Aspects Regarding the Evaluation of the Gearing Tooth Stiffness

2020 ◽  
pp. 313-323
Author(s):  
Daniela Ghelase ◽  
Luiza Daschievici
Keyword(s):  
Tooth Stiffness

Delay-Bond Graph Models for Geared Torsional Systems

1974 ◽  
Vol 41 (2) ◽  
pp. 366-370 ◽  
Author(s):  
N. T. Tsai ◽  
S. M. Wang
Keyword(s):  
Transmission Line ◽  
Gear Tooth ◽  
Nonlinear Damping ◽  
Bond Graph ◽  
Dynamic Responses ◽  
State Variables ◽  
Graph Models ◽  
Wave Variables ◽  
Tooth Stiffness ◽  
Line Elements

The dynamic responses of geared torsional systems are analyzed with the delay-bond graph technique. By transforming the power variables into torsional wave variables, the torsional elements are modeled as transmission line elements. The nonlinear elements, e.g., varying tooth stiffness, gear-tooth backlash, and nonlinear damping, are incorporated into the ideal transmission line element. A computational algorithm is established where the state variables of the system are expressed in terms of wave scattering variables and the dynamic responses are then obtained in both time and space domains. The simulation results of several simple examples of linear and nonlinear geared torsional systems are presented to demonstrate the feasibility of this algorithm.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

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.

Vibration-Based Early Crack Diagnosis With Machine Learning for Spur Gears

2020 ◽  
Author(s):  
Fatih Karpat ◽  
Ahmet Emir Dirik ◽  
Onur Can Kalay ◽  
Oğuz Doğan ◽  
Burak Korcuklu
Keyword(s):  
Machine Learning ◽  
Fault Diagnosis ◽  
High Speed ◽  
Crack Detection ◽  
Power Transmission ◽  
Calculated Data ◽  
Design Parameters ◽  
Tooth Stiffness ◽  
Vibration Responses ◽  
Root Crack

Abstract Gear mechanisms are one of the most significant components of the power transmission systems. Due to increasing emphasis on the high-speed, longer working life, high torques, etc. cracks may be observed on the gear surface. Recently, Machine Learning (ML) algorithms have started to be used frequently in fault diagnosis with developing technology. The aim of this study is to determine the gear root crack and its degree with vibration-based diagnostics approach using ML algorithms. To perform early crack detection, the single tooth stiffness and the mesh stiffness calculated via ANSYS for both healthy and faulty (25-50-75-100%) teeth. The calculated data transferred to the 6-DOF dynamic model of a one-stage gearbox, and vibration responses was collected. The data gathered for healthy and faulty cases were evaluated for the feature extraction with five statistical indicators. Besides, white Gaussian noise was added to the data obtained from the 6-DOF model, and it was aimed at early fault diagnosis and condition monitoring with ML algorithms. In this study, the gear root crack and its degree analyzed for both healthy and four different crack sizes (25%-50%-75%-100%) for the gear crack detection. Thereby, a method was presented for early fault diagnosis without the need for a big experimental dataset. The proposed vibration-based approach can eliminate the high test rig construction costs and can potentially be used for the evaluation of different working conditions and gear design parameters. Therefore, catastrophic failures can be prevented, and maintenance costs can be optimized by early crack detection.

LOAD AND STRESS ANALYSIS OF CYLINDRICAL WORM GEARING USING TOOTH SLICING METHOD

2006 ◽  
Vol 30 (1) ◽  
pp. 97-111 ◽  
Author(s):  
A.H. Falah ◽  
A.H. Elkholy
Keyword(s):  
Spur Gear ◽  
Operating Conditions ◽  
Stress Distributions ◽  
Worm Gearing ◽  
Tooth Stiffness ◽  
Worm Gears ◽  
Foundation Deformation ◽  
Stiffness Variation ◽  
Slicing Method

A method for the determination of load and stress distributions of the instantaneously engaged teeth of cylindrical worm gears is represented in this paper. The method is based on the assumption that both the worm and gear can be modeled as a series of spur gear slices. The exact geometry and point of load application of each slice depends on its location within the mesh. By calculating the applied load and stress for each slice, the same can be determined for the entire worm gear set. The method takes into consideration tooth stiffness variation from root to tip, tooth bending deflection, local contact deformation, tooth foundation deformation and, the influence of gear parameters on load and stress. Calculated results were found to be in agreement with experimental and analytical ones obtained from literature under given operating conditions.

scholarly journals Enhanced application limits for crossed helical gearboxes using new geometries for smaller sliding paths or smaller contact pressures

2019 ◽  
Vol 287 ◽  
pp. 01010
Author(s):  
Christoph Boehme ◽  
Dietmar Vill ◽  
Peter Tenberge
Keyword(s):  
Calculation Method ◽  
Helix Angle ◽  
Helical Gear ◽  
Design Parameters ◽  
Helical Gears ◽  
Positive Effects ◽  
Tooth Stiffness ◽  
Lubrication Condition ◽  
Overlap Ratio ◽  
Helical Gear Pair

Crossed-axis helical gear units are used as actuators and auxiliary drives in large quantities in automotive applications such as window regulators, windscreen wipers and seat adjusters. Commonly gear geometry of crossed helical gears is described with one pitch point. This article deals with an extended calculation method for worm gear units. The extended calculation method increases the range of solutions available for helical gears. In general, for a valid crossed helical gear pair, the rolling cylinders do not have to touch each other. In mass production of many similar gears, individual gears can be reused because they can be paired with other centre distances and ratios. This also allows the use of spur gears in combination with a worm, making manufacturing easier and more efficient. By selecting design parameters, for example the axis crossing angle or the helix angle of a gear, positive effects can be achieved on the tooth contact pressure, the overlap ratio, the sliding paths, the lubrication condition, the tooth stiffness and, to a limited extent, on the efficiency of the gearing. It can be shown that for involute helical gears, in addition to the known insensitivity of the transmission behaviour to centre distance deviations, there is also insensitivity to deviations of the axis crossing angle. This means that installation tolerances for crossed helical gearboxes can be determined more cost-effectively.

Investigating Vibration Sources of Faulty Gear Units

2008 ◽  
Vol 385-387 ◽  
pp. 601-604
Author(s):  
Ales Belsak ◽  
Joze Flasker
Keyword(s):  
Signal Analysis ◽  
Analysis Tool ◽  
Tooth Root ◽  
Dynamic Parameters ◽  
Unit Operation ◽  
Time Frequency ◽  
Tooth Stiffness ◽  
Non Stationary Signal ◽  
High Degree ◽  
Very High

A crack in the tooth root is the least desirable damage of gear units, which often leads to failure of gear unit operation. A possible damage can be identified by monitoring vibrations. The influences that a crack in the tooth root of a single-stage gear unit has upon vibrations are dealt with. Changes in tooth stiffness are much more expressed in relation to a fatigue crack in the tooth root, whereas in relation to other faults, changes of other dynamic parameters are more expressed. Signal analysis has been performed in relation to a non-stationary signal, by means of the Time Frequency Analysis tool, such as Wavelets. Typical scalogram patterns resulting from reactions to faults or damages indicate the presence of faults or damages with a very high degree of reliability.

The torsional stiffness of involute spur gears

2004 ◽  
Vol 218 (1) ◽  
pp. 131-142 ◽  
Author(s):  
J Wang ◽  
I Howard
Keyword(s):  
Finite Element ◽  
Gear Tooth ◽  
Torsional Stiffness ◽  
Spur Gears ◽  
Adaptive Meshing ◽  
Mesh Stiffness ◽  
Finite Element Program ◽  
Tooth Stiffness ◽  
Element Program ◽  
The Individual

This paper presents the results of a detailed analysis of torsional stiffness of a pair of involute spur gears in mesh using finite element methods. Adaptive meshing has been employed within a commercial finite element program to reveal the detailed behaviour in the change over region from single- to double-tooth contact zones and vice versa. Analysis of past gear tooth stiffness models is presented including single- and multitooth models of the individual and combined torsional mesh stiffness. The gear body stiffness has been shown to be a major component of the total mesh stiffness, and a revised method for predicting the combined torsional mesh stiffness is presented. It is further shown tha the mesh stiffness and load sharing ratios will be a function of applied load.

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