The dynamic model of 12-degrees-of-freedom for spur gears pair accounting for nonlinear time-varying stiffness, damping, and coefficient of friction along the path of contact obtained from experimental tests is investigated. The Newmark's integration method is used to solve the equations and obtain the dynamic responses. Elementary mass, stiffness, and damping matrices with torsional and translational coupled effects were detailed. The lens of this work is to start from a nonlinear dynamic model to evaluate the influence of dynamic effects and lubrication on meshing gears power loss for different spur gear geometries within various operating conditions. The results reveal some useful references to vibration control, dynamic design, and efficiency improvement.

Self-loosening of bolts is a problem encountered in many industrial fields, and especially in aviation. The purpose of this paper is to study the self-loosening phenomenon numerically through an assembly consisting of two plates assembled by a bolt and subjected to a transversal dynamic load. First, a 3D finite element model is developed, with contact elements and all geometrical details, including the real thread geometry with its helix angle. This leads to many degrees of freedom and long calculation time. Then a 1D simulation is made, based on a simplified model with only 4 degrees of freedom and few contact conditions. Calculation is nearly instantaneous. Both models describe the succession of sticking and slipping on contact surfaces and predict loosening of the assembly. They provide close results. The next step will be to compare their behaviour with an experimental approach, in order to validate and fit the models.

Purpose – The purpose of this paper is to study the influence of friction phenomenon generated by a disc brake on the dynamic behaviour of a one-stage spur gear. Design/methodology/approach – A theoretical model is proposed and is based on both theories of Coulomb and Dahl in order to analyse the influence of disc brake friction phenomenon on the dynamic behaviour of one-stage spur gear transmission. Findings – The influence of brake friction on the dynamic behaviour of the transmission is investigated using the proposed model and leads to observe higher vibration levels when the braking is occurring as well as the emergence of significant efforts at the gear teeth. Originality/value – A new numerical model based on the implicit numerical integration technique of Newmark coupled with Newton-Raphson method is proposed to study the influence of friction phenomenon of a disc brake on the dynamic behaviour of one-stage spur gear.

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