Asymmetric Spur Research Articles

A Comparative Study of Tooth Wear, Mechanical Power Losses and Efficiency in Normal and High Contact Ratio Asymmetric Spur Gears

The surface tooth wear which occurs at the gear contact region due to inadequate contact strength of the tooth is one of the predominant modes of gear failures. Currently, higher contact ratio spur gears are increasingly used in power transmission applications such as aircraft, wind turbine, automobiles and compact tracked vehicles due to their high load carrying capacity. In this work, the direct design is found to be one of the efficient gear design methods to reduce the tooth surface wear on high contact ratio asymmetric spur gears. Asymmetric gear tooth is defined as one whose tooth geometry of the drive and coast sides is not symmetric. Asymmetry between tooth sides is achieved by providing two different pressure angles at the respective coast and drive side pitch circles. The area of existence diagrams for normal and high contact ratio gears have been developed to select suitable design solution with the given variables of gear ratio, contact ratio and teeth number. The contact load capacity, wear resistance, power losses and mechanical efficiency have also been deduced for directly designing normal and high contact ratio asymmetric spur gears.

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.

Selection of Pressure Angle based on Dynamic Effects in Asymmetric Spur Gear with Fixed Normal Contact Ratio

Asymmetric spur gears are finding application in many fields including aerospace propulsion and automobile which demand unidirectional or relatively higher load on one side of the gear flank. Design intend to maximise the load carrying capacity of the drive side of asymmetric gear by increasing the pressure angle is achieved at the expense of coast side capacity. Multiple solution for coast to drive side pressure angle exist for a given contact ratio and each of these have relative merits and demerits. In the present work asymmetric spur gears of theoretically equal contact ratio as that of corresponding symmetric gears are selected to investigate the change in gear tooth static transmission error and dynamic behaviour with coast and drive side pressure angle. Study shows that dynamic factor of normal contact ratio asymmetric spur gears below resonance speed are relatively lower than corresponding symmetric gears of same module, contact ratio, number of teeth, coast side pressure angle and fillet radii. Results also show that, coast and drive side pressure angle can be suitably selected for a given contact ratio to reduce the single tooth and double tooth contact static transmission error and dynamic factor of asymmetric spur gears.

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.

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.

A model for evaluating the meshing characteristics and vibration characteristics of asymmetric spur gears with tooth modifications

Based on the potential energy method and slice assumption, an analytical model is proposed to evaluate the meshing characteristics and vibration characteristics of asymmetric spur gear pairs with tooth modifications. Considering the extended tooth contact, the nonlinear Hertzian contact, the revised foundation stiffness and the tooth modifications, the meshing characteristics of asymmetric spur gear pairs can be accurately evaluated. The time-varying mesh stiffness and contact stress obtained from the proposed method are compared with that obtained from the finite element method. The results show that the two methods are in good agreement but the computational efficiency of the proposed method is much higher than the finite element method. With the increase of the pressure angle on driving side, the contact ratio and the contact stress decrease and the mesh stiffness increases. On the basis of the meshing characteristics model, the dynamic model of asymmetric spur gear pairs is established to evaluate vibration characteristics. With the increase of the pressure angle on driving side, the amplitude of vibration increases and the first natural frequency decreases slightly. The proposed model can provide the theoretical basis for the parameter design of asymmetric spur gear pairs with tooth modifications.

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.

Fatigue Fracture Behaviour of Asymmetric Spur Gear Tooth Under Cyclic Loading

When the research on the gears are investigated, it is seen that there are different studies on the design and analysis. In the majority of research studies, the tooth root curve is designed as a trochoid curve as a results of production method. According to literature, application of the circular fillet method instead of the trochoid curve in the tooth root would increase the strength of the tooth root.Fatigue life will also be positively affected with increase of tooth strength. Because the less stress will develop in the tooth root, the fatigue life of the gear tooth will increase. In this study, we have designed and manufactured involute profile asymmetric spur gears using the circular fillet method in tooth root region.Involute profile asymmetric gears tooth have lower contact stress and superior tooth root strength than symmetric gears tooth. In this work, fatigue damages on asymmetric gear tooth caused by cyclic loads and effects of material hardness on fatigue life of gear tooth were investigated.In the extent of the study, a new single-tooth bending fatigue test apparatus (STBFT) was developed to investigate the fatigue performance of the gears. Low-cycle and high-cycle tests were done to detect the fatigue performance of the asymmetric gears.

Effect of Adjacent Teeth Load on Bending Strength of High Contact Ratio Asymmetrical Spur Gear Drive

This paper describes methodology for predicting the bending stress of the spur gear accurately by including the load on the adjacent teeth for high contact ratio asymmetric spur gear drive. Higher contact ratio is obtained by enlarging the addendum from the standard addendum value where as the asymmetric is achieved by keeping various pressure angles (170, 200 and 220) at non drive side while the drive side pressure angle was kept as 200. The bending stress developed for the given load according to the load sharing calculated by using stiffness based method along with the effect of adjacent teeth loads are explored in this work. Computer aided design tool is used for generating the gear tooth profile and ANSYS is used to carry out the finite element analysis. The result shows that the maximum bending stress level in a mesh cycle is increased when the load on adjacent teeth are taken into account. The higher pressure angle at the non-drive side yields lesser stress at the fillet region when compared to the lower pressure angle.

On the optimization of the asymmetric spur gears fillet geometry using Bézier curves

Recent research on asymmetric spur gears are focused on the geometry of the gear fillet. This happens because it is very important to avoid the high level of bending stress of the teeth. There are some authors that show how bending stress level can get lower using a proper geometry of the fillet curve. In this paper, there is presented a new concept to optimizing the geometry of the fillet curve. There is used the reasoning of finding a regular curve with minimum length that doesn't affect the functionality of the gear. Because the procedure of finding this curve is a difficult one, there is presented a special kind of curves that can accomplish all the technical requirements. The procedure is based on the considerations that are illustrated bellow.

Analytical and Numerical Tooth Contact Analysis (TCA) of Standard and Modified Involute Profile Spur Gear

Among all the common mechanical transmission elements, gears still playing the most dominant role especially in the heavy duty works offering extraordinary performance under extreme conditions and that the cause behind the extensive researches concentrating on the enhancement of its durability to do its job as well as possible. Contact stress distribution within the teeth domain is considered as one of the most effective parameters characterizing gear life, performance, efficiency, and application so that it has been well sought for formal gear profiles and paid a lot of attention for moderate tooth shapes. The aim of this work is to investigate the effect of pressure angle, speed ratio, and correction factor on the maximum contact and bending stress value and principal stresses distribution for symmetric and asymmetric spur gear. The analytical investigation adopted Hertz equations to find the contact stress value, distribution, and the contact zone width while the numerical part depends on Ansys software version 15, as a FE solver with Lagrange and penalty contact algorithm. The most fruitful points to be noticed are that the increasing of pressure angle and speed ratio trends to minimize all the induced stresses for the classical gears and the altered teeth shape with larger loaded side pressure angle than the unloaded side one behave better than the symmetric teeth concerning the stress reduction.
 

FINITE ELEMENT MODELING AND BENDING STRESS ANALYSIS OF NON STANDARD SPUR GEAR

Gears are toothed wheels, transmitting power and motion from one shaft to another by means of successive engagement of teeth. Having a higher degree of reliability, compactness, high velocity ratio and finally able to transmit motion at a very low velocity, gears are gaining importance as the most efficient means for transmitting power. A gearing system is susceptible to problems such as interference, backlash and undercut. The contact portions of tooth profiles that are not conjugate is called interference. Furthermore due to interference and in the absence of undercut, the involute tip or face of the driven gear tends to dig out the non-involute flank of the driver. The response of a spur gear and its wear is an engineering problem that has not been completely overcome yet. With the perspective of overcoming such defects and for increase the efficiency of gearing system, the use of a non-standard spur gear i.e., an asymmetric spur gear having different pressure angles for drive and coast side of the tooth comes into picture. This paper emphasis on the generation of an asymmetric spur gear tooth using modeling software and bending stress at the root of Asymmetric spur gear tooth is estimated by finite element analysis using ANSYS software and results were compared with the standard spur gear tooth.

Characteristic of involute slope modification of asymmetric spur gear

The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained. Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters. The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore, the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.

Estimation of tooth form factor for normal contact ratio asymmetric spur gear tooth

To estimate the tooth form factor for a loaded symmetric spur gear tooth, some normalized standards like International Organization for Standardization (ISO) and American Gear Manufacturers Association (AGMA) are available. However, the tooth form factor for a loaded asymmetric spur gear tooth cannot be estimated through the available standards. An asymmetric spur gear tooth is one whose drive side pressure angle is different from the coast side pressure angle. In the present work, the standard ISO B methodology has been adapted suitably for estimating the tooth form factor and the stress correction factor in asymmetric spur gear tooth. Also, the critical root fillet parameters (critical root tooth thickness, bending moment arm and radius of curvature) and the tooth form factor for asymmetric spur gear tooth with several sets of drive side and coast side pressure angles are determined through an adapted ISO method and a comparative study with FEM is also carried out.

Review of Composite Asymmetric Spur Gear

Gears made from composite materials are widely used in many power and motion transmission applications. Due to lower weight to stiffness ratio, composite gears may be replaced by conventional material gears in power transmission systems.

Research on the Design and Modification of Asymmetric Spur Gear

A design method for the geometric shape and modification of asymmetric spur gear was proposed, in which the geometric shape and modification of the gear can be obtained directly according to the rack-cutter profile. In the geometric design process of the gear, a rack-cutter with different pressure angles and fillet radius in the driving side and coast side was selected, and the generated asymmetric spur gear profiles also had different pressure angles and fillets accordingly. In the modification design of the gear, the pressure angle modification of rack-cutter was conducted firstly and then the corresponding modified involute gear profile was obtained. The geometric model of spur gears was developed using computer-aided design, and the meshing process was analyzed using finite element simulation method. Furthermore, the transmission error and load sharing ratio of unmodified and modified asymmetric spur gears were investigated. Research results showed that the proposed gear design method was feasible and desired spur gear can be obtained through one time rapid machining by the method. Asymmetric spur gear with better transmission characteristic can be obtained via involute modification.

Effect of Drive Side Contact Ratio on Direct Design Asymmetric High Contact Ratio Spur Gear Based on Load Sharing

The aim of this paper is to determine the effect on direct design asymmetric high contact ratio spur gear based on tooth load sharing. A unique Ansys parametric design language code is developed for this study. The load sharing based bending and contact stresses are determined for different drive side contact ratios. In addition to that the location of critical loading point is determined. Because the critical loading point for high contact ratio spur gear not lies on fixed point like normal contact ratio spur gears namely highest point of single tooth contact. In conclusion an increase in drive side contact ratio leads to increase in the load sharing based bending stress and decrease in the contact stress at the critical loading point.