Oscillations Caused by Solid Friction : Part 4, Experimental Study

Nonlinear friction forces are a problem in classical Brownian motion for a long time [1]. They are described either by Langevin or by Fokker-Planck equations [2-4]. However, the rigorous generalized Langevin equation is linear, which points out that nonlinear friction forces possess a macroscopic hydrodynamic origin [1]. For this reason, they are not present in the modern quantum theory of open systems [5]. The scope of the present paper is to investigate the nonlinear friction effect on quantum mechanics. The analysis is based on a dissipative Madelung quantum hydrodynamics. Thus, the nonlinear friction is a result of nonlinear non-equilibrium thermodynamics in contrast to the traditional mechanical nonlinear friction forces. A quantum particle in vacuum is described by the Schrodinger equation

The vital purpose of a vehicle suspension system is to isolate the car body and hence passengers, from roadway unevenness disturbances. Implementation of passive suspension systems has continuously improved disconnection from disturbances through available deflection constraints to provide maximum isolation. In the majority of relevant reported research studies, a quarter car is modelled as moving vertically straight for both a viscous damper and a stiffness spring. The motivation for this study, reported here, is to extend the modelling to take account of the actual configuration of a test rig system. Accordingly, a new passive suspension system model is presented, which includes nonlinear lubricant friction forces that affect the linear support body bearings. The friction model established relies on dynamic system analysis and the fact of slipping body on lubricant bearings; this model captures most of the friction behaviours that have been observed experimentally. The suspension model is composed of a car body and wheel unit, and only vertical motion (bounce mode) is addressed. In addition, an active actuator is used to generate the system inputs as a road simulator. Therefore, a nonlinear hydraulic actuator, including the dynamic of servovalve and proportional–integral controller model, is established. This study is validated by experimental work, with simulations achieving C++compiler. As a result, a good agreement is obtained between the experimental and simulation results, that is, the passive suspension system with considered nonlinear friction and the nonlinear hydraulic actuator with servovalve equation models are entirely accurate and useful. The suggested proportional–integral controller successfully derives the hydraulic actuator to validate the control scheme. The ride comfort and handling response are close to that expected for the passive suspension system with road disturbances.

This paper presents the new vibration model of the horizontal washing machine (HWM) using a nonlinear geographic of the suspension system with nonlinear friction force - velocity (F-V) relationship of dampers obtained from experiment. Furthermore, using the dissipated energy function of dampers (Ed) criteria, some results of the effect of the spring stiffness on the dampers’ loading level are achieved. The simulation was done in Matlab/Simulink® environment. The results were then compared with experimental validation results to determine the suitability of the model. The conclusions can provide some available evidences for the design and improvement of nonlinear dampers.

In the machine tool industry and the semiconductor manufacture fields, the necessity of high precision and fast response is rapidly spreading. In general, it is well known that a positioning control system contains nonlinear friction force; it may cause a serious disadvantage on control performances such as tracking errors, limit cycles and undesired stick-slip motion at very low motion velocity. In order to achieve the high level control performance, the frictional effects have to be removed. This paper presents a novel nonlinear friction compensation approach based on the idea of P, PI/I-P+FF control with sliding mode compensator for a high precision stage using a synchronous piezoelectric device driver. P, PI/I-P+FF control consists of Proportional position control and Proportional-Integral/Integral-Proportional velocity control with velocity Feed-Forward compensator. Experimental results are given to show the effectiveness of our proposed control method compared to the conventional P, PI/I-P+FF control method. Especially, the positioning error of our proposed control was reduced by more than 2/3 compared to the case of the conventional control at a stepping motion.

In this paper, a graphical prediction method is developed to effectively predict the existence of the limit cycles induced by nonlinear friction force in an electro‐hydraulic control system. The friction‐induced nonlinearity is linearized by its corresponding describing function. Then the stability equation method, accompanied by the parameter plane method, provides a useful tool for the establishment of necessary conditions to sustain a limit cycle in the controller coefficient plane. Henceforth, the limit cycles are predicted in a graphical way, and simulations are carried out to verify the accuracy of the prediction method.

A digital signal processor (DSP)-based complementary sliding mode control (CSMC) with Sugeno type fuzzy neural network (SFNN) compensator is proposed in this study for the synchronous control of a dual linear motors servo system installed in a gantry position stage. The dual linear motors servo system comprises two parallel permanent magnet linear synchronous motors (PMLSMs). The dynamics of the single-axis motion system with a lumped uncertainty which contains parameter variations, external disturbances and nonlinear friction force is briefly introduced first. Then, a CSMC is designed to guarantee the precision position tracking requirement in single-axis control for the dual linear motors. Moreover, to enhance the robustness to uncertainties and to eliminate the synchronous error of dual linear motors, the CSMC with a SFNN compensator is proposed where the SFNN compensator is designed mainly to compensate the synchronous error. Finally, some experimental results are illustrated to show the validity of the proposed control approach.

A field-programmable gate array (FPGA) based functional link radial basis function network (FLRBFN) control is proposed in this study to control the mover of a permanent magnet linear synchronous motor (PMLSM) servo drive system to track periodic reference trajectories. First, the dynamics of the field-oriented control PMLSM servo drive with a lumped uncertainty, which contains parameter variations, external disturbances and nonlinear friction force, is derived. Then, to achieve accurate trajectory tracking performance with robustness, an intelligent control approach using FLRBFN is proposed for the field-oriented control PMLSM servo drive system. The proposed FLRBFN is a radial basis function network (RBFN) embedded with a functional link neural network (FLNN). Moreover, the on-line learning algorithm of the FLRBFN, including the connective weights, the centers and the centers' width of the receptive field functions, are derived using back-propagation (BP) method. Furthermore, an FPGA chip is adopted to implement the developed control and on-line learning algorithms for possible low-cost and high-performance industrial applications using PMLSM. Finally, some experimental results are illustrated to show the validity of the proposed control approach.

A modified second-order sliding mode control (MSOSMC) combined with radial basis function (RBF) network estimator is developed and proposed to achieve accurate speed tracking performance for synchronous reluctance motor (SynRM). The dynamic model of SynRM system has the properties of parameter variations, external disturbance, and nonlinear friction force. The MSOSMC method that utilizes continuous control input is applied to reduce the chattering phenomenon. Also, this method utilizes two sliding surfaces to solve the problem of system uncertainty and reduce motor power consumption. The RBF network is developed in MSOSMC scheme to estimate the lumped uncertainty in an on-line fashion. The proposed MSOSMC method uses the system error and control input as the convergence criteria. The adaptation scheme adjusts the parameter vectors based on the Lyapunov theorem approach, so that the asymptotic stability of the developed motor system can be guaranteed. Experimental results show that the MSOSMC structure achieves the better tracking performances in terms of root-mean-square error compared with the traditional SOSMC method under different speed tracking conditions.

Aiming at problems of vibration, impact, and noise, the nonlinear dynamic characteristics of servo hydraulic cylinder are studied by using combination of theoretical derivation and simulation experiment methods. The nonlinear effect rules of spring force and friction force are analyzed based on nonlinear dynamic theory; it can be derived that the coupling effect rules of nonlinear spring force and friction force can be described by Duffing–Van Der Pol equation. The dynamic simulation model of servo hydraulic cylinder is established by using SimHydraulics software. The numerical simulation and experiment results showed that nonlinear vibration of servo hydraulic cylinder is mainly caused by exciting force, spring force, and friction force; the system has different motion states when the parameters take different values, which lays a good foundation for the optimal designs and precise control of hydraulic cylinder.

Using the perturbation theory, a class of relative rotation nonlinear dynamical model possessing nonlinear elastic force, friction force and multi-frequency excitation is investigated. The relations for the frequency syntheses are investigated, and the conditions under which multi-typical resonance happens at the same time are given. Using the renormalization method, the asymptotic expansions for the solutions of the model under corresponding conditions are obtained.

For the dynamic response of multilayer sheet structures it is important to take nonlinear contact and friction forces between the layers into account. The nonlinearities inside the joints can significantly influence the dynamic behavior of the entire structure. For the dynamic analysis of such structures conventional computational approaches have an unbalanced ratio between computational time and accuracy. In order to overcome this problem, so‐called “Joint Interface Modes” (JIMs) are used. These JIMs, which are problem‐oriented trial vectors, extend the reduction base of classical trial vector based reduction methods. In this contribution a new calculation approach for JIMs based on trial vector derivatives is introduced. The result quality of the presented method is comparable to the direct finite element method but the computational effort is extremely low due to model order reduction. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The use of composite materials is widely spread across the Aerospace sector. Scarf and step lap joints are amongst the most commonly used methods for flush joint repairs; they restore original stiffness and nearly original strength. Prior investigations conducted by the authors have shown that bonded and hybrid step lap joints have superior static strength capabilities than bolted joints. Hybrid step lap joints have shown the highest fatigue resistance than its bolted and bonded counterparts. This investigation aims at optimising the previous step lap joint design containing five steps with a 90 mm long overlap length in order to improve joint efficiency. Four new step lap joint configurations are considered based on a parametric study conducted using Abaqus; two of which contain seven steps and a 130 mm long overlap (bonded and hybrid) whilst the other two contain six steps and a 105 mm long overlap (bonded and hybrid) with a tapered outer step region. Experimental tests right through to numerical modelling using three-dimensional (3D) finite element (FE) models have been investigated. Adhesive non-linear material properties, fastener contacts and friction forces were all included in the 3D FE models. The Multicontinuum Theory (MCT) is used to simulate the progressive failure process and determine the stress states in the four configurations. Overall the FE models are able to accurately predict the bonded and hybrid joint strengths and highlights the importance of not only optimising the number of steps and their lengths but also the individual step heights. This is a parameter which has often been overlooked by fellow researchers. Experimental results showed that all four step lap joint configurations have significant improvement under static and fatigue load cases; the greatest improvement is seen in the two bonded step lap joint configurations. Overall the hybrid joint configuration consistently outperformed the bonded joint configurations. The presence of fasteners supress crack propagation, minimise peak peeling stresses at the ends of the overlap and increase the durability of the joint. This enables early crack detection which can assist composite joint repair certification.

An iterative non-linear stress analysis considering the thermal expansion and the dynamic effect of the poloidal field coil support in JT-60U tokamak are described. In the JT -60U design, the large electromagnetic forces and smaller space between the toroidal field coil and the vacuum vessel result in a marginal design of the poloidal field coil support structures with small safety margin. Moreover, the complicated geometry of the structure is not easily modeled into the finite elements in the stress analysis and the non-linear friction force applied from the poloidal field coils is difficult to represent realistically. To accurately analyze the deformation and the stress, an iterative method which can treat the friction force as nonlinear force is proposed and applied to the actual design analysis in JT-60U. The deformation calculated from the iterative method is approximately four times of the result in the case of conservative linear friction force. Simple dynamic analysis about the combination of the poloidal field coil, support and the vacuum vessel was carried out to evaluate the dynamic effect with plasma disruption. The results indicated that the serious dynamic resonance can not be expected.

In this study, an extension of linear-quadratic-Gaussian (LQG) control theory is used to determine the optimal state feedback controller for a nonlinear energy harvesting system that is driven by a stochastic disturbance. Specifically, the energy harvester is a base-excited single-degree-of-freedom (SDOF) resonant oscillator with an electromagnetic transducer embedded between the ground and moving mass. The electromagnetic transducer used to harvest energy from the SDOF oscillator introduces a nonlinear Coulomb friction force into the system, which must be accounted for in the design of the controller. As such, the development of the optimal controller for this system is based on statistical linearization, whereby the Coulomb friction force is replaced by an equivalent linear viscous damping term, which is calculated from the stationary covariance of the closed-loop system. It is shown that the covariance matrix and optimal feedback gain matrix can be computed by implementing an iterative algorithm involving linear matrix inequalities (LMIs). Simulation results are presented for the SDOF energy harvester in which the performance of the optimal state feedback control law is compared to the performance of the optimal static admittance over a range of disturbance bandwidths.

The dynamic response of a structure, which consists of jointed substructures, may be influenced by the nonlinear contact and friction forces inside the joints, even if the deformations are small. In case of joints with a large spatial distribution, like in car bodies or leaf springs, these nonlinearities dominate the overall system behavior. The use of the direct finite element method or a standard model order reduction technique leads to either huge computational costs or inaccurate results. So called ‘Joint Interface Modes’ (JIMs) overcome that problem. They represent a problem oriented extension of classical trial vectors for structures with bolted joints, spot welded seems and similar joints. The result quality is comparable to that one of a direct finite element analysis without losing the efficiency of model order reduction. In this paper a new approach for the computation of such JIMs is presented. The approach is based on so called trial vector derivatives which will be outlined in the theory part of the paper. At the end of the paper, the theory is applied to a static and dynamic example in order to underline the methods accuracy and efficiency.KeywordsModel reductionJointed structuresLap jointsInterface reduction