Tooth profile shift will change the thickness of gear teeth and a part of geometrical parameters of a gear pair, thus influencing its mesh stiffness and consequently the dynamic performances. In this paper, an analytical mesh stiffness calculation model for an internal gear pair in mesh considering the tooth profile shift is developed based on the potential energy principle. Geometrical representations of the tooth profile shift are firstly derived, and then fitted into the analytical tooth stiffness model of gears. This model could supply a convenient way for mesh stiffness calculation of profile shifted spur gears. Then, simulation studies are conducted based on the developed model to demonstrate the effects of tooth profile shift coefficient on the tooth compliances and the mesh stiffness of the internal spur gear pair. The results show that tooth profile shift has an obvious influence on the mean value, amplitude variation and phase of the mesh stiffness, from which it can be predicted that the dynamic response of an internal gear transmission system will be affected by the tooth profile shift.

Mesh stiffness evaluation of an internal spur gear pair with tooth profile shift

This thesis evaluates the service life of the spur gear in industry, showing that innovative techniques are required to resolve the problem of gear failure that occurs due to flank surface pitting and tooth breakage. Such techniques involve theoretical calculation, finite element analysis, hardness testing and selecting the appropriate material for the spur gear. Calculations were performed to measure contact stress, bending stress, and safety factor of the spur gear. This was followed by a finite element analysis (FEA) and software simulation. Then, the hardness test to compare the hardness of the materials was conducted. The material for the spur gear is chosen based on its mechanical properties. In this dissertation, the mechanical properties of currently used material C45 is compared to a new material, 19MnCr5. 
The aim of the research was to increase the service life of the spur gear pair using suitable and reliable material. To expand the purpose of the study, attention has also been paid to the ISO 6336 standard-based calculation for the load-carrying capacity of the spur gear; FEA simulation using ANSYS software, and Rockwell hardness test were both conducted. From material analysis, the study found that the 19MnCr5 material has more fatigue strength, tensile strength, and better yield point as compared to C45 material. Also, through mathematical and FEA comparison, the study establishes that the gear designed with 19MnCr5 material fulfils the prescribed safety limits and would operate for its recommended service life. Furthermore, it is clear from a series of Rockwell hardness tests conducted, that after achieving higher hardness values by using 19MnCr5 rather than the C45 grade material, the gear would work without breakage. 
For future study, it is suggested that there is a need to assess the effect of stress distribution variance over the flank and root of the spur gears, as this aspect has not been covered in the current context. Also, the stresses over the sub-surface of the gear teeth should be investigated. Besides this, research to find compatible lubricants for 19MnCr5 material is also required. Finally, observed differences in the hardness value at the rim and the tooth of the gear call for deeper analysis of the hardness testing process.

/pdf/finite-element-analysis-of-spur-gear-323c8nlaaj.pdf

Finite element analysis of spur gear

The effective case depth (ECD) plays an important role in the meshing strength of internal gear transmissions. Carburizing quenching heat treatment is commonly used to enhance gear strength and wear resistance. However, the different ECDs in internal and external gears caused by heat treatment significantly affect the meshing strength, causing vibration, reducing gear service life, and hastening malfunction in internal gear transmission. In this study, we conducted an investigation of different ECDs by the heat treatment of carburized gear pairs by numerical simulation with the finite element method (FEM) and experiment tests. We analyzed three different carburized layer models, with the ECD in the internal gear being greater than, less than, and equal to the ECD in the external gear. In addition, we investigated the ability to distinguish between hardness gradients in gear teeth by dividing the carburized depth into seven layers to improve modeling accuracy. Results revealed that the meshing strength of internal gear transmission could be significantly enhanced by adopting the model with the ECD in the internal gear being less than the ECD in the external gear, and moreover, the shear stress of carburized gears initially increased and then decreased along with depth direction, and the maximum value appeared in the middle of the lower surface.

/pdf/modeling-and-analysis-of-effective-case-depth-on-meshing-30rufnittn.pdf

Modeling and Analysis of Effective Case Depth on Meshing Strength of Internal Gear Transmissions

ABSTRAC: The various needs of power and motion transmission in drives are undoubtedly fulfilled by gears. Satisfying the needs required for efficient and effective transmission depends on the tooth geometry. Hence, gear design involves a detail study of the tooth geometry as it determines various performance aspects regarding to load carrying capacity, wear characteristics, efficiency and noise. Among them the load carrying capacity is a fundamental requisite which depends on the bending strength calculated using Lewis equation which was formulated one hundred years ago. Most often, the tooth geometry of standard gears fail to meet certain needs, hence it is modified for better performance. The most common way of modifying the tooth geometry is by profile shift by using S-gearing, such profile shifting of gears influence the performance. As an alternative to S-gearing, it is proposed to modify the tooth geometry by altering the tooth-sum of a gear pair when center distance and module are specified. This involves increase or decrease of tooth-sum with eventual negative or positive profile shift respectively. With such alteration the gears are found to have different tooth geometry with unique benefits that are studied. The amount of profile shift for altering the tooth-sum of a gear pair can be calculated by the established equations of involutometry and trigonometry. The load distribution along the path of contact of such altered tooth-sum gears is understood using load sharing diagram that indicates the pattern of loading along the path of contact. This study considers spur gears under static loading, it involves comparison and analysis of load distribution on the gear tooth along the path of contact for both standard as well as altered tooth-sum gears.

Investigation of Tooth Load Distribution along the Path of Contact in Altered Tooth-Sum Gears

A comprehensive review on design and analysisof spur gears

Power transmission between shafts that need positive drive is well assured by gears. The size and shape of the gear tooth is a critical consideration if specific drive requirements are imposed. Thus, design of gears calls for a detailed study of the tooth geometry that defines the performances like load carrying capacity, wear characteristics, efficiency and noise. Among them load carrying capacity is one of the fundamental requirements which depends on bending strength that can be computed using well known Lewis equation. Most often, tooth geometry is modified using S-gearing to influence the performance that may be either So or S+ type. Tooth geometry can also be modified by way of altering the tooth-sum of meshing gears for a standard center distance and module. Such modifications have some inherent benefits that are unique. Hence, this study is focused on analysis of bending stress as well as contact ratio in altered toothsum gears using load sharing diagram. The diagram clearly shows the loading pattern and contact length for both standard and altered tooth-sum gears at different points of contact. The load sharing analysis is carried out for altered tooth-sum spur gears having tooth-sum 100, 2 mm module, face width 10 mm and 20 o pressure angle with a tangential load of 9.81N/mm of face

http://www.idpublications.org/wp-content/uploads/2014/12/LOAD-SHARING-ANALYSIS-OF-BENDING-STRENGTH-IN-ALTERED-TOOTH-SUM-GEARS-Full-Paper.pdf

Load sharing analysis of bending strength in altered tooth-sum gears operating between a standard center distance and module

Altered tooth-sum gearing is a unique type of non-standard gearing having their profiles shifted due to altering the tooth-sum for a specified center distance and module. This approach is aptly termed as Z± gearing because it involves increasing the sum of teeth (positively altered toot-sum or aptly Z+ gearing) or decreasing the sum of teeth (negatively altered tooth-sum or aptly Z− gearing) of the mating gears working on an operating pressure angle. Here, both the center distance and gear ratio remains unaltered, such a study is less explored in gear research. This paper deals with determining experimental bending stress in standard and altered tooth-sum spur gears having involute form, further the results are compared with AGMA bending stress. For this purpose a Gear Tooth Bending Test (GTBT) fixture is developed which uses a single tooth specimen having a strain gauge bonded in its fillet region. Under the application of load a strain indicator reads out the strain. The specimen is a single tooth model having accurate involute profile and circular fillet, it is developed using advanced modeling software and manufactured using CNC machine. From the experiment it is observed that the tooth of Z− gearing subjected to positive profile shift has a lower bending stress (favorable) and the tooth of Z+ gearing subjected to negative profile shift has a higher bending stress (unfavorable, of course with higher contact ratio) compared to the tooth of standard gearing. This infers that the bending strength of a gear tooth can be influenced by altered tooth-sum design. The results obtained closely agree with AGMA values.

/pdf/design-and-testing-of-gears-operating-between-a-specified-w4f7buutqf.pdf

K. A. Venugopal

Papers

Load sharing analysis of bending strength in altered tooth-sum gears operating between a standard center distance and module

Design and Testing of Gears Operating between a Specified Center Distance Using Altered Tooth-sum Gearing (Z± Gearing)