Semi-analytic contact technique in a non-linear parametric model order reduction method for gear simulations

Abstract

In this work we present a novel method for the solution of gear contact problems in flexible multibody. These problems are characterized by significant variation in the location and size of the contact area, typically requiring a high number of degrees of freedom to correctly capture deformation and stress fields. Therefore fully dynamic simulation is computationally prohibitive. To overcome these limitations, we exploit a combined analytic-numerical contact model within a Parametric Model Order Reduction (PMOR) scheme. The reduction space consists of a truncated set of eigenvectors augmented with a parameter dependent set of residual static shape vectors. Each static shape is computed by interpolating among a set of displacement modes of the interacting bodies, obtained from a series of precomputed static contact analyses. During the contact analyses, an analytic model based on the Hertz theory describes the teeth local deformation. We implement the proposed method in an in-house code and we apply it to spur and helical gears dynamic contact analyses. We compare the results with classical PMOR schemes highlighting how the combined use of the semianalytic contact model allows to decrease further the model complexity as well as the computational burden, for both static and dynamic cases. Finally, we validate the methodology by means of a comparison with experimental data found in literature, showing that the numerical method is able to capture quantitatively the static transmission error measurements in case of both helical and spur geared transmission for different torque levels.

12 Model order reduction and digital twins

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“…While the first point is important but out of the scope of this chapter, the second and third bullets highlight how available techniques that can be found in the literature [3] have been enhanced thanks to a cooperation between Siemens PLM Software and the Mechanical Engineering Department of KU Leuven (Section 12.4.2). These developments lead to a method based on MOR [102,12,16] that allows to describe in an accurate way the gear contact stiffness, including effects such as gear body deforma- tion, Hertzian nonlinear stiffness, and teeth convective couplings, while remaining extremely efficient. The reasons for the efficiency and accuracy of the method are: -Efficiency: The problem is treated quasi-statically; thanks to the MOR technique, very few degrees of freedom are retained to describe the teeth deformation.…”

A Detailed Investigation of Gear Body-Induced Tooth Deflections and Development of an Improved Analytical Solution

“…But, they did not give details how the formula was derived. Cappellini et al [22] developed a combined analytic-numerical contact In Ref. [1], gear teeth were assumed to be rigid in evaluating gear-body induced tooth deflections in their finite element model.…”

“…But, they did not give details how the formula was derived. Cappellini et al [22] developed a combined analytic-numerical contact model to simulate gear dynamics, but they did not specifically investigate gear body induced tooth deflections. Table 1.…”

An Integrated Approach to Characterize the Dynamic Behaviour of a Mechanical Chain Tensioner by Functional Tolerancing

“…2 di 11 change. Examples of such assemblies include civil, military, automotive, naval and aerospace applications [4][5][6].…”