Static-transmission-error vibratory-excitation contributions from plastically deformed gear teeth caused by tooth bending-fatigue damage

2007 ◽  
Vol 21 (2) ◽  
pp. 885-905 ◽  
Author(s):  
W.D. Mark ◽  
C.P. Reagor
Keyword(s):  
Fatigue Damage ◽  
Transmission Error ◽  
Bending Fatigue ◽  
Gear Teeth ◽  
Static Transmission Error

Analytical approximations to damaged gear tooth transmission-error contributions for gear-health monitoring

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1157-1182 ◽  
Author(s):  
William D Mark
Keyword(s):  
Fatigue Damage ◽  
Gear Tooth ◽  
Transmission Error ◽  
Generic Model ◽  
Model Framework ◽  
Bending Fatigue ◽  
New Methods ◽  
Analytical Approximations ◽  
Significant Damage ◽  
Higher Harmonic

A generic model of transmission-error contributions arising from gear-tooth damage is developed. Damage is modeled as material removed from tooth-working-surfaces. Regions of modeled tooth damage are of limited size as in pitting damage or are extended to full working surfaces as in tooth-bending-fatigue damage. Results are computed for a wide variety of damage forms and formulated for any collection of teeth experiencing damage. Final results are expressed as transmission-error rotational-harmonic amplitudes arising from damage. Rotational-harmonic regions experiencing significant damage contributions from pitting/spalling damage and from tooth-bending-fatigue damage are delineated. Increases in higher harmonic-number amplitudes arising from transmission-error discontinuities are formulated. The overall model framework can be used to explain and interpret observed features of gear transmission-error spectra arising from gear-tooth damage and to develop new methods of detecting and assessing the severity of such damage.

2D nonlinear and non-Hertzian gear teeth deflection model for static transmission error calculation

2021 ◽  
Vol 166 ◽  
pp. 104471
Author(s):  
Fabio Bruzzone ◽  
Tommaso Maggi ◽  
Claudio Marcellini ◽  
Carlo Rosso
Keyword(s):  
Transmission Error ◽  
Gear Teeth ◽  
Error Calculation ◽  
Static Transmission Error

scholarly journals Study of the tooth contact for high contact ratio spur gears with long tip relief

2019 ◽  
Vol 287 ◽  
pp. 01004
Author(s):  
José I. Pedrero ◽  
Miguel Pleguezuelos ◽  
Miryam B. Sánchez
Keyword(s):  
Load Sharing ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Tooth Contact ◽  
Gear Teeth ◽  
Profile Modification ◽  
Static Transmission Error ◽  
Tooth Pair

Profile modifications are commonly used to avoid shocks between meshing gear teeth produced by the delay of the driven gear, and the subsequent sooner start of contact, due to the teeth deflections. A suitable tip relief at the driven tooth shifts the start of contact to the proper location at the theoretical inner point of contact. The shape of the relief governs the loading curve of the tooth pair, while the length of relief determines the intervals in which this actual loading curve differs from the theoretical one of unmodified teeth. As at least one tooth pair should be in contact at the unmodified involute profile interval, the length of modification should be smaller than the length of the intervals of two pair tooth contact; otherwise, a shock at the end of contact of the previous pair is unavoidable. However this problem does not occur for high contact ratio spur gears, in which at least two couples of teeth are in contact at any moment. In this work, a study on the load sharing and the quasi-static transmission error for high contact ratio spur gears with long profile modification has been performed, and a model for the tooth contact has been developed.

Behavior of the average-log-ratio ALR gear-damage detection algorithm in cases of a single damage form

2020 ◽  
pp. 095440622097166
Author(s):  
William D Mark
Keyword(s):  
Damage Detection ◽  
Gear Tooth ◽  
Transmission Error ◽  
Detection Algorithm ◽  
Frequency Spectra ◽  
Bending Fatigue ◽  
Static Transmission Error ◽  
Parseval’S Theorem ◽  
Log Ratio ◽  
Tooth Pair

A mathematical model of static-transmission-error frequency-domain contributions caused by a single generic form of gear-tooth damage is used to explain observed behavior of the average-log-ratio (ALR) gear-damage detection algorithm applied to a case of tooth-bending-fatigue damage. The periodic behavior of rotational-harmonic frequency spectra resulting from tooth damage is explained and experimentally verified. Monotonic increases in ALR contributions in the rotational-harmonic region below the tooth-meshing fundamental harmonic are unambiguously related to increasing gear damage by use of Parseval’s theorem for the discrete Fourier transform. Computation of ALR using rotational-harmonic bands between adjacent tooth-meshing harmonics is suggested for early detection of gear damage. Large high-frequency ALR contributions are explained by transmission-error jump (step) discontinuities caused by large tooth-pair deformations, indicating a severe state of damage.

Effects of the Gear Tooth Modification on the Nonlinear Dynamics of Gear Transmission System

2010 ◽  
Vol 97-101 ◽  
pp. 2764-2769
Author(s):  
Si Yu Chen ◽  
Jin Yuan Tang ◽  
C.W. Luo
Keyword(s):  
Nonlinear Dynamics ◽  
Gear Tooth ◽  
Simulation Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Meshing Stiffness ◽  
Gear Transmission System ◽  
Tooth Modification ◽  
Static Transmission Error ◽  
Misalignment Error

The effects of tooth modification on the nonlinear dynamic behaviors are studied in this paper. Firstly, the static transmission error under load combined with misalignment error and modification are deduced. These effects can be introduced directly in the meshing stiffness and static transmission error models. Then the effect of two different type of tooth modification combined with misalignment error on the dynamic responses are investigated by using numerical simulation method. The numerical results show that the misalignment error has a significant effect on the static transmission error. The tooth crowning modification is generally preferred for absorbing the misalignment error by comparing with the tip and root relief. The tip and root relief can not resolve the vibration problem induced by misalignment error but the crowning modification can reduce the vibration significantly.

Dynamic Analysis of a Multi-Mesh Helical Gear Train

1992 ◽  
Author(s):  
Ahmet Kahraman
Keyword(s):  
Loading Condition ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Gear Train ◽  
Loading Conditions ◽  
Gear Mesh ◽  
Natural Modes ◽  
Static Transmission Error

Abstract In this paper, the dynamic behavior of a multi-mesh helical gear train is studied. The gear train consists of three helical gears, with one of the gears in mesh with the other two. An 18-degree-of-freedom dynamic model which includes transverse, torsional, axial and rotational (rocking) motions of the flexibly mounted gears is developed. Two different loading conditions are identified. For case I, the system is driven by the gear in the middle, and for case II, the system is driven by one of the gears at either end of the gear train. Gear mesh phases under each loading condition are determined. The natural modes are predicted, and effects of the helix angle and the loading condition on the natural modes are explained. The forced response, which includes dynamic mesh and bearing forces, due to the static transmission error excitation is found. Effects of loading conditions and asymmetric positioning on the response are also explored. The results suggest that the dynamic forces are lower if the number of teeth of the gear in the middle is (i) an odd number for case I type loading, and (ii) an even number for case II type loading.

An Analytical and Numerical Investigation of Modulation Sidebands of a Planetary Gear Under Fluctuated External Torque

2018 ◽  
Author(s):  
Yunbo Yuan ◽  
Wei Liu ◽  
Yahui Chen ◽  
Donghua Wang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Operating Conditions ◽  
Radial Acceleration ◽  
External Torque ◽  
Gear Mesh ◽  
Planetary Gear Sets ◽  
Static Transmission Error ◽  
Frequency Modulations ◽  
Mesh Phasing

Certain operating conditions such as fluctuation of the external torque to planetary gear sets can cause additional sidebands. In this paper, a mathematical model is proposed to investigate the modulation mechanisms due to a fluctuated external torque (FET), and the combined influence of such an external torque and manufacturing errors (ME) on modulation sidebands. Gear mesh interface excitations, namely gear static transmission error excitations and time-varying gear mesh stiffness, are defined in Fourier series forms. Amplitude and frequency modulations are demonstrated separately. The predicted dynamic gear mesh force spectra and radial acceleration spectra at a fixed position on ring gear are both shown to exhibit well-defined modulation sidebands. Comparing with sidebands caused by ME, more complex sidebands appear when taking both FET and ME into account. An obvious intermodulation is found around the fundamental gear mesh frequency between the FET and ME in the form of frequency modulations, however, no intermodulation in the form of amplitude modulations. Additionally, the results indicate that some of the sidebands are cancelled out in radial acceleration spectra mainly due to the effect of planet mesh phasing, especially when only amplitude modulations are present.

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