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Hertzian contact theory

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Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006792
EISBN: 978-1-62708-295-2
.... A brief discussion on coatings to improve surface-initiated fatigue and wear is included, due to the similarity to RCF and the increasing criticality of this failure mode. The article presents a working knowledge of Hertzian contact theory, describes the life prediction of rolling-element bearings...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009224
EISBN: 978-1-62708-176-4
... of hardness theory—those having high values of stiffness to flow stress ( E / Y ), and those having low values of E / Y . When loaded by a blunt indenter, the materials having high values of E / Y (metals) appear to develop a Hertzian stress distribution over the contact. Materials having low values of E...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002401
EISBN: 978-1-62708-193-1
... Abstract The mechanism of contact fatigue can be understood in terms of several sources of stress concentration, or stress raisers, within the macroscopic Hertzian stress field. This article focuses primarily on rolling contact fatigue of hardened bearing steels. It discusses Hertzian shear...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003564
EISBN: 978-1-62708-180-1
... to 1 3 of the circumference of a circle. These circular cracks have been studied extensively. The fundamental basis for an explanation of the ring and cone fracture is provided by the Hertz theory of elastic contact. Traditionally, Hertzian cone cracks have been most widely studied in flat...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006399
EISBN: 978-1-62708-192-4
..., the surface of the sphere at the point of contact flattens (its deformation follows Hertzian contact theory, as discussed later) if the flat counterface surface is assumed to be ideally rigid. The footprint shape becomes a small circle of a few tenths of a millimeter radius subjected to high pressures...
Book Chapter

Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006358
EISBN: 978-1-62708-192-4
... as it moves between the inner and outer bearing races. A given point on the surface of the ball may not be stressed once per revolution of the inner race but rather, because of compound motions, may bear a Hertzian contact stress only occasionally. The center of the bearing race groove, on the other hand...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006354
EISBN: 978-1-62708-192-4
... to Hertzian stress high enough to cause permanent plastic deformation of the contacting surfaces. It is characterized by permanent deformation (without loss of material or change of surface texture), which can occur during a single load event. For example, true brinelling of a rolling element bearing...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006403
EISBN: 978-1-62708-192-4
... tribological action on a component (e.g., piston ring/cylinder liner; bearing shell/shaft). The contact-area-to-wear-track ratio is an important factor in developing suitable methods for testing. Fig. 4 Basic contact conditions for (a) conformal and (b) counterformal contact, with Hertzian contact...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003563
EISBN: 978-1-62708-180-1
... 2001 86. Johnson K.L. , Greenwood J.A. , and Poon S.Y. , A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication , Wear , Vol 19 , 1972 , p 91 – 108 87. Berthe D. , Flamand L. , and Godet M. , Micropitting in Hertzian Contacts , J. Lubr...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006409
EISBN: 978-1-62708-192-4
... a counter surface is measured. High accuracy is mainly achieved with the increased thermoelectric effect from dissimilar materials and with the use of a very small contact area that is typical for Hertzian contact of a spherical slider against a flat surface. Because of the thin junction, thermocouples can...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006820
EISBN: 978-1-62708-329-4
..., and the contact areas see the same Hertzian fatigue stress seen by rolling-element bearings, plus surface fatigue stress. Adding to the complexity, except for worm gears, the contact between mating teeth involves both rolling and sliding, and the sliding motion changes velocity and direction during that contact...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006834
EISBN: 978-1-62708-329-4
... are specifically heat treated to a surface hardness of 58 + 4 HRC over a sufficient thickness to resist the triaxial Hertzian stresses built under the surface of the raceways and the rolling elements; the triaxial Hertzian stresses are generated by the external normal compressive load. Under repeated contact loads...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006829
EISBN: 978-1-62708-295-2
... will be exposed to the ambient air, and the reciprocating sliding condition will prevail. If the transition from partial to gross slip is clearly established by contact mechanics and formalized by the Mindlin theory for Hertzian interfaces (i.e., sphere-on-flat and cylinder-on-flat contacts) ( Ref 45...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006377
EISBN: 978-1-62708-192-4
... increase in contact pressure ( Ref 27 ). Instead, Karpe proposed that the decrease in friction coefficient with increasing load could be explained by the Hertzian elastic contact model. This model has been subsequently and successfully used by many others for a wide range of MoS 2 -base coatings...
Book Chapter

Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006359
EISBN: 978-1-62708-192-4
..., and the Hertzian contact stresses arising in this contact, which are due to the prescribed impact cycles. The instantaneous wear state at the peak of the N th impact would include the instantaneous peak contact radius, a , peak maximum pressure, q , and others. The common experience with moderately stressed...
Book Chapter

Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003544
EISBN: 978-1-62708-180-1
... 1010-E96 for gears. In order to improve communication, it is recommended to maintain compatible nomenclature per ANSI/AGMA 1010-E96 such that: Macropitting is a general term that includes spalling and other forms of macroscale damage ( Table 1 ) caused by Hertzian contact fatigue. Macropitting...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006379
EISBN: 978-1-62708-192-4
... and/or elastically deform under the applied compressive stress. Under the assumption of mainly elastic deformation, the Greenwood-Williamson (GW) model ( Ref 8 , 9 ) provides an accurate description of the contact mechanics involved. It assumes a Gaussian distribution of asperity summit heights and employs Hertzian...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006779
EISBN: 978-1-62708-295-2
... the characteristics of fatigue fractures followed by a discussion on the effects of loading and stress distribution, and material condition on the microstructure of the material. In addition, general prevention and characteristics of corrosion fatigue, contact fatigue, and thermal fatigue are also presented...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006361
EISBN: 978-1-62708-192-4
... is a concern. These include: Flat-on-flat Conforming surfaces (belt on a drum, plain bearings, and so forth) Hertzian contact These systems are illustrated in Fig. 11 . It could be argued that when wear occurs, all surfaces become conforming. This is true for all systems but those where...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006393
EISBN: 978-1-62708-192-4
.... The Hertzian pressure profile ( Ref 21 , 22 ) associated with curved surfaces can be parabolic (line contact) or ellipsoidal (elliptical contacts). Figure 3 shows a parabolic contact stress profile, where the maximum pressure is labeled P . It should be noted that even cylindrical roller bearings can have...