Tooth Root Bending 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.

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.

Performance reliability evaluation of high‐pressure internal gear pump

AbstractWith the development of the high‐end equipment technology, the performance requirements of the internal gear pump (IGP) under high pressure are also increasing. However, the increase of working pressure will lead to the instability of gear pump performance in terms of volumetric efficiency, noise, reliability and so on, it is necessary to reasonably evaluate the reliability level of high‐pressure IGP. The reliability analysis of the high‐pressure IGP is carried out from the aspects of flow, noise, and gear strength in this paper. First, the output flow rate and far‐field flow‐induced noise of the high‐pressure IGP were obtained through fluid numerical simulation, and experimental verification was conducted. Then, based on the time‐varying meshing stiffness, backlash function and static transmission error of the gear pair, a nonlinear dynamic model of the internal meshing gear pair was established. The time‐varying meshing force was obtained through the dynamic model of the gear pair, and then the tooth contact stress and tooth root bending stress were obtained. Finally, considering the uncertain factors affecting the performance of the high‐pressure IGP, Latin hypercube sampling (LHS) combined with dendrite network (DD) was used for random response modeling. The performance reliability of the high‐pressure IGP, including output flow rate, far‐field flow‐induced noise, and the strength of gear pair, were estimated based on the fourth moment‐based saddlepoint approximation (FMSA). The reliability analysis results can provide a theoretical basis for the structural optimization design of the high‐pressure IGP.

Theoretical and experimental research on tooth root bending stress of face gear

A tooth root bending stress analysis method is proposed to study the tooth surface load distribution and tooth root bending stress during the meshing process of orthogonal face gear. Firstly, the tooth surface equation, transition surface equation and tooth width constraints are derived. Then, Through the tooth contact analysis (TCA), the contact path and spots of the face gear pair are obtained. What’s more, the proposed method based on Load tooth contact analysis (LTCA) is utilized to calculate the tooth surface load distribution and root bending stress of the face gear along the mesh cycle and compared with the finite element method. Meanwhile, root bending stress tests were carried out to verify the proposed method. The comparisons indicate that the proposed method has higher computational efficiency compared with the finite element method (e.g. the finite element method takes about 5 h for a mesh cycle and the proposed method costs 40 s). The results show that the tooth surface load distribution and root bending stress of the proposed method are consistent with those obtained by the finite element method and gear root stress experiment.

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear’s resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems.

The Design, Analysis, and Optimization of a New Pitch Mechanism for Small Wind Turbines

This article proposes and designs a novel variable pitch adjustment device for small wind turbines. The generator spindle is designed to be hollow so that the drive rod passes through it and connects the pitch drive mechanism to the pitch actuator. The article introduces the basic structure and working principle of the pitch mechanism and verifies the feasibility of the pitch device by using 3D printing technology to produce a small-scale model. The stress analysis of the wind turbine was carried out using the unidirectional fluid–structure coupling method. The results show that the maximum equivalent stress of the pitch mechanism is 27.42 MPa, the maximum tooth surface contact stress of the gear is 38.40 MPa, and the maximum tooth root bending stress is 18.13 MPa. The rack synchronous disk, blade handle, and gear rack mechanism were designed with light weight using various optimization schemes. The results of the optimization showed that the overall mass of the pitch mechanism was reduced by 33.2%, improving the applicability of the new pitch mechanism.

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.

Research on the Strength Calculation Method and Effects of Gear Parameters for High-Coincidence High-Tooth Gears

This article studies the calculation method for the tooth root bending stress of a high-tooth gear pair with a high contact ratio. The boundary point of the double-tooth meshing zone of the high-tooth gear pair is used as the loading point for the load, and the calculation formula for the bending stress at the dangerous section of the tooth root is obtained. By using ANSYS finite element simulation, the effect of the addendum coefficient, pressure angle, and other gear parameters on the bending stress of the tooth root is studied. The analysis shows that increasing the pressure angle will reduce the bending strength of the tooth root. Increasing the coefficient of a tooth’s top height will lead to an increase in the bending strength of the tooth root. Comparing the finite element analysis (FEA) results with the theoretical calculation results, the analysis shows that under low loads, the maximum error of the theoretical calculation values of the driving toothed gear and driven gear shall not exceed 13.53% and 15.42%, respectively. Under high loads, the maximum theoretical errors of the driving toothed gear and driven gear shall not exceed 8.78% and 10.91%, respectively. This verifies the correctness of the calculation method, which is of great significance for improving the load-bearing capacity of high-tooth gears and for guiding tooth shape design.

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.

Design, Stress Analysis, and FEA Prediction of Nutation Drive with Face Gear

Background: Nutation face gear transmission is a patent about a new type of transmission based on meshing between two face gears. It replaces spur gear with internal face gear to form a “faceface” meshing gear pair and actualizes its deceleration function by combining the nutation principle, which has the advantages of both face gear and nutation drive. Objective: The purpose of this paper is to study the designing and manufacturing of a nutation face gear reducer to derive the force calculation formulas of the face gear, input shaft and bearings, calculate the contact stress of tooth surface and bending stress of tooth root, determine the basic parameters of the prototype, and analyze the processing points for the core parts of the prototype. Methods: Using the dynamic meshing force analysis method by combining it with modern digital design and manufacturing methods, the designing and manufacturing of a nutation face gear reducer are studied. Results: In the theoretical calculation, the maximum contact stress of the fixed side tooth surface is about 433MPa, and the average contact stress is about 345MPa; the maximum contact stress of the tooth surface on the rotating side is about 579MPa, with an average of about 502MPa; the comparison of which with the finite element analysis results verifies the theoretical calculation results. Conclusion: The dynamic meshing force analysis method of nutation face gear transmission is deduced and given. Based on this, gear tooth surface transient contact stress and tooth root bending stress are calculated.

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.

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.

Numerical Study of the Impact of Shot Peening on the Tooth Root Fatigue Performances of Gears Using Critical Plane Fatigue Criteria

Gears are one of the the most widespread mechanical components and their design is supported by standard calculation methods. Among all the possible failure modes of gears, tooth root bending is the most critical and could lead to catastrophic failures. In this regard, different surface treatments could be exploited to improve the gear strength. Among them, shot peening is the most common. The aim of this study is to evaluate the effectiveness of shot peening on improving the tooth root bending resistance. This is achieved by exploiting the Finite Element Method (FEM) in combination with advanced multiaxial fatigue criterion based on the critical plane concept. A standard Single Tooth Bending Fatigue test was reproduced numerically via FEM. Beside the wrought gears, shot peened ones were also simulated. The state of stress induced by the shot peening was obtained numerically by simulating the surface treatment itself with non-linear dynamic analyses. The results have shown quantitatively how the residual stresses promote an improvement in the resistance and how the local hardening could lead to different early paths of nucleation and propagation of cracks on the tooth fillet.

소형 수문 권양기용 피니언의 강도설계

This paper presents an approach for the strength design of the pin jack-type gear system, that is, roller rack pinion (RRP) system, typically employed in small to mid-sized sluice gate devices. First, the load distribution of the pinion in the section of double tooth contact (DTC) was presented by the introduction of the load sharing factor considering the gear precision. Notably, the higher the gear precision, the lower was the contact force, contact stress, and tooth root bending stress (TRBS) in the section of DTC. Meanwhile, as the mounting distance (MD) increased, the pressure angle and geometry factor for the TRBS increased, and the tooth equivalent curvature decreased. Consequently, the change in contact force according to the increase of the MD was insignificant. However, the contact stress and TRBS significantly decreased, and the fatigue lifetime of the pinion increased.

기어 정밀도를 고려한 CRP 시스템 랙의 굽힘 강도설계

본 논문에서는 기존 랙-피니언의 인벌류트 피니언 치를 롤러로 대체한 CRP(cam rack pinion) 시스템 랙의 기어 정밀도(gear accuracy grade)를 고려하지 않았을 때와 고려하였을 때의 이뿌리 굽힘응력(TRBS: tooth root bending stress) 거동을 비교 고찰하였다. 하중전담구간(STC: single tooth contact)에서의 TRBS 거동은 기어 정밀도와 무관하게 거의 일치하였으나 STC 최고위치인 HPSTC(highest point of STC)를 지난 이후의 하중분담구간(DTC: double tooth contact)에서의 TRBS는 기어 정밀도에 따라 상당한 차이를 보였다. 또 설계제원 중 롤러 피니언 모듈이 증가하면 압력각의 감소로 최대 접촉력은 약간 감소하나 형상계수(bending strength geometry factor)의 감소로 인해 TRBS가 증가함을 확인하였다.

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.

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.