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%.

Braking Impact of Normal Dither Signals

2006 ◽  
Vol 129 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Jeff Badertscher ◽  
Kenneth A. Cunefare ◽  
Aldo A. Ferri
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%.

The Effect of Thermo-Hydrodynamics on Manual Automotive Transmissions Gear Rattle

2009 ◽  
Author(s):  
Miguel De la Cruz ◽  
Stephanos Theodossiades ◽  
Homer Rahnejat ◽  
Patrick Kelly
Keyword(s):  
Contact Stiffness ◽  
Hertzian Contact ◽  
Transmission Model ◽  
System Response ◽  
Common Denominator ◽  
Gear Teeth ◽  
Lubricated Contacts ◽  
Engine Order ◽  
Dynamic Transmission Model ◽  
Gear Rattle

Manual transmission gear rattle is the result of repetitive impacts of gear meshing teeth within their backlash. This NVH phenomenon is a major industrial concern and can occur under various loaded or unloaded conditions. It fundamentally differs from other transient NVH phenomena, such as clonk or thud, which are due to impulsive actions. However, they all have their lowest common denominator in the action of contact/impact forces through lubricated contacts. Various forms of rattle have, therefore, been defined: idle rattle, drive rattle, creep rattle and over-run rattle. This paper presents a dynamic transmission model for creep rattle conditions (engaged gear at low engine RPM). The model takes into account the lubricated impact force between a gear teeth pair during a meshing cycle as well as the friction between their flanks. Hertzian contact conditions are applied to the gear pair along the torque path. Additionally, isoviscous hydrodynamic regime of lubrication is assumed for unselected (loose gear pairs) with lightly loaded impact conditions. The highly non-linear impacts induce a range of system response frequencies. These include engine order harmonics, harmonics of meshing frequency and natural frequencies related to contact stiffness. The last of these are dependent on the contact geometry and lubricant rheology. The analysis includes lubricant viscosity variation due to generated contact pressures as well as temperature. For loose gears, subject to oscillations on their retaining bearings, bearing friction is also considered.

Motion of masses with asymmetric and symmetric friction. Application to fault sliding

2021 ◽  
Author(s):  
Rui Xiang Wong ◽  
Elena Pasternak ◽  
Arcady Dyskin
Keyword(s):  
Frictional Force ◽  
Normal Load ◽  
Power Spectra ◽  
Inertial Force ◽  
Friction Reduction ◽  
Relative Mass ◽  
Hydraulic Fractures ◽  
Driving Frequency ◽  
Stick Slip ◽  
Friction Forces

<p>This study analyses a situation when a geological fault contains a section of anisotropic gouge with inclined symmetry axes (e.g. inclined layering), Bafekrpour et al. [1]. Such gouge in a constrained environment induces, under compression, asymmetric friction (different friction forces resisting sliding in the opposite directions). The rest of the gouge produces conventional symmetric friction. A mass-spring model of the gouge with asymmetric and symmetric friction sections is proposed consisting of a mass with asymmetric friction connected through a spring to another mass with symmetric friction. These masses are set on a base subjected to vibration. A parametric analysis is performed on this system. Two distinct characteristic regimes were observed: <em>recurrent movement</em> resembling stick-slip motion similar to predicted by [2] and <em>sub-frictional movement</em>. Recurrent movement arises when the inertial force is sufficient to overcome frictional force of a block with symmetric friction. Sub-frictional movement occurs when the inertial force is not sufficient to overcome frictional force of an equivalent system with only symmetric friction. The sub-frictional movement is produced by the force in the connecting spring increased due to the movement of the asymmetric friction block in the direction characterised by low friction. We formulate the criterion at which sub-frictional movement occurs. The occurrence of sub-frictional depends upon the relative mass of the symmetric and asymmetric friction sections, as well as the amplitude and driving frequency of the excitation. Power spectra of the produced vibrations are determined for both regimes. The results can shed light on mechanisms of sliding over pre-existing discontinuities and their effect on seismic event generation and propagation of hydraulic fractures in the presence of discontinuities.</p><p>[1] Bafekrpour,<strong> </strong>E., A.V. Dyskin, E. Pasternak, A. Molotnikov and Y. Estrin (2015), Internally architectured materials with directionally asymmetric friction. <em>Scientific Reports</em>, 5, Article 10732.</p><p>[2] Pasternak, E. A.V. Dyskin and I. Karachevtseva, 2020. Oscillations in sliding with dry friction. Friction reduction by imposing synchronised normal load oscillations. <em>International Journal of Engineering Science</em>, 154, 103313.</p><p><strong>Acknowledgement</strong>. AVD and EP acknowledge support from the Australian Research Council through project DP190103260.</p>

scholarly journals Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Measurement Data ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Rolling Elements ◽  
Localized Defects

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

2018 ◽  
Vol 85 (10) ◽  
Author(s):  
Shun-hua Zhou ◽  
Peijun Guo ◽  
Dieter F. E. Stolle
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Scaling Law ◽  
Interaction Model ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Spherical Particles ◽  
Thin Coating ◽  
Normal Contact ◽  
Laboratory Test Results

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3,  1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3,  1].

Friction Induced Vibrations in Aircraft Disk Brakes

1997 ◽  
Author(s):  
Lisle B. Hagler ◽  
Per G. Reinhall
Keyword(s):  
Friction Coefficient ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Rotational Model ◽  
Stick Slip ◽  
Numeric Simulation ◽  
Constant Friction ◽  
The Stability ◽  
Rotor Stiffness ◽  
Friction Induced Vibration

Abstract This paper presents a detailed analysis of the dynamic behavior of a single rotor/stator brake system. Two separate mathematical models of the brake are considered. First, a non-rotational model is constructed with the purpose of showing that friction induced vibration can occur in the stator without assuming stick-slip behavior and a velocity dependent friction coefficient. Self-induced vibrations are analyzed via the application of the method of multiple scales. The stability boundaries of the primary resonance, as well as the super-harmonics and sub-harmonics are determined. Secondly, rotational effects are investigated by considering a mathematical brake model consisting of a spinning rotor engaging against a flexible stator. Again, a constant friction coefficient is assumed. The stability of steady whirl is determined as a function of the system parameters. We demonstrate that only forward whirl is stable for no-slip motion of the rotor. The interactions between chatter, squeal, and rotor whirl are investigated through numeric simulation. It is shown that rotor whirl can be an important source of the torsional oscillations (squeal) of the stator and that the settling time to no-slip decreases as the ratio of the stator to rotor stiffness is increased.

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.

STRENGTH DEGRADATIONS FROM HERTZIAN CONTACT DAMAGES IN NITRIDED PRESSURELESS SINTERED SILICON NITRIDE CERAMICS

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1819-1826 ◽  
Author(s):  
KIL HO GUAHK ◽  
IN SUB HAN ◽  
KEE SUNG LEE
Keyword(s):  
Silicon Nitride ◽  
Hard Spheres ◽  
Continuous Process ◽  
Theoretical Models ◽  
Strength Loss ◽  
Indentation Load ◽  
Hertzian Contact ◽  
Pressureless Sintering ◽  
Nitride Ceramics ◽  
Number Of Cycles

Strength degradations in silicon nitride ceramics subject to damage from contact with hard spheres are investigated. Strengths against indentation load, number of cycles in contact, or stress-rate parameter are reported and compared with theoretical models. Silicon nitride ceramics are prepared by nitride pressureless sintering (NPS) process, which process is the continuous process of nitridation reaction of Si metal combined with subsequent pressureless sintering. Microstructure characterizations reveal silicon nitride fabricated by NPS process exhibits a quasi-plastic mode, with continuous strength loss beyond a load above the onset of yield, and falloff at high number of cycles, > 105 at contact load, P = 950 N , using WC sphere r = 1.98 mm . The strength degradation is substantially faster by dynamic fatigue. Failures originated from contact damages, quasi-plastic microcrack zones, with developing radial cracks during strength test. The implication is that quasi-plastic damage of NPS silicon nitride itself can preserve benefits from the inherent higher damage tolerance at lower number of cycles of contacts, but fatigue susceptibility at multicycle contacts and lower stressing rate.

scholarly journals Finger pad friction and its role in grip and touch

2013 ◽  
Vol 10 (80) ◽  
pp. 20120467 ◽  
Author(s):  
Michael J. Adams ◽  
Simon A. Johnson ◽  
Philippe Lefèvre ◽  
Vincent Lévesque ◽  
Vincent Hayward ◽  
...  
Keyword(s):  
Contact Zone ◽  
Coefficient Of Friction ◽  
Normal Load ◽  
Theoretical Models ◽  
Tactile Perception ◽  
Major Influence ◽  
Sliding Velocity ◽  
Stick Slip ◽  
The Coefficient Of Friction ◽  
Finger Pad

Many aspects of both grip function and tactile perception depend on complex frictional interactions occurring in the contact zone of the finger pad, which is the subject of the current review. While it is well established that friction plays a crucial role in grip function, its exact contribution for discriminatory touch involving the sliding of a finger pad is more elusive. For texture discrimination, it is clear that vibrotaction plays an important role in the discriminatory mechanisms. Among other factors, friction impacts the nature of the vibrations generated by the relative movement of the fingertip skin against a probed object. Friction also has a major influence on the perceived tactile pleasantness of a surface. The contact mechanics of a finger pad is governed by the fingerprint ridges and the sweat that is exuded from pores located on these ridges. Counterintuitively, the coefficient of friction can increase by an order of magnitude in a period of tens of seconds when in contact with an impermeably smooth surface, such as glass. In contrast, the value will decrease for a porous surface, such as paper. The increase in friction is attributed to an occlusion mechanism and can be described by first-order kinetics. Surprisingly, the sensitivity of the coefficient of friction to the normal load and sliding velocity is comparatively of second order, yet these dependencies provide the main basis of theoretical models which, to-date, largely ignore the time evolution of the frictional dynamics. One well-known effect on taction is the possibility of inducing stick–slip if the friction decreases with increasing sliding velocity. Moreover, the initial slip of a finger pad occurs by the propagation of an annulus of failure from the perimeter of the contact zone and this phenomenon could be important in tactile perception and grip function.

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