scholarly journals Revised Lewis Bending Stress Capacity Model

2020 ◽  
Vol 14 (1) ◽  
pp. 1-14
Author(s):  
Edward. E. Osakue ◽  
Lucky Anetor
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Gear Tooth ◽  
Shear Stresses ◽  
Bending Stress ◽  
Moment Arm ◽  
Contact Ratio ◽  
Helical Gears ◽  
Cylindrical Gears

Background: During operation, cylindrical gearset experiences tangential, radial, and axial (helical gears only) force components that induce bending, compressive, and shear stresses at the root area of the gear tooth. Accurate estimation of the effective bending stress at the gear root is a challenge. Lewis was the first person who attempted estimating the root bending stress of spur gears with some reasonable accuracy. Various gear standards and codes in use today are modifications and improvements of the Lewis model. Objective: This research aims at revising the Lewis model by making adjustments for dynamic loads, shear stresses, axial bending stress for helical gears, and stress concentration factor that is independent on the moment arm of tangential or axial force component. Methods: An analytical approach is used in formulating a modified formula for the root bending stress in cylindrical gears starting with the original Lewis model. Intermediate expressions are developed in the process and works from many previous authors are reviewed and summarized. The new model developed is used to estimate the root bending stress in four example gearsets of 0o to 41.41o helix angle and the results are compared with those of AGMA (American Gear Manufacturers Association) formula. Results: Analysis from the examples shows that neglecting the radial compressive stress over-estimated the root bending stress by 5.27% on average. When shear stresses are ignored, the root bending stress is under-estimated by 7.49% on average. It is important, therefore, to account for both compressive and shear stresses in cylindrical gear root bending stress. When the root bending stress estimates from the revised Lewis model were compared with AGMA results, deviations in the range of -4.86% to 26.61% were observed. The stress estimates from the revised Lewis formulae were mostly higher than those of AGMA. Conclusion: The new root bending stress model uses stress concentration factors (normal and shear) that are independent of the point of load application on the gear tooth. This decoupling of stress concentration factor from the load moment arm distinguishes the new model from AGMA formula and brings bending stress analysis in gear design in line with classical bending stress analysis of straight and curved beams. The model can be used for both normal contact ratio and high contact ratio cylindrical gears.

Stress Concentration factor Analysis of Helical Gear Drives with Asymmetric Teeth Profiles

2018 ◽  
Vol 24 (5) ◽  
pp. 14
Author(s):  
Mohammad Qasim Abdullah ◽  
Mohammed Abdulaal Kadum
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Bending Strength ◽  
Spur Gear ◽  
Helical Gear ◽  
Tooth Profile ◽  
Bending Stress ◽  
Pressure Angle ◽  
Side Pressure

This study investigates the influence of asymmetric involute teeth profiles for helical gears on the bending stress. Theoretically, bending stress has been estimated in spur involute gears which have symmetric teeth profile by based on the Lewis, 1892 equation. Later, this equation is developed by, Abdullah, 2012. to determine the effect of an asymmetric tooth profile for the spur gear on the bending stress. And then these equations are applied with stress concentration factor once for symmetric and once other for asymmetric teeth profile. In this paper, the bending stresses for various types of helical gear with various types of asymmetric teeth profile are calculated numerically for defined the stress concentration factor. The numerical solution based on the finite element method technique which that done by using the software simulation SolidWorks 2016. The results of this study indicate that the helical gear drive with asymmetric teeth profile having 'loaded side pressure angle' of ( ) and 'unloaded side pressure angle' of ( ) is better than a helical gear with standard teeth profile having pressure angle of ( ) from the regarding of tooth bending strength. Also, notes that the great enhancement in the results of maximum tooth bending stress for modified involute of tooth profile compared with the standard teeth profile. In addition to, predict the equation of stress concentration factor which is a function of both unloaded side pressure angle and helix angle and then it used with Abdullah equation for to determine the nominal stresses in the root fillet.  

Influence of Gear Tooth Geometry on Tooth Stress of External and Internal Gears

1990 ◽  
Vol 112 (4) ◽  
pp. 575-583 ◽  
Author(s):  
H. von Eiff ◽  
K. H. Hirschmann ◽  
G. Lechner
Keyword(s):  
Stress Concentration ◽  
Tangential Stress ◽  
Infinite Number ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Gear Tooth ◽  
Maximum Tangential Stress ◽  
Number Of Teeth ◽  
Involute Gears ◽  
Gear Geometry

Type and geometry of the cutter influence the generated fillet in a gear tooth. Thus optimization of the cutter dimensions is an important step in minimizing gear stress. Gear tooth geometry of external and internal involute gears can be described by the same equations, if we apply the following rule: The number of teeth is positive in external gears and negative in internal gears; the rack has an infinite number of teeth. We demonstrate that both gear geometry and tooth stress, i.e., the location of maximum tangential stress, the amount of tooth stress and the stress concentration factor, change continuously from external to internal gears. The results obtained by FEM computations are verified by photoelastic experiments. Data for calculation of gears, especially internal gears, are presented and discussed.

Research on the Maximum Bending Stress on Driving Tine of SCMW

2012 ◽  
Vol 184-185 ◽  
pp. 445-449 ◽  
Author(s):  
Yang Zhi Chen ◽  
Shun Ke Liang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Theoretical Result ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Helix Angle ◽  
Bending Stress ◽  
Actual Result ◽  
Two Factors

In this study, equations of the maximum bending stress (MBS) on the root of driving tine of the space-curve meshing-wheel (SCMW) are deduced. Four factors have an impact on stress concentration of the driving tines, the helix angle, the fillet, the diameter of driving tines and the radius of the spiral curve for driving tine. They have been studied by Finite Element Method (FEM). Results show the former two factors have great impact on stress concentration while the last two could be ignored. Then the method to gain the stress concentration factor is proposed. It makes the theoretical result of the MBS on the root of driving tine match the actual result.

scholarly journals A novel thread connection structure of slimehole drilling tool in ultra-deep natural gas well

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110264
Author(s):  
Zhang Ying ◽  
Lian Zhanghua ◽  
Gao Anqi ◽  
Yang Kun
Keyword(s):  
Fatigue Life ◽  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Sensitivity Coefficient ◽  
Notch Sensitivity ◽  
Sensitivity Factor ◽  
Drilling Tool ◽  
Gas Well ◽  
Thread Connection

The thread connection’s root fillet radius of 0.038″ size is the greatest weakness of the API NC type joints and thread. During the slimehole drilling, especially in the deep and ultra-deep gas well, its stress concentration factor and notch sensitivity factor are very high A novel thread connection design (TM) of a drilling tool is proposed to decrease the fatigue failure of the slimehole drilling tool in the deep and the ultra-deep gas well in the Tarim oilfield China. The novelty in the TM thread structure is, reducing the threads per inch, extending the distance from the last engaged thread to the external shoulder of the pin and adding three threads to the conventional connection. The novel thread connection will improve the slimehole drilling tool’s anti-fatigue life due to its improved elasticity and rigidity. Furthermore, the TM can transfer the maximum stress at the connection root to the loaded surface, which can effectively lower the fatigue notch’s sensitivity coefficient. In this paper, the finite element method (FEM) is applied to carry out the detailed comparative analysis of the TM with existing thread connection NC38, TX60 and TH90. The TM has the lowest stress concentration factor and fatigue notch sensitivity coefficient, so its anti-fatigue life is the highest. In addition, TM is manufactured and is tested at Tarim oilfield in China.

Stress Concentration of Periodic Collinear Square Holes in an Infinite Plate in Tension

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Changqing Miao ◽  
Yintao Wei ◽  
Xiangqiao Yan
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Infinite Plate ◽  
Numerical Approach ◽  
Numerical Examples ◽  
Calculated Stress ◽  
Bueckner’S Principle

A numerical approach for the stress concentration of periodic collinear holes in an infinite plate in tension is presented. It involves the fictitious stress method and a generalization of Bueckner's principle. Numerical examples are concluded to show that the numerical approach is very efficient and accurate for analyzing the stress concentration of periodic collinear holes in an infinite plate in tension. The stress concentration of periodic collinear square holes in an infinite plate in tension is studied in detail by using the numerical approach. The calculated stress concentration factor is proven to be accurate.

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