# Geometry - Search Results

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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.

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.

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.

Traditionally, gear rating procedures consider manufacturing accuracy in the application of the dynamic factor, but only indirectly through the load distribution are such errors in the calculation of stresses used in the durability and gear strength equations. This paper discusses how accuracy affects the calculation of stresses and then uses both statistical design of experiments and Monte Carlo simulation techniques to quantify the effects of different manufacturing and assembly errors on root and contact stresses.

The 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.

This paper shows a method to calculate the occurring tooth root stress for involute, external gears with any form of fillets very precisely within a few seconds.

This article 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.

I have outsourced gear macrogeometry due to lack of resources. Now I received the output from them and one of the gears is with â€”0.8Ă— 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 â€”0.8Ă— module â€” is quite high â€” 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?

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.

The paper is not the proof of a discovery, but it is the description of a method: the optimization of the microgeometry for cylindrical gears. The method has been applied and described on some transmissions with helical gears and compound epicyclic, used on different hybrid vehicles. However, the method is also valid for industrial gearboxes.

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?

Beginning with our June Issue, Gear Technology is pleased to present a series of full-length chapters excerpted from Dr. Hermann J. Stadtfeldâ€™s latest scholarly â€” yet practical â€” contribution to the gear industry â€” 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 â€” Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius â€” lays out a practical approach for predicting the approximate top-land thicknesses at certain points of interest â€” 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. â€” 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.

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.

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!

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.

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.

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.

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 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.

Although there is plenty of information and data on the determination of geometry factors and bending strength of external gear teeth, the computation methods regarding internal gear design are less accessible. most of today's designs adopt the formulas for external gears and incorporate some kind of correction factors for internal gears. However, this design method is only an approximation because of the differences between internal gears and external gears. Indeed, the tooth shape of internal gears is different from that of external gears. One has a concave curve, while the other has a convex curve.

This article 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.

Q&A is an interactive gear forum. Send us you gear design, manufacturing, inspection or other related questions, and we will pass them to our panel of experts.

This study emphasizes the importance of a closed-loop approach togear design and manufacturing to assure designed root fillet shapes are attained in production, and gears meet the design intent.

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.

Involute spur gears are very sensitive to gear misalignment. Misalignment will cause the shift of the bearing contact toward the edge of the gear tooth surfaces and transmission errors that increase gear noise. Many efforts have been made to improve the bearing contact of misaligned spur gears by crowning the pinion tooth surface. Wildhaber(1) had proposed various methods of crowning that can be achieved in the process of gear generation. Maag engineers have used crowning for making longitudinal corrections (Fig. 1a); modifying involute tooth profile uniformly across the face width (Fig. 1b); combining these two functions in Fig. 1c and performing topological modification (Fig. 1d) that can provide any deviation of the crowned tooth surface from a regular involute surface. (2)

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.

Examples from gears in wind turbine, automotive and industrial applications.

Minimizing gear losses caused by churning, windage and mesh friction is important if plant operating costs and environmental impact are to be minimized. This paper concentrates on mesh friction losses and associated scuffing risk. It describes the preliminary results from using a validated, 3-D Finite Element Analysis (FEA) and Tooth Contact Analysis (TCA) program to optimize cylindrical gears for low friction losses without compromising transmission error (TE), noise and power density. Some case studies and generic procedures for minimizing losses are presented. Future development and further validation work is discussed.

This article discusses applications of statistical process capability indices for controlling the quality of tooth geometry characteristics, including profile and lead as defined by current AGMA-2015, ISO-1328, and DIN-3960 standards. It also addresses typical steps to improve manufacturing process capability for each of the tooth geometry characteristics when their respective capability indices point to an incapable process.

Quality gear manufacturing depends on controlled tolerances and geometry. As a result, ferritic nitrocarburizing has become the heat treat process of choice for many gear manufacturers. The primary reasons for this are: 1. The process is performed at low temperatures, i.e. less than critical. 2. the quench methods increase fatigue strength by up to 125% without distorting. Ferritic nitrocarburizing is used in place of carburizing with conventional and induction hardening. 3. It establishes gradient base hardnesses, i.e. eliminates eggshell on TiN, TiAIN, CrC, etc. In addition, the process can also be applied to hobs, broaches, drills, and other cutting tools.

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).

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.

Traditionally, high-quality gears are cut to shape from forged blanks. Great accuracy can be obtained through shaving and grinding of tooth forms, enhancing the power capacity, life and quietness of geared power transmissions. In the 1950s, a process was developed for forging gears with teeth that requires little or no metal to be removed to achieve final geometry. The initial process development was undertaken in Germany for the manufacture of bevel gears for automobile differentials and was stimulated by the lack of available gear cutting equipment at that time. Later attention has turned to the forging of spur and helical gears, which are more difficult to form due to the radial disposition of their teeth compared with bevel gears. The main driver of these developments, in common with most component manufacturing, is cost. Forming gears rather than cutting them results in increased yield from raw material and also can increase productivity. Forging gears is therefore of greater advantage for large batch quantities, such as required by the automotive industry.

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 Youngâ€™s modulus -- theoretically enhances performance when compared to the solid-steel design.

The hobbing and generation grinding production processes are complex due to tool geometry and kinematics. Expert knowledge and extensive testing are required for a clear attribution of cause to work piece deviations. A newly developed software tool now makes it possible to simulate the cutting procedure of the tool and superimpose systematic deviations on it. The performance of the simulation software is illustrated here with practical examples. The new simulation tool allows the user to accurately predict the effect of errors. With this knowledge, the user can design and operate optimal, robust gearing processes.

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.

Due to increasing requirements regarding the vibrational behavior of automotive transmissions, it is necessary to develop reliable methods for noise evaluation and design optimization. Continuous research led to the development of an elaborate method for gear noise evaluation. The presented methodology enables the gear engineer to optimize the microgeometry with respect to robust manufacturing.

An analysis of possibilities for the selection of tool geometry parameters was made in order to reduce tooth profile errors during the grinding of gears by different methods. The selection of parameters was based on the analysis of he grid diagram of a gear and a rack. Some formulas and graphs are presented for the selection of the pressure angle, module and addendum of the rack-tool. The results from the grinding experimental gears confirm the theoretical analysis.

While designing gear and spline teeth, the root fillet area and the corresponding maximum tensile stress are primary design considerations for the gear designer. Root fillet tensile stress may be calculated using macro-geometry values such as module, minor diameter, effective fillet radius, face width, etc.

Free form milling of gears becomes more and more important as a flexible machining process for gears. Reasons for that are high degrees of freedom as the usage of universal tool geometry and machine tools is possible. This allows flexible machining of various gear types and sizes with one manufacturing system. This paper deals with manufacturing, quality and performance of gears made by free form milling. The focus is set on specific process properties of the parts. The potential of free form milling is investigated in cutting tests of a common standard gear. The component properties are analyzed and flank load-carrying capacity of the gears is derived by running trials on back-to-back test benches. Hereby the characteristics of gears made by free form milling and capability in comparison with conventionally manufactured gears will be shown.

Although gear geometry and the design of asymmetric tooth gears are well known and published, they are not covered by modern national or international gear design and rating standards. This limits their broad implementation for various gear applications, despite substantial performance advantages in comparison to symmetric tooth gears for mostly unidirectional drives. In some industries â€” like aerospace, that are accustomed to using gears with non-standard tooth shapes â€” the rating of these gears is established by comprehensive testing. However, such testing programs are not affordable for many other gear drive applications that could also benefit from asymmetric tooth gears.

Highly loaded gears are usually casehardened to fulfill the high demands on the load-carrying capacity. Several factors, such as material, heat treatment, or macro and micro geometry, can influence the load-carrying capacity. Furthermore, the residual stress condition also significantly influences load-carrying capacity. The residual stress state results from heat treatment and can be further modified by manufacturing processes post heat treatment, e.g. grinding or shot peening.

This paper analyzes the different influences of the deviations between nominal and actual geometry for a first-cut bevel gear. In each section, the customary tolerances are quantified and the possibilities to reduce them are discussed.

In many gear transmissions, tooth load on one flank is significantly higher and is applied for longer periods of time than on the opposite one; an asymmetric tooth shape should reflect this functional difference. The advantages of these gears allow us to improve the performance of the primary drive tooth flanks at the expense of the opposite coast flanks, which are unloaded or lightly loaded during a relatively short work period by drive flank contact and bending stress reduction. This article is about the microgeometry optimization of the spur asymmetric gearsâ€™ tooth flank profile based on the tooth bending and contact deflections.

Inspection of the cutting blades is an important step in the bevel gear manufacture. The proper blade geometry ensures that the desired gear tooth form can be achieved. The accuracy of the process can be compromised when the blade profile consists of several small sections such as protuberance, main profile, top relief and edge radius. Another common obstacle - are outliers which can be caused by dust particles, surface roughness and also floor vibrations during the data acquisition. This paper proposes the methods to improve the robustness of the inspection process in such cases.

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.

New software from AGMA helps gear designers calculate geometry and ratings for all types of bevel gears.

In the last section, we discussed gear inspection; the types of errors found by single and double flank composite and analytical tests; involute geometry; the involute cam and the causes and symptoms of profile errors. In this section, we go into tooth alignment and line of contact issues including lead, helix angles, pitch, pitchline runout, testing and errors in pitch and alignment.

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.

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.

The Pentac Plus is the latest generation of Gleasonâ€™s Pentac bevel gear cutting system. It is designed to allow much higher tool life and improved productivity, especially for cutters using multiple face blade geometry.

The objective of this paper is to demonstrate that transmission gears of rotary-wing aircraft, which are typically scrapped due to minor foreign object damage (FOD) and grey staining, can be repaired and re-used with signifi cant cost avoidance. The isotropic superfinishing (ISF) process is used to repair the gear by removing surface damage. It has been demonstrated in this project that this surface damage can be removed while maintaining OEM specifications on gear size, geometry and metallurgy. Further, scrap CH-46 mix box spur pinions, repaired by the ISF process, were subjected to gear tooth strength and durability testing, and their performance compared with or exceeded that of new spur pinions procured from an approved Navy vendor. This clearly demonstrates the feasibility of the repair and re-use of precision transmission gears.

The fundamental purpose of gear grinding is to consistently and economically produce "hard" or "soft" gear tooth elements within the accuracy required by the gear functions. These gear elements include tooth profile, tooth spacing, lead or parallelism, axial profile, pitch line runout, surface finish, root fillet profile, and other gear geometry which contribute to the performance of a gear train.

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.

In this paper, an accurate FEM analysis has been done of the â€śtrueâ€ť stress at tooth root of spur gears in the function of the gear geometry. The obtained results confirm the importance of these differences.

This paper presents an approach that provides optimization of both gearbox kinematic arrangement and gear tooth geometry to achieve a high-density gear transmission. It introduces dimensionless gearbox volume functions that can be minimized by the internal gear ratio optimization. Different gearbox arrangements are analyzed to define a minimum of the volume functions. Application of asymmetric gear tooth profiles for power density maximization is also considered.

The quality of the finished gear is influenced by the very first machining operations of the blank. Since the gear tooth geometry is generated on a continuously rotating blank in hobbing or shaping, it is important that the timed relationship between the cutter and workpiece is correct. If this relationship is disturbed by eccentricities of the blank to its operating centerline, the generated gear teeth will not be of the correct geometry. During the blanking operations, the gear's centerline and locating surfaces are established and must be maintained as the same through the following operations that generate the gear teeth.

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.

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.

Our research group has been engaged in the study of gear noise for some nine years and has succeeded in cutting the noise from an average level to some 81-83 dB to 76-78 dB by both experimental and theoretical research. Experimental research centered on the investigation into the relation between the gear error and noise. Theoretical research centered on the geometry and kinematics of the meshing process of gears with geometric error. A phenomenon called "out-of-bound meshing of gears" was discovered and mathematically proven, and an in-depth analysis of the change-over process from the meshing of one pair of teeth to the next is followed, which leads to the conclusion we are using to solve the gear noise problem. The authors also suggest some optimized profiles to ensure silent transmission, and a new definition of profile error is suggested.

A study of AGMA 218, the draft ISO standard 6336, and BS 436: 1986 methods for rating gear tooth strength and surface durability for metallic spur and helical gears is presented. A comparison of the standards mainly focuses on fundamental formula and influence factors, such as the load distribution factor, geometry factor, and others. No attempt is made to qualify or judge the standards other than to comment on the facilities or lack of them in each standard reviewed. In Part I a comparison of pitting resistance ratings is made, and in the subsequent issue, Part II will deal with bending stress ratings and comparisons of designs.

Whether gear engineers have to replace an old gear which is worn out, find out what a gear's geometry is after heat treatment distortion, or just find out parameters of gears made by a competitor, sometimes they are challenged with a need to determine the geometry of unknown gears. Depending on the degree of accuracy required, a variety of techniques are available for determining the accuracy of an unknown gear. If a high degree of precision is important, a gear inspection device has to be used to verify the results. Frequently, several trial-and-error attempts are made before the results reach the degree of precision required.

The design of any gearing system is a difficult, multifaceted process. When the system includes bevel gearing, the process is further complicated by the complex nature of the bevel gears themselves. In most cases, the design is based on an evaluation of the ratio required for the gear set, the overall envelope geometry, and the calculation of bending and contact stresses for the gear set to determine its load capacity. There are, however, a great many other parameters which must be addressed if the resultant gear system is to be truly optimum. A considerable body of data related to the optimal design of bevel gears has been developed by the aerospace gear design community in general and by the helicopter community in particular. This article provides a summary of just a few design guidelines based on these data in an effort to provide some guidance in the design of bevel gearing so that maximum capacity may be obtained. The following factors, which may not normally be considered in the usual design practice, are presented and discussed in outline form: Integrated gear/shaft/bearing systems Effects of rim thickness on gear tooth stresses Resonant response

The 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.

Ausforming, the plastic deformation of heat treatment steels in their metastable, austentic condition, was shown several decades ago to lead to quenched and tempered steels that were harder, tougher and more durable under fatigue-type loading than conventionally heat-treated steels. To circumvent the large forces required to ausform entire components such as gears, cams and bearings, the ausforming process imparts added mechanical strength and durability only to those contact surfaces that are critically loaded. The ausrolling process, as utilized for finishing the loaded surfaces of machine elements, imparts high quality surface texture and geometry control. The near-net-shape geometry and surface topography of the machine elements must be controlled to be compatible with the network dimensional finish and the rolling die design requirements (Ref. 1).

In recent years, gear inspection requirements have changed considerably, but inspection methods have barely kept pace. The gap is especially noticeable in bevel gears, whose geometry has always made testing them a complicated, expensive and time-consuming process. Present roll test methods for determining flank form and quality of gear sets are hardly applicable to bevel gears at all, and the time, expense and sophistication required for coordinate measurement has limited its use to gear development, with only sampling occurring during production.

Recent advances in spiral bevel gear geometry and finite element technology make it practical to conduct a structural analysis and analytically roll the gear set through mesh. With the advent of user-specific programming linked to 3-D solid modelers and mesh generators, model generation has become greatly automated. Contact algorithms available in general purpose finite element codes eliminate the need for the use and alignment of gap elements. Once the gear set it placed in mesh, user subroutines attached to the FE code easily roll it through mesh. The method is described in detail. Preliminary result for a gear set segment showing the progression of the contact line load is given as the gears roll through mesh.

In this paper the effects of thermally induced geometry distortions on load distribution and transmission error have been analyzed.

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