![]() ![]() suggested a new idea of calculating the load transmission error (LTE) by considering the effect of the bearing supports. Some researchers are focused on the effect of faults on the dynamic behavior of gear pairs. Lin and Wu theoretically and experimentally showed that increasing the contact ratio has a significant effect on the vibration of helical curve-face gear pair. The two considered STEs are predesigned parabolic function and the sine function. analyzed the effect of two different STEs on the dynamic response of SBG. presented two finite element models (two-dimensional and three-dimensional) to achieve mesh stiffness (MS) and derived a simple formula for calculating MS. studied the optimization of straight bevel gear models by the Tredgold method. offered a nonlinear dynamic model for the SBG pair of a train with considering the effect of the shafts and the bearings stiffnesses. achieved a new mathematical model of elastic ring squeeze film dampers (ERSFDs) based on the Reynolds equation and presented a semi-analytical method to estimate the elastic ring deformation of ERSFDs. In their research, face width, module, and teeth number are considered as the design parameters for optimization. carried out a study on optimizing the straight bevel gear volume by means of a genetic algorithm. investigated three different algorithms to discriminate proper contact patterns from improper ones with considering different speeds. Recently, researches on SBG are mainly focused on the tooth contact analysis to obtain the static transmission error (STE) which is marked as the main source of the vibration. A method to minimize vibration of the SBG is presented with the meshing impact model by Mu et al. The vibration has affected the bending, pressure, and fatigue life of the gear systems. Durability and vibration are two main aspects in which researchers study interestingly. Spiral bevel gear (SBG) is applicable to transfer the torque between non-parallel high-speed axes. The results show that the spiral bevel gear pair may comprise chaotic response with periodic torque excitation if the bearing supports locate far enough from the gears. To scrutinize the dynamic behavior of the spiral bevel gear-pair in a nearly real situation, the input driver torque is periodically variable. The nonlinear dynamics of the spiral bevel gear pair under two different support situations is investigated in this paper. What is done in the present paper can be mentioned in three main parts: The periodic torque causes undesirable responses such as chaos and bifurcation and period-doubling responses. Moreover, while the input torque is constant, the support movement does not cause undesirable responses such as chaotic or period-doubling responses. By investigating the effect of shaft stiffness, results show that when the support is far away from gear, the vibration response increased by 67.5%. Particular vibrational behaviors such as “chaos” and “period-doubling” phenomena are illustrated with details. Vibrational phenomena are illustrated by means of bifurcation diagrams, RMS, and Poincaré maps. The equations are nonlinear due to backlash and time-varying coefficients as the results of GSOS variation. To illustrate the dynamic behavior, the governing differential equations are solved numerically according to the Runge–Kutta method. Besides, to study the effect of torque, two main types are considered: constant and periodic excitation torque. The first case is presented by locating the support close to the gear, and in the latter one, the distance between gear and support is increased. ![]() In order to investigate the effects of shaft stiffness and elastic deformation, two different cases with different support locations are considered. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. \) direction (Figure 17.13a).This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. ![]()
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