Rotational Vibration Response of Power Transmission Systems

4th International Pipeline Conference, Parts A and B ◽

10.1115/ipc2002-27285 ◽

2002 ◽

Author(s):

Sidi M. Berri

Keyword(s):

Power Transmission ◽

Spur Gear ◽

Crack Size ◽

Integration Scheme ◽

Transmission Systems ◽

Coupled Equations ◽

Numerical Integration Scheme ◽

Wide Range ◽

Power Transmission Systems ◽

Rotational Vibration

The main goal of monitoring systems for rotary machinery is to provide sufficient time between warning and failure of machine elements so that safety procedures can be implemented. The present study investigates the dynamics of transmission systems by interpreting the interaction dynamic loads of the elements of the system. This phase of the effort concerns itself with the determination of the relationship of the dynamic tooth loads to the crack size of a single cracked tooth of a spur gear pair. A mathematical model of the test rig used for the general study is proposed. In addition to accounting for the time-varying stiffness of the meshing tooth pair, the model also includes gear errors and damping. A Newmark-Beta numerical integration scheme is used to solve the system of non-linear coupled equations. Results for the dynamic tooth loads as a function of crack size are presented for a wide range of rotational speeds. Simulated and experimental vibrational signals are also presented.

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Dynamics of a Transmission System Having a Cracked Gear Tooth

Volume 6: 8th International Power Transmission and Gearing Conference ◽

10.1115/detc2000/ptg-14443 ◽

2000 ◽

Author(s):

Sidi M. Berri ◽

J. M. Klosner

Keyword(s):

Power Transmission ◽

Gear Tooth ◽

Crack Size ◽

Analytical Investigation ◽

Transmission System ◽

Integration Scheme ◽

System Of Nonlinear Equations ◽

Gear Mesh ◽

Numerical Integration Scheme ◽

Vibrational Characteristics

Abstract The present study is a combined experimental/analytical investigation of the effect of a cracked pinion tooth on the vibrational characteristics of a power transmission system. It is part of an ongoing effort to develop strategies for locating and quantifying local defects by properly processing and interpreting the output signals. Presented, is a system of nonlinear equations representing the analytical model of an experimental test rig. The model includes the effect of crack size on the time-varying gear mesh stiffness, and the equations are solved by using a Newmark-Beta numerical integration scheme. The numerically and experimentally obtained signals, processed by using the wavelet transform, show excellent agreement over a range of crack sizes and running speeds, thus suggesting that mathematical simulation can provide a useful tool for quantifying cracks.

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Simulation of the Rotational Vibration Response of a Spur Gear Pair With One Cracked Tooth

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education ◽

10.1115/2000-gt-0357 ◽

2000 ◽

Author(s):

Sidi M. Berri ◽

J. M. Klosner

Keyword(s):

Differential Equations ◽

Power Transmission ◽

Equations Of Motion ◽

Spur Gear ◽

Crack Size ◽

Vibration Response ◽

Time Varying ◽

Gear Pair ◽

Rotational Vibration ◽

Tooth Pair

The present study introduces a developed simulator on rotational vibrations of a power transmission spur gear set with one cracked pinion tooth. The simulator computes the expected vibration response of the meshing gears by solving the differential equations of motion. In additions to accounting for the time-varying stiffness of the meshing tooth pair, the simulator also includes gear errors and damping. Dynamic tooth loads as a function of crack size are also computed. The simulated outputs depict precisely the experimental behaviors. Results for rotational vibrations of the power transmission system are presented as a function of crack size.

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