Nonlinear Friction-Induced Vibration of a Slider–Belt System

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Zilin Li ◽  
Huajiang Ouyang ◽  
Zhenqun Guan
Keyword(s):  
Nonlinear System ◽  
Transient Analysis ◽  
Contact Stiffness ◽  
Linear Part ◽  
Realistic Model ◽  
Complex Eigenvalue ◽  
Nonlinear Stiffness ◽  
Model Of Friction ◽  
Mass Spring ◽  
Friction Induced Vibration

A mass–spring–damper slider excited into vibration in a plane by a moving rigid belt through friction is a major paradigm of friction-induced vibration. This paradigm has two aspects that can be improved: (1) the contact stiffness at the slider–belt interface is often assumed to be linear and (2) this contact is usually assumed to be maintained during vibration (even when the vibration becomes unbounded at certain conditions). In this paper, a cubic contact spring is included; loss of contact (separation) at the slider–belt interface is allowed and importantly reattachment of the slider to the belt after separation is also considered. These two features make a more realistic model of friction-induced vibration and are shown to lead to very rich dynamic behavior even though a simple Coulomb friction law is used. Both complex eigenvalue analyses of the linearized system and transient analysis of the full nonlinear system are conducted. Eigenvalue analysis indicates that the nonlinear system can become unstable at increasing levels of the preload and the nonlinear stiffness, even if the corresponding linear part of the system is stable. However, they at a high enough level become stabilizing factors. Transient analysis shows that separation and reattachment could happen. Vibration can grow with the preload and vertical nonlinear stiffness when separation is considered, while this trend is different when separation is ignored. Finally, it is found that the vibration magnitudes of the model with separation are greater than the corresponding model without considering separation in certain conditions. Thus, ignoring the separation is unsafe.

Does a Predictive Minimal Model of Friction-Induced Vibration Exist?

2010 ◽  
Author(s):  
Tore Butlin ◽  
Jim Woodhouse
Keyword(s):  
Minimal Model ◽  
Mode Coupling ◽  
Test System ◽  
Minimal Models ◽  
Pin On Disc ◽  
Limited Frequency ◽  
Extensive Program ◽  
Negative Damping ◽  
Model Of Friction ◽  
Friction Induced Vibration

Highly idealised models of friction-induced vibration have been motivated by an attempt to capture what is essential to the phenomenon. This approach has resulted in a few simple mechanisms that are thought to capture common routes to instability. This paper aims to determine how well these perform as approximations to a more complex system, and whether the essential ingredients needed for a minimal model can be identified. We take a reduced-order model that exemplifies ‘mode-coupling’ and explore the extent to which it can approximate predictions based on an experimentally identified test-system. For the particular test system under study, two-mode ‘mode-coupling’ is rarely a good approximation and three modes are usually required to model a limited frequency range. We then compare predictions with results from an extensive program of sliding contact tests on a pin-on-disc rig in order to identify which ingredients are needed to explain observed squeal events. The results suggest that several minimal models would be needed to describe all observed squeal initiations, but the ‘negative-damping’ route to instability, which requires a velocity-dependent friction law, convincingly accounts for one cluster.

Transient Calculation of Electric Power Circuits with Special Reference to Magnetizing Nonlinearity

2016 ◽  
Vol 25 (06) ◽  
pp. 1650054
Author(s):  
Xiaoqin Zhang
Keyword(s):  
Electric Power ◽  
Nonlinear Differential Equations ◽  
Linear Part ◽  
Realistic Model ◽  
Power Circuit ◽  
Runge Kutta Method ◽  
Proposed Model ◽  
Power Circuits ◽  
Set Up ◽  
Reduced Scale

This paper proposes a realistic model of magnetizing branches for transient calculation of electric power circuits. The model represents the nonlinear relationship between flux linkage and exciting current of magnetizing branches with a major loop and a family of minor loop trajectories, which has the capability of simulating the multi-valued hysteresis behavior. By applying the proposed model to transient calculation, an efficient algorithm is developed for obtaining the transient responses in electric power circuits. In the algorithm, the electric power circuit is divided into the magnetizing branches and the remaining linear part. The nonlinear differential equations are set up for the magnetizing branches and solved by the semi-explicit Runge–Kutta method. The transient calculation for the remaining linear part is performed on the basis of the solution to the magnetizing branches. Then, a laboratory measurement is made with a reduced-scale experimental arrangement. The measured results are compared with the calculated ones and a reasonable agreement is shown between them.

S-synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems

2020 ◽  
Vol 21 (6) ◽  
pp. 323-336
Author(s):  
N. N. Karabutov
Keyword(s):  
Nonlinear System ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Structural Parameters ◽  
Linear Part ◽  
Structural Identification ◽  
Nonlinear Dynamic Systems ◽  
Necessary Condition ◽  
Structural Identifiability ◽  
Nonlinear Part

An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.

scholarly journals Analytical Modeling of a Ball Screw Feed Drive for Vibration Prediction of Feeding Carriage of a Spindle

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lei Zhang ◽  
Taiyong Wang ◽  
Songling Tian ◽  
Yong Wang
Keyword(s):  
Mathematical Model ◽  
Analytical Modeling ◽  
Contact Stiffness ◽  
Ball Screw ◽  
Linear Guide ◽  
Feed Drives ◽  
Vibration Prediction ◽  
Spring System ◽  
Mass Spring ◽  
Screw Feed

An analytical modeling approach for ball screw feed drives is proposed to predict the dynamic behavior of the feeding carriage of a spindle. Mainly considering the rigidity of linear guide modules, a ball-screw-feeding spindle is modeled by a mass-spring system. The contact stiffness of rolling interfaces in linear guide modules is accurately calculated according to the Hertzian theory. Next, a mathematical model is derived using the Lagrange method. The presented model is verified by conducting modal experiments. It is found that the simulated results correspond closely with the experimental data. In order to show the applicability of the proposed mathematical model, parameter-dependent dynamics of the feeding carriage of the spindle is investigated. The work will contribute to the vibration prediction of spindles.

State Feedback Guaranteed Cost Control of Parameter Uncertain Nonlinear System

2011 ◽  
Vol 58-60 ◽  
pp. 803-809
Author(s):  
Chuan Feng Li ◽  
Yong Ji Wang ◽  
Yun Xing Shu ◽  
Zhi Shen Wang
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Linear Part ◽  
Nonlinear Function ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Actual System ◽  
Model Combining ◽  
Guaranteed Cost ◽  
Nonlinear Features

In an actual system, the effects of nonlinear factors are inevitable. So in real practice, when a model for complex system is being built, all the features in it will be linearized. Though simplifying the designing and analyzing process, the model being built in this way is thought to be incapable of revealing the true characteristics of the system. In order to solve this problem, the paper analyzes a model combining both linear and nonlinear features while taking the parameter perturbation of the linear part into consideration, which enables the model to retain as many characteristics of the actual system as possible. Provided that the nonlinear function satisfies the Lipschitz constraint conditions, the robust guaranteed cost state feedback control law of nonlinear system is deduced using the Lyapunov function and then converted into the feasible solutions of linear matrix inequality (LMI). The proposed method optimizes the design of controller by modifying the previous oversimplified models that fail to reveal the real characteristics of the actual system, and the effectiveness of the proposed method is being verified through an algorithm simulation example.

The Effect of Hertzian, Bending and Shearing Stiffness on Noise and Vibration

2001 ◽  
Author(s):  
Jamil Abdo ◽  
Kambiz Farhang ◽  
Mousa Mohsen
Keyword(s):  
Mathematical Model ◽  
Contact Stiffness ◽  
Hertzian Contact ◽  
Hertz Contact ◽  
Resonant Frequencies ◽  
Tangential Contact ◽  
Apparent Stiffness ◽  
Fundamental Understanding ◽  
The Mathematical Model ◽  
Friction Induced Vibration

Abstract Since the apparent stiffness due to contact of one surface on another relates directly to the localized resonant frequencies, it is believed that accurate account of this property will lead to the fundamental understanding of causes of friction-induced vibration and noise. The mathematical model of contact is utilized to develop formulae for normal and tangential contact stiffness. The inclusion of a study in which the various modes of elastic deflections of an asperity are also considered, as well as their effects. The bending, shear and Hertz contact modes of elastic deflection are assumed to simultaneously occur for an asperity. Investigation of the combined effect of bending, shear and Hertzian contributions to the contact stiffness is indicating that the equivalent contact stiffness is best represented, among the three types of stiffness, by that due to Hertzian contact.

The Effect of Spring Mass on Nonlinear System Dynamic Behavior

2012 ◽  
Vol 197 ◽  
pp. 120-123
Author(s):  
Qing Chao Yang ◽  
Jing Jun Lou ◽  
Hai Ping Wu ◽  
Si Mi Tang
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Dynamic Behavior ◽  
Phase Plane ◽  
Dead Zone ◽  
Great Influence ◽  
System Dynamic ◽  
Motion Trajectories ◽  
Mass Spring ◽  
The Impact

A model is established in this paper about the impact of mass spring on the particle in nonlinear systems with dead-zone and the particle’s subsequent synchronised movement with spring. Simulates are conducted under different conditions, and it is found that when the spring mass is large, the phase plane of particle’s motion trajectories change significantly to the condition when spring is no mass. It is concluded that the spring mass have a great influence on the dynamic behavior of nonlinear systems with dead-zone.

Dynamics Characteristic of a Linear Oscillator with Nonlinear Damped Attachment as Energy Absorber

2010 ◽  
Vol 44-47 ◽  
pp. 2651-2655 ◽  
Author(s):  
Jian Lian Cheng
Keyword(s):  
Numerical Analysis ◽  
Nonlinear System ◽  
Periodic Orbits ◽  
Dynamic Structure ◽  
Nonlinear Stiffness ◽  
Complex Dynamic ◽  
Energy Absorber ◽  
Energy Pumping ◽  
Two Degree Of Freedom ◽  
Dynamics Characteristic

The dynamics of a two-degree-of-freedom (2-DOF) nonlinear system, consisting of a grounded linear coupled to an attachment by means of an essentially nonlinear stiffness, is studied. The essential nonlinearity of the attachment enable it to resonate with any of the linearized modes of the substructure leading to energy pumping phenomena, irreversible transfer of energy from the substructure to the attachment. We then study analytically the periodic orbits of the system using a complexification/averaging technique in order to determine the frequency contents of the fundamental branches of solutions, and to understand the types of oscillation performed by the system at different regimes of the motion. The results of numerical analysis show complex dynamic structure of the system.

scholarly journals A Novel Method for Fault Diagnosis of the Two-Input Two-Output Nonlinear Mass-Spring-Damper System Based on NOFRF and MBPCA

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jialiang Zhang ◽  
Jie Wu ◽  
Xiaoqian Zhang
Keyword(s):  
Principal Component Analysis ◽  
Fault Diagnosis ◽  
Nonlinear System ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Principal Component ◽  
Component Analysis ◽  
Novel Method ◽  
Mass Spring

For fault diagnosis of the two-input two-output mass-spring-damper system, a novel method based on the nonlinear output frequency response function (NOFRF) and multiblock principal component analysis (MBPCA) is proposed. The NOFRF is the extension of the frequency response function of the linear system to the nonlinear system, which can reflect the inherent characteristics of the nonlinear system. Therefore, the NOFRF is used to obtain the original fault feature data. In order to reduce the amount of feature data, a multiblock principal component analysis method is used for fault feature extraction. The least squares support vector machine (LSSVM) is used to construct a multifault classifier. A simplified LSSVM model is adopted to improve the training speed, and the conjugate gradient algorithm is used to reduce the required storage of LSSVM training. A fault diagnosis simulation experiment of a two-input two-output mass-spring-damper system is carried out. The results show that the proposed method has good diagnosis performance, and the training speed of the simplified LSSVM model is significantly higher than the traditional LSSVM.

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