An efficient multibody dynamic model of three-dimensional meshing contacts in helical gear-shaft system and its solution

Liu, Jiawei; Liu, Jiapeng; Shu, Xuan-Bo; Mikkola, Aki; Ren, Gexue

doi:10.1016/j.mechmachtheory.2019.103607

Cited by 24 publications

(12 citation statements)

References 45 publications

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“…Actually, only the patch pairs near the line of engagement generate contact forces. The hierarchical oriented bounding box (OBB) method 35,43 is adopted to detect the contact boundary. The key procedures include construction of the hierarchical OBB‐tree and overlap detection.…”

Section: Contact Algorithmmentioning

confidence: 99%

“…The above results obtained from the three methods are in good agreement. To provide a quality measure for the accuracy of stress, the normalized root mean square deviation (NRMSD) is introduced as the error measure 15,35 . This error measure accounts for the complete time interval of a stress curve and is normalized with respect to the range given by the FE result

$$ \mathrm{NRMSD}=\frac{\sqrt{\sum \limits_{i=1}^n{\left({\sigma}_i-{\sigma}_i^{\mathrm{FE}}\right)}^2}}{\sigma_{\mathrm{max}}^{\mathrm{FE}}-{\sigma}_{\mathrm{min}}^{\mathrm{FE}}}.

…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Using the ALE formulation, the contact states during a full gear revolution can be described by defining interface DOFs only on the current potential contact tooth‐faces. This model is also developed in helical gear‐shaft systems 35 . However, the additional computational effort of updating the modal basis matrix, stiffness matrix, and mass invariants is introduced, and the low‐frequency approximation assumption restricts the application to the working condition with high‐frequency excitation.…”

Section: Introductionmentioning

confidence: 99%

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A free‐interface component mode synthesis of moving contact multibodies and its application to gear contacts

Yao

Shu

Ren

2022

Numerical Meth Engineering

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Moving contact components are common in mechanical systems, and they exhibit a large rigid motion with linear‐elastic deflection under contact boundary conditions. The finite element method can capture local deformation and high gradient stresses, but finely meshed contact interfaces lead to numerous degrees of freedom. Model order reduction techniques for multibodies are effective, but moving contact interfaces also introduce multiple interface degrees of freedom. In the present method, the interface degrees of freedom are retained to ensure the accuracy of the local response induced by contacts, but the computational scale is not further enlarged. The motion of moving contact components is described by the floating frame of reference formulation. A free‐interface component mode synthesis method is proposed for model order reduction. Kept free‐interface normal modes represent global flexibility and residual modes accurately compensate for the local quasi‐static responses of omitted modes induced by contacts. The contribution of residual modes is represented by interface load coordinates, which can be directly evaluated by contact forces. The contacts are calculated with the present contact algorithm. The accuracy and efficiency of the proposed method are fully demonstrated through correlation with the finite element method in gear meshing simulations.

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Section: Contact Algorithmmentioning

confidence: 99%

$$ \mathrm{NRMSD}=\frac{\sqrt{\sum \limits_{i=1}^n{\left({\sigma}_i-{\sigma}_i^{\mathrm{FE}}\right)}^2}}{\sigma_{\mathrm{max}}^{\mathrm{FE}}-{\sigma}_{\mathrm{min}}^{\mathrm{FE}}}.

…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A free‐interface component mode synthesis of moving contact multibodies and its application to gear contacts

Yao

Shu

Ren

2022

Numerical Meth Engineering

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“…Slave contact points are used to find the corresponding master point (potential contact point) on the rigid body using an orthogonality condition. 6,9,10,35 The orthogonality condition states that the line connecting potential contact points is perpendicular to the tangent lines at the contact points.…”

Section: Contact Descriptionmentioning

confidence: 99%

Procedure for non-smooth contact for planar flexible beams with cone complementarity problem

Matikainen

Harish

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part K:

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Contact description plays an important role in modeling of applications involving flexible multibody dynamics. Example of such applications include contact between a belt and pulley, crash-worthiness analysis in aerospace and automotive engineering. Approaches such as the linear complementarity problem (LCP), nonlinear complementarity problem (NCP) and penalty method have been proposed for contact detection and imposition of contact constraints. Contact description within multibody dynamics, however, continues to be a challenging topic, particularly in the case of flexible bodies. This paper describes and compares the use of two contact descriptions in the framework of flexible multibody dynamics; (1) the use of nonlinear cone complementarity approach (CCP) and (2) the penalty method. Both contact models are presented together with a master-slave detection algorithm. The modified form of node-to-node approach presented facilitates creation of pseudo-nodes where gap function can be calculated. This reduces the cumbersome effort of contact search. Since large deformations can be an important phenomenon in flexible multibody applications, beam elements based on the absolute nodal coordinate formulation (ANCF) are implemented in this study. To make a comparison of two approaches, the damping component is included in the penalty method by using the continuous contact model introduced by Hunt and Crossley. Numerical results are based on the simulation of ANCF beam contact with rigid ground, rigid body with an arbitrary shape and pendulum contact. Although kinematic results show a good agreement between both approaches when the coefficient of restitution is zero, the unphysical interpenetration appears in the penalty method. Nonlinear minimization problem solved by CCP approach helps to prevent the penetration during contact event. Furthermore, the proposed contact detection algorithm is proved to be capable of being used for multiple contact between beam and arbitrary shape rigid body; different contact types, such as side-by-side and corner-by-side, can be performed without prediction.

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“…gears rotate around fixed (or moving) axes transmitting the power via meshing teeth [6]. generally, a gear train can be modelled as a flexible multibody system that, owing to the interaction of deformable bodies [7], leads to the identification of the system response.…”

mentioning

confidence: 99%

A Multibody Dynamic Model for Evaluating the Vibrating Modes of Gear Train Systems

Monteiro¹,

Vidoni²,

Concli³

2021

Int. J. TDI

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A multibody dynAmic model for evAluAting the vibrAting modes of geAr trAin systems r. P. monteiro, r. vidoni & f. concli faculty of science and technology, free university of bozen-bolzano, italy AbstrAct nowadays, the use of gearboxes in the mechanical sector has significantly increased due to the various possible applications and new materials available on the market. moving through each application, from robotics to the automotive sector, the use of gearboxes ensures high efficiency with a compact structure. generally, gearboxes are composed by gears, shafts and bearings, and each of these components can be subjected to failures. therefore, in the analysis of each mechanical component it is central to let the system operate properly. in fact, the presence of a damage can lead to a slight variation of system properties (e.g. stiffness). to design even more reliable gearboxes, it results fundamental to monitor the system's health state and the damage progress. to better understand these phenomena, a numerical study is here presented. A back-to-back gear rig (fixed-axis two-stage test rig) is used as reference. it was developed an effective multibody dynamic model that exploits a combination of two different approaches -the lumped Parameter method (lPm) and the finite element method (fem). in this work, the effect of different operative and loading conditions was studied. in particular, the effect of damages on the eigenfrequencies and on the vibrational spectra was investigated based on numerical simulations. the stiffnesses of the gear train components, used in the lPm, were estimated by means of dedicated fem simulations. the results of the lPm were validated with experimental data acquired on a real healthy back-to-back rig. moreover, the effect of a tooth root damage on the vibrational spectra was analysed. the stiffnesses of the system's components affect considerably the eigenfrequencies. As predicted by the fem simulations, in presence of damage, the stiffness of the teeth varies significantly, affecting the vibrational spectra. therefore, this work can be an effective starting point to setup a monitoring strategy of gearboxes.

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An efficient multibody dynamic model of three-dimensional meshing contacts in helical gear-shaft system and its solution

Cited by 24 publications

References 45 publications

A free‐interface component mode synthesis of moving contact multibodies and its application to gear contacts

A free‐interface component mode synthesis of moving contact multibodies and its application to gear contacts

Procedure for non-smooth contact for planar flexible beams with cone complementarity problem

A Multibody Dynamic Model for Evaluating the Vibrating Modes of Gear Train Systems

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