COBEM99

S9 Fenômenos Não-Lineares e Caóticos em Engenharia

Title:

ANALYSIS OF REGULAR AND IRREGULAR DYNAMICS OF A NON-IDEAL GEAR RATTLING PROBLEM

Summary :

THIS PAPER PRESENTS A STUDY ON THE DYNAMICS OF THE RATTLING PROBLEM IN GEAR BOXES UNDER NON-IDEAL EXCITATION. THE SUBJECT HAS BEEN ANALYZED BY A NUMBER OF AUTHORS, SUCH AS KARAGIANNIS AND PFEIFFER (1991), FOR THE IDEAL EXCITATION CASE. AN INTERESTING MODEL OF THIS SAME PROBLEM BY MOON (1992) HAS BEEN RECENTLY USED BY SOUZA AND CALDAS (1999) TO DETECT CHAOTIC BEHAVIOR. WE CONSIDER TWO SPUR GEARS WITH DIFFERENT DIAMETERS AND GAPS BETWEEN THE TEETH. SUPPOSE THE MOTION OF ONE GEAR TO BE GIVEN WHILE THE MOTION OF THE OTHER IS GOVERNED BY ITS DYNAMICS. IN THE IDEAL CASE, THE DRIVING WHEEL IS SUPPOSED TO UNDERGO A SINUSOIDAL MOTION WITH GIVEN CONSTANT AMPLITUDE AND FREQUENCY. IN THIS PAPER, WE CONSIDER THIS MOTION TO BE A FUNCTION OF THE SYSTEM RESPONSE AND A LIMITED ENERGY SOURCE IS ADOPTED. THUS, AN EXTRA DEGREE OF FREEDOM IS INTRODUCED IN THE PROBLEM. THE EQUATIONS OF MOTION ARE OBTAINED VIA A LAGRANGIAN APPROACH WITH SOME ASSUMED CHARACTERISTIC TORQUE CURVES. NEXT, EXTENSIVE NUMERICAL INTEGRATION IS USED TO DETECT SOME INTERESTING GEOMETRICAL ASPECTS OF REGULAR AND IRREGULAR MOTIONS OF THE SYSTEM RESPONSE. KEY-WORDS: GEAR RATTLING, NON-LINEAR DYNAMICS, NON-IDEAL SYSTEMS.

Author :

Balthazar, J. M.
Brasil, R. M.L.R.F.
Caldas, I. L.
Souza, S. L.T.

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