Tooth surface modification of double-helical gears for compensation of shaft deflections

Based on gear meshing theory, the tooth surface equation with tooth profile modification parameters is deduced, the tooth surfaces of unmodified and modified gears are constructed, the three-dimensional model of unmodified and modified double helical gear-shaft-bearing system is established and then the three-dimensional contact finite element model of double helical gear-shaft-bearing system is established and the load-bearing contact analysis of the tooth surface is carried out. The actual contact state of the tooth surfaces of double helical gears under different shaft stiffness and power transmission paths is investigated, and the influence of tooth modification parameters on the load distribution of the tooth surfaces of double helical gear pairs is studied. The results show that the tooth surface bearing the contact of the herringbone gear system has the phenomenon of partial load due to the supporting deformation, and the unmodified herringbone gear has obvious contact stress concentration. However, the phenomenon of partial load and stress concentration can be effectively improved by gear tooth modification.

Recent Progress and Prospect on Tooth Modification of Involute Cylindrical Gear

Background: Recent reviews on tooth modification of involute cylindrical gear are presented. Gear pairs are widely employed in motion and power transmission systems. Manufacturing and assembling errors of gear parts, time-varying mesh stiffness and transmission error of gear pair, usually induce vibration, noise, non-uniformly load distribution and stress concentration, resulting in earlier failure of gear. Tooth modification is regarded as one of the most popular ways to suppress vibration, reduce noise level, and improve load distribution of gear pairs. Objective: To provide an overview of recent research and patents on tooth modification method and technology. Methods: This article reviews related research and patents on tooth modification. The modification method, evaluation, optimization and machining technology are introduced. Results: Three types of modifications are compared and analyzed, and influences of each on both static and dynamic performances of gear pair are concluded. By summarizing a number of patents and research about tooth modification of cylindrical gears, the current and future development of research and patent are also discussed. Conclusion: Tooth modification is classified into tip or root relief along tooth profile, lead crown modification along tooth width and compound modification. Each could be applied in different ways. In view of design, optimization under given working condition to get optimal modification parameters is more practical. Machining technology and device for modified gear is a key to get high quality performance of geared transmission. More patents on tooth modification should be invented in future.

Tooth flank modification to reduce transmission error and mesh-in impact force in consideration of contact ratio for helical gears

In this paper, a new tooth modification method considering the contact ratio of gears and a new method for calculating the mesh-in impact force of modified helical gears are proposed. The new method for calculating the mesh-in impact force is based on tooth contact analysis and loaded tooth contact analysis. The mesh-in impact position can be calculated accurately via the new method. First, the procedures for creating the new tooth modification and the details of calculation method of the mesh-in impact force are exhibited. Second, the optimal modification of the tooth flank is achieved by solving the optimization problem. Third, a dynamic model of the gear system considering the loaded transmission error and the mesh-in impact force is used to study the dynamic characteristics. Ultimately, numerical examples are presented and the simulation results suggest that the amplitude of the loaded transmission error and the mesh-in impact force can be reduced more effectively based on the introduced new tooth modification method. And the mesh-in impact effects should not be neglected in gear dynamic analysis, regardless of whether the tooth modified or not, especially for high-speed gears.

Geometric characteristics and tooth modification for variable speed pinion–rack drive

Variable speed steering system has been used by cars of various brands, including BMW and Toyota, with the purpose of improving the stationarity and controllability of the vehicle. Until now, relevant investigations are focused on the theory and traditional application, while the geometric characteristics and tooth modification for the rack are left untouched upon, hindering the prospect of a wider application. Focusing on this, the paper synthesizes the mathematical model, geometry characteristics, and tooth modification method for the variable pinion–rack drive. The major contributions lie in the contact analysis and the modification methodology for the pinion–rack drive, which combined forms a solid foundation for the application that has never been discussed.

Reliability sensitivity analysis of tooth modification on dynamic transmission error of helical planetary gears

As one of the most influential factors leading to gear vibrations, transmission errors of the engaging gears must be controlled to achieve a desirable dynamic performance for a power transmission system. It is well known that tooth modification is an effective way to reduce the fluctuations of the transmission error of a gear pair. The challenge is determining how to establish a quantitative relationship between the tooth modification parameters and the transmission error fluctuations of a gear pair. The present study aims to reveal the sensitivity of the tooth modification parameters on the transmission error fluctuations of a helical planetary gear train in a wind turbine gearbox. For this purpose, a sophisticated parametric three-dimensional contact model that included the micro-geometries of the tooth modification is developed in the ROMAX® environment. Based on this model, a loaded tooth contact analysis is carried out to compute the meshing characteristics, such as the contact pressure and transmission error of each gear pair in the planetary gear train. With the obtained meshing characteristics, the tooth modification amounts of the engaging gears were determined using empirical formulas. These modification amounts are designated as the mean values of the samples generated by the central composite method. After repeating the loaded tooth contact analysis process for each generated sample, a quadratic polynomial function is derived using the response surface method to describe the quantitative relationship between the tooth modification parameters and the dynamic transmission error fluctuations. A large number of random samples are generated using a Monte Carlo method, and the corresponding dynamic transmission error fluctuations are determined with the aforementioned quadratic polynomial function. Based on these samples, a reliability sensitivity analysis is carried out to demonstrate the effects of the tooth modification parameters on the dynamic transmission error fluctuations of the helical planetary gear train.

Fatigue Analysis of Bearings in Planetary Gearboxes of Turbofan Engines Taking into Account Dynamic Loading

This paper presents a calculation method for assessing dynamic loading of bearings in satellites of planetary gearboxes of turbofan engines. The method is based on the analysis of a dynamic model of a planetary gearbox with lumped parameters for a planetary gear set with a fixed carrier. Simulation of the variable stiffness function of gear tooth meshing using the finite element method in a quasistatic formulation is employed for a more accurate assessment of the main source of excitation in the tooth meshing, that is the kinematic error, which includes both tooth deformations under load and technological deviations. Based on the comparison of the frequency response of the dynamic coefficient with and without tooth modification, it is established that the introduction of a modification reduces the dynamic coefficient in some modes by 2 times. The calculation results demonstrate that without taking into account the dynamic loading of the bearings, the bearing life is overestimated by about 11%. The design of a gearbox with satellite bearings on rolling bearings is considered.