Analysis of the Vibration Response of a Gearbox With Gear Tooth Faults

2004 ◽  
Author(s):  
Xinhao Tian ◽  
Ming J. Zuo ◽  
Ken R. Fyfe
Keyword(s):  
Gear Tooth ◽  
Spur Gear ◽  
Vibration Response ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Vibration Model ◽  
Vibration Signatures ◽  
Potential Energy Method ◽  
The Relationship

In this study, the steady-state vibration response of a gearbox with gear tooth faults is investigated. Based on the analytical expression of the position-dependent mesh stiffness of the gear with perfect gear teeth derived with the potential energy method and the characteristics of involute gear teeth, expressions of the mesh stiffness of a gear with tooth faults such as tooth chip, tooth crack, and tooth breakage are derived. Using a coupled lateral and torsional vibration model of a one-stage spur gear pair, we have numerically solved a set of nonlinear equations and obtained typical vibration response diagrams of the gear pair with perfect gears and gears with tooth faults. This study reveals the relationship between the waveforms of the vibration and the types of local faults of the gear. These results are useful for identification of vibration signatures when there are these types of tooth faults.

Mesh Stiffness Calculation of Spur Gears With Tooth Surface Crack

2019 ◽  
Author(s):  
Luke Zhang ◽  
Yimin Shao
Keyword(s):  
Surface Crack ◽  
Theoretical Basis ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Early Failure ◽  
Proposed Model ◽  
Potential Energy Method ◽  
The Relationship

Abstract Tooth surface crack is an early fault before spalling, which has an important influence on mesh stiffness and vibration characteristics of the gear system. However, the researches on tooth surface crack are limited as scholars pay little attention to this early fault. In this study, an analytical model of spur gears with tooth surface crack is established. Using the potential energy method, the equations for mesh stiffness calculation of spur gears with tooth surface crack are derived. By adopting the proposed model, the influences of tooth surface crack fault on mesh stiffness of gear tooth are studied. The relationship between tooth surface crack and mesh stiffness of gear tooth under different lengths and depths can be further calculated. This study provides a theoretical basis for the diagnosis of early failure of spalling.

Analysis of parametric stability for a spur gear pair system considering the effect of extended tooth contact

2009 ◽  
Vol 223 (8) ◽  
pp. 1787-1797 ◽  
Author(s):  
Q Han ◽  
J Wang ◽  
Q Li
Keyword(s):  
High Speed ◽  
Floquet Theory ◽  
Gear Tooth ◽  
Spur Gear ◽  
Parametric Vibration ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Parametric Stability ◽  
Tooth Contact ◽  
Speed Range

In spur gear dynamic analysis, rectangular waves are often used to approximate the mesh stiffness alternating between one and two pairs of teeth in contact. But in actual practice, extended tooth contact (ETC) occurs due to gear tooth deflection under load. Considering the effect of ETC, the mesh stiffness in the pre-mature and post-mature contact regions is gradually rather than abruptly varying with time, which would influence the parametric stability of the geared system significantly. Therefore, research on parametric stability for a spur gear pair system considering the effect of ETC is carried out in this article. First, a torsional parametric vibration model for a spur gear pair system is established and the periodically time-varying mesh stiffness is approximated linearly by trapezoidal waveforms (with the effect of ETC) and rectangular waves (without the effect of ETC). Then, the Floquet theory for stability analysis (including two key elements: one is the derivation of state transition matrix (STM); the other is the stability criterion for parametric vibration system) is presented briefly. Based on these, the stabilities (stable and unstable regions) of a practically used high-speed and heavy-load spur gear pair with and without taking into account ETC are determined utilizing Floquet theory, respectively, and the differences between the two cases in three ranges of operating speeds for the system (low speed range, middle speed range, and high speed range) are contrasted in detail. In addition, various values of operating torques and mesh damping of the gear pair are also simulated and discussed for their influences upon unstable regions.

Numerical Simulation of Nonlinear Spur Gear Dynamics

1999 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
C. Nataraj
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Spur Gear ◽  
Journal Bearings ◽  
Accurate Estimation ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

Abstract An analytical investigation of the nonlinear dynamics of a high-speed spur-gear pair supported on journal bearings is presented. Dynamic tooth loads result from the interaction between periodic variation of gear mesh stiffness, involute tooth profile errors and gear rotor dynamics. Accurate estimation of dynamic tooth loads, as the gear teeth engage and disengage, is critical for fatigue life estimation. Load-deflection characteristics of a spur gear mesh and the periodically varying gear mesh stiffness is developed using a finite element model. Relative displacement between the gear teeth (transmission error) due to tooth deflection along the line of action is evaluated. The coupled torsional-lateral vibrations of a spur-gear pair supported on journal bearings is modeled as a six degree of freedom system. The time dependent radial and tangential forces acting on the gear shaft supported on journal bearings is evaluated. Short bearing theory is used for modeling the journal bearing dynamics. The resulting nonlinear equations of motion are numerically integrated to obtain gear and pinion whirl orbits due to unbalance excitation and dynamic tooth load variation. Dynamic tooth loads are compared with the mean load due to torque transmission.

Influence of simultaneous time-varying bearing and tooth mesh stiffness fluctuations on spur gear pair vibration

2019 ◽  
Vol 97 (2) ◽  
pp. 1403-1424 ◽  
Author(s):  
Guanghui Liu ◽  
Jun Hong ◽  
Robert G. Parker
Keyword(s):  
Spur Gear ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness

Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nan Gao ◽  
Shiyu Wang ◽  
Muhammad Asad Ur Rehman Bajwa
Keyword(s):  
Nonlinear Dynamics ◽  
Amplitude Modulation ◽  
Spur Gear ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Chaotic Motions ◽  
Content Type ◽  
Modulation Function ◽  
Nonlinear Behaviors

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair

2001 ◽  
Vol 123 (3) ◽  
pp. 311-317 ◽  
Author(s):  
J. H. Kuang ◽  
A. D. Lin
Keyword(s):  
Dynamic Load ◽  
Sliding Wear ◽  
Vibration Spectrum ◽  
Tooth Wear ◽  
Spur Gear ◽  
Damping Factor ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Wear Process ◽  
The Mathematical Model

In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The wear prediction model proposed by Flodin et al. is used to simulate the tooth profile wear process. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.

Dynamic Analysis of Sliding Friction in a Gear Pair

2003 ◽  
Author(s):  
Rajendra Gunda ◽  
Rajendra Singh
Keyword(s):  
Load Distribution ◽  
Sliding Friction ◽  
Spur Gear ◽  
Time Instant ◽  
Friction Torque ◽  
Speed Ratio ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Static Mode

Chief objective of this article is to evaluate the role of sliding friction in gear dynamics, and more specifically the effect of the periodic variations in mesh stiffness, load distribution and friction torque during a mesh cycle. A non-unity speed ratio spur gear is considered. Only the torsional degree of freedom of the gear pair, with ideal Coulomb friction law, is analyzed. Previous studies by Vaishya and Singh [1–3] make idealized assumptions about temporal (or spatial) variation of mesh stiffness and load sharing in order to obtain more tractable analytical solutions. In our formulation, an accurate Finite Element/Contact Mechanics analysis code [4] is run in the static mode to compute the mesh stiffness and load distribution at every time instant of the mesh. The computed parametric variation of stiffness is then incorporated into our dynamic formulation that includes frictional torques. Next, we use appropriate numerical techniques to solve for the dynamic response in time domain. This study, though preliminary in nature, examines the effects of pinion speed, coefficient of friction and mean input torque. This, along with work in progress, should yield further insights into the role of friction sources in gear vibro-acoustics.

scholarly journals Nonlinear Dynamic Characteristic Analysis of a Coated Gear Transmission System

Coatings ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Yangyi Xiao ◽  
Liyang Fu ◽  
Jing Luo ◽  
Wankai Shi ◽  
Minglin Kang
Keyword(s):  
Dynamic Characteristic ◽  
Time History ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Phase Curve ◽  
Gear Pair ◽  
Characteristic Analysis ◽  
Mesh Stiffness ◽  
Gear Transmission System

Coatings can significantly improve the load-carrying performance of a gear surface, but how they affect the vibration characteristic of the system is an urgent issue to be solved. Taking into account the nonlinear factors like the variable mesh stiffness, friction, backlash, and transmission error, a six-degree-of-freedom spur gear transmission system with coatings is presented. Meanwhile, the finite element method is applied to acquire the time-varying mesh stiffness of the coated gear pair in the engagement process. With the support of the time-history curve, phase curve, Poincare map, and fast Fourier transform spectrum, the dynamic characteristics and the effects of the coating elastic modulus on vibration behaviors of a gear transmission system are minutely dissected by using a numerical integration approach. Numerical cases illustrate that the dynamic characteristic of a gear transmission system tends toward a one-period state under the given operating condition. They also indicate that, compared with softer coatings, stiffer ones can properly enhance the transmission performance of the coated gear pair. Numerical results are also compared with previous studies, and can establish a theoretical basis for dynamic design and vibration control of the coated gear transmission system.

Sign in / Sign up

Export Citation Format

Share Document