Hertzian Contact Stress Research Articles

Near-zero-wear with super-hard WB4 and a self-repairing tribo-chemical layer

Achieving near-zero-wear remains a major challenge in mechanical engineering and material science. Current ultra-low wear materials are typically developed based on the self-consumption strategy. Here, we demonstrate a new self-repairing approach to achieve near-zero-wear. We find that the WB4-βB/WC tribo-pair has a low wear rate of 10−8 mm3 N−1 m−1 in low vacuum conditions, under a maximum Hertzian contact stress of 2.23 GPa over 1 × 105 friction cycles. Additionally, we observe an abnormal wear phenomenon after 5 × 104 friction cycles, characterized by an increase in the dimensions of the tribo-pair. This near-zero-wear mechanism is attributed to the synergistic action of the super-hard WB4-βB substrate and the self-repairing tribo-oxide layer. This research provides a new approach for advancing wear-resistant materials and enhancing material longevity.

Effect of external magnetic field on the fretting wear mechanism of the ferromagnetic materials

With the widespread implementation of maglev technology in fields such as rail transit and military, it is imperative to investigate the effects of magnetic fields on fretting damage in metallic materials. This study conducted multi-parameter fretting wear tests on typical ferromagnetic counterparts in the presence of an external permanent magnetic field. Subsequently, the wear behavior and damage mechanism of the fretting interface were elucidated through multi-scale characterization analysis. The results indicated that the operation state of the fretting interface was shifted towards the partial slip regime under the magnetic field. Meanwhile, the external magnetic field transformed the dominant wear mechanism from abrasive wear to adhesive wear. The influence of the external magnetic field on fretting wear has been demonstrated to manifest in dual aspects: Firstly, the Hertzian contact stress at the interface is enhanced by the magnetic field induction force, resulting in a remarkable reduction of about 79.83 % in accumulated dissipation energy; Secondly, the effectiveness of debris being expelled from the worn interface decreased, and the wear progression was further impeded by the accumulated debris, so that the abrasion loss is significantly reduced by about 60.66 %. These findings provide valuable theoretical data and practical reference for the protection of fretting damage in ferromagnetic materials under the action of a magnetic field.

TCT-381 Safety and Effectiveness of a Novel Intravascular Lithotripsy Device Using the Hertz Contact Stress Mechanism for Calcium Fragmentation: Six-Month Outcomes of the PINNACLE I Clinical Trial

TCT-381 Safety and Effectiveness of a Novel Intravascular Lithotripsy Device Using the Hertz Contact Stress Mechanism for Calcium Fragmentation: Six-Month Outcomes of the PINNACLE I Clinical Trial

Cold Spray Deposition of MoS2- and WS2-Based Solid Lubricant Coatings

The cold spray deposition technique has been used to produce a new class of solid lubricant coatings using powder feedstocks of the metal disulfides WS2 or MoS2, either pure or mixed with Cu and Ni metal powders. Friction and cycle lives were obtained using ball-on-flat reciprocating tribometry of coated 304 SS flats in dry nitrogen and vacuum at higher Hertzian contact stresses (Smax = 1386 MPa (201 ksi)). The measured friction and thickness of the coatings were much lower than for previous studies (COF = 0.03 ± 0.01 and ≤1 µm, respectively), which is due to their high metal disulfide:metal ratios. Cu-containing metal sulfide coatings exhibited somewhat higher cycle lifetimes than the pure metal sulfide coatings, even though the Cu content was only ~1 wt%. Profiling of wear tracks for coatings tested to 3000 cycles (i.e., pre-failure) yielded specific wear rates in the range 3–7 × 10−6 mm3N−1m−1, similar to other solid lubricant coatings. When compared to other coating techniques, the cold spray method represents a niche that has heretofore been vacant. In particular, it will be useful in many precision ball-bearing applications that require higher throughput and lower costs than sputter-deposited MoS2-based coatings.

Failure Mechanism of Bearings under Extremely Cryogenic Conditions

Bearing, as one of the most core components of rotating equipment, is prone to wear under cryogenic conditions, which seriously affects the efficiency of the whole system. Therefore, it is necessary to study the failure mechanism of bearing under cryogenic conditions. In this paper, friction and wear behavior of the bearings under cryogenic conditions is verified by using bearing simulation test platform. The results show that the bearing surface of raceway is prone to wear failure under cryogenic conditions, but the ball wear amount per unit time is small. This is because the cryogenic conditions seriously change the performance of the bearing material, the plasticity and strength of the material will be seriously reduced, and the brittleness will increase. Therefore, when the bearing ball and the bearing raceway surface contact friction, under the action of Hertz contact stress, the raceway surface is easy to produce pits and spalling, resulting in serious fatigue on the surface of the friction pair. The research provides a strongly theoretical and technical support for further improving the bearing performance and developing the tribological design of bearings.

Failure Analysis of a Needle Roller Bearing in a Megawatt Reciprocating Pump

In this paper, bearing failure was reported for a needle roller bearing used as intermediate support in a pinion shaft system. Severe deformation and wear were noticed on the working surface of the failed needle roller and around the window lintel of the bearing cage. The geometry, materials and hardness of the failed needle roller bearing were analyzed. Appearance detection, SEM and EDS analyses were carried out for clarifying the potential reasons of the needle roller bearing failure. The effect of radial displacement, Hertz contact stress and misalignment on the service life of the needle roller bearing were discussed. The excessive deformation and misalignment, resulting from the unbalanced loading and improper assembly, are the likely cause of the needle roller bearing failure.

Fully ceramic versus steel gears: Potential, feasibility and challenges

The most common gear strength calculations performed in accordance with ISO/TC 60/SC 2 include surface durability and root bending strength. Typical geared power transmissions are characterized by high Hertzian contact stresses (surface durability) on the flanks – frequently in the order of 103 MPa – versus almost half an order magnitude lower first principal stresses on the tooth root (tooth bending strength). Therefore, the use of high strength special steel alloys is almost mandatory, especially in high-end applications, mainly to withstand the high contact stress values. Ceramic materials are typically characterized by high compressive strength versus very low flexural strength that at first glance makes them inefficient for gear transmissions since they are unlikely to withstand the tensile root stresses. Nevertheless, ceramic materials possess a number of advantages that makes them potential candidates for geared transmissions, such as their exceptional thermal properties, their low density (weight), their excellent wear characteristics and limited lubrication demands. The present work investigates the main challenges of using high-end ceramic gears and attempts to provide an insight on defining the design envelope of such gears to counter the main disadvantages. The increase of the normal pressure angle beyond the 25° limit set by ISO 6336 is primarily investigated, since in minimizes the tensile tooth root stresses, while also increasing the curvature of the contact surfaces without greatly increasing Hertzian stresses. Comparative assessment of the performance of fully ceramic gear designs versus their conventional steel counterparts is performed through quasi-static FEA simulations to set the basic design requirements for such gears and to promote further investigation of the feasibility of their usage in high power density applications.

Effect of pv values on dry fretting and wear characteristics of aromatic thermosetting co-polyester (ATSP)-MoS2 coatings

For components affected by vibration, fretting wear is one of the most common failure types. In this work, the fretting behavior of ATSP-MoS2 coating was investigated and analyzed in detail. The tested coating only has two fretting states: partial slip regime (PSR) and gross slip regime (GSR). The coefficient of friction (COF) can be maintained at 0.1 when the pv＜1 MPa·m·s−1, meanwhile the COF and wear rate are significantly affected by the Hertzian contact stress p. The wear mechanism of the coating mainly includes three aspects, the mechanical damage of the original coating, especially the abrasive wear, the densification of surface film, as well as the formation and rupture of blisters on the surface film.

Test and analysis of the tribofilm and surface state during rolling contact under lubrication condition

This study aimed to investigate the formation and alteration of tribofilm during pure rolling contact under sufficient lubrication. The surface state changes were also analyzed. Rolling contact experiments with varying stress cycles were conducted using a ball-rod testing machine. Characterizations on surface state including morphology, roughness and plastic deformation were executed and chemical composition and valence state of tribofilm were detected for different rolling periods. The results indicated tribofilm was formed and evolved due to the effect of Hertz Contact stress. Surface morphology changes and plastic deformation were caused by Hertz Contact, simultaneously. The micro-sliding destroyed the tribofilm to a certain degree, resulting in the change of surface state and tribofilm composition compared to the pure rolling region.

Tribological parameters analysis of cam and follower pair used in IC engine using ANSYS

The cam and follower pair play an essential role in the valve train mechanism in IC engines. An IC engine has a specific form of contact condition called cam and follower contact. The tribological parameters related to this contact are vital for engine performance. In this paper, the cam and follower pair are analyzed, and improvements to the traditional material used for making the cam and follower are suggested. A 3D geometry of the disc type cam and spherical follower used in a typical IC engine is designed using Solidworks software, and Finite Element Analysis (FEA) of the cam and follower assembly is done using the CAE software ANSYS Mechanical. The materials taken for this analysis are structural steel and grey cast iron. We have done analyses of two of the most important tribology parameters: contact pressure and Hertzian contact stress. The maximum value of contact pressure and Hertzian contact stress is calculated for both types of material, and the results are presented and compared in tabular form and using graphical plots. The results showed that the contact pressure, Hertzian contact stress increase linearly with each other for both type of materials. Also, the maximum values of Hertzian contact stress and contact pressure were lower for grey cast iron material. So, it is a preferable substitute to structural steel for making the cam and follower pair of a motorcycle IC engine. A good agreement of results showed that our model provided a reliable prediction of the tribological characteristics of the cam follower contact.

A comprehensive study on Hertzian contact stress behaviour of engineering thermoplastic gears using 3D finite element analysis

Two-dimensional Finite Element Analysis is frequently utilized to determine the behaviour of gear contact stress due to its computational time and higher efficiency. Based on the gear tooth-to-face width ratio, either plane stress or plane strain was selected in the investigations. However, the existing investigations failed to explain the above selection criteria. Thus, the present work attempted to do detailed contact stress investigations for all thermoplastic gears using 3D FEA and compared them with 2D FEA. Based on the criteria, the face widths of 5 and 20 mm were selected during the 3D analyses, replicating the plane stress and plane strain conditions of the 2D analysis. Contact stress variations with respect to face width were extracted at 10 distinct locations. For both 5 and 20 mm gears, higher contact stresses were obtained on gear edges, whereas lesser contact stresses were in the centre regions of the gear. For all the analysed thermoplastic gears, 5 and 20 mm face-width gears exhibited plane stress conditions. Subsurface and surface stress was detected during 3D and 2D analysis for both gears. For PP, the maximum contact stress occurred at the lowest depth value of 0.15–0.155 mm, and PC exhibited maximum contact stress at 0.275–0.28 mm depth. A dimensionless ratio of proportional limit – to – young’s modulus was introduced to predict the maximum contact stress depth for the thermoplastic gears. And it was observed that the ratio is directly proportional to the maximum contact stress depth value.

Estimation of contact stresses in EN31 rolling contact bearings for screw compressor using Gauss quadrature & statistical analysis

ABSTRACT The aim of this work is to estimate Hertzian contact stresses in EN31 alloy steel and to obtain the line of best fit using statistical analysis. In refrigerant screw compressors, EN31 is used as a material of construction for cylindrical roller bearings. The Hertzian contact with friction between the outer surface of the inner race of the rolling contact bearing & the outer surface of the cylindrical roller is simulated using pin-on-disk tribometer. Measurement of friction coefficient was carried out by sliding different cylinders of hardened EN31 material against the hardened EN31 disk of the pin-on-disk tribometer. A total 16 tests, each of 1 minute time duration, are performed for the estimation of friction coefficient with varying loads from 20 N to 100 N and speeds in the range of 50 RPM to 200 RPM. The magnitude of Von Mises stress induced in the inner race of the bearing is estimated using Gauss quadrature method with the help of a self-developed MS Excel program. Statistical analysis showed that the stress magnitude increases with the increase in the load & decreases with an increase in speed.

Contact stress analysis of external non-variable multi-modulus spur gear pairs

The conditions of correct gear engagement of a pair of involute gears and the principle of geometric relationship of involute tooth profile are derived to determine the pitch point of externally meshing non-variable multi-modulus spur gear pairs into the double tooth engagement region. The Hertzian contact stress model is used as the basis to derive the contact stress calculation equations for pitch point and other characteristic contact points, and the variation of the contact stress distribution on the contact line with the module ratio is analyzed. The results demonstrate that when the number of teeth of the gear pairs is determined, the larger the value of the module difference, the easier it is for the pitch point of the gear pairs to be in the double tooth meshing zone. Except for the double tooth meshing out point, the contact stress decreases with the increase of module ratio, and the maximum point of contact stress is at the upper boundary point of the single tooth meshing zone.

Effect of shatterproof polymer film application on the fracture types and strength of glass subject to bending load

Shatterproof polymer films are widely for windows used because they can be easily installed on existing glass windows to improve safety. Applying them to glass plates has been reported to not only prevent fragments from scattering but also increase load-bearing capacity and penetration resistance. However, the clarification of their mechanism and quantitative evaluation are still insufficient because the effect of film application on the strength and failure mode of glass under quasi-static loading has not been investigated. In this study, three-point bending tests and fracture surface observations were conducted on a float glass with a shatterproof polymer film. The stress field formed inside the glass was visualised during the tests using the photoelastic method. By varying the support span of the specimen, the deformation mode was varied to generate three types of failures: bending, shear caused by Hertzian contact stress, and mixed-mode failures. Under the conditions in the present study, the breaking loads of the specimens with and without film were almost the same; however, the fracture surface observation indicated that the area subjected to shear failure caused by Hertzian contact stress was larger with film application. Finally, the effect of the film thickness on the breaking load due to bending deformation was theoretically predicted.

Silicon wafer as a feasible candidate for tribological characterization of thin coatings under high contact stress?

Silicon (Si) wafer is generally used as the substrate for structural analysis and residual stress measurement of thin coatings. A few studies can be found for mechanical and tribological characterization wherein Hertzian contact stress never exceeded 1 GPa. Si, being single crystal, pure, and having low surface roughness (Ra) is an ideal potential candidate for thin coating analysis. However, Si wafer breaks immediately under higher contact stress. The current study aims to push the contact stress limit to test thin coatings on Si wafer especially for friction and wear testing. To serve the purpose, different bias DLC coatings (−120 V, −80 V, −40 V, Zero V, +40 V, +80 V, +120 V) were deposited on Si wafer employing closed field unbalanced magnetron sputtering (CFUMS) system. Using conveniently available experimental approach, Hertzian contact stress in tribological tests has been pushed up to 2.6 GPa successfully on DLC coated Si wafer. Thus, it is feasible to test thin coatings on Si wafer at high contact stress which will provide useful and consistent friction and wear data such that further test using the steel substrate will be reduced by a significant margin. A thorough mechanical, tribological and structural (Raman) analysis is presented. It was found that −120 V possessed the highest hardness (H: 17.6 GPa), modulus (E: 184 GPa) and residual stress (4.5 GPa). The same coating produced the lowest sp2/sp3 ratio, wear rate using contact stress (0.092 × 10−13 mm4/N) and wear/friction energy (0.071 × 10−13 mm3/J2) in comparison to other coatings used in the study. Counter body analysis for −120 V shows the minimum scratch area depicting friction between transfer film and DLC hence the lowest coefficient of friction (0.061) was obtained. Moreover, surface topography is explained with the aid of atomic force microscope (AFM) images and surface roughness (Ra) data. AFM revealed craters and bumpy like surfaces for positive and negative biased samples respectively.

Whole Field Analysis of Asymmetric Helical Gear Using Photo Stress Method and FEA Method

Objectives: To carry out dynamic state analysis of asymmetrical helical gears for contact stresses using photo stress technique and suitable finite element software. Methods: Currently the Hertz contact stress equation is used to calculate the contact stress which is based on certain speculations. The value of load transmitted by a gear may be known but whether it is taken by a single or more pairs of teeth are based on some assumptions and stresses thus calculated may not be true stresses. To get precise evaluation of stress field in gear tooth it is decided to carry out experimental work on asymmetric helical gear in actual working condition. The photo stress method not only provide magnitude of stress but also gives idea about stress distribution in gear. Finite element method is used for asymmetrical helical gear to validate experimental results. Findings: The stress values obtained by photostress method and FEA method has minimum error of 2.17% and maximum of 8.89% respectively. The error values are less than 10% and within the limit. We can observe close agreement between these two methods. Novelty: This study has provided a more accurate result than theoretical method of stress calculation. Photostress analysis method is one of the best test methods for evaluation of contact stress of asymmetric helical gear with different torque condition in actual working that is dynamic condition. Maximum error of 8.89% has been found with photostress method. Keywords: Asymmetric Gears; Contact Stress; Experimental Method; Reflection Polariscope; PhotoStress; Finite Element Analysis

Investigation on 3D fatigue crack propagation in pitch bearing raceway of offshore wind turbines

In complex marine environments, pitch bearings are more prone to crack initiation, propagation, and evolution, which leads to contact fatigue problems. Accurately identifying and predicting the evolution of early crack extensions in pitch bearings can effectively prevent major economic losses caused by failure. The two limitations of the current research on pitch bearing cracking are the low efficiency of the simulation and the fact that the contact fatigue models are mostly simplified to two-dimensional models. These models do not accurately reflect the influence of the raceway geometry parameters on the real situation. This study combined Bladed and MATLAB for an integrated life cycle simulation using Python and a cloud platform to reduce the simulation duration. A three-dimensional modelling method was proposed to calculate the crack propagation in pitch bearings throughout the full life cycle. The effects of different operating conditions, crack depths, and initial crack angles were investigated and analyzed. The results suggested that the maximum Hertz contact stress was 2961.4 MP. When the initial crack angle was greater than 0°, the crack generally propagated towards the core area. When the crack angle was less than 30°, the crack propagated gradually in depth and towards the surface. The fatigue life at an initial crack angle of 60° was 1.5 times that of an initial crack angle of 30°.

2D and 3D numerical investigation on contact stress behaviour on different combinations of gear pair

Polyamide (PA6) polymer gear tremendously expanded its usage in power transmission applications. PA6 gear were engaged with different combinations of gear pairs (STEEL – PA6, PA6 – STEEL, and PA6 – PA6) were utilized in those applications. Normally gears are subjected to Hertzian contact stress due to their non-conformal contact and ANSYS is one of the widely used Finite Element Analysis (FEA) tool to determine the contact stress behaviour of those gears. Even though numerous 2D and 3D FEA investigation were performed to determine the gear contact stress behaviour, the occurrence of surface and subsurface stresses for different combination of gear pair was not explored especially for PA6 gears. Thus, the work attempted to study the surface and subsurface contact stress behaviour of three combination of gear pairs (STEEL – PA6, PA6 – STEEL, and PA6 – PA6) using 2D (plane stress with thickness condition) and 3D FE analysis (ANSYS APDL). The optimum mesh sizes were selected from the convergence study and further simulations were performed. From the analysis, the stress was observed maximum at the contact pitch point for 2D analysis, whereas, 3D analysis showed the maximum stress at a depth below the contact surface (subsurface stress) for all the combinations of gear pairs. Different trend pattern was obtained between the stress plot of 2D (surface stress) and 3D (subsurface stress) analysis for all the gear pairs. The variation in depth occurrence of maximum stress was observed for Steel-PA6 (0.16 mm depth), PA6-Steel (0.16 mm depth) and PA6-PA6 (0.25 mm depth) gear pairs. And, the Polymer – Polymer (PA6-PA6) gear pair exhibited higher depth occurrence compared to Steel – PA6 and PA6 – Steel gear pairs.

Contact Stress-Induced Wear Mechanism Transitions of PcBN/Al2O3 Under Vacuum and Air Conditions

Abstract Since the millennium, incremental breakthroughs in aerospace have attracted widespread attention from countries around the world on deep space exploration. Technological innovations in ceramic and superhard materials have also played a key role in deep space exploration. Inspired by this, a tribological ball-disk experiment of polycrystalline cubic boron nitride (PcBN) sliding against aluminum oxide (Al2O3) was implemented in air and vacuum conditions, in order to evaluate the friction and wear properties of PcBN based on drilling in the deep space environment. The results prove that the coefficient of friction (CoF) is interrelated with load and wear conditions, where CoFs gradually decrease with load growth in both air and vacuum. When the loads keep increasing, however, the wear mechanisms finally change under the high Hertz contact stress and lead to the CoF lift. Detailed characterizations were made to verify the tribological behaviors of the microscopic surface and chemical composition. Finally, by analyzing the surface topographies and chemical residues, it is certain that the wear mechanisms change due to the high Hertz contact stress. As a result, abrasive wear and adhesive wear turn to furrow wear in air and three-body wear in vacuum. These results can influence actual work in deep space by reducing large stress loads to avoid the impact of severe vibrations on precision instruments during work and improving cutting removal efficiency by selecting the appropriate loading.

Prediction of rolling contact fatigue crack propagation in bearing steels using experimental crack growth data and linear elastic fracture mechanics

Rolling contact fatigue (RCF) is a major life limiting factor for machine elements that employ non-conformal, rolling sliding, lubricated contacts such as rolling bearings and gears. This paper explores the application of linear elastic fracture mechanics (LEFM) principles, as commonly used in structural fatigue, for prediction of RCF crack propagation. A triple-disc contact fatigue machine is used to generate RCF cracks of varying lengths in AISI 52100 bearing steel roller specimens. Crack propagation rates across the surface are measured using optical inspection of test specimens and the final crack geometry is established through specimen sectioning. A numerical finite element model of surface breaking RCF cracks based on LEFM methods is devised to predict the evolution of stress intensity factors (SIFs) during over-rolling of the contact over the experimentally observed crack geometries. The model employs a suitable fracture mechanics mesh to resolve stresses at the crack tip and accounts for Hertzian contact stresses, contact friction and crack face friction. Potential effects of lubricant pressurisation within the crack are not modelled. The predicted SIFs are then related to the experimentally measured crack propagation rates to establish the applicability of the LEFM principles to RCF crack propagation. Results show that LEFM can be used to predict the growth of surface braking RCF cracks. For cracks longer than about 100 μm, a Paris law relationship with the stress intensity exponent of about 4 is derived. Mode II was seen to be the dominant mode of propagation for surface braking RCF cracks. Mode I SIFs are much smaller but can exhibit significant values when the contact is located just ahead of the crack mouth. Decreasing the crack face friction significantly increases mode II stress intensity suggesting that this is one important mechanism by which lubricant entry into the surface braking crack can accelerate its propagation. The findings can help in improving the reliability of mechanical systems by supporting the development of new tools for prediction of remaining useful life of machine components such as bearings and gears.