A dynamic model of double-mesh helical gear set was established including the torsional vibration, axial vibration and time varying mesh stiffness. The natural modes were systematically analyzed and classified into three types: rotational vibration mode, axial vibration mode and overall vibration mode. The influence of time varying mesh stiffness and the dynamic responses of the gear set were also investigated. The results showed that several natural frequencies are excited in the dynamic response and there is a frequency sensitive area which may cause large dynamic load.
This paper takes a helical gear shaft as research subject and discusses the main structural parameters to see how it would affect natural frequency sensitivity. The parametrical model of helical gear shaft is created by using software PROE3.0. The natural frequencies and vibration shapes are calculated by the modal analysis. The relationship between the structural parameters and the natural frequency sensitivity can be obtained by means of ANSYS. The result shows that the structural parameters can affect the natural frequency sensitivity. The variation in low order natural frequency is similar to that in high order natural frequency. The effect of module on the natural frequency sensitivity is more remarkable comparing with pressure angle, modification coefficient and helical angle. Selecting structural parameters reasonably may reduce vibration and noise of the helical gear shaft effectively.
In this paper, we first investigate the classification of positively homogeneous equations (φp(u )) + q(t)φp(u) = 0, u(0) = 0 = u(1), where p > 1 is fixed, φp(u) = |u| p−2 u and q ∈ L ∞ (0, 1), and then discuss the existence of solutions for non-homogeneous equations. The main method of classification is by using a generalized Prufer equationwhere sinp : R → [−1, 1] is a periodic function and cosp t = d sinp t/dt for t ∈ R.
The three-dimensional helical gear model based on the geometric parameters is created by using software called PROE3.0. The natural characteristics of helical gear are analyzed by using the finite element method. The natural frequency of the helical gear is calculated by the software ANSYS and the principal mode of vibration is discussed. There are four vibration modes, which are circular vibration, torsional vibration, radial vibration and umbrella vibration. The phenomenon of resonance of the helical gear can be avoided by choosing suitable parameters and changing the natural frequency of the helical gear.
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