Seismic Pounding Model Using Hertzian Contact

2018 ◽  
Author(s):  
Arthur Mereles ◽  
Marcus Varanis ◽  
José Manoel Balthazar ◽  
Angelo Marcelo Tusset
Keyword(s):  
Hertzian Contact ◽  
Seismic Pounding

scholarly journals Improved design criterion for frictionally engaged contacts in overrunning clutches

2021 ◽  
Author(s):  
Nadine Nagler ◽  
Armin Lohrengel
Keyword(s):  
Design Process ◽  
Contact Area ◽  
Axial Load ◽  
State Of The Art ◽  
Tangential Force ◽  
Design Criterion ◽  
Hertzian Contact ◽  
Loss Of Function ◽  
Axial Loads ◽  
Improved Design

AbstractOverrunning clutches, also known as freewheel clutches, are frictionally engaged, directional clutches; they transmit torque depending on the Freewheel clutch rings’ rotation directions. The torque causes a tangential force in the Hertzian contact area. The hitherto “state-of-the-art design criterion” bases on this load situation. In practice, axial loads additionally act on the frictionally engaged Hertzian contact area. This additional axial load can cause the loss of the friction connection and so the freewheel clutch slips. This publication presents an improved design criterion for frictionally engaged contacts in freewheel clutches. It allows to consider tangential as well as axial loads during the design process. Additionally, it offers the possibility to estimate the probability of frictional engagement loss and gross slip based on the freewheel clutch’s application scenario. This publication points out how to use the improved design criterion to design freewheel clutches that are more robust against a loss of function.

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.

scholarly journals Analysis of the Viscoelastic Sphere Impact against a Viscoelastic Uflyand-Mindlin Plate considering the Extension of Its Middle Surface

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yury A. Rossikhin ◽  
Marina V. Shitikova ◽  
Phan Thanh Trung
Keyword(s):  
Contact Force ◽  
Middle Surface ◽  
Hertzian Contact ◽  
Mindlin Plate ◽  
Strong Discontinuity ◽  
Time Duration ◽  
Suggested Approach ◽  
Viscoelastic Sphere ◽  
The Impact ◽  
Contact Domain

In the present paper, the problem on impact of a viscoelastic sphere against a viscoelastic plate is considered with due account for the extension of plate’s middle surface and local bearing of sphere and plate’s materials via the Hertz theory. The standard linear solid models with conventional derivatives and with fractional-order derivatives are used as viscoelastic models, respectively, outside and within the contact domain. As a result of impact, transient waves (surfaces of strong discontinuity) are generated in the plate, behind the wave fronts of which up to the boundaries of the contact domain the solution is constructed in terms of one-term ray expansions due to short-time duration of the impact process. The motion of the contact zone occurs under the action of extension forces acting in the plate’s middle surface, transverse force, and the Hertzian contact force. The suggested approach allows one to find the time-dependence of the impactor’s indentation into the target and the Hertzian contact force.

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.

Surface Durability of Spur Gears at Hertzian Stresses Over Shakedown Limit

1974 ◽  
Vol 96 (2) ◽  
pp. 359-372 ◽  
Author(s):  
Akira Ishibashi ◽  
Taku Ueno ◽  
Shigetada Tanaka
Keyword(s):  
Fatigue Testing ◽  
Testing Machine ◽  
Carbon Steels ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Load Testing ◽  
Short Period ◽  
Hertzian Contact Stress ◽  
Surface Durability ◽  
Shakedown Limit

Using a new type of gear-load testing machine and a disk-type rolling fatigue testing machine designed and made by the authors, the upper limits of Hertzian contact stress allowable on rolling contact surfaces were investigated. It was shown conclusively that gears and rollers made of soft carbon steels could be rotated beyond 108 revolutions at Hertzian stresses over shakedown limit (≈ 0.4 HB). In the case of gears, pits having a pitting area ratio of 0.04 percent occurred during 1.16 × 108 rotations at a Hertzian stress of 0.50 HB. However, no pitting occurred on the roller rotated through 1.20 × 108 revolutions at a Hertzian stress of 0.71 HB, although appreciable changes in texture were observed at the subsurface. In order to rotate gears or rollers at Hertzian stresses over shakedown limit, their surface must either be very smooth initially or after a short period of running, and an oil film must be formed between contacting surfaces.

Estimation of Crack Growth Life in Rail with a Squat Defect

2009 ◽  
Vol 417-418 ◽  
pp. 313-316 ◽  
Author(s):  
Hyun Kyu Jun ◽  
Won Hee You
Keyword(s):  
Growth Rate ◽  
Crack Growth Rate ◽  
Crack Growth ◽  
Rail Steel ◽  
Crack Tip ◽  
Cost Effective ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Maintenance Strategy ◽  
Whole Life Cycle

Rolling contact fatigue initiated defects such as surface corrugation, head check, squat, are one of growing problems in high speed railway line. A squat is generally developed below the rail surface and grows parallel to surface until it turns down into rail. Estimation of critical crack size and crack growth rate is an essential to prevent rail from failure and develop cost effective railway maintenance strategy. In this study, we predict crack growth rate of a rail with a squat defect. For this purpose, a rail model with a squat defect is developed. Timoshenko’s beam theory is applied to calculate the global bending stress at the crack tip and Hertzian contact model is applied to calculate the local contact stresses at the surface of rail by simulating rolling over a railway wheel on a rail. Stress intensity factors are calculated from the total stress at the crack tip. Fatigue crack growth curve of 60kg rail steel is applied to calculated crack growth rate. Software to predict crack growth life through whole life cycle is developed. We expect that we can make a more cost effective rail maintenance strategy by considering the crack growth analysis for a defective rail.

Observation of Fatigue Fracture on PEEK Shaft against Alumina Bearing’s Ball under One-Point Rolling Contact

2016 ◽  
Vol 878 ◽  
pp. 137-141 ◽  
Author(s):  
Hitonobu Koike ◽  
Genya Yamaguchi ◽  
Koshiro Mizobe ◽  
Yuji Kashima ◽  
Katsuyuki Kida
Keyword(s):  
Fatigue Fracture ◽  
Rolling Contact Fatigue ◽  
Rolling Direction ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Subsurface Crack ◽  
Mechanical Elements ◽  
The One ◽  
Alumina Ball

Tribological fatigue failure of the machined PEEK shaft was investigated through the one-point type rolling contact fatigue test between a PEEK shaft and an alumina ball, in order to explore fatigue fracture mechanism of frictional parts working at high frequency in various mechanical elements. Due to Hertzian contact of cyclic compressive stress, the subsurface crack occurred within approximately 300 μm depth from thesurface and propagated along the rolling direction. After that, the subsurface crack propagation direction changed toward the surface. The flaking occurred on the raceway of the PEEK shaft when the subsurface crack reached to the PEEK shaft surface.

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.

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