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.

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.

Analysis of the Housing Vibration of a Rotorcraft Planetary Gear Using a Finite Element/Contact Mechanics Model

2017 ◽  
Author(s):  
Christopher G. Cooley ◽  
Adrian A. Hood
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Planetary Gear ◽  
Time Instant ◽  
Frequency Content ◽  
Contact Conditions ◽  
Gear Teeth ◽  
Mechanics Model ◽  
Parametric Studies ◽  
Frequency Components

This study investigates the planetary gear housing vibration for rotorcraft systems with equally spaced and diametrically opposed planets using a finite element/contact mechanics model. This approach permits accurate housing deflection calculations at each time instant that result from the changing contact conditions on all gear teeth and elastic deformations of each gear. Planetary gears with diametrically opposed planets have larger amplitude vibrations and more frequency content than those with equally spaced planets. Parametric studies show that although the frequency content does not change with changes in the system’s parameters, the amplitudes of response at these frequencies are meaningfully impacted. The frequency components of the acceleration spectra can have additional content when the planetary gear has manufacturing and assembly errors. Each error case results in different frequency content in the acceleration spectra. Understanding these housing vibrations is beneficial for interpreting measured accelerometer signals to detect and classify damage.

scholarly journals A Method of Selecting Grid Size to Account for Hertz Deformation in Finite Element Analysis of Spur Gears

1982 ◽  
Vol 104 (4) ◽  
pp. 759-764 ◽  
Author(s):  
J. J. Coy ◽  
C. Hu-Chih Chao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Gear Tooth ◽  
Spur Gear ◽  
Grid Size ◽  
Spur Gears ◽  
Element Analysis ◽  
Element Size ◽  
Full Effect ◽  
The Finite Element Analysis

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classic Hertzian solution for deflection. Many previous finite element studies of gear tooth deflection have not included the full effect of the Hertzian deflection. The present results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

scholarly journals Optimization of Tooth Root Profile Using Bezier Curve with G2 Continuity to Reduce Bending Stress of Asymmetric Spur Gear Tooth

2018 ◽  
Vol 237 ◽  
pp. 03010 ◽  
Author(s):  
Priyakant Vaghela ◽  
Jagdish Prajapati
Keyword(s):  
Stress Concentration ◽  
Gear Tooth ◽  
Spur Gear ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Tooth Root ◽  
Geometric Continuity ◽  
Bending Stress ◽  
Gear Design ◽  
G2 Continuity

This research describes simple and innovative approach to reduce bending stress at tooth root of asymmetric spur gear tooth which is desire for improve high load carrying capacity. In gear design at root of tooth circular-filleted is widely used. Blending of the involute profile of tooth and circular fillet creates discontinuity at root of tooth causes stress concentration occurs. In order to minimize stress concentration, geometric continuity of order 2 at the blending of gear tooth plays very important role. Bezier curve is used with geometric continuity of order 2 at tooth root of asymmetric spur gear to reduce bending stress.

Further Evaluation of Spur Gear Tooth Profile Designs Used in Heavily Loaded Transmissions

2011 ◽  
Author(s):  
Nihat Yıldırım ◽  
Hakan I˙s¸c¸i ◽  
Abdullah Akpolat
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Profile ◽  
Design Parameters ◽  
Preference Order ◽  
Spur Gears ◽  
Tooth Root ◽  
Contact Ratio ◽  
Practical Applications

Aerospace applications require special procedures for component design and manufacturing. Spur gears of different designs, because of their simpler geometries, are used in vital units-transmissions of helicopters and alike aerospace vehicles. In this study, performances of various profile designs of previously researched low and high contact ratio spur gears with some realistic design parameters are studied. Effects of the realistic parameters of variable tooth pair stiffness, relief shape, and adjacent pitch error on Transmission Error (TE), tooth loads and root stresses are presented; composition of these parameters determines the efficiency of the gearbox assembly. Detail of minimization of tooth root stress through optimized/proper design of relief is described. More comprehensive comparison of the gear tooth profile design cases is done to be able to guide aerospace transmission designers for practical applications with realistic parameters for each of the design cases. A preference order is done among the design cases, depending on effect of some design parameters on the results such as tooth loads, tooth root stresses, TE curves and peak-to-peak TE values.

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