The Static Transmission Error of Cracked Spur Gear Teeth Using FEA

1998 ◽  
Author(s):  
Seney Sirichai ◽  
Ian Howard ◽  
Laurie Morgan ◽  
Kian Teh
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Mesh Stiffness ◽  
Element Analysis ◽  
Angular Rotation ◽  
Simple Strategy ◽  
Static Transmission Error ◽  
The Individual

Abstract This paper considers a Finite Element Model which is used to predict the torsional mesh stiffness and static transmission error of a pair of spur gears in mesh. The model involves the use of 2D plain strain elements, coupled with contact elements at the points of contact between the meshing teeth. A simple strategy of how to determine an appropriate value of the penalty parameter of the contact elements (gap element) is also presented. When gears are unloaded, a pinion and gear with perfect involute profiles, should theoretically run with zero transmission error. However, when gears with involute profiles are loaded, the individual torsional mesh stiffness of each gear changes throughout the mesh cycle, causing variations in angular rotation of the gear body and subsequent transmission error. The theoretical changes in the torsional mesh stiffness throughout the mesh cycle are developed using finite element analysis and related to the static transmission error. A 5mm through thickness tooth crack is also modelled, and the comparison of the torsional mesh stiffness and static transmission error with and without the tooth crack is discussed.

An Experimental Investigation of the Static Transmission Error and Torsional Mesh Stiffness of Nylon Gears

2007 ◽  
Author(s):  
Chuan Wen Chi ◽  
Ian Howard ◽  
Jian De Wang
Keyword(s):  
Experimental Investigation ◽  
Research Work ◽  
Transmission Error ◽  
Statistical Data Analysis ◽  
Mesh Stiffness ◽  
Element Analysis ◽  
Static Transmission Error ◽  
Series Of Experiments ◽  
The Individual ◽  
The Relationship

This paper details an investigation of the relationship between the static individual torsional mesh stiffness and the static transmission error of gears in mesh. The investigations of the individual torsional mesh stiffness are one of the fundamental concepts in gear analysis and behaviour that have been used in recent years for predicting transmission error. The research work for this paper has two main parts. The first part involved measuring the static transmission error of gears through a series of experiments. An existing test rig was used for the experimental investigation where a nylon gear was placed in mesh with a fixed aluminium gear under various torques. Measurements of the rotation of the nylon gear at precise angular positions throughout the mesh cycle were used as a basis for determining the torsional mesh stiffness and the static transmission error. The second part involved the use of numerical analysis tools (FEA) to calculate the theoretical static transmission error and the individual torsional mesh stiffness in the same conditions as the experiments. The validity of the theory of individual torsional mesh stiffness was investigated, through a comparison between the experimental results and the FEA modelling results. The work included experiments, finite element analysis modelling, and statistical data analysis. The final results of this paper showed that individual torsional mesh stiffness theory can effectively predict transmission error in gear transmission systems, however some improvements need to be made to both the theory and the experiments.

BIDIMENSIONAL FINITE ELEMENT ANALYSIS OF SPUR GEAR: STUDY OF THE MESH STIFFNESS AND STRESS AT THE LEVEL OF THE TOOTH FOOT

2009 ◽  
Vol 33 (2) ◽  
pp. 175-187 ◽  
Author(s):  
Mohamed Nizar Bettaieb ◽  
Mohamed Maatar ◽  
Chafik Karra
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Spur Gear ◽  
Fortran Program ◽  
Mesh Stiffness ◽  
Element Analysis ◽  
Gear Mesh ◽  
Finite Element Software ◽  
Time Calculation ◽  
Finite Element Meshing

The purpose of this work is to determine the spur gear mesh stiffness and the stress state at the level of the tooth foot. This mesh stiffness is derived from the calculation of the normal tooth displacements: local displacement where the load is applied, tooth bending displacement and body displacement [15]. The contribution of this work consists in, basing on previous works, developing optimal finite elements model in time calculation and results precision. This model permits the calculation of time varying mesh stiffness and the evaluation of stress state at the tooth foot. For these reasons a specific Fortran program was developed. It permit firstly, to obtain the gear geometric parameters (base radii, outside diameter,…) and to generate the data base of the finite element meshing of a tooth or a gear. This program is interfaced with the COSMOS/M finite element software to predict the stress and strain state and calculate the mesh stiffness of a gear system. It is noted that the mesh stiffness is periodic and its period is equal to the mesh period.

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

Numerical and experimental investigation of a spur gear pair with unloaded static transmission error

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Duncai Lei ◽  
Xiannian Kong ◽  
Siyu Chen ◽  
Jinyuan Tang ◽  
Zehua Hu
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Content Type ◽  
High Order Harmonic ◽  
Static Transmission Error ◽  
Harmonic Components

Purpose The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE). Design/methodology/approach A simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally. Findings The predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load. Originality/value This study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

Effects of tip relief on vibration responses of a geared rotor system

2013 ◽  
Vol 228 (7) ◽  
pp. 1132-1154 ◽  
Author(s):  
Hui Ma ◽  
Jian Yang ◽  
Rongze Song ◽  
Suyan Zhang ◽  
Bangchun Wen
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Spur Gear ◽  
Rotor System ◽  
Time Varying ◽  
Frequency Range ◽  
Mesh Stiffness ◽  
Resonance Frequencies ◽  
Vibration Responses

Considering tip relief, a finite element model of a spur gear pair in mesh is established by ANSYS software. Time-varying mesh stiffness under different amounts of tip relief is calculated based on the finite element model. Then, a finite element model of a geared rotor system is developed by MATLAB software considering the effects of time-varying mesh stiffness and constant load torque. Emphasis is given to the effects of tip relief on the lateral–torsional coupling vibration responses of the system. The results show that as the amount of tip relief increases, the saltation of time-varying mesh stiffness reduces at the position of approach action and transition mesh region from the single tooth to double tooth. A number of primary resonances and some super-harmonic of gears 1 and 2 are excited by time-varying mesh stiffness in amplitude frequency responses. As the amount of tip relief increases, some super-harmonic responses change due to the variation in the higher frequency components of time-varying mesh stiffness. After tip relief, the vibration and meshing force decrease obviously at lower mesh frequency range except at some resonance frequencies; however, tip relief is not effective in reducing the vibration at higher mesh frequency range. The amplitude fluctuation of the vibration acceleration reduces evidently after considering tip relief, which is not remarkable with the increase of meshing frequency.

scholarly journals Dynamic Analysis of Geared Rotors by Finite Elements

1992 ◽  
Vol 114 (3) ◽  
pp. 507-514 ◽  
Author(s):  
A. Kahraman ◽  
H. Nevzat Ozguven ◽  
D. R. Houser ◽  
J. J. Zakrajsek
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Axial Loading ◽  
Element Model ◽  
Transmission Error ◽  
Analysis Procedure ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Transverse Vibrations ◽  
Forced Vibration Analysis

A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.

An Estimate of Mesh Stiffness and Load Sharing Ratio of a Spur Gear Pair

1992 ◽  
Author(s):  
J. H. Kuang ◽  
Y. T. Yang
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Spur Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Stiffness Constant ◽  
Generating Method ◽  
Single Tooth ◽  
Tooth Stiffness ◽  
Involute Gears

Abstract A curve fitted tooth stiffness equation was developed to calculate directly the variable gear mesh stiffness. To improve the accuracy, a tooth profile generating method introduced by Litvin (1989) was employed for finite element idealization. A quadratic finite element model was employed in deriving the tooth stiffness constant at the successive positions of a single tooth as it passed through the zone of loading. The developed stiffness equation is applicable to both the standard full-depth or addendum modified involute gears. Variation of the shared loads introduced by the consideration of mesh stiffness was also investigated.

Strength Evaluation of Polymer Composite Spur Gear by Finite Element Analysis

2008 ◽  
Author(s):  
Mohammad Robiul Hossan ◽  
Zhong Hu
Keyword(s):  
Finite Element ◽  
Polymer Composite ◽  
Volume Fraction ◽  
Gear Tooth ◽  
Axial Stress ◽  
High Stress ◽  
Element Model ◽  
Simulation Method ◽  
Spur Gear ◽  
Element Analysis

Modern advanced polymer composite materials have opened a new level of noiseless, lubricant free, high resilience and precision gearing in power and motion transmission. The proper understanding and evaluation of gear strength and performance is an important prerequisite for any reliable application. In this paper, a 20% short glass fiber reinforced nylon66 spur gear fabricated by injection molding has been carefully investigated. A three-dimensional finite element model was used to simulate the multi-axial stress-strain behaviors of a gear tooth under the dynamic load for a complete working cycle with a special geometry, operating condition, fiber orientation and volume fraction. The strength of composite gears has been compared with isotropic un-reinforced nylon66 and steel gears. The tooth root region of a gear which usually experiences high stress and potential to failure has been carefully investigated. This computer simulation method can be used as a useful tool for evaluating strength and predicting failure of the polymer composite gears.

Sign in / Sign up

Export Citation Format

Share Document