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Articles About Geometric

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1 Product News (August 2014)

The complete Product News section from the August 2014 issue of Gear Technology.

2 The Application of Geometrical Product Specification (GPS) - Compatible Strategies for Measurement of Involute Gears (November/December 2019)

During the revision of ISO 1328-1:2013 Cylindrical gears — ISO system of flank tolerance classification, ISO Technical Committee TC 60 WG2 delegates discussed proposals that the standard should be modified to ensure that it is compatible with the ISO Geometrical Product Specification (GPS) series of standards (Refs. 1-3). This seems sensible because the gears are geometrical components, but after reviewing the implications, it was rejected because ISO TC 60 WG2 did not think the gear manufacturing industry was ready for such a radical change in measurement strategy. The feasibility of the implementation of gears into the GPS matrix of standards has been carried out and the results conclude that this is practical, provided some key issues related to measurement uncertainty and establishing appropriate KPIs are addressed.

3 Influence of Geometrical Parameters on the Gear Scuffing Criterion - Part I (March/April 1987)

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.

4 Influence of Geometrical Parameters on the Gear Scuffing Criterion - Part 2 (May/June 1987)

In ParI 1 several scuffing (scoring) criteria were shown ultimately to converge into one criterion, the original flash temperature criterion according to Blok. In Part 2 it will be shown that all geometric influences may be concentrated in one factor dependent on only four independent parameters, of which the gear ratio, the number of teeth of the pinion, and the addendum modification coefficient of the pinion are significant.

5 The Geometric Design of Internal Gear Pairs (May/June 1990)

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.

6 Hard Gear Finishing with a Geometrically Defined Cutting Edge (November/December 1999)

The market demand for gear manufacturers to transmit higher torques via smaller-sized gear units inevitably leads to the use of case-hardened gears with high manufacturing and surface quality. In order to generate high part quality, there is an increasing trend towards the elimination of the process-induced distortion that occurs during heat treatment by means of subsequent hard finishing.

7 Point-Surface-Origin Macropitting Caused by Geometric Stress Concentration (January/February 2011)

Point-surface-origin (PSO) macropitting occurs at sites of geometric stress concentration (GSC) such as discontinuities in the gear tooth profile caused by micropitting, cusps at the intersection of the involute profile and the trochoidal root fillet, and at edges of prior tooth damage, such as tip-to-root interference. When the profile modifications in the form of tip relief, root relief, or both, are inadequate to compensate for deflection of the gear mesh, tip-to-root interference occurs. The interference can occur at either end of the path of contact, but the damage is usually more severe near the start-of-active-profile (SAP) of the driving gear.

8 Metallurgical Aspects to be Considered in Gear and Shaft Design (March/April 1999)

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.

9 Hypoid Gears with Involute Teeth (May 2015)

This paper presents the geometric design of hypoid gears with involute gear teeth. An overview of face cutting techniques prevalent in hypoid gear fabrication is presented. Next, the specification of a planar involute rack is reviewed. This rack is used to define a variable diameter cutter based upon a system of cylindroidal coordinates; thus, a cursory presentation of cylindroidal coordinates is included. A mapping transforms the planar involute rack into a variable diameter cutter using the cylindroidal coordinates. Hypoid gears are based on the envelope of this cutter. A hypoid gear set is presented based on an automotive rear axle.

10 Micropitting of Large Gearboxes: Influence of Geometry and Operating Conditions (September/October 2014)

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.

11 Press Quenching and Effects of Prior Thermal History on Distortion during Heat Treatment (March/April 2014)

Precision components (industrial bearing races and automotive gears) can distort during heat treatment due to effects of free or unconstrained oil quenching. However, press quenching can be used to minimize these effects. This quenching method achieves the relatively stringent geometrical requirements stipulated by industrial manufacturing specifications. As performed on a wide variety of steel alloys, this specialized quenching technique is presented here, along with a case study showing the effects of prior thermal history on the distortion that is generated during press quenching.

12 Gear Standards and ISO GPS (October 2013)

In today’s globalized manufacturing, all industrial products having dimensional constraints must undergo conformity specifications assessments on a regular basis. Consequently, (standardization) associated with GD&T (geometrical dimensioning and tolerancing) should be un-ambiguous and based on common, accepted rules. Of course gears - and their mechanical assemblies - are special items, widely present in industrial applications where energy conversion and power transmission are involved.

13 High-Performance Sintered-Steel Gears for Transmissions and Machinery: A Critical Review (August 2012)

Except for higher-end gear applications found in automotive and aerospace transmissions, for example, high-performance, sintered-steel gears match wrought-steel gears in strength and geometrical quality. The enhanced P/M performance is due largely to advances in powder metallurgy over last two decades, such as selective surface densification, new materials and lubricants for high density and warm-die pressing. This paper is a review of the results of a decade of research and development of high- performance, sintered-steel gear prototypes.

14 Properties of Tooth Surfaces due to Gear Honing with Electroplated Tools (November/December 2001)

In recent years, the demands for load capacity and fatigue life of gears constantly increased while weight and volume had to be reduced. To achieve those aims, most of today's gear wheels are heat treated so tooth surfaces will have high wear resistance. As a consequence of heat treatment, distortion unavoidably occurs. With the high geometrical accuracy and quality required for gears, a hard machining process is needed that generates favorable properties on the tooth surfaces and the near-surface material with high reliability.

15 Comparative Load Capacity Evaluation of CBN-Finished Gears (May/June 1990)

Cubic boron nitride (CBN) finishing of carburized gearing has been shown to have certain economic and geometric advantages and, as a result, it has been applied to a wide variety of precision gears in many different applications. In critical applications such as aerospace drive systems, however, any new process must be carefully evaluated before it is used in a production application. Because of the advantages associated with this process, a test program was instituted to evaluate the load capacity of aerospace-quality gears finished by the CBN process as compared to geometrically identical gears finished by conventional grinding processes. This article presents a brief description of the CBN process, its advantages in an aerospace application, and the results of an extensive test program conducted by Boeing Helicopters (BH) aimed at an evaluation of the effects of this process on the scoring, surface durability, and bending fatigue properties of spur gears. In addition, the results of an x-ray diffraction study to determine the surface and subsurface residual stress distributions of both shot-peened and nonshot-peened CBN-ground gears as compared to similar conventionally ground gears are also presented.

16 Structural Analysis of Teeth With Asymmetrical Profiles (July/August 1997)

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.

17 Grinding of Spur and Helical Gears (July/August 1992)

Grinding is a technique of finish-machining, utilizing an abrasive wheel. The rotating abrasive wheel, which id generally of special shape or form, when made to bear against a cylindrical shaped workpiece, under a set of specific geometrical relationships, will produce a precision spur or helical gear. In most instances the workpiece will already have gear teeth cut on it by a primary process, such as hobbing or shaping. There are essentially two techniques for grinding gears: form and generation. The basic principles of these techniques, with their advantages and disadvantages, are presented in this section.

18 The Involute Helicoid and The Universal Gear (November/December 1990)

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.

19 Gear Noise and the Making of Silent Gears (March/April 1990)

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.

20 Calculation of Optimum Tooth Flank Corrections for Helical Gears (September/October 1988)

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.

21 Software-Based Process Design in Gear Finish Hobbing (May 2010)

In this paper, the potential for geometrical cutting simulations - via penetration calculation to analyze and predict tool wear as well as to prolong tool life - is shown by means of gear finish hobbing. Typical profile angle deviations that occur with increasing tool wear are discussed. Finally, an approach is presented here to attain improved profile accuracy over the whole tool life of the finishing hob.

22 Gear Data Exchange Format (March/April 2005)

VDI has created a data exchange format that allows for the electronic exchange of all geometric parameters for cylindrical gears.

23 Gear Failure Analysis Involving Grinding Burn (January/February 2009)

When gears are case-hardened, it is known that some growth and redistribution of stresses that result in geometric distortion will occur. Aerospace gears require post case-hardening grinding of the gear teeth to achieve necessary accuracy. Tempering of the case-hardened surface, commonly known as grinding burn, occurs in the manufacturing process when control of the heat generation at the surface is lost.

24 Gear Mathematics for Bevel & Hypoid Gears (August 2015)

The calculation begins with the computation of the ring gear blank data. The geometrically relevant parameters are shown in Figure 1. The position of the teeth relative to the blank coordinate system of a bevel gear blank is satisfactorily defined with...