Asymmetric Tooth Research Articles

Power loss prediction in asymmetric spur gear considering gear tooth dynamic load

In many gear drives, one side of the flank is subjected to relatively higher load for a longer duration than the other side. Asymmetric spur gears with drive side pressure angle higher than the coast side reflects this functional difference. Conventional design criteria and procedures followed for symmetric spur gears are suitably modified and applied to predict the gear tooth bending, contact stress and power loss in asymmetric spur gears. Quasi-static gear tooth load and empirical friction coefficient formulae were applied in the past to predict the sliding power loss in asymmetric spur gears. In the present work, Finite element method is used to determine the time varying mesh stiffness of the normal contact ratio asymmetric spur gear tooth. Computed gear tooth stiffness is used to predict the dynamic load at two different speeds under non-extended contact condition. Sliding power loss during the course of meshing is analytically calculated under quasi static and dynamic load conditions. Study demonstrates the difference in sliding power loss computed based on friction formulae and empirical friction coefficient formulae under static and dynamic load.

ARCHED TRANSMISSIONS TEETH GEOMETRY WITHIN OFFSET OF INITIAL PROFILE

There has been researched teeth geometry of cylindrical arched teeth gears, cut with rod instrument, teeth of which profiled by arbitrary curve in normal cross-section and in linear direction within initial profile offset.Toothing of instrumental rod with arched teeth with gears within initial profile offset is an analogue of the process of cutting teeth with rod instrument by means of enveloping. Surfaces of gear teeth within toothing with rod are enveloping of teeth surfaces of the last one.If teeth surfaces of instrumental rods for cutting pinion teeth and gear are non-congruous, then we have case of dotty toothing of pinion and gear. If initial profiles are non-congruous, then contact dot moves from one side of the tooth to another.It was obtained equations of teeth surfaces, while writing down coordinates of toothing surfaces in coordinate systems X 1 Y 1 Z 1 andX 2 Y 2 Z 2 , connected with pinion and gear. While making such a transition, we have equations of surfaces of convex side of pinion teeth and concave side of gear teeth. In common case those equations are equations of helical lines of variable pitch. These equations can be used within the determination of toothing field borders, appropriate to the tops of the pinion and the gear teeth. Within this case two types of toothed gears with arched teeth will differ: gears with symmetric arched teeth (teeth are symmetric relatively to the plane and asymmetric arched teeth (working area of teeth surface is situated from one side of plane.Received results can be used within the determination of indices of loading ability and other characteristics of cylindrical arched transmissions with generalized teeth geometry within initial profile offset.

Unilateral Mastication Evaluated Using Asymmetric Functional Tooth Units as a Risk Indicator for Hearing Loss.

BackgroundSome previous studies reported hearing ability can be reduced by impaired masticatory ability, but there has been little evidence reported of an association between hearing loss and unilateral mastication. Therefore, this study aimed to investigate the relationship between unilateral mastication (UM), estimated from individual functional tooth units (FTUs), and hearing loss in a representative sample of Korean adults.MethodsThe analyzed data were obtained from 1,773 adults aged 40–89 years who participated in Korean national survey. Hearing loss was defined as a pure-tone average of >25 dB at frequencies of 0.5, 1, 2, and 4 kHz in either ear. In each subject, UM was calculated as the difference in the sums of the FTU scores, which is an index of posterior tooth occlusion, on the two sides of the oral cavity. The scores were used to classify the UM into low, moderate, and high. The adjusted odds ratios (aORs) and their 95% confidence intervals (CIs) were calculated in multivariable logistic regression analyses.ResultsWhen controlling for sociodemographic factors, the aOR for hearing loss was 3.12 (95% CI, 1.21–8.03) for high UM relative to low UM. This association remained in a fully-adjusted model containing factors related to noise exposure (aOR 2.88; 95% CI, 1.12–7.46).ConclusionAdults with high UM as measured using FTUs showed a higher occurrence of hearing loss than those with low UM.

Optimization of asymmetric tooth root generated with protuberance hob

The Direct Gear Design method optimizes various parameters and elements of gear tooth geometry to achieve the required gear drive performance. One such critical element of the tooth profile is the root fillet. Previous publications had considered asymmetric tooth root fillet optimization assuming that the tooth involute flanks and root fillets are processed (machined) simultaneously. However, there are many applications that require high gear tooth flank accuracy and high load capacity in combination with minimized gear production cost. In order to satisfy these requirements, the tooth involute flanks and root fillets are processed separately. A gear blank is machined by a topping protuberance hob that finalizes the root fillet, tooth tip diameter and chamfers, leaving stock for the tooth flank grinding. Then, after the gear’s heat treatment (carburizing + case hardening) and in some cases shot peening of the tooth root, the tooth flanks are processed using highly productive generating grinding, removing the grinding stock. As a result, the full residual stress developed by case hardening is retained. This fabrication sequence is most typical for automotive transmission gears.

A comparative numerical study of forged bi-metal gears: Bending strength and dynamic response

In this paper, an evaluation of the static and dynamic behavior of bimetallic spur gears with different gear parameters is performed numerically. Bimetallic lightweight spur gears working without a decrease in the performance of the gear mechanisms have many potential benefits in automotive and aerospace applications. A bimetallic spur gear consists of two metals which are steel on the gear teeth and aluminum on the hub region. The dynamic performance of these gears is evaluated by using a two degree of freedom (2-DOF) dynamic model. The finite element method is used to calculate maximum root stress for varying ring thicknesses and other gear parameters for gears with symmetric and asymmetric teeth. These stress values and the weight reduction ratios are taken into consideration to optimize the ring thickness. Tooth deflection is also calculated to determine tooth stiffness by finite element analysis (FEA). Dynamic simulations are carried out to investigate the effects of gear parameters on the dynamic force and static transmission error (STE). Sample simulation results are illustrated with numerical examples. The results indicate that, if properly designed, bimetallic gears can provide a high potential to reduce the weight in power transmission systems without adverse effects on stress and dynamic behavior.

Development of a Radial-Flux Slotted Limited-Angle Torque Motor With Asymmetrical Teeth for Torque Performance Improvement

Although conventional slotted limited-angle torque motors (LATMs) have a high torque density, its fatal shortcoming of non-uniform torque profile makes it difficult to apply for precise positioning systems. This paper presents a novel radial-flux slotted LATM with asymmetrical teeth for the torque performance improvement including average output torque and angular operation range. A magnetic equivalent circuit (MEC) for radial-flux slotted LATMs is first derived and implemented in the design process. Then, the finite-element analysis is utilized to validate the related analytical equations and to make the comparison of the torque performance between the radial-flux conventional and proposed LATMs. Finally, a prototype machine of the proposed LATM is accomplished, and its torque characteristic experiment is carried out to confirm the torque performance improvement. The related experimental results are presented and discussed.

On-load Back-EMF Optimization Based on the Back-EMF MST Method and Parametric Optimization

This paper proposes an optimal design for a surface mounted permanent magnet synchronous machine (SM-PMSM) based on parametric optimization process to reduce the on-load Back-EMF distortions caused by an increase in the electromagnetic load and in the saturation. Unlike conventional methods described in the literature, the optimization approach proposed here accounts for the saturation effects, air gap flux density distribution and the evaluation of the on-load Back-EMF by means of finite element analysis, allied to the most recent on-load Back-EMF evaluation method, known as the Back-EMF MST (Maxwell stress tensor) method. Furthermore, the optimization process is performed considering either the machine's physical symmetry (based on pole numbers) and its nonevident symmetry (based on saturation effects and on the relevance of each tooth in the Back-EMF waveform), which is identified using the Back-EMF MST method. The proposed optimization process also analyzes different sets of variables based on symmetric and asymmetric tooth dimensions. The result is a machine with a reasonably improved design, higher average torque, lower torque ripple and smaller volume. In addition, the on-load Back-EMF is almost identical to the no-load one. Hence, the on-load cogging torque is almost identical to the no-load cogging torque.

Influence of Addendum Modification Factor on Root Stresses in Normal Contact Ratio Asymmetric Spur Gears

Tooth root crack is considered as one of the crucial causes of failure in the gearing system and it occurs at the tooth root due to an excessive bending stress developed in the root region. The modern power transmission gear drives demand high bending load capacity, increased contact load capacity, low weight, reduced noise and longer life. These subsequent conditions are satisfied by the aid of precisely designed asymmetric tooth profile which turns out to be a suitable alternate for symmetric spur gears in applications like aerospace, automotive, gear pump and wind turbine industries. In all step up and step down gear drives (gear ratio > 1), the pinion (smaller in size) is treated as a vulnerable one than gear (larger in size) which is primarily due to the development of maximum root stress in the pinion tooth. This paper presents an idea to improve the bending load capacity of asymmetric spur gear drive system by achieving the same stresses between the asymmetric pinion and gear fillet regions which can be accomplished by providing an appropriate addendum modification. For this modified addendum the pinion and gear teeth proportion equations have been derived. In addition, the addendum modification factors required for a balanced maximum fillet stress condition has been determined through FEM for different parameters like drive side pressure angle, number of teeth and gear ratio. The bending load capacity of the simulated addendum modified asymmetric spur gear drives were observed to be prevalent (very nearly 7%) to that of uncorrected asymmetric gear drives.

Performance enhancement of spur gear formed through asymmetric tooth

Tooth fracture and surface wear are the major failure causes in a gearing system. With increasing demand for high power density gear applications, the need of effective gear design becomes an important requirement to improve gear life. This article presents a method to enhance the load carrying capacity in bending and contact, as well as wear resistance to increase gear efficiency through asymmetric tooth. Asymmetric gear is the one whose pressure angles at pitch circle on drive and coast sides are different. In the present investigation, the load shared by a teeth pair, fillet and contact stresses, wear resistance, frictional power losses and the respective mechanical efficiencies have been determined for comparative performance assessment of symmetric and asymmetric spur gears.

Determination of load dependent gear loss factor on asymmetric spur gear

This paper shows the prediction of coefficient of friction and load dependent loss factor for spur gear drives with asymmetric tooth. An accurate evaluation of gear loss factor is important to exactly calculate the power loss and the corresponding mechanical efficiency of the asymmetric spur gear drive. In the present investigative research work, a formulation to accurately estimate the gear loss factor on asymmetric gear has been developed. The tooth load and the corresponding contact stress that develops at the symmetric and asymmetric gear contact surfaces are also evaluated through finite element method in order to deduce the friction coefficient and loss factor. The suitability of three distinct models is studied and compared in this paper. The asymmetric gear pair is analyzed and the loss factor is predicted for influence over the major drive parameters. It is revealed that the approach employed facilitate substantial enhancement in the efficiency which is confined by the detailed parametric study.

Dynamics of underwater gas bubbles impact on a ratchet with gradient inclination

An underwater gas bubble may have a unidirectional movement, after impacting with a ratchet, which consists of asymmetric teeth with gradient inclination. In this work, the corresponding movements were first experimentally investigated. Small bubbles are easily pinned on a ratchet surface. In contrast, large bubbles have directional transportation from large to small inclination areas. Since the detected motions could not be interpreted using existing propulsive mechanisms, a new propulsive mechanism was then developed. Based on the new mechanism, two approaches to manipulate bubbles have been investigated experimentally.

Parametric analysis of asymmetric involute spur gear tooth

The focus of this work is a geometric parameter of an asymmetric involute spur gear tooth. Gear strength is influenced by tooth geometry. So, knowledge of tooth geometric is required which will help to improve the strength of a gear tooth. In this article, a data generated from an equations and presented in form of graph for better interpretation of the effect of drive side pressure angle on various parameters like contact ratio, HPSTC radius, load angle, tip thickness, thickness of tooth at pitch circle radius, critical section thickness, bending moment arm height, etc. Parametric analysis of gear tooth gives an idea about how different parameters affect tooth geometry of an asymmetric involute spur gear tooth which is essential for modelling and manufacturing. Parametric analysis helps to calculate optimise drive side pressure angle. It is also predicted or calculates % reduction in bending stress at the root of the tooth without using FEA. It is explained with illustration and results are compared to justify it.

Parametric analysis of asymmetric involute spur gear tooth

The focus of this work is a geometric parameter of an asymmetric involute spur gear tooth. Gear strength is influenced by tooth geometry. So, knowledge of tooth geometric is required which will help to improve the strength of a gear tooth. In this article, a data generated from an equations and presented in form of graph for better interpretation of the effect of drive side pressure angle on various parameters like contact ratio, HPSTC radius, load angle, tip thickness, thickness of tooth at pitch circle radius, critical section thickness, bending moment arm height, etc. Parametric analysis of gear tooth gives an idea about how different parameters affect tooth geometry of an asymmetric involute spur gear tooth which is essential for modelling and manufacturing. Parametric analysis helps to calculate optimise drive side pressure angle. It is also predicted or calculates % reduction in bending stress at the root of the tooth without using FEA. It is explained with illustration and results are compared to justify it.

Crack detection for spur gears with asymmetric teeth based on the dynamic transmission error

Gears are one of the most important power transmission elements in every area of the industry. Because of its importance, the gear design must be carefully performed. Unfortunately, due to the changing of the boundary conditions, gears are exposed to failures such as cracks, pitting, tooth missing etc. during the operation. Thus the gear diagnostic and monitoring become a very critical phenomenon for the gearboxes. A dynamic transmission error (DTE) based numerical fault detection model is proposed. Firstly, numerical finite element model is created to calculate single tooth stiffness with different crack levels. Furthermore, the model is used for the asymmetric gear profile which has a great importance nowadays for different areas. After that, the time-varying mesh stiffness is calculated by using single tooth stiffness with different crack levels for both symmetric and asymmetric types of the gears. To understand the effects of the gear cracks along the tooth thickness on dynamic transmission error of the gear system and to detect the gear crack faults for symmetric and asymmetric gear profiles, a four-degree of freedom dynamic model is created. The results show that with the increment of the crack level, the mesh stiffness of the gears is decreased.

Kinematic Errors on a C-Type Gear with a Parabolic Surface

Abstract An asymmetric tooth is used to develop a mathematical model of an imaginary skewed rack cutter. Using this imaginary skewed rack cutter and the theory of gearing, a pair of helical gears with asymmetric, straight teeth and a parabolic surface is created. Using tooth contact analysis, this mathematical model of a pair of helical gears with a parabolic surface is used to study the kinematic errors that occur because of assembly errors. Using a computer-aided software package to simulate the scenario, the kinematic errors for the gear set when it is ideally assembled and inaccurately assembled are presented. The contact pattern between the pair of helical gears is obtained. A pair of helical gears is created by rapid prototype machining and is used to observe the actual contact conditions of the gears.

Lévy flights on a comb and the plasma staircase.

We formulate the problem of confined Lévy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V(x)∝|Δx|^{n} within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Lévy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n>4-μ, where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ=1), n>3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.

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

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.

Design principle and modeling method of asymmetric involute internal helical gears

In the field of mechanical engineering, involute helical gears are widely used. Compared with the involute spur gear, helical gears have a high bearing strength, more smooth transmission, less impact and less noise. The internal gear pairs have the features of large transmission ratio, low vibration, low noise and low wear and hence are widely used in planetary gear transmission systems. In order to meet the requirements of high strength, high speed of the modern gear transmission systems, a new type of asymmetric involute internal helical gears is designed based on conventional involute gears. This paper discusses the gear shaper cutter modeling for machining this new gear, analyzes the formation principle of asymmetric tooth profile and establishes a three-dimensional modeling by SolidWorks. Through MATLAB simulation, pressure angle, tooth number, coefficient of displacement and contact ratio of conventional and asymmetric gear are compared and analyzed. Using ANSYS, two types of gears are compared on strength in order to demonstrate superiority of asymmetric tooth and further study about the asymmetric internal helical gears.

Search method applied for gear tooth bending stress prediction in normal contact ratio asymmetric spur gears

Various analytical methods have been developed by designers to predict gear tooth bending stress in asymmetric spur gears with an intention to improve the accuracy of predicted results and to reduce the need for time consuming finite element analysis at the early stages of gear design. Asymmetry in the drive and coast side of asymmetric spur gears poses difficulty in direct application of well-known procedures like American Gear Manufacturers Association and International Organization for Standardization in the prediction of gear tooth bending stress. In earlier works, ISO-6336-3 methodology was suitably modified and adapted to predict asymmetric spur gear tooth bending stress. This approach is based on certain assumptions on the location of critical section which could introduce error in the predicted maximum bending stress. The present work is to analytically predict gear tooth bending stress in normal contact ratio asymmetric spur gears based on a more rigorous analytical approach. This includes a fundamental study on the gear tooth orientation used to define the coordinate system, determination of maximum bending stress by search along the fillet profile and to obtain stress profile along the fillet. Gear tooth bending stress obtained from the present work using Search method is compared against the results obtained from earlier adapted International Organization for Standardization method and Finite Element Analysis. This study recommends a new coordinate system and method for analytical prediction of gear tooth bending stress in normal contact ratio asymmetric spur gears.

Optimization of Tooth Root Profile Using Bezier Curve with G2 Continuity to Reduce Bending Stress of Asymmetric Spur Gear Tooth

This research describes simple and innovative approach to reduce bending stress at tooth root of asymmetric spur gear tooth which is desire for improve high load carrying capacity. In gear design at root of tooth circular-filleted is widely used. Blending of the involute profile of tooth and circular fillet creates discontinuity at root of tooth causes stress concentration occurs. In order to minimize stress concentration, geometric continuity of order 2 at the blending of gear tooth plays very important role. Bezier curve is used with geometric continuity of order 2 at tooth root of asymmetric spur gear to reduce bending stress.