2D nonlinear and non-Hertzian gear teeth deflection model for static transmission error calculation

Bruzzone, Fabio; Maggi, Tommaso; Marcellini, Claudio; Rosso, Carlo

doi:10.1016/j.mechmachtheory.2021.104471

Cited by 15 publications

(11 citation statements)

References 33 publications

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“…As detailed in [50] during engagement the elastic deformation of the meshing teeth pairs causes a relative sliding between the contacting flanks causing a subsequent shift of the contact point where the load should be applied. Since the contact point changes, the stiffness of the engaged pair changes thus also altering the load sharing characteristics.…”

Section: Nonlinear Algorithmmentioning

confidence: 99%

“…where s = p, g. To solve the problem stated in Equation ( 15) and satisfy all the conditions a two nested sub-iterative processes are needed, as detailed in [50,58] to remove the residual traction stresses and to obtain the correct total transmitted force based on the computed force at the k th iteration f k and the value at the previous one f k−1 . The first one is used to identify the correct contact footprint devoid of tension forces given a certain initial indentation h 0 , while the second is used to estimate the correct indentation to impose to the profiles so that the resulting transmitted force is within tolerance of the applied load.…”

Section: Non-hertzian Contact Modelmentioning

confidence: 99%

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Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

et al. 2021

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In this paper, a three-dimensional model for the estimation of the deflections, load sharing attributes, and contact conditions will be presented for pairs of meshing teeth in a spur gear transmission. A nonlinear iterative approach based on a semi-analytical formulation for the deformation of the teeth under load will be employed to accurately determine the point of application of the load, its intensity, and the number of contacting pairs without a priori assumptions. At the end of this iterative cycle the obtained deflected shapes are then employed to compute the pressure distributions through a contact mechanics model with non-Hertzian features and a technique capable of obtaining correct results even at the free edges of the finite length contacting bodies. This approach is then applied to a test case with excellent agreement with its finite element counterpart. Finally, several results are shown to highlight the influence on the quasi-static behavior of spur gears of different kinds and amounts of flank and face-width profile modifications.

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Section: Nonlinear Algorithmmentioning

confidence: 99%

Section: Non-hertzian Contact Modelmentioning

confidence: 99%

Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

et al. 2021

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“…Mechanical contact problems arise naturally in countless industrial and scientific applications. Classical examples include the study of the deformation and stress in gear teeth [1–3], ball bearings and ball joints [4], impact absorbers [5], propagation of stress waves in colliding solids [6], and models of granular materials [7]. Contact problems also frequently arise in problems relating to material characterization, where a localized indenter is used to infer properties of solid substrates [8].…”

Section: Introductionmentioning

confidence: 99%

Impact of a rigid sphere onto an elastic membrane

Alventosa

Harris

et al. 2022

Proc. R. Soc. A.

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We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion of the sphere and the membrane during contact. The free-boundary problem of finding the contact surface, over which forces caused by the collision act, is solved by an iterative method. This results in a model that produces detailed predictions of the trajectory of the sphere, the deflection of the membrane, and the pressure distribution during contact. Our model predictions are validated against our direct experimental measurements. Moreover, we identify new phenomena regarding the behaviour of the coefficient of restitution for low impact velocities, the possibility of multiple contacts during a single rebound, and energy recovery on subsequent bounces. Insight obtained from this model problem in contact mechanics can inform ongoing efforts towards the development of predictive models for contact problems that arise naturally in multiple engineering applications.

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“…Pleguezuelos et al [13] presented a simple analytical model for the transmission error for spur gears with profile modification under non-nominal load conditions. Bruzzone et al [14] established a bi-dimensional approach under quasi-static conditions to model the deflection and the load sharing characteristics of spur gears, and investigated the effects of different profile modifications on the static transmission error. Lee et al [15] establish a robust algorithm to analyze the influence of system uncertainties on the transmission error of a spur gear pair.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling and analysis of elastic isolation damping gears

Jiang¹,

Liu²

2022

J. vibroeng.

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Transmission error is the main excitation source of gear vibration and noise, how to reduce the transmission error has always been the focus of the research on gear dynamics. In this study, a new type of cylindrical spur gear with elastic isolation is developed for the reduction of transmission error. The elastic isolation damping gear includes three parts: the gear body, the elastic isolation layer, and the involute profile body. Dynamic models are established with the elastic isolation damping gear using lumped parameter method. Dynamic characteristics are simulated via spur gear pair examples by the Runge-Kutta algorithm. By comparing the simulation results of three gear models, the dynamic response of the elastic isolation damping gear with sliding friction is illustrated. The influence of different parameters of the elastic isolation layer on the dynamic response for the elastic isolation damping gear model is carried out. The results indicate that the proposed elastic isolation damping gear model is effective in reducing dynamic transmission error, especially for torque fluctuation, high-speed and heavy-duty conditions. Parameter influence analysis guides the design of elastic isolation damping gears with low transmission error.

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2D nonlinear and non-Hertzian gear teeth deflection model for static transmission error calculation

Cited by 15 publications

References 33 publications

Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

Gear Teeth Deflection Model for Spur Gears: Proposal of a 3D Nonlinear and Non-Hertzian Approach

Impact of a rigid sphere onto an elastic membrane

Dynamic modeling and analysis of elastic isolation damping gears

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