Prediction of machining deformation and reasonable design of gear blank for split straight bevel gear

The deformation of gear blank is serious in the machining process of the split straight bevel gear,considering the material and the design of gear blank, the relationship between the change of additional stress and bending deformation of gear blank is studied, and the calculation model of the internal additional stress and additional torque during the gear cutting is established.According to the moment-area method, the calculation formula of the bending deformation of gear blank is derived, and combined with the time-varying stiffness, the mathematical model of the gear blank deformation is obtained. The theoretical calculation, finite element analysis and experimental results are highly consistent.Based on the above research, the internal relationships between the machining deformation and the geometric parameters such as the thickness, diameter and gear module of the split gear blank is analyzed, and the reasonable design of the geometric parameters of the split gear blank and the reasonable dividing law of the gear blank are explored.

Residual Stress and Deformation Analysis in Machining Split Straight Bevel Gears

In the machining of split straight bevel gears, the stiffness changes and internal stress are redistributed, which leads to serious deformation of the gear blank after machining. To rectify this problem, q finite element model is established by transforming the processing information of the gear blank into the finite element simulation calculation information, and the gear machining simulation of split straight bevel gear is carried out. Considering the material, design, and machining process of the gear blank, the characteristics and laws of internal stress variation during the gear machining are studied, and the internal mechanism and deformation law of split straight bevel gear are explored. Finally, the gear machining experiment, and the gear blank measurement are carried out. The results show that the deformation law of simulation is consistent with that of the experiment and the deformation characteristics of the split straight bevel gear are consistent with the change law of initial residual stress.

Software Application for Design of Straight Bevel Gear with Localization of Bearing Contact

Разработан программный комплекс для проектирования прямозубых конических передач с локализованным контактом. Предложена методика построения 3D-моделей активных поверхностей зубьев, обеспечивающая получение требуемой локализации контакта. Одно из колес передачи выполнено с эвольвентными прямыми зубьями. Выбор боковых поверхностей зубьев сопряженного колеса для реализации локализованного контакта осуществляется на основе решения задачи условной оптимизации. Представлен алгоритм оценки характеристик зацепления и контакта в модифицированной передаче. Целевой функцией, подлежащей минимизации, является максимальное контактное давление в период работы одной пары зубьев. Варьируемыми являются параметры синтеза, определяющие положение центра локализованного пятна контакта и его размеры. Ограничением при решении задачи выступает предотвращение кромочного контакта. Предложен итерационный эвристический алгоритм для решения задачи минимизации целевой функции. В начале работы алгоритма выбирается начальная точка. На каждой итерации с некоторым шагом рассчитываются несколько точек кандидатов для следующего начального приближения. Переход совершается в ту точку с наименьшим значением целевой функции, где отсутствует кромочный контакт. При невозможности перехода уменьшается шаг для расчета точек-кандидатов. Алгоритм завершает работу при невозможности найти подходящую точку или слишком малом шаге. Дан пример расчета.

Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.