Gear transmission is widely used in engineering machinery, vehicles, ships, aerospace and other fields. As one of the core components, the dynamic characteristics of the gear system directly affect the working performance and service life of the whole machine. The research on the dynamics of gear systems has achieved fruitful results in the field of gear theory. Considering time-varying mesh stiffness and backlash, AlShyyab et al. established a centralized parameter dynamic model for a second-order spur gear set, and solved for the first-order steady-state response and forced response using multi-scale harmonic balance method, discrete Fourier transform, and parameter continuation method. A multi factor bending torsion coupled nonlinear dynamic model is established for an orthogonal gear system, and the dimensionless dynamic differential equations of the system are solved using the 4-5 order variable step Runge Kutta method. The dynamic response of the hypoid gear system under dynamic excitation was analyzed, and the lateral, longitudinal, and axial vibration responses of the gearbox bearing seat and the surface vibration acceleration response of the gearbox were measured. The fully coupled vibration problem of the gear system was studied. On the basis of precise tooth surface geometry modeling, a linear dynamic model is proposed to study the dynamic behavior of hypoid gear pairs under transmission error excitation, and the influence of design parameters and operating conditions on vibration modes and responses is analyzed. Afterwards, they also established a 14 degree of freedom dynamic model considering factors such as time-varying mesh stiffness, transmission error, and backlash, clarifying that transmission error is the main excitation source of vibration. Taking into account factors such as time-varying mesh stiffness, mesh damping, and backlash, a nonlinear time-varying dynamic model of a hypoid gear system is proposed to study the effect of asymmetric mesh stiffness on the dynamic response of gear teeth on the working and non working sides. Introducing dynamic meshing stiffness and quantifying meshing through a nonlinear dynamic model of hyperbolic gears The interaction between stiffness and dynamic meshing force. This paper elaborates on the torque generated by meshing force and damping force in different meshing regions under multi tooth meshing conditions, further enriching the nonlinear system dynamics equation of hyperbolic gears. The influence of time-varying friction coefficient on dynamic meshing force and transmission error was analyzed using a 14 degree of freedom nonlinear dynamic model of hyperbolic gears under mixed elastohydrodynamic lubrication conditions.
Since the emergence of circular arc gears, they have been widely used in high-speed and heavy-duty parallel shaft transmissions, but the emergence of hard tooth involute gears has hindered their promotion process. However, the spatial meshing relationship and machining process of involute spur bevel gears and bevel bevel gears under intersecting and staggered axis conditions are complex, and the comprehensive advantages are not obvious. In order to meet the demand for large bias and excellent NVH performance interleaved shaft transmission technology in the vehicle field, Circular arc gear a hyperbolic normal circular arc gear transmission is proposed. At present, the hyperbolic normal circular arc gear is still in the theoretical development stage, and dynamic research is needed to reveal the evolution law of gear system dynamic behavior under multi-source excitation, clarify the mapping relationship between dynamic characteristics and gear geometric parameters and transmission errors, and provide a basis for subsequent parameter optimization and fault diagnosis.
During the meshing process, the inter tooth force can be decomposed into radial, axial, and tangential components, which respectively cause bending vibration, axial vibration, and torsional vibration of the gear. Consider two gears as rigid bodies, and the contact between gear teeth is represented by springs, damping elements, error elements, and clearance parameters, which respectively represent the time-varying meshing stiffness of the gear pair Establish a discrete mathematical model for gear pair meshing based on meshing damping, Circular arc gear static transmission error, and backlash. Due to time-varying mesh stiffness and static transmission errors, Circular arc gear the differential equations of gear transmission dynamics exhibit time-varying and strong nonlinearity, making it difficult to obtain exact solutions through analytical methods. Generally, the fourth-order Runge Kutta method is used for numerical solution.
Referring to the working conditions of automobiles, the small gear speed of the hyperbolic normal arc gear pair is set to 2000r/min. Based on this, the dynamic model of the gear pair is solved and calculated to obtain the vibration displacement response curve and dynamic meshing force curve of the gear pair. At the same time, the mean values of the vibration displacement response and dynamic meshing force are calculated. On the basis of dynamic models and dynamic differential equations, the effects of time-varying meshing stiffness, static transmission error, Circular arc gear and backlash on the dynamic response of hyperbolic normal circular arc gear pairs were studied separately. Among them, the backlash has the greatest impact on the vibration displacement response, followed by time-varying mesh stiffness. Although static transmission errors have little effect on the mean square value of the vibration displacement response, they significantly change the fluctuation range of the vibration displacement response; The maximum impact on dynamic meshing force is the backlash and time-varying meshing stiffness. Circular arc gear To reduce the vibration displacement response of the gear pair, the first step is to reduce the backlash within a reasonable range, and consider how to increase the stiffness and reduce the static transmission error from the perspective of structural parameters.