil model by considering the Coulomb friction effects, the wave-induced seabed instability has been investigated. An analytical solution is derived for soil response of a finite depth seabed under surface water wave. The effects of wave parameters and soil characteristics on the seabed instability are addressed for three types of soil. Finally, the roles of Coulomb friction stability are then analyzed as well.

Time-optimal control of a single-DOF mechanical system with friction

Presents the exact solution to the minimum-time optimal control problem of a single-degree-of-freedom (DOF) mechanical systems with friction. In particular, the optimal control input can be synthesized in feedback form. The effect of Coulomb friction, which has been ignored or precompensated in prior works, is taken into full account. As a result, the admissible range of control input can be maximized so as to achieve faster responses. A practical example using a direct-driven single-DOF robotic manipulator is discussed to demonstrate the practical use of the optimal solution.