The Prediction of the Dynamic Transmission Error for the Helical Gear System

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.

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Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications

Journal of Mechanical Design ◽

10.1115/1.4043586 ◽

2019 ◽

Vol 141 (10) ◽

Cited By ~ 8

Author(s):

M. Benatar ◽

M. Handschuh ◽

A. Kahraman ◽

D. Talbot

Keyword(s):

Dynamic Models ◽

Nonlinear Behavior ◽

Transmission Error ◽

Helical Gear ◽

Forced Response ◽

Test Machine ◽

Response Curves ◽

Gear Mesh ◽

Dynamic Transmission Error ◽

Static Transmission Error

This paper presents a set of motion transmission error data for a family of helical gears having different profile and lead modifications operated under both low-speed (quasi-static) and dynamic conditions. A power circulatory test machine is used along with encoder and accelerometer-based transmission error measurement systems to quantify motion transmission behavior within wide ranges of torque and speed. Results of these experiments indicate that the tooth modifications impact the resultant static and dynamic transmission error amplitudes significantly. A design load is shown to exist for each gear pair of different modifications where static transmission error amplitude is minimum. Forced response curves and waterfall plots are presented to demonstrate that the helical gear pairs tested act linearly with no signs of nonlinear behavior such as tooth contact separations. Furthermore, static and dynamic transmission error amplitudes are observed to be nearly proportional, suggesting that static transmission error can be employed in helical gear dynamic models as the main gear mesh excitation. The data presented here is intended to fill a void in the literature by providing means for validation of load distribution and dynamic models of helical gear pairs.

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Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/14613484211065742 ◽

2021 ◽

pp. 146134842110657

Author(s):

Hao Dong ◽

Yue Bi ◽

bo Wen ◽

Zhen-bin Liu ◽

Li-bang Wang

Keyword(s):

Frequency Response ◽

Dynamic Modeling ◽

External Load ◽

Transmission Error ◽

Helical Gear ◽

Gear System ◽

Time Varying ◽

Vibration Displacement ◽

Meshing Stiffness ◽

Nonlinear Dynamic Modeling

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

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

Volume 7: 10th International Power Transmission and Gearing Conference ◽

10.1115/detc2007-34078 ◽

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.

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

Journal of Mechanical Design ◽

10.1115/1.2890115 ◽

2008 ◽

Vol 130 (5) ◽

Cited By ~ 23

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.657.649 ◽

2014 ◽

Vol 657 ◽

pp. 649-653 ◽

Cited By ~ 4

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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