A Method for Constructing Standard Involute Gear Tooth Profile

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

Nowadays the design constructional process is almost exclusively aided with CAD/CAE/CAM systems. It is evaluated that nearly 80% of design activities have a routine nature. These design routine tasks are highly susceptible to automation. Design automation is usually made with API tools which allow building original software responsible for adding different engineering activities. In this paper the original software worked out in order to automate engineering tasks at the stage of a product geometrical shape design is presented. The elaborated software works exclusively in NX Siemens CAD/CAM/CAE environment and was prepared in Microsoft Visual Studio with application of the .NET technology and NX SNAP library. The software functionality allows designing and modelling of spur and helicoidal involute gears. Moreover, it is possible to estimate relative manufacturing costs. With the Generator module it is possible to design and model both standard and non-standard gear wheels. The main advantage of the model generated in such a way is its better representation of an involute curve in comparison to those which are drawn in specialized standard CAD systems tools. It comes from fact that usually in CAD systems an involute curve is drawn by 3 points that respond to points located on the addendum circle, the reference diameter of a gear and the base circle respectively. In the Generator module the involute curve is drawn by 11 involute points which are located on and upper the base and the addendum circles therefore 3D gear wheels models are highly accurate. Application of the Generator module makes the modelling process very rapid so that the gear wheel modelling time is reduced to several seconds. During the conducted research the analysis of differences between standard 3 points and 11 points involutes was made. The results and conclusions drawn upon analysis are shown in details.

According to Jarvis March method and characteristics of non-circular gear's tooth profile, a numerical algorithm of non-circular gear's tooth profile based on Jarvis March has been proposed. This method can calculate the non-circular gear's tooth profile with the help of improved Jarvis March method. And improve efficiency and accuracy by simplify shaper cutter model and envelope process. So this method can calculate the non-circular gear's tooth profile accurately and efficiently. In order to detect the correctness and efficiency of this method, the method has been used to calculate the tooth profile's curve data of non-circular gear. In the end, good results have been obtained and indirectly verify the correctness and efficiency of this method.

This paper describes an experimental study of the wear of injection molded acetal gears on tooth flank.For the driving gear, general-purpose acetal copolymer is used, while for the driven gear, 12 kinds of acetal resin for friction performance are used. The gear parameters are module=1.0mm, number of teeth=37, pressure angle=20° and face width=6.0mm. The gear precision for the driving and driven gears are JGMA Grade 0 to 3. The conditions of this experiment are as follows; fixed torque=0.3N·m, rotation rate=1000rpm, total number of revolutions=1×106 times.This experiment concentrated on the following 4 points. 1) Amount of wear, 2) Change on tooth flank, 3) Gear accuracy, 4) State of tooth surface (using a SEM).The above observation shows that low friction coefficient acetal gears, with a few exceptions, are effective for wear decrease generally in proportion to their mechanical properties. Grading by JIS and by JGMA standards for gear accuracy do not always coincide, because these methods are basically different. Furthermore, a significant change in the tooth surface is seen around the pitch and this change depends on the combination of intermeshing gears. Lubrication of the driven gear also plays an important role in the state of wear and in friction performance. Therefore it is evident that the choice of the gear material has a great influence on the usage.

IN text books on gears and gear teeth the form of the tooth below the base circle is usually dismissed with a few words of advice on the evils of undercutting, and while formulae for calculating the form of the involute curve abound, no one worries about the epitrochoid which is the form of the curve below the base circle. This may be because the involute is a self‐respecting curve that never varies except in size while the epitrochoid varies as the distance below the base circle and the ratio of the rolling circles vary. Of course in the case of generated gears, provided that the root diameter gives sufficient clearance the cutter will sweep out its own correct path, but with gears ground with formed wheels the question of the form below the base circle does arise, especially with small pump gears of about nine to sixteen teeth. The easiest way to examine the form of the root is by projection and here comes the problem of drawing the correct form.

In this paper the problem of the failure of gear in speed reduction gearbox developed by Laxmi Hydraulic Pump (LHP) Pvt Ltd, Solapur is resolved by replacing the existing material by a material SAE8620. The Gear and Pinion using AGMA and FEM analysis Method. In the gear design, the bending stress and surface strength of the gear tooth are considered to be one of the main factors to the failure of the gear. In this paper bending and contact stresses are calculated by using analytical method as well as Finite Element Method. To estimate bending stress modified Lewis beam strength method is used as well as AGMA method. Software is used to generate the 3-D solid model of helical gear. Ansys software package is used to analyze the bending stress. Contact stresses are calculated using modified AGMA contact stress method. Ansys software package is used to analyze the contact stress and bending stress. The main objective of this study has to investigate the stresses induced by gear tooth profile. Finally, the results obtained by theoretical analysis and Finite Element Analysis are compared to check the correctness. Estimated stress is used to calculate module of gear which can withstand easily at given loading conditions. A conclusion has arrived on the material which is best suited for helical gear based on the results.

This paper presents an iterative method for calculating the effective contact ratio and the bending tooth stress for a pair of plastic/plastic and plastic/steel spur gears with an involute profile. In this method, the pinion and the gear are modeled, at each moment of the mesh cycle, as equivalent springs in parallel undergoing the same displacement along the line of action. This leads to the calculation of the bending stress by taking into account the number of teeth initially in contact and those which enter in contact prematurely. We also investigate the influence of certain gear parameters, such as, the number of teeth, the pressure angle, and the module on the behavior of a pair of meshed gears. In addition, the variation of the bending stress at the tooth fillet is investigated for a pair of plastic/plastic and a pair of plastic/steel spur gears, in order to determine the critical configurations for which the bending stress is maximum. In general, the results obtained from the present method also show that the stress variation in plastic/plastic gears differs markedly from that in plastic/steel gears.

Deproximating Tredgold's Approximation

Determination of the ISO tooth form factor for involute spur and helical gears

A hybrid strategy is proposed to meet the challenge of obtaining the profile of micro gear teeth with a small modulus. Firstly, the contact probe segmentally obtained the falling flank profiles with an auxiliary lifting mechanism to avoid interference when it climbs on the rising slope. Then, the noncontact chromatic confocal displacement sensor efficiently acquired the gear peak positions to carry out the two-point error separation with the gear peak positions from the probe measurement. Finally, actual experiments were carried out to obtain the profile of a harmonic drive flexspline. Compared with the commercial ultraprecise profiler, the proposed method provides measurement results with a deviation of less than 20 μm. In conclusion, the hybrid strategy is feasible and accurate for drawing the micro gear teeth profile without any collision between the measuring probes and the measured workpiece.

In this article, the simultaneous influence of profile shape variation and running-in of the involute gear teeth on the surface load capacity of cylindrical gear pair was examined. Experimental investigations were carried out on spur gears in laboratory conditions, using a back-to-back gear test rig. Different involute profile shapes are achieved by varying the gear teeth pressure angle. Different running-in regimes were achieved by varying the torque of the gear pair in the initial period of operation. By modifying the profile and adequate running-in in short period of time, the following are reduced: the intensity of wear, the amount of surface damage, and friction on the contact surfaces of gear teeth. Greater benefits of a higher pressure angle and running-in were observed with driven gears. It is shown that the negative sliding on the dedendum of the driving gears teeth has a greater effect on the generation of surface fatigue compared to the driven gears teeth, due to the direction of the friction force. The obtained results indicate that by varying the shape of the involute profile and running-in parameters, the surface load capacity of spur gears can be significantly improved, such that a longer operational life and greater efficiency of the gear drive in exploitation can be achieved.

Study of the influence of the design parameters on the efficiency of spur gears

The cutter systems of hypoid gear cutting machines contain groups of inside and outside blades. In these cutter systems, the side cutting edges of the blades machine the convex and concave gear teeth while rotating about the cutter rotation axis. The side cutting edges lay on the rake face formed through the blade, rake, and relief angles; hence, the normal cross-section of the cutter swept surface forms hyperboloid gear teeth. Using the accurate geometry of the cutter system, a relationship between the pressure and spiral angles of the gear tooth and the parameters of the cutter system is developed for the FORMAT machining of a hypoid gear. A new parameterization of the gear tooth surfaces is introduced to determine these angles for the accurate gear tooth by the accurate cutter system. A numerical example with different cutter systems and blade parameters is presented, demonstrating the effects of rake and relief angles over the pressure and spiral angles on mean point projections and gear tooth surface. Finally, the change in pressure and spiral angles with respect to the rake and relief angles are plotted, and the results are analyzed. Finally, it is concluded that the pressure and spiral angles are changed up to a few seconds of a degree in the operating area of the tooth with the change in the back and side rake angles. The side relief angle exhibited little or no effect over the geometry of the gear tooth.

Computer modeling of rack-generated spur gears

The logarithmic spiral bevel gear is a new type of spiral bevel gear and has received great attention in the industry for its excellent engineering characteristics. The objective of this study is to develop an accurate geometric model for the logarithmic spiral bevel gear. Based on the gear tooth flank formation mechanism, a conical logarithmic spiral curve with a constant spiral angle was constructed as the tooth trace curve. The profiles for the exterior and interior transverse of the tooth were built with an accurate involutes curve, with transition being circular arcs and straight lines. The first tooth model was established by sweeping the tooth profile accurately along the tooth trace curve, and the rest of the teeth were created by an array operation. The accurate three-dimensional model of logarithmic spiral bevel gear was finally obtained by means of a Boolean addition operation among all of the gear teeth and the root cone. An experimental study was carried out for such a gear whose number of teeth was 37, with modules being 4.5 mm, normal pressure angle being 20° and spiral angle being 35°. A DMU 40 monoBLOCK five-axis computer numerical control milling machine tool was used to produce the prototype, and a Zeiss CONTURA G3 three-dimensional coordinate instrument was employed to measure the exterior transverse addendum diameter. The linear error between the theoretical model value and the measured average value was 0.0027 mm, indicating the effectiveness and practicability of this modeling method, which provides an accurate geometric model for design and for subsequent tasks like computer-aided engineering analysis and manufacturing.