Root Fillet Research Articles

Composite failure analysis of an aero-engine inter-shaft bearing inner ring

The inter-shaft bearing is a critical component in dual rotors aero-engine. Due to the complex and severe loads caused by the interactive excitation of HP and LP rotors during operation, the inter-shaft bearing is prone to damage accumulation and failure. Focusing on a typical failure of inter-shaft bearing inner ring fragmentation and cannot be spliced together completely in high thrust-weight ratio turbofan engine, this paper conducted morphological investigation, fractographic analysis, vibration signal processing, finite element numerical simulation, and fully studied the failure mechanism of this failure.The results indicated that: there exists an uncoordinated resonance speed of the HP rotor in close proximity to the operating speed. This puts the rotor in non-synchronous procession state, accompanied by the uncoordinated angular displacement of the inner and outer rings, which resulting in a lager rolling dynamic load in bearing inner ring. This further leads to high tangential impact load at the root fillet of the anti-rotation pin, causing significant stress concentration, and eventually leads to the generation of initial cracks. These cracks persist and propagate into fatigue oblique fracture over time. After oblique fracture, the modal frequencies of the inner ring become more dispersed. Under the rolling dynamic load (traveling wave load), nodal diameter vibration occurs, causing high stress vibration fatigue damage, and ultimately leading to multiple-point simultaneous fragmentation.The investigation suggests that reducing the stress levels at the root fillet of the anti-rotation pin of the inner ring is an effective approach to prevent bearing failure. This can be achieved through two methods: one is optimizing the rotor structure to decrease the rolling dynamic load on the inner ring, the other is eliminating the anti-rotation pin and appropriately reducing the tightening torque of the compression nut and the interference between the bearing inner ring and the HP turbine rear journal.

A Modified Approach to the Rack Generation of Beveloid Gears

The purpose of this paper is to present an easier and more efficient method for the determination of the geometry of a bevelled gear tooth. Based on a method that provides an easier way for the rack generation of involute helical gears, the mathematical model of a beveloid gear is studied. The mathematical procedure for developing two-dimensional cross-sections has been extended to three-dimensional gear models. A computer programme is developed to obtain generating and generated surfaces. The proposed algorithm is compared with the previous studies for verification and validation. The results demonstrate that the coordinates obtained from the given method are nearly the same on the start and end points of the main gear parts, such as the involute and root fillets regions. Also, between the limits, the values can be considered acceptable. A coordinate deviation of the gear profile has been observed in the mathematical model, because of the profile shift. Modifications have been developed in the equations to eliminate these cases. The main advantage of the proposed method is to obtain mathematical models without carrying out some of the calculation steps used in previous studies. Eventually, this feature will provide an easier and faster method to develop computer-aided models of the beveloid gear types.

Effect of tooth root fillet on root bending stress

The tooth root fillet exerts a significant effect on the root bending stress of gear teeth. However, the current study predominantly focuses on theoretical analysis and numerical methods, with insufficient emphasis on effective experimental verification. Therefore, this paper completes root bending stress tests on gear teeth and conducts an analysis of how the tooth root fillet impacts root bending stress. Firstly, the paper provides a summary of the generation theory of the tooth root fillet using rack cutters/hobs, which serves as the foundational machining principle for tooth root fillet. Secondly, using three typical tooth root fillet as examples, the study conducts root bending stress tests. The R-S-N curves corresponding to these three tooth root fillet profiles are derived using both conventional group methods and a variable load approach, involving lifting and lowering. Finally, the paper analyses the influence of these three types of tooth root fillet on the root bending stress of gear teeth. Through a comparison of S-N curves at the same reliability level, it identifies the optimal tooth root fillet among the three.

Effects of Profile Shifting of a Cosine Gear

Cosine gears are a special type of gear drive, in which the tooth profile of the theoretical generating rack is described by the cosine function. According to recent research results, the cosine gear drive has a lower slip coefficient and the contact and bending stresses supported by the teeth during the load are smaller than those occurring in involute gears. The main advantage of the cosine drive pair lies in the apparent higher rigidity of the gear tooth: this can reduce flank wear and increase gear life, especially in heavy load and highspeed applications. In contrast to involute profile gears, cosine gears do not show undercut root fillet, even with small teeth number. This paper deals with cosine gear tooth profile design and the meshing of the cylindrical cosine gear pair conceived without, or with the application of the profile shifting. The mathematical model of the meshing was implemented in a Mathcad environment, showing that there exists a significant difference compared to the well-known involute gears. The simulation of the motion during the rolling of the gear pairs was realized with the Autolisp programming interface. Solid models were created and tested in the Autodesk Inventor environment.

Influences of Root Fillet and Dihedral Angle of Bowed Stator Blade on Aerodynamic Performance of Low-Speed Single-Stage Axial Compressor

Influences of Root Fillet and Dihedral Angle of Bowed Stator Blade on Aerodynamic Performance of Low-Speed Single-Stage Axial Compressor

Parametric Modeling of Curvic Couplings and Analysis of the Effect of Coupling Geometry on Contact Stresses in High-Speed Rotation Applications

Curvic couplings are used in applications demanding high positional accuracy and high torque transmission; therefore, improving their design and enhancing their load-carrying capacity is crucial. This study introduced the kinematic model Curvic3D, which was developed to produce the accurate geometry of both members of a curvic coupling using a CAD system. The model enabled the complete parametrization and customization of the coupling design using important geometric parameters. The couplings produced using Curvic3D were then imported into a finite element analysis model also developed as part of this study. A detailed analysis of the stresses developed on the teeth of the concave and convex parts provided information about the behavior of the coupling under different loading conditions. Finally, a series of geometric parameters, such as the number of teeth, the number of half pitches, the root fillet radius, and gable angle were examined as to their influence on the load-carrying capacity of the curvic coupling. The study concluded that all the examined parameters have a significant effect on the tooth flank and root area stresses.

Influence of the Slot Fillet and Vane Root Fillet on the Turbine Vane Endwall Cooling Performance

Due to machining techniques and dust deposition, gas turbine upstream slots and vane roots are always filleted, significantly affecting the cooling performance of the endwall. The effects of upstream slot fillet and vane root fillet on the cooling performance of the gas turbine endwall were investigated by solving the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations with the shear stress transport (SST) k–ω turbulence model. The results indicate that the velocity distribution of the slot coolant is effectively changed by introducing the upstream slot fillets. Among the four cases, the largest adiabatic cooling effectiveness was obtained for the case with two similar fillets, with a 42% increase in effective cooling area compared to the traditional slot. At MFR = 0.75%, the horseshoe vortex is weakened by the introduction of the vane fillet with a small radius, with a 53% increase in effective cooling area compared to the baseline. However, the vane fillet with a large radius makes the boundary layer flow separately prematurely, decreasing the cooling performance. The lateral coverage of the coolant jet from the filmhole embedded in the vane root fillet is greatly enhanced by increasing the vane root fillet radius. However, the streamwise coverage is decreased and the thermodynamic loss is increased.

Effect of Geometric Variation of Root Fillet on the Flow Characteristic of a Transonic Compressor Rotor

Effect of Geometric Variation of Root Fillet on the Flow Characteristic of a Transonic Compressor Rotor

Failure analysis of an aero-engine inter-shaft bearing due to clearance between the outer ring and its housing

The inter-shaft bearing is a critical but vulnerable component of dual rotors, because of the severe operational conditions and loads. This paper investigates the failure mechanism of a fractured inter-shaft bearing belonging to a high thrust-weight ratio turbofan engine. Fractographic and microscopic analyses of the fracture surfaces were conducted, followed by vibration signal processing. Finite element analyses of the outer ring were also performed considering the centrifugal, thermal, and roller-raceway loads. What’s more, using the linear elastic fracture mechanics theory, the crack growth path simulation was obtained, whose result showed good agreement with the real fracture morphologies. The results indicated that due to the clearance between the outer ring and its housing during the operation, the anti-rotation tabs of the outer ring were subjected to non-uniform load, thus several tabs might suffer large stress concentrations at the root fillets, which could lead to the crack initiation. During the following operation of the aero-engine, the crack propagated through the outer ring and cause the fatigue fracture of tabs. The investigation provided herein suggests that the outer ring and its housing should be redesigned to eliminate the clearance during the operation, an outer ring formed integrally with the bearing housing flange is one of the failure preventions of this failure mode.

Evaluation of root stresses of a rattling gear pair

Gear rattle is a major noise problem in certain powertrains systems, especially those that are driven by internal combustion engines such as timing gear drives, engine balancers or manual transmissions. Teeth lose contact intermittently to commit impacts along the drive and coast sides of the gear pairs having backlash. Most of the studies on this topic focused exclusively on the noise and vibration consequences of rattle with a very little attention given to its influence on system durability. This study presents an experimental investigation of tooth root stresses of a spur gear pair during periodic and chaotic rattling motions caused by a harmonically time-varying input torque. Root stresses of certain teeth of one of the gears are measured in the instances when these teeth are in gear mesh zone when impacts occur. Changes to root stress time histories due to drive and coast-side impacts are documented to show that root stress amplitudes are increased significantly by impacts. Measurements also indicate that most impacts generate families of fully-released strain peaks that contribute the fatigue damage along the drive and coast sides root fillets. A deformable-body model was shown to simulate the experiments accurately, so that it can be used to predict statistical distributions for root stress duty cycles for estimation of fatigue lives of rattling gears.

An analytical approach for the determination of helical gear tooth geometry

Purpose This paper aims to present an analytical approach for the determination of helical gear tooth geometry and introduces the necessary parameters. Tooth geometry including tooth chamfer, involute curve, root fillet, helix as well as tooth microgeometry can be obtained using the presented approach. Design/methodology/approach The presented analytical approach involves deriving the equivalent equations at the transverse plane rather than the normal plane. Moreover, numerical evaluation of microgeometry modifications is presented for tooth profile, tooth lead and flank twist. Findings An analytical approach is presented and equations are derived and explained in detail for helical gear tooth geometry calculation, including tooth microgeometry. Method 1, which was presented by Lopez and Wheway (1986) for obtaining the root fillet, is examined and it is proven that it does not work accurately for helical gears, but rather it works perfectly in the case of spur gears. Changing the normal plane parameters in Method 1 to the transverse plane ones does not give correct results. Two alternative methods, namely, Methods 2 and 3, are developed in the current research for the calculation of the tooth root fillet of helical gears. The presented methods and also the numerical evaluation presented for microgeometry modification are examined against the geometry obtained from Windows LDP software. The results show very good agreement, and it is feasible to apply the approach using the presented equations. Originality/value In the gear design process, it is important to model the correct gear tooth geometry and deliver all related dimensions and calculations accurately. However, the determination of helical gear tooth geometry has not been presented adequately by equations to facilitate gear modelling. The detailed helical gear tooth root has been enveloped using software tools that can simulate the cutter motion. Deriving those equations, presented in this article, provides gear design engineers and researchers with the possibility to model helical gears and perform design calculations in a structured, applicable and accurate method.

COMPARISON OF STANDARD AND NONSTANDARD GEAR ROOT FILLET CONSIDERING ROOT STRESS AND MANUFACTURING POSSIBILITIES

In this paper, root stress, manufacturing possibilities and limitations of standard and nonstandard tooth root fillet of spur gears are examined. Nowadays, standard trochoidal root fillet is used the most as an economical trade-off between tooth strength and manufacturing complexity. A disadvantage of the trochoidal root fillet, especially in spur gears with less than 17 teeth, is undercutting which minimises strength of tooth root, introduces stress concentration, and deteriorates meshing conditions. This study focuses on different root designs, namely elliptical and novel cycloidal root fillets. Root stress in gears with different root designs is analysed by FEM and compared with analytical equations according to ISO. The possibility of producing nonstandard root fillet gears by hobbing and limitations of surface finishing are considered as well. Analysis reveals stress differences between each of the root fillet shapes and their relative advantages and disadvantages.

Research on the time-varying mesh stiffness method and dynamic analysis of cracked spur gear system considering the crack position

The occurrence of a crack could change the gear mesh stiffness and consequently influence gear vibration properties. Cracks may occur on the tooth root and tooth surface, but the surface crack type has been seldomly concerned. This study proposes a comprehensive time-varying mesh stiffness (TVMS) calculation method in which the crack position is considered and emphasized. Two tooth crack types (Root crack type: the crack occurs on the root fillet; Surface crack type: the crack occurs on the tooth surface) are modeled and analyzed, and corresponding analytical calculation expressions of TVMS are derived. The finite element method is applied to validate the applicability and accuracy of the proposed analytical method for both root and surface crack types. Besides, by establishing a nonlinear dynamic model for a spur gear system, the influences of the crack depth and crack position on the gear dynamic characteristics are investigated. Several statistic parameters are also applied to evaluate the health conditions for the spur gear system. The method and analysis results reported here may be of interest to researchers and engineers attempting to handle the gear fault analysis analytically and effectively.

Balanced bending fatigue life for helical gear drives to enhance the power transmission capacity through novel rack cutters

This article proposes an idea for balancing the bending fatigue life between the gear and pinion of a novel helical gear drive. In this study, the helical gear is developed through analytical equations based on a novel rack cutter tooth thickness factor, and the estimation of principal stress and strain at the critical root fillet of the helical gear teeth is carried out through finite element analysis. Further, the fatigue module in COMSOL- Multiphysics software is employed to determine the bending fatigue life through strain life approach based on Smith-Watson-Topper with Neuber’s rule and fatigue usage factor based on Findley criteria. The effect of major gear parameters such as helical angle, pressure angle, teeth number, gear ratio, addendum height and addendum modification factor (S+, S− and S0) on bending fatigue life are computed based on novel helical gear with different rack cutter tooth thickness factor of gear and pinion. Finally, the above parametric study shows an optimum rack cutter tooth thickness factor between the gear and pinion to achieve a balanced bending fatigue life and fatigue usage factor, which aids in improving the power transmission capacity of the helical gear drive.

Crack initiation and propagation analysis for fisheye failures in high-strength gears

Lightweight design has had an important role to play in recent gear developments. One way of reducing gear weight is to apply a shot-peening process in addition to the usual case-hardening because the higher compressive residual stresses within the material mean that the same torque values can be transmitted with smaller gears. However, due to the compressive residual stresses, fisheye failures at non-metallic inclusions can occur, which have an effect on the endurance fatigue strength of high-strength gears, especially in the very high cycle fatigue range. This paper presents a detailed FEM simulation of the stress state at a non-metallic inclusion in the tooth root fillet of such high-strength gears. The aim is to explain certain fracture characteristics, which differ from fisheye failures of standard specimens. With the results of the simulation und taking into consideration the fracture characteristics determined in a SEM, a fracture analysis for fisheye failures in the tooth root fillet of high-strength gears is carried out that links different theories found in the literature. Subsequently, this analysis and the influence of residual stresses are compared with data and further fracture analyses from experimental investigations found in the literature.

Study on excitation and time-varying mesh characteristics of straight bevel gears considering modification and friction

An accurate and numerically efficient nonlinear coupled excitation model for straight bevel gears (SBG) with linear and point contact is proposed. This model incorporates stiffness, load distribution, and transmission error (TE) models. Considering root fillet and axial mesh force components, energy equivalence principle, accumulated integral potential energy method, and segment coupling theory, single mesh stiffness (SMS) models with and without coupling effect are proposed. On this basis, the formula for calculating SMS under the action of friction is given. Time-varying mesh stiffness (TVMS), load distribution, and TE models were established using the deformation compatibility condition and principle of force balance. The proposed model was verified by comparing the calculation results with those obtained using the finite element method (FEM). The semi-analytical TVMS model used in this study could be solved accurately and quickly. The meshing characteristics and changing rules of SBG under the influence of different modification methods, modification amounts, and friction coefficients were analyzed. This study is expected to help further enrich and develop gear stiffness theory and provide a theoretical tool for gear dynamics research.

Improvement on the machining accuracy of titanium alloy casing during counter-rotating electrochemical machining by using an insulation coating

Counter-rotating electrochemical machining (CRECM) is an innovative ECM method that can be used to manufacture revolving parts, especially thin-walled casings with complex convex structures. As titanium alloys are easy to passivate and difficult to machine, active NaCl solution is often used to obtain a good surface quality from ECM. However, the top surfaces of convex structures will be subjected to severe over cutting using NaCl solution, resulting in poor machining accuracy. Therefore, an insulation coating is employed to protect the non-processed area by shielding stray currents in this paper. A simulation model is established to investigate the evolution of convex structures with an insulation coating. According to the simulated convex structures, the top of the convex structure suffers from serious stray corrosion without the protection of insulation coating, and the sidewall inclination angle is 25.42°. However, the insulation coating enables convex structures without over cutting, achieving a sidewall inclination angle of only approximately 1.1°. Under the protection of insulation coating, the width and height decrease linearly with time, and the radius of the root fillet increases towards an approximately constant value. The experimental results indicate that stray currents can be shielded completely with an insulation coating, and no electrochemical dissolution occurs on the top of the convex structure. The deviation between simulation and experimental results does not exceed 10 %, demonstrating reliability of the proposed model. Cylindrical and conical parts with a grid-like convex structure are successfully produced with a surface roughness value of Ra1.8 μm. This fully verifies the effectiveness of an insulation coating and demonstrates the excellent processing capability of CRECM.

A computerized method of contact pressure and load distribution for crossed beveloid gears

Exact contact pressure and load distribution are key evaluation indices for beveloid gear design. A numerical calculation approach of contact pressure and load distribution for crossed beveloid gears is proposed, as opposed to the traditional method based on a finite element modeling software package. To acquire the flexibility properties of beveloid gear tooth surfaces, an accurate finite element (FE) model about a beveloid gear tooth with root fillets is first built. A solution model for crossed beveloid gears is developed using the influence coefficients technique. An enhanced solving approach is presented to improve the robustness of the solving model by addressing the limitation of the influence coefficients method. In addition, a unique contact pressure is presented. The numerical example proposed can be used to test the proposed methodology.

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.

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.