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.

Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair

2018 ◽  
Vol 19 (3) ◽  
pp. 306 ◽  
Author(s):  
Yong Yang ◽  
Jiaxu Wang ◽  
Qinghua Zhou ◽  
Yanyan Huang ◽  
Jinxuan Zhu ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Analytical Description ◽  
Element Model ◽  
Spur Gear ◽  
Tooth Profile ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Proposed Model ◽  
Tooth Stiffness ◽  
Gear Mesh Stiffness

Some tooth profile geometric features, such as root fillet area, flank modification and wear are of nonnegligible importance for gear mesh stiffness. However, due to complexity of analytical description, their influence on mesh stiffness was always ignored by existing research works. The present work derives analytical formulations for time-varying gear mesh stiffness by using parametric equations of flank profile. Tooth geometry formulas based upon a rack-type tool are derived following Litvin's vector approach. The root fillet area and tooth profile deviations can therefore be fully considered for spur gear tooth stiffness evaluation. The influence of gear fillet determined by tip fillet radius of the rack-type tool is quantified parametrically. The proposed model is validated to be effective by comparing with a finite element model. Further, the model is applied to investigate the stiffness variations produced by tooth addendum modification, tooth profile nonuniform wear and modification.

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.

Coupled Bending-Torsion Vibration of Geared Rotors

1995 ◽  
Author(s):  
J. S. Rao ◽  
J. R. Chang ◽  
T. N. Shiau
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Mesh Stiffness ◽  
Present Program ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Torsion Vibration ◽  
Gear Mesh Stiffness

Abstract A general finite element model is presented for determining the coupled bending-torsion natural frequencies and mode shapes of geared rotors. Uncoupled bending and torsion frequencies are obtained for examples available in literature and the present program is verified against these. The effect of the gear box is considered to determine the coupled frequencies. Parameters studied include the pressure angle, gear mesh stiffness, and bearing properties. The gear pressure angle is shown to have no effect on the natural frequencies of rotors supported on isotropic bearing supports. Several case studies with bending-torsion coupling are considered and the results obtained are compared with those available in literature. The results of a general rotor system with 8lodes are also presented.

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.

Evaluation of spur gear mesh compliance using the finite element method

1999 ◽  
Vol 213 (6) ◽  
pp. 569-579 ◽  
Author(s):  
M H Arafa ◽  
M M Megahed
Keyword(s):  
Finite Element ◽  
Experimental Methods ◽  
Spur Gear ◽  
Spur Gears ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Fe Modelling ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

This paper presents a finite element (FE) modelling technique to evaluate the mesh compliance of spur gears. Contact between the engaging teeth is simulated through the use of gap elements. Analysis is performed on several gear combinations and the variation in tooth compliance along the contact location is presented in a non-dimensional form. Results are compared with earlier predictions based on analytical, numerical and experimental methods. Load sharing among the mating gear teeth is discussed, and the overall gear mesh stiffness together with its cyclic variation along the path of contact is evaluated.

Dynamic Features of Gear System With Tooth Crack and Tooth Surface Sliding due to Speed Variation

2012 ◽  
Author(s):  
Liming Wang ◽  
Zaigang Chen ◽  
Yimin Shao ◽  
Xi Wang
Keyword(s):  
Degrees Of Freedom ◽  
Surface Friction ◽  
Element Model ◽  
Spur Gear ◽  
Gear System ◽  
Tooth Surface ◽  
Dynamic Features ◽  
Mesh Stiffness ◽  
Speed Variation ◽  
Gear Mesh

It was found that the vibration features resulted from tooth crack and sliding on the contact interfaces due to speed variation are very similar with each other, which is difficult to distinguish. So, it is meaningful to study whether they are the same or not. Firstly, a finite element model of a spur gear pair in mesh with tooth crack at pitch circle is established to calculate the effect of tooth crack on gear mesh stiffness. Then, combined with the tooth crack through mesh stiffness, a spur gear dynamic model with six degrees of freedom (dof) is developed to extract the dynamic features affected by the tooth crack. The tooth surface friction due to different relative velocity is also involved to study its effects on the dynamic characteristics of the gear system. Finally, comparisons are made between the dynamic features of the gear system with tooth crack and the tooth surface sliding to expose their effects to supply some theoretical guidance on fault detection.

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.

Study on Minimum Teeth without Undercutting of Involute Gears with 14.5 Degree Pressure Angle

2013 ◽  
Vol 544 ◽  
pp. 497-501
Author(s):  
Chao Zhang ◽  
Jia Ning He ◽  
Yong Gao ◽  
Xu Lei Deng
Keyword(s):  
Spur Gear ◽  
Bevel Gear ◽  
Theoretical Derivation ◽  
Cylindrical Gear ◽  
Correct Number ◽  
Pressure Angle ◽  
Generating Method ◽  
Involute Gears

Study on minimum teeth without undercutting for considering the rack cutter’s addendum c*m of a kind of gear with 14.5 degree pressure angle, and the gear standard No is B436-1940 and used in UK. Based on the generating method, reasons for undercut phenomena is analyzed, and the numbers of minimum teeth without undercutting of the involute spur gear, involute helical cylindrical gear and involute spur bevel gear are theoretically analyzed and figured out. The correct number of minimum teeth without undercutting of gear with 14.5 degree pressure angle is given, and also illustrated the validity of theoretical derivation.

scholarly journals Improvement on Meshing Stiffness Algorithms of Gear with Peeling

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 609
Author(s):  
Lingli Cui ◽  
Tongtong Liu ◽  
Jinfeng Huang ◽  
Huaqing Wang
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Gear Wheel ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Involute Gears ◽  
Gear Mesh Stiffness ◽  
Meshing Process

This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.

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