Tooth Root Bending Strength Research Articles

Prediction of residual stress depth profiles in case-carburized gears

Residual stresses have a significant influence on the load carrying capacity of gears. High near-surface compressive residual stresses can increase pitting strength and tooth root bending strength up to 50%. Tooth flank fracture (TFF) is a gear fatigue failure mode, which is in contrast to pitting or tooth root breakage not initiated at the surface or close to the surface but in larger material depths beneath the active gear flank. Therefore, the residual stresses in larger material depths are decisive for TFF. In these larger material depths, the residual stress conditions are almost unknown up to now. It is assumed that tensile residual stresses are present in these areas, which can negatively influence the TFF load carrying capacity. So far, no validated methods are known to estimate or predict these tensile residual stresses. As a result, the tensile residual stresses could not be considered in the calculation methods for the risk of TFF at all until recently.This paper presents a method to predict the residual stresses in case-carburized gears based on comprehensive numerical simulations of case-carburizing processes of different-sized gears. The calculated residual stress profiles also consider the tensile residual stresses in larger material depths.

Advantages in the production of power transmitting gears by fineblanking

Fineblanking of gears has an enormous time and cost saving potential as well as the potential to significantly reduce CO2 emissions compared to conventional manufacturing of gears. Conventional manufacturing of gears consists of at least three steps such as milling, case hardening, and grinding. With fineblanking, only one manufacturing step is necessary. However, the load-carrying capacity regarding different gear fatigue failure modes, such as pitting or tooth root breakage, is stated significantly lower for the commonly used shear-cutting steels compared to the conventional case-hardened gears made out of high-strength hardened steels. This work shows the possibility of utilizing compressive residual stresses that are induced by the fineblanking process to increase the load-carrying capacity regarding tooth root breakage up to the level of case-carburized gears. Pinions and wheels made of S355MC (1.0976) and S500MC (1.0984) are fineblanked using parameters determined in previous works with a focus on the induction of high compressive residual stresses into the finished products. The variants are investigated regarding, e.g., cut surface characteristics, hardness, and residual stresses. For the two steels, as well as a stress relived variant, the tooth root bending strength is also determined in pulsator tests with the fineblanked pinions.

Improve wind gears bending performance by means of IGS (Improved gear surface)

Gearbox power density plays a decisive role in wind energy competitiveness. As wind turbines become larger to reduce the levelized cost of energy (LCOE), bending fatigue plays a higher role in gearbox design. Shot peening (SP) has been introduced frequently as a technique to increase wind gearbox bending capacity, but other techniques, such as root grinding (RG) and superfinishing (SF), remain insufficiently explored. This paper investigates the tooth root bending strength of the case-carburized gears of a normal modulemn = 10 with different root finishing conditions. The results show no relevant influence of SF after SP. In contrast, RG prior to SP shows a potential capacity increase. However, high cycle subsurface failures must be considered for this potential capacity increase.

A Comparison between Two Statistical Methods for Gear Tooth Root Bending Strength Estimation Starting from Pulsator Data

Due to their cost-effectiveness, pulsator tests are widely adopted as a testing methodology for the investigation of the effects of material and heat and surface treatment on the gear strength with respect to tooth root fatigue fracture. However, since no meshing contact is present in pulsator tests, there are differences between the test case and the real-world application scenario where gears are rotating under load. Those differences are related to both statistical and fatigue phenomena. Over the years, several methodologies have been developed in order to handle this problem. This article summarizes them and proposes a first comparison. However, no complete comparison between the different estimation methodologies has been conducted so far. This article aims to partially cover this gap, first by presenting and comparing the methodologies proposed in the literature and then via a deeper comparison between two different elaboration methodologies. Those two methodologies, which have been developed by examined to the same test rig configuration, are also discussed in detail. The comparison is performed based on an actual database composed of 1643 data points from case-hardened gears, divided into 76 experimental campaigns. Good agreement between the estimated gear strengths was found. The database is also adopted in order to make further considerations about one methodology, providing additional validation and defining the specimen numerosity required.

Material influence on mechanical properties of gears with alternative microstructures

AbstractCase hardening represents the most important heat treatment process to increase the load carrying capacity of gear components. Beside predominantly martensitic surface layers with low proportion of retained austenite, there were investigated material structures with differing properties in preceding research work.In a previous publication, the results of three variants made of the material 20MnCr5, which is typically used for gears, were presented. The reference heat treatment was a conventional carburizing with subsequent case hardening. The second variant was also gas carburized, but with a high proportion of retained austenite. The last presented variant had a bainitic structure in the surface layer. The second and the third variant showed a similar tooth root bending strength compared to the reference. The numbers of the pitting resistance were significantly higher than for the reference variant.This paper presents the results of further investigations on the influence of different microstructures on the gear load carrying capacity. For this purpose, gears made of 18CrNiMo7‑6 were tested with regard to their load carrying capacity. 18CrNiMo7‑6 is a case hardening steel like 20MnCr5, too, which is often applied in big gear components. The tooth root bending strength was approximately constant, whereas the pitting resistance decreased compared to the corresponding variants of the material 20MnCr5. In comparison to the carburized 20MnCr5 reference variant, only the 18CrNiMo7‑6 variant with a large proportion of retained austenite showed a higher pitting resistance.The tooth root bending strength investigations took place in the cycle regime of limited life as well in the high cycle fatigue regime. The pitting resistance was only determined in the cycle regime of limited life.

Tooth Root Bending Fatigue Performance of Shot Peening TM210A Steel Spur Gear

Tooth root bending fatigue performance is the primary consideration in gear design. To investigate the difference between the tooth root fatigue performances of shot peened and base material, TM210A steel gears and double-tooth pulsating bending fatigue experiment with a stress ratio of 0.05 was carried out on the experimental gears by the group method and the staircase method. The fatigue life of experimental gears with different stress levels and the conditional fatigue limit under 1 × 107 cycles were obtained, and the S-N curves were fitted by the double-weighted least squares method. The tooth root residual stress of the shot peened gear was measured by the X-ray diffraction method, the stress field at the tooth root was calculated by the finite element method, and the fatigue failure mechanism of the shot peened gear tooth root was analyzed. The results show that shot peening can significantly enhance the tooth root bending fatigue life and strength of TM210A steel gear, and the tooth root bending fatigue limit of shot peened gear is about 2.18 times that of base material gear. The residual stress generated by shot peening keeps the fatigue source away from the tooth root surface, and the smaller the external load stress, the farther the fatigue source is from the surface, and the smaller the range where the fatigue source can occur.

Rapid hob tip corner optimization of spur gears for increasing bending strength

Spur gears are widely applied in transmissions of heavy load cases, such as turbines, ships, mining devices, and other industrial applications. Increasing the tooth root bending strength offers great potential to increase the power density of gearboxes. To obtain a higher bending strength without increasing manufacturing costs, this study intends to find an optimal tooth root contour by optimizing the hob tip corner geometry. A rapid optimization method is thus proposed, consisting of a quick hobbing simulation to generate the tooth root fillet for arbitrary hob tip corners, a fast meshing adaptation mapping rule to guarantee the high mesh quality of different gear tooth geometries, and an analytical equation for calculating the maximum principal stress of the tooth root margin. The results show that the computing time only takes 5–8 min for each optimization, and an average potential of 15% is obtained for various gear parameters. Furthermore, a unified optimal hob tip contour, suitable for a wide range of gears, is also found with an average optimization potential of 13%. This study contributes greatly to the rapid optimization of the tooth root geometry and the corresponding hob tip geometry for high bending strength.

Flame and Induction Hardening – An Advantageous Alternative to Case Hardening for Large Size Gears?

Abstract Surface hardening is an economical and technological alternative to case hardening, especially for larger gear sizes. Due to the high carburization depths required for case hardening with large component dimensions and technological limitations (e. g. furnace size), typical surface hardening processes such as flame or induction hardening show advantages here. In this publication, a flame-spin-hardened variant is compared with an induction-hardened variant using the gap-by-gap method. Both variants have a gear size of mn = 14 mm. A comparison is also made with a case-hardened, shot-peened reference variant of comparable size. In the comparison, the chemical composition, microstructural properties, hardness-depth characteristics and experimental results of the tooth root bending strength tests on the pulsator test rig are presented, comparatively evaluated and discussed. The experimentally determined tooth root load carrying capacities of the two surface-hardened variants are then classified with the reference variant in the state of the art.

Investigation of the effects of surface roughness and shot peening on the tooth root bending strength of case-carburized gears

Investigation of the effects of surface roughness and shot peening on the tooth root bending strength of case-carburized gears

In-depth analysis of crack area characteristics of fisheye failures influenced by the multiaxial stress condition in the tooth root fillet of high-strength gears

Modern high-strength gears have to satisfy many requirements, such as improved tooth root bending strength. The process of shot-peening is correlated to the introduction of compressive residual stresses in the surface layer of a gear to achieve a higher tooth root bending strength. However, due to the compressive residual stresses fisheye failures can occur and can have a determining effect on the endurance of high-strength gears. By preventing such failures, it should be possible to increase further the tooth root bending strength of high-strength gears. However, this requires a deeper understanding of the crack initiation and propagation processes. Especially the unique multiaxial stress condition in the tooth root fillet of a gear could influence the crack area characteristics significantly. Though, in the literature there is no proper characterization of crack area characteristics in the tooth root fillet of gears in detail, so far. Furthermore, in previous work a model approach for the evaluation of the tooth root bending strength of gears was presented, which is based on the results of Murakami. A first comparison with experimental data showed a basic applicability of the model approach on gears. However, the derived model approach showed some room for improvement. Questions arose as to whether the approach is really fully applicable to gears, whether further modifications are needed, or whether further extension is even practical, since the fisheye fracture characteristics of gears might differ significantly from those of standard specimens. The aim of this paper is therefore to present an extensive in-depth analysis of the crack area characteristics in the event of tooth root fracture damages caused by a fisheye failure in high-strength gears. Furthermore, a case study is used to verify whether a detailed evaluation of the characteristics of non-metallic inclusions leads to more accurate results of the model approach.

Influence of Heating Rate and Soaking Temperature during Case-Hardening on the Hardness and Grain Size of Ultra-Clean Gear Steels

AbstractIn the framework of a research project, the tooth root bending strength of high-strength gears is investigated. The most common type of failure encountered with these shot-peened, case-hardened gears is tooth root breakage caused by a crack initiation below the surface at a non-metallic inclusion (fisheye failure). However, it is well known that case-hardening depth and quenching grain size can have a great influence on a gear’s load carrying capacity. To ensure that this research project solely investigates the influence of non-metallic inclusions, any cross-influences must be excluded or minimized, or at least known. However, in the case of such ultra-clean gear steels, no recommendations or investigations of the influence of case-hardening on material properties are currently available. Therefore, in the framework of this paper, extended investigations are conducted into the effects of different process steps during case-hardening on the resulting material properties of ultra-clean gear steels.

Influence of grinding zones on the tooth root bending strength of case carburized gears

Knowledge of the expected tooth root bending strength plays a decisive role in the design of gear sets. Due to dimensional and shape changes resulting from distortion due to the heat treatment, unintentional, partial grinding in the tooth root area may occur, particularly in the application range of large gears. The influences of an unintentional grinding zone on the tooth root bending strength have not yet been clarified with sufficient accuracy. As a result, grinding zones lead to uncertainties when evaluating the tooth root bending strength and thus to a loss of time and cost in the field of industrial practice.This paper presents experimental investigations on the influence of grinding zones on the tooth root bending strength of case carburized gears. For the experimental investigations, there are three unground reference variants with different blasting treatments: non-blasted, mechanical cleaned by shot blasting and shot peened. The unground reference variants are examined regarding their tooth root bending strength. For the other test gear variants, different grindings zones are applied resulting in light and strong material removal by grinding. The variants with the different grinding zones are examined analogously regarding their tooth root bending strength and are subsequently compared to the reference variants.The results of the experimental investigations show that grinding zones can have diverse influences on the tooth root bending strength of case carburized gears– Non-blasted gears do not show changes regarding the tooth root bending strength with regard to light or strong grinding zones applied within this investigation.– Shot blasted (mechanical cleaned) gears show no change in the tooth root bending strength for light grinding zones (grinding application does not significantly alter the original residual stress state in the tooth root area).– Shot blasted (mechanical cleaned) gears show a reduction of the tooth bending strength of up to 20 % with regard to strong grinding zones (grinding application does significantly alter the original residual stress state in the tooth root area).– Shot peened gears show a behavior similar to that of shot blasted gears with reductions of the tooth root bending strength of up to 30 %.– Shot peening the strong grinding zones as a repair measure can increase the reduced tooth root bending strength again. However, for the investigated test gears, the resulting tooth root bending strength was below the shot blasted reference variant.The results of this paper help to evaluate the influence of grinding zones on the tooth root bending strength of case carburized gears more precisely compared to the generalized reductions of current standards and classifications. The results can be incorporated in standards such as DIN 3390 as well as ISO 6336 and can be applied in the field of industrial practice. Eventually, the findings help to reduce the current loss of time and cost caused by uncertainties regarding grinding zones.

Deep nitriding—contact and bending strength of gears with increased nitriding hardening depth

The load carrying capacity of gears can be significantly increased by nitriding. However, the required nitriding hardening depth depends on the stress level and the gear size. In order to achive a high fatigue resistance and durability of nitrided gears an adequate nitriding hardening depth is necessary. In industrial practice, a nitriding hardening depth (NHD) of about 0.6 mm is currently regarded as the upper limit that can be reached within a reasonable time and cost. This also limits of the load carrying capacity of nitrided gears, in particular with increasing gear sizes. Therefore, case hardening is the main treatment used with increasing gear sizes, although nitriding provides some advantages over case hardening. However, with an increased nitriding hardening depth, a significant increase in the load carrying capacity of nitrided gears for medium and larger gear sizes could be expected, which will be discussed in this publication. In order to evaluate the expected potential of the load carrying capacity of nitrided gears with an increased nitriding hardening depth of NHD ≈ 0.8 to 1.0 mm (deep nitriding heat treatment) made out of the materials 31CrMoV9 (1.8519), 30CrNiMo8 (1.6580) and 32CDV13 (alloy for aerospace applications according to AIR 9160), experimental investigations were carried out, which will be discussed in this publication. Both, the tooth root bending strength and the flank load carrying capacity were investigated.

Tooth Root Bending Strength of Gears: Dimensional Effect for Small Gears Having a Module below 5 mm

Downsizing is a more and more widespread trend in many industrial sectors, and, among the others, the automotive industry is pushing the design of its components towards increasingly compact, lightweight, efficient, and reliable solutions. In the past, the drivetrains for automotive were designed and manufactured with gears having modules in the range 3 to 10. In this respect, the main actual European standards for gear design such as ISO 6336:2019 (based on the DIN 3990:1987) are validated in the 3 to 10 mm range only. Moreover, it is well known that, by increasing the gear size, the gear size factor for tooth bending YX reduces. However, nowadays the advances in terms of materials and design knowledge have made possible the realization of miniaturized gearboxes with gears having normal modules below 3 mm with comparable (or better) reliability. In this scenario, understanding how the size affects (positively) the load-carrying capacity for tooth root bending for small modules below 5 mm is fundamental to maximize the design effectiveness in case of downsizing of the drivetrains. In this paper an experimental study was performed on small gears made of 39NiCrMo3 having a normal module of 2 mm to verify the load-carrying capacity for tooth root bending. Based on the experimental evidences and additional data from literature and past studies by the author, an extended formula for the size factor YX (according to ISO 6336) is proposed.

Shear cutting induced residual stresses in involute gears and resulting tooth root bending strength of a fineblanked gear

The manufacturing of case-hardened gears usually consists of several complex and expensive steps to ensure high load carrying capacity. The load carrying capacity for the main fatigue failure modes pitting and tooth root breakage can be increased significantly by increasing the near surface compressive residual stresses. In earlier publications, different shear cutting techniques, the near-net-shape-blanking processes (NNSBP’s), were investigated regarding a favorable residual stress state. The influence of the process parameters on the amount of clean cut, surface roughness, hardness and residual stresses was investigated. Furthermore, fatigue bending tests were carried out using C-shaped specimens. This paper reports about involute gears that are manufactured by fineblanking. This NNSBP was identified as suitable based on the previous research, because it led to a high amount of clean cut and favorable residual stresses. For the fineblanked gears of S355MC (1.0976), the die edge radii were varied and the effects on the cut surface geometry, hardness distribution, surface roughness and residual stresses are investigated. The accuracy of blanking the gear geometry is measured, and the tooth root bending strength is determined in a pulsating test rig according to standardized testing methods. It is shown that it is possible to manufacture gears by fineblanking with a high precision comparable to gear hobbing. Additionally, the cut surface properties lead to an increased tooth root bending strength.

Investigations on the Micro-Pitting and Wear Behavior of Nitrided Internal Gears

Nitriding processes can significantly increase the load carrying capacity of gears, compared e.g. to through hardened gears. Nitrided gears are generally characterized by a thin and hard compound layer on the surface and an adjacent diffusion layer that extends deeper into the material. Structure and properties of the compound layer significantly determine especially the tribologically dominated load carrying capacity characteristics of the tooth flank surface such as micro-pitting and wear. Previous investigations on nitrided gears were mainly focused on fatigue limits for the surface durability against pitting and tooth root bending strength. Furthermore, mostly external nitrided gears were investigated. Results of systematic investigations on the wear and micro-pitting behavior of nitrided internal gears are scarcely available. Based on the investigations in the research project FVA 482 IV, experimental test results confirm that nitrided internal gears in the material pairing “case hardened/nitrided” provide a significantly better performance regarding wear compared to through hardened or case hardened internal gears. Furthermore, it was shown that nitriding can have a positive influence on the micro-pitting behavior. A detailed analysis of the microstructure shows that the properties of the compound layer are primarily responsible for both, the micro-pitting and wear behavior.

Design optimisation of mating helical gears with profile shift using nature inspired algorithms

ABSTRACT Profile shift of the gear significantly affects its form, zone, stress factors, transversal and face load factors. In this paper, an optimum solution to the problem of mating helical gears design considering profile shift is given. The objective of the problem is to minimise volume taking into account tooth root bending strength, contact pressure, face width, and addendum modification coefficients as constraints. The design variables, namely, the module, the face width, the number of teeth, and profile shift coefficients of both gears are considered. Nature-inspired algorithms, namely, Simulated Algorithm (SA), Fire Fly Algorithm (FA), Cuckoo Search (CS), Particle Swarm Optimisation (PSO) and Teaching Learning-Based Optimisation (TLBO) algorithms are employed. Results of simulation with and without profile shift, performance of various algorithms are analysed and validated with literature. Results show that CS and PSO algorithms give the best optimum volume. They also significantly reduce volume by 1.91%, when compared to literature. CS algorithm gives the best optimum design parameters. Furthermore, results show the volume of the mating helical gears with profile shift is much lesser than the pair without profile shift.

Bending stress analysis of eccentric straight and helical curve-face gear pair

As a new type of gear transmission developed in recent years, curve-face gear transmission has not appeared before. In order to solve the problem of root bending strength of the eccentric straight and helical curve face gear, a calculating method of the tooth root bending strength was proposed. According to the principle of space meshing, differential geometry and design of machinery, the parametric equations of pitch curve was obtained, the pressure angle and the contact ratio in the meshing process were derived. The plane equivalent pitch curve was obtained, and the formula for calculating the equivalent tooth form factor and the equivalent stress correction factor was acquired. The calculation method of the bending strength of the gear pair was established, and the influence of the basic structural parameters on the bending stress was also analyzed in detail. The position of the stress hazard of the eccentric curve-face gear was determined. Through the finite element analysis and transmission experiment, the accuracy of the calculation method of strength of the gear pair was verified.

Effects of Prestressing of the Ring Gear in Interference Fit on Flexural Fatigue Strength of Tooth Root

When the gearbox body interference is connected to the ring gear, prestressing occurs in the ring gear, which has a significant impact on the strength and life of the gear. Research on the prestressing of the inner ring gear is in the preliminary stage, and the distribution rule of the prestressing and the influence of each parameter on the interference prestressing have not been derived. In this paper, based on the method of calculating the prestressing of the thick cylinder in interference fit, the ring gear is found to be equivalent to a thick cylinder, and the distribution rule of prestressing of the ring gear in the interference fit is inferred. Then, by modeling and analyzing the gearbox body and ring gear in the interference fit using ABAQUS, the distribution rule of prestressing the ring gear in the interference fit is obtained through a numerical simulation. Finally, the prestressing of the ring gear in the interference fit is measured using X-ray diffraction, and the distribution rule of prestressing of the ring gear in the interference fit is obtained through analysis. Compared with the distribution rule of prestressing in theory, numerical simulation, and experiment, the theoretical distribution rule of prestressing is amended through a statistical method, and a more accurate formula of prestressing is obtained. Through the calculation of the stress and bending moment in the dangerous section of the ring gear through prestressing, the formula for checking the tooth root flexural fatigue strength in the interference fit prestressing is inferred. This research proposes a tooth root bending strength conditional formula for the inner ring gear of the interference fit, which serves as a guide for the design and production of the actual interference joint inner ring gear.

Effects of low-temperature treatments on surface hardness, retained austenite content, residual stress condition and the resulting tooth root bending strength of case-hardened 18CrNiMo7-6 gears

This paper contains parts of the research project FVA 612 and investigates the correlation between low-temperature treatments of case-hardened gears made from the material 18CrNiMo7-6 and the resulting surface hardness, retained austenite content, and residual stress condition. These parameters were further investigated with regard to the tooth root bending strength obtained with pulsating test rigs. The tested gears were subjected to various low-temperature treatments including different temperature levels before or after tempering. Other investigated parameters were the application of a shot blasting treatment and the effect of low-temperature treatments on gears with increased retained austenite content after the carburizing process.