Nonlinear Dynamic Analysis of a New Antibacklash Gear Mechanism Design for Reducing Dynamic Transmission Error

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
S. R. Besharati ◽  
V. Dabbagh ◽  
H. Amini ◽  
Ahmed A. D. Sarhan ◽  
J. Akbari ◽  
...  
Keyword(s):  
Mechanism Design ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Transmission Error ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Dynamic Transmission Error ◽  
Gear Mechanism ◽  
Lower Transmission ◽  
Input Torque

In this study, a new antibacklash gear mechanism design comprising three pinions and a rack is introduced. This mechanism offers several advantages compared to conventional antibacklash mechanisms, such as lower transmission error as well as lower required preload. Nonlinear dynamic modeling of this mechanism is developed to acquire insight into its dynamic behavior. It is observed that the amount of preload required to diminish the backlash depends on the applied input torque and nature of periodic mesh stiffness. Then, an attempt is made to obtain an approximate relation to find the minimum requiring preload to preserve the system’s antibacklash property and reduce friction and wear on the gear teeth. The mesh stiffness of the mated gears, rack, and pinion is achieved via finite element method. Assuming that all teeth are rigid and static transmission error is negligible, dynamic transmission error (DTE) would be zero for every input torque, which is a unique trait, not yet proposed in previous research.

Nonlinear Dynamic Analysis of a Multi-Gear Train With Time-Varying Mesh Stiffness Including Modification Coefficient Effect

2011 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
K. H. Huang ◽  
C. J. Cheng ◽  
C. R. Wang
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Gear Train ◽  
Work Piece ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Harmonic Motion ◽  
Gear Profile

The nonlinear dynamic analysis of a multi-gear train with time-varying mesh stiffness on account of the modification coefficient effect is in vestigated in this paper. The proposed application of the modification coefficient will revise the center distance of the gear pair, avoid undercut and raise the mesh stiffness of the designed gear system. In this study, the gear profile is generated from the relationship between the rack cutter and the gear work piece by using the envelope theory. The rack cutter with the modification coefficient increases the mesh stiffness and thus enhances the strength of the gear tooth. Then the time-varying mesh stiffness at the contact position of the gear pair is calculated from the tooth deflection analysis using the generated gear profile. With the obtained time-varying mesh stiffness, the nonlinear dynamic behavior of multi-gear train is investigated by using Runge-Kutta integration method. The numerical results of the studied examples show the harmonic motion, sub-harmonic motion, chaotic motion and bifurcation phenomenon of the gear train.

Analysis of Gear Noise and Dynamic Transmission Error Measurements

2004 ◽  
Author(s):  
Mats Henriksson
Keyword(s):  
Dynamic Properties ◽  
Transmission Error ◽  
Gear System ◽  
Gear Pair ◽  
Gear Noise ◽  
Gear Teeth ◽  
Opposite Trend ◽  
Dynamic Transmission Error

Measurements of dynamic transmission error (DTE) and noise have been performed on a truck gearbox. The DTE is related to the dynamic properties of the complete gear system. To investigate the coupling between noise and DTE, the correlation between noise and DTE is calculated for fixed speeds, as the torque is increased. The highest correlation is found for the low split gear pair, which is located closest to the gearbox housing. When the correlation is low, one of the reasons can be a resonance of the shafts, although not all resonances effect the correlation between noise and DTE. The DTE is also compared to calculated static TE for the gear teeth. Both the DTE and noise for the fifth gear increases as the torque is increased. The calculated static TE shows the opposite trend and decreases as the torque is increased.

Nonlinear dynamic analysis of gear system in shearer cutting section under wear failure

2021 ◽  
pp. 146441932110535
Author(s):  
Lianchao Sheng ◽  
Wei Li ◽  
Guo Ye ◽  
Ke Feng
Keyword(s):  
Nonlinear Dynamic Analysis ◽  
Transmission Error ◽  
Gear System ◽  
Radial Clearance ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Vibration Impact ◽  
Coupling Factors ◽  
Dynamic Meshing ◽  
Internal Error

Gear wear failure is one of the important failures of the gear system in the shearer cutting section. To reveal the influence mechanism of shearer cutting gear wear on the system dynamic characteristics, considering coupling factors such as time-varying meshing stiffness, dynamic gear clearance, internal error excitation, end load constraint and bearing radial clearance under wear failure, an improved dynamic model of shearer drive gear system is introduced to present an in-depth investigation of uniform wear of gear teeth effect. The dynamic meshing stiffness of gears under different degrees of wear is analysed. Furthermore, the bifurcation diagram is utilized to observe the motion state of the system experiencing different excitation frequencies, support damping as well as terminal loads. It is demonstrated that the gear surface wear could bring a change in gear dynamic transmission error, vibration impact state and amplitude, which is mainly manifested in increasing the unstable area and the vibration amplitude of the gear system, providing a method for monitoring and diagnosing of gear surface faults.

Analytical Study of Helical Gear Dynamics With Sliding Friction Using Floquet Theory

2007 ◽  
Author(s):  
Song He ◽  
Rajendra Singh
Keyword(s):  
Floquet Theory ◽  
Sliding Friction ◽  
Initial Conditions ◽  
Transmission Error ◽  
Helical Gear ◽  
Degree Of Freedom ◽  
Analytical Models ◽  
Mesh Stiffness ◽  
Forcing Function ◽  
Dynamic Transmission Error

Analytical models of a helical gear pair are developed in order to examine the effect of sliding friction on the dynamic transmission error. Simplified 6 degree-of-freedom and single degree-of-freedom analytical models are developed. These models characterize the contact plane dynamics and capture the velocity reversal at the pitch line due to sliding friction. By assuming a constant mesh stiffness density along the contact lines, a linear time-varying model (with parametric excitation) is obtained. The effect of sliding friction is quantified by an effective mesh stiffness term. Floquet theory is then used to obtain closed-form solutions to the dynamic transmission error given periodic piece-wise linear tooth stiffness function. Responses to both initial conditions and forcing function under a nominal torque are derived. Analytical models are validated by comparing predictions with numerical simulations. Finally, parametrically-induced instability issues are briefly mentioned.

Nonlinear dynamic analysis of spur gear system based on fractional-order calculus

2020 ◽  
Vol 34 (36) ◽  
pp. 2050420
Author(s):  
Jingyu Hou ◽  
Shaopu Yang ◽  
Qiang Li ◽  
Yongqiang Liu
Keyword(s):  
Fractional Order ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Balance Method ◽  
Spur Gear ◽  
Nonlinear Dynamic Model ◽  
Mesh Stiffness ◽  
Incremental Harmonic Balance Method ◽  
Internal Excitation

In this paper, nonlinear dynamic model of spur gear pairs with fractional-order damping under the condition of time-varying stiffness, backlash and static transmission error is established. The general formula of fractional-order damping term is derived by using the incremental harmonic balance method (IHBM), and the approximate analytical solution of the system is obtained by use of the iterative formula. The correctness of the results is verified by comparing with the numerical solutions in the existing literature. The effects of mesh stiffness, internal excitation amplitude and fractional order on the dynamic behavior of the system are analyzed. The results show that changing the fractional order can effectively control the resonance position and amplitude in the meshing process. Both the mesh stiffness and internal excitation can control the collision state and the stability.

Dynamic Transmission Error Prediction of Helical Gear Pair Under Sliding Friction Using Floquet Theory

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Song He ◽  
Rajendra Singh
Keyword(s):  
Floquet Theory ◽  
Sliding Friction ◽  
Initial Conditions ◽  
Transmission Error ◽  
Helical Gear ◽  
Marginal Effect ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Dynamic Transmission Error ◽  
Helical Gear Pair

An analytical solution to the dynamic transmission error of a helical gear pair is developed by using a single-degree-of-freedom model with piecewise stiffness functions that characterize the contact plane dynamics and capture the velocity reversal at the pitch line. By assuming a constant mesh stiffness density along the contact lines, a linear time-varying model (with parametric excitations) is obtained, where the effect of sliding friction is quantified by an effective mesh stiffness term. The Floquet theory is then used to obtain closed-form solutions to the dynamic transmission error, and responses are derived to both initial conditions and the forced periodic function under a nominal preload. Analytical models are validated by comparing predictions with numerical simulations, and the effect of viscous damping is examined. Stability analysis is also briefly conducted by using the state transition matrix. Overall, the sliding friction has a marginal effect on the dynamic transmission error of helical gears, as compared with spur gears, in the context of the torsional model.

The Effect of Tooth Wear on the Dynamic Transmission Error of Helical Gears with Smaller Number of Pinion Teeth

2014 ◽  
Vol 657 ◽  
pp. 649-653 ◽  
Author(s):  
Virgil Atanasiu ◽  
Cezar Oprişan ◽  
Dumitru Leohchi
Keyword(s):  
Dynamic Contact ◽  
Tooth Wear ◽  
Transmission Error ◽  
Analytical Investigation ◽  
Helical Gear ◽  
Wear Depth ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Dynamic Transmission Error

The paper presents an analytical investigation of the effect of the tooth wear on the dynamic transmission error of helical gear pairs with small number of pinion teeth. Firstly, the dynamic analysis is conducted to investigate only the effect of the time-varying mesh stiffness on the variation of dynamic transmission error along the line of action. Then, the tooth wear effect on the dynamics of helical gear with small number of pinion teeth is being researched. In the analysis, instantaneous dynamic contact analysis is used in wear depth calculations. A comparative study was performed to investigate the relation between total contact ratio, mesh stiffness and dynamic transmission error of helical gear pairs with small number of teeth.

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