A Study of Spur Gear Geometry Factor Through Complex Potential Analysis

1989 ◽  
Vol 111 (3) ◽  
pp. 433-438 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Complex Potential ◽  
Sliding Friction ◽  
Spur Gear ◽  
Potential Method ◽  
Theory Of Elasticity ◽  
Spur Gears ◽  
Geometry Factor ◽  
The Coefficient Of Friction ◽  
Bending Stresses ◽  
Complex Potential Method

Bending stresses in spur gears have been obtained analytically using the Complex Potential Method of the two-dimensional theory of elasticity and conformal mapping of the tooth profile. Effects of profile shift and sliding friction on geometry factor have been studied for 20 deg pressure angle and numbers of teeth ranging from 20 to 150. It has been shown how these results can be applied to obtain a geometry factor corrected to include either the profile or the coefficient of friction effect in a given gear pair.

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.

Complex Analysis of Plane Problem of Two-Dimensional Quasicrystals

2012 ◽  
Vol 236-237 ◽  
pp. 52-54
Author(s):  
Lin Yang ◽  
Qin He ◽  
Shu Yong Zhou ◽  
Wu Li
Keyword(s):  
Stress Concentration ◽  
Plane Problem ◽  
Complex Potential ◽  
Fracture Behavior ◽  
Complex Analysis ◽  
Potential Method ◽  
Two Dimensional ◽  
Complex Potential Method ◽  
Important Significance

The fracture behavior of materials and structures are always caused by stress concentration near the defects in materials. This article describes the complex potential method for solving plane problems of quasicrystalline materials with defects. In order to prove effectiveness and success of the method, an example is given, and the results have very important significance in studying two-dimensional quasicrystals.

The Interaction between a Dislocation and Circular Inhomogeneity in 1D Hexagonal Quasicrystals

2010 ◽  
Vol 34-35 ◽  
pp. 429-434
Author(s):  
Ya Qun Hu ◽  
Ping Xia ◽  
Ke Xiang Wei
Keyword(s):  
Elastic Constant ◽  
Complex Potential ◽  
Image Force ◽  
Potential Method ◽  
Complex Potentials ◽  
Explicit Solutions ◽  
Circular Inhomogeneity ◽  
The Matrix ◽  
Complex Potential Method ◽  
1D Hexagonal Quasicrystals

The interaction between a dislocation and circular inhomogeneity in 1D hexagonal quasicrystals is investigated. By using the complex potential method, explicit solutions of complex potentials are obtained. The image force acting on the dislocation are also derived. The results show that the interface attracts the dislocation inside both the matrix and the inhomogeneity under most condition. The attraction increase with the increase of the elastic constant of phason field and the phonon-phason coupling elastic constant.

A New Photoelastic Investigation of the Dynamic Bending Stress of Spur Gears

2003 ◽  
Vol 125 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Ming-Jong Wang
Keyword(s):  
Critical Points ◽  
Gear Tooth ◽  
Spur Gear ◽  
Behavioral Characteristics ◽  
Spur Gears ◽  
Bending Stress ◽  
Dynamic Effects ◽  
Contact Points ◽  
Photoelastic Investigation ◽  
Bending Stresses

In this paper, the maximum tensile bending stress (MTBS) and the critical point in the root fillet of spur gear tooth during transmission are determined by a digital photoelastic system involving real time imaging. The behavioral characteristics of the bending stresses of the gear tooth are analyzed at different rotation speeds, transmitted torques, and contact points. Then, the dynamic effects, the various critical points and the maximum tensile bending stresses are compared experimentally and theoretically, and discussed. Finally, the best approaches for determining the maximum bending stress and its position in the root fillet of spur gear tooth are recommended.

scholarly journals Interaction between a Macrocrack and a Cluster of Microcracks by Muskhelishvili’s Complex Potential Method

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Xu Li ◽  
Xiaotao Li ◽  
Hongda Yang ◽  
Xiaoyu Jiang
Keyword(s):  
Inclination Angle ◽  
Complex Potential ◽  
Great Influence ◽  
Tensile Load ◽  
Potential Method ◽  
Elastic Plane ◽  
Inclination Angles ◽  
Complex Potential Method ◽  
Stress Boundary Conditions ◽  
Stress Boundary

The interaction between a macrocrack and a cluster of microcracks has been investigated based on Muskhelishvili’s complex potential method. A step-by-step subproblem procedure is used to satisfy the stress boundary conditions on each crack surface. The interactions between a cluster of microcracks and a macrocrack and the interaction among microcracks are analyzed. Three damage configurations as chained, reverse-chained, and randomly distributed microcracks have been designed to simulate the damage around the macrocrack tip. The solution of an infinite elastic plane containing a macrocrack and a cluster of microcracks is presented for the plane subjected to a uniform tensile load. The stress intensity factor (SIF) at the macrocrack tip and the microcrack tips is obtained. The results show that the inclination angle of the microcrack and the distance between the macrocrack and microcracks have a great influence on SIF. When the inclination angle is small, the SIF at microcrack tips may be larger than other inclination angles. These results are helpful to analyze the fracture or damage behaviors of materials.

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