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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.
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.
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.
Introduction The standard profile form in cylindrical gears is an involute. Involutes are generated with a trapezoidal rack — the basis for easy and production-stable manufacturing (Fig. 1).
An analysis of possibilities for the selection of tool geometry parameters was made in order to reduce tooth profile errors during the grinding of gears by different methods. The selection of parameters was based on the analysis of he grid diagram of a gear and a rack. Some formulas and graphs are presented for the selection of the pressure angle, module and addendum of the rack-tool. The results from the grinding experimental gears confirm the theoretical analysis.
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.
The authors have developed a rack-type rolling process in which a rack tool is used to roll gear teeth. The results and analysis show that the proposed method reduces errors.
Zerol bevel gears are the special case of spiral bevel gears with a spiral angle of 0°. They are manufactured in a single-indexing face milling process with large cutter diameters, an extra deep tooth profile and tapered tooth depth.
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.
Load-carrying capacity of gears, especially the surface durability, is influenced by their tooth surface roughness in addition to their tooth profiles and tooth traces.
Since the design of involute splines and their manufacture requires considerable knowledge, not only of the basic properties of the involute profile, but also of various other elements which affect the spline fit and the sometimes complex principles underlying manufacturing and checking equipment, the question is frequently raised as to why the involute profile is given preference in designing splines over the seemingly simpler straight sided tooth profile.
Point-surface-origin (PSO) macropitting occurs at sites of geometric stress concentration (GSC) such as discontinuities in the gear tooth profile caused by micropitting, cusps at the intersection of the involute profile and the trochoidal root fillet, and at edges of prior tooth damage, such as tip-to-root interference. When the profile modifications in the form of tip relief, root relief, or both, are inadequate to compensate for deflection of the gear mesh, tip-to-root interference occurs. The interference can occur at either end of the path of contact, but the damage is usually more severe near the start-of-active-profile (SAP) of the driving gear.
This paper describes the research and development of the first production gearbox with asymmetric tooth profiles for the TV7-117S turboprop engine. The paper also presents numerical design data related to development of this gearbox.
This article describes a method and a computer program that were developed for 3-D finite element analysis of long-fiber reinforced composite spur gears, in which long fibers are arranged along tooth profiles. For such a structure, the gear is composed of two regions; namely the long fiber reinforced and the chopped-fiber reinforced regions.
Gear shaving is a free-cutting gear finishing operation which removes small amounts of metal from the working surfaces of the gear teeth. Its purpose is to correct errors in index, helical angle, tooth profile and eccentricity. The process can also improve tooth surface finish and eliminate, by crowned tooth forms, the danger of tooth end load concentrations in service. Shaving provides for form modifications that reduce gear noise. These modifications can also increase the gear's load carrying capacity, its factor of safety and its service life.
Almost any external tooth form that is uniformly spaced around a center can be hobbed. Hobbing is recognized as an economical means of producing spur and helical gears with involute tooth profiles.
Gear shaving is a free-cutting gear finishing operation which removes small amounts of metal from the working surfaces of gear teeth. Its purpose is to correct errors in index, helix angle, tooth profile and eccentricity. The process also improves tooth surface finish and eliminates by means of crowned tooth forms the danger of tooth end load concentrations in service.
Gear shaving is a free-cutting gear finishing operation which removes small amounts of metal from the working surfaces of the gear teeth. Its purpose is to correct errors in index, helical angle, tooth profile and eccentricity.
Involute spur gears are very sensitive to gear misalignment. Misalignment will cause the shift of the bearing contact toward the edge of the gear tooth surfaces and transmission errors that increase gear noise. Many efforts have been made to improve the bearing contact of misaligned spur gears by crowning the pinion tooth surface. Wildhaber(1) had proposed various methods of crowning that can be achieved in the process of gear generation. Maag engineers have used crowning for making longitudinal corrections (Fig. 1a); modifying involute tooth profile uniformly across the face width (Fig. 1b); combining these two functions in Fig. 1c and performing topological modification (Fig. 1d) that can provide any deviation of the crowned tooth surface from a regular involute surface. (2)
Gear shaving is a free cutting gear finishing operation which removes small amounts of metal from the working surfaces of gear teeth. Its purpose is to correct errors in index, helix angle, tooth profile and eccentricity.
In this article, the authors calculated the numerical coordinates on the tooth surfaces of spiral bevel gears and then modeled the tooth profiles using a 3-D CAD system. They then manufactured the large-sized spiral bevel gears based on a CAM process using multi-axis control and multi-tasking machine tooling. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. Moreover, the gears were meshed with each other and the tooth contact patterns were investigated. As a result, the validity of this manufacturing method was confirmed.
This paper presents an approach that provides optimization of both gearbox kinematic arrangement and gear tooth geometry to achieve a high-density gear transmission. It introduces dimensionless gearbox volume functions that can be minimized by the internal gear ratio optimization. Different gearbox arrangements are analyzed to define a minimum of the volume functions. Application of asymmetric gear tooth profiles for power density maximization is also considered.
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.
In order to grind gears burn-free and as productively as possible, a better understanding of the process is required.
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.
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 processes—threaded wheel and profile grinding. In addition, more difficult modifications—such as defined flank twist or topological flank corrections—will also be described in this paper.
A graphical procedure for selecting optimum combinations of profile and lead modifications.
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.
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.
Glancing back now, The Falk Corp. looks to have had a straight path toward power transmission when it opened in 1892.
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.
Measurement institutions of seven different countries — China, Germany, Japan, Thailand, Ukraine, United Kingdom and the U.S. — 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.
It is very common for those working in the gear manufacturing industry to have only a limited understanding of the fundamental principals of involute helicoid gear metrology, the tendency being to leave the topic to specialists in the gear lab. It is well known that quiet, reliable gears can only be made using the information gleaned from proper gear metrology.
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.
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.
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.
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.
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.
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.
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?
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.
How does one determine the center of a worm and a worm wheel? Also, what are the differences between the common worm tooth forms?
This paper discusses the influence of tip relief, root relief, load modification, end relief and their combinations on gear stresses and transmission errors due to shaft deflections.
The two-flank roll test measures kickout (tooth-to-tooth composite error) and tooth thickness. In this article, it will be shown that measured values vary with the number of teeth on the master gear.
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.
Wait a minute, we don't measure pitch diameter. We're sometimes asked to measure it by customers, though, especially ones with older drawings.
Influences of Load Distribution and Tooth Flank Modifications as Considered in a New, DIN/ISO-Compatible Calculation Method
This article is part four of an eight-part series on the tribology aspects of angular gear drives. Each article will be presented first and exclusively by Gear Technology, but the entire series will be included in Dr. Stadtfeld’s upcoming book on the subject, which is scheduled for release in 2011.
A study was performed to evaluate fault detection effectiveness as applied to gear-tooth pitting-fatigue damage. Vibration and oil-debris monitoring (ODM) data were gathered from 24 sets of spur pinion and face gears run during a previous endurance evaluation study.
Tooth contact under load is an important verification of the real contact conditions of a gear pair and an important add-on to the strength calculation according to standards such as ISO, AGMA or DIN. The contact analysis simulates the meshing of the two flanks over the complete meshing cycle and is therefore able to consider individual modifications on the flank at each meshing position.
Bevel gear systems are particularly sensitive to improper assembly. Slight errors in gear positioning can turn a well-designed, quality manufactured gear set into a noisy, prone-to-failure weak link in your application.
The development of a new gear strength computer program based upon the finite element method, provides a better way to calculate stresses in bevel and hypoid gear teeth. The program incorporates tooth surface geometry and axle deflection data to establish a direct relationship between fillet bending stress, subsurface shear stress, and applied gear torque. Using existing software links to other gear analysis programs allows the gear engineer to evaluate the strength performance of existing and new gear designs as a function of tooth contact pattern shape, position and axle deflection characteristics. This approach provides a better understanding of how gears react under load to subtle changes in the appearance of the no load tooth contact pattern.
A single tooth bending (STB) test procedure has been developed to optimally map gear design parameters. Also, a test program on case-carburized, aerospace standard gears has been conceived and performed in order to appreciate the influence of various technological parameters on fatigue resistance and to draw the curve shape up to the gigacycle region.
As is well known in involute gearing, “perfect” involute gears never work perfectly in the real world. Flank modifications are often made to overcome the influences of errors coming from manufacturing and assembly processes as well as deflections of the system. The same discipline applies to hypoid gears.
With the right selection of nonstandard center distance and tool shifting, it may be possible to use standard tools to improve the gear set capacity with a considerable reduction in cost when compared to the use of special tools.
Your May/June issue contains a letter from Edward Ubert of Rockwell International with some serious questions about specifying and measuring tooth thickness.
Calculation of gear tooth flexibility is of interest for at least two reasons: (a) It controls, at least in part, the vibratory properties of a transmission system hence, fatigue resistance and noise: (b) it controls load sharing in multiple tooth contact.
After a period of operation, high-speed turbo gears may exhibit a change in longitudinal tooth contact pattern, reducing full face width contact and thereby increasing risk of tooth distress due to the decreased loaded area of the teeth. But this can be tricky—the phenomenon may or may not occur. Or, in some units the shift is more severe than others, with documented cases in which shifting occurred after as little as 16,000 hours of operation. In other cases, there is no evidence of any change for units in operation for more than 170,000 hours. This condition exists primarily in helical gears. All recorded observations here have been with case-carburized and ground gear sets. This presentation describes phenomena observed in a limited sampling of the countless high-speed gear units in field operation. While the authors found no existing literature describing this behavior, further investigation suggests a possible cause. Left unchecked and without corrective action, this occurrence may result in tooth breakage.
The effect of load speed on straight and involute tooth forms is studied using several finite-element models.
The manufacturing quality of spiral bevel gears has achieved a very high standard. Nevertheless, the understanding of the real stress conditions and the influences. of certain parameters is not satisfactory.
This presentation introduces a new procedure that - derived from exact calculations - aids in determining the parameters of the validation testing of spiral bevel and hypoid gears in single-reduction axles.
In this paper a new method for the introduction of optimal modifications into gear tooth surfaces—based on the optimal corrections of the profile and diameter of the head cutter, and optimal variation of machine tool settings for pinion and gear finishing—is presented. The goal of these tooth modifications is the achievement of a more favorable load distribution and reduced transmission error. The method is applied to face milled and face hobbed hypoid gears.
Quality gear inspection means doing the "right" inspections "right." A lot of time and money can be spent doing the wrong types of inspections related to function and doing them incorrectly. As we will discover later, such things as runout can creep into the manufacturing and inspection process and completely ruin any piece of data that is taken. this is one of the most important problems to control for quality inspection.
In some gear dynamic models, the effect of tooth flexibility is ignored when the model determines which pairs of teeth are in contact. Deflection of loaded teeth is not introduced until the equations of motion are solved. This means the zone of tooth contact and average tooth meshing stiffness are underestimated, and the individual tooth load is overstated, especially for heavily loaded gears. This article compares the static transmission error and dynamic load of heavily loaded, low-contact-ratio spur gears when the effect of tooth flexibility has been considered and when it has been ignored. Neglecting the effect yields an underestimate of resonance speeds and an overestimate of the dynamic load.
Analysis of helical involute gears by tooth contact analysis shows that such gears are very sensitive to angular misalignment leading to edge contact and the potential for high vibration. A new topology of tooth surfaces of helical gears that enables a favorable bearing contact and a reduced level of vibration is described. Methods for grinding helical gears with the new topology are proposed. A TCA program simulating the meshing and contact of helical gears with the new topology has been developed. Numerical examples that illustrate the proposed ideas are discussed.
In recent years, gear inspection requirements have changed considerably, but inspection methods have barely kept pace. The gap is especially noticeable in bevel gears, whose geometry has always made testing them a complicated, expensive and time-consuming process. Present roll test methods for determining flank form and quality of gear sets are hardly applicable to bevel gears at all, and the time, expense and sophistication required for coordinate measurement has limited its use to gear development, with only sampling occurring during production.
In the last section, we discussed gear inspection; the types of errors found by single and double flank composite and analytical tests; involute geometry; the involute cam and the causes and symptoms of profile errors. In this section, we go into tooth alignment and line of contact issues including lead, helix angles, pitch, pitchline runout, testing and errors in pitch and alignment.
In this paper, two developed methods of tooth root load carrying capacity calculations for beveloid gears with parallel axes are presented, in part utilizing WZL software GearGenerator and ZaKo3D. One method calculates the tooth root load-carrying capacity in an FE-based approach. For the other, analytic formulas are employed to calculate the tooth root load-carrying capacity of beveloid gears. To conclude, both methods are applied to a test gear. The methods are compared both to each other and to other tests on beveloid gears with parallel axes in test bench trials.
This paper will provide examples of stress levels from conventional root design using a hob and stress levels using an optimized root design that is now possible with PM manufacturing. The paper will also investigate how PM can reduce stresses in the root from transient loads generated by abusive driving.
Indiana Technology and Manufacturing Companies (ITAMCO) has released iBlue—the first handheld bluetooth transmitter that gathers crucial production data and sends it to bluetooth-enabled smartphones, tablets and computers.
In the majority of spiral bevel gears, spherical crowning is used. The contact pattern is set to the center of the active tooth flank and the extent of the crowning is determined by experience. Feedback from service, as well as from full-torque bench tests of complete gear drives, has shown that this conventional design practice leads to loaded contact patterns, which are rarely optimal in location and extent. Oversized reliefs lead to small contact area, increased stresses and noise, whereas undersized reliefs result in an overly sensitive tooth contact.
The complete and accurate solution t the contact problem of three-dimensional gears has been, for the past several decades, one of the more sought after, albeit elusive goals in the engineering community. Even the arrival on the scene in the mid-seventies of finite element techniques failed to produce the solution to any but the most simple gear contact problems.
The first commandment for gears reads "Gears must have backlash!" When gear teeth are operated without adequate backlash, any of several problems may occur, some of which may lead to disaster. As the teeth try to force their way through mesh, excessive separating forces are created which may cause bearing failures. These same forces also produce a wedging action between the teeth with resulting high loads on the teeth. Such loads often lead to pitting and to other failures related to surface fatigue, and in some cases, bending failures.
In the design of any new gear drive, the performance of previous similar designs is very carefully considered. In the course of evaluating one such new design, the authors were faced with the task of comparing it with two similar existing systems, both of which were operating quite successfully. A problem arose, however, when it was realized that the bending stress levels of the two baselines differed substantially. In order to investigate these differences and realistically compare them to the proposed new design, a three-dimensional finite-element method (FEM) approach was applied to all three gears.
Helical gears can drive either nonparallel or parallel shafts. When these gears are used with nonparallel shafts, the contact is a point, and the design and manufacturing requirements are less critical than for gears driving parallel shafts.
An analytical method is presented to predict the shifts of the contact ellipses on spiral bevel gear teeth under load. The contact ellipse shift is the motion of the point to its location under load. The shifts are due to the elastic motions of the gear and pinion supporting shafts and bearings. The calculations include the elastic deflections of the gear shafts and the deflections of the four shaft bearings. The method assumes that the surface curvature of each tooth is constant near the unloaded pitch point. Results from these calculations will help designers reduce transmission weight without seriously reducing transmission performance.
The curved tooth cylindrical gear is one of ancient design. Samples which date from the period of the Warring State (475-221 BC) have been excavated from archeological sites in China. One such sample is now on display in the Xi'an Clay figures of Warriors and Horses Exhibition Hall. This example is about 3/4" in diameter and made of bronze. It was used in the famous model, "Ancient Chinese Vehicle With a Wooden Figure Always Pointing to the South." Although this early gear is handmade and somewhat crude, it is a viable model.
CNC technology offers new opportunities for the manufacture of bevel gears. While traditionally the purchase of a specific machine at the same time determined a particular production system, CNC technology permits the processing of bevel gears using a wide variety of methods. The ideological dispute between "tapered tooth or parallel depth tooth" and "single indexing or continuous indexing" no longer leads to an irreversible fundamental decision. The systems have instead become penetrable, and with existing CNC machines, it is possible to select this or that system according to factual considerations at a later date.
The load carrying behavior of gears is strongly influenced by local stress concentrations in the tooth root and by Hertzian pressure peaks in the tooth flanks produced by geometric deviations associated with manufacturing, assembly and deformation processes. The dynamic effects within the mesh are essentially determined by the engagement shock, the parametric excitation and also by the deviant tooth geometry.
Service performance and load carrying capacity of bevel gears strongly depend on the size and position of the contact pattern. To provide an optimal contact pattern even under load, the gear design has to consider the relative displacements caused by deflections or thermal expansions expected under service conditions. That means that more or less lengthwise and heightwise crowning has to be applied on the bevel gear teeth.
This article also appears as Chapter 1 in the Gleason Corporation publication "Advanced Bevel Gear Technology." Gearing Principles in Cylindrical and Straight Bevel Gears The purpose of gears is to transmit motion and torque from one shaft to another. That transmission normally has to occur with a constant ratio, the lowest possible disturbances and the highest possible efficiency. Tooth profile, length and shape are derived from those requirements.
News Items About tooth profile
1 Ikona and Magna Advanced Technologies Partner for Gear Tooth Profile (January 6, 2005)
Ikona Gear International and Magna Advanced Technologies have jointly introduced a patented gear technology that utilizes a newly designe... Read News