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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.
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.
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.
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.
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.
This article summarizes results of research programs on RCF strength of wrought steels and PM steels.
The purpose of this paper is to present a method of designing and specifying gear teeth with much higher bending and surface contact strength (reduced bending and surface contact stresses). This paper will show calculation procedures, mathematical solutions and the theoretical background equations to do this.
Examining the history of software in mechanical engineering
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.
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.
Dear Editor: In Mr. Yefim Kotlyar's article "Reverse Engineering" in the July/August issue, I found an error in the formula used to calculate the ACL = Actual lead from the ASL = Assumed lead.
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.
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.
Changes in the third edition of parts 1, 2, 3, 5 and 6 compared to the previous edition (from the year 2006 for parts 1, 2, 3, 6 and from the year 2003 for part 5).
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.
This is part II of a two-part paper that presents the results of extensive test programs on the RCF strength of PM steels.
How local stresses obtained from FEA can be used to determine fatigue strength of worm wheel teeth.
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.
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.
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 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.
The present article contains a preliminary description of studies carried out by the authors with a view toward developing asymmetrical gear teeth. Then a comparison between numerous symmetrical and asymmetrical tooth stress fields under the same modular conditions follows. This leads to the formulation of a rule for similar modules governing variations of stress fields, depending on the pressure angle of the nonactive side. Finally a procedure allowing for calculations for percentage reductions of asymmetrical tooth modules with respect to corresponding symmetrical teeth, maximum ideal stress being equal, is proposed. Then the consequent reductions in size and weight of asymmetrical teeth are assessed.
This article illustrates a structural analysis of asymmetrical teeth. This study was carried out because of the impossibility of applying traditional calculations to procedures involved in the specific case. In particular, software for the automatic generation of meshes was devised because existing software does not produce results suitable for the new geometrical model required. Having carried out the structural calculations, a comparative study of the stress fields of symmetrical and asymmetrical teeth was carried out. The structural advantages of the latter type of teeth emerged.
Columbus' first voyage to the Americas is not the only anniversary worthy of celebration this year. In 1892, on October 15, Wilfred Lewis gave an address to the Engineer's Club of Philadelphia, whose significance, while not as great as that of Columbus' voyage, had important results for the gearing community. In this address, Lewis first publicly outlined his formula for computing bending stress in gear teeth, a formula still in use today.
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.
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.
The geometry factor, which is a fundamental part of the AGMA strength rating of gears, is currently computed using the Lewis parabola which allows computation of the Lewis form factor.(1) The geometry factor is obtained from this Lewis factor and load sharing ratio. This method, which originally required graphical construction methods and more recently has been computerized, works reasonably well for external gears with thick rims.(2-6) However, when thin rims are encountered or when evaluating the strength of internal gears, the AGMA method cannot be used.
The 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.
A method to extrapolate running gear bending strength data from STF results for comparing bending performance of different materials and processes.
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.
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.
News Items About strength calculation
1 KISSsoft Examines Gear Strength Calculation with Load Collectives (September 2, 2021)
Load spectra can be derived from time series - a measured time-torque-speed curve or one derived from simulations. For time series with o... Read News
2 KISSsoft Offers Standards in the Shaft Strength Calculation (February 27, 2014)
For an analytical strength assessement, in the first instance the currently valid standard has to be applied. Therefore, an essential tas... Read News