SPIRAL BEVEL GEAR: THE NONLINEAR ANALYSES OF THE MESH STIFFNESS

Spiral Bevel Gears (SBG) are key components of power transmission systems, where it is required to transfer power between intersected shafts. Understanding the dynamics of the system necessitates identifying the main sources of nonlinearity and time dependency. In addition to bearings and backlash, mesh stiffness is the parameter that introduces not only nonlinearity but also time dependency into the dynamical model. The time dependency mainly stems from the number of mated teeth, and the nonlinearity arises from the Hertzian effect. The transmission system undergoes different vibration levels; consequently, the gear pairs operate under varying load conditions, influencing the dynamic behavior of the system. Indeed, the dynamic mesh torque (DMT) on the SBG-pair teeth varies due to system vibrations, even though a constant input torque is assumed. Due to the complex geometry of the SBG, many studies on the vibration of the transmission system have considered a linear function for the torque and torsional deflection curve. However, this is not an accurate assumption due to the Hertzian effect. In the present study, a thorough analysis is carried out to propose an approach for obtaining mesh stiffness at different vibration levels. The accuracy of the proposed method is validated with verified results extracted from Finite Element Analysis (FEA). Analyzing the force-deflection curve reveals two different working ranges: normal, and high torque ranges. The normal torque range is where nonlinearity plays a significant role in the mesh stiffness, while the latter working range shows less nonlinearity. A comparison is carried out to represent dynamically the difference between average mesh stiffness, where a linear function is considered, and adaptive mesh stiffness, where a smooth function is considered for the force-deflection curve.