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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 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.
The design of any gearing system is a difficult, multifaceted process. When the system includes bevel gearing, the process is further complicated by the complex nature of the bevel gears themselves. In most cases, the design is based on an evaluation of the ratio required for the gear set, the overall envelope geometry, and the calculation of bending and contact stresses for the gear set to determine its load capacity. There are, however, a great many other parameters which must be addressed if the resultant gear system is to be truly optimum. A considerable body of data related to the optimal design of bevel gears has been developed by the aerospace gear design community in general and by the helicopter community in particular. This article provides a summary of just a few design guidelines based on these data in an effort to provide some guidance in the design of bevel gearing so that maximum capacity may be obtained. The following factors, which may not normally be considered in the usual design practice, are presented and discussed in outline form: Integrated gear/shaft/bearing systems Effects of rim thickness on gear tooth stresses Resonant response
The present article contains a preliminary description of studies carried out by the authors with a view toward developing asymmetrical gear teeth. Then a comparison between numerous symmetrical and asymmetrical tooth stress fields under the same modular conditions follows. This leads to the formulation of a rule for similar modules governing variations of stress fields, depending on the pressure angle of the nonactive side. Finally a procedure allowing for calculations for percentage reductions of asymmetrical tooth modules with respect to corresponding symmetrical teeth, maximum ideal stress being equal, is proposed. Then the consequent reductions in size and weight of asymmetrical teeth are assessed.
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.
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.
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.
In this study, the combined influence of shaft misalignments and gear lead crown on load distribution and tooth bending stresses is investigated. Upon conclusion, the experimental results are correlated with predictions of a gear load distribution model, and recommendations are provided for optimal lead crown in a given misalignment condition.
At first sight the appearance of 5-axis milling for bevel gears opens new possibilities in flank form design. Since in comparison to existing machining methods applying cutter heads no kinematic restrictions exist for 5-axis milling technology, any flank form can be machined. Nevertheless the basic requirements for bevel gears did not change. Specifications and functional requirements like load carrying capacity and running behavior are still increasing demands for design and manufacturing. This paper describes the demands for gear design and gives an overview about different design principles in the context of the surrounding periphery of the gear set.
This paper presents the results of a study performed to measure the change in residual stress that results from the finish grinding of carburized gears. Residual stresses were measured in five gears using the x-ray diffraction equipment in the Large Specimen Residual Stress Facility at Oak Ridge National Laboratory.
In this paper, an accurate FEM analysis has been done of the “true” stress at tooth root of spur gears in the function of the gear geometry. The obtained results confirm the importance of these differences.
Traditionally, gear rating procedures consider manufacturing accuracy in the application of the dynamic factor, but only indirectly through the load distribution are such errors in the calculation of stresses used in the durability and gear strength equations. This paper discusses how accuracy affects the calculation of stresses and then uses both statistical design of experiments and Monte Carlo simulation techniques to quantify the effects of different manufacturing and assembly errors on root and contact stresses.
How local stresses obtained from FEA can be used to determine fatigue strength of worm wheel teeth.
This paper presents the results of research directed at measuring the total stress in a pair of statically loaded and carburized spur gears. Measurements were made to examine the change in total stress as a function of externally applied load and depth below the surface.
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.
How does one determine the center of a worm and a worm wheel? Also, what are the differences between the common worm tooth forms?
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 high precision and heavily loaded spur gears, the effect of gear error is negligible, so the periodic variation of tooth stiffness is the principal cause of noise and vibration. High contact ration spur gears can be used to exclude or reduce the variation of tooth stiffness.
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 describes the investigation of a steel-and-plastic gear transmission and presents a new hypothesis on the governing mechanism in the wear of plastic gears.
Gear-loaded tooth contact analysis is an important tool for the design and analysis of gear performance within transmission and driveline systems. Methods for the calculation of tooth contact conditions have been discussed in the literature for many years. It's possible the method you've been using is underestimating transmission error in helical gears. Here's why.
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).
In terms of the tooth thickness, should we use the formulation with respect to normal or transverse coordinate system? When normalizing this thickness in order to normalize the backlash (backlash parameter), we should divide by the circular pitch. Thus, when normalizing, should this circular pitch be defined in the normal or traverse coordinate system, depending on which formulation has been used? Is the backlash parameter always defined with respect to the tangential plane or normal plane for helical gears?
One of the most effective methods in solving the edge loading problem due to excess misalignment and deflection in aerospace actuation gearing is to localize tooth-bearing contact by crowning the teeth. Irrespective of the applied load, if the misalignment and/or deflection are large enough to cause the contact area to reduce to zero, the stress becomes large enough to cause failure. The edge loading could cause the teeth to break or pit, but too much crowning may also cause the teeth to pit due to concentrated loading. In this paper, a proposed method to localize the contact bearing area and calculate the contact stress with crowning is presented and demonstrated on some real-life examples in aerospace actuation systems.
Transmission errors, axial shuttling forces and friction result in bearing forces that serve as the major excitations of gear noise. This paper will use these factors as well as gear stresses and tribological factors to assist in obtaining optimal gear designs.
Using the DANTE software, a finite element simulation was developed and executed to study the response of a carburized 5120 steel helical gear to quenching in molten salt. The computer simulation included heat-up, carburization, transfer and immersion in a molten salt bath, quenching, and air cooling. The results of the simulation included carbon distribution of phases, dimensional change, hardness, and residual stress throughout the process. The predicted results were compared against measured results for hardness, dimensions and residual stress. The excellent agreement between predictions and measured values for this carburized 5120 steel gear provides a basis for assessing the various process parameters and their respective importance in the characteristics of not only these heat-treated parts, but of other compositions and shapes.
When hardened steel components are ground, there is always the possibility of damage to the steel in the form of residual stress or microstructural changes. Methods for detecting this sort of damage have always had one or more drawbacks, such as cost, time, complexity, subjectivity, or the use of hazardous chemicals.
Bending stress evaluation in modern gear design is generally based on the more-than-one-hundred-year-old Lewis equation.
Gleason 350GMS helps put higher quality, more reliable gears into its next-generation TC10 automatic transmission.
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.
I have heard that X-ray diffraction does not tell the whole story and that I should really run a fatigue test. I understand this may be the best way, but is there another method that gives a high degree of confidence in the residual stress measurement?
Contact fatigue and bending fatigue are two main failure modes of steel gears, while surface pitting and spalling are two common contact fatigue failures -- caused by alternating subsurface shear stresses from the contact load between two gear mates. And when a gear is in service under cyclic load, concentrated bending stresses exist at the root fillet -- the main driver of bending fatigue failures. Induction hardening is becoming an increasingly popular response to these problems, due to its process consistency, reduced energy consumption, clean environment and improved product quality -- but not without issues of its own (irregular residual stresses and bending fatigue). Thus a new approach is proposed here that flexibly controls the magnitude of residual stress in the regions of root fillet and tooth flank by pre-heating prior to induction hardening. Using an external spur gear made of AISI 4340 as an example, this new concept/process is demonstrated using finite element modeling and DANTE commercial software.
A very important parameter when designing a gear pair is the maximum surface contact stress that exists between two gear teeth in mesh, as it affects surface fatigue (namely, pitting and wear) along with gear mesh losses. A lot of attention has been targeted to the determination of the maximum contact stress between gear teeth in mesh, resulting in many "different" formulas. Moreover, each of those formulas is applicable to a particular class of gears (e.g., hypoid, worm, spiroid, spiral bevel, or cylindrical - spur and helical). More recently, FEM (the finite element method) has been introduced to evaluate the contact stress between gear teeth. Presented below is a single methodology for evaluating the maximum contact stress that exists between gear teeth in mesh. The approach is independent of the gear tooth geometry (involute or cycloid) and valid for any gear type (i.e., hypoid, worm, spiroid, bevel and cylindrical).
Several trends in mechanical engineering are leading to greater surface stress on components and thus to unacceptable wear. These trends include greater stresses due to increased power densities; the need to maintain high precision of components throughout their service life; and the environmental imperative to reduce use of lubricants and additives.
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.
The traditional way of controlling the quality of hypoid gears' tooth flank form is to check the tooth flank contact patterns. But it is not easy to exactly judge the tooth flank form quality by the contact pattern. In recent years, it has become possible to accurately measure the tooth flank form of hypoid gears by the point-to-point measuring method and the scanning measuring method. But the uses of measured data of the tooth flank form for hypoid gears have not yet been well developed in comparison with cylindrical involute gears. In this paper, the tooth flank form measurement of generated face-milled gears, face-hobbed gears and formulate/generated gears are reported. The authors discuss the advantages and disadvantages of scanning and point-to-point measuring of 3-D tooth flank forms of hypoid gears and introduce some examples of uses of measured data for high-quality production and performance prediction.
An offshore jack-up drilling rig is a barge upon which a drilling platform is placed. The barge has legs that can be lowered to the sea floor to support the rig. Then the barge can be “jacked up” out of the water, providing a stable work platform from which to drill for oil and gas. Jack-up drilling rigs were first introduced in the late 1950s. Rack-and- pinion-type jack-up units were introduced soon after that and have dominated the industry ever since.
Gears with an asymmetric involute gear tooth form were analyzed to determine their bending and contact stresses relative to symmetric involute gear tooth designs, which are representative of helicopter main-drive gears.
The connection between transmission error, noise and vibration during operation has long been established. Calculation methods have been developed to describe the influence so that it is possible to evaluate the relative effect of applying a specific modification at the design stage. These calculations enable the designer to minimize the excitation from the gear pair engagement at a specific load. This paper explains the theory behind transmission error and the reasoning behind the method of applying the modifications through mapping surface profiles and determining load sharing.
With the publishing of various ISO draft standards relating to gear rating procedures, there has been much discussion in technical papers concerning the various load modification factors. One of the most basic of parameters affecting the rating of gears, namely the endurance limit for either contact or bending stress, has not, however, attracted a great deal of attention.
Induction hardening is widely used in both the automotive and aerospace gear industries to minimize heat treat distortion and obtain favorable compressive residual stresses for improved fatigue performance. The heating process during induction hardening has a significant effect on the quality of the heat-treated parts. However, the quenching process often receives less attention even though it is equally important.
This article includes a brief summary of the characteristics of involute asymmetric teeth and the problems connected with the related bending tests.
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.
Wait a minute, we don't measure pitch diameter. We're sometimes asked to measure it by customers, though, especially ones with older drawings.
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.
Influences of Load Distribution and Tooth Flank Modifications as Considered in a New, DIN/ISO-Compatible Calculation Method
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.
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.
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.
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.
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.
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.
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.
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.
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.
This section will deal with the use of gear inspection for diagnostic purposes rather than quality determination. The proper evaluation of various characteristics in the data can be useful for the solution of quality problems. It is important to sort out whether the problem is coming from the machine, tooling and/or cutters, blanks, etc. An article by Robert Moderow in the May/June 1985 issue of Gear Technology is very useful for this purpose.
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.
This article offers an overview of the practical design of a naval gear for combined diesel or gas turbine propulsion (CODOG type). The vibration performance of the gear is tested in a back-to-back test. The gear presented is a low noise design for the Royal Dutch Navy's LCF Frigate. The design aspects for low noise operation were incorporated into the overall gear system design. Therefore, special attention was paid to all the parameters that could influence the noise and vibration performance of the gearbox. These design aspects, such as tooth corrections, tooth loading, gear layout, balance, lubrication and resilient mounting, will be discussed.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
In a modern truck, the gear teeth are among the most stressed parts. Failure of a tooth will damage the transmission severely. Throughout the years, gear design experience has been gained and collected into standards such as DIN (Ref. 1) or AGMA (Ref. 2). Traditionally two types of failures are considered in gear design: tooth root bending fatigue, and contact fatigue. The demands for lighter and more silent transmissions have given birth to new failure types. One novel failure type, Tooth Interior Fatigue Fracture (TIFF), has previously been described by MackAldener and Olsson (Refs. 3 & 4) and is further explored in this paper.