Meshing Stiffness Analysis of Gear Using the Ishikawa Method

Shi, Jia Lian; Xiao, Gang; Xu, Changjun; Zang, Sheng Ju

doi:10.4028/www.scientific.net/amm.401-403.203

Cited by 21 publications

(16 citation statements)

References 1 publication

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“…The L j is the thickness of infinitesimal element, ω x is the load angle, and A i is the area of the infinitesimal element, S ij is the distance from the infinitesimal element to the loading points. More detailed parameters are given in the reference [17].…”

Section: ( )mentioning

confidence: 99%

The Influences of Gradual Wears and Bearing Clearance of Gear Transmission on Dynamic Responses

et al. 2019

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Gears are important components of the transmission system. Tooth wear and bearing clearance are significant factors affecting the dynamics of the gear system. In order to reveal the effects of gradual wears and bearing clearance on the gear system dynamics, a six-degrees-of-freedom bending-torsion coupled model of gear-rotor-bearing which considers surface wear, bearing clearance and backlash is established. The Rung-Kutta method is used to solve the nonlinear dynamic system, and the dynamic responses of the system are obtained. The results show that the time-varying mesh stiffness decreases with the tooth surface from the unworn phase to severe wear phase. At the same time, the change of the mesh stiffness in the double-tooth mesh area and single-tooth area are different. Moreover, the amplitude of the X-displacement, Y-displacement and relative gear mesh displacement will be enlarged slightly with the increase of wear depth or bearing clearance. By analyzing variation tendency in the frequency domain, the different order harmonics show the different change characteristic with the variation of the wear phases or bearing clearances. This study provides a theoretical basis for improving the transmission performance and the selection of the bearing clearances in the gear system.

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Section: ( )mentioning

confidence: 99%

The Influences of Gradual Wears and Bearing Clearance of Gear Transmission on Dynamic Responses

et al. 2019

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“…The normal synthetic mesh stiffness of gears can be solved using the Ishikawa equation [24]. Take the external meshing for instance, 1 and 2 denote the sun-planet mesh stiffness of the 1st stage and the 2nd stage planetary gear system, respectively.…”

Section: Sensitivity To Mesh Stiffnessmentioning

confidence: 99%

Analytical coupling characterization of multi-stage planetary gear free vibration considering flexible structure

Zhang¹,

Wei²,

Qin³

et al. 2017

J. vibroeng.

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The mode characteristics and the parameter sensitivity for a two-stage NGW spur planetary gear system are studied based on the principles of structure natural dynamical characteristics. Considering the influence of flexible structure including shaft, the planet carrier, and the ring-gear, the coupled lateral-torsional-axial vibration dynamical model of the planetary gear system is established under the generalized coordinate system using the shafting element method. With the model, the natural frequency and vibration mode are solved, and the results indicate that the flexibility of ring-gear has a greater effect on natural frequency. Several distinct types of vibration mode are summarized, such as planet torsional mode, sun-gear shaft axial mode, ring-gear axial mode and so on. However, the translational mode which is one of the modes in the coupled lateral-torsional lumped mass model is not found in this study. Within the scope of the time-varying, mesh stiffness mainly affects the planet torsional mode of corresponding stage. Furthermore, the variation of radial bearing stiffness will also do effect on axial vibration mode, and the variation of bearing stiffness not only affects the vibration modes of adjacent stage of planetary gear train, but also affects the nonadjacent stage. The results demonstrate the coupling characteristics of the system under the free vibration condition.

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“…2, a linear addendum modification of face gears could be equivalent to that of involute gears, and could be simplified as shown in Fig. 3, according to Ishikawa model [15].…”

Section: Calculation Solutions and Influence Mechanisms Of Linear Addmentioning

confidence: 99%

“…According to the reference [15], each part flexibility of Ishikawa model can be calculated, as listed in Table 1.…”

Section: Calculation Solutions and Influence Mechanisms Of Linear Addmentioning

confidence: 99%

“…The symbols , , , , and are a bending flexibility of the rectangle part, a bending flexibility of the trapezoid part, a shear flexibility, a contact flexibility, and the flexibilities induced by base rotations of teeth and rotations of wheel bodies, respectively, is a modulus of elasticity, is a Poisson ratio, and are tooth numbers, and are rim diameters, and are reference circle diameters of pinions and face gears, respectively, is a drive ratio, as well as , and ℎ , ℎ , ℎ are an acting angle and the geometry parameters of gears, which can be expressed as [15]:…”

Section: Calculation Solutions and Influence Mechanisms Of Linear Addmentioning

confidence: 99%

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Influence comparisons of two version tooth profile modifications on face gear dynamic behaviors

Li¹,

Wang²,

Zhu³

2016

J. vibroeng.

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Face gear drives in first-stage gear drives of helicopter main gearboxes occupy several strong points versus traditional spiral bevel gear drives, and are addressed by many scholars. However, face gear vibration suppressions, such as calculation solutions of face gear dynamics associated with tooth profile modifications and influences of tooth profile modifications on face gear dynamic behaviors, are not to be investigated, according to the limited published issues. Thus, in the study, influence mechanisms of two version tooth profile modifications, namely, linear addendum modifications of face gears and arcuate dedendum modifications of pinions, on face gear dynamic base parameters, such as mesh stiffness and static transmission errors, are discussed, and calculation solutions of two version tooth profile modifications are constructed. Meanwhile, an equivalent evaluation solution between linear addendum modifications of face gears and arcuate dedendum modifications of pinions is proposed, and a four degree-of-freedom dynamic model of face gear drives is established. Furthermore, dynamic behaviors of an example case of face gear drives associated with two version tooth profile modifications are simulated. The results indicate dynamic behavior crises of face gear drives would not to be caused by two version tooth profile modifications, and when two version tooth profile modifications are equivalent, the effect of linear addendum modifications of face gears on dynamic mesh force suppressions at whole frequencies is better than that caused by arcuate dedendum modifications of pinions, while, as for mesh frequency, the dynamic mesh force suppression effect caused by arcuate dedendum modifications of pinions is better, and considered dynamic mesh force suppression average values associated with two version tooth profile modifications, arcuate dedendum modifications of pinions are recommended. These contributions would improve modification developments and engineering applications of face gear drives in the future.

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Meshing Stiffness Analysis of Gear Using the Ishikawa Method

Cited by 21 publications

References 1 publication

The Influences of Gradual Wears and Bearing Clearance of Gear Transmission on Dynamic Responses

The Influences of Gradual Wears and Bearing Clearance of Gear Transmission on Dynamic Responses

Analytical coupling characterization of multi-stage planetary gear free vibration considering flexible structure

Influence comparisons of two version tooth profile modifications on face gear dynamic behaviors

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