Spiral Bevel Gears: nonlinear dynamic model based on accurate static stiffness evaluation

Molaie, Moslem; Samani, Farhad S.; Zippo, Antonio; Pellicano, Francesco

doi:10.1016/j.jsv.2022.117395

Cited by 14 publications

(8 citation statements)

References 31 publications

(33 reference statements)

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“…Typically, in gearboxes the driven shaft is connected to big inertial masses; therefore, 𝜃 𝑙 can be neglected in Eqs. ( 16)- (19). The four-DOF system is then reduced to a three-DOF system as represented in Eqs.…”

Section: System With Three-dofmentioning

confidence: 99%

“…Following Refs. [12], [16]- [19], we can introduce the parameter 𝜆 of Eq. ( 11) and the following parameters:…”

Section: System With Single Dofmentioning

confidence: 99%

“…FEM is well-established for providing affordable and reliable results within a reasonable time. More specifically, nonlinear FEM has become increasingly popular thanks to the possibility of including contact nonlinearities throughout the analysis [18], [19], [24], [25].…”

Section: Mesh Stiffness Calculationmentioning

confidence: 99%

See 2 more Smart Citations

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

Molaie,

Samani,

Zippo

et al. 2023

Chaos, Solitons & Fractals

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Section: System With Three-dofmentioning

confidence: 99%

“…Following Refs. [12], [16]- [19], we can introduce the parameter 𝜆 of Eq. ( 11) and the following parameters:…”

Section: System With Single Dofmentioning

confidence: 99%

See 1 more Smart Citation

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

Molaie,

Samani,

Zippo

et al. 2023

Chaos, Solitons & Fractals

Self Cite

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“…This clearance introduces a piecewise characteristic in the system which is modelled by a continuous function of class C 0 , as typically happens in engineering applications (e.g. see [6,8,9,26,42,43,45,50,60]). Systems with similar properties fall in the category of the piecewise-smooth continuous systems for which the Picard-Lindelöf Theorem guarantees the uniqueness and existence of the solution in the whole domain.…”

Section: Introductionmentioning

confidence: 99%

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

2023

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In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

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“…Ambarisha et al 27 used mathematical modeling and finite element to simulate the planetary gear system's nonlinear dynamic behavior and to demonstrate the efficacy of mathematical model construction. Molaie et al 28 established the dynamic model of a single pair of bevel gears based on the static stiffness, and the nonlinear phenomenon with back contact and damping is analyzed. The meshing stiffness of the gear is coupled with its own motion to obtain a stiffness calculation model under multiple working conditions in Song's work.…”

Section: Introductionmentioning

confidence: 99%

Study on nonlinear vibration and primary resonance characteristics of helicopter face gear-planetary gear coupling transmission system

Huang

Liu

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part K:

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In order to explore the dynamic response and primary resonance characteristics of the gear transmission system of the helicopter main reducer. The face gear-planetary gear torsion-translation vibration dynamics model is established, and the time-varying meshing stiffness, gear backlashes, gear eccentricity error, and friction are considered. The four-order variable-step Runge–Kutta was used to solve the dynamic response of the system, and the nonlinear dynamic characteristics of the system were described by time domain diagram, phase trajectory plane, Poincaré map, 3D frequency spectrum, and bifurcation diagram. Additionally, using the face gear-spur gear system's transmission as an example, the multi-scale method is used to analyze the face gear-spur gear system's primary resonance characteristics. The influence of load fluctuation amplitude, meshing damping, and meshing stiffness on its amplitude-frequency characteristics is also investigated. It is found that when external load excitation frequency changes, the vibration response of the whole system changes synchronously, which exhibits periodic, multi-periodic, and chaotic motion. In addition, according to the primary resonance analysis, the system's stability will be harmed by increasing the external load fluctuations’ amplitude, lowering the meshing damping, and raising the meshing stiffness.

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Spiral Bevel Gears: nonlinear dynamic model based on accurate static stiffness evaluation

Cited by 14 publications

References 31 publications

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

Study on nonlinear vibration and primary resonance characteristics of helicopter face gear-planetary gear coupling transmission system

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