Experimental Response of a Preloaded Vibro-Impacting Hertzian Contact

2001 ◽  
Author(s):  
Emmanuel Rigaud ◽  
Joël Perret-Liaudet
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Primary Resonance ◽  
External Input ◽  
Hertzian Contact ◽  
Normal Forces ◽  
Linear Dynamic ◽  
Input Amplitude ◽  
Linear Resonance ◽  
Amplitude System

Abstract This paper concerns the non-linear dynamic response of a vibro-impacting Hertzian contact. Sinusoidal and random external normal forces are considered. We focus on the primary resonance and include vibro-impact responses in order to analyze the main characteristics of the system associated to both Hertzian and contact loss non-linearities. Under very small input amplitude, contact exhibits an almost linear resonance. Linearized resonance frequency and damping ratio are identified. Increasing the external input amplitude, the softening behaviour induced by Hertzian nonlinear stiffness is clearly demonstrated for both sinusoidal and random inputs. For higher input amplitude, system exhibits vibro-impacts. The contact loss non-linearity strongly governs the dynamic behaviour of the system.

Motion of a Ball in a Ball Bearing

1973 ◽  
Vol 95 (1) ◽  
pp. 263-268
Author(s):  
H. Portig ◽  
H. G. Rylander
Keyword(s):  
Deformation Theory ◽  
Coulomb Friction ◽  
Ball Bearing ◽  
Digital Simulation ◽  
Equations Of Motion ◽  
Unsteady Motion ◽  
Hertzian Contact ◽  
Contact Deformation ◽  
Normal Forces ◽  
Simulation Language

A method is developed which allows the digital simulation of the unsteady motion of a single ball constrained only by two moving bearing races. Any desired motion of the races can be simulated. Normal forces acting on the ball are calculated by Hertzian contact deformation theory. If there is slippage between ball and races, Coulomb friction is assumed to occur. Solutions to the differential equations of motion were obtained on a computer with the digital simulation language MIMIC. The phenomenon of ball control as well as the behavior of the ball as it reached a controlled state from rest were observed. This analysis can produce more realistic results than methods that assume that the ball is controlled at all times, especially when the races are radially or angularly displaced with respect to each other.

The Dynamic Behaviour of Passively Compensated, Hydrostatic Journal Bearings with Various Numbers of Recesses

1976 ◽  
Vol 18 (6) ◽  
pp. 292-302 ◽  
Author(s):  
P. B. Davies
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
Flow Equation ◽  
External Excitation ◽  
Signal Flow Graphs ◽  
Flow Compensation ◽  
Circular Functions ◽  
Flow Graphs

A previously established small-perturbation analysis is developed to express the unsteady-state continuity-of-flow equation for an isolated recess in a passively compensated, multirecess, hydrostatic journal bearing in terms of generalized co-ordinates. The concise form of this equation enables motion of the shaft about the concentric position to be described by equations which are derived in closed form for bearings with orifice, capillary or constant flow compensation and any number of recesses. These equations of motion, and hence the expressions for the receptances which describe the response of a bearing to external excitation, are shown to be of exactly the same form for all bearings of the type considered. Furthermore, the damping ratio and natural frequency in any particular case are determined by a single dynamic constant which is shown to be equal to a linear combination of circular functions and a limited number of coefficients which may be found explicitly by routine use of signal flow graphs. The results of the analysis, which is exact within the stated assumptions, are compared with those of other workers and the steady-state solution of the equations of motion is shown to give an expression for static stiffness which is useful for design purposes. Numerical values of the dynamic constant for bearings with between 3 and 20 recesses are given graphically.

A Study of Effect of Various Normal Force Loading Forms on Frictional Stick-Slip Vibration

2021 ◽  
Author(s):  
Xiaocui Wang ◽  
◽  
Runlan Wang ◽  
Bo Huang ◽  
Jiliang Mo ◽  
...  
Keyword(s):  
Dynamic Behaviour ◽  
Normal Force ◽  
Time Varying ◽  
Stick Slip ◽  
Vibration Signals ◽  
Theoretical Methods ◽  
Normal Forces ◽  
Frequency Domains ◽  
Amplitude Vibration ◽  
Fourier Spectra

In this work, a comparative study is performed to investigate the influence of time-varying normal forces on the friction properties and friction-induced stick-slip vibration by experimental and theoretical methods. In the experiments, constant and harmonic-varying normal forces are applied, respectively. The measured vibration signals under two loading forms are compared in both time and frequency domains. In addition, mathematical tools such as phase space reconstruction and Fourier spectra are used to reveal the science behind the complicated dynamic behaviour. It can be found that the friction system shows steady stick-slip vibration, and the main frequency does not vary with the magnitude of the constant normal force, but the size of limit cycle increases with the magnitude of the constant normal force. In contrast, the friction system harmonic normal force shows complicated behaviour, for example, higher-frequency larger-amplitude vibration occurs as the frequency of the normal force increases. The interesting findings offer a new way for controlling friction-induced stick-slip vibration in engineering applications.

The complex stiffnes method to detect and identify non-linear dynamic behaviour of SDOF systems

1989 ◽  
Vol 3 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Mertens ◽  
H. Van der Auweraer ◽  
P. Vanherck ◽  
R. Snoeys
Keyword(s):  
Dynamic Behaviour ◽  
Linear Dynamic ◽  
Non Linear

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%.

Analysis on Impact Loading at Rail Welds at High Speed

2008 ◽  
Author(s):  
Guangwen Xiao ◽  
Xinbiao Xiao ◽  
Zefeng Wen ◽  
Xuesong Jin
Keyword(s):  
Impact Loading ◽  
High Speed ◽  
Hertzian Contact ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Explicit Integration ◽  
Normal Forces ◽  
Rail Irregularity ◽  
Multi Body ◽  
The Impact

When a railway vehicle passes through a track with different weld irregularities at high speed, the impact loading of the vehicle coupled with the track is investigated in detail using a coupled vehicle/track model. In this model, a half vehicle is considered and modeled as a multi-body system. In the track model, a Timoshenko beam resting on discrete sleepers is applied to model each rail. Each sleeper is modeled as a rigid body accounting for its vertical, lateral, roll motions. A moving sleeper support model is used to simulate the interaction of the vehicle and the track. The ballast bed is replaced with equivalent masses. The equivalent dampers and springs are used to replace the connections between the parts of the vehicle and track. In calculating the coupled vehicle and track dynamics, Hertzian contact theory and the creep force theory by Shen et al. are, respectively, used to calculate the normal forces and the creep forces between the wheels and the rails. The motion equations of the vehicle-track are solved by means of an explicit integration method. The weld rail irregularity is modeled by setting a local track vertical deviation at a rail weld joint, which is described with a simplified cosine function. In the numerical analysis the effect of the different wavelength, depth, the position of the welded joint in a sleeper span, and vehicle speed is taken into account. The numerical results obtained are greatly useful in the tolerance design of welded rail profile irregularity caused by damage and hand-grinding after rail welding.

An Investigation of Steady-State Dynamic Response of a Sphere-Plane Contact Interface With Contact Loss

2006 ◽  
Vol 74 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Q. L. Ma ◽  
A. Kahraman ◽  
J. Perret-Liaudet ◽  
E. Rigaud
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Numerical Solutions ◽  
Fourier Transforms ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Hertzian Contact ◽  
Contact Interface ◽  
Discrete Fourier Transforms ◽  
Plane Contact

In this study, the dynamic behavior of an elastic sphere-plane contact interface is studied analytically and experimentally. The analytical model includes both a continuous nonlinearity associated with the Hertzian contact and a clearance-type nonlinearity due to contact loss. The dimensionless governing equation is solved analytically by using multi-term harmonic balance method in conjunction with discrete Fourier transforms. The accuracy of the dynamic model and solution methods is demonstrated through comparisons with experimental data and numerical solutions for both harmonic amplitudes of the acceleration response and the phase difference between the response and the force excitation. A single-term harmonic balance approximation is used to derive a criterion for contact loss to occur. The influence of harmonic external excitation f(τ) and damping ratio ζ on the steady state response is also demonstrated.

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