Study on Induction Heating Characteristics of Spiral Bevel Gear Excited by Selective Laser Melting Coil

ABSTRACTA thermal elastohydrodynamic lubrication model is combined with a wear model under mixed lubrication to investigate the lubrication performance and wear characteristics of double‐circular‐arc spiral bevel gears for nutation drive. Moreover, the effects of operating conditions on the characteristic parameters of the film are analysed under the mixed lubrication point‐contact conditions. Furthermore, the characteristics of gears in terms of friction coefficient and wear depth are discussed. According to the results, the performance of lubrication and wear during the mutual meshing of the convex tooth surface of the external bevel gear and the concave tooth surface of the inner bevel gear is better than that during the mutual meshing of the other pair of tooth surfaces. The minimum film thickness of the whole meshing process occurs near the inner of the bevel gear due to the joint action of the load and the end edge effect. Moreover, an increase in torque at a certain rotational speed is favourable to the lubrication performance of the meshing process. The wear depth in the double‐circular‐arc spiral bevel gears' meshing process is heavily influenced by the roughness of the tooth surface.

In recent years, spiral bevel gears have been used in various fields. Therefore, it is one of the most important subjects in the gear field to develop gears which are effective to reduce vibration and transmission noise. However, there have been very few studies hitherto which deal with vibration and noise of spiral bevel gears, and many problems still remain to be solved. Considering the meshing characteristics of the Oerlikon-type spiral bevel gears under various running conditions in a case when the module is changed, the authors examined tooth bearing, acceleration at the gear housing and stresses at the tooth root of drive and driven gears. From this study, meshing characteristics of the Oerlikon-type spiral bevel gears (drive and driven gears) could be clarified in the case in which the module is changed.

The article contains the results of research on the automation of control of the geometric characteristics of gears. The use of coordinate measuring machines can significantly improve the productivity and accuracy of measurements. However, their use for testing gears requires the use of special programs for carrying out and processing the results of measurements of products with complex surface shapes. The use of software for metrological control of the geometric characteristics of worm and bevel gears makes it possible to achieve high accuracy of control and measurement work. To automate the control of geometric characteristics of worm and bevel gears, an additional module has been created for the standard program. With its help, all points of the measured curved surface of gears, obtained by contact method according to a standard measurement program, are structured into a single data array with a measurement protocol. Based on these data, the module generates a profile of the measured surface of a wheel tooth and builds a geometric contour of the profile of the measured tooth. The result of the module's operation is the formation of a general profile of the entire gear and its comparison with the original (theoretical) profile of the gear as a whole. The control process itself is carried out in a short time interval, which makes it possible to use the proposed approach to automating the control of gear profiles in small-scale production.

Spiral bevel gears have the advantage of transmitting high torque and power comparing to helical gear and straight bevel gear. However, they are susceptible to wear due to factors such as high loads, poor lubrication, and surface imperfections resulting from machining. In this study, we propose an autonomous model for predicting tooth wear and analyze the meshing characteristics of spiral bevel gear (SBG) pairs under different assembly errors. Concurrently, we establish a finite element model to validate the accuracy of our meshing characteristic analyses. We also compare the distribution patterns of wear depth on the tooth surface with existing literature. Our investigation delves into meshing characteristics, encompassing transmission errors and Time-varying mesh stiffness (TVMS), considering wear evolution under assembly errors. The results demonstrate that the fluctuations in TVMS remain consistent across all four types of assembly errors examined. Gear tooth wear leads to an increase in gear backlash and fluctuations in unloaded transmission error. The meshing stiffness fluctuation of the SBG pair enlarges under wear evolution. Assembly errors result in shifts in the initial contact line and contact pattern, subsequently altering the distribution of wear depth. Different forms of assembly errors may cause a similar effect on the distribution of wear depth and meshing characteristics.

High-speed heavy-load spiral bevel gears put forward high requirement for flexural strength; shot peening is a technique that greatly improves the bending fatigue strength of gears. During shot peening, a large number of fine pellets bombard the surface of the metal target material at very high speeds and let the target material undergo plastic deformation, at the same time strengthening layer is produced. Spiral bevel gear as the object of being bombarded inevitably brought the tooth surface micro-morphology changes. In this article, we aim to reveal the effect of microtopography of tooth shot peening on gear lubrication in spiral bevel gear, try to establish a reasonable description of the microscopic morphology for tooth surface by shot peening, to reveal the lubrication characteristics of spiral bevel gears after shot peening treatment based on the lubrication theory, and do comparative research on the surface lubrication characteristics of a variety of microstructures.

The spiral bevel gears of attack helicopter transmission systems are taken as an object in this paper. The numerical analysis model for starved elastohydrodynamic lubrication (SEHL) of spiral bevel gears is established on the basis of the analysis of load tooth contacts analysis and SEHL in elliptical contacts. The SEHL characteristics of spiral bevel gears are also analyzed. The results are as follows: during the course of a gear-tooth meshing cycle of the spiral bevel gear, the extremum of minimal film thickness and maximal film pressure occurs near midpoint of the path of contact, and leans to dedendum. The minimal value of the minimal film thickness is 0.39 um, and the maximal value of the maximal film pressure is 0.69 GPa. The value of minimal film thickness gradually increases with the increasing of meshing point velocity. When the velocity of meshing point exceeds 110 m/s, the increase became tardiness. As the load of meshing point increases, the value of minimal film thickness gently diminishes.

Based on the principle of the duplex spread blade method, the mathematic model of small-module spiral bevel gear has been established. The solid model and finite element model of the gear pair have been developed. The shaft-bearing-gear coupling system has been established to obtain the comprehensive errors of alignment and investigate the influence of the error on the contact characteristic of small-module spiral bevel gear under the rated condition. The results show that the position of contact patter moves from root side to top side of tooth flank considering the comprehensive errors of alignment, the top edge contact area appears, and the root bending stress and tooth contact stress increase obviously. The contact characteristic of spiral bevel gears becomes worse when comprehensive errors of alignment are considered.

Study on spatial curve meshing and its application for logarithmic spiral bevel gears

With the increasing speed of aviation spiral bevel gears, the load-independent windage power losses caused by hydrodynamic have increasingly more influence on gear transmission efficiency. Firstly, a test rig for the windage power loss of spiral bevel gear under oil-jet lubrication is established, and on this basis, a method for measuring windage torque is proposed. Next, the interactive effects of different injection lubrication parameters on the windage power loss were studied by orthogonal experiment, and the formula for calculating the windage loss was obtained by fitting the experimental data. Then, the fluid distribution, velocity field and pressure field around the gear were analysed by using a computational fluid dynamics (CFD) numerical model, and the mechanical and energy characteristics of the gear windage power loss were obtained. Finally, the dimensionless processing of the windage moment was carried out, and the variation of the dimensionless windage moment coefficient with the rotational Reynolds number is obtained. The comparison between the dimensionless windage moment coefficient of experimental data and simulation results shows that the CFD values are in good agreement with the measured data. This study provides experimental and methodological guidance for the calculation of windage power loss and windage reduction design of aviation gear pair under oil injection lubrication.

High-speed overloading puts forward very strict requirements on the bending strength of spiral bevel gears, and shot blasting is a technological process method to increase gear bending fatigue strength significantly. During the process of shot blasting, a large number of tiny pellets bombard metal target material surface at very high speed in order to let the target material form plastic deformation and form strengthened layer at the same time. As the bombarded target, the microstructure of gear surface spiral bevel gear is inevitably changed. This paper aims at revealing how the shot peened surface microstructure of the spiral bevel gear affects lubrication of gear and establishes a reasonable microstructure description model of the shot blasting surface of the spiral bevel gear, revealing the tribological characteristics of spiral bevel gears after shot blasting treatment based on the elastohydrodynamic lubrication theory. Also, comparative research is carried out on a variety of lubrication characteristics of the microstructure surface.

Contact pattern and transmission error were compared for two different methods of simulating tooth generation and power transmission characteristics of hypoid gears. One method incorporates pinion and gear tooth flanks that are generated individually as a function of the parameters of the tooth cutting machine, and the other method uses the same gear tooth flank, but a different pinion tooth flank. The reference pinion tooth flank is a virtual one generated mathematically by a computer and it is conjugate to the gear tooth flank. The latter method uses the composite error surface of mating tooth flanks in the analysis. The calculated results were also compared with measured results obtained for four hypoid gear with four different kinds of tooth contact patterns. These investigations show the validity of the latter method for simulating the performance of hypoid gears. With this method, a gear engineer can apply knowledge of cylindrical involute gears to hypoid or bevel gears in predicting their performance.

The fundamental geometrical characteristics of bevel gears have been discussed in this study. The mathematical modeling of the tooth surface geometry of bevel gears can be developed based on the basic gearing kinematics and involute geometry along with the tangent planes geometry. The parametric representations of the spherical involute and the involute spiraloid, which are the tooth surface geometry of straight bevels and spiral bevels, respectively, have been derived in this paper. This study may provide some fundamentals for computer numerical controlled manufacturing of bevel gears.

Calculation methods of load distribution ratio for spiral bevel gear

High speed and heavy load put forward demanding requirements for the bending strength of spiral bevel gear. Shot peening, as a technological method, can greatly improve the bending strength of gear. During shot peening, a large number of subtle projectiles bombard the tooth surface of spiral bevel gear at an extremely high speed, which makes the latter produce plastic deformation and strengthened layer. Serving as the bombarded target, spiral bevel gear inevitably leads to the change of tooth surfaces microstructure. This paper aims at revealing the coupling law between microstructure and lubrication characteristics and establishing a reasonable model that can describe the tooth surface microstructure of shot peened spiral bevel gear. Besides, this paper brings insight into the lubrication characteristics of shot peened spiral bevel gears. Based on the elastohydrodynamic lubrication (EHL) theory, a comparative research on tooth surface lubrication characteristics has been conducted by various microscopic morphologies in this study.

Spiral bevel gears (SBG) are the core transmission elements for realizing intersection shaft driving. Owing to the outstanding advantages of finishing efficiency and capability, electrochemicalmechanical finishing (ECMF) is used to finish the tooth surfaces of SBG for improving surface quality and accuracy.The forming ECMFmethod is put forward, the influence of processing parameters on the surface roughness is studied, and the influence of the forming ECMF method on the accuracy of SBG’s tooth profile is studied experimentally. The results indicate that the surface roughness R a is reduced from 1.6 μm to 0.05 μm. After finishing, the dimensional accuracy between teeth can be enhanced by 1∼2 grades compared with the technical specifications before finishing and the accuracy of gear teeth profile are also improved.