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MATHEMATICAL MODEL OF A TIME AND POSITION VARIANT EXTERNAL LOAD ON A GEAR TOOTH USING THE MODIFIED TIMOSHENKO BEAM EQUATION
Author(s) -
AMIROUCHE F. M. L.,
TAJIRI G. C.,
VALCO M. J.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960630)39:12<2073::aid-nme943>3.0.co;2-3
Subject(s) - involute , spur gear , timoshenko beam theory , kinematics , cantilever , beam (structure) , structural engineering , non circular gear , gear tooth , position (finance) , involute gear , base (topology) , tooth surface , spiral bevel gear , finite element method , cycloid gear , engineering , coordinate system , physics , mathematics , mechanical engineering , geometry , mathematical analysis , classical mechanics , cycloid , finance , reducer , economics
A piece wise continuous closed‐form dynamic model of spur gear teeth meshing, using the modified Timoshenko beam equation for a stubby cantilever beam of varying cross‐sectional area, is presented. The kinematics and kinetic relationships of a shaft‐driven spur gear are used to determine the force on the involute surface of the gear tooth. A convenient set of equations, used to locate this force, is presented. The co‐ordinates of this force are given with respect to a gear fixed coordinate system, located at the base of the gear tooth. The governing equations of motion were then numerically solved, and dynamic simulations of the gear tooth response at different gear speeds were performed. This model was then compared with the empirical data from research performed at the NASA Lewis Research Center.