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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.
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.
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 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 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 load capacity rating of gears had its beginning in the 18th century at Leiden University when Prof. Pieter van Musschenbroek systematically tested the wooden teeth of windmill gears, applying the bending strength formula published by Galilei one century earlier. In the next centuries several scientists improved or extended the formula, and recently a Draft International Standard could be presented.
A method to extrapolate running gear bending strength data from STF results for comparing bending performance of different materials and processes.
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.
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.
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.
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.
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 itâ€™s important to know which defect limits the strength of a gear.
Reduced component weight and ever-increasing power density require a gear design on the border area of material capacity. In order to exploit the potential offered by modern construction materials, calculation methods for component strength must rely on a deeper understanding of fracture and material mechanics in contrast to empirical-analytical approaches.
To achieve the requested quality, most gears today are ground. The usual grinding process includes treating the gear flank but disengaging before reaching the root rounding area. If the gear is premanufactured with a tool without protuberance, then at the position where the grinding tool retracts from the flank a grinding notch in the tooth root area is produced. Such a notch may increase the bending stresses in the root area, thus reducing the strength rating.
In Part I differences in pitting ratings between AGMA 218, the draft ISO standard 6336, and BS 436:1986 were examined. In this part bending strength ratings are compared. All the standards base the bending strength on the Lewis equation; the ratings differ in the use and number of modification factors. A comprehensive design survey is carried out to examine practical differences between the rating methods presented in the standards, and the results are shown in graphical form.
Surface-hardened, sintered powder metal gears are increasingly used in power transmissions to reduce the cost of gear production. One important problem is how to design with surface durability, given the porous nature of sintered gears. Many articles have been written about mechanical characteristics, such as tensile and bending strength, of sintered materials, and it is well-known that the pores existing on and below their surfaces affect their characteristics (Refs. 1-3). Power transmission gears are frequently employed under conditions of high speed and high load, and tooth surfaces are in contact with each other under a sliding-rolling contact condition. Therefore it is necessary to consider not only their mechanical, but also their tribological characteristics when designing sintered gears for surface durability.
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.
The properties of both shot-peened and cold rolled PM gears are analyzed and compared. To quantify the effect of both manufacturing processes, the tooth root bending fatigue strength will be evaluated and compared to wrought gears.
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.
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 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.
How local stresses obtained from FEA can be used to determine fatigue strength of worm wheel teeth.
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.
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.
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.
The present article contains a preliminary description of studies carried out by the authors with a view toward developing asymmetrical gear teeth. Then a comparison between numerous symmetrical and asymmetrical tooth stress fields under the same modular conditions follows. This leads to the formulation of a rule for similar modules governing variations of stress fields, depending on the pressure angle of the nonactive side. Finally a procedure allowing for calculations for percentage reductions of asymmetrical tooth modules with respect to corresponding symmetrical teeth, maximum ideal stress being equal, is proposed. Then the consequent reductions in size and weight of asymmetrical teeth are assessed.
This article summarizes results of research programs on RCF strength of wrought steels and PM steels.
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.
A common design goal for gears in helicopter or turboprop power transmission is reduced weight. To help meet this goal, some gear designs use thin rims. Rims that are too thin, however, may lead to bending fatigue problems and cracks. The most common methods of gear design and analysis are based on standards published by the American Gear Manufacturers Association. Included in the standards are rating formulas for gear tooth bending to prevent crack initiation (Ref. 1). These standards can include the effect of rim thickness on tooth bending fatigue (Ref 2.). The standards, however, do not indicate the crack propagation path or the remaining life once a crack has started. Fracture mechanics has developed into a useful discipline for predicting strength and life of cracked structures.
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.
This article includes a brief summary of the characteristics of involute asymmetric teeth and the problems connected with the related bending tests.
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.
The effect of load speed on straight and involute tooth forms is studied using several finite-element models.
A single tooth bending (STB) test procedure has been developed to optimally map gear design parameters. Also, a test program on case-carburized, aerospace standard gears has been conceived and performed in order to appreciate the influence of various technological parameters on fatigue resistance and to draw the curve shape up to the gigacycle region.
In this study, the combined influence of shaft misalignments and gear lead crown on load distribution and tooth bending stresses is investigated. Upon conclusion, the experimental results are correlated with predictions of a gear load distribution model, and recommendations are provided for optimal lead crown in a given misalignment condition.
The powder metal (P/M) process is making inroads in automotive transmission applications due to substantially lower costs of P/M-steel components for high-volume production, as compared to wrought or forged steel parts. Although P/M gears are increasingly used in powered hand tools, gear pumps and as accessory components in automotive transmissions, P/M-steel gears are currently in limited use in vehicle transmission applications. The primary objective of this project was to develop high-strength P/M-steel gears with bending fatigue, impact resistance and pitting fatigue performance equivalent to current wrought steel gears.
Gears with an asymmetric involute gear tooth form were analyzed to determine their bending and contact stresses relative to symmetric involute gear tooth designs, which are representative of helicopter main-drive gears.
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.
Three samples of quenched and tempered 4140 steel, with varying levels of oxygen and sulfur, were submitted to a series of bending fatigue tests.
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.
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.
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.
This is part II of a two-part paper that presents the results of extensive test programs on the RCF strength of PM steels.