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.

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.

Influence of gear tooth addendum and dedendum on the helical gear optimization considering mass, efficiency, and transmission error

2021 ◽  
Vol 166 ◽  
pp. 104476
Author(s):  
Chanho Choi ◽  
Hyoungjong Ahn ◽  
Young-jun Park ◽  
Geun-ho Lee ◽  
Su-chul Kim
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Helical Gear

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

scholarly journals Towards an integrated forecasting system for fisheries on habitat-bound stocks

Ocean Science ◽  
2013 ◽  
Vol 9 (2) ◽  
pp. 261-279 ◽  
Author(s):  
A. Christensen ◽  
M. Butenschön ◽  
Z. Gürkan ◽  
I. J. Allen
Keyword(s):  
Climatic Variability ◽  
Maximum Sustainable Yield ◽  
Ecosystem Dynamics ◽  
Fish Stock ◽  
Generic Model ◽  
Sustainable Yield ◽  
Model Framework ◽  
The North ◽  
Basin Scale ◽  
Forecasting System

Abstract. First results of a coupled modelling and forecasting system for fisheries on habitat-bound stocks are being presented. The system consists currently of three mathematically, fundamentally different model subsystems coupled offline: POLCOMS providing the physical environment implemented in the domain of the north-west European shelf, the SPAM model which describes sandeel stocks in the North Sea, and the third component, the SLAM model, which connects POLCOMS and SPAM by computing the physical–biological interaction. Our major experience by the coupling model subsystems is that well-defined and generic model interfaces are very important for a successful and extendable coupled model framework. The integrated approach, simulating ecosystem dynamics from physics to fish, allows for analysis of the pathways in the ecosystem to investigate the propagation of changes in the ocean climate and to quantify the impacts on the higher trophic level, in this case the sandeel population, demonstrated here on the basis of hindcast data. The coupled forecasting system is tested for some typical scientific questions appearing in spatial fish stock management and marine spatial planning, including determination of local and basin-scale maximum sustainable yield, stock connectivity and source/sink structure. Our presented simulations indicate that sandeel stocks are currently exploited close to the maximum sustainable yield, even though periodic overfishing seems to have occurred, but large uncertainty is associated with determining stock maximum sustainable yield due to stock inherent dynamics and climatic variability. Our statistical ensemble simulations indicates that the predictive horizon set by climate interannual variability is 2–6 yr, after which only an asymptotic probability distribution of stock properties, like biomass, are predictable.

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