Tooth Root Bending Fatigue Research Articles

Analysis of rolling contact and tooth root bending fatigue in a new high-strength steel: Experiments and micromechanical modelling

To find materials that meet the future requirements of increasing load density in wind turbine gear structures, the commonly used reference material, 18CrNiMo7-6, and another high-strength steel were analysed. Their fatigue properties were studied through rolling contact fatigue (RCF) and gear tooth root bending fatigue (TRBF) tests. The reference steel exhibited better fatigue performance under RCF conditions compared to the new steel; however, it was outperformed by the new steel under TRBF conditions. This study aims to understand gear contact fatigue at the microscopic level, moving beyond the macroscopic focus that dominates current research literature. To establish the causal link between the varied fatigue performance observed in these materials, we proposed a multiscale modelling workflow based on crystal plasticity. This crystal plasticity framework is combined with the fatigue indicator parameter (FIP) to explore the fatigue resistance of materials subjected to RCF and TRBF conditions. Emphasis has been placed on the role of retained austenite (RA) in fatigue performance. Utilizing representative elementary volumes (REVs) generated based on statistically representative crystallographic features and measured size distribution of RA, we examined the effects of various RA levels on fatigue resistance. Our findings reveals that the fatigue damage accumulation is significantly influenced by the level of RA. Different fatigue damage accumulation behaviours were observed under RCF and TRBF conditions. These insights offer new perspectives on RA’s role in fatigue resistance and highlight its complex influence under varied loading conditions.

Load distribution and tooth root stress of highly crowned spherical gear couplings working at high misalignment angles

Spherical gear couplings are commonly used mechanical components to transmit power between highly misaligned rotating shafts. For that, gear couplings are manufactured with high longitudinal crowning and are usually small due to space restrictions, with the probability to contain undercutting sections. High misalignment angles cause the number of teeth in contact to decrease drastically, resulting in the failure of the component by tooth root fatigue breakage.This paper investigates the load distribution and the tooth root stress of highly crowned spherical gear couplings working at high misalignment angles using a finite element model. Moreover, a deep understanding of the bending tooth root stresses in terms of the operating conditions is presented, which is novel for such high misalignment angles (γ≥3∘). Results show that different mechanical behaviors are observed at low or high misalignment angles since teeth in the pivoting position lose contact. This results in a tooth root stress history change from a sinusoidal cycle to a pulsating cycle. Finally, this study shows evidence that current sizing methods are not suitable, and underlines the need for further research to determine the spherical gear coupling life to tooth root bending fatigue.

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.

Gear Tooth Root Bending Strength Estimation under the Assumption of Fatigue Limit Existence

Being able to properly predict gear failure is a key aspect to achieve a reliable light-weight gearbox. Among the several gear failures, tooth root bending fatigue is considered as the most dangerous one because it implies the stoppage of the whole gearbox. In order to characterize a gear for this phenomena, Single Tooth Bending Fatigue (STBF) tests are the most performed ones. However, as in STBF test THERE IS no sliding/rolling contact and as the specimens are teeth rather than gears, some differences occur between the test conditions and those of the real case. This paper deals with the statistical ones that is the estimation of the gear SN curve starting from the teeth one. The teeth SN curve has been estimated by means of a statistical model developed considering Murakami’s idea of nonpropagating crack. Then, a methodology based on statistic of extreme is adopted for the purpose of estimating the gear SN curve.

Establishment of the integrated safety domain for spur gear pair and its safety characteristics in the domain

In order to reveal the evolutionary mechanism of the safety characteristics for the gear transmission system, the integrated safety domain is established and the safety characteristics of the spur gear pair in it are researched according to our previous research results. An integrated safety domain including 8 safety grades of the spur gear pair considered its multi-state meshing characteristics is established. Single and double drive-side meshing, tooth disengagement, single and double back-side contacting and the tooth surface contact fatigue, tooth surface plastic deformation and tooth root bending fatigue under drive-side meshing and back-side contacting are included in the established integrated safety domain. The calculated multi-initial values bifurcation diagrams, the calculated safety characteristic transition curves and the constructed bifurcation & safety dendrogram are used in combination to investigate the transition process of the system motion and its safety characteristics. Phase portraits, Poincaré maps and safe basins are used in combination to investigate the transition mechanism of the system motion and its safety characteristics. The influences of load on the system safety characteristics in three different safety domains are analyzed comparatively when the multi-state meshing characteristic of spur gear pair is considered. The influences of the meshing frequency and the fluctuation amplitude of meshing stiffness on the safety characteristics of the system in the established integrated safety domain are investigated. The transition mechanism of the system safety characteristics and the range of three sensitive parameters are obtained. The identification method of the safety characteristic considering the integrated safety domains and the fractal degree of the safety basin is introduced. The study is helpful in the selection of system parameters for mitigation and design against fatigue or improving safety. It is also helpful for grading safety early warning of the gear transmission system and the corresponding safety protection measures or adjusting system parameters can be taken according to actual engineering requirements.

Gear root bending strength: statistical treatment of Single Tooth Bending Fatigue tests results

Gear tooth failure due to tooth root bending fatigue is one of the most dangerous failure modes in gears. Therefore, the precise definition of gear bending fatigue strength is a key aspect. Furthermore, in order to calculate the service life of a gear component, an accurate estimation of the S‑N curve is required. This curve must properly account for the slope of the fatigue strength region, the slope of the region ahead the fatigue knee, as well as the position of the knee itself. Hence, in order obtain a curve at different reliability levels, a proper estimation of the dispersion associated with the experimental points is required. Usually, Single Tooth Bending Fatigue (STBF) tests are used to investigate the gear load carrying capacity with respect to the bending failure mode. Then, starting from the gear specimen test data, the S‑N curve that has to be used in the rating method has to be determined. Maximum Likelihood Estimation (MLE), a statistical tool capable of considering also interrupted tests (e.g. runouts) has been used to estimate, in the most reliable way, the S‑N curve from experimental points. Furthermore, if the STBF test is performed in a symmetrical configuration, i.e. two teeth loaded at the same time, also the survival of one of the two teeth represents an information that can be taken into account thanks to MLE.Moreover, additional effects must be considered to obtain the S‑N curve of a real component starting from STBF tests. In reality, the load history and the statistical behaviour are different, since in a meshing gear the strength is determined by its weakest tooth, while in a STBF test the failing tooth is predetermined. The latter effect is considered by means of the statistic of extremes, which enables the estimation of the strength of the weakest tooth and therefore of the gear. This paper describes in detail the proposed calculation method and explains its application to determine the S‑N curve in practical cases.

Estimation of gear SN curve for tooth root bending fatigue by means of maximum likelihood method and statistic of extremes

Gear failure due to tooth root bending fatigue is one of the most dangerous gear failure modes. Therefore, the precise definition of gear bending fatigue strength is a key aspect in gear design. As a matter of fact, in order to assess a gear component, an accurate estimation of the component SN curve is required. This curve must properly take into account three main aspects: the slope of the fatigue strength region, the slope of the region ahead the fatigue knee and the position of the knee itself. In addition, with the aim of being able of considering different reliability levels, a proper estimation of the associated dispersion is required too.Single Tooth Bending Fatigue (STBF) tests are usually used to investigate the tooth load carrying capacity with respect to the bending failure mode. However, due to the test rig configuration, two main differences between test and real case are present. Firstly, the statistical behavior is different, since in the meshing gear the strength is determined by its weakest tooth, while in a STBF test the failing tooth is predetermined. Secondly, the load history is different.Therefore, additional effects have to be taken into account to obtain the gear SN curve starting from STBF tests. In this article, due to its capability of handling interrupted tests (e.g. runouts), Maximum Likelihood Estimation (MLE) has been used to estimate, in the most reliable way, the SN curve from experimental points. SoE (Statistic of Extremes) has been adopted to move from the STBF SN curve to the gear one, as, by means of a simple mathematical passage, SoE enables the estimation of the strength of the weakest tooth among the z gear teeth and, as a consequence, of the gear. The effect of the different load history is considered by adopting a literature-based approach (i.e. use of corrective coefficient).This paper describes in detail the proposed calculation method and shows its application to determine the SN curve in a practical case.

On the determination of the bending fatigue strength in and above the very high cycle fatigue regime of shot-peened gears

Demands on modern gearboxes are constantly increasing, for example to comply with lightweight design goals or new CO2 thresholds. Normally, to increase performance requires making gearboxes and powertrains more robust. However, this increases the weight of a standard gearbox. The two trends therefore seem contradictory. To satisfy both of these goals, gears in gearboxes can be shot-peened to introduce high compressive residual stresses and improve their bending fatigue strength. To determine a gear’s tooth root bending fatigue strength, experiments are conducted up to a defined number of load cycles in the high cycle fatigue range. However, investigations of shot-peened gears have revealed tooth root fracture damage initiated at non-metallic inclusions in and above the very high cycle fatigue range. This means that a further reduction in bending load carrying capacity has to be expected at higher load cycles, something which is not covered under current standard testing conditions. The question is whether there is a significant decrease in the bending load carrying capacity and, also, if pulsating tests conducted at higher load cycles—or even tests on the FZG back-to-back test rig—are necessary to determine a proper endurance fatigue limit for shot-peened gears. This paper examines these questions.

Analysis of safety characteristics by nonlinear dynamics and safety basin methods for the spur gear pair in the established teeth contact safety domain

The safe operation of gear pairs is the basic safety guarantee of the machine. The safety of the gear pair may be destroyed due to transfinite of kinematic variables and system parameters. In order to reveal its evolutionary mechanism, the safety characteristics of the spur gear pair are researched under the established safety domain. A nonlinear dynamics model of the spur gear pair considered multi-state meshing is introduced. The comprehensive teeth contact safety domain of the spur gear pair to prevent tooth surface contact fatigue, tooth surface plastic deformation and tooth root bending fatigue is established. A method of judging safety characteristics of the system is given. The safety basins, phase portraits and Poincaré mappings are computed to reveal the distribution of the coexistence attractors and judge the safety characteristics of the system motions under the established safety domain in the state space. Multi-initial values bifurcation diagrams and the corresponding top Lypunov exponents (TLE) via the change of the backlash, the fluctuation coefficient of the comprehensive transmission error and the external load are used to catch the motions in the studied state space and study their transition. Bifurcation & safety dendrograms are constructed to study the evolutionary processes of the system safety characteristics. System parameters are divided into two types according to their influence on the erosion and bifurcation of the system safety basins. Two patterns to change the system safety characteristics from safe to unsafe are found. The sensitive parameters of meshing state change the safety characteristics by one-to-two bifurcation. The sensitive parameters of dynamic characteristics mainly affect the safety characteristics by changing the amplitude of kinematic variables and the dynamic response of the tooth disengagement or back-side teeth contacting state. The study is helpful in the selection of system parameters for mitigation and design against fatigue.

High-strength gears produced by powder metallurgical processes – KL500/93-2

Purpose The purpose of this study is to optimize high-strength gears produced by powder metallurgical process and to provide a material model to predict the tooth root bending fatigue strength. Powder metal (PM) technology offers great opportunities for the reduction of the carbon footprint and improvement of the cost efficiency of gear production. PM gears can achieve flank load-carrying capacities comparable to wrought steel gears if the loaded volume is fully densified. Still, the tooth root strength is of particular importance. Design/methodology/approach The tooth root stresses can be minimized by optimizing the tooth root geometry. This usually leads to a target conflict, as fully optimized tooth root geometries cannot be manufactured by generating processes such as hobbing, generating-grinding or rolling. To use the increase in tooth root load-carrying capacity of fully optimized root geometry on PM gears, a non-generating method for surface densifying is needed. The shot-peening process is used as an alternative densification process for PM gears. The properties of both shot peened and cold-rolled PM gears are analyzed and compared. To quantify the effect of both manufacturing processes, the tooth root bending fatigue strength will be evaluated and compared to wrought gears. Findings From the fatigue strength perspective, a material model is developed, which is able to predict local endurable stress amplitudes. The model is gained through regression varying carbon content, density and size effect on bending specimens. Originality/value It is transferable to PM gears of the same material using a load transfer coefficient.

Study on the gear fatigue behavior considering the effect of residual stress based on the continuum damage approach

The fatigue failures of gears have great influence on lifetime and reliabilities of mechanical transmissions. Initial residual stress (IRS) induced in the manufacturing process, together with the applied loading stress, contributes to gear fatigue behavior. Gear fatigue behavior represents a continuous damaging process during a high-cycle period. In the present work, a damage-coupled numerical model considering the effect of IRS is developed to investigate the gear fatigue performance. The deterioration of gear material, the detailed evolution of damage and the stress response during the cyclic loading process are calculated and recorded based on the continuum damage mechanics (CDM) using a user material subroutine (UMAT) in ABAQUS. Both the tooth surface contact fatigue and tooth root bending fatigue of the gear are evaluated, and the influence of IRS on stress response and damage evolution is analyzed. Results show that the risk of surface contact fatigue failure of this gear is much greater than that of the tooth bending fatigue. The initial compressive residual stress has positive effect on contact fatigue performance while the initial tensile residual stress with amplitude of 380 MPa would reduce the gear contact fatigue life by 20%.

Tooth Root Bending Fatigue Strength of High-Density Sintered Small-Module Spur Gears: The Effect of Porosity and Microstructure

The present paper is aimed at investigating the effect of porosity and microstructure on tooth root bending fatigue of small-module spur gears produced by powder metallurgy (P/M). Specifically, three steel variants differing in powder composition and alloying route were subjected either to case-hardening or sinter-hardening. The obtained results were interpreted in light of microstructural and fractographic inspections. On the basis of the Murakami a r e a method, it was found that fatigue strength is mainly dictated by the largest near-surface defect and by the hardness of the softest microstructural constituent. Owing to the very complicated shape of the critical pore, it was found that its maximum Feret diameter is the geometrical parameter that best captures the detrimental effect on fatigue.

The role of pores and microstructural heterogeneity on the tooth root fatigue strength of sintered spur gears

The automotive industry employs a considerable amount of sintered parts, mainly as transmission and engine components. Gears are the parts that mostly benefit, in terms of cost saving, from the near net shape P/M technology. However, the porosity along with the heterogeneous microstructure can detrimentally affect the mechanical behaviour, especially the fatigue strength. The possibility of increasing sintered density up to 90% and more, the use of high strength alloys, as well as post sintering treatments have been extensively investigated obtaining consistent increases in the fatigue strength. The present study focuses on the effects of porosity and microstructure on tooth root bending fatigue of small module spur gears. The aim is to investigate the synergistic contribution of pore morphology and microstructure heterogeneity to the initiation of fatigue cracks and to the following crack paths. High density parts produced by high strength pre-alloyed powders were studied. Part of the specimens was case-hardened to obtain a martensitic/bainitic microstructure in the surface layer. Bending fatigue tests up to a fatigue endurance of three million cycles were performed. A careful fractographic analysis was conducted. The obtained results were discussed using the fracture mechanics approach of Murakami, considering the pores as pre-existing defects, whose propagation strongly depends on the microstructural heterogeneity.

Alternative microstructures and their influence on mechanical properties of case-hardened gears

Case hardening is one of the most common heat treatment processes for highly loaded shafts and gears. Due to numerous investigations, a microstructure consisting of martensite with retained austenite (less than 30%) represents a high sustainable microstructure. Besides this, there are some alternative microstructures compared to the commonly specified martensitic layer. The central question is how they influence the load carrying capacity of gears. A former research project was focused on the mechanical properties of carbonitrided parts by varying the amount of retained austenite. The investigations revealed that a microstructure containing a significantly increased amount of retained austenite can increase the flank load carrying capacity in comparison to standard case carburized gears. The tooth root bending strength was not influenced in a negative way. A microstructure containing an increased amount of retained austenite can also be reached by gas carburizing. Furthermore, a variant containing bainite in the case hardened layer was adjusted. In an actual research project, the influence on the load carrying capacity of gears made out of the material 20MnCr5 was investigated in experimental test-runs, using spur gears. The results of the variants with alternative microstructure show some differences, e. g. in the hardness profiles, compared to results of standard case hardened gears. In comparison to the case hardened reference, the flank load capacity of the gears with the alternative microstructures showed increased flank load capacity numbers, whereas the tooth root bending fatigue was not influenced in a negative way.

Parameter Sensitivity Analysis of Gear Contact in Gear-Bearing-Rotor System Based on Romax

Gear transmission is one of the most important mechanical transmissions. It is widely used because of its high efficiency, compact structure, stable transmission ratio, etc. In general, the failure of gear transmission is mainly due to the failure of tooth. Tooth broken main failure mode of gear tooth is mainly due to the role of the tooth root bending fatigue. So, researching both tooth root bending fatigue strength and tooth surface contact fatigue strength are of great significance for the guarantee of gear life. Basing on romax this paper chooses a gear-bearing-rotor system as the research background to conduct parameter sensitivity analysis of gear contact and simulate the changes of tooth root bending stress and contact lines position in the whole meshing process of gear pair.

Dynamics Analysis and Optimization of Gear Transmission System

The gear transmission system was parametric modeled in the software Pro/E to establish the prototype, and imported into ADAMS. The meshing force curves of time domain and frequency domain were reached through dynamic simulation. Then the gear system was optimized with several constraint conditions, such as the number of surface modes, helix angle, cutting conditions, minimum tooth width, the contact fatigue strength, and tooth root bending fatigue strength. The optimization was calculated with these constraint conditions, and got the best design of gear system. After optimization, the gear transmission system was simulated again to reach the dynamic analysis and made a contract with the former simulation results. The simulation of the optimized gear system shows that the optimized gear has good mechanical properties.

42CrMo Hard Surface Gear Intensity Tests and Modified Parameter Correction

Hard surface gears drive is considering mainly how to improve the tooth root bending fatigue strength and wear resistance of the teeth. Based on the analysis of sliding ratio, coincidence degree and the gear tooth root bending fatigue strength, basic parameters of gear can be modified to improve strength. Although these gears must be cut by the standard tools, high strength gears are needed in machinery. In this research, intensity experiments were conducted with 42CrMo modified and standard hard surface gears. Experiment results show that the improvements of 42CrMo gear parameters are effective and teeth strength is improved for the modified parameters of gears.

Effect of Mezzo-Heterogeneous Microstructure and Rolling on the Tooth Root Bending Fatigue Properties of Sintered Ni Alloy Steel Gears

This study aims at reducing costs of high load gear manufacturing, and substituting P/M gears for conventional wrought steel gears. In order to improve the fatigue strength of P/M gears, we focused on the rolling and the high performance sintered and heat treated 4600 series alloy steels with mezzo-heterogeneous microstructure which were made from the mixed elemental powders. The fatigue strength was determined by single tooth root bending fatigue test machine, and the effect of mezzo-heterogeneous microstructure and rolling on the fatigue strength was mainly investigated. The endurance limit at N=3.0×106 of the 500 μm rolled 6 % Ni alloy steel gear compact showed 950 MPa which value is about 2/3 of the case hardened wrought steel (SCM415) gears. However, the endurance limit of rolled and heat treated gear compact showed lower value (630 MPa) as compared to as-rolled gear compact. This seems to be due to the decreasing the compressive residual stress by heat treatment and unfavorable mezzo-heterogeneous microstructures.

鉄系焼結合金歯車の歯元曲げ疲労強度に及ぼす転造の影響

Sintered ferrous alloy gears are used in wide engineering fields. However, it is difficult for them to be applied to the parts loading at high stress levels, because their strength is poorer than that of the wrought materials. In this study, sintered ferrous alloy gears were rolled and their tooth root bending fatigue strengths were investigated. The effect of rolling conditions on the porosity distribution and hardness at tooth root, and the tooth root bending fatigue strength were determined. As the amount of stock rolled was increased, the porosity of the vicinity of the surface was decreased and the hardness was increased, and also the tooth root bending fatigue strength was increased to certain level, and then the fatigue strength was decreased. This seemed to be due to the shaving when the gear was rolled.