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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 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.
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.
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.
In his Handbook of Gear Design (Ref.1), Dudley states (or understates): "The best gear people around the world are now coming to realize that metallurgical quality is just as important as geometric quality." Geometric accuracy without metallurgical integrity in any highly stressed gear or shaft would only result in wasted effort for all concerned - the gear designer, the manufacturer, and the customer - as the component's life cycle would be prematurely cut short. A carburized automotive gear or shaft with the wrong surface hardness, case depth or core hardness may not even complete its basic warranty period before failing totally at considerable expense and loss of prestige for the producer and the customer. The unexpected early failure of a large industrial gear or shaft in a coal mine or mill could result in lost production and income while the machine is down since replacement components may not be readily available. Fortunately, this scenario is not common. Most reputable gear and shaft manufacturers around the world would never neglect the metallurgical quality of their products.
Designers are constantly searching for ways to reduce rotocraft drive system weight. Reduced weight can increase the payload, performance, or power density of current and future systems. One example of helicopter transmission weight reduction was initiated as part of the United States Army Advanced Rotocraft Transmission program. This example used a split-torque, face-gear configuration concept (Ref. 1). compared to a conventional design with spiral-bevel gears, the split-torque, face-gear design showed substantial weight savings benefits. Also, the use of face gears allows a wide-range of possible configurations with technical and economic benefits (Ref. 2).
I must admit that after thumbing through the pages of this relatively compact volume (113 pages, 8.5 x 11 format), I read its three chapters(theory of gearing, geometry and technology, and biographical history) from rear to front. It will become obvious later in this discussion why I encourage most gear engineers to adopt this same reading sequence!
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.
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.
A universal gear is one generated by a common rack on a cylindrical, conical, or planar surface, and whose teeth can be oriented parallel or skewed, centered, or offset, with respect to its axes. Mating gear axes can be parallel or crossed, non-intersecting or intersecting, skewed or parallel, and can have any angular orientation (See Fig.1) The taper gear is a universal gear. It provides unique geometric properties and a range of applications unmatched by any other motion transmission element. (See Fig.2) The taper gear can be produced by any rack-type tool generator or hobbing machine which has a means of tilting the cutter or work axis and/or coordinating simultaneous traverse and infeed motions.
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.
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 paper describes a procedure for the design of internal gear pairs, which is a generalized form of the long and short addendum system. The procedure includes checks for interference, tip interference, undercutting, tip interference during cutting, and rubbing during cutting.
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 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).
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?
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.
Gears are manufactured with thin rims for several reasons. Steel gears are manufactured with thin rims and webs where low weight is important. Nonmetallic gears, manufactured by injection molding, are designed with thin rims as part of the general design rule to maintain uniform thickness to ensure even post-mold cooling. When a thin-rimmed gear fails, the fracture is thought the root of the gear, as shown in Fig. 1a, rather than the usual fillet failure shown in Fig. 1b.
Gear design has long been a "black art." The gear shop's modern alchemists often have to solve problems with a combination of knowledge, experience and luck. In many cases, trial and error are the only effective way to design gears. While years of experience have produced standard gearsets that work well for most situations, today's requirements for quieter, more accurate and more durable gears often force manufacturers to look for alternative designs.
A gear shaper cutter is actually a gear with relieved cutting edges and increased addendum for providing clearance in the root of the gear being cut. The maximum outside diameter of such a cutter is limited to the diameter at which the teeth become pointed. The minimum diameter occurs when the outside diameter of the cutter and the base circle are the same. Those theoretical extremes, coupled with the side clearance, which is normally 2 degrees for coarse pitch cutters an d1.5 degrees for cutters approximately 24-pitch and finer, will determine the theoretical face width of a cutter.
Plastic gears are serious alternatives to traditional metal gears in a wide variety of applications. The use of plastic gears has expanded from low-power, precision motion transmission into more demanding power transmission applications. As designers push the limits of acceptable plastic gear applications, more is learned about the behavior of plastics in gearing and how to take advantage of their unique characteristics.
Powder metallurgy (P/M) is a precision metal forming technology for the manufacture of parts to net or near-net shape, and it is particularly well-suited to the production of gears. Spur, bevel and helical gears all may be made by made by powder metallurgy processing.
When designing a gear set, engineers usually want the teeth of the gear (Ng) and the pinion (Np) in a "hunting" mesh. Such a mesh or combination is defined as one in which the pinion and the gear do not have any common divisor by a prime number. If a mesh is "hunting," then the pinion must make Np x Ng revolutions before the same pinion tooth meshes with the same gear space. It is often easy to determine if a mesh is hunting by first determining if both the pinion and the gear teeth are divisible by 2,3,5,7,etc. (prime numbers). However, in this age of computerization, how does one program the computer to check for hunting teeth? A simple algorithm is shown below.
The primary objective in designing reliable gear drives is to avoid failure. Avoiding failure is just as important for the manufacturer and designer as it is for the end user. Many aspects should be considered in order to maximize the potential reliability and performance of installed gearing.
For a long time, relatively high noise levels have been generally accepted for industrial gear units in the 10-100 kW power range. However, due to changing environmental awareness - both in and around industrial sites - customers expectations have moved drastically towards low noise as a key differentiating factor.
Friction weighs heavily on loads that the supporting journals of gear trains must withstand. Not only does mesh friction, especially in worm gear drives, affect journal loading, but also the friction within the journal reflects back on the loads required of the mesh itself.
Material selection can play an important role in the constant battle to reduce gear noise. Specifying tighter dimensional tolerances or redesigning the gear are the most common approaches design engineers take to minimize noise, but either approach can add cost to the finished part and strain the relationship between the machine shop and the end user. A third, but often overlooked, alternative is to use a material that has high noise damping capabilities. One such material is cast iron.
Designing a gear set implies a considerable effort in the determination of the geometry that fulfills the requirements of load capacity, reliability, durability, size, etc. When the objective is to design a new set of gears, there are many alternatives for the design, and the designer has the freedom to choose among them. Reverse engineering implies an even bigger challenge to the designer, because the problem involves already manufactured gears whose geometry is generally unknown. In this case, the designer needs to know the exact geometry of the actual gears in order to have a reference for the design.
Helical gear pairs with narrow face width can be theoretically classified into three categories over the contact ration domain whose abscissa is the transverse contact ration and whose ordinate is the overlap contact ratio. There is a direct relation between vibration magnitude and shaft parallelism deviation. To clarify the effect of the tooth deviation types on the vibration behavior of helical gear pairs, performance diagrams on vibration are introduced. the acceleration levels of gear pairs are shown by contour lines on the contact ratio domain. Finally, the performance of gears with bias-in and bias-out modifications is discussed considering the effect of the shaft parallelism deviation with use of the developed simulator on a helical gear unit. It becomes clear that there is an asymmetrical feature on the relation between the vibration magnitude of a gear pair and the direction of each deviation.
Gear designers today are continually challenged to provide more power in less space and improve gear performance. The following article looks at some of the most common ways to increase the power density or improve the performance of gear trains. The author also takes an in-depth look at the case of a steel worm mating with a plastic helical gear and explores ways to optimize this increasingly common configuration.
Gear design and specification are not one and the same. They are the first two steps in making a gear. The designer sits down and mathematically defines the gear tooth, working with the base pitch of the gear, the pressure angle he wants to employ, the number of teeth he wants, the lead, the tooth thickness, and the outside, form and root diameters. With these data, the designer can create a mathematical model of the gear. At this stage, he will also decide whether the gear will be made from existing cutting tools or whether new tools will be needed, what kind of materials he will use, and whether or not he will have the gear heat treated and finished.
Planetary gear transmissions are compact, high-power speed reducers that use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane transmission, the planet gear has no size of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary transmission with a fixed size, gear ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives, which point to an optimal planetary reduction ratio in the neighborhood of four to five.
Computers are everywhere. It's gotten so that it's hard to find an employee who isn't using one in the course of his or her day - whether he be CEO or salesman, engineer or machinist. Everywhere you look, you find the familiar neutral-colored boxes and bright glowing screens. And despite the gear industry's traditional reluctance to embrace new technology, more and moe of what you find on those screens are gears.
simplified equations for backlash and roll test center distance are derived. Unknown errors in measured tooth thickness are investigate. Master gear design is outlined, and an alternative to the master gear method is described. Defects in the test radius method are enumerated. Procedures for calculating backlash and for preventing significant errors in measurement are presented.
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.
The efficient and reliable transmission of mechanical power continues, as always, to be a central area of concern and study in mechanical engineering. The transmission of power involves the interaction of forces which are transmitted by specially developed components. These components must, in turn, withstand the complex and powerful stresses developed by the forces involved. Gear teeth transmit loads through a complex process of positive sliding, rolling and negative sliding of the contacting surfaces. This contact is responsible for both the development of bending stresses at the root of the gear teeth and the contact stresses a the contacting flanks.
A major source of helicopter cabin noise (which has been measured at over 100 decibels sound pressure level) is the gearbox. Reduction of this noise is a NASA and U.S. Army goal. A requirement for the Army/NASA Advanced Rotorcraft Transmission project was a 10 dB noise reduction compared to current designs.
The Hobbing Process The hobbing process involves a hob which is threaded with a lead and is rotated in conjunction with the gear blank at a ratio dependent upon the number of teeth to be cut. A single thread hob cutting a 40-tooth gear will make 40 revolutions for each revolution of the gear. The cutting action in hobbing is continuous, and the teeth are formed in one passage of the hob through the blank. See Fig. 1 for a drawing of a typical hob with some common nomenclature.
The first part of this article describes the analytical design method developed by the author to evaluate the load capacity of worm gears. The second part gives a short description of the experimental program and testing resources being used at CETIM to check the basic assumptions of the analytical method; and to determine on gears and test wheels the surface pressure endurance limits of materials that can be used for worm gears. The end of the article compares the results yielded by direct application of the method and test results.
One of the most frequently neglected areas of gear design is the determination of "form diameter". Form diameter is that diameter which specifies the transition point between the usable involute profile and the fillet of the tooth. Defining this point is important to prevent interference with the tip of the mating gear teeth and to enable proper preshave machining when the gear is to be finished with a shaving operation.
Since size and efficiency are increasingly important considerations in modern machinery, the trend is gear design is to use planetary gearing instead of worm gearing and multi-stage gear boxes. Internal gearing is an important part of most of planetary gear assemblies. In external gearing, if the gears are standard (of no-modified addenda), interference rarely happens. But in an internal gearing, especially in some new types of planetary gears, such as the KHV planetary, the Y planetary, etc., (1) various types of interference may occur. Therefore, avoiding interference is of significance for the design of internal gearing.
Plastic gears are being used increasingly in applications, such as printers, cameras, small household appliances, small power tools, instruments, timers, counters and various other products. Because of the many variables involved, an engineer who designs gear trains on an occasional basis may find the design process to be somewhat overwhelming. This article outlines a systematic design approach for developing injection molded plastic spur and helical gears. The use of a computer program for designing plastic gears is introduced as an invaluable design tool for solving complex gearing equations.
Gear shaping is one of the most popular production choices in gear manufacturing. While the gear shaping process is really the most versatile of all the gear manufacturing methods and can cut a wide variety of gears, certain types of gears can only be cut by this process. These are gears closely adjacent to shoulders; gears adjacent to other gears, such as on countershafts; internal gears, either open or blind ended; crown or face gears; herringbone gears of the solid configuration of with a small center groove; rack; parts with filled-in spaces or teeth, such as are used in some clutches.
This article discusses an application driven approach to the computer-aided sizing of spur gear teeth. The methodology is bases on the index of tooth loading and environment of application of the gear. It employs handbook knowledge and empirical information to facilitate the design process for a novice. Results show that the approach is in agreement with the textbook data. However, this technique requires less expert knowledge to arrive at the conclusion. The methodology has been successfully implemented as a gear tooth sizing module of a parallel axis gear drive expert system.
How dynamic load affects the pitting fatigue life of external spur gears was predicted by using NASA computer program TELSGE. TELSGE was modified to include an improved gear tooth stiffness model, a stiffness-dynamic load iteration scheme and a pitting-fatigue-life prediction analysis for a gear mesh. The analysis used the NASA gear life model developed by Coy, methods of probability and statistics and gear tooth dynamic loads to predict life. In general, gear life predictions based on dynamic loads differed significantly from those based on static loads, with the predictions being strongly influenced by the maximum dynamic load during contact.
In principal, the design of internal helical gear teeth is the same as that for external helical gears. Any of the basic rack forms used for external helical gears may be applied to internal helical gears. The internal gear drive, however, has several limitations; not only all those which apply to external gears, but also several others which are peculiar to internal gears. As with external gears, in order to secure effective tooth action, interferences must be avoided. The possible interferences on an internal gear drive are as follows: 1. Involute interference. To avoid this, all of the working profile of the internal tooth must be of involute form.
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.
Involute Curve Fundamentals. Over the years many different curves have been considered for the profile of a gear tooth. Today nearly every gear tooth uses as involute profile. The involute curve may be described as the curve generated by the end of a string that is unwrapped from a cylinder. (See Fig. 1) The circumference of the cylinder is called the base circle.
The south-pointing chariot exhibited at the Smithsonian Institution, Washington, D.C., (circa 2600 BC)is shown in Fig. 1. Although the mechanism is ancient, it is by no means either primitive or simplistic. The pin-tooth gears drive a complex system, wherein the monk on the top of the chariot continues to point in a preset direction, no matter what direction the vehicle in moved, without a slip of the wheels.(1)
Primitive gears were known and used well over 2,000 years ago, and gears have taken their place as one of the basic machine mechanisms; yet, our knowledge and understanding of gearing principles is by no means complete. We see the development of faster and more reliable gear quality assessment and new, more productive manufacture of gears in higher materials hardness states. We have also seen improvement in gear applications and design, lubricants, coolants, finishes and noise and vibration control. All these advances push development in the direction of smaller, more compact applications, better material utilization and improved quietness, smoothness of operation and gear life. At the same time, we try to improve manufacturing cost-effectiveness, making use of highly repetitive and efficient gear manufacturing methods.
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.
In our last issue, the labels on the drawings illustrating "Involutometry" by Harlan Van Gerpan and C. Kent Reece were inadvertently omitted. For your convenience we have reproduced the corrected illustrations here. We regret any inconvenience this may have caused our readers.
In many gear transmissions, a tooth load on one flank is significantly higher and is applied for longer periods of time than for the opposite one; an asymmetric tooth shape reflects this functional difference. This paper describes an approach that rationalizes the degree of asymmetry (or asymmetry factor K) selection to meet a variety of operating conditions and requirements for custom gear drives.
Cutter Sharpening Cutter sharpening is very important both during manufacturing and subsequently in resharpening after dulling. Not only does this process affect cutter "over cutting edge" quality and the quality of the part cut, but it can also affect the manner in which chip flow takes place on the cutter face if the surface finished is too rough or rippled.
Many CAD (Computer Aided Design) systems have been developed and implemented to produce a superior quality design and to increase the design productivity in the gear industry. In general, it is true that a major portion of design tasks can be performed by CAD systems currently available. However, they can only address the computational aspects of gear design that typically require decision-making as well. In most industrial gear design practices, the initial design is the critical task that significantly effects the final results. However, the decisions about estimating or changing gear size parameters must be made by a gear design expert.
Today's high technology hobs are visible different from their predecessors. Gear hobs have taken on a different appearance and function with present day technology and tool and material development. This article shows the newer products being offered today and the reasons for investigating their potential for use in today's modern gear hobbers, where cost reduction and higher productivity are wanted.
The use of dimensionless factors to describe gear tooth geometry seems to have a strong appeal to gear engineers. The stress factors I and J, for instance, are well established in AGMA literature. The use of the rack shift coefficient "x" to describe nonstandard gear proportions is common in Europe, but is not as commonly used in the United States. When it is encountered in the European literature or in the operating manuals for imported machine tools, it can be a source of confusion to the American engineer.
The 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.
This is Part II of a two-part series on the basics of gear hobbing. Part I discussed selection of the correct type of hobbing operation, the design features of hobs and hob accuracy. This part will cover sharpening errors and finish hob design considerations.
The quality of the material used for highly loaded critical gears is of primary importance in the achievement of their full potential. Unfortunately, the role which material defects play is not clearly understood by many gear designers. The mechanism by which failures occur due to material defects is often circuitous and not readily apparent. In general, however, failures associated with material defects show characteristics that point to the source of the underlying problem, the mechanism by which the failure initiated, and the manner in which it progressed to failure of the component.
Questions: I have heard the terms "safety factor," "service factor," and "application factor" used in discussing gear design. what are these factors an dhow do they differ from one another? Why are they important?
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
This is a three-part article explaining the principles of gear lubrication. It reviews current knowledge of the field of gear tribology and is intended for both gear designers and gear operators. Part 1 classifies gear tooth failures into five modes and explains the factors that a gear designer and operator must consider to avoid gear failures. It defines the nomenclature and gives a list of references for those interested in further research. It also contains an in-depth discussion of the gear tooth failure modes that are influenced by lubrication and gives methods for preventing gear tooth failures.
Engineering design requires many different types of gears and splines. Although these components are rather expensive, subject to direct wear, and difficult to replace, transmissions with gears and splines are required for two very simple reasons: 1) Motors have an unfavorable (disadvantageous) relation of torque to number of revolutions. 2)Power is usually required to be transmitted along a shaft.
What follows is Part 2 of a three-part article covering the principles of gear lubrication. Part 2 gives an equation for calculating the lubricant film thickness, which determines whether the gears operate in the boundary, elastohydrodynamic, or full-film lubrication regime. An equation for Blok's flash temperature, which is used for predicting the risk of scuffing, is also given.
This is the final part of a three-part series on the basics of gear lubrication. It covers selection of lubricant types and viscosities, the application of lubricants, and a case history
The finished gear engineer, the man who is prepared for all emergencies, must first of all know the basic design principles. Next he must be well versed in all sorts of calculations which come under the heading of "involute trigonometry."
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?
For high-quality carburized, case hardened gears, close case carbon control is essential. While tight carbon control is possible, vies on what optimum carbon level to target can be wider than the tolerance.
"Design for manufacturability" (DFM) is a well-established practice, essential to realizing the successful transformation of concepts into mass-produced gears and motion control devices. And yet, all too often issues that could have been avoided are identified very late in the process that impact production costs and schedules. This suggests that key DFM principles are often underutilized in practice and are not applied consistently - or to the degree necessary - to avoid these negative results.
"Gear Train" is a new Gear Technology section focusing on training and education in the gear industry. For the first installment, we've focused on AGMA's online and video training programs.
What is the difference between pressure angle and operating pressure angle?
A gear design optimization approach applied to reduce tooth contact temperature and noise excitation of a high-speed spur gear pair running without lubricant. Optimum gear design search was done using the Run Many Cases software program. Thirty-one of over 480,000 possible gear designs were considered, based on low contact temperature and low transmission error. The best gear design was selected considering its manufacturability.
Flank breakage is common in a number of cylindrical and bevel gear applications. This paper introduces a relevant, physically based calculation method to evaluate flank breakage risk vs. pitting risk. Verification of this new method through testing is demonstrably shown.
Romax Technology, the gearbox, bearing and driveline engineering specialist, has launched a new design software package that will increase speed, quality, creativity and innovation when designing gearboxes and drivelines. Called Concept, the new product delivers on the Romax vision of streamlining the end-to-end, planning-to-manufacture process with open, easy to use software solutions. It has been developed in close collaboration with engineers in the largest ground vehicle, wind energy and industrial equipment companies around the globe.
While external involute gears are very tolerant of center distance variations, what are the center distance constraints for internal gears?
This article discusses the relationships among the fillet stress on a thin rim planet gear, the radial clearance between the gear rim and the gear shaft, the tooth load, the rim thickness, the radius of curvature of the center line of the rim, the face width and the module.
This paper presents approximate and accurate methods to generate solid models of involute cylindrical gears using Autodesk Inventor 3-D CAD software.
Three experts tackle the question of profile shift in this issue's edition of "Ask the Expert."
Gearbox performance, reliability, total cost of ownership (energy cost), overall impact on the environment, and anticipation of additional future regulations are top-of-mind issues in the industry. Optimization of the bearing set can significantly improve gearbox performance.
By increasing the number of gears and the transmission-ratio spread, the engine will run with better fuel efficiency and without loss of driving dynamics. Transmission efficiency itself can be improved by: using fuelefficient transmission oil; optimizing the lubrication systems and pumps; improving shifting strategies and optimizing gearings; and optimizing bearings and seals/gaskets.
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.
For metal replacement with powder metal (PM) of an automotive transmission, PM gear design differs from its wrought counterpart. Indeed, complete reverse-engineering and re-design is required so to better understand and document the performance parameters of solid-steel vs. PM gears. Presented here is a re-design (re-building a 6-speed manual transmission for an Opel Insignia 4-cylinder, turbocharged 2-liter engine delivering 220 hp/320 N-m) showing that substituting a different microgeometry of the PM gear teeth -- coupled with lower Young’s modulus -- theoretically enhances performance when compared to the solid-steel design.
Bevel Gear Technology Chapter 6
What is the point of using two idler gears in a geartrain?
A best practice in gear design is to limit the amount of backlash to a minimum value needed to accommodate manufacturing tolerances, misalignments, and deflections, in order to prevent the non-driving side of the teeth to make contact and rattle. Industry standards, such as ANSI/AGMA 2002 and DIN3967, provide reference values of minimum backlash to be used in the gear design. However, increased customers’ expectations in vehicle noise eduction have pushed backlash and allowable manufacturing tolerances to even lower limits. This is especially true in the truck market, where engines are quieter because they run at lower speeds to improve fuel economy, but they quite often run at high torsional vibration levels. Furthermore, gear and shaft arrangements in truck transmissions have become more complex due to increased number of speeds and to improve efficiency. Determining the minimum amount of backlash is quite a challenge. This paper presents an investigation of minimum backlash values of helical gear teeth applied to a light-duty pickup truck transmission. An analytical model was developed to calculate backlash limits of each gear pair when not transmitting load, and thus susceptible to generate rattle noise, through different transmission power paths. A statistical approach (Monte Carlo) was used since a significant number of factors affect backlash, such as tooth thickness variation; center distance variation; lead; runout and pitch variations; bearing clearances; spline clearances; and shaft deflections and misalignments. Analytical results identified the critical gear pair, and power path, which was confirmed experimentally on a transmission. The approach presented in this paper can be useful to design gear pairs with a minimum amount of backlash, to prevent double flank contact and to help reduce rattle noise to lowest levels.
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.
The increasing demands in the automotive industry for weight reduction, fuel efficiency and a reduced carbon footprint need to be addressed urgently. Up until now, widely used conventional steels have lived up to expectations. However, with more stringent emissions standards, demands on materials are increasing. Materials are expected to perform better, resulting in a need for increased fatigue strength. A possibility to increase torque on current generations without design changes can be achieved by selecting suitable materials.
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).
When compared with the traditional gear design approach — based on pre-selected, typically standard generating rack parameters — the alternative Direct Gear Design method provides certain advantages for custom, high-performance gear drives.
Light-weight construction and consideration of available resources result in gearbox designs with high load capacity and power density. At the same time, expectations for gear reliability are high. Additionally, there is a diversity of planetary gears for different applications.
There is a great need for future powertrains in automotive and industrial applications to improve upon their efficiency and power density while reducing their dynamic vibration and noise initiation. It is accepted that planetary gear transmissions have several advantages in comparison to conventional transmissions, such as a high power density due to the power division using several planet gears. This paper presents planetary gear transmissions, optimized in terms of efficiency, weight and volume.
With all the advantages of building float into a planetary gear system, what advantages are there to using a carrier in the first place, rather than simply having your planets float in the system?
It has been documented that epicyclic gear stages provide high load capacity and compactness to gear drives. This paper will focus on analysis and design of epicyclic gear arrangements that provide extremely high gear ratios. Indeed, a special, two-stage planetary arrangement may utilize a gear ratio of over one hundred thousand to one. This paper presents an analysis of such uncommon gear drive arrangements and defines their major parameters, limitations, and gear ratio maximization approaches. It also demonstrates numerical examples, existing designs, and potential applications.
Gears with a diametral pitch 20 and greater, or a module 1.25 millimeters and lower, are called fine-pitch or low-module gears. The design of these gears has its own specifics.
Optimizing the running behavior of bevel and hypoid gears means improving both noise behavior and load carrying capacity. Since load deflections change the relative position of pinion and ring gear, the position of the contact pattern will depend on the torque. Different contact positions require local 3-D flank form optimizations for improving a gear set.
Bending stress evaluation in modern gear design is generally based on the more-than-one-hundred-year-old Lewis equation.
The configuration of flank corrections on bevel gears is subject to relatively narrow restrictions. As far as the gear set is concerned, the requirement is for the greatest possible contact zone to minimize flank compression. However, sufficient reserves in tooth depth and longitudinal direction for tooth contact displacement should be present. From the machine - and particularly from the tool - point of view, there are restrictions as to the type and magnitude of crowning that can be realized. Crowning is a circular correction. Different kinds of crowning are distinguished by their direction. Length crowning, for example, is a circular (or 2nd order) material removal, starting at a reference point and extending in tooth length or face width.
Users of gear-cutting tools probably do not often consciously consider the raw material from which those hobs, broaches or shavers are made. However, a rudimentary awareness of the various grades and their properties may allow tool users to improve the performance or life of their tools, or to address tool failures. The high-speed steel from which the tool is made certainly is not the only factor affecting tool performance, but as the raw material, the steel may be the first place to start.
Crown gearings are not a new type of gear system. On the contrary, they have been in use since very early times for various tasks. Their earliest form is that of the driving sprocket, found in ancient Roman watermills or Dutch windmills. The first principles of gear geometry and simple methods of production (shaper cutting) were developed in the 1940s. In the 1950s, however, crown gears' importance declined. Their tasks were, for example, taken over by bevel gears, which were easier to manufacture and could transmit greater power. Current subject literature accordingly contains very little information on crown gears, directed mainly to pointing out their limitations (Ref. 1).
Early in the practice of involute gearing, virtually all gears were made with the teeth in a standard relationship to the reference pitch circle. This has the advantages that any two gears of the same pitch, helix angle and pressure angle can operate together, and that geometry calculations are relatively simple. It was soon realized, though, that there are greater advantages to be gained by modifying the relationship of the teeth to the reference pitch circle. The modifications are called profile shift.
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.
Two-shaft planetary gear drives are power-branching transmissions, which lead the power from input to output shaft on several parallel ways. A part of the power is transferred loss-free as clutch power. That results in high efficiency and high power density. Those advantages can be used optimally only if an even distribution of load on the individual branches of power is ensured. Static over-constraint, manufacturing deviations and the internal dynamics of those transmission gears obstruct the load balance. With the help of complex simulation programs, it is possible today to predict the dynamic behavior of such gears. The results of those investigations consolidate the approximation equations for the calculation of the load factors...
The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.
In general, bevel gears and curvic couplings are completely different elements. Bevel gears rotate on nonintersecting axis with a ratio based on the number of teeth. Curvic couplings work like a clutch (Fig. 1).
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.
Noncircular gearing is not new. There are well-documented articles covering standard and high order elliptical gears, sinusoidal gears, logarithmic spiral gears, and circular gears mounted eccentrically. What these designs have in common is a pitch curve defined by a mathematical function. This article will cover noncircular gearing with free-form pitch curves, which, of course, includes all the aforementioned functions. This article also goes into the generation of teeth on the pitch curve, which is not usually covered in the technical literature. Needless to say, all this is possible only with the help of a computer.
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.
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.
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.
The lifetime of worm gears is usually delimited by the bronze-cast worm wheels. The following presents some optimized cast bronzes, which lead to a doubling of wear resistance.
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.
This paper reviews the necessity for detailed specification, design and manufacture to achieve required performance in service. The precise definition of duty rating and a thorough understanding of the environmental conditions, whether it is in a marine or industrial application, is required to predict reliable performance of a gearbox through its service life. A case study relating to complex marine gears and other general practice is presented to review the techniques used by Allen Gears to design and develop a gearbox that integrates with the requirements of the whole machinery installation. Allen Gears has considerable experience in the design of a variety of industrial and marine gears(Ref. 1,2).
The load capacity of worm gears is mainly influenced by the size and the position of the contact pattern.
In the last couple of years, many research projects dealt with the determination of load limits of cylindrical worm gears. These projects primarily focused on the load capacity of the worm wheel, whereas the worm was neglected. This contribution presents investigations regarding damages such as large scores and cracks on the flanks of case-hardened worms.
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.
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.
The need for improved power transmissions that use gears and gearboxes with smaller overall dimensions and with lower noise generation has left manufacturing engineers searching for different methods of gear processing. This search has led to the requirement of hardened gears.
Gear pitting is one of the primary failure modes of automotive transmission gear sets. Over the past years, many alternatives have been intended to improve their gear surface durability. However, due to the nature of new process development, it takes a length of time and joint efforts between the development team and suppliers to investigate and verify each new approach.
There are numerous engineering evaluations required to design gear sets for optimum performance with regard to torque capacity, noise, size and cost. How much cost savings and added gear performance is available through optimization? Cost savings of 10% to 30% and 100% added capacity are not unusual. The contrast is more pronounced if the original design was prone to failure and not fit for function.
Modern gear design is generally based on standard tools. This makes gear design quite simple (almost like selecting fasteners), economical, and available for everyone, reducing tooling expenses and inventory. At the same time, it is well known that universal standard tools provide gears with less than optimum performance and - in some cases - do not allow for finding acceptable gear solutions. Application specifies, including low noise and vibration, high density of power transmission (lighter weight, smaller size) and others, require gears with nonstandard parameters. That's why, for example, aviation gear transmissions use tool profiles with custom proportions, such as pressure angle, addendum, and whole depth. The following considerations make application of nonstandard gears suitable and cost-efficient:
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.
The selection of the proper steel for a given gear application is dependent on many factors. This paper discusses the many aspects related to material, design, manufacture, and application variables. The results of several studies on the optimization of alloy design for gas- and plasma- carburization processing and reviewed.
Plastic gears and transmissions require a different design approach than metal transmissions. Different tools are available to the plastic transmission designer for optimizing his geared product, and different requirements exist for inspection and testing. This paper will present some of the new technology available to the plastic gear user, including design, mold construction, inspection, and testing of plastic gears and transmissions.
Selection of the number of teeth for each gear in a gear train such that the output to input angular velocity ratio is a specified value is a problem considered by relatively few published works on gear design.
News about the latest products in the industry.
THE FINAL CHAPTER This is the last in the series of chapters excerpted from Dr. Hermann J. Stadtfeld’s Gleason Bevel Gear Technology — a book written for specialists in planning, engineering, gear design and manufacturing. The work also addresses the technical information needs of researchers, scientists and students who deal with the theory and practice of bevel gears and other angular gear systems. While all of the above groups are of course of invaluable importance to the gear industry, it is surely the students who hold the key to its future. And with that knowledge it is reassuring to hear from Dr. Stadtfeld of the enthusiastic response he has received from younger readers of these chapter installments.
Gear designs are evolving at an ever accelerating rate, and gear manufacturers need to better understand how the choice of materials and heat treating methods can optimize mechanical properties, balance overall cost and extend service life.
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.
This article presents some of the findings of cutting investigations at WZL in which the correlation of cutting parameters, cutting materials, tool geometry and tool life have been determined.
The cutting process consists of either a roll only (only generating motion), a plunge only or a combination of plunging and rolling. The material removal and flank forming due to a pure generating motion is demonstrated in the simplified sketch in Figure 1 in four steps. In the start roll position (step 1), the cutter profile has not yet contacted the work. A rotation of the work around its axis (indicated by the rotation arrow) is coupled with a rotation of the cutter around the axis of the generating gear (indicated by the vertical arrow) and initiates a generating motion between the not-yet-existing tooth slot of the work and the cutter head (which symbolizes one tooth of the generating gear).
Could you explain to me the difference between spiral bevel gear process face hobbing-lapping, face milling-grinding and Klingelnberg HPG? Which one is better for noise, load capacity and quality?
Following is a report on the R&D findings regarding remediation of high-value, high-demand spiral bevel gears for the UH–60 helicopter tail rotor drivetrain. As spiral bevel gears for the UH–60 helicopter are in generally High-Demand due to the needs of new aircraft production and the overhaul and repair of aircraft returning from service, acquisition of new spiral bevel gears in support of R&D activities is very challenging. To compensate, an assessment was done of a then-emerging superfinishing method—i.e., the micromachining process (MPP)—as a potential repair technique for spiral bevel gears, as well as a way to enhance their performance and durability. The results are described in this paper.
Gear tooth wear and micropitting are very difficult phenomena to predict analytically. The failure mode of micropitting is closely correlated to the lambda ratio. Micropitting can be the limiting design parameter for long-term durability. Also, the failure mode of micropitting can progress to wear or macropitting, and then go on to manifest more severe failure modes, such as bending. The results of a gearbox test and manufacturing process development program will be presented to evaluate super-finishing and its impact on micropitting.
Heat treat suppliers look to the gear industry and the upcoming combined Gear Expo/Heat Treat 2013 for new business.
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.
Manufacturing involute gears using form grinding or form milling wheels are beneficial to hobs in some special cases, such as small scale production and, the obvious, manufacture of internal gears. To manufacture involute gears correctly the form wheel must be purpose-designed, and in this paper the geometry of the form wheel is determined through inverse calculation. A mathematical model is presented where it is possible to determine the machined gear tooth surface in three dimensions, manufactured by this tool, taking the finite number of cutting edges into account. The model is validated by comparing calculated results with the observed results of a gear manufactured by an indexable insert milling cutter.
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.
An accurate and fast calculation method is developed to determine the value of a trigonometric function if the value of another trigonometric function is given. Some examples of conversion procedures for well-known functions in gear geometry are presented, with data for accuracy and computing time. For the development of such procedures the complete text of a computer program is included.
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.
I have outsourced gear macrogeometry due to lack of resources. Now I received the output from them and one of the gears is with —0.8× module correction factor for m = 1.8 mm gear. Since bending root stress and specific slide is at par with specification, but negative correction factor —0.8× module — is quite high — how will it influence NVH behavior/transmission error? SAP and TIF are very close to 0.05 mm; how will that influence the manufacturing/cost?
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 article summarizes results of research programs on RCF strength of wrought steels and PM steels.
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.
Beginning with our June Issue, Gear Technology is pleased to present a series of full-length chapters excerpted from Dr. Hermann J. Stadtfeld’s latest scholarly — yet practical — contribution to the gear industry — Gleason Bevel Gear Technology. Released in March, 2014 the book boasts 365 figures intended to add graphic support of a better understanding and easier recollection of the covered material.
The geometry of the bevel gear is quite complicated to describe mathematically, and much of the overall surface topology of the tooth flank is dependent on the machine settings and cutting method employed. AGMA 929-A06 — Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius — lays out a practical approach for predicting the approximate top-land thicknesses at certain points of interest — regardless of the exact machine settings that will generate the tooth form. The points of interest that AGMA 929-A06 address consist of toe, mean, heel, and point of involute lengthwise curvature. The following method expands upon the concepts described in AGMA 929-A06 to allow the user to calculate not only the top-land thickness, but the more general case as well, i.e. — normal tooth thickness anywhere along the face and profile of the bevel gear tooth. This method does not rely on any additional machine settings; only basic geometry of the cutter, blank, and teeth are required to calculate fairly accurate tooth thicknesses. The tooth thicknesses are then transformed into a point cloud describing both the convex and concave flanks in a global, Cartesian coordinate system. These points can be utilized in any modern computer-aided design software package to assist in the generation of a 3D solid model; all pertinent tooth macrogeometry can be closely simulated using this technique. A case study will be presented evaluating the accuracy of the point cloud data compared to a physical part.
There are different types of spiral bevel gears, based on the methods of generation of gear-tooth surfaces. A few notable ones are the Gleason's gearing, the Klingelnberg's Palloid System, and the Klingelnberg's and Oerlikon's Cyclo Palliod System. The design of each type of spiral bevel gear depends on the method of generation used. It is based on specified and detailed directions which have been worked out by the mentioned companies. However, there are some general aspects, such as the concepts of pitch cones, generating gear, and conditions of force transmissions that are common for all types of spiral bevel gears.
In the past gear manufacturers have had to rely on hob manufacturers' inspection of individual elements of a hob, such as lead, involute, spacing, and runout. These did not always guarantee correct gears, as contained elements may cause a hob to produce gears beyond tolerance limits.
In 1961 I presented a paper, "Calculating Conjugate Helical Forms," at the semi-annual meeting of the American Gear Manufacturers Association (AGMA). Since that time, thousands of hobs, shaper cutters and other meshing parts have been designed on the basis of the equations presented in that paper. This article presents the math of that paper without the formality of its development and goes on to discuss its practical application.
The focus of the following presentation is two-fold: 1) on tests of new geometric variants; and 2) on to-date, non-investigated operating (environmental) conditions. By variation of non-investigated eometric parameters and operation conditions the understanding of micropitting formation is improved. Thereby it is essential to ensure existent calculation methods and match them to results of the comparison between large gearbox tests and standard gearbox test runs to allow a safe forecast of wear due to micropitting in the future.
In the past, the blades of universal face hobbing cutters had to be resharpened on three faces. Those three faces formed the active part of the blade. In face hobbing, the effective cutting direction changes dramatically with respect to the shank of the blade. Depending on the individual ratio, it was found that optimal conditions for the chip removal action (side rake, side relief and hook angle) could just be established by adjusting all major parameters independently. This, in turn, results automatically in the need for the grinding or resharpening of the front face and the two relief surfaces in order to control side rake, hook angle and the relief and the relief angles of the cutting and clearance side.
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.
Bevel gear manufacturers live in one of two camps: the face hobbing/lapping camp, and the face milling/grinding camp.
In a previous article, the authors identified two misconceptions surrounding gear superfinishing. Here, they tackle three more.
Dutch design and Swiss ingenuity cause transmission breakthrough. Updated examples of Cylkro face gears in action.
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.
This article is part five 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.
In earlier studies, surface roughness has been shown to have a significant influence on gear pitting life. This paper discusses how high surface roughness introduces a wear mechanism that delays the formation of pits. Accompanied by a full-page technical review.
In addition to the face milling system, the face hobbing process has been developed and widely employed by the gear industry. However, the mechanism of the face hobbing process is not well known.
Superfinishing the working surfaces of gears and their root fillet regions results in performance benefits.
Non-uniform gear wear changes gear topology and affects the noise performance of a hypoid gear set. The aggregate results under certain vehicle driving conditions could potentially result in unacceptable vehicle noise performance in a short period of time. This paper presents the effects of gear surface parameters on gear wear and the measurement/testing methods used to quantify the flank wear in laboratory tests.
Curved face width (CFW) spur gears are not popular in the gear industry. But these non-metallic gears have advantages over standard spur gears: higher contact ratio, higher tooth stiffness, and lower contact and bending stresses.
Results from the Technical University of Munich were presented in a previous technical article (see Ref. 4). This paper presents the results of Ruhr University Bochum. Both research groups concluded that superfinishing is one of the most powerful technologies for significantly increasing the load-carrying capacity of gear flanks.
Surface coatings or finishing processes are the future technologies for improving the load carrying capacity of case hardened gears. With the help of basic tests, the influence of different coatings and finishing processes on efficiency and resistance to wear, scuffing, micropitting, and macropitting is examined.
Most research on micropitting is done on small-sized gears. This article examines whether those results are also applicable to larger gears.
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.
Bevel gears have been the standard for several decades in situations where power transmission has to occur between shafts mounted at a given angle. Now a new approach has been developed that challenges the bevel gear's de facto monopoly in such applications. The concept is based on the principle of the crown gear; i.e., a cylindrical pinion mates with a face gear. Crown Gear B.V. in Enschede, Holland, is the developer of these specialty gear teeth, which are marketed under the trade name Cylkro.
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.
Rotary gear honing is a crossed-axis, fine, hard finishing process that uses pressure and abrasive honing tools to remove material along the tooth flanks in order to improve the surface finish (.1-.3 um or 4-12u"Ra), to remove nicks and burrs and to change or correct the tooth geometry. Ultimately, the end results are quieter, stronger and longer lasting gears.
Surface roughness measuring of gear teeth can be a very frustrating experience. Measuring results often do not correlate with any functional characteristic, and many users think that they need not bother measuring surface roughness, since the teeth are burnished in operation. They mistakenly believe that the roughness disappears in a short amount of time. This is a myth! The surface indeed is shiny, but it still has considerable roughness. In fact, tests indicate that burnishing only reduces the initial roughness by approximately 25%.
Face-milled hypoid pinions produced by the three-cut, Fixed Setting system - where roughing is done on one machine and finishing for the concave-OB and convex-IB tooth flanks is done on separate machines with different setups - are still in widespread use today.
Could the tip chamfer that manufacturing people usually use on the tips of gear teeth be the cause of vibration in the gear set? The set in question is spur, of 2.25 DP, with 20 degrees pressure angle. The pinion has 14 teeth and the mating gear, 63 teeth. The pinion turns at 535 rpm maximum. Could a chamfer a little over 1/64" cause a vibration problem?
The working surfaces of gear teeth are often the result of several machining operations. The surface texture imparted by the manufacturing process affects many of the gear's functional characteristics. To ensure proper operation of the final assembly, a gear's surface texture characteristics, such as waviness and roughness, can be evaluated with modern metrology instruments.
Gear surface fatigue endurance tests were conducted on two groups of 10 gears each of carburized and hardened AlSI 9310 spur gears manufactured from the same heat of material
Spiral-bevel gears, found in many machine tools, automobile rear-axle drives, and helicopter transmissions, are important elements for transmitting power.
Rotary gear honing is a hard gear finishing process that was developed to improve the sound characteristics of hardened gears by: Removing nicks and burrs; improving surface finish; and making minor corrections in tooth irregularities caused by heat-treat distortion.
Spur gear surface endurance tests were conducted to investigate CBN ground AISI 9310 spur gears for use in aircraft applications, to determine their endurance characteristics and to compare the results with the endurance of standard vitreous ground AISI 9310 spur gears. Tests were conducted with VIM-VAR AISI 9210 carburized and hardened gears that were finish ground with either CBN or vitreous grinding methods. Test conditions were an inlet oil temperature of 320 K (116 degree F), an outlet oil temperature of 350 K (170 degree F), a maximum Hertz stress of 1.71 GPa (248 ksi), and a speed of 10,000 rpm. The CBN ground gears exhibited a surface fatigue life that was slightly better than the vitreous ground gears. The subsurface residual stress of the CBN ground gears was approximately the same as that for the standard vitreous ground gears for the CBN grinding method used.
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.
Applying "Dynamic Block Contours" allows the designer to predict gear quality at the earliest stage of the design process.
Romax Technology is automating the design iteration process to allow companies to be faster to market with the highest quality, most robust gear products.
A graphical procedure for selecting optimum combinations of profile and lead modifications.
This paper presents a unique approach and methodology to define the limits of selection for gear parameters. The area within those limits is called the “area of existence of involute gears” (Ref. 1). This paper presents the definition and construction of areas of existence of both external and internal gears. The isograms of the constant operating pressure angles, contact ratios and the maximum mesh efficiency (minimum sliding) isograms, as well as the interference isograms and other parameters are defined. An area of existence allows the location of gear pairs with certain characteristics. Its practical purpose is to define the gear pair parameters that satisfy specific performance requirements before detailed design and calculations. An area of existence of gears with asymmetric teeth is also considered.
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.
LMS International helped a Fiat subsidiary develop a new, dynamic vibro-acoustic prediction method to reduce design time and engineering costs through accurate prediction of gear noise in the design phase.
In this article, a new tip relief profile modification for spur gears is presented. The topography proposed here is a classical linear profile modification with a parabolic fillet.
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.
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.
Above all, a gear is not just a mechanical transmission, but is developed to a system fulfilling multiple demands, such as clutch integration, selectable output speeds, and controls of highest electronic standards. This paper shows the basics for high-speed gear design and a selection of numerous applications in detailed design and operational needs.
MASTA 4.5.1 models complete transmissions and includes 3-D stress analysis.
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.
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.
A series of bench-top experiments was conducted to determine the effects of metallic debris being dragged through meshing gear teeth. A test rig that is typically used to conduct contact fatigue experiments was used for these tests. Several sizes of drill material, shim stock and pieces of gear teeth were introduced and then driven through the meshing region. The level of torque required to drive the “chip” through the gear mesh was measured. From the data gathered, chip size sufficient to jam the mechanism can be determined.
When specifying a complete gear design, the novice designer is confronted with an overwhelming and frequently confusing group of options which must be specified. This array of specifications range from the rather vague to the very specific.
When a gear set is to be designed for a new application, the minimum size gears with the required capacity are desired. These gears must be capable of meeting the power, speed, ratio, life, and reliability requirements.
Traditionally, a worm or a multi-stage gear box has been used when a large speed ratio is required. However, such boxes will become obsolete as size and efficiency become increasingly important considerations for a modern transmission. The single-enveloped worm gear has a maximum speed ratio of only 40 to 60. Its efficiency is only 30 to 60 per cent. The necessity of using bronze for the worm gear and grinding nitoalloy steel for the worm drives up material and manufacturing costs.
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.
Consisting of only a ring gear b meshing with one or two planets a, a carrier H and an equal velocity mechanism V, a KHV gearing(Fig. 1) is compact in structure, small in size and capable of providing a large speed ratio. For a single stage, its speed ratio can reach up to 200, and its size is approximately 1/4 that of a conventional multi-stage gear box.
The following is a general overview of some of the different factors that lead to the specific design. and the selection of the correct tool for a given hobbing application.
In designing involute gear teeth, it is essential that the fundamental properties of the involute curve be clearly understood. A review of "the Fundamental Laws of the Involute Curve" found in last issue will help in this respect. It has previously been shown that the involute curve has its origin at the base circle. Its length, however, may be anything from zero at the origin or starting point on to infinity. The problem, therefore, in designing gear teeth, is to select that portion of the involute, which will best meet all requirements.
Bradley University and Winzeler Gear collaborate on the design and development of an urban light vehicle.
In comparison with the traditional gear design approach based on preselected, typically standard generating rack parameters, the Direct Gear Design method provides certain advantages for custom high-performance gear drives that include: increased load capacity, efficiency and lifetime; reduced size, weight, noise, vibrations, cost, etc. However, manufacturing such directly designed gears requires not only custom tooling, but also customization of the gear measurement methodology. This paper presents definitions of main inspection dimensions and parameters for directly designed spur and helical, external and internal gears with symmetric and asymmetric teeth.
An update on the latest gear design software from several vendors, plus what gear design engineers can expect next.
A gear can be defined as a toothed wheel which, when meshed with another toothed wheel with similar configuration, will transmit rotation from one shaft to another. Depending upon the type and accuracy of motion desired, the gears and the profiles of the gear teeth can be of almost any form.
If a gear system is run continuously for long periods of time—or if the starting loads are very low and within the normal operating spectrum—the effect of the start-up conditions may often be insignificant in the determination of the life of the gear system. Conversely, if the starting load is significantly higher than any of the normal operating conditions, and the gear system is started and stopped frequently, the start-up load may, depending on its magnitude and frequency, actually be the overriding, limiting design condition.
In the field of large power transmission gear units for heavy machine industry, the following two development trends have been highly influential: use of case hardened gears and a branching of the power flow through two or more ways.
The common calculation methods according to DIN 3990 and ISO 6336 are based on a comparison of occurring stress and allowable stress. The influence of gear size on the load-carrying capacity is considered with the size factors YX (tooth root bending) and ZX (pitting), but there are further influences, which should be considered. In the following, major influences of gear size on the load factors as well as on the permissible tooth root bending and contact stress will be discussed.
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.
How the latest techniques and software enable faster spiral bevel and hypoid design and development.
In most transmission systems, one of the main power loss sources is the loaded gear mesh. In this article, the influences of gear geometry parameters on gear efficiency, load capacity, and excitation are shown.
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.
Austempered 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.
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 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.
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.
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.
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.
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.
The main theme of this article is high-capacity, high-speed load gears in a power transmission range between 35 MW and 100 MW for generators and turbo-compressors driven by gas or steam turbines.
Excess lubricant supply in gearing contributes to power loss due to churning as well as the requirements of the lubrication system itself. Normally, a much larger amount of oil than required is used for cooling because so much of it is thrown away by centrifugal force. To lower the amount of lubricant required and reduce those losses, it is necessary to discover the ideal location of the supplying nozzle.
High speed gearing, operating with low viscosity lubricants, is prone to a failure mode called scoring. In contrast to the classic failure modes, pitting and breakage, which generally take time to develop, scoring occurs early in the operation of a gear set and can be the limiting factor in the gear's power capability.
In today’s manufacturing environment, shorter and more efficient product development has become the norm. It is therefore important to consider every detail of the development process, with a particular emphasis on design. For green machining of gears, the most productive and important process is hobbing. In order to analyze process design for this paper, a manufacturing simulation was developed capable of calculating chip geometries and process forces based on different models. As an important tool for manufacturing technology engineers, an economic feasibility analysis is implemented as well. The aim of this paper is to show how an efficient process design—as well as an efficient process—can be designed.
The use of plastic gearing is increasing steadily in new products. This is due in part to the availability of recent design data. Fatigue stress of plastic gears as a function of diametral pitch, pressure angle, pitch line velocity, lubrication and life cycles are described based on test information. Design procedures for plastic gears are presented.
Gear engineers have long recognized the importance of considering system factors when analyzing a single pair of gears in mesh. These factors include important considerations such as load sharing in multi-mesh geartrains and bearing clearances, in addition to the effects of flexible components such as housings, gear blanks, shafts and carriers for planetary geartrains. However, in recent years, transmission systems have become increasingly complex—with higher numbers of gears and components—while the quality requirements and expectations in terms of durability, gear whine, rattle and efficiency have increased accordingly.
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.
Advancements in machining and assembly techniques of thermoplastic gearing along with new design data has lead to increased useage of polymeric materials. information on state of the art methods in fabrication of plastic gearing is presented and the importance of a proper backlash allowance at installation is discussed. Under controlled conditions, cast nylon gears show 8-14 dBA. lower noise level than three other gear materials tested.
The effect of load speed on straight and involute tooth forms is studied using several finite-element models.
The latest software for gear design, engineering and manufacturing.
The method of cutting teeth on a cylindrical gear by the hobbing process has been in existence since the late 1800s. Advances have been made over the years in both the machines and the cutting tools used in the process. This paper will examine hob tool life and the many variables that affect it. The paper will cover the state-of-the-art cutting tool materials and coatings, hob tool design characteristics, process speeds and feeds, hob shifting strategies, wear characteristics, etc. The paper will also discuss the use of a common denominator method for evaluating hob tool life in terms of meters (or inches) per hob tooth as an alternative to tool life expressed in parts per sharpening.
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.
The contact lines of a pair of helical gears move diagonally on the engaged tooth faces and their lengths consequently vary with the rotation of the gears.
The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.