Thin-rimmed Gears Research Articles

Investigation of Crack Propagation Behaviour in Thin-Rim Gears: Experimental Tests and Numerical Simulations.

Thin-rim gears are widely used in industrial fields such as aerospace and electric vehicles due to the advantage of light weight. Yet, the root crack fracture failure of thin-rim gears significantly limits their application and further affects the reliability and safety of high-end equipment. In this work, the root crack propagation behavior of thin-rim gears is experimentally and numerically investigated. The crack initiation position and crack propagation path for different backup ratio gears are simulated using gear finite element (FE) models. The crack initiation position is determined using the maximum gear root stress position. An extended FE method coupled with commercial software ABAQUS is used to simulate the gear root crack propagation. The simulation results are then verified by conducting experimental tests for different backup ratio gears based on a dedicated designed single-tooth bending test device.

DIC analysis of gears in bending condition

Thin rim gears present a complex strain and stress field due to its particular geometry, above all in bending problems. From this point of view, the position of the most stressed point and the corresponding equivalent stress value are useful for an accurate design of thin rim gears. More in detail, in case of bending failure, both crack initiation point and corresponding propagation path are strictly related to the gear’s geometry.In this work, an experimental analysis was performed to evaluate how light weight gears geometry may influence the strain field close to the tooth root.To this aim, an experimental activity was carried on by a dedicated equipment for bending tests and the gear deformation was monitored by using the 3D Digital Image Correlation (DIC) technique.The local strain field in both tooth and web portions was measured for two types of gears (standard gear and thin-rim gear) in order to identify the stress condition due to the bending loading. A particular attention was devoted to point out the most stressed point for both gears. Results were also compared with XFEM model available in literature.

Experimental investigation on crack propagation paths in spur gears

Spur gears subjected to bending fatigue may nucleate cracks at the tooth root fillet. In thin rim gears these cracks may propagate in a safe way (through the tooth) or in catastrophic way (through the rim). Crack propagation direction is mainly influenced by both wheel geometry parameters and crack initiation point, as already pointed out by theoretical and numerical results available in literature. Aim of this work is to set up an experimental activity in order to verify the onset of the bending crack and its propagation path in spur gears with different geometries. In particular, a special device connected to a standard fatigue machine was realized to perform bending tests for both standard and thin rim gears. During bending tests, an IR thermocamera was utilized to monitor the surface thermal profile in the tooth root fillet zone.

A flexible-helical-geared rotor dynamic model based on hybrid beam-shell elements

Considering the flexibility of gear foundations and rotational effects, a geared rotor dynamic model for thin-rimmed helical gears is established. The deformable shafts and gear foundations are modelled by Timoshenko beam elements and Mindlin-Reissner shell elements, respectively. The beam element and the shell element are connected using the ‘interfacial coupling element’. Then the modal superposition method is adopted to improve the computational efficiency. The proposed dynamic model is verified through the comparison between the simulated responses and experimental results in a published literature. Based on the proposed dynamic model, the effects of the web thickness, the rotational effects and the helix angle on the dynamic behaviors are discussed. The results show that the dynamic responses of thin-rimmed gears obtained from the traditional dynamic model and the proposed model are quite different, which emphasizes the significances of the flexible body modeling. Compared to the centrifugal stiffening and the spin softening, the gyroscopic effect has more significant effect on dynamic characteristics. The nodal diameter vibration cannot be excited due to the absence of the axial exciting force when helix angle is zero. The increase of the helix angle will lead to more significant out-of-plane vibration of the gear foundation.

Hybrid Dynamic Modeling and Analysis of High-Speed Thin-Rimmed Gears

Abstract In this study, a hybrid dynamic model of high-speed thin-rimmed gears is developed. In this model, the translational and angular displacements (including the rigid and vibration displacements) with a total of six degrees-of-freedom (DOFs) are selected as the generalized coordinates for each gear, and the meshing force distributions along the contact line and between the teeth are considered. Thus, the model can be implemented under stationary and nonstationary conditions. The condensed finite element models (FEMs) are developed with the centrifugal and inertia forces for gear bodies. This paper proposes a novel method to couple the lumped-parameter model and condensed finite element model for the hybrid dynamic model system, which considers the variation of the meshing tooth during the gear operation, namely, the variations of the acting point of meshing force. Based on the model, the dynamic analysis of high-speed thin-rimmed gears is conducted under stationary speed and acceleration processes. The effects of the flexible gear body, high speed, and tooth errors on the system dynamics and tooth load distribution are investigated. The analysis results are also compared with the current reference and pure finite element method to validate the proposed model.

Design and analysis of thin wall gear structure with Tio2/GF reinforced Nylon66 composites

In machineries, to increase or decrease the speed, gear is very much needed. Such machineries are now days are compact design with less weight. Gears must occupy minimum spaces and materials reduction is required. For that, one of the best options is rimmed gears. The aim of the paper is to design and analysis of different thin-rimmed gear for high strength with high speed of rotations under harsh condition. The composite materials are in trend in recent years. High heat resistance and low wear characterized composite materials such as Nylon66 with TiO2, with and without glass; fibres are implemented in thinned rimmed gears. With TiO2, volume of percentage varies from 0% to 6%, which are used in analysing the individual gear models. The effect of web thickness, web positions, rim thickness, module, hub thickness and face width parameters are analysed to find out the strength that depends on the type of materials and gears, which are analysed in this paper.

Effects of tooth modifications on the dynamic characteristics of thin-rimmed gears under surface wear

Considering the thin rim structure and gear tooth modifications, a three-dimensional wear prediction model is proposed. Unitizing the proposed model, the contact pattern and the wear distribution are analyzed. For gear pairs with asymmetric rim structure, obvious stress concentration will lead to the severe wear on one edge of the gear tooth. Aiming at balancing the wear distribution and reducing vibration, an optimization scheme of the tooth modification (including the tip relief and the helix angle modification) is proposed. After adopting tooth modifications, the severe wear at one edge is almost eliminated. The fluctuation of the transmission error decreases significantly. The dynamic characteristics of thin-rimmed gears over the whole wear process are analyzed. It is found that the tooth modification is beneficial to shorten the running-in period and decelerate the failure process in the period of performance degradation.

Modular hybrid models to simulate the static and dynamic behaviour of high-speed thin-rimmed gears

Several modular hybrid gear dynamic models are presented which account for both the local phenomena associated with the instant contact conditions between the tooth flanks and the more global aspects related to shafts, bearings and particularly the contributions of light thin-rimmed/-webbed gear bodies. The proposed models combine sub-structures, lumped parameter and beam elements to simulate components with linear behaviour such as webs, rims, shafts, etc. while local mesh elasticity is simulated by time-varying, possibly non-linear Winkler foundations. A specific interface has been developed to connect discretised tooth contact lines with continuous finite element models and avoid singularities in tooth load distributions. A number of comparisons with numerical and experimental results show that the proposed modelling is sound and can capture most of the quasi-static and dynamic behaviour of single stage reduction units with thin-webbed gears and/or pinions. Finally, the modelling strategy is applied to the analysis of high–speed industrial gears and results are presented which illustrate the interest of the proposed methodology compared with the classic gear dynamic models.

Crack growth modeling in spur gear tooth and its effect on mesh stiffness using extended finite element method

Abstract The manuscript is devoted to determine the time variable mesh stiffness (TVMS) and crack propagation behaviour in spur gear tooth using extended finite element method (XFEM). The TVMS of gear pairs provides significant information about the condition of the gear system. Thus, the accurate estimation of TVMS is essential to get the information of the primary source of vibration and noise. Extended finite element method is very effective for discontinuity due to faults like cracks etc. The capability of XFEM to enrich approximate spaces locally makes it appropriate method to compute the values of TVMS in spur gear. A gear tooth crack problem has been solved using XFEM and the obtained results are compared with the analytical results for validation. Further, a problem of crack at the root resign in thin rim gear is simulated to investigate the effect of rim thickness on gear tooth crack propagation path. The estimated crack propagation path shows good agreement with the results available in literature.

Influence of high speed on crack propagation path in thin rim gears

AbstractThin rim gears need accurate design as cracks nucleated at the tooth root fillet may propagate in a safe way (through the tooth) or in catastrophic way (through the rim). Crack propagation direction is mainly influenced by both wheel geometry parameters and crack initiation point. For specific geometry configurations, crack propagation path may be influenced also by other parameters such as the centrifugal load. For this reason, in this work the effect of the centrifugal load (proportional to wheel speed), related to the bending one, has been investigated. The stress field at the tooth root fillet and near the crack has been considered to evaluate the crack initiation point and to explain the propagation direction. This research activity has been carried out by means of numerical models (traditional 2D and 3D finite elements and extended finite elements (XFEM)). Results show that both crack initiation point and crack propagation path are strongly influenced by the centrifugal load entity; this effect is mainly evident in the uncertainty zone of the backup ratio.

Investigation about crack propagation paths in thin rim gears

Crack propagation in gears is a problem related not only to the life of the components, but also to the concept of failsafe design. Fail safe design means to design a component in order that, if a failure occurs, this may cause a “safe failure”. This aspect is very important above all in aerospace industry. As a matter of fact, in aerospace application, the need of reducing weight brings to produce gears with very thick rim and web. Considering thin rim gears, when a crack is nucleated near the tooth root, it may propagate through the tooth (causing the loss of the entire tooth or a portion of it) or the propagation may follow a path across the wheel diameter (causing the projection of big parts of the gear that may break the gearbox and may cause serious damage to the aircraft). The first failure mode is define as “failsafe failure” and the second one as “catastrophic failure” and of course has to be avoided. Designers need to have robust design criteria in order to predict crack propagation paths and to avoid catastrophic failures. In literature, few works are present concerning this topic, in particular related to the effect of geometrical parameters that may affect the crack propagation. In this work a numerical analysis about crack propagation in gears with respect to the backup ratio (ratio between tooth height and rim thickness), initial crack position and shape has been done by means of the Extended FEM (XFEM) technique, realizing 3D models. XFEM 3D is a relatively new technique consisting in enriching traditional finite elements with more complex shape functions; in this way it is possible to propagate crack also between mesh nodes and to have mesh independent results. Aim of this paper is to highlight the crack propagation path in order to give to designers an high confident design criterion, related to the gear geometry. In particular, the effect of both rim thickness and orientation of the initial crack have been considered in order to enrich the literature knowledge. Numerical results obtained in this work have been compared with those found in the literature, showing a very good correlation.

314 薄肉ウェブ構造はすば歯車の歯元応力と伝達トルクに及ぼすねじれ角の影響

314 薄肉ウェブ構造はすば歯車の歯元応力と伝達トルクに及ぼすねじれ角の影響

1208 薄肉ウェブ構造はすば歯車の曲げ疲労強度に及ぼすねじれ角の影響(歯車(1))

1208 薄肉ウェブ構造はすば歯車の曲げ疲労強度に及ぼすねじれ角の影響(歯車(1))

S112012 一対の平歯車の平等歯元曲げ強さの設計に関する研究([S112-01]伝動装置の基礎と応用(1))

A pinion and a gear of a pair of spur gears usually have different the maximum root bending stresses because of using profile-shifted gears or thin-rimmed gears or internal gears. Because of inequality of the maximum root bending stresses, load-carrying capacity of the gear with smaller root bending stress is limited by the gear with larger one. If this limit can be removed, this pair of the gears can have greater load-carrying capacity than it has before. So, this paper presents an idea to remove this limit through designing a pair of spur gears with uniform maximum root bending stresses. It is realized through changing the tooth thickness of the racks on the pitch lines from a standard tooth thickness into a non-standard one. Tooth root stresses and surface contact stresses of a pair of spur gears with standard and non-standard tooth thicknesses are analyzed by loaded tooth contact analysis using the finite element method (FEM). Calculation results show that the load-carry capacity of the pair of the gears become greater when the pinion and the gear have the same maximum root bending stresses.

S112013 薄肉ウェブ構造はすば歯車の歯元応力と曲げ疲労強度に及ぼすリム・ウェブ厚さおよびウェブ構造の影響([S112-01]伝動装置の基礎と応用(1))

S112013 薄肉ウェブ構造はすば歯車の歯元応力と曲げ疲労強度に及ぼすリム・ウェブ厚さおよびウェブ構造の影響([S112-01]伝動装置の基礎と応用(1))

Effects of centrifugal load on tooth contact stresses and bending stresses of thin-rimmed spur gears with inclined webs

Firstly, centrifugal deformation and stresses of thin-rimmed spur gears with inclined webs are analyzed in this paper with the finite element method (FEM) when the gears run at very high speeds. It was found that centrifugal load has a significant effect on tooth root bending stresses of the thin-rimmed gears at high speeds. So, it is necessary to consider the effect of the centrifugal load on tooth root bending stresses into bending strength calculations of the thin-rimmed gears when the gear speed is greater than 10,000min−1. Secondly, loaded tooth contact analyses (LTCA) are conducted for the thin-rimmed inclined web gears when they are deformed by the centrifugal load and engaged with a solid mating gear. FEM combined with a mathematical programming method is used to do the analyses. Tooth contact stresses and root bending stresses of the thin-rimmed gears are calculated under a torque load. It was found that the centrifugal deformation of the thin-rimmed inclined web gears almost has no effects on the tooth contact stresses and root bending stresses. This conclusion is different from the one obtained from the thin-rimmed straight web gears. Li (2008) [5] reported that the centrifugal deformation of the thin-rimmed straight web gears had significant effects on the tooth contact stresses and root bending stresses of the contact teeth. Finally, it is explained why the centrifugal deformation of the thin-rimmed inclined web gears does not affect the tooth contact stresses and root bending stresses.

Contact Stress and Root Stress Analyses of Thin-Rimmed Spur Gears With Inclined Webs

Loaded tooth contact analysis (LTCA), deformation, and stress calculations of three types of thin-rimmed spur gears with inclined webs at the left side, the center, and the right side of the tooth are conducted in this paper with finite element methods (FEM) combined with a mathematical programming method when these gears are engaged with a solid mating gear. The contact stresses on the tooth surfaces, the bending stresses at the tooth roots, and the joint stresses of the rim and the web are analyzed as the web position and the web angle are changed. It was found that the web position and the web angle of the thin-rimmed gears have a significant effect on the tooth contact stresses, the root bending stresses, and the joint stresses. The maximum contact stress of the right web gear becomes very small when the web is inclined from 0 to 30 deg, and it increases again when the web angles are changed from 45 to 60 deg. This interesting relationship between the web angle and the tooth contact stresses of thin-rimmed right inclined web gears is used to absorb the misalignment errors in the gears and improve the partial tooth contact pattern resulting from the misalignment errors. A calculation example is provided to illustrate how to improve the partial tooth contact patterns in gears with misalignment errors.

Effects of Rim and Web Thicknesses on Root Stresses of Thin-Rimmed Helical Gear

This paper presents a study on root stresses of thin-rimmed helical gears with web arrangement of various rim and web thickness. Thin-rimmed helical gears used in this study were meshed with solid helical gear. Root stresses were measured from the beginning of engagement to the end of engagement by using the strain gauge method. The changes of root stresses from the beginning of engagement to the end of engagement were examined and the meshing position where the maximum root stress occurred (worst loading position) was determined. Effects of rim and web thickness on the root stress, the maximum root stress and the position of maximum root stress were clarified.

Effect of Rotational Speed on Thin-Rim Gear Bending Fatigue Crack Initiation Life

Thin-rim gears are often used in aircraft applications in order to reduce weight. The objective of this study is to investigate the effect of rotational speed (centrifugal force) on bending fatigue crack initiation life of thin-rim gear manufactured from case carburized 14NiCrMo13-4 steel. Stresses in gear are determined from two-dimensional finite element model, assuming plane stress conditions. The fact that, in actual thin-rim gear operation, a significant reversed stress occurs at the root of the tooth adjacent to the loaded tooth is considered. Material is assumed to be homogenous, isotropic and linear elastic. Elastic strains are calculated from obtained stresses and corrected using Neuber’s rule to account plasticity effects. The number of load cycles required to initiate bending fatigue crack is predicted using strain-life approach for variety of gear rotational speeds and rim thicknesses. Strain-controlled fatigue properties were approximated from material hardness, while the mean stress as well as residual stress effects are included through Morrow’s mean stress correction. The proposed approach is validated by comparison with available experimental data from literature and used for parametric studies. Predicted numbers of load cycles required to initiate potential bending fatigue crack are presented for the variety of cases studied.

Prediction of thin-rimmed gear crack propagation from a factorial design approach

Gear failure involving bending fatigue can have catastrophic consequences depending on the propagation path direction. Therefore, anticipating and preventing eventual critical fracture are crucial at the design stage. However, none of the methods available can give rapid and quantitative evaluation of gear fatigue crack evolution. Aiming to provide fast predictions of crack propagation paths, this paper proposes a factorial design approach for gear bending fatigue simulation. Six parameters related to gear geometry and initial crack configuration are considered in this study. Factorial design experiments are numerically conducted with an efficient 2D boundary element model assuming linear elasticity. Then, bending fatigue damage is modelled using polynomial functions. The resulting prediction model can instantly establish the crack trajectory in thin-rimmed gear for any cycle numbers. Application of the approach is illustrated by several case studies, while its precision and reliability are demonstrated through an exhaustive validation procedure.