Parametric Vibration Analysis of Transmission Mechanisms Using Numerical Methods

Transmission mechanisms are frequently used in machines for power transmission, varia‐ tion of speed and/or working direction and conversion of rotary motion into reciprocating motion. At high speeds, the vibration of mechanisms causes wear, noise and transmission errors. The vibration problem of transmission mechanisms has been investigated for a long time, both theoretically and experimentally. In dynamic modelling, a transmission mecha‐ nism is usually modelled as a multibody system. The differential equations of motion of a multibody system that undergo large displacements and rotations are fully nonlinear in n generalized coordinates in vector of variable q [1–4].

[1]  W. Hahn,et al.  Theorie der Stabilität einer Bewegung , 1959 .

[2]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[3]  L. Cesari,et al.  Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations , 1960 .

[4]  Lamberto Cesari,et al.  Asymptotic Behavior and Stability Problems in Ordinary Differential Equations , 1963 .

[5]  J. I. Vul'fson.  Analytical investigation of the vibration of mechanisms caused by parametric impulses , 1975 .

[6]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[7]  R. G. Fenton,et al.  Steady-state vibrational response of high-speed flexible mechanisms , 1984 .

[8]  E. Rivin,et al.  Vibroactivity of branched and ring structured mechanical drives , 1989 .

[9]  Hans Dresig,et al.  Dynamik der Mechanismen , 1989 .

[10]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[11]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[12]  Josef Stoer,et al.  Numerische Mathematik 2 , 1990 .

[13]  H. Troger,et al.  Nonlinear stability and bifurcation theory , 1991 .

[14]  Peter Lugner,et al.  Systemdynamik und Regelung von Fahrzeugen , 1994 .

[15]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[16]  Chandramouli Padmanabhan,et al.  Analysis of periodically forced nonlinear Hill’s oscillator with application to a geared system , 1996 .

[17]  Robert G. Parker,et al.  NON-LINEAR DYNAMIC RESPONSE OF A SPUR GEAR PAIR: MODELLING AND EXPERIMENTAL COMPARISONS , 2000 .

[18]  Giorgio Dalpiaz,et al.  Effectiveness and Sensitivity of Vibration Processing Techniques for Local Fault Detection in Gears , 2000 .

[19]  S. Theodossiades,et al.  NON-LINEAR DYNAMICS OF GEAR-PAIR SYSTEMS WITH PERIODIC STIFFNESS AND BACKLASH , 2000 .

[20]  Ian Howard,et al.  THE DYNAMIC MODELLING OF A SPUR GEAR IN MESH INCLUDING FRICTION AND A CRACK , 2001 .

[21]  Phong Dien Nguyen,et al.  Beitrag zur Diagnostik der Verzahnungen in Getrieben mittels Zeit-Frequenz-Analyse , 2002 .

[22]  R. Huston,et al.  Dynamics of Mechanical Systems , 2002 .

[23]  Nguyen Van Khang,et al.  Modelling Parametric Vibration of Gear-Pair Systems as a Tool for Aiding Gear Fault Diagnosis , 2004 .

[24]  Arend L. Schwab,et al.  Dynamics of Multibody Systems , 2007 .

[25]  Van Khang Nguyen,et al.  Linearization and parametric vibration analysis of some applied problems in multibody systems , 2009 .

[26]  Claus Führer,et al.  Numerical Methods in Multibody Dynamics , 2013 .