Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation

In this study, the dynamic response of a pair of spur gears is analyzed when the gear set has translational motion due to bearing deformation. A new dynamic model for the gear set, considering translational motion, is proposed, in which the distance between the centers of a pinion and a gear varies with time. Therefore, the proposed model regards the pressure angle and the contact ratio as time-varying variables, while the previous model regards them as constants. After deriving nonlinear equations of motion for the gear set, the dynamic responses are computed by applying the Newmark time integration method. This paper claims that the new model produces more accurate dynamic responses in comparison to those of the previous model. Some dynamic response differences between the new and previous models are demonstrated, and the effects of damping and stiffness upon the dynamic responses are also investigated.

[1]  R. Cornell Compliance and Stress Sensitivity of Spur Gear Teeth , 1981 .

[2]  Ahmet Kahraman,et al.  Effect of Involute Contact Ratio on Spur Gear Dynamics , 1999 .

[3]  Robert G. Parker,et al.  Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems , 2002 .

[4]  Kiyohiko Umezawa,et al.  Simulation of Rotational Vibration of Spur Gears , 1984 .

[5]  Rajendra Singh,et al.  Non-linear dynamics of a geared rotor-bearing system with multiple clearances , 1991 .

[6]  Jao-Hwa Kuang,et al.  THEORETICAL ASPECTS OF TORQUE RESPONSES IN SPUR GEARING DUE TO MESH STIFFNESS VARIATION , 2003 .

[7]  P. Velex,et al.  Dynamic tooth loads and quasi-static transmission errors in helical gears – Approximate dynamic factor formulae , 2007 .

[8]  Fakher Chaari,et al.  Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission , 2008 .

[9]  Rajendra Singh,et al.  Non-linear dynamics of a spur gear pair , 1990 .

[10]  P. Velex,et al.  A MATHEMATICAL MODEL FOR ANALYZING THE INFLUENCE OF SHAPE DEVIATIONS AND MOUNTING ERRORS ON GEAR DYNAMIC BEHAVIOUR , 1996 .

[11]  Ahmet Kahraman,et al.  Load sharing characteristics of planetary transmissions , 1994 .

[12]  A. Kahraman Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair , 2021 .

[13]  H. N. Özgüven,et al.  Dynamic analysis of high speed gears by using loaded static transmission error , 1988 .

[14]  Marco Amabili,et al.  A METHOD TO IDENTIFY MODAL PARAMETERS AND GEAR ERRORS BY VIBRATIONS OF A SPUR GEAR PAIR , 1998 .

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

[16]  Tzong-Shi Liu,et al.  Dynamic analysis of a spur gear by the dynamic stiffness method , 2000 .

[17]  Donald R. Houser,et al.  Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears , 1986 .