Probabilistic Analysis of MEMS Asymmetric Gear Tooth

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Fatih Karpat ◽  
Stephen Ekwaro-Osire ◽  
Morshed P. H. Khandaker
Keyword(s):  
Gear Tooth ◽  
Load Capacity ◽  
Probability Of Failure ◽  
Mems Devices ◽  
Contact Ratio ◽  
Microelectromechanical System ◽  
Gear Teeth ◽  
Failure Theory ◽  
Gear Drives ◽  
Root Stress

Currently, there is an increased interest in the application of microelectromechanical system (MEMS) gear drives. Additionally, requirements for transmitted power and related reliability issues have increased. Reliability issues often occur due to uncertainties of material, geometry, and loading conditions of the MEMS gears. Asymmetric gear teeth are used to improve the performance of gears by increasing the load capacity or by reducing vibrations. In this paper, asymmetric gear teeth are proposed for MEMS applications. The objective of this research is to investigate the feasibility of applying asymmetric gears for MEMS devices while accounting for uncertainty. The Weibull failure theory was applied to four different MEMS gear configurations. The following analyses were carried out in this research: (i) for the calculation of root stress, four different asymmetric gears were used; (ii) for the calculation of the probability of failure, the Weibull failure theory formulization was used, and (iii) the efficacy of the various asymmetric tooth configurations was discussed. Specifically, the probability of failure of the asymmetric gear was extracted for various parameters. The parameters considered included pressure angle, tooth height, and contact ratio. The efficacy of using asymmetric gear teeth was shown in this study.

Probabilistic Analysis of MEMS Asymmetric Gear Tooth

2006 ◽  
Author(s):  
F. Karpat ◽  
S. Ekwaro-Osire ◽  
M. P. H. Khandaker
Keyword(s):  
Finite Element ◽  
Probabilistic Analysis ◽  
Gear Tooth ◽  
Load Capacity ◽  
Probability Of Failure ◽  
Mems Devices ◽  
Contact Ratio ◽  
Finite Element Program ◽  
Gear Teeth ◽  
Element Program

Asymmetric gear teeth are used to improve the performance of gears by increasing the load capacity or by reducing vibrations. Recently these types of gears have found application in MEMS devices where the use of gears is on the rise. In this research a probabilistic computer program, in conjunction with a commercially available finite element program, is developed and the reliability of the asymmetric gear tooth is studied. Specifically, the probability of failure of the asymmetric gear is extracted for various parameters. The parameters considered included pressure angle, tooth height, and contact ratio. The efficacy of using asymmetric gear tooth is shown in this study.

Analysis of Spur Gear with Tooth Circular Discontinuity for Weight Reduction

2018 ◽  
Vol 17 (02) ◽  
pp. 249-265 ◽  
Author(s):  
R. Ravichandran ◽  
S. Neelakrishnan
Keyword(s):  
Internal Stress ◽  
Weight Reduction ◽  
Gear Tooth ◽  
Stress Relief ◽  
Spur Gear ◽  
Contact Ratio ◽  
Tangential Load ◽  
Single Tooth ◽  
Gear Drives ◽  
Root Stress

The design of gears and gear drives are becoming challenging in automobile applications in which low contact ratio gears are required to transmit higher loads and be lighter in weight. There are various methods available for optimizing the design. Some researches have been taken place in the areas of gear tooth profile modifications for providing internal stress relief and weight reduction. In most cases, the maximum loads are assumed to be acting on the tip of the tooth. In this study, investigations are carried out on the effect of circular discontinuity on the weight reduction without affecting the root stress. The maximum tangential load is applied on the highest point of single tooth contact. The results show that with the modified gear tooth having a combination of two circular discontinuities of size 0.4 times the module not only provides weight reduction but also gives stress relief at the root.

Determination of Addendum Modification Coefficients for Spur Gears Operating at Non-Standard Center Distances

2003 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Performance Variables ◽  
Practical Design ◽  
Gear Drives ◽  
Maximum Contact ◽  
Center Distance

Although it is possible to find some recommended conventional values both for the sum of the addendum modification coefficients and for the allocation of the sum of the addendum modification coefficients (e.g. ISO/TR 4467), a detailed analysis is necessary to determine the addendum modification coefficient values for the desired optimization criteria and the performance since the main objective of the above mentioned sources is to facilitate practical design of non-standard gear drives which will not have problems while operating. They give practical average values within a safe range. In this study, by considering the required gear ratio, center distance and the desired backlash, alternative gear pairs are determined and corresponding gear performance variables are calculated in order to allocate the addendum modification coefficients for the pinion and the gear by using criteria such as: not having undercut or pointed (or excessively-thinned-tip) tooth, having desired proportions for the lengths of the dedendum and addendum portions of the line of action, having maximum contact ratio, having sufficient bottom clearance, having minimum contact stresses, having balanced pinion and gear tooth root stresses, having equal pinion and gear lives, etc.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

2007 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Advantages And Disadvantages ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.

Influence of Pressure Angle on Load Sharing Based Stresses in Asymmetric Normal Contact Ratio Spur Gear Drives

2013 ◽  
Vol 465-466 ◽  
pp. 1229-1233 ◽  
Author(s):  
P. Marimuthu ◽  
G. Muthuveerappan
Keyword(s):  
Parametric Design ◽  
Load Sharing ◽  
Spur Gear ◽  
Contact Model ◽  
Contact Ratio ◽  
Element Analysis ◽  
Normal Contact ◽  
Gear Teeth ◽  
Pressure Angle ◽  
Gear Drives

The aim of this paper is to investigate the influence of pressure angle on drive and coast sides in conventional design asymmetric normal contact ratio spur gear, considering the load sharing between the gear teeth pair. The multi pair contact model in finite element analysis is used to find the load sharing ratio and respective stresses. It has been found out that the predictions through multipoint contact model are in good agreement with the available literature. A unique Ansys parametric design language code is developed for this study. It is found that, the maximum fillet stress decreases up to the threshold point for drive side (35o) and coast side (25o) pressure angles, beyond this point it increases. The load share based maximum fillet and contact stresses are lower in the high pressure angle side than that of the low pressure angle side, when it is loaded at the critical loading points.

Gear Transmission Density Maximization

2011 ◽  
Author(s):  
Alexander L. Kapelevich ◽  
Viacheslav M. Ananiev
Keyword(s):  
Gear Tooth ◽  
Load Capacity ◽  
Gear Ratio ◽  
Gear Transmission ◽  
Gear Trains ◽  
Reduced Costs ◽  
Gear Drives ◽  
Internal Gear ◽  
Ratio Optimization ◽  
Volume Functions

Maximization of the gear transmission density presents an important task. It allows to increase the output torque within given dimensional constrains that is critical, for instance, in racing gearboxes, or to reduce size and weight of aerospace gear drives. It can also lead to reduced costs for automotive and consumer product gear trains, etc. There are several ways to increase gear drive load capacity, including advanced design, materials, and technologies. This paper presents an approach that allows optimizing gearbox kinematic arrangement and gear tooth geometry to achieve high gear transmission density. It introduces dimensionless gearbox volume functions, which can be minimized by the internal gear ratio optimization. Different gearbox arrangements are analyzed to define a minimum of the volume functions. Application of the asymmetric gear tooth profiles power density maximization is also considered.

Optimum Gear Tooth Geometry for Minimum Fillet Stress Using BEM and Experimental Verification With Photoelasticity

2005 ◽  
Vol 128 (5) ◽  
pp. 1159-1164 ◽  
Author(s):  
Vasilios A. Spitas ◽  
Theodore N. Costopoulos ◽  
Christos A. Spitas
Keyword(s):  
Gear Tooth ◽  
Optimization Procedure ◽  
Computational Time ◽  
Design Parameters ◽  
Gear Teeth ◽  
Design Variables ◽  
Maximum Root ◽  
Stress Minimization ◽  
Complex Algorithm ◽  
Root Stress

This paper introduces the concept of nondimensional gear teeth to be used in gear stress minimization problems. The proposed method of modeling reduces the computational time significantly when compared to other existing methods by essentially reducing the total number of design variables. Instead of modeling the loaded gear tooth and running BEA to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously by applying the BEM on nondimensional models corresponding to different combinations of the design parameters. The complex algorithm is used for the optimization and the root stresses of the optimum gears are compared with the stresses of the standard gears for the same transmitted torque. Reduction in stress up to 36.5% can be achieved in this way. This reduction in stress has been confirmed experimentally with two-dimensional photoelasticity.

Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears

1991 ◽  
Vol 113 (4) ◽  
pp. 473-480 ◽  
Author(s):  
Chinwai Lee ◽  
Hsiang Hsi Lin ◽  
Fred B. Oswald ◽  
Dennis P. Townsend
Keyword(s):  
Computer Simulation ◽  
Contact Stress ◽  
Dynamic Load ◽  
Applied Load ◽  
Gear Tooth ◽  
Load Force ◽  
Loading Conditions ◽  
Contact Ratio ◽  
Profile Modification ◽  
Root Stress

This paper presents a computer simulation for the dynamic response of high-contact-ratio spur gear transmissions. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this paper examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. This paper shows that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.

Performance Rating and Optimization of Spur Gear Drives With Small Number of Teeth

2000 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Spur Gear ◽  
Maximum Length ◽  
Performance Rating ◽  
Tooth Root ◽  
Contact Ratio ◽  
Geometry Factor ◽  
Factor I ◽  
Number Of Teeth ◽  
Gear Drives

Abstract Performance rating of spur gear drives with small number of teeth is made and variations of contact ratio, circular tooth thicknesses at pinion and gear tooth tips, lengths of the pinion addendum and dedendum portions of the line of action, AGMA geometry factor J for the pinion and the gear and their ratio, and AGMA geometry factor I with addendum modification coefficient are determined. Thus, it is made possible to design gear drives with properties such as, maximum possible contact ratio, maximum length of the pinion addendum portion of the line of action, maximum length of the pinion dedendum portion of the line of action, equal AGMA geometry factors J for the pinion and the gear (i.e. equal pinion and gear tooth root stresses), and maximum AGMA geometry factor I (i.e. minimum tooth contact stress). Rack cutter tip fillet radius and rack cutter geometry are considered in the analysis, which are the basic factors that determine the gear tooth fillet profile.

A Weibull Failure Theory for Contact Loading in Gears With Asymmetric Teeth

2008 ◽  
Author(s):  
M. Dhorje ◽  
S. Ekwaro-Osire ◽  
M. P. H. Khandaker ◽  
F. Karpat
Keyword(s):  
Stress Gradient ◽  
High Stress ◽  
Probability Of Failure ◽  
Contact Loading ◽  
Gear Teeth ◽  
Stress Gradients ◽  
Failure Theory ◽  
The Face ◽  
Modified Weibull ◽  
Material Mismatch

Meshing gear pairs have regions of high stress gradients due to contact loading. In other applications, high stress gradients can also be generated due to geometric irregularities, material mismatch, or thermal mismatch. In meshing gear pairs, the extent of the region with a high stress gradient depends on the material and the geometric properties. It is common that failure, through crack initiation, will occur in the region of high stress and strain gradients. The conventional Weibull failure theory fails to accurately predict the probability of failure of components with high stress gradients. In this research, the contact loading in a gear pair, with asymmetric teeth, is analyzed. Thus, the objective of this work is to develop a Weibull failure theory to handle the high stress gradients due to contact loading in gear pairs with asymmetric teeth. The modified Weibull failure theory developed uses the weight function approach to account for the variation of the critical stress along the face of natural flaws. For contacting gear teeth, it is demonstrated that the modified Weibull failure theory generates monotonous trends for the probability of failure with respect to increasing Weibull modulus.

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