Multiple Solutions in an Amplitude Limited Jeffcott Rotor Including Rubbing and Stick-Slip Effect

2005 ◽  
Author(s):  
Jan-Olov Aidanpa¨a¨
Keyword(s):  
Bifurcation Diagram ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Slip Effect ◽  
Chaotic Motions ◽  
Stick Slip ◽  
Diagram Method ◽  
Machine Failure ◽  
Jeffcott Rotor ◽  
Stable Solutions

The non-linear behaviour of rub-impact rotors have been studied in several papers. In such systems rich dynamics have been found together with the coexistence of solutions within some specific parameter ranges. In this paper an attempt is made to find all stable solutions for an amplitude limited Jeffcott rotor including rubbing and stick-slip effect. The recently suggested “multi bifurcation diagram method” is used to find and extract stable sets of bifurcation diagrams. A system is chosen where the linear stationary amplitude only exceeds the clearance in a narrow region near the natural frequency. Therefore large regions in frequency are expected to have only the linear stationary response. The results show that it is only for very low frequencies that one single solution exists. Even though periodic motions are dominant, there exist large ranges in frequency with quasi-periodic or chaotic motions. For the studied cases, three coexisting stable solutions are most common. In one case as many as four stable solutions was found to coexist. For rotors with large clearances (no impacts necessary) it is still possible to find several coexisting motions. For all cases the stick motion is the most severe one with large amplitudes and high backward whirl frequencies. In real situations the consequence of this stick motion is machine failure. These high amplitude motions were found to be stable over large frequency ranges. From the stability analysis it was found that this rolling motion can be avoided by low spin speed, low contact stiffness, low coefficient of friction, small ratio of disc radius/clearance or high damping ratio. In a design situation the parameters are seldom known with high accuracy. Therefore, it is of interest to know all solutions for parameter intervals. The multi-bifurcation diagram can be used in such situations to design a robust machine or at least be prepared for unwanted dynamics.

scholarly journals A Prediction Method with Altering Equivalent Stiffness for Damping Evaluation of Shrouded Bladed Disk Dynamic Systems

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 413
Author(s):  
Shimin Gao ◽  
Yanrong Wang ◽  
Zhiwei Sun ◽  
Siyuan Chen
Keyword(s):  
Contact Surface ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Characteristic Curve ◽  
Prediction Method ◽  
Blade Vibration ◽  
Stick Slip ◽  
Bladed Disk ◽  
Damping Characteristics ◽  
Vibration Stress

In turbomachinery bladed disks are typical cyclic symmetric structures where high-cycle fatigue of the blades can easily occur. Increasing the shroud structure is an effective blade vibration reduction method using the dry friction of the shroud contact surface to dissipate vibration energy. During one vibration cycle of the blade, the contact surface of the shroud may have one or several states of stick, slip, and separation due to the different amplitude of blade, which affects not only the damping, but also the stiffness of the system. This paper proposes a method to analyze the damping characteristics of blades with shroud considering the change of equivalent contact stiffness of the shroud by using the finite element method. With a 2D contact model, this method calculates the equivalent damping and obtains the damping characteristic curve to evaluate the damping of shroud. During the design phase, the objective is that when resonance occurs, the shroud can provide the optimal damping ratio under the allowable vibration stress of the blade. The parameter sensitivity of the damping characteristic for one bladed disk with parallel shroud is investigated. It is shown that vibration phase angle, contact stiffness, contact force, friction coefficient significantly influence the damping characteristics.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Simulacija i odstranjivanje stick-slip efekta servosistema sprovodnog aparata hidraulične turbine

2021 ◽  
Vol 23 (1) ◽  
pp. 37-41
Author(s):  
Darko Babunski ◽  
◽  
Emil Zaev ◽  
Atanasko Tuneski ◽  
Laze Trajkovski ◽  
...  
Keyword(s):  
Hydraulic Cylinder ◽  
Friction Model ◽  
Slip Effect ◽  
Hydraulic Systems ◽  
Hydraulic Actuator ◽  
Stick Slip ◽  
Hydro Turbine ◽  
Servo Mechanism ◽  
The Mathematical Model ◽  
Slip Phenomenon

Friction is a repeatable and undesirable problem in hydraulic systems where always has to be a tendency for its removal. In this paper, the friction model is presented through which the most accurate results are achieved and the way of friction compensation, approached trough technique presented with the mathematical model of a hydraulic cylinder of a hydro turbine wicket gate controlled by a servomechanism. Mathematical modelling of a servo mechanism and hydraulic actuator, and also the simulation of hydraulic cylinder as a part of a hydro turbine wicket gate hydraulic system where the stick-slip phenomenon is present between the system components that are in contact is presented. Applied results in this paper and the theory behind them precisely demonstrate under what circumstances the stick-slip phenomenon appears in such a system. The stick-slip effect is simulated using Simulink and Hopsan software and the analysis of the results are given in this paper. Removal of the stick-slip effect is presented with the design of a cascade control implemented to control the behaviour of the system and remove the appearance of a jerking motion.

A Novel Trans-Scale Precision Positioning Stage Based on the Stick-Slip Effect

2012 ◽  
Vol 2 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Bowen Zhong ◽  
Liguo Chen ◽  
Zhenhua Wang ◽  
Lining Sun
Keyword(s):  
Friction Model ◽  
Slip Effect ◽  
Precision Positioning ◽  
Stick Slip ◽  
Kinematics Model ◽  
Lugre Friction Model ◽  
Positioning Stage ◽  
Simulation Results ◽  
Relationship Of ◽  
The Relationship

This article focuses on developing a novel trans-scale precision positioning stage based on the stick-slip effect. The stick-slip effect is introduced and the rigid kinematics model of the stick-slip driving is established. The forward and return displacement equations of each step of the stick-slip driving are deduced. The relationship of return displacement and the acceleration produced by friction are obtained according to displacement equations. Combining with LuGre friction model, the flexible dynamics model of the stick-slip driving is established and simulated by using Simulink software. Simulation results show that the backward displacement will reduce with the acceleration of the slider produced by dynamic friction force, the rigid kinematics model is also verified by simulation results which are explained in further detail in the article.

scholarly journals Load-dependent surface nanomechanical properties of poly-HEMA hydrogels in aqueous medium

Soft Matter ◽  
2019 ◽  
Vol 15 (38) ◽  
pp. 7704-7714 ◽  
Author(s):  
Gen Li ◽  
Illia Dobryden ◽  
Eric Johansson Salazar-Sandoval ◽  
Mats Johansson ◽  
Per M. Claesson
Keyword(s):  
Aqueous Medium ◽  
Cross Linking ◽  
Slip Effect ◽  
Stick Slip ◽  
Nanomechanical Properties ◽  
Combined Action

The combined action of load and shear results in the formation of a temporary sub-micrometer hill in front of the tip. As the tip pushes against such hills, a pronounced stick-slip effect is observed for the hydrogel with low cross-linking density.

Non-Linear Coupled Dynamics of a Flexible Propeller-Shaft System Supported by Water Film Bearings

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Chang-Gang Lin ◽  
Ming-Song Zou ◽  
Can Sima ◽  
Li-Bo Qi ◽  
Yue Yu
Keyword(s):  
Nonlinear Vibration ◽  
Damping Ratio ◽  
Water Film ◽  
Vibration Characteristics ◽  
Superposition Method ◽  
Propeller Shaft ◽  
Chaotic Motions ◽  
Mode Superposition Method ◽  
Shaft System ◽  
Slice Method

Abstract A slice method to determine the boundary conditions between the stern bearing and shaft by dividing the journal in the stern bearing into several slice elements along the axial direction is proposed for the first time. A comprehensive finite element model considering the nonlinear force of the water film and the flexibility of the propeller blade is established for a propeller-shaft system. The long bearing approximation is adopted to calculate the pressure distribution around each journal element in the stern bearing. The mode superposition method is employed. The nonlinear equation of motion is solved iteratively using the Newmark method. A parametric study is implemented to analyze the nonlinear vibration characteristics of the system. It is shown that the real motion state of the journal in the stern bearing can be simulated more precisely by the slice method proposed. The responses of the system alternate among period-one, quasi-periodic, multi-periodic, and chaotic motions as the rotating speed increases. The damping ratio has a significant effect on the dynamic characteristics of the propeller-shaft system. The motion of the system is unstable when the damping ratio is very small. At this time, the modes of the flexible propeller blades can be excited readily. The slice method, which can also be extensively used in similar rotor-bearing systems in the engineering field, is very simple and efficient to analyze the nonlinear vibration characteristics of a flexible propeller-shaft system supported by water film bearings.

Stick-Slip Behaviour of Seals With Respect to Time Dependent Friction Forces

2004 ◽  
Author(s):  
Markus Lindner ◽  
Matthias Kro¨ger ◽  
Karl Popp ◽  
Manuel Gime´nez
Keyword(s):  
Stability Analysis ◽  
Time Dependent ◽  
Dynamic Friction ◽  
Slip Effect ◽  
Stick Slip ◽  
Friction Forces ◽  
Seal Design

In the present paper dynamic friction processes in seals are investigated. The undesired stick-slip effect of these components under real technical conditions is analyzed. Starting with the basics of stick-slip vibrations the development of an advanced seal design with improved properties is presented that prevents stick-slip. Finally, an optimization based on the extensive but simple stability analysis is shown by an expanded theory of stick-slip simulations.

Braking Impact of Normal Dither Signals

2005 ◽  
Author(s):  
Jeff Badertscher ◽  
Kenneth A. Cunefare
Keyword(s):  
Contact Stiffness ◽  
Frequency Control ◽  
Primary Resonance ◽  
Theoretical Models ◽  
Friction Reduction ◽  
Hertzian Contact ◽  
Brake Squeal ◽  
Stick Slip ◽  
Friction Oscillator ◽  
Braking Torque

Dither control is a method of introducing high frequency control efforts into a system to suppress a lower frequency disturbance. One application of dither control is the suppression of automotive brake squeal. Brake squeal is a problem that has plagued the automotive industry for years. Placing a piezoceramic stack actuator in the piston of a floating caliper brake creates an experimental normal dither system. Many theoretical models indicate a reduction in the braking torque due to the normal dither signal. Using a Hertzian contact stiffness model the loss in friction is due to lowering the average normal force. There are also theories that the dither signal eliminates the ‘stick-slip’ oscillation causing an effective decrease in the friction force. Yet another theory indicates that the effective contact area is reduced, lowering the mean coefficient of friction. A particular approach considering a single degree of freedom friction oscillator predicts a maximum friction reduction of 10%, occurring at the primary resonance of the system. This paper will concentrate on validating this claim by experimentally determining braking torque reduction for a variety of dither control signals. Several dither control frequencies were chosen at system resonances, while others were chosen at frequencies most likely to provide control of the system. These frequencies were chosen based on previous squeal suppression research. The results indicate that dither control frequencies at system resonances have a greater impact on the braking system’s performance. In general, dither control reduces braking torque by no more than 2%.

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