Hertzian Contact Stress Research Articles

Analysis of Elliptical Rolling Contact Joints in Compression

AbstractThis paper presents elliptical rolling contact joints in compression as an alternative to circular rolling contact and conventional revolute joints where high quality force transmission—low friction and backlash—with variable output are desired. Parameters specific to the joint and its position are defined in terms of relative link angles and elliptical surface geometry. These relationships allow elliptical rolling contact joints to be incorporated in vector loop summations used in kinematic analysis. Notably, elliptical rolling contact is developed as the more general case of which circular rolling contact is a subset. Elliptical rolling contact joints are shown to offer several benefits over circular rolling contact, including reduced Hertz contact stresses, variable output velocity, maximum use of contact interface by distributing small rotations across surfaces of small curvature, reduced forces on constraining members, and no-slip pure rolling provided by either connecting links or flexures, without the need for gear teeth or friction.

Rolling contact fatigue in high vacuum using ion plated nickel-copper-silver solid lubrication

Ion plated, nickel-copper-silver coated steel ball bearings that were tested in rolling contact fatigue (RCF) experiments in high vacuum are presented in this article. ANSI T5 ball bearings were coated with approximately 10 nm of nickel-copper followed by 100 nm of silver using a dc ion plating process. The balls were then tested for RCF in vacuum in the 10−7 Torr range at 130 Hz rotational speed and at 4.1 GPa Hertzian contact stress. The significance of this work is in the extension of RCF testing to an ultrahigh vacuum (UHV) application using silver as a lubricant instead of oil. The effects of pressure and voltage on the ion plating process were also investigated using scanning electron microscopy and RCF life testing in UHV. Test results with a ball size of 5/16 in. in UHV show that deposition at voltages greater than 2.5 kV shortens the RCF life and introduces a unique failure mode. Voltage and pressure fluctuations during the deposition process result in significant thickness monitor measurement errors as well. A regulator control scheme that minimizes the process pressure overshoot is also simulated.

S113014 円すいローラねじ機構の概要とローラ支持構造 : 円すいローラねじ機構の研究([S11301]機械システムの要素技術と設計(1))

In this paper, we first introduce the outline of the conic roller screw mechanism, a new device for converting rotary motion to linear motion, and explain on its roller supporting structure. The new mechanism achieves high durability by reducing Hertzian contact stress on rolling contact by bringing roller into line contact with screw shaft, and also maintains high mechanical efficiency by minimizing partial slip on the contact line. Each of three rollers that contact with screw shaft is supported by holder through tapered roller bearings, and they are permitted to tilt. The load center of tapered roller bearing is located to the proper position. This roller supporting structure is considered for long life of the tapered roller bearing. The method of mechanical efficiency estimation for the roller supporting structure is also explained, and results of the estimation varying coefficients of rolling friction are showed. It's confirmed that the roller supporting structure can hold good mechanical efficiency.

Study of Inner Micro Cracks on Rolling Contact Fatigue of Bearing Steels Using Ultrasonic Nano-Crystalline Surface Modification

The purpose of this study is to analyze the effect of ultrasonic nano-crystalline surface modification (UNSM) treatment on rolling contact fatigue (RCF) characteristics of bearing steels. It was found that severe plastic deformation occurred at surface by over 100 µm after UNSM treatment. The micro surface hardness was increased by 18%, and the measured compressive residual stress was as high as -700~-900MPa. The polymet RCF-2 roller type RCF test showed over 2 times longer fatigue lifetime after UNSM treatment under Hertzian contact stress of 425.2kg/mm2 and 8,000 rpm. And SEM study showed a spalling phenomenon at the samples which went through the RCF test after UNSM treatment. Samples before UNSM treatment produced surface initiated spalls and multi shear lips by progressive spalling at the end along the rolling direction, but sub-surface initiated spalls were formed without multi shear lips after UNSM treatment. The spalling occurred at once, and the size and depth of spalls were larger than those before UNSM treatment. And micro cracks were found to form within the spallings after UNSM treatment, and stress distribution at the maximum Herzian shear stress through these micro cracks is thought to improve the fatigue lifetime of bearing materials.

Acoustic Method And Apparatus For Fracture Detection Of Ball Bearings

A method for testing ball bearings includes applying a Hertzian contact stress on a ball bearing to provide a fracture of the ball bearing that releases acoustic energy, establishing a signal representing the acoustic energy, and identifying occurrence of the fracture based upon the signal.

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.

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.

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.

Effect of Lubricant on Surface Rolling Contact Fatigue Cracks

This study performed the finite element analysis of the cycle of stress intensity factors at the surface initiated rolling contact fatigue crack tip under Hertzian contact stress including an accurate model of friction between the faces of the crack and the effect of fluid inside the crack. A two-dimensional model of a rolling contact fatigue crack has been developed with FRANC-2D software. The model includes the effect of Coulomb friction between the faces of the crack. The fluid in the crack was assumed not only to lubricate the crack faces and reduce the crack face friction coefficient but also to generate a pressure.

Rolling Contact Fatigue Life and Spall Propagation of AISI M50, M50NiL, and AISI 52100, Part I: Experimental Results

This article is the first part of a three-part series that investigates the rolling contact fatigue (RCF) initiation and spall propagation characteristics of three bearing materials, namely, AISI 52100, VIM-VAR AISI M50, and VIM-VAR M50NiL steels. Although there is substantial prior work published on the rolling contact fatigue initiation of these materials, little has been published on their spall propagation characteristics after spall initiation. It is recognized that rapid spall growth can lead to catastrophic bearing failure. Hence, understanding the spall growth phase and factors that may cause accelerated growth rates is key to achieving a reliable and robust bearing design. The end goal is to identify control parameters for optimizing bearing materials for improved spall growth resistance. This first part study features the experimental results from 208-size (40 mm bore) angular-contact ball bearings endurance life tested at maximum Hertzian contact stress levels of 3.10 GPa and bearing outer race temperatures up to 131°C. Spall propagation experiments were conducted on new and life tested bearings at 2.10 and 2.41 GPa maximum contact stress. Spall propagation experiments show that all materials exhibit a rapid or critical spall growth rate after undergoing an initial low-rate spall growth period. The time-to-critical growth rate is dependent on contact stress and was swiftest in AISI 52100 steel. To better understand the underlying physics, the driving factors, and failure mechanisms, the state of stress is modeled using finite element analysis in Part II and an in-depth microstructural analysis of selected bearings is presented in Part III.

하이포 트로코이드 기어 펌프의 건식 마멸 최적설계

A disadvantage in the design of a hypotrochoidal gear pump as in a gerotor pump is a lack of parts that can be adjusted to compensate for wear in the rotor set, and as a consequence, it causes a sharp reduction of volumetric efficiency. In this paper, an attempt has been made to reduce the wear rate between the rotors of a hypotrochoidal gear pump. Using the knowledge of shape design on the rotors, the contact stresses without hydrodynamic effect between the rotors' teeth are evaluated through the calculation of the Hertzian contact stress. Based on the above result and the sliding velocity between the rotors, a genetic algorithm (GA) is used as an optimization technique for minimizing the wear rate proportional factor (WRPF). The result shows that the wear rate or the WRPF can be reduced considerably, e.g. approximately 12.8% in this paper, throughout the optimization using GA.

The mechanisms of gross slip fretting wear on nickel oxide/Ti6Al4V mated surfaces

The objective of this work was to determine the mechanisms of tribofilm formation during the gross slip fretting wear of Ti6Al4V and a thick nickel oxide film. This was accomplished by conducting bench level fretting wear experiments on Ti6Al4V surfaces mated with ∼75 μm thick nickel oxide scale. The nickel oxide scale was grown by oxidizing commercially pure nickel at 1000 °C. The fretting wear experiments were conducted at room temperature, 150, 300, and 450 °C, with a stroke length of 250 μm, at oscillation speeds of 2 and 30 Hz, and an approximate Hertzian contact stress of 650 MPa. It has been shown that at elevated temperatures, lubricious nanocrystalline tribofilms were formed in the fretting wear contact via a tribo-sintering mechanism. These tribofilms formed as transfer layers on the mated Ti6Al4V interface, and reduced the friction and wear on the mated surface at elevated temperatures.

Discussion: “A Deterministic-Chaos Study of Electron Triboemission Outputs” (Molina, G. J., Furey, M. J., and Kajdas C., 2007, ASME J. Tribol., 129(3), pp. 679–683)

The authors observed that the strength of triboemission, for diamond-Si and diamond-Ge pairs, decreased as contact progressed over the same wear track. Nakayama and Fujimoto (1) observed similar tendencies although accompanied by occasional high strength emission peaks. Nakayama and Fujimoto proposed that the weak signals are due to their samples being mono-crystalline silicon, whereas they suggested that the strong signals are probably due to contamination of samples by formation of oxides during pre-experimental surface preparation in air. This author suggests that the observed triboemission behavior in the present work and the work of Nakayama is a consequence of a pressure-induced metallization of silicon. Repeated passing of the diamond stylus on the same wear track, under suitable conditions, would induce metallization (2). Such a notion is supported by the observation of plastically extruded silicon plastically extruded silicon (PES) along the wear track (3). The presence of PES suggests a pressure induced semi-conductor-to-metal phase transformation, i.e., the formation of the metallic phase Si-II (β-tin) which has low electrical resistivity (4). This low electrical resistivity can explain the observed emission behavior. For mono-crystalline silicon transformation from Si-I to the metallic phase Si-II takes place in the pressure range 8.5 GPa <P< 12 GPa. Using 1200 GPa and 110 GPa for the moduli of elasticity, 0.2 and 0.28 for Poisson's ratio for diamond and silicon, respectively, and considering the experimental conditions of Nakayama, calculation of the Hertzian contact stress yields a value of 9.6 GPa. This value favors a transition from the semi-conductor phase to a metallic phase. Further using the Johnson solution for pressure under a conical indenter considering the experimental conditions, reported by the current authors, we reach a similar conclusion.The energy of the electron emission depends on the strength of the electric field generated by tribo-charging (surface potential). This depends, principally, on the electric resistivity of the solid. If the resistivity remains constant for the duration of the scratch, then the strength and the counts of the emission will remain fairly constant and donators of the emission will remain unaffected. Experimental observations, however, suggest that the resistivity changes during scratching as evidenced by the reported short-lived emission bursts, strength of emission that rapidly grows weak in time, in addition to the changes in the work function as pointed out by the authors. Using the resistivity values for Si-II (5), we can verify that the strength of emission of the metallic phase to that of the semi-conductor phase is detectable only in the time range 1E−8 s<t<1E−04 s where the ratio of strengths is in the range of 0.999 to 0.75. Thus beyond the few initial ten thousandths of a second the emission will not be of detectable strength. This is because the transformed phase, which is metallic, is incapable of emitting particles of detectable strength. Any contribution to particle counts at this point would likely originate from the recovering material in the wake of the slider. The phase of the recovering material, the PES, is a-Si (amorphous silicon). This phase is capable of emitting particles of detectable strength and is the source of the observed emission since it rubs against the sides of the diamond slider.

Nanostructural, electrical, and tribological properties of composite Au–MoS 2 coatings

Considerable research has been done on the tribological properties of cosputtered metal/MoS 2 solid lubricant films with low metal content (< 20 at.%) because of their usefulness in applications at high Hertzian contact stress (around 1 GPa). However, cosputtered Au–MoS 2 coatings with a much higher range of metal contents up to (95 at.%) have shown surprisingly good performance at low contact stresses (as low as 0.1 MPa). In the present study, transmission electron microscopy, X-ray diffraction and electrical resistance measurements of cosputtered Au–MoS 2 coatings reveal them to be composites of nanocrystalline Au particles within an amorphous MoS 2 matrix. Electrical conductivity images of the coatings displayed metallic (Au) and semi-conducting (MoS 2) domains of nanometer dimensions. Auger Nanoprobe analyses confirmed that sliding on the coatings causes the formation of a pure MoS 2 layer about a nanometer thick on top of the bulk of the coatings. Lattice resolution atomic force microscopy revealed that this nanometer-thick MoS 2 layer is crystalline, and oriented with the basal plane (0001) parallel to the coating surface. Electrical resistance obtained during sliding and pull-off force measurements was consistent with the structure of the coatings. Sliding friction data on the coatings support previous results showing that performance at different Hertzian contact stresses correlated strongly with Au content.

Micro-to-nano triboactivity of hydrogenated DLC films

In this paper, we present the results of a systematic study directed toward submicrometric scale triboactivity of a range of hydrogenated diamond-like-carbon (H : DLC) films derived from source gases with different hydrogen-to-carbon ratios. The H : DLC films were deposited on Si substrates in a plasma enhanced chemical vapour deposition system. Specifically, we produced three kinds of H : DLC films, using pure acetylene, pure methane and 25% methane + 75% hydrogen as the precursor source gases. Samples were subjected to wettability and depth sensing ultramicroindentation tests, and micro-to-nanoscale friction and wear studies using a nanotribometer and an atomic force microscope. The results of our study revealed a very close correlation between the wettability and the tribo-mechanical response of the H : DLC films at micro-to-nanoscales and their hydrogen-to-carbon ratio, i.e. lower hydrogen-to-carbon ratio leads to higher hardness (H) and lower water contact angles. Moreover, our results indicated a strong correlation between the hardness of the films and the threshold for severe wear damage. This threshold can be expressed by the ratio between the average Hertzian contact stress and the hardness which, in this study, is close to unity.

Silicon Nitride Tools for Hot Rolling of High-Alloyed Steel and Superalloy Wires

For hot rolling wires of high-alloyed steels or superalloys tools are nowadays made of ce¬mented carbides. In service they suffer from roughening of the surfaces and severe wear, which de¬teriorates the surface quality of the wires and restricts the lifetime of the tool. Due to their high hard¬ness and good high-temperature properties, improvements in tool behaviour can be expected by the use of silicon nitride tools. Experiments with several types of rollers were performed in commercial rolling mills. At modest and medium severe loaded positions (e.g. in the case of guidance rolls) silicon nitride rolls show superior performance to conventional steel or cemented carbide rolls. At the most severe loaded positions silicon nitride rolls were also superior to conventional rolls when rolling high strength steel wires. But for rolling superalloy wires, cracks, which limited further applications of the rolls, appeared in the roll surface profile (calibre). Cracks in the surface of the rollers are in general caused by Hertzian contact stresses, which can reach several hundred MPa. These cracks come into existence if a limiting load is exceeded. Then small flaws can quickly extend to a length of more then one millimetre, and then they stop again (pop in behaviour). Popped in cracks can slowly extend by cyclic fatigue up to a length where breaking out of large fragments of the rollers occurs. The critical load depends on the flow curve of the rolled materials and on the design of the rolls. For the analysed design it is exceeded when rolling superalloy wires, but it is not exceeded when rolling materials having a lower flow curve.

A Study of the Apparent Modulus of Elasticity and Maximum Contact Stress of Timothy Stem Nodes in Relation to Disinfesting Hessian Fly Puparia in Hay Rebaling Processing

To disinfest Hessian fly in timothy hay bales by mechanical compression, the crushing strength of timothy stem nodes was investigated using an Instron testing machine. Unbaled first-cut timothy hay of the 2007 crop year was used in the test. Before testing, stem segments with nodes were equilibrated to moisture contents of 12.19% and 14.13% wet basis (w.b.). According to its position in the hay stalk, the node on each stem was designated as a top, middle, or bottom node. The force-deformation curves for the nodes as affected by the node position on the stem, node size, and moisture content were obtained under a constant rate of deformation of 1 mm min-1. Equations based on Hertz's contact stress theory for cylindrical bodies radially compressed between two parallel flat plates were employed for calculation of the apparent modulus of elasticity and maximum contact stress of the timothy stem nodes. The apparent modulus of elasticity and maximum contact stress values were affected by node moisture content, size, and position on the stalk. The uniaxial compression test showed that the nodes had no elastic behavior. The apparent moduli of elasticity of timothy stem nodes for this study ranged from 24.86 to 39.82 MPa at 12.19% moisture content and from 35.67 to 53.98 MPa at 14.13% moisture content. Maximum contact stress of 8.22 MPa with a standard deviation of 3.52 MPa was obtained for timothy stem nodes at moisture content of 14.13% and size less than 1.60 mm. The maximum contact stress values obtained for the stem nodes in this study indicated that sufficient pressures were applied to Hessian fly puparia in the field tests (12.41 MPa) within 99% probability. These pressures were influenced by the moisture content, node size, and node position. The apparent modulus of elasticity and maximum contact stress values increased with increasing moisture content and decreased with increasing node size, and these values decreased from top position to bottom position on the stem.

A guided wave approach to defect detection under shelling in rail

Rail defects are responsible for many railroad accidents. Trains are derailed and serious consequences often occur. Traditional bulk wave testing wheel probes are often inadequate for finding all defects in a rail, especially under shelling. Shelling takes place as a result of wheel to rail Hertzian contact stresses that lead to surface and subsurface defects, as a result of high stresses below the surface of the rail. Guided waves can detect shelling, if so desired, by employing the proper mode and frequency. Guided waves can also detect transverse cracking under shelling by selecting a mode and frequency insensitive to the shelling, but sensitive to transverse cracking under the shelling. Special modes and frequencies can also be used to detect defects in the web or base of a rail. The guided wave methodology of using a hybrid analytical-FEM technique to accomplish the sensor design and subsequent scattering analysis is presented in this paper. Sensor design to generate rail boundary conditions via dispersion curve and wave structure analysis is illustrated along with a few static shots of animations of wave propagation and reflection from defects in a rail.

Excellent durability of DLC film on carburized steel (JIS-SCr420) under a stress of 3.0 GPa

To improve durability of transmission gears, Diamond Like Carbon (DLC) film coated on roller was estimated as well as TiN film. These films were coated on JIS-SCr420 steel, which was carburized, quenched, and tempered. DLC and TiN films were deposited by PCVD and PVD process, respectively. These surface modified rollers were estimated by usual metallurgical methods (observation of microstructure by optical microscope, SEM, and TEM, measurement of hardness by Vickers hardness tester and nano-indentator), measurement of friction coefficient by ball-on-disk in dry atmosphere, analysis of carbon by Raman spectroscopy and hydrogen by EDRA, and lifetime of pitting by the roller-pitting test. The hardness values were 21 GPa and 26 GPa, the elasticity coefficients were 192 GPa and 336 GPa, the friction coefficients were 0.1~0.15 and 0.5~0.6 for DLC and TiN films, respectively. The present DLC was a typical DLC called as hydrogenated amorphous carbon (a-C: H). The hydrogen content was about 20 %. The surface fatigue resistance of DLC-coated specimen had 100 times longer life than that the carburized and quenched one even under Hertzian contact stress of 3.0 GPa. TiN coated specimen was failed at 3.0 GPa by 5.17·105 cycles despite that the strength of the surface of the substrate was reduced due to the exposure at higher temperature in the coating process than the temperature for tempering.

Analytical Wear Model of a Gerotor Pump without Hydrodynamic Effect

The contact stress in a gerotor pump is addressed in this paper because the gerotor pump cannot be adjusted for wear. The first part of this paper presents a simple and exact rotor profile equations of the gerotor pump. In the second part of this paper, an explicit formula to avoid undercut in the inner-rotor of the gerotor pump is proposed by examining the minimum radius of curvature of the inner-rotor tooth profile on the convex section. It is found that undercut does not occur so long as the minimum value of the radius of curvature on the convex section is not less than zero. Next, the contact stresses without hydrodynamic effect between the inner and outer-rotors are evaluated through the calculation of the Hertzian contact stress in the rotor teeth. Based on the above results, we finally present the wear characteristics of pHVs factor, which is proportional to the wear rate, between the rotors of the gerotor pump under quasi-static and dry contact conditions.