Proceedings of the Institution of Mechanical Engineers,Part C: Journal of Mechanical Engineering Science

In this study, a theoretical investigation on the overall loaded motion transmission error of planetary gear sets is presented. Planetary gear set load distribution model is employed to predict the input-to-output transmission error of planetary gear sets having distinct planet phasing conditions, to establish nominal transmission error behavior. Impact of carrier manufacturing errors resulting in unequal planet-to-planet load sharing on the gear set transmission error is quantified. Gear manufacturing imperfections such as run-out errors at their relative angles are introduced to observe their signatures on the resultant transmission error. Simplified formulations are presented to combine individual gear mesh transmission error functions with required modifications in order to obtain the overall transmission error. The predicted transmission error time histories are examined in the frequency domain to explore their diagnostic value in determining what errors the gear set possesses.

This paper is aimed at analysing the influence of local tooth faults such as pitting on the dynamic behaviour of planetary gears. A model of one-stage planetary gear combining lumped parameters and Timoshenko beam elements is presented, which accounts for deformable shafts and ring gears. Local tooth fault are simulated by material removal from tooth flanks, which can be positioned on the sun-gear, the planets and the ring-gear. The corresponding state equations are solved by combining a Newmark time-step integration scheme combined with a unilateral normal contact algorithm, which verifies that all contact forces on gear teeth are compressive and that no contact can occur outside the contact areas. A number of results are presented, which show the influence of tooth fault positions, depths and extents on displacement and acceleration signals. The contribution of a deformable ring-gear is analysed and the possibility to detect such localised tooth faults from vibration monitoring is discussed.

In this paper, a hybrid model is used to investigate the dynamic behavior of planetary gears. Sun-gear, planets, and ring-gear are modeled using lumped parameters elements, while planet carrier is integrated via a condensed finite element model. This approach intends to be more precise than the traditional lumped parameter models while keeping acceptable computational times. In some aeronautical applications, tooth lead modifications can be necessary to counterbalance the effect of planet carrier deflections on tooth load distribution. This study focuses on the influence of various lead modifications on the dynamic behavior of double helical planetary gears over a broad range of loads.

A complete procedure for the whining noise computation of a planetary gear set induced by the multi-mesh excitations is presented. This procedure is divided into three main steps. First, the parametrical internal excitations are simultaneously characterized by considering all contacts at the multiple gear meshes. Secondly, a finite element model of the planetary gear set is built. Finally, the coupled equations of motion are projected onto the modal basis and the stationary dynamic response is computed using an iterative spectral method.

There are several cases where it is not possible to test a gearbox in its actual size. Consequently, planetary gear stages with an actual size, that does not fit, need to be scaled. Unfortunately, scaling a gear stage in general, especially a planetary gear stage, leads to a conflict between the various gear stage properties. Therefore, it is necessary to develop a scaling process of a planetary gear stage, with the purpose of maintaining excitation similarity between the original and the scaled gearbox. Finally, the scaling process is illustrated by scaling down a wind turbine gearbox.

Tooth modification is critical when designing high-performance gear transmission systems. However, it is difficult to accurately calculate the system deformation and tooth modification amount using the traditional empirical formula. Although the finite element method provides accurate results, it is time consuming and its direct application to tooth modification for multistage geared systems is difficult. This study proposes a novel methodology to define tooth modification in both width and profile directions, which can be used for multistage spur gears. First, a housing-transmission coupled dynamic model is built, and the actual meshing state of each gear pair is obtained from dynamic simulation. Lead and profile modification are then conducted sequentially using the actual meshing state as an input. As the optimal tooth modification parameter is determined by the system dynamic response, and the tooth modification in turn influences the system dynamic response, the “dynamic simulation” and “tooth modification” are repeated iteratively until the modification parameter converges. Taking the drum driving system of a shearer as an example, the optimal tooth modification parameter is obtained after three iterations, and the dynamic factor and maximum tooth contact stress clearly decreased after applying the optimal tooth modification.

The article discusses the problem of a torque ripple on the output shaft of a cycloidal gearbox. To investigate the phenomenon, numerical simulations were performed and compared with the experimental results. Simulations were performed with multibody dynamic software—one with rigid and second with flexible elements. The dynamic model of the gearbox for the determination of the amplitude of the torque change was introduced, where the model utilizes periodical change of the stiffness of gear components as well as geometrical parameters, which are the results of machining and assembly tolerances. The test was made on a gearbox that was calculated, designed, and tested by the authors of the article. To perform the test, a test bench was built. The bench included electric motors, torque meters, and a control application.

The objective of this paper is to analyse the effect of centrifugal effects on thin-rimmed/-webbed gears. To this end, an original hybrid gear model is used, which combines lumped parameter elements, finite elements and condensed sub-structures along with a mortar-based mesh interface aiming at coupling mismatched models. It is shown that due to gear body flexibility, centrifugal effects can strongly modify geometry and, consequently, tooth load distributions at high speeds. The possibility to counterbalance these effects by introducing profile and lead modification is investigated. It is finally shown that for the effective tooth design, both thin-rimmed gear geometry and operating conditions must be accounted for.

Metaheuristic methods have proved to be suitable for solving complex multi-criteria optimization problems. In this paper, a modified particle swarm algorithm has been implemented in order to improve the quasi-static behavior of a power transmission gearbox, thus optimizing various objectives such as the maximum contact pressure on the gear flanks, the root-mean-square of the loaded transmission error signal, the tooth bending stress, and/or the pressure-speed factor. For narrow-faced spur gears, the comparison between optimal solutions found by the algorithm and the so-called master curve shows quite good agreements. The chosen form of the profile modifications, linear or quadratic, is then discussed. Finally, the robustness of the optimal solutions is tested to guarantee their efficiency against variable shaft misalignments.

Demands for higher performance have caused a need for improved component characteristics, e.g. through surface strengthening of gears and increased cleanliness of gear steels. Unfortunately, a resultant drawback is that cracks in such high-strength gears are more often initiated in the material matrix at nonmetallic inclusions and not at the surface. In standardized calculation methods, the degree of cleanliness of steels is not yet directly correlated to the tooth root load-carrying capacity. This paper considers the effects of nonmetallic inclusions in the steel matrix on the tooth root strength based on the theoretical approach of Murakami.

An environmentally friendly design of gearboxes means to increase the utilization of material steadily. This leads to in many ways optimized constructions, which require an exact prediction of occurring stresses under given load-carrying capacity to guarantee sufficient endurance. This paper shows a very precise method to calculate the occurring tooth root stress for involute, external gearings with any form of fillets within a few seconds. A two-dimensional Boundary–Element–Model is used to receive the notch stresses of the fillets which are linked to a high quality analytical tooth contact analysis to consider the exact relations of the gear meshing. The introduced model also allows a calculation of the occurring tension and compression stresses along the whole fillet for different meshing positions. This paper shows the optimization potential by using the described method in comparison to a standard approach.

Future trends indicate that the demands on bevel and hypoid gears for higher power transmission and lower weight are continuously increasing. Beside typical fatigue failures such as pitting, tooth root breakage, and tooth flank fracture, spontaneous failures such as scuffing are often observed if the load-carrying capacity of the tribological system consisting of gears and lubricant is exceeded. This paper gives an overview of the newest findings on scuffing specifically on bevel and hypoid gears and discusses the hypoid-specific decisive influence parameters. Furthermore, the newly developed calculation method as well as its verification with test results and results from field application are presented.

This paper contains data of the research project FVA 293 III by Schurer et al. and investigates the tooth root bending strength and the fatigue fracture characteristics of case-carburized and shot-peened gears of different sizes. The investigated carburized and shot-peened gears are made out of high-purity steel batches of the materials 20MnCr5 and 18CrNiMo7-6. Three different gear sizes with the normal modules m_n = 1.5, 5, and 10 mm are examined in pulsator test rigs. Additionally, gear running tests in the FZG back-to-back gear test rigs for the gear size m_n = 1.5 are performed.

This paper contains parts of the research project FVA 612 and investigates the correlation between low-temperature treatments of case-hardened gears made from the material 18CrNiMo7-6 and the resulting surface hardness, retained austenite content, and residual stress condition. These parameters were further investigated with regard to the tooth root bending strength obtained with pulsating test rigs. The tested gears were subjected to various low-temperature treatments including different temperature levels before or after tempering. Other investigated parameters were the application of a shot blasting treatment and the effect of low-temperature treatments on gears with increased retained austenite content after the carburizing process.

On universal milling machines, bevel gears can be produced with standard end mills. Due to the flexible process kinematics, there are fewer restrictions with regard to implementable component geometries compared to conventional gear-cutting processes. The quality requirements for bevel gears allow deviations of only a few micrometers. For this reason, small production-related deviations can lead to the exceedance of the permissible tolerances. Furthermore, surface integrity is decisive for the load-carrying capacity of gears. In this report, the influence of the process on the bevel gear quality and the properties of the near surface zone is analyzed.

A parametric mathematical model is presented, by which it is possible to determine the machined gear tooth surface topography cut by a pinion shaper cutter. Arbitrary internal or external helical gears designs can be considered, the gear and the shaper cutter must only share a basic rack design. The basic rack has here an elliptical fillet, as it allows fewer tool tooth numbers without the risk of undercut. The machined tooth surface is presented in three dimensions and by surface roughness parameters R z , R m , and R a . A novel method to choose cutting parameters and tool design is also presented.

For manufacturing bevel gears, special tool systems consisting of a cutterhead and carbide stick blades are used. Due to the complex relationship between the machine and process kinematics, however, an analytical analysis of the cutting process has been proven to be very difficult. For this reason, a manufacturing simulation based on planar penetration has been developed. In this paper, the algorithm is to be extended to generate processes for the first time. The concluding validation ensures that the simulated values match the actual cutting conditions. The result is a validated extension of the existing manufacturing simulation.

The tooth normal force is one of the main influencing factors for calculating the pitting load-carrying capacity of gears. In the current standards for cylindrical gears, it is calculated without regard to the friction force’s influence. This paper presents a simple local calculation approach for determining the friction force and driving direction’s influence on the tooth normal force of cylindrical gears on the whole tooth flank. Unlike previous models, without the need to set up a dynamic model of the gear mesh and having to solve differential equations numerically. For two exemplary spur and one helical gear set, the tooth normal forces are calculated considering the friction force and the driving direction’s influence and without regard to these effects. A comparison is carried out and the results are discussed thoroughly.

A comparative study of a cycloidal gearbox working with a different kind of bearings is presented in the article. Two kinds of the bearings used in the cycloidal gearbox are taken into consideration: sleeves and needle bearings. The theoretical efficiency calculation for both types of the bearing was compared with experimental results. The experiment was performed on a one-stage cycloidal gearbox designed, calculated, and manufactured during the research. The test was made under different working conditions, input speeds, and the braking torques. The results show an increase in the efficiency for the needle bearings compared to sleeves. The value of the efficiency is strictly connected with the braking torque of the gearbox as well as with the velocity. The article shows a very good correlation between calculated efficiency and the efficiency determined during the tests.

In recent years, the computational fluid dynamics method has developed into very useful tools for investigating the oil flow and the no-load losses in geared transmissions. It has neither restriction on the housing shape nor limitations on the lubrication configuration. For this work, a computational fluid dynamics method model based on the finite volume method of a single-stage, injection-lubricated gearbox was built. The influence of different parameters including the injection volume, oil viscosity, and gear speed on the oil supply and distribution were investigated. The results also include a comparison of the simulated no-load losses with empirical no-load loss equations. This work provides first results on computational fluid dynamics method investigations of injection-lubricated geared transmissions and a starting point for comprehensive validation and more complex modeling.

In order to calculate the efficiency of an automotive manual transmission, taking into consideration the effect of its most power consuming components – gears and bearings – as well as the interactions between them is of high importance. In this paper, a dynamic model has been developed which can predict the frictional losses of a complete gearbox as a system and, thus, its efficiency. The effect of temperature on bearing preload is also considered and taken into account from a system perspective identifying its effect on the bearings frictional losses (as well as the overall efficiency). The operating conditions used are snapshots of the Real Driving Emissions driving cycle, which is a standard metric for automotive manufacturers. Results show that doubling the temperature can lead to 120% increase of the bearing losses and up to 140% increase of the total transmission losses. The effect of the variation of operating conditions (velocity and torque) is also taken into account. The novelty of this paper lays in the development of a dynamic model which takes into account the performance of a complete gearbox under transient operating conditions, as well as the interaction among its main components and the ability to make changes on the influencing factors of transmission efficiency so that their effect on the complete gearbox efficiency can be tracked. This has not been yet reported in the relevant literature which mainly focuses on the influencing factors of transmission power loss and efficiency experimental measurements under various operating conditions for gear pairs instead of complete gearboxes.