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Micropitting, pitting and wear are typical gear failure modes that can occur on the flanks of slowly operated and highly stressed internal gears. However, the calculation methods for the flank load-carrying capacity have mainly been established on the basis of experimental investigations of external gears. This paper describes the design and functionality of the newly developed test rigs for internal gears and shows basic results of the theoretical studies. It furthermore presents basic examples of experimental test results.
Instances of damage to discontinuous form ground and surface-hardened gears, especially of large scale, have recently increased. This may be attributed partly to a faulty grinding process with negative effects on the surface zones and the surface properties.
The objective of this study was to investigate the limits concerning possible reduction of lubricant quantity in gears that could be tolerated without detrimental effects on their load carrying capacity.
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.
In order to improve load-carrying capacity and noise behavior, gears usually have profile and lead modifications. Furthermore, in gears where a specified tooth-flank load application direction (for drive and coast flanks) is a design enhancement, or even compulsory, the asymmetric tooth profile is a further solution. Nowadays, many gears need to be hard finished. Continuous generating grinding offers a very high process efficiency, but is this process able to grind all modifications, especially asymmetric gears? Yes, it is!
Influences of Load Distribution and Tooth Flank Modifications as Considered in a New, DIN/ISO-Compatible Calculation Method
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.
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 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.
We need a method to analyze cumulative fatigue damage to specify and to design gear drives which will operate under varying load. Since load is seldom constant, most applications need this analysis.
Recently, there has been increased interest in the dynamic effects in gear systems. This interest is stimulated by demands for stronger, higher speed, improved performance, and longer-lived systems. This in turn had stimulated numerous research efforts directed toward understanding gear dynamic phenomena. However, many aspects of gear dynamics are still not satisfactorily understood.
Crossed helical gear sets are used to transmit power and motion between non-intersecting and non-parallel axes. Both of the gears that mesh with each other are involute helical gears, and a point contact is made between them. They can stand a small change in the center distance and the shaft angle without any impairment in the accuracy of transmitting motion.
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.
The Integral Temperature Method for the evaluation of the scoring load capacity of gears is described. All necessary equations for the practical application are presented. The limit scoring temperature for any oil can be obtained from a gear scoring test.
This article describes some of the most important tests for prototypes conducted at Winergy AG during the product development process. It will demonstrate that the measurement results on the test rig for load distribution are in accordance with the turbine measurements.
In epicyclic gear sets designed for aeronautical applications, planet gears are generally supported by spherical roller bearings with the bearing outer race integral to the gear hub. This article presents a new method to compute roller load distribution in such bearings where the outer ring can’t be considered rigid.
In this study, limiting values for the load-carrying-capacity of fine-module gears within the module range 0.3–1.0 mm were determined and evaluated by comprehensive, experimental investigations that employed technical, manufacturing and material influence parameters.
This paper presents an original method to compute the loaded mechanical behavior of polymer gears. Polymer gears can be used without lubricant, have quieter mesh, are more resistant to corrosion, and are lighter in weight. Therefore their application fields are continually increasing. Nevertheless, the mechanical behavior of polymer materials is very complex because it depends on time, history of displacement and temperature. In addition, for several polymers, humidity is another factor to be taken into account. The particular case of polyamide 6.6 is studied in this paper.
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.
Spiral-bevel gears, found in many machine tools, automobile rear-axle drives, and helicopter transmissions, are important elements for transmitting power.
Helical gears can drive either nonparallel or parallel shafts. When these gears are used with nonparallel shafts, the contact is a point, and the design and manufacturing requirements are less critical than for gears driving parallel shafts.
The power of high speed gears for use in the petrochemical industry and power stations is always increasing. Today gears with ratings of up to 70,000kW are already in service. For such gears, the failure mode of scoring can become the limiting constraint. The validity of an analytical method to predict scoring resistance is, therefore, becoming increasingly important.
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.
In order to properly select a grease for a particular application, a sound knowledge of the influence of different grease components and operating conditions on the lubrication supply mechanism and on different failure modes is of great benefit.
Helical gear teeth are affected by cratering wear — particularly in the regions of low oil film thicknesses, high flank pressures and high sliding speeds. The greatest wear occurs on the pinion — in the area of negative specific sliding. Here the tooth tip radius of the driven gear makes contact with the flank of the driving gear with maximum sliding speed and pressure.
How should we consider random helix angle errors fHβ and housing machining errors when calculating KHβ? What is a reasonable approach?
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.
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 objective of this work is to introduce a method for the calculation of the tooth root load carrying capacity for gears, under consideration of the influence of the defect size on the endurance fatigue strength of the tooth root. The theoretical basis of this method is presented in this paper as well as the validation in running tests of helical and beveloid gears with different material batches, regarding the size distribution of inclusions. The torque level for a 50 percent failure probability of the gears is evaluated on the test rig and then compared to the results of the simulation. The simulative method allows for a performance of the staircase method that is usually performed physically in the back-to-back tests for endurance strength, as the statistical influence of the material properties is considered in the calculation model. The comparison between simulation and tests shows a high level of accordance.
The usage of modern thrusters allows combining the functions of the drive and the ship rudder in one unit, which are separated in conventional ship propulsion systems. The horizontally oriented propeller is supported in a vertically rotatable nacelle that is mounted underneath the ship's hull. The propeller can directly or indirectly be driven by an electric motor or combustion engine. Direct drive requires the installation of a low-speed electric motor in the nacelle. This present paper concentrates on indirect drives where the driving torque is transferred by bevel gear stages and shafts from the motor to the propeller.
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 finite elements-based contact model is developed to predict load distribution along the spline joint interfaces; effects of spline misalignment are investigated along with intentional lead crowning of the contacting surfaces. The effects of manufacturing tooth indexing error on spline load distributions are demonstrated by using the proposed model.
The goal of gear drive design is to transit power and motion with constant angular velocity. Current trends in gear drive design require greater load carrying capacity and increased service life in smaller, quieter, more efficient gearboxes. Generally, these goals are met by specifying more accurate gears. This, combined with the availability of user-friendly CNC gear grinding equipment, has increased the use of ground gears.
In some gear dynamic models, the effect of tooth flexibility is ignored when the model determines which pairs of teeth are in contact. Deflection of loaded teeth is not introduced until the equations of motion are solved. This means the zone of tooth contact and average tooth meshing stiffness are underestimated, and the individual tooth load is overstated, especially for heavily loaded gears. This article compares the static transmission error and dynamic load of heavily loaded, low-contact-ratio spur gears when the effect of tooth flexibility has been considered and when it has been ignored. Neglecting the effect yields an underestimate of resonance speeds and an overestimate of the dynamic load.
Because of the better thermal conductivity of CBN abrasives compared to that of conventional aluminum oxide wheels, CBN grinding process, which induces residual compressive stresses into the component, and possibly improves the subsequent stress behavior. This thesis is the subject of much discussion. In particular, recent Japanese publications claim great advantages for the process with regard to an increased component load capacity, but do not provide further details regarding the technology, test procedures or components investigated. This situation needs clarification, and for the this reason the effect of the CBN grinding material on the wear behavior and tooth face load capacity of continuously generated ground gears was further investigated.
The load capacity of worm gears is mainly influenced by the size and the position of the contact pattern.
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.
In this paper, two developed methods of tooth root load carrying capacity calculations for beveloid gears with parallel axes are presented, in part utilizing WZL software GearGenerator and ZaKo3D. One method calculates the tooth root load-carrying capacity in an FE-based approach. For the other, analytic formulas are employed to calculate the tooth root load-carrying capacity of beveloid gears. To conclude, both methods are applied to a test gear. The methods are compared both to each other and to other tests on beveloid gears with parallel axes in test bench trials.
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.
Solutions to the governing equations of a spur gear transmission model, developed in a previous article are presented. Factors affecting the dynamic load are identified. It is found that the dynamic load increases with operating speed up to a system natural frequency. At operating speeds beyond the natural frequency the dynamic load decreases dramatically. Also, it is found that the transmitted load and shaft inertia have little effect upon the total dynamic load. Damping and friction decrease the dynamic load. Finally, tooth stiffness has a significant effect upon dynamic loadings the higher the stiffness, the lower the dynamic loading. Also, the higher the stiffness, the higher the rotating speed required for peak dynamic response.
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.
It was very interesting to see Robert Smith's article on single-flank testing of gears...
Presumably, everyone who would be interested in this subject is already somewhat familiar with testing of gears by traditional means. Three types of gear inspection are in common use: 1) measurement of gear elements and relationships, 2) tooth contact pattern checks and 3) rolling composite checks. Single Flank testing falls into this last category, as does the more familiar Double Flank test.
Gear flank breakage can be observed on edge zone-hardened gears. It occurs, for example, on bevel gears for water turbines, on spur gears for wind energy converters and on single- and double-helical gears for other industrial applications.
Anyone involved in the design, manufacture and use of gears is concerned with three general characteristics relative to their application: noise, accuracy, and strength or surface durability. In the article, we will be dealing with probably the most aggravating of the group, gear noise.
Joe Arvin comments on his recent trip to Scandinavia and how U.S. defense dollars are being spent overseas. J.D. Smith responds to an article on gear noise from the previous issue.
AGMA introduced ANSI/AGMA 2015–2–A06— Accuracy Classification System: Radial System for Cylindrical Gears, in 2006 as the first major rewrite of the double-flank accuracy standard in over 18 years. This document explains concerns related to the use of ANSI/AGMA 2015–2–A06 as an accuracy classification system and recommends a revised system that can be of more service to the gearing industry.
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.
The concept of "transmission error" is relatively new and stems from research work in the late 1950s by Gregory, Harris and Munro,(1) together with the need to check the accuracy of gear cutting machines. The corresponding commercial "single flank" testing equipment became available in the 1960s, but it was not until about ten years ago that it became generally used, and only recently has it been possible to test reliably at full load and full speed.
Most research on micropitting is done on small-sized gears. This article examines whether those results are also applicable to larger gears.
Modern gearboxes are characterized by high torque load demands, low running noise and compact design. In order to fulfill these demands, profile and lead modifications are being applied more often than in the past. This paper will focus on how to produce profile and lead modifications by using the two most common grinding processes—threaded wheel and profile grinding. In addition, more difficult modifications—such as defined flank twist or topological flank corrections—will also be described in this paper.
This article was originally published 20 years ago, in Gear Technology’s first issue. It describes a method of evaluating the smoothness, or lack of smoothness, of gear motion. This lack of smoothness of motion, known as “transmission error,” is responsible for excitation of gear noise and problems of gear accuracy and sometimes has a relationship to gear failure.
Much of the information in this article has been extracted from an AGMA Technical Paper, &quot;What Single Flank Testing Can Do For You&quot;, presented in 1984 by the author
As is well known in involute gearing, “perfect” involute gears never work perfectly in the real world. Flank modifications are often made to overcome the influences of errors coming from manufacturing and assembly processes as well as deflections of the system. The same discipline applies to hypoid gears.
"Frenco--Inspecting All Flanks in Minutes."
More strength, less noise. Those are two major demands on gears, including bevel and hypoid gears.
The presence of significant errors in the two-flank roll test (a work gear rolled in tight mesh against a master gear) is well-known, but generally overlooked.
This paper discusses the influence of tip relief, root relief, load modification, end relief and their combinations on gear stresses and transmission errors due to shaft deflections.
Question: What is functional measurement and what is the best method for getting truthful answers?
Quality gear inspection means doing the "right" inspections "right." A lot of time and money can be spent doing the wrong types of inspections related to function and doing them incorrectly. As we will discover later, such things as runout can creep into the manufacturing and inspection process and completely ruin any piece of data that is taken. this is one of the most important problems to control for quality inspection.
The manufacturing quality of spiral bevel gears has achieved a very high standard. Nevertheless, the understanding of the real stress conditions and the influences. of certain parameters is not satisfactory.
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 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.
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.
There is an increasing significance of screw helical and worm gears that combine use of steel and plastics. This is shown by diverse and continuously rising use in the automotive and household appliance industries. The increasing requirements for such gears can be explained by the advantageous qualities of such a material combination in comparison with that of the traditional steel/bronze pairing.
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.
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.
An experimental effort has been conducted on an aerospace-quality helical gear train to investigate the thermal behavior of the gear system as many important operational conditions were varied.
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.
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.
It is very common for those working in the gear manufacturing industry to have only a limited understanding of the fundamental principals of involute helicoid gear metrology, the tendency being to leave the topic to specialists in the gear lab. It is well known that quiet, reliable gears can only be made using the information gleaned from proper gear metrology.
This section will deal with the use of gear inspection for diagnostic purposes rather than quality determination. The proper evaluation of various characteristics in the data can be useful for the solution of quality problems. It is important to sort out whether the problem is coming from the machine, tooling and/or cutters, blanks, etc. An article by Robert Moderow in the May/June 1985 issue of Gear Technology is very useful for this purpose.
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.
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.
Part I of this paper, which appeared in the January/February issue of Gear Technology, described the theory behind double-flank composite inspection. It detailed the apparatus used, the various measurements that can be achieved using it, the calculations involved and their interpretation. The concluding Part II presents a discussion of the practical application of double-flank composite inspection -- especially for large-volume operations. It also addresses statistical techniques that can be used in conjunction with double-flank composite inspection, as well as an in-depth analysis of gage R&R for this technique.
Part I of this paper describes the theory behind double-flank composite inspection, detailing the apparatus used, the various measurements that can be achieved using it, the calculations involved and their interpretation. Part II, which will appear in the next issue, includes a discussion of the practical application of double-flank composite inspection, especially for large-volume operations. Part II covers statistical techniques that can be used in conjunction with double-flank composite inspection, as well as an in-depth analysis of gage R&R for this technique.
This paper intends to determine the load-carrying capacity of thermally damaged parts under rolling stress. Since inspection using real gears is problematic, rollers are chosen as an acceptable substitute. The examined scope of thermal damage from hard finishing extends from undamaged, best-case parts to a rehardening zone as the worst case. Also, two degrees of a tempered zone have been examined.