•The friction heat generation of the spiral bevel gear is analysed by FE method.•The distribution of the contact stress and heat flux on the tooth are evaluated.•Both the steady state and transient ...temperature fields are explored.•The contact patterns are obtained for better efficiency and anti-scuffing capacity.
Friction loss and scuffing failure are two primary research subjects in improving the performance of spiral bevel gears. Aimed at improving the thermal characteristics with machine-setting parameter adjustment, a coupled thermo-elastic 3D finite element model has been developed to analyse the frictional heat generation and transient thermal behaviour of spiral bevel gears. The heat fluxes due to friction effects are applied to the gear tooth to investigate thermal characteristics and prediction of transient temperature fields. The resulting thermal characteristics agree with earlier work, thus verifying the model and numerical approach. This study permits an in-depth understanding of the temperature fields, together with the frictional heat generation process. Furthermore, by investigating the transient thermal behaviour among different pinion machine-setting parameters, the tilted and extended tooth contact pattern achieved by adjusting the machine-setting parameters can result in an optimal tooth contact pattern that produces a uniform temperature field of much lower value, thereby achieving higher efficiency of transmission along with stronger anti-scuffing performance.
In this paper, a nonlinear time-varying dynamic model of a drivetrain composed of a spiral bevel gear pair, shafts and bearings is developed. Gear shafts are modeled by utilizing Timoshenko beam ...finite elements, and the mesh model of a spiral bevel gear pair is used to couple them. The dynamic model includes the flexibilities of shaft bearings as well. Gear backlash and time variation of mesh stiffness are incorporated into the dynamic model. Clearance nonlinearity of bearings is assumed to be negligible, which is valid for preloaded rolling element bearings. Furthermore, stiffness fluctuations of bearings are disregarded. Multi-term harmonic balance method (HBM) is applied on the system of nonlinear differential equations in order to obtain a system of nonlinear algebraic equations. Utilizing receptance method, system of nonlinear algebraic equations is grouped in nonlinear and linear sets of algebraic equations where the nonlinear set can be solved alone decreasing the number of equations to be solved significantly. This reduces the computational effort drastically which makes it possible to use finite element models for gear shafts. In the calculation of Fourier coefficients, continuous-time Fourier transform as opposed to the gear dynamics studies that utilize discrete Fourier Transform is used. Thus, convergence problems that arise when the number of nonlinear DOFs is large are avoided. Moreover, analytical integration is employed for the calculation of Fourier coefficients rather than numerical integration in order to further reduce the computational time required. Nonlinear algebraic equations obtained are solved by utilizing Newton’s method with arc-length continuation. Direct numerical integration is employed to verify the solutions obtained by HBM. Several case studies are carried out, and the influence of backlash amount, fluctuation of gear mesh stiffness and variation of bearing stiffness are investigated. In addition to these, the response of the coupled gear system model is compared with that of gear torsional model in order to study the influence of the coupling on dynamics of the system.
To predict the churning power losses in a gearbox with spiral bevel geared transmission, based on the Computational Fluid Dynamics (CFD) method, a numerical simulation model for the splash ...lubrication of the intermediate gearbox of a helicopter including gear box housing, a spiral bevel gear pair and an oil guide device is established and validated by the churning power losses prediction of experiments showing a good agreement. With the model, churning power losses of a gearbox with spiral bevel geared transmission are obtained; influences of gear rotational speed, oil fill level, oil temperature, oil dynamic viscosity, oil density, and tilt angle of the helicopter, on the churning power losses are analyzed.
•CFD calculations of churning power losses of a gearbox with spiral bevel geared transmission are performed.•The churning power losses increase with the increase of the rotational speed and the oil fill level of gears•The churning power losses increase with the increase of the dynamic viscosity and density of the oil.•The influence of the helicopter tilt angle on the churning power losses is small and regular.•The present numerical model is validated by experimental results.
•A novel multi-channel signal processing method named LQSSA is proposed.•Lanczos method is used in the decomposition to reduce calculation time.•Filter factor is obtained by introducing Lagrange ...multiplier to improve signal purity.•Each LQSSC is derived from multi-channel signals by periodic similarity.•Simulation and experimental signals of bevel gear verify the effectiveness and superiority of LQSSA.
Multi-channel signals collected by multiple sensors contain more operating information than single-channel signal, so multi-channel signal processing method can improve confidence level and accuracy of fault diagnosis. Multivariate empirical mode decomposition (MEMD) is the most widely used multi-channel signal method, however, it has the problem of mode mixing. Quaternion singular spectrum analysis (QSSA) is an effective multi-channel signal denoising method with three defects. It needs huge calculation time, the contribution of irrelevant components exists in selected singular values, and the obtained denoising signal derives from certain single-channel signal. Hence, a novel multi-channel signal processing method called Lanczos quaternion singular spectrum analysis (LQSSA) is proposed in this paper. First, LQSSA uses Lanczos method during the decomposition of the proposed method, which reduces the calculation time greatly. Then, filter value factor is obtained by introducing Lagrange multiplier to suppress the contribution of the irrelevant components and improve the purity of required signal. Finally, periodic similarity is used to obtain Lanczos quaternion singular spectrum components (LQSSCs) by taking the signal components as a whole, so it breaks the restriction between different channels. The proposed method is applied to simulated signals and experimental signals of bevel gear, and the analysis results show that the proposed method can extract the fault characteristic frequency from the multi-channel signals effectively.
•Tooth flank grinding using double helical method for non-orthogonal aerospace spiral bevel gears.•Data-driven local bearing contact prediction considering three given evaluations.•Loaded contact ...pressure distribution considering time-varying meshing characteristics.•Adaptive collaborative decision model considering tooth flank geometric and local bearing contact evaluations.•Collaborative decision process by using sensitivity analysis strategy.
It is very different with the recent tooth flank grinding, an innovative collaborative optimization considering both geometric accuracy and local bearing contact evaluations is proposed for non-orthogonal aerospace spiral bevel gears. In particular, its data-driven prediction and adaptive control is developed. Firstly, tooth flank grinding using double helical method is simulated to establish mathematical model of the whole tooth flank including work flank and root fillet. Then, prediction of local bearing contact evaluations including geometric topography, loaded contact pressure and loaded contact deformation is performed by correlating with numerical loaded tooth contact analysis (NLTCA). Where, loaded contact pressure and its distribution considering time-varying meshing characteristics are developed, respectively. Moreover, an adaptive collaborative control model is established by extending the conventional machine tool settings modification only considering geometric accuracy to case that collaborative optimization. In the normal direction, loaded contact deformation of material removal point is predicated in the geometric accuracy control. In tooth flank tangential plane, the material removal points are constrained within the prescribed boundary. Finally, the sensitivity analysis strategy is used to select the optimal design variables, and control mode is solved for accurate machine tool settings. The given numerical instances can verify the proposed method.
The paper presents a novel method for evaluation of assembly of spiral bevel gears. The examination of the approaches to the problem of gear control diagnostics without disassembly has revealed that ...residual processes in the form of vibrations (or noise) are currently the most suitable to this end. According to the literature, contact pattern is a complex parameter for describing gear position. Therefore, the task is to determine the correlation between contact pattern and gear vibrations. Although the vibration signal contains a great deal of information, it also has a complex spectral structure and contains interferences. For this reason, the proposed method has three variants which determine the effect of preliminary processing of the signal on the results. In Variant 2, stage 1, the vibration signal is subjected to multichannel denoising using a wavelet transform (WT), and in Variant 3 – to a combination of WT and principal component analysis (PCA). This denoising procedure does not occur in Variant 1. Next, we determine the features of the vibration signal in order to focus on information which is crucial regarding the objective of the study. Given the lack of unequivocal premises enabling selection of optimum features, we calculate twenty features, rank them and finally select the appropriate ones using an algorithm. Diagnostic rules were created using artificial neural networks. We investigated the suitability of three network types: multilayer perceptron (MLP), radial basis function (RBF) and support vector machine (SVM).
•A new method for evaluation of spiral bevel gear assembly is proposed.•A parameter describing correctness of spiral bevel gear assembly is determined.•A vibration signal processing method ensuring higher diagnostic accuracy is proposed.•The suitability of applying the MLP, RBF, SVM neural networks is verified.
Display omitted
•Proposes an analytical dynamic model of face-milling for spiral bevel gear.•Investigates the un-deformed chip geometry and static cutting force for spiral bevel gear.•Discusses the ...dynamic equation and semi-discretization method for chatter stability analysis.•Validates the proposed model through the simulation and experiment.
For an efficient and precise machining of spiral gear, the special face-milling process for spiral bevel gear is developed and widely used, exhibiting great difference from the general milling process in cutting machine, cutter and cutting kinematics. The un-deformed chip geometry, cutting force model and regenerating mechanism are hence complexly different, bringing great challenge to the modeling of cutting dynamics. In this regard, no relevant work can be found at present.
To overcome this problem, through fully investigating the cutting force regenerating mechanism under complicated cutting kinematics, this paper first develops an analytical cutting force prediction model by classifying the chip geometry into 6 cases, and then a simplified dynamic chip model by assuming the chip geometry cases unchanged and ignoring edge alteration.
On such basis, the model for prediction of the cutting dynamics and the chatter stability are developed and validated. Besides, the 3D stability lobe for face-milling of spiral bevel gear is presented and the cutting system tends to be stable with high cutter gear ratio and cutting speed.
•Carburizing-meshing coupling effect in loaded contact pattern area of aerospace spiral bevel gears.•Data-driven prediction of tooth flank heat treatment deformation considering coupling ...effect.•Adaptive tooth flank heat treatment deformation optimization model.•Sensitivity analysis strategy-based adaptive data-drive optimization of tooth flank heat treatment deformation.
In the current tooth flank manufacturing of aerospace spiral bevel gears, accurate prediction and optimization of heat treatment deformation is of paramount significance to high accuracy improvement. In particular, the loaded elastic contact mechanical variation can directly affect tooth flank heat treatment geometric topography in micro-scale. An innovative adaptive data-driven prediction and optimization of tooth flank heat treatment deformation for spiral bevel gears by considering carburizing-meshing coupling effect is proposed in this work. At first, numerical loaded tooth contact analysis (NLTCA) based on data-driven tooth flank finite element modeling is integrated into tooth flank carburizing to get an accurate data-driven determination of carburizing-meshing coupling effect. Then, machine settings are used as the basic data to perform the data-driven tooth flank deformation prediction. The recent machine tool settings modification is extended to the case that the loaded contact deformation is predicted as the important tooth flank geometric accuracy. Finally, an adaptive data-driven optimization of tooth flank heat treatment deformation considering carburizing-meshing coupling effect is proposed for a high-accuracy tooth flank manufacturing. The given numerical instance can verify the proposed method.
Windage effects becomes prevailing in high speed areo-engine applications. The present paper is to provide some theoretical findings to predict the windage power loss for spiral bevel gears. Firstly, ...a quasi-analytical model detailing the flow pattern surrounding the spiral bevel gear including the toe, heel and gear teeth. Then, the developed physical model achieves good results in comparison with sets of experimental findings and the quasi-analytical formulas applied to predict windage power loss for spiral bevel gears under high-speed condition are set up. Finally, the influence of the specific role, such as pitch cone angle and spiral angle, on the windage power losses of the bevel gear is examined by calculating the theoretical model.
•A quasi-analytical model is developed for predicting the windage power losses of a spiral bevel gear.•The developed physical model achieves good results in comparison with sets of experimental evidence.•Influence of reference cone angle and spiral angle on the windage power losses of the gear is examined.
Finishing of bevel gears is an important requirement in many machining shop floors. Variants of abrasive flow machining (AFM) could be plausible solutions for finishing such parts with intricate ...geometries. In the present work, a relatively new variant of AFM called ultrasonically assisted abrasive flow machining (UAAFM) technique was employed to finish bevel gears made of EN8 steel. An analysis of the process has been presented with suitable illustrations. A finite element simulation of the behavior of the medium during finishing of bevel gears using the UAAFM process has been presented. A 3D model was constructed to simulate the flow of medium through the outer wall of the gear tooth surface using computational fluid dynamics (CFD) approach. The velocity, pressure and temperature values along the length of the workpiece were computed for both UAAFM and the conventional AFM processes. Further, the effectiveness of the process was investigated through experimental trials by conducting a comparison study between classical AFM and UAAFM. Ultrasonic frequency, extrusion pressure, processing time and the media flow rate were considered as the input variables while improvements in surface finish and material removal were considered as the monitored outputs. Results confirm that improvements in surface roughness and material removal are significantly higher than those obtained with conventional abrasive flow machining. The study further reveals that, the applied high frequency (ultrasonic) vibration to the workpiece has the maximum influence on the process responses among the variables considered.
•Analysis of a new variant of abrasive flow machining (AFM) has been presented.•Finite element simulation of media flow behavior in UAAFM is presented.•Mechanism of workpiece-abrasive interaction in the UAAFM has been explained.•Application of the UAAFM process in finishing bevel gear has been demonstrated.
PDF
