Spiral Bevel Gears Research Articles

Transmission Efficiency Optimal Design of Spiral Bevel Gear Based on Hybrid PSOGSA (Particle Swarm Optimization—Gravitational Search Algorithm) Method

Transmission efficiency is a significant index of the transmission system. Even though much research has been carried out to calculate gear transmission efficiency, only a few of them studied spiral bevel gear due to its complexity. Moreover, spiral bevel gear does not have a “standard surface”, which means more complex coupling relations between different parameters and makes efficiency optimal design more difficult. Therefore, an instantaneous transmission efficiency computing model of a spiral bevel gear was set up based on loaded tooth contact analysis and hybrid elasto-hydrodynamic lubrication theory. Then, the particle swarm optimization–gravitational search algorithm (PSOGSA) optimal model was constructed to obtain the best parameters that maximize the average transmission efficiency of spiral bevel gears. Control parameters and machining parameters are optimized in sequence based on the proposed optimal model. The results showed that both optimal designs could help improve transmission efficiency, but the range of machining parameters is limited in a small interval because of the complex coupling relations. Therefore, the machining parameters optimization are conducted after control parameters optimization, which showed good results. Transmission efficiency was finally improved to 98.78%, which increased more than 4% at least. The proposed optimal model could also be applied into other gear design methods or even other fields.

Dynamic Induction Heating Temperature Field Analysis of Spiral Bevel Gears

Combining tooth surface induction heating and shot peening is an efficient method to improve tooth surface performance. Reasonable designs of the induction coil structure and parameters are essential for achieving uniform and efficient tooth surface heating. In this work, to precisely control the tooth surface temperature field and improve the heat uniformity across the tooth surface, a transverse coil (TC) and a longitudinal coil (LC) were designed, and the gear was set to rotate at a constant speed of 20 r/min, dividing the tooth surface is into a shot-peening area and heating area. Further, dynamic numerical simulations were performed using COMSOL Multiphysics in combination with the uniform rotation of gears to investigate the effect of the coil structure on the temperature field of the outer surface of gears. The results of the analyses combining the effects of different electrical parameters revealed that the gear surface temperature under LC heating was more uniformly distributed in the axial and circumferential directions, the tooth surface temperature fluctuations were smaller, the temperature difference between the root and top of the tooth was smaller, an coil heating was more efficient. Thus, the LC was deemed suitable for use as the spiral bevel gear induction heating coil. Finally, heating experiments were conducted using the LC to validate the simulation model. The results show that the use of LC heating can achieve the research goals of uniform temperature field distribution on the tooth surface and efficient temperature rise, providing the prerequisite for shot peening.

A standardizable approach for Tooth Flank Fracture

Ultrasonic scanning of large spiral bevel gears and the subsequent fracture analyses of early-stage tooth flank fractures imply a mode II crack initiation under surface-parallel, orthogonal shear stresses. An iteration of the Dang Van criterion is presented that focuses exclusively on surface-parallel material planes, yielding a standardizable approach for the study of tooth flank fracture in spiral bevel gears. It is shown that Dang Van’s shear stress amplitude and maximum hydrostatic stress along a surface-perpendicular path can adequately be described by the Hertzian orthogonal shear stress amplitude and Lang’s compressive residual stress. The fatigue properties along the same path are estimated from Thomas’ hardness model and augmented by ISO-inspired lifetime, size and conversion factors. The article closes with a comparison between the commonly used Witzig-Boiadjiev, Hertter-Wirth, DNV subsurface fatigue and the herein proposed, rationalized Dang Van criterion.

Optimal tool path generation and cutter geometry design for five-axis CNC flank milling of spiral bevel gears

Abstract Computer numerical control milling provides greater flexibility and universality for machining complex gears compared to dedicated gear manufacturing. A critical challenge in popularizing the use of five-axis flank milling to spiral bevel gears is to achieve acceptable machining accuracy that ensures the meshing performance of the finished gears. Previous studies, which used approaches such as gear design modification, using multiple tool paths, and end milling, failed to resolve this issue. Thus, this paper proposes a computational scheme to improve the machining accuracy of five-axis flank milling of spiral bevel gears by optimizing the tool path and cutter geometry. The scheme minimizes the geometric deviations between the machined surface and original design using heuristics and optimization algorithms. A simplified tooth contact analysis method was developed to quantitatively evaluate the contact path of the meshing gears. The simulation results of real gears show that the proposed scheme outperforms previous methods in reducing machining errors and further enhance the meshing performance by optimizing the design of form cutters. This work developed an effective approach for flexible and low-cost manufacturing of complex gears.

Correction to: Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD‑based model

Correction to: Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD‑based model

Research on Nonlinear Dynamic Characteristics of Spiral Bevel Gear with Time-Varying Thermal Deformation and Time-Varying Friction

Research on Nonlinear Dynamic Characteristics of Spiral Bevel Gear with Time-Varying Thermal Deformation and Time-Varying Friction

An investigation into the impact of grinding residual stress on the meshing stress of spiral bevel gear

An investigation into the impact of grinding residual stress on the meshing stress of spiral bevel gear

Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD-based model

Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD-based model

Modal Analysis of Aeronautic Spiral Bevel Gear in the Temperature Field

The temperature of the bevel gear tooth surface will increase greatly because of its special structure. Modal is the characteristic of reaction structure. In order to design and manufacture higher quality aerial bevel gears, it is necessary to study the modal of aerial bevel gears under the action of the temperature field. Firstly, a temperature field calculation model is established according to heat transfer theory. Then, based on the traditional linear modal theory, the modal analysis model under the influence of temperature was established considering the influence of rotational speed and temperature field on the stiffness. Based on the model, modal analysis of the driven gear of a certain aviation bevel gear is carried out. It can be seen from the analysis results that the speed has a great influence on the gear stiffness, and the positive and negative effects are related to the direction of the centrifugal force. Secondly, the inhomogeneity of temperature field distribution also affects the natural frequency and then the gear stiffness. When the speed field and temperature field work together, the pitch shape changes the most, so it is necessary to consider temperature as an influencing factor in the design of aerial bevel gears.

Analysis on wear patterns and mechanisms of carbide tool for face-hobbing of spiral bevel gear

Spiral bevel gear is widely used in the automotive and aerospace manufacturing industries, and the machining process is complex and the material is difficult to cut. The characteristics of high hardness, strong chemical reactivity and poor heat dissipation make the machinability of 20CrMnTi poor for face-hobbing machining of spiral bevel gear. In the process of cutting, there are some problems such as severe tool wear, poor machining quality and low machining efficiency caused by higher cutting force and higher cutting temperature. Therefore, it is necessary to study and analyze the wear experiment of the cutting tools of spiral bevel gear for face-hobbing deeply. Firstly, under the single factor experimental conditions, the wear patterns of inside blade and outside blade are observed and analyzed at different rotational speeds, and the tool wear conditions are detected and measured analysis. Secondly, the tool wear morphology and element distribution of rake face and flank face of inside blade and outside blade are analyzed by scanning electron microscope and energy spectrometer, and the tool wear mechanism for face-hobbing of spiral bevel gear is discussed in depth. The results demonstrate that chipping and fracture are the main patterns of tool wear; the tool wear mechanism are mainly embodied in adhesive wear, diffusion wear and oxidation wear. The tool wear is mainly distributed on the main cutting edge, top edge and corner radius, and the top edge and corner radius are more seriously worn. The research results can provide an effective basis for exploring the tool wear mechanism and improving the tool life, and provide technical support for the design and development of gear machining tools.

Mathematical Modeling and Machining of the Internal Double-Arc Spiral Bevel Gear by Finger Milling Cutters for the Nutation Drive Mechanism

A method of machining the internal double-arc spiral bevel gear with a finger milling cutter was presented. The mathematical model of the internal spiral bevel gear tooth profile was established considering the principle of machining a spiral bevel gear by the generating method, and a three-dimensional (3D) tooth profile graph was developed. Subsequently, by applying the gear meshing theory, the 3D model of the tooth alignment curve for the finger milling cutter was established. Based on the tooth surface equation of crown gear, the cutter intercept equation was derived. The cutter was divided into four finger milling cutters considering the design difficulty of the cutter, which is used to manufacture different arc segments of the double-arc tooth profile, respectively. The special machining tool model of the internal spiral bevel gear was further developed by using SolidCam, and the simulation experiment was carried out. The simulated gear model was compared with the theoretical gear model and the error of the simulation experiment was estimated. Actual machining on the machine tool and the internal spiral bevel gear were inspected. The maximum error is 0.035 mm, and the minimum error is 0.005 mm. The machining accuracy meets the requirements. The feasibility of machining the internal double-arc spiral bevel gear with a finger milling cutter was verified.

Loaded and unloaded tooth contact analysis of spiral bevel gears in consideration of misalignments

Bevel gear pairs are employed extensively in transmission systems, such as vehicle transmissions (rear axle drive), aircraft engines/turbines and helicopter gears, to transfer power between non-parallel shafts at high speed or high torque. The most complex form of bevel gear is the spiral bevel gear (SBG). SBG pairs are commonly used in applications that require high load capacity at higher operating speeds than are typically possible with other types of bevel gear. When manufactured in a metal-cutting process, spiral bevel gears can either be produced using single indexing (a face-milling method, which is considered in this study) or continuous indexing (a face-hobbing method). Due to manufacturing imperfections and the flexibility of components, the system might experience misalignments that intensify or exert a destructive effect on the gear vibration, which causes disruption in the stress distribution, thereby decreasing the lifetime of the gearbox. The main purpose of this study is to carry out loaded tooth contact analysis (LTCA) and unloaded tooth contact analysis (UTCA) for an SBG pair in the presence of two types of misalignment, axial and radial misalignment, and represent their effects on the mesh stiffness (MS). To calculate the MS, it is essential to determine the geometrical mismatch between two mating tooth profiles by means of UTCA. To conduct LTCA, three main approaches can be utilised: the finite element method (FEM) and experimental and analytical approaches. Due to the development of software packages during the last decade, Transmission3D-Calyx, an FEM-based software, is used in this study to carry out LTCA and UTCA. Finally, the MS for different misalignment cases is compared to represent the effect of misalignment on the SBG pair.

Data-driven bending fatigue life forecasting and optimization via grinding Top-Rem tool parameters for spiral bevel gears

To establish a bridge between grinding tool parameters and loaded tooth fatigue life, an innovative data-driven root flank bending fatigue life forecasting and optimization via Top-Rem tool parameters was proposed for grinding spiral bevel gears. The recent machine settings modification is extended into grinding Top-Rem tool parameters modification in case that geometric accuracy and root bending fatigue life are integrated into a collaborative optimization. The proposed Top-Rem modification includes three key steps: (I) arc-shaped blade, (II) top part, and (III) top fillet part. Then, while root bending stress is determined by using finite element method (FEM)-based simulated loaded tooth contact analysis (SLTCA), data-driven fatigue life forecasting is developed by correlating with the multiaxial fatigue damage model based assessment. Moreover, data-driven bending fatigue life optimization model is established by using Top-Rem tool parameters modification, where the important constraints in target flank determination includes: (i) root overcutting, (ii) geometric accuracy, and, (iii) fatigue life. For high accuracy and efficiency, two different strategies are proposed: (i) the different parameters modification types; and, (ii) sensitivity analysis of grinding Top-Rem tool parameters. Finally, proposed method can verify that bending fatigue life can be significantly improved by modifying the key Top-Rem tool parameters in early stage of the whole life product development for spiral bevel gears.

Reverse-adjustment algorithm of tooth surface precision control design for spiral bevel gears

As aerospace requirements for low noise and high strength spiral bevel gear transmission continue to increase, tooth surface precise control is becoming increasingly important in design and manufacture. The previous design depended significantly on ease off the tooth surface and using the tooth surface optimization approach. It’s a parameter design technique that goes from the design tooth surface to the target tooth surface without accounting for the reaction of the tooth surface to machine tool machining errors. This study proposes a new algorithm for reverse adjustment of tooth face accuracy control. A mathematical model of the tooth face is initially built using the local synthesis method to replicate the genuine machining process. Second, the machine setup settings are chosen as multi-objective optimization parameters, and the reverse adjustment model is constructed to investigate the machine’s machining error on the tooth surface, as well as the reverse adjustment model’s effects on contact and robustness characteristics. Finally, numerical calculations and comparisons with the findings of existing design approaches are used to verify the validity and effectiveness of the reverse adjustment algorithm in the design of tooth surface accuracy control of curved bevel gears.

Optimization of high-efficiency tooth surface accuracy of spiral bevel gears considering machine-tool motion errors

With the continuous improvement of the requirements of spiral bevel gear transmission for low noise and high precision, the optimization of high-efficiency tooth surface accuracy considering the motion axis error of machining machine tool has become a key point in the process of designing and manufacturing spiral bevel gear. Based on the theory of the multi-body dynamics system and the principle of gear meshing, a new tooth surface error model of spiral bevel gear considering the error of machine-tool moving axis is proposed and optimized, so as to obtain higher tooth surface accuracy and meshing efficiency. Firstly, according to the motion and machining principle of spiral bevel gear NC grinding machine, the corresponding relationship between the motion error of each axis of the NC gear grinding machine and the variation of cutting parameters of spiral bevel gear is analyzed, and the geometric motion error model of spiral bevel gear grinding machine is given; secondly, the tooth surface equation of the spiral bevel gear considering the machine-tool motion axis error is established; then, in view of Powell's dog leg optimization algorithm, the tooth surface considering the motion axis error of the machine tool is optimized, and the optimal cutting parameters of spiral bevel gear tooth surface machining are obtained. Finally, the simulation results show that the difference between the peak and peak values of transmission error and the maximum contact stress of the tooth surface is reduced by 72.6% and 1.62%, respectively, and the meshing efficiency is improved from 0.9798 to 0.9803 after optimization; by comparing the rolling experiment and simulation results, the maximum error between the quantitative parameters of the two groups of tooth surface contact marks is no more than 9%, which verifies the effectiveness and feasibility of this method, and provides a certain theoretical basis for practical production and processing.

Top-Rem grinding tool modification considering loaded edge contact for spiral bevel gears

Focusing on the collaborative manufacturing requiring meshing interface physical performances, an innovative Top-Rem grinding tool modification considering loaded edge contact is proposed for spiral bevel gears. Accurate Top-Rem grinding tool parameters can instead of machine-tool settings and their impact in the sophisticated flank topography correction technique. At first, the whole Top-Rem tool modification includes: i) arc-shaped blade part; ii) Top-Rem part; iii) top fillet part. Then, grinding tool modification model considering both loaded contact and geometric accuracy is established. Where, three important constraint conditions were taken into accounts: i) geometric boundary considering loaded edge contact, ii) root overcutting, and iii) flank geometric accuracy. Moreover, two kinds of optimization strategies are proposed to improve the accuracy and efficiency of the whole modification: i) two types of modification by the different tool modification parameters; ii) sensitivity analysis with respect to ease-off for optimization operation of the unknown variables. Finally, the given instances can verify that it can get accurate and effective loaded contact performance optimization in early stage of full life cycle product development.

Surface integrity and transmission performance of spiral bevel gears subjected to shot peening: A comparison between concave and convex surfaces

As a typical surface strengthening method, shot peening can effectively enhance the bending fatigue resistance of spiral bevel gears by improving the surface integrity parameters. Due to the complex geometry of spiral bevel gears, one group of shot-peening parameters can hardly satisfy the performance requirements of concave and convex surfaces. Thus, the effect mechanism of shot peening on both surfaces needs a thorough understanding. Meanwhile, the effect of shot peening on the transmission performance of gears is still somewhat cloudy and controversial, which confuses the optimization of shot-peening parameters. To address this issue, the effect of shot peening on the surface integrity and transmission performance of spiral bevel gears is systematically investigated by experiments. The results show that due to the smaller curvature radius, the surface integrity of the concave surface is better than that of the convex surface before and after shot peening. Specifically, for the shot-peened gears, the dislocation density at the concave surface is 9.1 % higher than that at the convex surface; the intergranular oxidation (IGO) layer for the concave surface is 2.1 % shallower than that for the convex surface; the maximum compressive residual stress for the concave surface in the profile direction is 6.9 % higher than that for the convex surface; the peak value of hardness for the concave surface is 3.5 % higher than that for the convex surface. Furthermore, smoother tooth flanks can lead to better transmission performance of gears, and shot peening has side effects on it. The transmission performance in the drive condition is better than that in the coast condition before and after shot peening.

Novel kinematic and geometric views for improving tooth contact analysis of spatial gears

AbstractTooth contact analysis (TCA) has been widely applied to evaluate the working performance of gear pairs. TCA is often formulated with five unknowns and five independent scalar equations. The solution process involves a global optimization problem with strong nonlinearity and numerical instability, especially for spatial gears with complicated tooth geometries. This study proposes novel kinematic and geometric views of gearing that reveal insights into the meshing process of spatial gears. One unknown can be removed from the position and normal equations of the TCA formulation. To solve the remaining four unknowns, a simplified optimization model with two unknowns is proposed, and the other two unknowns are obtained by using geometric iterative methods or directly from explicit expressions in some cases. A general algorithm was developed to solve the simplified TCA. The test results of both the spiral bevel and face gear drives validate the effectiveness of the proposed method.

Numerical study on mixed thermal-elastohydrodynamic lubrication of grease lubricating lubricated spiral bevel gear for heavy-duty unmanned aerial vehicle

Aiming to solve the problem of the gear lubrication of unmanned aerial vehicles (UVAs), a grease mixed Thermal-elastohydrodynamic lubrication (TEHL) model is established, and the lubrication state of the gearbox of oil-powered heavy-duty UAVs is numerically analyzed. In this study, grease is regarded as a non-Newtonian fluid whose properties change nonlinearly with respect to pressure, temperature, and other conditions. The complex meshing state of a spiral bevel gear tooth surface is analyzed using the loaded tooth contact analysis (LTCA) method, and three points on the tooth surface are selected as samples to describe the lubrication state of the entire tooth surface. The thickness of grease film and the temperature rise of the tooth surface are studied in detail, considering the natural roughness of the tooth surface and influence of different greases. The results show that the established model agrees with results from the literature. The dangerous point of tooth surface lubrication is at the meshing midpoint. Under cruise conditions, the lubricating grease viscosity significantly influences the temperature rise of the tooth surface.

Cutterhead approximation machining method of line contact spiral bevel gear pairs based on controlling topological deviations

To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, a cutterhead approximation machining method based on controlling geometric topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be machined by cutterheads. First, a mathematical model of the line contact conjugate flank was established, and the geometric topological deviations model of the comparison between the machining tooth flank and the theoretical tooth flank was obtained. Second, the deviation of each tooth flank point was calculated by the topological differential calculus analysis. Finally, with the machining tooth flank approaching the theoretical tooth flank as the modification objective, the additional cutting motions and machining compensation parameters of cutterheads were obtained to control the machining tooth flank deviations and reduce them to the allowable deviations of the theoretical tooth flank, and the cutterhead approximation machining of line contact spiral bevel gear pairs with tapered teeth depth was realized. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and the feasibility of the cutterhead approximation machining method.