Hertzian Stress Research Articles

Celtic Stone Dynamics Revisited Using Dry Friction and Rolling Resistance

The integral model of dry friction components is built with assumption of classical Coulomb friction law and with specially developed model of normal stress distribution coupled with rolling resistance for elliptic contact shape. In order to avoid a necessity of numerical integration over the contact area at each the numerical simulation step, few versions of approximate model are developed and then tested numerically. In the numerical experiments the simulation results of the Celtic stone with the friction forces modelled by the use of approximants of different complexity (from no coupling between friction force and torque to the second order Padé approximation) are compared to results obtained from model with friction approximated in the form of piecewise polynomial functions (based on the Taylor series with hertzian stress distribution). The coefficients of the corresponding approximate models are found by the use of optimization methods, like as in identification process using the real experiment data.

Effect of sulphide inclusions on rolling contact fatigue life of bearing steels

Flaking failure in rolling contact fatigue (RCF) of hardened bearing steel under well controlled lubrication is known to originate primarily from non-metallic inclusions. Among several different types of defects inevitably present in steels, the influence of sulphides on the RCF performance of steel is an issue that still raises many questions and controversies. In the present study, our objective is to investigate this matter by observing cracks initiating from sulphides after RCF testing. To accelerate bearing failure, high Hertzian stresses of 5·3 GPa were used. It was found that cracks initiated from the elongated tips of sulphides and propagated to a direction parallel to the direction of load movement. This rule was true regardless of the relationship between the direction of load movement and the elongation direction of sulphides. We concluded that sulphides could be a dominant factor in RCF life when the harmful oxide effect was excluded.

Celtic stone dynamics revisited using dry friction and rolling resistance

The integral model of dry friction components is built with assumption of classical Coulomb friction law and with specially developed model of normal stress distribution coupled with rolling resistance for elliptic contact shape. In order to avoid a necessity of numerical integration over the contact area at each the numerical simulation step, few versions of approx- imate model are developed and then tested numerically. In the numerical experiments the simulation results of the Celtic stone with the friction forces modelled by the use of approximants of different complexity (from no coupling between friction force and torque to the second order Pade approximation) are compared to results obtained from model with friction approximated in the form of piecewise polynomial functions (based on the Taylor series with hertzian stress distribution). The coefficients of the corresponding approximate models are found by the use of optimization methods, like as in identification process using the real experiment data.

An interaction stress analysis of nanoscale elastic asperity contacts

A new contact mechanics model is presented and experimentally examined at the nanoscale. The current work addresses the well-established field of contact mechanics, but at the nanoscale where interaction stresses seem to be effective. The new model combines the classic Hertz theory with the new interaction stress concept to provide the stress field in contact bodies with adhesion. Hence, it benefits from the simplicity of non-adhesive models, while offering the same applicability as more complicated models. In order to examine the model, a set of atomic force microscopy experiments were performed on substrates made from single-walled carbon nanotube buckypaper. The stress field in the substrate was obtained by superposition of the Hertzian stress field and the interaction stress field, and then compared to other contact models. Finally, the effect of indentation depth on the stress field was studied for the interaction model as well as for the Hertz, Derjaguin-Muller-Toporov, and Johnson-Kendall-Roberts models. Thus, the amount of error introduced by using the Hertz theory to model contacts with adhesion was found for different indentation depths. It was observed that in the absence of interaction stress data, the Hertz theory predictions led to smaller errors compared to other contact-with-adhesion models.

Bearing Fatigue Life Tests of Two Advanced Base Oils for Space Applications Under Vacuum and Atmospheric Environments

Four series of rolling-element bearing fatigue tests were conducted with 51104 size thrust ball bearings with three balls made from SUJ2 (AISI 52100) steel lubricated with two advanced synthetic base oils used for space applications. The test lubricants were perfluoropolyether (PFPE) and multiply alkyated cyclopentane (MAC). Each oil was tested with bearings under vacuum and atmospheric environments. The bearings were tested at a maximum Hertzian stress of 4 GPa on the inner and outer races. The outer race was rotated at a speed of 250 rpm. A pool lubrication system was used. Fresh lubricant was used for each test bearing. Testing in vacuum conditions was at 5 × 10−2 Pa. The test oils were analyzed to determine whether changes occurred as a result of operating in air and in a vacuum. In a vacuum environment, the PFPE 815Z oil exhibited a longer fatigue life than the MAC 2001A oil. However, in an air environment, the MAC 2001A oil had a longer L10 fatigue life than the PFPE 815Z oil. The fatigue life tests of PFPE 815Z oil in vacuum resulted in a longer L10 life than when tested in an air environment. In an air environment, hydrogen fluoride was generated in the bearing tests with the PFPE 815Z oils. Under vacuum conditions, hydrogen fluoride was not generated with the PFPE 815Z oil, resulting in longer bearing fatigue lives. The fatigue life tests of MAC 2001A oil in a vacuum resulted in shorter L10 fatigue life than in an air environment. The shorter life was attributed to the lower elastohydrodynamic oil film formation with the MAC 2001A oil because of a higher operating temperature and decomposition of the oil in vacuum.

Effect of residual stresses on the onset of yielding in a Zr-based metallic glass

Indentation experiments were performed on as-cast and elastically-bent-and-constrained Zr-based metallic glass samples to investigate the effect of strain rate and residual stresses on the onset of yielding in the material. The critical shear stress for the onset of yielding in the as-cast sample was found to be insensitive to the applied strain rate. By contrast, in the elastically-stressed sample, the maximum contact pressure from the Hertzian stress field at the onset of yielding was found to largely decrease under tensile residual stress, but only slightly increase under compressive residual stress. Despite the different residual stresses, the effective shear stress, i.e. the superimposition of residual and Hertzian stress fields, for the onset of yielding in the Zr-based metallic glass was essentially a constant. The constancy of the effective stress for the onset of yielding was discussed in light of a critical excess volume associated with the atomic structure upon loading.

A new analytical formulation for contact stress and prediction of crack propagation path in rolling bodies and comparing with finite element model (FEM) results statically

Rails fracture by the growth of fatigue crack or critical crack is one of the prevalent defects in railway. The rail fracture, failure and analysis of stress should be studied to prevent rail fracture and events. In this paper, new formulation of contact stress for two rolling bodies is presented, and its results are close to the hertz stress formulation. The analysis of stress is done by Finite Element Model (FEM) and it is compared with hertz stress and new stress formulation results. Then, the analysis of stress, fracture, prediction of fracture and path of crack motion in rail and wheel are studied, statically which plays an important role in this field. The methods of analysis of stress theory fracture with numerical and FEM are compared and consequently, it was proved that these approaches have acceptable results compared with other results. So we can rely on these methods and their results. The relation between maximum displacement and maximum stress is presented, and the path of crack growth and fracture is predicted. To analyze the pressure of collection of the wheel and rail instead of elliptical contact surface, quadrant of elliptical contact surface is assumed. With this assumption, acceptable results will be attained. Key words: Rail fracture, maximum stress, Hertz’s elliptic, reformation coefficients, negative discharge energy hole, crack growth.

Designing the fiber volume ratio in SiC fiber-reinforced SiC ceramic composites under Hertzian stress

Finite element method (FEM) analysis and experimental studies are undertaken on the design of the fiber volume ratio in silicon carbide (SiC) fiber-reinforced SiC composites under indentation contact stresses. Boron nitride (BN)/Pyrocarbon (PyC) are selected as the coating materials for the SiC fiber. Various SiC matrix/coating/fiber/coating/matrix structures are modeled by introducing a woven fiber layer in the SiC matrix. Especially, this study attempts to find the optimum fiber volume ratio in SiC fiber-reinforced SiC ceramics under Hertzian stress. The analysis is performed by changing the fiber type, fiber volume ratio, coating material, number of coating layers, and stacking sequence of the coating layers. The variation in the stress for composites in relation to the fiber volume ratio in the contact axial or radial direction is also analyzed. The same structures are fabricated experimentally by a hot process, and the mechanical behaviors regarding the load–displacement are evaluated using the Hertzian indentation method. Various SiC matrix/coating/fiber/coating/matrix structures are fabricated, and mechanical characterization is performed by changing the coating layer, according to the introduction (or omission) of the coating layer, and the number of woven fiber mats. The results show that the damage mode changes from Hertzian stress to flexural stress as the fiber volume ratio increases in composites because of the decreased matrix volume fraction, which intensifies the radial crack damage. The result significantly indicates that the optimum fiber volume ratio in SiC fiber-reinforced SiC ceramics should be designed for inhibiting the flexural stress.

Wear behavior of HPPMS deposited (Ti,Al,Si)N coating under impact loading

AbstractOver the last decade the interest in High Power Pulse Magnetron Sputtering (HPPMS) and High impulse Magnetron Sputtering (HiPIMS) has undergone a considerable increase. This is mainly due to the fact that several researchers have shown that in these processes a distinct increase of the ionization of deposition species is observable. However, there is only little known about the performance of these films with regard to applications. Recently Hovsepian et al. [1] and Bobzin et al. [2] presented cutting results of different films. Both authors show that films deposited using HPPMS or HiPIMS outperform state‐of‐the‐art coatings. Depending on the cutting process, besides hardness and adhesion also excellent impact behavior is required. Therefore this work deals with the impact behavior of (Ti,Al,Si)N which was deposited using HPPMS for the application in interrupted cutting process. The impact behavior of HPPMS coating under normal and tangential loads is analyzed. During impact tests number of impacts, loads and inclination angle of the samples with regard to the load direction are varied. (Ti,Al,Si)N shows an excellent endurance even at very high loads causing Hertzian stresses in the range of 10–13 GPa. At an inclination angle of 10° and an impact load of 100 N, which corresponds to app. 10 GPa initial Hertzian stress, no damage was observed after 800×103 impacts.

A Study on Interface Strength of a-Si:H-DLC Film

In this study a method to deposit a-Si:H-DLC film at room temperature has been explored by CVD. The interface structure of a-Si:H-DLC film and the compositions of DLC film were studied, the adhesion strength of DLC film deposited directly on metal substrates was very poor, there was an almost complete crack at interface between DLC film and metal substrates, the local shedding could also be observed on surface of DLC film. After inserting a-Si:H intermediate material into the interface, the adhesion strength of a-Si:H-DLC film was improved well, the a-Si:H intermediate layer with about 0.2μm thickness was formed, and was very impact. In addition the structures of DLC film mainly were graphite structure with SP2 bonding, and contain a certain amount of diamond structure with SP3 bonding. Load capacity of a-Si:H-DLC film deposited on the metal substrates was also evaluated, as the contact stress (Hertz stress) was less than 544MPa for the film with 1μm-thickness, the failure life was up to 100 million cycles or more by using “ball- on- disk” wear testing machine, therefore it could be used in practice. Changes in load had little effect on friction coefficient.

Rolling Contact Fatigue Evaluation of Advanced Bearing Steels with and Without the Oil Anti-Wear Additive Tricresyl Phosphate

The effect of the oil anti-wear additive tricresyl phosphate (TCP) on rolling contact fatigue (RCF) life of advanced bearing steels—AISI VIMVAR M50, CSS 42L, Pyrowear 675, and Cronidur 30 was investigated with silicon nitride balls at 177 °C and at a maximum Hertzian stress of 5.5 GPa. TCP at 1% additive concentration was blended into a synthetic polyol ester turbine engine lubricant basestock having a nominal viscosity of 3 cSt at 100 °C. Additionally, the basestock was fortified with the anti-oxidants dioctyl-diphenyl amine (DODPA) and phenyl-α-napthyl amine (PANA) at 1% concentration each. The presence of TCP has a measurable positive effect on RCF life and wear. Also, all the advanced bearing materials exhibited superior fatigue life compared to conventional bearing steel M50, both with and without TCP. The study indicates that current gas turbine lubricant formulations with TCP have positive effects on fatigue life and wear performance of M50, Pyrowear 675, CSS 42L, and Cronidur 30.

Silicon nitride nanoceramics densified by dynamic grain sliding

The densification behaviors of two silicon nitride nanopowder mixtures based respectively on α-Si3N4and β-Si3N4as the major phase constituent were studied by spark plasma sintering. Sintering conditions were established where a low viscous liquid not in equilibrium with the main crystalline constituent(s) stimulated the grain sliding yet did not activate the reprecipitation mechanism that unavoidably yields grain growth. By this way of dynamic grain sliding full densification of silicon nitride nanoceramics was achieved with no noticeable involvement of α- to β-Si3N4phase transformation and grain growth. This processing principle opens the way toward flexible and precise tailoring of the microstructures and properties of Si3N4ceramics. The obtained silicon nitride nanoceramics showed improved wear resistance, particularly under higher Hertzian stresses.

Critical Flaw Size in Silicon Nitride Ball Bearings

Silicon nitride balls, used in hybrid ball bearings, are susceptible to failure from fatigue spalls emanating from preexisting partial cone cracks that can grow under rolling contact fatigue (RCF). We simulate the range of three-dimensional nonplanar surface flaw geometries subject to RCF to calculate mixed mode stress intensity factors to determine the critical flaw size (CFS) or the largest allowable flaw that does not grow under service conditions. The cost of nondestructive evaluation (NDE) methods for silicon nitride balls scales exponentially with decreasing CFS and increasing ball diameter and can become a significant fraction of the overall manufacturing cost. Stress intensity factor variability is analyzed for variations of the location and orientation of the load relative to the crack, the geometry of load, and full-slip traction. The modeling techniques utilized in the creation of a three-dimensional (3D) finite element analysis (FEA) model is discussed and the maximum tensile contact periphery stress is examined for effect on crack driving force under RCF. The CFS results are presented as a function of Hertzian contact stress, traction magnitude, and crack size.

Uncertainty analysis for rolling contact fatigue failure probability of silicon nitride ball bearings

Uncertainty analysis and parametric studies are presented for estimating the fatigue failure probability of surface cracks in silicon nitride ball bearings subjected to rolling contact fatigue. Uncertainty quantification of input parameters are presented first based on experimental data, inspection capability, and geometric reasoning. Surrogate models for equivalent stress intensity factors are then used for uncertainty propagation, which are built upon high fidelity finite element modeling with half-penny-shaped surface cracks. Instead of black-box type surrogate modeling, physical observations are employed to decompose the high dimensional surrogate model into multiple one-dimensional models. The cross-validation technique is used to find the best surrogate that has the smallest prediction variance. The probability of failure is estimated using Monte Carlo simulation and surrogate models. The parametric studies show that reducing the maximum crack size (by limiting inspection threshold) and increasing the fatigue threshold (by improving fracture toughness of a material) are the most effective ways of reducing the probability of failure. For example, decreasing the maximum crack size by 4.4% and increasing the lowest fracture threshold by 2.8% results in the reduction of probability of failure by 40%. Ball survivability increases with decreasing ball diameter, for a given peak Hertzian stress. In order to apply the current study to hybrid ball bearing design, the survivability results are generalized through non-dimensionalization.

Friction and wear mechanisms in MoS2/Sb2O3/Au nanocomposite coatings

Fundamental phenomena governing the tribological mechanisms in sputter deposited amorphous MoS 2 /Sb 2 O 3 /Au nanocomposite coatings are reported. In dry environments the nanocomposite has the same low friction coefficient as pure MoS 2 (∼0.007). However, unlike pure MoS 2 coatings, which wear through in air (50% relative humidity), the composite coatings showed minimal wear, with wear factors of ∼1.2–1.4 × 10 −7 mm 3 Nm −1 in both dry nitrogen and air. The coatings exhibited non-Amontonian friction behavior, with the friction coefficient decreasing with increasing Hertzian contact stress. Cross-sectional transmission electron microscopy of wear surfaces revealed that frictional contact resulted in an amorphous to crystalline transformation in MoS 2 with 2H-basal (0 0 0 2) planes aligned parallel to the direction of sliding. In air the wear surface and subsurface regions exhibited islands of Au. The mating transfer films were also comprised of (0 0 0 2)-oriented basal planes of MoS 2 , resulting in predominantly self-mated “basal on basal” interfacial sliding and, thus, low friction and wear.

Impact Behaviour of PtIr-Based Coatings with Different Interlayers for Glass Lens Moulding

Over the last decades demands for optical systems and complex optical products made of glass increased steadily. Precision glass moulding has a great potential for the bulk production of complex lenses with high precision and low costs. To prevent sticking or reactions between hot glass and moulding, and to reduce abrasive wear of the die a protective coating is deposited on the tool. In this research two coating systems suitable for this application are compared by analysing their behaviour under an impact load. The PVD (Physical Vapor Deposition) coating PtIr with two different bond coatings Ni or Cr is analysed. During impact test number of impacts and loads are varied. Compared to industrially used coating system PtIr with a Ni interlayer the adhesion can be improved by using a Cr interlayer. The PtIr-based coating with Cr as bond coating shows an excellent endurance even at very high loads causing Hertzian stresses in the range of 10 14 GPa. An impact load of 600 N which corresponds to a contact pressure of app. 13.2 GPa generates almost no damage after 200,000 impacts.

Sleeved rolls: old idea, new possibilities

The idea of sleeving is rather old, but the presence of permanent tensile stress in sleeves that may lead to cracks handicapped these types of rolls. The developments in mathematical modelling, metallurgy, non-destructive metal testing and other technologies have enabled the production of sleeved rolls with similar or better properties than the solid ones. The paper deals with techniques that allow reduction in the level of permanent tensile stresses, such as computer simulation. Complex design of sleeved rolls including the shape optimalisation of sleeve and arbour, design of chamfers on back-up rolls reducing Hertzian contact stresses and design of roll grinding will be described. A comparison of measured and computed residual stresses in the sleeve after a thermal treatment will be presented. Finally, practical experience with sleeved rolls in hot rolling mills will be discussed.

Influence of a white layer on the performance of hard machined surfaces in rolling contact

This study investigates the influence of a machining-induced white layer on the performance of hard machined surfaces in rolling contact. Based on the residual stress and microhardness distribution of a specimen without a white layer and one with a white layer, fatigue parameters are computed to investigate its effect on the fatigue performance. Fatigue tests are then performed to substantiate the computations. It is noted that the white layer moves the crack initiation depth to a deeper location at low maximum Hertzian stresses, whereas it moves the crack initiation depth to a shallower location at the highest maximum Hertzian stress. The white layer can increase the maximum shear stress at crack initiation depth by 54 per cent. The white layer can reduce the crack initiation life by 75 per cent, while reducing the crack propagation life by 89 per cent. Accordingly, it can reduce the fatigue life by 85 per cent. The effect of the white layer on crack initiation life, crack propagation life, and fatigue life decreases significantly as the loading increases. The presented results demonstrate that the white layer induces a highly variable change in fatigue parameters, and its effect on fatigue performance can be significantly lessened if the loading is increased.

Non-undercutting region and property evaluation of epitrochoidal gerotor geometry

The gerotor pump is widely used for industrial applications. In this paper, the inner rotor profile is an equidistant epitrochoidal curve, and the outer rotor is generated by the inner rotor profile. This paper discusses an undercutting analysis of the rotor profile, in which the undercutting equations are derived by the theory of gearing. The non-undercutting region is determined by the undercutting curves of the inner and the outer rotors. Numerical examples show that the non-undercutting region on the gerotor profiles only needs to consider the lower part of the undercutting curve of the inner rotor. Besides, the curvature equations of the outer and inner rotors are derived for evaluating the rotor profile properties such as assessing the sealing property and the Hertz stress forecast. The theoretical stress and software simulations proved the stress forecast. The results obtained are important for using the gerotor profile in optimum design.

Surface durability of WC/C-coated case-hardened steel gear

The purpose of this study is to investigate the influence of tungsten carbide/carbon (WC/C) coating on the surface durability of casehardened steel gear. Two kinds of WC/C coatings were deposited on the ground gear pair made of chromium molybdenum steel with carburizing and quenching. One is the conventional WC/C coating, and the other is WC/C coating with about 1 μm CrN interlayer. Here, the WC/C-coated test pinion and the WC/C-coated one with CrN interlayer are represented by WT and ST, respectively. Non-coated test pinion is represented by NT. The surface roughness along the tooth profile direction of WT and ST was almost the same as that of NT. A spur gear test was carried out with an IAE power circulating type gear test rig under EP gear oil lubricating condition. The fatal failure mode of the test pinions was pitting due to surface cracking. The fatigue life of WT was longer than that of NT under a maximum Hertzian stress pmax=1700 MPa. On the other hand, under pmax=1900 MPa, that of WT was as long as that of NT due to the peeling occurrence of the coated layer. Under the comparatively low load condition without peeling occurrence, the surface roughness of WT decreased with the increasing number of cycles, and their fatigue life became longer than that of NT. On the contrary, in the case of ST, the peeling of the coated layer occurred at a comparatively early stage of the gear test, and the dedendum was worn by tens of micrometers. Therefore, in the case of ST, the effect of the WC/C coating disappeared at a comparatively small number of cycles.