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The gear tooth fillet is an area of maximum bending stress concentration. However, its profile is typically less specified in the gear drawing and hardly controlled during gear inspection in comparison with the gear tooth flanks. This paper presents a fillet profile optimization technique for gears with symmetric and asymmetric teeth based on FEA and a random search method. It allows achieving substantial bending stress reduction in comparison with traditionally designed gears. This bending stress reduction can be traded for higher load capacity, longer lifetime, lower noise and vibration and cost reduction.
This article describes a root fillet form calculating method for a helical gear generated with a shaper cutter.
The fundamental purpose of gear grinding is to consistently and economically produce "hard" or "soft" gear tooth elements within the accuracy required by the gear functions. These gear elements include tooth profile, tooth spacing, lead or parallelism, axial profile, pitch line runout, surface finish, root fillet profile, and other gear geometry which contribute to the performance of a gear train.
In this article, a new tip relief profile modification for spur gears is presented. The topography proposed here is a classical linear profile modification with a parabolic fillet.
Introduction The standard profile form in cylindrical gears is an involute. Involutes are generated with a trapezoidal rack â€” the basis for easy and production-stable manufacturing (Fig. 1).
A programmable algorithm is developed to separate out the effect of eccentricity (radial runout) from elemental gear inspection date, namely, profile and lead data. This algorithm can be coded in gear inspection software to detect the existence, the magnitude and the orientation of the eccentricity without making a separate runout check. A real example shows this algorithm produces good results.
Base helix error - the resultant of lead and profile errors is the measured deviation from the theoretical line of contact (Fig. 1). It can be measured in the same way that lead error on a spur gear is measured, namely, by setting a height gage to height H based on the radial distance r to a specified line of contact (Fig. 2), rotating the gear so as to bring a tooth into contact with the indicator on the height gage, and then moving the height gage along two or more normals to the plane of action. The theoretical line of contact on helical gear must be parallel to the surface plate, which is attained by mounting the gear on a sine bar (Fig. 3).
Early in the practice of involute gearing, virtually all gears were made with the teeth in a standard relationship to the reference pitch circle. This has the advantages that any two gears of the same pitch, helix angle and pressure angle can operate together, and that geometry calculations are relatively simple. It was soon realized, though, that there are greater advantages to be gained by modifying the relationship of the teeth to the reference pitch circle. The modifications are called profile shift.
In this article, equations for finding profile and base pitch errors with a micrometer are derived. Limitations of micrometers with disc anvils are described. The design of a micrometer with suitable anvils is outlined.
Three experts tackle the question of profile shift in this issue's edition of "Ask the Expert."
Vibration and noise from wind turbines can be significantly influenced - and therefore reduced - by selecting suitable gearing modifications. New options provided by manufacturers of machine tools and grinding machines, and especially state-of-the-art machines and controls, provide combined gearing modifications - or topological gearing corrections - that can now be reliably machined. Theoretical investigations of topological modifications are discussed here with the actual machining and their possible use.
Measurement institutions of seven different countries â€” China, Germany, Japan, Thailand, Ukraine, United Kingdom and the U.S. â€” participated in the implementation of the first international comparison of involute gear measurement standards. The German metrology institute Physikalisch-Technische Bundesanstalt (PTB) was chosen as the pilot laboratory as well as the organizer. Three typical involute gear measurement standards provided by the PTB were deployed for this comparison: a profile, a helix and a pitch measurement standard. In the final analysis, of the results obtained from all participants, the weighted mean was evaluated as reference value for all 28 measured parameters. However, besides the measurement standards, the measured parameters, and, most importantly, some of the comparison results from all participants are anonymously presented. Furthermore, mishandling of the measurement standards as occurred during the comparison will be illustrated.
The name Gleason is practically synonymous with gear manufacturing. Since the company was founded in 1865, the technology of gear manufacturing has been its focus, its core and its competitive advantage.
Helical gear teeth are affected by cratering wear â€” particularly in the regions of low oil film thicknesses, high flank pressures and high sliding speeds. The greatest wear occurs on the pinion â€” in the area of negative specific sliding. Here the tooth tip radius of the driven gear makes contact with the flank of the driving gear with maximum sliding speed and pressure.
A major source of helicopter cabin noise (which has been measured at over 100 decibels sound pressure level) is the gear box. Reduction of this noise is a NASA and U.S. Army goal.
Chapter 2, Continued In the previous sections, development of conjugate, face milled as well as face hobbed bevel gearsets - including the application of profile and length crowning - was demonstrated. It was mentioned during that demonstration that in order to optimize the common surface area, where pinion and gear flanks have meshing contact (common flank working area), a profile shift must be introduced. This concluding section of chapter 2 explains the principle of profile shift; i.e. - how it is applied to bevel and hypoid gears and then expands on profile side shift, and the frequently used root angle correction which - from its gear theoretical understanding - is a variable profile shift that changes the shift factor along the face width. The end of this section elaborates on five different possibilities to tilt the face cutter head relative to the generating gear, in order to achieve interesting effects on the bevel gear flank form. This installment concludes chapter 2 of the Bevel Gear Technology book that lays the foundation of the following chapters, some of which also will be covered in this series.
This paper presents a new approach to repair industrial gears by showing a case study where pressure angle modification is also considered, differently from the past repairing procedures that dealt only with the modification of the profile shift coefficient. A computer program has been developed to automatically determine the repair alternatives under two goals: minimize the stock removal or maximize gear tooth strength.
The deformation of the gear teeth due to load conditions may cause premature tooth meshing. This irregular tooth contact causes increased stress on the tooth flank. These adverse effects can be avoided by using defined flank modifications, designed by means of FE-based tooth contact analysis.
In order to improve load-carrying capacity and noise behavior, gears usually have profile and lead modifications. Furthermore, in gears where a specified tooth-flank load application direction (for drive and coast flanks) is a design enhancement, or even compulsory, the asymmetric tooth profile is a further solution. Nowadays, many gears need to be hard finished. Continuous generating grinding offers a very high process efficiency, but is this process able to grind all modifications, especially asymmetric gears? Yes, it is!
A reader asks: We are currently revising our gear standards and tolerances, and a few problems with the new standard AGMA 2002-C16 have arisen. Firstly, the way to calculate the tooth thickness tolerance seems to need a "manufacturing profile shift coefficient" that isn't specified in the standard; neither is another standard referred to for this coefficient. This tolerance on tooth thickness is needed later to calculate the span width as well as the pin diameter. Furthermore, there seems to be no tolerancing on the major and minor diameters of a gear.
In many gear transmissions, tooth load on one flank is significantly higher and is applied for longer periods of time than on the opposite one; an asymmetric tooth shape should reflect this functional difference. The advantages of these gears allow us to improve the performance of the primary drive tooth flanks at the expense of the opposite coast flanks, which are unloaded or lightly loaded during a relatively short work period by drive flank contact and bending stress reduction. This article is about the microgeometry optimization of the spur asymmetric gearsâ€™ tooth flank profile based on the tooth bending and contact deflections.
A reader asks: We are currently revising our gear standards and tolerances and a few questions with the new standard AGMA 2002-C16 have risen. Firstly, the way to calculate the tooth thickness tolerance seems to need a "manufacturing profile shift coefficient" that isn't specified in the standard; neither is another standard referred to for this coefficient. This tolerance on tooth thickness is needed later to calculate the span width as well as the pin diameter. Furthermore, there seems to be no tolerancing on the major and minor diameters of a gear.
In this paper the effects of thermally induced geometry distortions on load distribution and transmission error have been analyzed.
Lately, the use of asymmetric gears in automotive and other applications is an upcoming trend, though few applications are known to have asymmetric teeth. However, an increased interest in asymmetric gears can be seen. Many companies have started to design and test such applications.
It isn't for everyone, but... Within the installed base of modern CNC gear profile grinding machines (approximately 542 machines worldwide), grinding from the solid isn't frequent, but a growing number of gear profile grinder users are applying it successfully using CBN-plated wheels.
When designing hardened and ground spur gears to operate with minimum noise, what are the parameters to be considered? should tip and/or root relief be applied to both wheel and pinion or only to one member? When pinions are enlarged and he wheel reduced, should tip relief be applied? What are the effects on strength, wear and noise? For given ratios with enlarged pinions and reduced wheels, how can the gear set sized be checked or adjusted to ensure that the best combination has been achieved?
This article presents a new spur gear 20-degree design that works interchangeably with the standard 20-degree system and achieves increased tooth bending strength and hence load carrying capacity.
In order to grind gears burn-free and as productively as possible, a better understanding of the process is required.
This article investigates fillet features consequent to tooth grinding by generating methods. Fillets resulting from tooth cutting and tooth grinding at different pressure angles and with different positions of grinding wheel are compared. Ways to improve the final fillet of the ground teeth with regard to tooth strength and noise, as well as the grinding conditions, are shown. "Undergrinding" is defined and special designs for noiseless gears are described.
For maximum life in carburized and ground gearing, I have been advised that fully grinding a radius into the root gives maximum resistance against fatigue failures. Others have advised that a hobbed and unground radius root form is best. Which is best, and why?
While designing gear and spline teeth, the root fillet area and the corresponding maximum tensile stress are primary design considerations for the gear designer. Root fillet tensile stress may be calculated using macro-geometry values such as module, minor diameter, effective fillet radius, face width, etc.
This study emphasizes the importance of a closed-loop approach togear design and manufacturing to assure designed root fillet shapes are attained in production, and gears meet the design intent.
This paper shows a method to calculate the occurring tooth root stress for involute, external gears with any form of fillets very precisely within a few seconds.
This article shows the newest developments to reduce overall cycle time in grinding wind power gears, including the use of both profile grinding and threaded wheel grinding.
Glancing back now, The Falk Corp. looks to have had a straight path toward power transmission when it opened in 1892.
Much information has been written on gear inspection, analytical. functional. semiautomatic and automatic. In most cases, the charts, (if you are lucky enough to have recording equipment) have been explained.
This paper will demonstrate that, unlike commonly used low-contact-ratio spur gears, high-contact-ratio spur gears can provide higher power-to-weight ratio, and can also achieve smoother running with lower transmission error (TE) variations.
A graphical procedure for selecting optimum combinations of profile and lead modifications.
Question: I have just become involved with the inspection of gears in a production operation and wonder why the procedure specifies that four involute checks must be made on each side of the tooth of the gear being produced, where one tooth is checked and charted in each quadrant of the gear. Why is this done? These particular gears are checked in the pre-shaved, finish-shaved, and the after-heat-treat condition, so a lot of profile checking must be done.
Modern gearboxes are characterized by high torque load demands, low running noise and compact design. In order to fulfill these demands, profile and lead modifications are being applied more often than in the past. This paper will focus on how to produce profile and lead modifications by using the two most common grinding processesâ€”threaded wheel and profile grinding. In addition, more difficult modificationsâ€”such as defined flank twist or topological flank correctionsâ€”will also be described in this paper.
Profile corrections on gears are a commonly used method to reduce transmission error, contact shock, and scoring risk. There are different types of profile corrections. It is a known fact that the type of profile correction used will have a strong influence on the resulting transmission error. The degree of this influence may be determined by calculating tooth loading during mesh. The current method for this calculation is very complicated and time consuming; however, a new approach has been developed that could reduce the calculation time.
The use of dimensionless factors to describe gear tooth geometry seems to have a strong appeal to gear engineers. The stress factors I and J, for instance, are well established in AGMA literature. The use of the rack shift coefficient "x" to describe nonstandard gear proportions is common in Europe, but is not as commonly used in the United States. When it is encountered in the European literature or in the operating manuals for imported machine tools, it can be a source of confusion to the American engineer.
The NASA Lewis Research Center investigated the effect of tooth profile on the acoustic behavior of spur gears through experimental techniques. The tests were conducted by Cleveland State University (CSU) in NASA Lewis' spur gear testing apparatus. Acoustic intensity (AI) measurements of the apparatus were obtained using a Robotic Acoustic Intensity Measurement System (RAIMS). This system was developed by CSU for NASA to evaluate the usefulness of a highly automated acoustic intensity measurement tool in the reverberant environment of gear transmission test cells.
The newer profile-shifted (long and short addendum) gears are often used as small size reduction gears for automobiles or motorcycles. The authors have investigated the damage to each cutting edge when small size mass-produced gears with shifted profiles are used at high speeds.
This article describes a method of obtaining gear tooth profiles from the geometry of the rack (or hob) that is used to generate the gear. This method works for arbitrary rack geometries, including the case when only a numerical description of the rack is available. Examples of a simple rack, rack with protuberances and a hob with root chamfer are described. The application of this technique to the generation of boundary element meshes for gear tooth strength calculation and the generation of finite element models for the frictional contact analysis of gear pairs is also described.
Our research group has been engaged in the study of gear noise for some nine years and has succeeded in cutting the noise from an average level to some 81-83 dB to 76-78 dB by both experimental and theoretical research. Experimental research centered on the investigation into the relation between the gear error and noise. Theoretical research centered on the geometry and kinematics of the meshing process of gears with geometric error. A phenomenon called "out-of-bound meshing of gears" was discovered and mathematically proven, and an in-depth analysis of the change-over process from the meshing of one pair of teeth to the next is followed, which leads to the conclusion we are using to solve the gear noise problem. The authors also suggest some optimized profiles to ensure silent transmission, and a new definition of profile error is suggested.
An investigation of transmission errors and bearing contact of spur, helical, and spiral bevel gears was performed. Modified tooth surfaces for these gears have been proposed in order to absorb linear transmission errors caused by gear misalignment and to localize the bearing contact. Numerical examples for spur, helical, and spiral bevel gears are presented to illustrate the behavior of the modified gear surfaces with respect to misalignment and errors of assembly. The numerical results indicate that the modified surfaces will perform with a low level of transmission error in non-ideal operating environments.
In this paper, an accurate FEM analysis has been done of the â€śtrueâ€ť stress at tooth root of spur gears in the function of the gear geometry. The obtained results confirm the importance of these differences.
On many occasions a reasonably approximate, but not exact, representation of an involute tooth profile is required. Applications include making drawings, especially at enlarged scale, and laser or EDM cutting of gears, molds, and dies used to produce gears. When numerical control (NC) techniques are to be used, a simple way to model an involute can make the NC programming task much easier.