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Mechanical Vibrations of the Gear Teeth

mohamedlamine's picture

Recent research work available on request.

 

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mohamedlamine's picture

You will find below the formulations of the related work:

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Université des Sciences et de la Technologie Houari-Boumediene (USTHB)

Faculté de Génie Mécanique et Génie de Procédés (FGM&GP)

Département de Construction Mécanique et Productique (CMP)

 

Mechanical Vibrations of the Gear Teeth

 

Introduction :

 

The aim of the present work is to study the dynamic behaviour of a gear teeth in the two-dimensional plane under the effect of excitation loads.

The equations of motion obtained by Lagrange's equations are developed for a  unitary volume. The displacements  and  are the unknowns of the problem.

The discretisation of the set of the governing partial differential equations is carried out by the forward time centered space (FTCS) scheme. The resulting equations will be then solved by the finite difference method on the domain. A spatial discretisation with  and  is established. The discretisation in time is also done. This process lead to a multigrid scheme giving a set of algebraic equations which define the dynamic behaviour of the vibrating teeth.

 

Formulations :

 

The total potential energy of the domain is   and the kinetic energy is   where is the strain energy and  is the work of external loads.

For an elementary volume :   

where are the strains in linear elasticity and

 is the matrix of  material properties for isotopic plane stress case.

 

We define + where  ρ  is the mass density of material point and k is the stiffness spring.

 

The applied Lagrange's equations are :

 

 

 and are all non-potential loads except of dissipative loads.

 

 

 

 

 

 

The obtained equations of motion are :

 

 

where  , ,  ,  elastic modulus and

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