Flexible three dimensional gear modelling
Keywords:
flexible mechanisms, finite rotations, nonlinear dynamicsAbstract
We present a formulation for describing flexible gear pairs in the three dimensional analysis of flexible mechanisms. The set of holonomic and no-holonomic constraint equations that defines the behavior of gears is developed. The formulation is capable of representing almost any kind of gears used in industry : spur gears, bevel gears, hypoid gears, racks, etc. All reaction forces due to gear engagement are accounted for. Teeth flexibility, clearance and mesh stiffness fluctuation are introduced in the model by relating deformation along the normal pressure line to the normal forces acting on teeth.
Downloads
References
[ACa89] A.Cardona. An Integrated Approach to Mechanism Analysis. PhD
thesis, Universite de Liege, Belgium, 1989. Collection des Publications
de la Faculte des Sciences Appliquees 127.
[ACa95] A. Cardona. Three dimensional gears modeling in multibody systems
analysis. 1995. submitted to International Journal for Numerical
Methods in Engineering.
[AKa94a] A.Kahraman. Load sharing characteristics of planetary transmissions.
Mech. Mach. Theory, 29:1151-1165, 1994.
[AKa94b] A.Kahraman. Planetary gear train dynamics. Journal of Mechanical
Design, 116:713-720, 1994.
[AKTS72] A.Kubo, K.Yamada, T.Aida, and S.Sato. Research on ultra speed
gear devices (reports 1-3). Transactions of the Japan Society of
Mechanical Engineers, 38:2692-2715, 1972.
[AM88] A. Cardona and M.Geradin. A beam finite element nonlinear theory
with finite rotations. Int. J. Num. Meth. Engng., 26:2403-2438,
[AM89] A. Cardona and M. Geradin. Time integration of the equations of
motion in mechanism analysis. Comput. €3 Structures, 33:801-820,
[AM94] A.Cardona and M.Geradin. Numerical integration of second order
differential - algebraic systems in flexible mechanism dynamics.
NATO ASI Series, 268:501-529, 1994. Computer - Aided Analysis
of Rigid and Flexible Mechanical Systems, ed. by M.F.O.Seabra
Pereira and J.A.C.Ambr6sio, Kluwer.
[AMD91] A.Cardona, M.Geradin, and D.B.Doan. Rigid and flexible joint
modeling in multibody dynamics using finite elements. Comput.
Methods Appl. Mech. Engrg., 89:395-418, 1991.
[DA89] D.Z.Xiao and A.T.Yang. Kinematics of three dimensional gearing.
Mech. Mach. Theory, 24:245-255, 1989.
[HD88a] H.N.Ozgii.ven and D.R.Houser. Dynamic analysis of high speed
gears by using loaded static transmission error. J.Sound Vibration,
:71-83, 1988.
[HD88b] H.N.Ozgii.ven and D.R.Houser. Mathematical models used in gear
dynamics- a review. J.Sound Vibration, 121:383-411, 1988.
[HN091] H.N.Ozgii.ven. A non-linear mathematical model for dynamic analysis
of spur gears including shaft and bearing dynamics. J.Sound
Vibration, 145:239-260, 1991.
[JJ80] J.E.Shigley and J.J.Uicker Jr. Theory of Machines and Mechanisms.
Me Graw-Hill, New York, 1980.
[MD86] M. Tavakoli and D.R.Houser. Optimum profile modification for the
minimization of static transmission errors of spur gears. Journal
of Mechanisms, Power, Transmissions, and Automation in Design,
Transactions of the ASME, 108:86-94, 1986.
[MG81] M.Geradin and G.Robert. Vibrations de Torsion et de Flexion d 'un
Train d'Engrenages. LTAS-Rapport VF-42, Universite de Liege,
Belgium, 1981.
[RG93] C.Rama Mohana Rao and G.Muthuveerappan. Finite element modeling
and stress analysis of helical gear teeth. Comp. €3 Struct.,
:1095-1106, 1993.
[SAM94] SAMCEF- Module d'Analyse de Mecanismes MECANO (Manuel
d 'Utilisation). 1994.
[SH93]
Flexible three dimensional gear modelling 691
O.S. Sener and H.N.Ozguven. Dynamic analysis of geared shaft
systems by using a continuous system model. J.Sound Vibration,
:539-556, 1993.
