Numerical Implementation of Complex Potentials for Gear Tooth Stress Analysis

1981 ◽  
Vol 103 (2) ◽  
pp. 460-465 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Mathematical Programming ◽  
Conformal Mapping ◽  
Stress Analysis ◽  
Gear Tooth ◽  
Spur Gear ◽  
Complex Potentials ◽  
Numerical Implementation ◽  
Gear Teeth ◽  
Transformation Parameters

Stresses in spur gear teeth can be calculated by the complex potentials method, using a generalization of Hirano’s conformal mapping. Mathematical programming is used to fit the transformation to a given profile as closely as desired. Complete formulas for stresses and displacements are given in terms of the transformation parameters. Results are compared with other published values.

Computer Implementation of an Optimal Conformal Mapping for Gear Tooth Stress Analysis

1989 ◽  
Vol 111 (2) ◽  
pp. 297-305 ◽  
Author(s):  
M. J. Richard ◽  
D. Pare ◽  
A. Cardou
Keyword(s):  
Conformal Mapping ◽  
Stress Analysis ◽  
Computer Aided Design ◽  
Gear Tooth ◽  
Spur Gear ◽  
Concentrated Load ◽  
New Approach ◽  
Gear Teeth ◽  
Aided Design ◽  
Mapping Theory

This paper describes a computerized version of the complex potential approach which is a comprehensive mathematical model for the stress analysis of spur gear teeth. The entire procedure is a basic application of Hirano’s conformal mapping theory in which laws of elasticity have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The algorithm is eminently well-suited for computer-aided-design of gear teeth; it serves as the basis for an interactive computer program which can model a gear tooth and can calculate the stresses and displacements within the tooth when subjected to a concentrated load. Results are compared with AGMA’s and other published values.

scholarly journals Study of Lubricant Jet Flow Phenomena in Spur Gears

1975 ◽  
Vol 97 (2) ◽  
pp. 283-288 ◽  
Author(s):  
L. S. Akin ◽  
J. J. Mross ◽  
D. P. Townsend
Keyword(s):  
Motion Picture ◽  
High Speed ◽  
Drop Size ◽  
Gear Tooth ◽  
Jet Flow ◽  
Spur Gear ◽  
Spur Gears ◽  
Gear Teeth ◽  
Flow Phenomena ◽  
Oil Jet

Lubricant jet flow impingement and penetration depth into a gear tooth space were measured at 4920 and 2560 using a 8.89-cm- (3.5-in.) pitch dia 8 pitch spur gear at oil pressures from 7 × 104 to 41 × 104 N/m2 (10 psi to 60 psi). A high speed motion picture camera was used with xenon and high speed stroboscopic lights to slow down and stop the motion of the oil jet so that the impingement depth could be determined. An analytical model was developed for the vectorial impingement depth and for the impingement depth with tooth space windage effects included. The windage effects on the oil jet were small for oil drop size greater than 0.0076 cm (0.003 in.). The analytical impingement depth compared favorably with experimental results above an oil jet pressure of 7 × 104 N/m2 (10 psi). Some of this oil jet penetrates further into the tooth space after impingement. Much of this post impingement oil is thrown out of the tooth space without further contacting the gear teeth.

Finite Element Application of Gear Tooth Analysis

2014 ◽  
Vol 889-890 ◽  
pp. 527-531
Author(s):  
V. Balambica ◽  
T. Jayachandra Prabhu ◽  
R. Venkatesh Babu
Keyword(s):  
Dynamic Load ◽  
Gear Tooth ◽  
Design Procedure ◽  
Spur Gear ◽  
Dynamic Loads ◽  
Historical Period ◽  
Simple Design ◽  
Gear Teeth ◽  
Gear Design ◽  
Stiffness Characteristics

Gears play an important role in every aspect of power and motion of transmission from historical period to modern day period . Due to this , gear design has become a complicated art.A considerable amount of research has been carried out to determine the amount of dynamic gear tooth loads acting.The findings of the dynamic load between the gear teeth results in difficulty for the designer.In this paper, an effort has been made to formulate a simple design procedure for calculating the dynamic load .Earlier the stiffness characteristics and deformation of the gear tooth were studied to predict the dynamic load acting. This was developed with the tooth assumed as a short cantilever.Whereas in reality, an involute profile exists in a spur gear tooth.Based on this reality, work has been done to model the exact profile of the tooth.Later ,the stiffness characteristics were carefully analysed and an improvement was thus made. It was proved that FEA is one such technique that can be used for predicting dynamic loads acting on a gear tooth.

scholarly journals An Analysis of the Surface Geometric Structure and Geometric Accuracy of Cylindrical Gear Teeth Manufactured with the Direct Metal Laser Sintering (DMLS) Method

2019 ◽  
Author(s):  
Jadwiga Małgorzata Pisula ◽  
Grzegorz Budzik ◽  
Łukasz Przeszłowski
Keyword(s):  
Surface Roughness ◽  
Geometric Structure ◽  
Gear Tooth ◽  
Spur Gear ◽  
Laser Sintering ◽  
Tooth Surface ◽  
Direct Metal Laser Sintering ◽  
Cylindrical Gear ◽  
Sand Blasting ◽  
Gear Teeth

This paper presents findings concerning the accuracy of the geometry of cylindrical spur gear teeth manufactured with the direct metal laser sintering (DMLS) method. In addition, the results of the evaluation of the tooth surface geometric structure are presented in the form of selected two-dimensional and three-dimensional surface roughness parameters. An analysis of the accuracy of the fabricated gear teeth was performed after gear sand-blasting and gear tooth milling processes. Surface roughness was measured before and after sand-blasting and gear tooth milling. The test gear wheel was manufactured from GP1 high-chromium stainless steel on an EOS M270 machine.

Analysis of the Vibration Response of a Gearbox With Gear Tooth Faults

2004 ◽  
Author(s):  
Xinhao Tian ◽  
Ming J. Zuo ◽  
Ken R. Fyfe
Keyword(s):  
Gear Tooth ◽  
Spur Gear ◽  
Vibration Response ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Vibration Model ◽  
Vibration Signatures ◽  
Potential Energy Method ◽  
The Relationship

In this study, the steady-state vibration response of a gearbox with gear tooth faults is investigated. Based on the analytical expression of the position-dependent mesh stiffness of the gear with perfect gear teeth derived with the potential energy method and the characteristics of involute gear teeth, expressions of the mesh stiffness of a gear with tooth faults such as tooth chip, tooth crack, and tooth breakage are derived. Using a coupled lateral and torsional vibration model of a one-stage spur gear pair, we have numerically solved a set of nonlinear equations and obtained typical vibration response diagrams of the gear pair with perfect gears and gears with tooth faults. This study reveals the relationship between the waveforms of the vibration and the types of local faults of the gear. These results are useful for identification of vibration signatures when there are these types of tooth faults.

Calculation of Spur Gear Tooth Flexibility by the Complex Potential Method

1985 ◽  
Vol 107 (1) ◽  
pp. 38-42 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Singular Point ◽  
Complex Potential ◽  
Gear Tooth ◽  
Contact Point ◽  
Spur Gear ◽  
Potential Method ◽  
Complex Potentials ◽  
Spur Gears ◽  
Tooth Contact ◽  
Complex Potential Method

Complex potentials have already been used to calculate analytically spur gear stresses. However, their application to the calculation of tooth flexibility is not so straightforward since displacements of interest are at the tooth contact point, which is a singular point for the equations being used. A method has been devised to circumvent this difficulty and to obtain the value of the displacement at each point of the line of action, and thus, the flexibility of a given pair of spur gears.

Gear tooth stress analysis by the complex potentials method

Meccanica ◽  
1992 ◽  
Vol 27 (2) ◽  
pp. 105-110 ◽  
Author(s):  
Gianni Nicoletto
Keyword(s):  
Stress Analysis ◽  
Gear Tooth ◽  
Complex Potentials

The Stress Intensity Factor and Stiffness for a Cracked Spur Gear Tooth

1994 ◽  
Vol 116 (3) ◽  
pp. 697-700 ◽  
Author(s):  
S. R. Daniewicz ◽  
J. A. Collins ◽  
D. R. Houser
Keyword(s):  
Stress Intensity ◽  
Gear Tooth ◽  
Fatigue Cracks ◽  
Spur Gear ◽  
Potential Method ◽  
Mapping Technique ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Face Width ◽  
Tooth Pair

The stiffness of a spur gear tooth mesh controls load sharing in an operating gearset as well as vibratory properties which further dictate fatigue resistance and gear noise. A spur gear mesh consisting of a pinion with a single cracked tooth and an uncracked gear is considered. Expressions are presented which allow the determination of stress intensity factors for small through face width fatigue cracks in spur gear teeth. Predictions of tooth pair stiffness for a cracked pinion tooth and uncracked gear tooth pair are made using an analytical model. The model is based on elastic energy methods and fracture mechanics principles. The model employs a conformal mapping technique from elasticity theory, often denoted in spur gear applications as the complex potential method, in which a gear tooth is mapped onto on elastic half-plane.

Contact between Logarithmic Crowned Teeth of Spur Gear Transmission

2015 ◽  
Vol 740 ◽  
pp. 69-78 ◽  
Author(s):  
Ting Ting Jin ◽  
Jiu Gen Wang ◽  
Shou Song Jin ◽  
Zhen Rong Wang
Keyword(s):  
Stress Concentration ◽  
Gear Tooth ◽  
Subsurface Layer ◽  
Spur Gear ◽  
Gear Transmission ◽  
Von Mises Stress ◽  
Tooth Surface ◽  
Gear Teeth ◽  
Deformation Equation ◽  
Von Mises

Gear tooth modification such as lead crowning can reduce stress concentration at the edges of the gear teeth; therefore prolong the fatigue life of gears. A logarithmical lead profile was applied on spur gears and the surface coordinate equation of logarithmic crowned tooth for manufacturing was established. On the basis of the contact mechanics model, the deformation equation of compatibility and load equilibrium equation were solved with an iterative numerical algorithm, and the corresponding programs were developed in Matlab to calculate the distributions of contact stress and von Mises stress field inside the subsurface layer at any meshing position. The numerical results of some typical examples show that the level of stress concentration before modification changes with the engaging locations of the gear teeth, and so does the amount of logarithmic modification along the line of contact, which can completely eliminate the edge effects of tooth surface at every meshing position during the spur gear transmission process, and thus improves the fatigue resistance of gear teeth surfaces.

The Stress Intensity Factor and Stiffness for a Cracked Spur Gear Tooth

1992 ◽  
Author(s):  
S. R. Daniewicz ◽  
J. A. Collins ◽  
Donald R. Houser
Keyword(s):  
Stress Intensity ◽  
Gear Tooth ◽  
Fatigue Cracks ◽  
Spur Gear ◽  
Potential Method ◽  
Mapping Technique ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Face Width ◽  
Tooth Pair

Abstract The stiffness of a spur gear tooth mesh controls load sharing in an operating gearset as well as vibratory properties which further dictate fatigue resistance and gear noise. A spur gear mesh consisting of a pinion with a single cracked tooth and an uncracked gear is considered. Expressions are presented which allow the determination of stress intensity factors for small through face width fatigue cracks in spur gear teeth. Predictions of tooth pair stiffness for a cracked pinion tooth and uncracked gear tooth pair are made using an analytical model. The model is based on elastic energy methods and fracture mechanics principles. The model employs a conformal mapping technique from elasticity theory, often denoted in spur gear applications as the complex potential method, in which a gear tooth is mapped onto an elastic half-plane.

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