Finite Element/Contact Mechanics Analysis of Spur Gear Pairs With Tooth Root Cracks

2021 ◽  
Author(s):  
Yaosen Wang ◽  
Adrian A. Hood ◽  
Christopher G. Cooley
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Contact Mechanics ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Root ◽  
Transmission Errors ◽  
Wide Range ◽  
Dynamic Transmission Error ◽  
Root Crack

Abstract This study analyzes the nonlinear static and dynamic response in spur gear pairs with tooth root crack damage. A finite element/contact mechanics (FE/CM) model is used that accurately captures the elastic deformations on the gear teeth due to kinematic motion, tooth and rim deformations, vibration, and localized increases in compliance due to a tooth root crack. The damage is modeled by releasing the connectivity of the finite element mesh at select nodes near a tooth crack. The sensitivity of the calculated static transmission errors and tooth mesh stiffnesses is determined for varying crack initial locations, final locations, and the path from the initial to final location. Gear tooth mesh stiffness is calculated for a wide range of tooth root crack lengths, including large cracks that extend through nearly all of the tooth. Mesh stiffnesses are meaningfully reduced due to tooth root crack damage. The dynamic response is calculated for cracks of varying length. Larger cracks result in increased peak dynamic transmission errors. For small tooth root cracks the spectrum of dynamic transmission error contains components near the natural frequency of the gear pair. The spectrum of dynamic transmission error has broadband frequency response for large tooth root cracks that extend further than one-half of the tooth’s thickness.

A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs

2006 ◽  
Vol 129 (1) ◽  
pp. 75-84 ◽  
Author(s):  
V. K. Tamminana ◽  
A. Kahraman ◽  
S. Vijayakar
Keyword(s):  
Dynamic Models ◽  
Deformable Body ◽  
Nonlinear Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear Mesh ◽  
Dynamic Factors ◽  
Wide Range ◽  
Dynamic Transmission Error ◽  
Torque Values

In this study, two different dynamic models, a finite-element-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torque values. Although similar models were proposed in the past, they were neither fully validated nor equipped to predict both DTE and different forms of DF. Accordingly, this study focuses on (i) validation of both models through an extensive set of experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles, and (ii) establishment of a direct link between DTE and different forms of DF, especially the ones based on tooth forces and the root stresses. The predicted DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior, such as tooth separations and jump discontinuities on DF, is also quantified.

Prediction and Experimental Correlation of Tooth Root Strains in Spur Gear Pairs

2015 ◽  
Author(s):  
Xiang Dai ◽  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Gear Tooth ◽  
Strain Curve ◽  
Spur Gear ◽  
Tooth Root ◽  
Contact Conditions ◽  
Tooth Contact ◽  
Mechanics Model ◽  
Large Amplitude Vibration

Spur gear tooth root strains are calculated using a finite element/contact mechanics formulation for varying gear speeds and applied torques. Extensive comparisons with experiments, including those from the literature and new ones, confirm that the finite element/contact mechanics formulation accurately predicts the quasi-static and dynamic tooth root strains. The finite element/contact mechanics model is used to investigate the features of the tooth root strain curves as the gears rotate kinematically and the tooth contact conditions change. Tooth profile modifications are shown to strongly affect the shape of the strain curve. At non-resonant speeds the dynamic tooth root strain curves have similar shapes as the quasi-static strain curves. At resonant speeds, however, the dynamic tooth root strain curves are drastically different because large amplitude vibration causes tooth contact loss.

Modeling the Nonlinear Vibration of a Spur Gear Pair

2000 ◽  
Author(s):  
R. G. Parker ◽  
S. M. Vijayakar ◽  
T. Imajou
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Surface ◽  
Nonlinear Phenomena ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Time Step ◽  
Mechanics Model ◽  
Wide Range

Abstract The dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model that offers significant advantages for dynamic gear analyses. The gear pair is analyzed across a wide range of operating speeds and torques. Comparisons are made to other researchers’ published experiments that reveal complex nonlinear phenomena. The nonlinearity source is contact loss of the meshing teeth, which, in contrast to the prevailing understanding, occurs even for large torques despite use of high-precision gears. A primary feature of the modeling is that dynamic mesh forces are calculated using detailed contact analysis at each time step as the gears roll through mesh; there is no need to externally specify the excitation in the form of time-varying mesh stiffness, static transmission error input, or the like. A semi-analytical model near the tooth surface is matched to a finite element solution away from the tooth surface, and the computational efficiency that results permits dynamic analysis. Two single degree of freedom models are discussed briefly. While one gives encouragingly good results, the second, which appears to have better mesh stiffness modeling, gives poor comparisons with experiments. The results indicate the sensitivity of such models to changing mesh stiffness representations.

3-D elastic coupling vibration and acoustical radiation characteristics of cracked gear under elastic support condition

2015 ◽  
Vol 23 (9) ◽  
pp. 1548-1568 ◽  
Author(s):  
Shao Renping ◽  
Purong Jia ◽  
Xiankun Qi
Keyword(s):  
Dynamic Response ◽  
Support System ◽  
Three Dimensional ◽  
Elastic Support ◽  
Dynamic Responses ◽  
Tooth Root ◽  
Support Condition ◽  
Elastic Boundary ◽  
Root Crack ◽  
Elastic Disc

According to the actual working condition of the gear, the supporting gear shaft is treated as an elastic support. Its impact on the gear body vibration is considered and investigated and the dynamic response of elastic teeth and gear body is analyzed. On this basis, the gear body is considered as a three-dimensional elastic disc and the gear teeth are treated as an elastic cantilever beam. Under the conditions of the elastic boundary (support shaft), combining to the elastic disk and elastic teeth, the influence of three-dimensional elastic discs on the meshing tooth response under an elastic boundary condition is also included. A dynamic model of the gear support system and calculated model of the gear tooth response are then established. The inherent characteristics of the gear support system and dynamics response of the meshing tooth are presented and simulated. It was shown by the results that it is correct to use the elastic support condition to analyze the gear support system. Based on the above three-dimensional elastic dynamics analysis, this paper set up a dynamics coupling model of a cracked gear structure support system that considered the influence of a three-dimensional elastic disc on a cracked meshing tooth under elastic conditions. It discusses the dynamic characteristic of the cracked gear structure system and coupling dynamic response of the meshing tooth, offering a three-dimensional elastic body model of the tooth root crack and pitch circle crack with different sizes, conducting the three-dimensional elastic dynamic analysis to the faulty crack. ANSYS was employed to carry out dynamic responses, as well as to simulate the acoustic field radiation orientation of a three-dimensional elastic crack body at the tooth root crack and pitch circle with different sizes.

On the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Three-Dimensional Gear Systems

2015 ◽  
Author(s):  
Nina Sainte-Marie ◽  
Philippe Velex ◽  
Guillaume Roulois ◽  
Franck Marrot
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
Test Rig ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Dynamic Transmission Error ◽  
Time Variations ◽  
The Relationship

A three-dimensional dynamic model is presented to simulate the dynamic behavior of single stage gears by using a combination of classic shaft, lumped parameter and specific 2-node gear elements. The mesh excitation formulation is based on transmission errors whose mathematical grounding is briefly described. The validity of the proposed methodology is assessed by comparison with experimental evidence from a test rig. The model is then employed to analyze the relationship between dynamic transmission errors and dynamic tooth loads or root stresses. It is shown that a linear dependency can be observed between the time variations of dynamic transmission error and tooth loading as long as the system can be assimilated to a torsional system but that this linear relationship tends to disappear when the influence of bending cannot be neglected.

Dynamic Transmission Error Measurements From Spur Gear Pairs Having Tooth Indexing Errors

2017 ◽  
Author(s):  
Brian Anichowski ◽  
Ahmet Kahraman ◽  
David Talbot
Keyword(s):  
High Speed ◽  
Transient Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Transient Effects ◽  
Dynamic Factors ◽  
Frequency Domains ◽  
Error Dynamic ◽  
Dynamic Transmission Error

This paper complements recent investigations [Handschuh et al (2014), Talbot et al (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur test gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. Both measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors.

scholarly journals Dynamic Response Analysis of Spur Gear System with Backlash

2021 ◽  
Vol 276 ◽  
pp. 01012
Author(s):  
Chao Li ◽  
Jigang Wang
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear System ◽  
Response Analysis ◽  
Response Curves ◽  
Nonlinear Dynamic Response ◽  
Dynamic Response Analysis ◽  
Return Difference

There are few studies on space-driven gear systems in the existing literature. In this paper, a spacedriven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. A nonlinear dynamic response analysis was performed. The backlash was introduced into the dynamic model, and the time-varying stiffness was corrected to make the theoretical model closer to reality. By comparing two kinds of dynamic response curves with and without return difference, it was illustrated that the influence of return difference on dynamic transmission error in a gear system. The results obtained in this paper provide a reference and basis for subsequent research.

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