Addendum Modification Research Articles

Choosing the optimal addendum modification coefficient of external involute spur gear

The influence of addendum modification coefficient (AMC) on the durability and load-carrying ability of gear pairs is widely adopted in the production of gears. However, the effect of AMC only surveyed at single-point, intermittent in the range of values that have not come up with the optimal value of them. In order to overcome these disadvantages, this study is proposed to develop a method for choosing the optimal AMC of external involute spur gear with the aim to improve load-carrying capacity of gears, reduce vibrations, suppress the noises and extend service life and so on. This paper investigates choosing the optimal AMC of gears based on all the necessary conditions according to the standard design that is selected. Three objectives are studied for optimal selection. As such, the combination of Pareto optimal and genetic algorithm methods is applied for gear optimization. Our method is shown to be better in the difference maximum of sliding factors and the difference of form base on the maximum of sum of AMC. The analysis results of tooth root stress and contact stress were decreased significantly. This implies the feasibility of the optimization design for increasing the gears’ properties by choosing the optimal AMC.

Impact of Structural Characteristics of Flexspline on the Stresses Occurring at the Tooth Space Bottom

The author of the article applied the boundary element method (BEM) to determine stresses occurring in a toothed rim of a flexspline. The relevant numerical calculations were conducted using software developed at the Faculty of Transport of the Silesian University of Technology. The numerical analysis conducted for flexsplines entailed the impact exerted by parameters of an indented toothed flexspline rim (number of teeth, addendum modification coefficient) and of a gear tool (gear tool head curve radius, pressure angle) on values of the stresses occurring at the tooth space bottom. Results of the said calculations have been depicted as curves of dependences between stresses at the tooth space bottom in the function of the number of flexspline rim teeth on constant values of the addendum modification coefficient. The cumulative diagrams developed based on the results of the calculations conducted may provide guidelines as to the manner of designing flexsplines for harmonic drives.

A Balanced Maximum Fillet Stresses on Normal Contact Ratio Spur Gears to Improve the Load Carrying Capacity Through Nonstandard Gears

This article presents an idea to remove the inequality in maximum fillet stresses developed between pinion and gear of a step up gear drive. This uniform fillet strength of the gear drive can be achieved by using nonstandard pinion and gear with appropriate addendum modifications generated by nonstandard basic racks of respective tooth thickness not equal to 0.5πm at the pitch circle. The influence of gear parameters such as gear ratio, pressure angle, addendum factor, pinion teeth number, and addendum modifications on the maximum fillet stress on the nonstandard pinion and gears of different tooth thickness has been analyzed through finite element method and finally the optimum value of rack tooth thickness coefficients (k pc and k gc ) are suggested for the given gear drive (defined by i) that improves the fillet capacity in bending. This study has been extended for various drives like S std , S o , S +, and S − drives.

Study of Formed Milling Cutter for Involute Gear with Small Numbers of Teeth

After its addendum modification and tangent modification of involute gear with fewer teeth, its addendum becomes pointed, which results in the bigger difference between the tooth profile of involute gear with fewer teeth and that of the standard. The equation of tooth profile is deduced in condition of pointed addendum of involute gear with fewer teeth and its 3D mathematic model is built. Based on the principle of form milling machining, relative position between the gear and workpiece is found when form machining. Then contact lines of cutter and workpiece are derived and revolution surface and axial section of formed cutter are obtained. Simulating machining is made after the cutter model is built in 3D software. It’s found that the gear obtained by simulating machining coincides fully with that built based on equation of tooth profile, which shows the validity of form milling machining.

Preliminary modeling of the oil trapping between teeth for spur gears

This study focuses on the phenomenon of oil trapping in the tooth spaces of spur gears. It presents the first obtained results in order to provide an estimation of the power losses due to the compression of the oil trapped between the inter teeth meshing spaces in a high-speed transmission for internal and external spur gears. It first allows, to model the inter teeth spaces at any time and offers limits for the trapped fluid volume and axial and radial discharge surfaces. The discretization impact result is discussed.Then, the influence of certain design and operating parameters such as module, pressure angle, addendum modification coefficient and rotational speed on these discharge surfaces and trapped volume is presented.

Effect of Backup Ratio and Cutter Tip Radius on Uniform Bending Strength Design of Spur Gears

In the higher speed ratio and profile shifted gear drives, the maximum fillet stress in the pinion and the gear is not equal. The load-carrying capacity of the gear drives can be improved by removing this unbalanced maximum fillet stress. This paper has explained an idea to remove this unbalanced maximum fillet stress and design the spur gear drives with uniform fillet strength. This uniform fillet strength of the gear drive can be achieved by changing the tooth thickness of basic racks on the pitch lines from the standard tooth thickness (0.5πm) in to a non-standard one (kgcπm, kgc≠0.5). The influence of gear parameters such as backup ratio, cutter tip radius and addendum modification factors on the maximum fillet stress has been analyzed through FEM with different values of tooth thickness coefficient and finally the optimum value of tooth thickness coefficient are suggested for the given spur gear drive that improve the fillet capacity in bending.

Design and Static Analysis of an Addendum Modified Helical Gear Tooth

A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. We have several types of gears among which spur gears are used as pinion and gear between parallel shafts.. When the involute portion of the tooth mates with the non-involute portion of the other tooth an undercut is formed. Due to this the mating gear will try to scoop out metal from the interfering portion. In order to avoid undercutting and interference, addendum modification of the gear tooth is carried out. This paper describes about the modeling meshing and the analysis techniques. Effort has been taken to develop the tooth profile involute as well as the fillet region by calculating the co-ordinates using C-language. The output file of the C-program is converted to modeling software PRO/E for 3-D modeling with the help of a coupler software DXF file converter. Those PRO/E models are imported to an analysis software ANSYS for the proposed stress analysis.

Structural and Technology Support Quality Improvement of Gear Coupling

In this work the question of sharing use a thermo-mechanical treatment method and forming spatial tool based on a kinematic method researches gearings, is considered. Also, the method of thermo mechanical treatment a gear couplings teeth, with the receiving a spatial teeth geometry and ensuring required physical- mechanical properties of them, is presented. For implementation of this method, the scheme of the device and the special tool is developed, which allows to fair blanking of spatially modified teeth. The design procedure a teeth tool’s geometric parameters of the line addendum modification are offered.

Explicit Parametric Method for Optimal Spur Gear Tooth Profile Definition

The gear tooth profile has an immense effect on the main operating parameters of gear pairs (load capacity, working life, efficiency, vibrations, etc). In current engineering research and practice, there is a strong need to develop methods for tooth profile optimization. In this paper a new method for selecting the optimal tooth profile parameters of spur gears is described. This method has been named the Explicit Parametric Method (EPM). The addendum modification coefficient, radius of root curvature, and pressure angle of the basic rack for cylindrical gears, have been identified as the main tooth profile parameters of spur gears. Therefore, the EPM selects the optimal values for these three tooth profile parameters. Special attention has been paid to develop a method of adjustment for the particular working conditions and explicit optimization requirements. The EPM for optimal tooth profile parameters of gears uses contact nonlinear Finite Element Analysis (FEA) for calculation of deformations and stresses of gear pairs, in addition to explicit comparative diagrams for optimal tooth profile parameter selection.

Optimal Selection of Addendum Modification Coefficients of Involute Cylindrical Gears

Based on the principles of equalized sliding coefficients and equalized t oo th bending strength, the optimization mathematical model for calculating and allocating the addendum modification coefficients of involute cylindrical gear is firstly established. Then the measures to calculate the tooth parameters in real-time during the optimization steps are achieved. Finally, the optimization program for calculating and allocating the modification coefficients is developed using the Optimization Toolbox in MATLAB combined with VC++. Compared with the traditional methods such as enclosed chart and graph method, the proposed optimization method in this paper can update the constraints during the optimization process and obtain the accurate modification coefficients. The examples show that the proposed optimization method is more rational and accurate .

スプライン穴付き歯車の押出し成形

The shaping conditions for a spur gear with an inner spline by cold extrusion are examined experimentally. The specifications of the spur gear examined are as follows: module m=1.25-2.0, number of teeth Z=18-13, pressure angle α=20°, and tooth depth h=2.25m; those of the inner spline are as follows: module ms=1.0, number of teeth Z=8-18, pressure angle α=20°, and tooth depth hs=1.25m. The tested material is low-carbon steel, S15C. The inner diameter of the workpiece, inner spline tooth depth, addendum modification coefficient, and module are varied to examine the effect of the reduction in area. It is found that well-shaped spur gears and inner splines can be produced. The shaping conditions are closely connected with the reduction in area. The accuracy of the shaped spur gear was about 7 Grade in the old JIS. The punch pressure needed for the shaping is much lower than the strength of the punch material.

Research on Increasing Hob Tip Fillet Radius to Decrease Addendum Modification Coefficient

Reasonable design of hob tip fillet and calculation of modification coefficients were researched to avoid undercutting in this paper. The undercut gears were generated in the virtual environment based on Pro / E software. Meanwhile, parametric finite element models of undercut gear, ordinary modified gear generated by standard hob and modified gear generated by hob with tip fillet radius increased,were founded by APDL (ANSYS Parametric Design Language).The results show that the minimum modification coefficients chosen to avoid undercutting by traditional modification method may not meet the requirements of contact ratio or addendum thickness.While through reasonable design of hob tip fillet, modification coefficients calculated not only avoid undercutting to improve the tooth bending strength but also meet the requirements of contact ratio ε>1.2 and addendum thickness δ>0.25m (module) .

A thermal finite line contact EHL model of a helical gear pair

A thermal finite line contact elastohydrodynamic lubrication (EHL) model is developed to study lubricated contact performance of a helical gear pair. Three typical engagement positions during a meshing cycle, i.e. the engage-in position, the engage-out position and the pitch point position are chosen to show effect of load, speed, and addendum modification on pressure distribution, film profile, temperature field, etc. Results show temperature rise increases as the load or the speed goes up. The temperature distribution when the gear pair engaging around the pitch point behaves like a V-shape with higher values at the end parts. For the case with a standard center distance, proper addendum modification, i.e., negative modification for the bigger gear and positive modification for the small gear is good for improving lubrication performance and the service life of the helical gear drive.

Research on Measure Method of Common Normal Length Variation of Bilateral Modification Gear

In the conditions of rationally selecting of the measure tooth number, this paper puts forward a new method to calculate the common normal length variation, which is based on coordinate measurement machine to collect the data of bilateral modification gear's outline. Firstly, the addendum modification coefficient and tangential modification coefficient are used to determine the optimum measure tooth number, and then the common normal length variation is determined according to the definition. The experiment has shown that this way has a lot of advantages, such as the intensive data of sample points, less human intervention and high measurement accuracy.

Comparison of tooth profiles and oil formulation focusing lower power losses

Environmental awareness, lower consumption of raw materials and longer life of equipment are main concerns nowadays and are leading to the research and development of lubricants and equipment to access those requirements. In this study, the power loss performance of three different tooth profile geometries, developed with the purpose of decreasing power losses while keeping the predicted life, were tested and evaluated in a FZG test rig. The path to reduce power losses was based on the decrease of the module, the increase of the helix angle and increase of the addendum modification coefficients in order to reduce the path of contact, i.e. the sliding velocity. The power loss behaviour of two different lubricants was also evaluated for each tooth profile geometry considered. The influence of the oil level in the gearbox was also evaluated. One of the lubricants has an ester base while the other has a polyalphaolefin base and both are fully formulated. An energetic model was developed for the FZG test gearbox and applied to these tests to improve the knowledge about the influence of tooth geometries as well as lubricant formulation in the power losses and coefficient of friction between gear teeth. The developed geometries showed that the path followed for the reduction of power losses produced the expected results and can be implemented with success on gear design.

Influence of the addendum modification on spur gear efficiency

Nowadays, in the field of transmissions, one of the most important objectives is to realize gears with high efficiency so as to reduce power losses, operating temperatures, noise and wear. The target of this work is to analyze spur gear efficiency through two different approaches for friction coefficient calculation along the line of action in order to evaluate the possible differences. The first method analyzed considers a mean friction coefficient that follows Niemann's equation, the second method considers a local value for the friction coefficient following Hai Xu studies. For this purpose the efficiency variation versus the addendum modification of the pinion is taken into consideration for each of the following: operating conditions, transmission ratio and sum of addendum modification coefficient variations. Moreover, using the results of the first part of the paper, some of the more used methods for gear teeth optimization, in terms of the apportion of the addendum modification coefficient, are investigated in depth and compared in terms of efficiency so as to find out the best behaviour about: load capacity, safety against wear, noise and vibration.

An analytical method to determine the addendum modification parameters of involute helical gears

Due to the simplified tooth profile and the complicated load distribution along the contact line, the traditional analytic method cannot satisfy the accuracy requirement while carrying out addendum modification of the helical gears. To overcome this disadvantage, a new way based on cross-section method is presented to calculate the deformation of helical tooth tip. First, the tooth is divided into copies of cross-section along face width and the moment of inertia for each section is calculated. Also, the load is distributed according to length of the contact line, and the effect of deflected load is taken into account as well. Based on these works, a general formula of helical tooth tip deformation is deduced. Then, this formula is applied to calculate the addendum modification width ac. In addition, considering that tooth tip modification will shorten the meshing line, three models used to control length of the remaining meshing line are proposed and addendum modification height hc is defined accordingly. Finally, an instance is given to verify the good agreement between results of this study and those of a finite element model. Apart from this, engineering application of this method is provided.

Maximum Fillet Stress Analysis Based on Load Sharing in Normal Contact Ratio Spur Gear Drives#

An optimum design of high-quality gears requires an accurate estimation of the tooth load. Since only a fraction of the total load is shared by each pair, when there is contact in more than one pair during transmission, the same has been estimated with a reasonable accuracy through the load-sharing ratio calculated using the single-point loaded model. The reliability of this method has also been justified by comparison with multipair contact models and also by checking with the values available in the literature. The influence of finite-element modeling, boundary conditions, gear ratio, teeth number, module, pressure angle at pitch circle, backup ratio, generating rack cutter tip radius, and addendum modification factor on the load-sharing ratio and in turn in the maximum fillet stress has been studied and discussed using single-point loaded model of normal contact ratio gear pairs in this study.

The Precise Forming of Automobile Start Gear Shaft

The start gear shaft is the key part of automobile starter, it is involute small module internal gear with addendum modification. It is step shaft with H/D>6 in the outline. Because of the concentric degree demand of the internal gear and the outline step shaft is higher, length of below shaft is large and diameter is small, So plastic forming of the shaft is very difficult. Meeting the needs of markets and improving comprehensive function of automobiles, the high efficient precision forming technology method of single-step chipless-forming for internal gear tooth surface and external step shaft is put forward based on analysis, study and repeated test. In the same time, a set of high accuracy die with simple novel structure and long service life is designed and manufactured. The advantages of the method have been verified that utilization ratio of material and production efficiency is high. For this reason, the method is profitable reference for producing the same type of complex shape gear shaft.

812 試料内径の拡張押出しによる歯車成形(GS1-(2) 通常セッション,オーガナイズドセッション)

The shaping of the spur gear by expanding the inner diameter was studied. That is the workpiece is set its inner diameter to the front part of the stepped mandrel, which is placed the expansion of its inner diameter, by passing through the rear part of the mandrel. The specification of the gear is as follows: module m=1.0mm, number of teeth z=26, pressure angle α=20°, whole depth h=2.25mm, addendum modification x=0.25. Criterion for the shaping of complete teeth is discussed in terms of reduction in area and expanding of the inner diameter of workpiece. It is shown that the reduction in area for shaping the complete teethed gears 8%. The required pressure of punch annd stepped mandrel for shaping is far below the strength of the punch and mandrel materials.