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.

scholarly journals An experimental method to measure gear tooth stiffness throughout and beyond the path of contact

2001 ◽  
Vol 215 (7) ◽  
pp. 793-803 ◽  
Author(s):  
R. G. Munro1 ◽  
D Palmer ◽  
L Morrish
Keyword(s):  
Gear Tooth ◽  
Contact Region ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Extended Contact ◽  
Tooth Stiffness ◽  
Simplifying Assumptions ◽  
Tooth Pair ◽  
Usual Problem

A method is presented that allows the accurate measurement of the tooth pair stiffness of a pair of spur gears. The method reveals the stiffness behaviour throughout the full length of the normal path of contact and also into the extended contact region when tooth corner contact occurs. The method makes use of the properties of transmission error plots for mean and alternating components over a range of tooth loads (Harris maps). It avoids the usual problem when measuring tooth deflections that deflections of other test rig components are difficult to eliminate. Also included are predicted Harris maps for a pair of high contact ratio spur gears, showing the effects of various simplifying assumptions, together with a measured map.

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.

A Novel Design Procedure for Reducing Vibration and Noise in Gears

1993 ◽  
Author(s):  
K. Y. Yoon ◽  
S. S. Rao
Keyword(s):  
Gear Tooth ◽  
Design Procedure ◽  
Transmission Error ◽  
Tooth Profile ◽  
Profile Modification ◽  
Noise Characteristics ◽  
Spline Curves ◽  
Involute Gears ◽  
Static Transmission Error ◽  
Novel Design

Abstract A new method is proposed for reducing vibration and noise of involute gears. The method is based on the use of cubic spline curves for gear tooth profile modification. The tooth profile is constrained to assume an involute shape during the loaded operation. Thus the new gear profile assures conjugate motion at all points along the line of action. The new profile is found to result in a more uniform static transmission error compared to standard involute profile thereby contributing to the improvement of vibration and noise characteristics of the gear.

A Study on Planetary Gear Dynamics With Tooth Profile Modification

2011 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Transmission Error ◽  
Tooth Profile ◽  
Peak Amplitude ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Static Transmission Error ◽  
The Impact

This study investigates the impact of tooth profile modification on planetary gear dynamic response. Micro-scale geometric deviations from an involute gear tooth profile add an additional excitation source, potentially reducing gear vibration. In order to take account of the excitation, tooth profile modification is included in an analytical planetary gear model. Nonlinearity due to tooth contact loss is considered. Time-varying mesh stiffness and both rotational and translational gear motions are modeled. The accuracy of the proposed model for dynamic analysis is correlated against a benchmark finite element analysis. Perturbation analysis is employed to obtain a closed-form approximation of planetary gear dynamic response with tooth profile modification. Mathematical expressions from the perturbation solution allow one to easily estimate the peak amplitude of resonant response using known parameters. Variation of the peak amplitude with the amount and the length of profile modification illustrates the effect of tooth profile modification on planetary gear dynamic response. For a given external load, the tooth profile modification parameters for minimal response are readily obtained. Static transmission error and dynamic response are minimized at different amounts of profile modification, which contradicts common practical thinking regarding strong correlation between static transmission error and dynamic response. Contrary to the expectation of further reduced vibration, the combination of the optimum sun-planet and ring-planet mesh tooth profile modifications that minimizes response when applied individually increases dynamic response.

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.

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