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The aim of our research is to clearly show the influence of defects on the bending fatigue strength of gear teeth. Carburized gears have many types of defects, such as non-martensitic layers, inclusions, tool marks, etc. It is well known that high strength gear teeth break from defects in their materials, so it’s important to know which defect limits the strength of a gear.
To mechanical engineers, the strength of gear teeth is a question of constant recurrence, and although the problem to be solved is quite elementary in character, probably no other question could be raised upon which such a diversity of opinion exists, and in support of which such an array of rules and authorities might be quoted. In 1879, Mr. John H. Cooper, the author of a well-known work on "Belting," made an examination of the subject and found there were then in existence about forty-eight well-established rules for horsepower and working strength, sanctioned by some twenty-four authorities, and differing from each other in extreme causes of 500%. Since then, a number of new rules have been added, but as no rules have been given which take account of the actual tooth forms in common use, and as no attempt has been made to include in any formula the working stress on the material so that the engineer may see at once upon what assumption a given result is based, I trust I may be pardoned for suggesting that a further investigation is necessary or desirable.
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.
The geometry factor, which is a fundamental part of the AGMA strength rating of gears, is currently computed using the Lewis parabola which allows computation of the Lewis form factor.(1) The geometry factor is obtained from this Lewis factor and load sharing ratio. This method, which originally required graphical construction methods and more recently has been computerized, works reasonably well for external gears with thick rims.(2-6) However, when thin rims are encountered or when evaluating the strength of internal gears, the AGMA method cannot be used.
The gear designer needs to know how to determine an appropriate case depth for a gear application in order to guarantee the required load capacity.
There are three distinct gear types in angle drives. The most commonly used are bevel and worm drives. Face gear drives are the third alternative.
The load capacity rating of gears had its beginning in the 18th century at Leiden University when Prof. Pieter van Musschenbroek systematically tested the wooden teeth of windmill gears, applying the bending strength formula published by Galilei one century earlier. In the next centuries several scientists improved or extended the formula, and recently a Draft International Standard could be presented.
A simple, closed-form procedure is presented for designing minimum-weight spur and helical gearsets. The procedure includes methods for optimizing addendum modification for maximum pitting and wear resistance, bending strength, or scuffing resistance.
The face load factor is one of the most important items for a gear strength calculation. Current standards propose formulae for face load factor, but they are not always appropriate. AGMA 927 proposes a simpler and quicker algorithm that doesn't require a contact analysis calculation. This paper explains how this algorithm can be applied for gear rating procedures.
Although there is plenty of information and data on the determination of geometry factors and bending strength of external gear teeth, the computation methods regarding internal gear design are less accessible. most of today's designs adopt the formulas for external gears and incorporate some kind of correction factors for internal gears. However, this design method is only an approximation because of the differences between internal gears and external gears. Indeed, the tooth shape of internal gears is different from that of external gears. One has a concave curve, while the other has a convex curve.
This article summarizes results of research programs on RCF strength of wrought steels and PM steels.
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.
A method to extrapolate running gear bending strength data from STF results for comparing bending performance of different materials and processes.
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.
This is part II of a two-part paper that presents the results of extensive test programs on the RCF strength of PM steels.
This is the third article in a series exploring the new ISO 6336 gear rating standard and its methods of calculation. The opinions expressed herein are htose of the author as an individual. They do not represent the opinions of any organization of which he is a member.
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 article illustrates a structural analysis of asymmetrical teeth. This study was carried out because of the impossibility of applying traditional calculations to procedures involved in the specific case. In particular, software for the automatic generation of meshes was devised because existing software does not produce results suitable for the new geometrical model required. Having carried out the structural calculations, a comparative study of the stress fields of symmetrical and asymmetrical teeth was carried out. The structural advantages of the latter type of teeth emerged.
Columbus' first voyage to the Americas is not the only anniversary worthy of celebration this year. In 1892, on October 15, Wilfred Lewis gave an address to the Engineer's Club of Philadelphia, whose significance, while not as great as that of Columbus' voyage, had important results for the gearing community. In this address, Lewis first publicly outlined his formula for computing bending stress in gear teeth, a formula still in use today.
QuesTek Innovations LLC is applying its Materials by Design computational design technology to develop a new class of high-strength, secondary hardening gear steels that are optimized for high-temperature, low-pressure (i.e., vacuum) carburization. The new alloys offer three different levels of case hardness (with the ability to “dial-in” hardness profiles, including exceptionally high case hardness), and their high core strength, toughness and other properties offer the potential to reduce drivetrain weight or increase power density relative to incumbent alloys such as AISI 9310 or Pyrowear Alloy 53.
Compared to non-heat-treated components, case-carburized gears are characterized by a modified strength profile in the case-hardened layer. The design of case-carburized gears is based on defined allowable stress numbers. These allowable stress numbers are valid only for a defined "optimum" case depth. Adequate heat treatment and optimum case depth guarantee maximum strength of tooth flank and tooth root.
The search for greater gear life involves improvement in cost, weight and increased power output. There are many events that affect gear life, and this paper addresses those relating to fatigue, gear tooth pitting, fatigue strength losses due to the heat treating processes and shot peening technique. The capability of shot peening to increase fatigue strength and surface fatigue life eliminate machine marks which cause stress risers, and to aid in lubrication when properly controlled, suggests increased use and acceptance of the process.
In Part I differences in pitting ratings between AGMA 218, the draft ISO standard 6336, and BS 436:1986 were examined. In this part bending strength ratings are compared. All the standards base the bending strength on the Lewis equation; the ratings differ in the use and number of modification factors. A comprehensive design survey is carried out to examine practical differences between the rating methods presented in the standards, and the results are shown in graphical form.
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 effort described in this paper addresses a desire in the gear industry to increase power densities and reduce costs of geared transmissions. To achieve these objectives, new materials and manufacturing processes, utilized in the fabrication of gears, and being evaluated. In this effort, the first priority is to compare the performance of gears fabricated using current materials and processes. However, once that priority is satisfied, it rapidly transforms to requiring accurate design data to utilize these novel materials and processes. This paper describes the effort to address one aspect of this design data requirement.
This is the fourth and final article in a series exploring the new ISO 6336 gear rating standard and its methods of calculation. The opinions expressed herein are those of the author as an individual. They do not represent the opinions of any organization of which he is a member.
For years, politicians, educators and business leaders have generated various ideas to revitalize U.S. manufacturing and engineering. These include manufacturing initiatives, internal training programs and an emphasis on science, technology, engineering and mathematics (STEM) in the classroom. The declining expertise in these fields, however, continues to be a growing problem in every facet of manufacturing and engineering.
A common design goal for gears in helicopter or turboprop power transmission is reduced weight. To help meet this goal, some gear designs use thin rims. Rims that are too thin, however, may lead to bending fatigue problems and cracks. The most common methods of gear design and analysis are based on standards published by the American Gear Manufacturers Association. Included in the standards are rating formulas for gear tooth bending to prevent crack initiation (Ref. 1). These standards can include the effect of rim thickness on tooth bending fatigue (Ref 2.). The standards, however, do not indicate the crack propagation path or the remaining life once a crack has started. Fracture mechanics has developed into a useful discipline for predicting strength and life of cracked structures.
Powder metal. To gear makers today, the phrase conjures images of low power applications in non-critical systems. As powder metal technology advances, as the materials increase in density and strength, such opinions are changing. It is an ongoing, evolutionary process and one that will continue for some time. According to Donald G. White, the executive director of the Metal Powder Industries Federation, in his State-of-the-P/M Industry - 1999 report. "The P/M world is changing rapidly and P/M needs to be recognized as a world-class process - national, continental and even human barriers and prejudices must be eliminated - we must join forces as a world process - unified in approach and goals."
Just back from IMTS and once again, I'm struck by the enormous vitality and strength of the manufacturing sector of the U.S. economy. It has made a phoenix-like rise from the grave dug for it by pundits in the '80s and has come back more robust and competitive than ever.
What Is Whisker-Reinforced Ceramic? Whisker-reinforced ceramic as applied to cutting tool inserts comprises a matrix of aluminum oxide into which approximately 50% by volume of high-purity silicon carbide "whiskers" are randomly dispersed. The "whiskers" are, in fact, single crystals having dimensions of approximately 0.6 microns in diameter x 10-80 microns in length. These "whiskers" have a tensile strength on the order of 1,000,000 psi (690 MPa). The composite material that is the best known and most widely applied using this technology is designated WG-300 and manufactured by the Greenleaf Corporation of Saegertown, PA.
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?
Ausforming, the plastic deformation of heat treatment steels in their metastable, austentic condition, was shown several decades ago to lead to quenched and tempered steels that were harder, tougher and more durable under fatigue-type loading than conventionally heat-treated steels. To circumvent the large forces required to ausform entire components such as gears, cams and bearings, the ausforming process imparts added mechanical strength and durability only to those contact surfaces that are critically loaded. The ausrolling process, as utilized for finishing the loaded surfaces of machine elements, imparts high quality surface texture and geometry control. The near-net-shape geometry and surface topography of the machine elements must be controlled to be compatible with the network dimensional finish and the rolling die design requirements (Ref. 1).
Surface-hardened, sintered powder metal gears are increasingly used in power transmissions to reduce the cost of gear production. One important problem is how to design with surface durability, given the porous nature of sintered gears. Many articles have been written about mechanical characteristics, such as tensile and bending strength, of sintered materials, and it is well-known that the pores existing on and below their surfaces affect their characteristics (Refs. 1-3). Power transmission gears are frequently employed under conditions of high speed and high load, and tooth surfaces are in contact with each other under a sliding-rolling contact condition. Therefore it is necessary to consider not only their mechanical, but also their tribological characteristics when designing sintered gears for surface durability.
Quality gear manufacturing depends on controlled tolerances and geometry. As a result, ferritic nitrocarburizing has become the heat treat process of choice for many gear manufacturers. The primary reasons for this are: 1. The process is performed at low temperatures, i.e. less than critical. 2. the quench methods increase fatigue strength by up to 125% without distorting. Ferritic nitrocarburizing is used in place of carburizing with conventional and induction hardening. 3. It establishes gradient base hardnesses, i.e. eliminates eggshell on TiN, TiAIN, CrC, etc. In addition, the process can also be applied to hobs, broaches, drills, and other cutting tools.
Composite spur gears were designed, fabricated and tested at NASA Glenn Research Center. The composite web was bonded only to the inner and outer hexagonal features that were machined from an initially all-metallic aerospace quality spur gear. The hybrid gear was tested against an all-steel gear and against a mating hybrid gear. Initial results indicate that this type of hybrid design may have a dramatic effect on drive system weight without sacrificing strength.
Carburized gears have higher strengths and longer lives compared with induction-hardened or quench-tempered gears. But in big module gears, carburizing heat-treatment becomes time-consuming and expensive and sometimes cannot achieve good hardness due to the big mass-effect. Also, it is not easy to reduce distortion of gears during heat treatment.
Carburized helical gears with high retained austenite were tested for surface contact fatigue. The retained austenite before test was 60% and was associated with low hardness near the case's surface. However, the tested gears showed good pitting resistance, with fatigue strength greater than 1,380 MPa.
Cracks initiated at the surface of case-hardened gears may lead to typical life-limiting fatigue failure modes such as pitting and tooth root breakage. Furthermore, the contact load on the flank surface induces stresses in greater material depth that may lead to crack initiation below the surface if the local material strength is exceeded. Over time the sub-surface crack propagation may lead to gear failure referred to as “tooth flank fracture” (also referred to as “tooth flank breakage”). This paper explains the mechanism of this subsurface fatigue failure mode and its decisive influence factors, and presents an overview of a newly developed calculation model.
Plastics as gear materials represent an interesting development for gearing because they offer high strength-to-weight ratios, ease of manufacture and excellent tribological properties (Refs. 1-7). In particular, there is a sound prospect that plastic gears can be applied for power transmission of up to 10 kW (Ref. 6).
Aurstempered irons and steels offer the design engineer alternatives to conventional material/process combinations. Depending on the material and the application, austempering may provide the producers of gear and shafts with the following benefits: ease of manufacturing, increased bending and/or contact fatigue strength, better wear resistance or enhanced dampening characteristics resulting in lower noise. Austempered materials have been used to improve the performance of gears and shafts in many applications in a wide range of industries.
Effective gear designs balance strength, durability, reliability, size, weight, and cost. Even effective designs, however, can have the possibility of gear cracks due to fatigue. In addition, truly robust designs consider not only crack initiation, but also crack propagation trajectories. As an example, crack trajectories that propagate through the gear tooth are the preferred mode of failure compared to propagation through the gear rim. Rim failure will lead to catastrophic events and should be avoided. Analysis tools that predict crack propagation paths can be a valuable aid to the designer to prevent such catastrophic failures.
Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ration under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque and power. Significant parameters in the design are the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near-optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.
Except for higher-end gear applications found in automotive and aerospace transmissions, for example, high-performance, sintered-steel gears match wrought-steel gears in strength and geometrical quality. The enhanced P/M performance is due largely to advances in powder metallurgy over last two decades, such as selective surface densification, new materials and lubricants for high density and warm-die pressing. This paper is a review of the results of a decade of research and development of high- performance, sintered-steel gear prototypes.
The large gears found in mining, steel, construction, off-road, marine and energy applications—massive and robust in nature—need to tackle the greatest production demands. This, in turn, means that a special emphasis must be put on the heat treating methods used to increase the wear resistance and strength properties of gears this size.
Induction hardening is a heat treating technique that can be used to selectively harden portions of a gear, such as the flanks, roots and tips of teeth, providing improved hardness, wear resistance, and contact fatigue strength without affecting the metallurgy of the core and other parts of the component that don’t require change. This article provides an overview of the process and special considerations for heat treating gears. Part I covers gear materials, desired microsctructure, coil design and tooth-by-tooth induction hardening.
The powder metal (P/M) process is making inroads in automotive transmission applications due to substantially lower costs of P/M-steel components for high-volume production, as compared to wrought or forged steel parts. Although P/M gears are increasingly used in powered hand tools, gear pumps and as accessory components in automotive transmissions, P/M-steel gears are currently in limited use in vehicle transmission applications. The primary objective of this project was to develop high-strength P/M-steel gears with bending fatigue, impact resistance and pitting fatigue performance equivalent to current wrought steel gears.
Borazon is a superabrasive material originally developed by General Electric in 1969. It is a high performance material for machining of high alloy ferrous and super alloy materials. Borazon CBN - Cubic Born Nitride - is manufactured with a high temperature, high pressure process similar to that utilized with man-made diamond. Borazon is, next to diamond, the hardest abrasive known; it is more than twice as hard as aluminum oxide. It has an extremely high thermal strength compared to diamond. It is also much less chemically reactive with iron, cobalt or nickel alloys.
This article focuses on bending fatigue strength improvements of P/M gearing from recent improvements in P/M technology, combined with shot peening.
More strength, less noise. Those are two major demands on gears, including bevel and hypoid gears.
The approximate tensile strength of any steel is measured by its hardness, Table 1. Since hardness is determined by both chemical composition and heat treatment, these are the two important metallurgical considerations in selecting gear steels.
The objective of this paper is to demonstrate that transmission gears of rotary-wing aircraft, which are typically scrapped due to minor foreign object damage (FOD) and grey staining, can be repaired and re-used with signifi cant cost avoidance. The isotropic superfinishing (ISF) process is used to repair the gear by removing surface damage. It has been demonstrated in this project that this surface damage can be removed while maintaining OEM specifications on gear size, geometry and metallurgy. Further, scrap CH-46 mix box spur pinions, repaired by the ISF process, were subjected to gear tooth strength and durability testing, and their performance compared with or exceeded that of new spur pinions procured from an approved Navy vendor. This clearly demonstrates the feasibility of the repair and re-use of precision transmission gears.
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.
The manufacturing process to produce a gear essentially consist of: material selection, blank preshaping, tooth shaping, heat treatment, and final shaping. Only by carefully integrating of the various operations into a complete manufacturing system can an optimum gear be obtained. The final application of the gear will determine what strength characteristics will be required which subsequently determine the material and heat treatments.
Anyone involved in the design, manufacture and use of gears is concerned with three general characteristics relative to their application: noise, accuracy, and strength or surface durability. In the article, we will be dealing with probably the most aggravating of the group, gear noise.
A study of AGMA 218, the draft ISO standard 6336, and BS 436: 1986 methods for rating gear tooth strength and surface durability for metallic spur and helical gears is presented. A comparison of the standards mainly focuses on fundamental formulae and influence factors, such as the load distribution factor, geometry factor, and others. No attempt is made to qualify or judge the standards other than to comment on the facilities or lack of them in each standard reviewed. In Part I a comparison of pitting resistance ratings is made, and in the subsequent issue, Part II will deal with bending stress ratings and comparisons of designs.
In a very general sense, increasing the hardness of a steel gear increases the strength of the gear. However, for each process there is a limit to its effectiveness. This article contains background information on each of the processes covered. In each section what is desired and what is achievable is discussed. Typical processes are presented along with comments on variables which affect the result. By reviewing the capabilities and processes, it is possible to determine the limits to each process.
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.
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.
Rules and Formula for worm gears, bevel gears and strength of gear teeth.
Almost all machines or mechanical systems contain precision contact elements such as bearings, cams, rears, shafts, splines and rollers. These components have two important common requirements: first, they must possess sufficient mechanical properties, such as, high hardness, fatigue strength and wear resistance to maximize their performance and life; second, they must be finished to close dimensional tolerances to minimize noise, vibration and fatigue loading.
Most gear cutting shops have shelves full of expensive tooling used in the past for cutting gears which are no longer in production. It is anticipated that these cutters will be used again in the future. While this may take place if the cutters are "standard," and the gears to be cut are "standard," most of the design work done today involves high pressure angle gears for strength, or designs for high contact ratio to reduce noise. The re-use of a cutter under these conditions requires a tedious mathematical analysis, which is no problem if a computer with the right software is available. This article describes a computerized graphical display which provides a quick analysis of the potential for the re-use of shaving cutters stored in a computer file.
Worm gears are among the oldest types of gearing, but that does not mean they are obsolete, antiquated technology. The main reasons for the bad experiences some engineers have with worm gearing are misapplication and misuse. No form of gearing works for every application. Strengths and weaknesses versus the application must be weighed to decide which form of gearing to use. For proper application and operation of worm gears, certain areas that may differ from other types of gearing need to be addressed.
News Items About strength
1 KISSsoft Offers Standards in the Shaft Strength Calculation (February 27, 2014)
For an analytical strength assessement, in the first instance the currently valid standard has to be applied. Therefore, an essential tas... Read News
2 Metal Bonding Adhesive Exhibits Superior Strength (March 30, 2009)
Master Bond's Supreme 10HT is a one-part heat resistant adhesive formulated to cure at elevated temperatures and effectively applied ... Read News
3 KISSsoft Releases Calculation for Shearing Strength for Plastic Worm Wheels (February 17, 2011)
For crossed axis helical gear designs where a worm meshes with a cylindrical worm wheel made of plasti... Read News