scholarly journals Vibrations of Misaligned Rotor System with Hysteretic Friction Arising from Driveshaft–Stator Contact under Dispersed Viscous Fluid Influences

2021 ◽  
Vol 11 (17) ◽  
pp. 8089
Author(s):  
Bernard Xavier Tchomeni ◽  
Alfayo Alugongo
Keyword(s):  
Viscous Fluid ◽  
Power Transmission ◽  
Viscous Medium ◽  
Rotor System ◽  
Hertzian Contact ◽  
Engineering Practice ◽  
Flexible Coupling ◽  
Parametric Studies ◽  
Cardan Joint ◽  
Hertzian Contact Theory

Dynamic analysis of a combination of misaligned rotors, the disturbance of the Cardan joint and the rotor–stator rubbing within a restricted clearance space in a viscous fluid is complex and can result in persistent vibration anomalies that are often misunderstood. It becomes increasingly important to gain some insights into how the transmission of coupled motion responds dynamically under a variety of conditions. This paper introduces an efficient simulation of the misaligned multi-degree-of-freedom rotor’s model, which was developed to predict the transient dynamic behaviours of a driveshaft deflection. The model accounts for tight clearance as a function of contact deformation according to nonlinear Hertzian contact theory. The paper also examines recent research by considering the influence of parameters such as eccentric masses, applied torques and flexible coupling joint perturbation introduced in the proposed rotor system. The simulation results indicated that the viscous fluid surrounding the driveshaft had sufficient torsional flexibility to dampen the rubbing impact to the driven shaft displacement. In addition, the torsional fluctuations of the flexible coupling abruptly increased, and then significantly impacted the vibration of the submerged driveshaft. Parametric studies involving the interconnected rotor models indicated that the effects of fluid on a close-bounds contact area can create partial disturbance reduction. The high rubbing contact is shown to be lost through the Hooke’s joints during power transmission. The speed-frequency spectrum maps provide valuable information on all the modelled excitations over the frequency of the twice-running speed resonance in a viscous medium. Further, nonlinear characteristics are reconstructed through orbit shapes and can be adopted in the condition monitoring of rotors in engineering practice.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

Critical examination of various approaches used for analysing helical cables

1994 ◽  
Vol 29 (1) ◽  
pp. 43-55 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Large Diameter ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Critical Examination ◽  
First Order ◽  
Wide Range ◽  
End Conditions ◽  
Parametric Studies ◽  
The Individual ◽  
Fixed End

Using theoretical parametric studies covering a wide range of cable (and wire) diameters and lay angles, the range of validity of various approaches used for analysing helical cables are critically examined. Numerical results strongly suggest that for multi-layered steel strands with small wire/cable diameter ratios, the bending and torsional stiffnesses of the individual wires may safely be ignored when calculating the 2 × 2 matrix for strand axial/torsional stiffnesses. However, such bending and torsional wire stiffnesses are shown to be first order parameters in analysing the overall axial and torsional stiffnesses of, say, seven wire stands, especially under free-fixed end conditions with respect to torsional movements. Interwire contact deformations are shown to be of great importance in evaluating the axial and torsional stiffnesses of large diameter multi-layered steel strands. Their importance diminishes as the number of wires associated with smaller diameter cables decreases. Using a modified version of a previously reported theoretical model for analysing multilayered instrumentation cables, the importance of allowing for the influence of contact deformations in compliant layers on cable overall characteristics such as axial or torsional stiffnesses is demonstrated by theoretical numerical results. In particular, non-Hertzian contact formulations are used to obtain the interlayer compliances in instrumentation cables in preference to a previously reported model employing Hertzian theory with its associated limitations.

Approximate Analytical Model for Hertzian Elliptical Wheel/Rail or Wheel/Crossing Contact Problems

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
F. D. Fischer ◽  
M. Wiest
Keyword(s):  
Contact Pressure ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Technical Accuracy ◽  
Elliptical Contact ◽  
Current Approximation ◽  
Analytical Expressions ◽  
Maximum Contact ◽  
Hertzian Contact Theory

The Hertzian contact theory is approximated according to a concept by Tanaka (2001, “A New Calculation Method of Hertz Elliptical Contact Pressure,” ASME J. Tribol., 123, pp. 887–889) yielding simple analytical expressions for the elliptical semi-axes, the maximum contact pressure, the mutual approach and the contact spring constant. Several configurations are compared using the exact Hertz theory and the current approximation. The results agree within technical accuracy.

Simulation of Traction Drive Ratio Changes

2000 ◽  
Author(s):  
Z. Zou ◽  
Y. Zhang ◽  
X. Zhang ◽  
W. Tobler
Keyword(s):  
Hertzian Contact ◽  
Contact Theory ◽  
Hydrodynamic Theory ◽  
Traction Drive ◽  
Input And Output ◽  
Piston Displacement ◽  
Simulation Results ◽  
Traction Drives ◽  
Stability And Accuracy ◽  
Hertzian Contact Theory

Abstract In the simulation model presented in this paper, the kinematic characteristics of traction drives are formulated using classical Hertzian contact theory and elasto-hydrodynamic theory. The roller swing motion is governed by an equation derived based on Newton’s Second Law and is coupled to the side slip, torque input and output, as well as ratio variations. A control strategy with feedbacks for both the roller swing and the piston displacement is applied for ratio control based on stability and responsiveness considerations. The model has been implemented systematically in Matlab/Simulink environment. The effectiveness of the ratio control system in terms of stability and accuracy is illustrated by the simulation results included in this paper.

Difference between the ideal and combined spherical joints and its effects on parallel manipulators

2019 ◽  
Vol 234 (5) ◽  
pp. 1112-1129
Author(s):  
Shuai Fan ◽  
Shouwen Fan
Keyword(s):  
Machine Tools ◽  
Parallel Manipulators ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Contact Deformation ◽  
Spherical Joint ◽  
Universal Joint ◽  
Deformation Models ◽  
Hertzian Contact Theory ◽  
The Ideal

When using parallel manipulators as machine tools, the spherical joint has been widely used and replaced by a combination of a universal joint and a rotating unit, but the introduced differences and effects have not been studied in detail. In this paper, an approach to establish the mathematical models of the ideal and combined spherical joints is presented, and the differences between the two spherical joints are given from the perspective of constraints, workspace, clearance, and contact deformation. First, the non-interference workspace of a class universal joint is investigated by using a simple and clear projection method, where the constraint domain and workspace of two spherical joints are proposed. Next, the approximate clearance models of these two spherical joints are analyzed, and the corresponding contact deformation models are also given based on the Hertzian Contact theory. Finally, a 1PU + 3UPS parallel manipulator is used to verify the discrepant effects of two spherical joints on parallel manipulators. If the combined spherical joint is used, the results indicate that the improvement in the workspace is significant, but the drop in stiffness is also evident. Thus, this paper provides a theoretical basis for researchers to use combined spherical joints.

Shock Isolation in Finite-Length Dimer Chains With Linear, Cubic, and Hertzian Spring Interactions

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Eric Smith ◽  
Aldo Ferri
Keyword(s):  
Numerical Simulations ◽  
Finite Length ◽  
Hertzian Contact ◽  
Mass Ratio ◽  
Transmitted Force ◽  
Parametric Studies ◽  
Shock Isolation ◽  
Isolation Systems ◽  
Chain Lengths ◽  
Isolation Performance

This paper investigates the use of finite 1:1 dimer chains to mitigate the transmission of shock disturbances. Dimer chains consist of alternating light and heavy masses with interconnecting compliance. Changing the mass ratio has provided interesting results in previous research. In particular, in the case of Hertzian contacts with zero-preload, certain mass ratios have revealed minimal levels of transmitted force. This paper examines this phenomenon from the perspective of utilizing it in practical isolation systems. The zero-preload Hertzian contact case is contrasted with chains connected by linear or cubic springs. Through numerical simulations, tradeoffs are examined between displacement and transmitted force. Parametric studies are conducted to examine how isolation performance changes with mass ratio, stiffness, and different chain lengths.

A Systematic Model for the Analysis of Contact, Side Slip and Traction of Toroidal Drives

1999 ◽  
Vol 122 (4) ◽  
pp. 523-528 ◽  
Author(s):  
Y. Zhang ◽  
X. Zhang ◽  
W. Tobler
Keyword(s):  
Traction Force ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Kinematic Parameters ◽  
Traction Drive ◽  
Continuously Variable Transmissions ◽  
Toroidal Traction ◽  
Hertzian Contact Theory ◽  
Slip Force ◽  
Ratio Range

This paper presents a systematic model for the design and analysis of toroidal traction drive continuously variable transmissions (CVT). The contacts between the input disk, the roller and the output disk of the traction drive are formulated using the classical Hertzian contact theory. The traction force and side slip force occurring in CVT operation are modelled based on the elasto-hydrodynammic theory and are correlated to the traction drive geometric and kinematic parameters. The model allows for the quantitative analysis of traction drive operation under various torque inputs and over the desired ratio range. [S1050-0472(00)01004-7]

Dynamic Analysis of a Nonlinear Torsional Flexible Coupling With Elastic Links

2003 ◽  
Vol 125 (3) ◽  
pp. 509-517 ◽  
Author(s):  
Charles W. Bert ◽  
Shiyuan Wu
Keyword(s):  
Dynamic Analysis ◽  
System Performance ◽  
Power Transmission ◽  
Angular Displacement ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Flexible Coupling ◽  
Elastic Links ◽  
Lagrange’S Equation ◽  
Power Transmission Systems

Torsional oscillations in mechanical power transmission systems are a significant source of dynamic loads which are harmful to the system performance. The effects can cause a drive shaft to become unstable and self-destructive at critical speeds. This research focuses on dynamic analysis of a nonlinear torsional flexible coupling with elastic links. The equations of motion are derived by means of Lagrange’s equation. These equations are used to obtain the quasi-static performance of torque vs. angular displacement at constant rotational velocity. An exact solution is also found for the phase-plane representation for free oscillation torque. The fluctuation ratios of input velocity vs. output velocity of the system are obtained for determining the system performance. The results of the analyses of steady running and transient oscillation performance are applied to the determination of optimum proportions of the couplings. Results are compared with those of rigid-link couplings to show the influence of elasticity of the link on dynamic behavior of the system.

Extension of Hertzian Theory for Bodies With a Single Coating

2003 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Numerical Solutions ◽  
Layered Materials ◽  
Sufficient Accuracy ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Numerical Analyses ◽  
Convenient Tool ◽  
Homogeneous Materials ◽  
Hertzian Contact Theory ◽  
Single Coating

The Hertzian theory is a convenient tool for analyzing counterformal bodies in mechanical contacts. However, it is limited to homogeneous materials. This paper reports the results from recent research that extends the Hertzian contact theory to layered materials. Numerical analyses are conducted to evaluate the accuracy of the formulas of the extended Hertzian theory, and the comparison with numerical solutions indicates that the formulas have sufficient accuracy.

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