scholarly journals Extended Hertz Theory of Contact Mechanics for Case-Hardened Steels With Implications for Bearing Fatigue Life

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Nikhil D. Londhe ◽  
Nagaraj K. Arakere ◽  
Ghatu Subhash
Keyword(s):  
Elastic Modulus ◽  
Fatigue Life ◽  
Contact Pressure ◽  
Effective Elastic Modulus ◽  
Hardened Steel ◽  
Hertzian Contact ◽  
Design Parameters ◽  
Case Hardening ◽  
Ball Bearings ◽  
Subsurface Stress

The analytical expressions currently available for Hertzian contact stresses are applicable only for homogeneous materials and not for case-hardened bearing steels, which have inhomogeneous microstructure and graded elastic properties in the subsurface region. Therefore, this article attempts to determine subsurface stress fields in ball bearings for graded materials with different ball and raceway geometries in contact. Finite element models were developed to simulate ball-on-raceway elliptical contact and ball-on-plate axisymmetric contact, to study the effects of elastic modulus variation with depth due to case hardening. Ball bearings with low, moderate, and heavy load conditions are considered. The peak contact pressure for case-hardened steel is always more than that of through-hardened steel under identical geometry and loading conditions. Using equivalent contact pressure approach, effective elastic modulus is determined for case-carburized steels, which will enable the use of Hertz equations for different gradations in elastic modulus of raceway material. Nonlinear regression tools are used to predict effective elastic modulus as a weighted sum of surface and core elastic moduli of raceway material and design parameters of ball–raceway contact area. Mesh convergence study and validation of equivalent contact pressure approach are also provided. Implications of subsurface stress variation due to case hardening on bearing fatigue life are discussed.

scholarly journals Experimental and Numerical Analysis of the Mechanical Properties of a Pretreated Shape Memory Alloy Wire in a Self-Centering Steel Brace

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 80
Author(s):  
Bo Zhang ◽  
Sizhi Zeng ◽  
Fenghua Tang ◽  
Shujun Hu ◽  
Qiang Zhou ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Energy Dissipation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Loading Rate ◽  
Effective Elastic Modulus ◽  
Maximum Energy ◽  
Numerical Results ◽  
Energy Dissipation Capacity

As a stimulus-sensitive material, the difference in composition, fabrication process, and influencing factors will have a great effect on the mechanical properties of a superelastic Ni-Ti shape memory alloy (SMA) wire, so the seismic performance of the self-centering steel brace with SMA wires may not be accurately obtained. In this paper, the cyclic tensile tests of a kind of SMA wire with a 1 mm diameter and special element composition were tested under multi-working conditions, which were pretreated by first tensioning to the 0.06 strain amplitude for 40 cycles, so the mechanical properties of the pretreated SMA wires can be simulated in detail. The accuracy of the numerical results with the improved model of Graesser’s theory was verified by a comparison to the experimental results. The experimental results show that the number of cycles has no significant effect on the mechanical properties of SMA wires after a certain number of cyclic tensile training. With the loading rate increasing, the pinch effect of the hysteresis curves will be enlarged, while the effective elastic modulus and slope of the transformation stresses in the process of loading and unloading are also increased, and the maximum energy dissipation capacity of the SMA wires appears at a loading rate of 0.675 mm/s. Moreover, with the initial strain increasing, the slope of the transformation stresses in the process of loading is increased, while the effective elastic modulus and slope of the transformation stresses in the process of unloading are decreased, and the maximum energy dissipation capacity appears at the initial strain of 0.0075. In addition, a good agreement between the test and numerical results is obtained by comparing with the hysteresis curves and energy dissipation values, so the numerical model is useful to predict the stress–strain relations at different stages. The test and numerical results will also provide a basis for the design of corresponding self-centering steel dampers.

scholarly journals Measurements of sea-ice flexural stiffness by pressure characteristics of flexural-gravity waves

2013 ◽  
Vol 54 (64) ◽  
pp. 51-60 ◽  
Author(s):  
Aleksey Marchenko ◽  
Eugene Morozov ◽  
Sergey Muzylev
Keyword(s):  
Elastic Modulus ◽  
Gravity Waves ◽  
Water Depth ◽  
Water Pressure ◽  
Field Measurements ◽  
Effective Elastic Modulus ◽  
Flexural Stiffness ◽  
Flexural Gravity Waves ◽  
Using Data ◽  
Relative Errors

Abstract A method to estimate the flexural stiffness and effective elastic modulus of floating ice is described and analysed. The method is based on the analysis of water pressure records at two or three locations below the bottom of floating ice when flexural-gravity waves propagate through the ice. The relative errors in the calculations of the ice flexural stiffness and the water depth are analysed. The method is tested using data from field measurements in Tempelfjorden, Svalbard, where flexural-gravity waves were excited by an icefall at the front of the outflow glacier Tunabreen in February 2011.

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.

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].

Nitriding Gears

2000 ◽  
pp. 133-158
Keyword(s):  
Fatigue Life ◽  
Liquid Medium ◽  
Case Studies ◽  
Alloy Steel ◽  
Fatigue Damage ◽  
White Layer ◽  
Case Hardening ◽  
Bending Fatigue ◽  
Gas Nitriding ◽  
Hardening Process

Abstract Nitriding is a case-hardening process used for alloy steel gears and is quite similar to case carburizing. Nitriding of gears can be done in either a gas or liquid medium containing nitrogen. This chapter discusses the processes involved in gas nitriding. It reviews the effects of white layer formation in nitrided gears and presents general recommendations for nitrided gears. The chapter describes the microstructure, overload and fatigue damage, bending-fatigue life, cost, and distortion of nitrided gears. Information on nitriding steels used in Europe and the applications of nitrided gears are also provided. The chapter presents case studies on successful nitriding of a gear and on the failure of nitrided gears used in a gearbox subjected to a load with wide fluctuations.

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