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This article summarizes results of research programs on RCF strength of wrought steels and PM steels.
This is part II of a two-part paper that presents the results of extensive test programs on the RCF strength of PM steels.
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.
Spur gear endurance tests were conducted to investigate the surface pitting fatigue life of noninvolute gears with low numbers of teeth and low contact ratios for the use in advanced application. The results were compared with those for a standard involute design with a low number of teeth. The gear pitch diameter was 8.89 cm (3.50 in.) with 12 teeth on both gear designs. Test conditions were an oil inlet temperature of 320 K (116 degrees F), a maximum Hertz stress of 1.49 GPa (216 ksi), and a speed of 10,000 rpm. The following results were obtained: The noninvolute gear had a surface pitting fatigue life approximately 1.6 times that of the standard involute gear of a similar design. The surface pitting fatigue life of the 3.43-pitch AISI 8620 noninvolute gear was approximately equal to the surface pitting fatigue life of an 8-pitch, 28-tooth AISI 9310 gear at the same load, but at a considerably higher maximum Hertz stress.
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.
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.
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).
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 it’s important to know which defect limits the strength of a gear.
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.
Review of "Gigacycle Fatigue in Mechanical Practice," by Claude Bathias and Paul C. Paris
A method to extrapolate running gear bending strength data from STF results for comparing bending performance of different materials and processes.
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.
In the past two years DSM has been conducting fatigue tests on actual molded gears in order to provide design data.
The aim of the study was to apply such a specialized tooth contact analysis method, well-used within the steel gear community, to a polymer gear application to assess what modifications need be made to these models for them to be applicable to polymer gears.
In several applications like hoisting equipment and cranes, open gears are used to transmit power at rather low speeds (tangential velocity < 1m/s) with lubrication by grease. In consequence those applications have particularities in terms of lubricating conditions and friction involved, pairing of material between pinion and gear wheel, lubricant supply, loading cycles and behavior of materials with significant contact pressure due to lower number of cycles.
How does one perform a contact analysis for worn gears? Our expert responds.
An experimental and theoretical analysis of worm gear sets with contact patterns of differing sizes, position and flank type for new approaches to calculation of pitting resistance.
Bevel gears must be assembled in a specific way to ensure smooth running and optimum load distribution between gears. While it is certainly true that the "setting" or "laying out" of a pair of bevel gears is more complicated than laying out a pair of spur gears, it is also true that following the correct procedure can make the task much easier. You cannot install bevel gears in the same manner as spur and helical gears and expect them to behave and perform as well; to optimize the performance of any two bevel gears, the gears must be positioned together so that they run smoothly without binding and/or excessive backlash.
Why is there so much emphasis on the tooth contact pattern for bevel gears in the assembled condition and not so for cylindrical gears, etc?
This article presents an analysis of asymmetric tooth gears considering the effective contact ratio that is also affected by bending and contact tooth deflections. The goal is to find an optimal solution for high performance gear drives, which would combine high load capacity and efficiency, as well as low transmission error (which affects gear noise and vibration).
Gear-loaded tooth contact analysis is an important tool for the design and analysis of gear performance within transmission and driveline systems. Methods for the calculation of tooth contact conditions have been discussed in the literature for many years. It's possible the method you've been using is underestimating transmission error in helical gears. Here's why.
A study was performed to evaluate fault detection effectiveness as applied to gear-tooth pitting-fatigue damage. Vibration and oil-debris monitoring (ODM) data were gathered from 24 sets of spur pinion and face gears run during a previous endurance evaluation study.
One of the major problems of plastic gear design is the knowledge of their running temperature. Of special interest is the bulk temperature of the tooth to predict the fatigue life, and the peak temperature on the surface of the tooth to avert surface failure. This paper presents the results of an experimental method that uses an infrared radiometer to measure the temperature variation along the profile of a plastic gear tooth in operation. Measurements are made on 5.08, 3.17, 2.54, 2.12 mm module hob cut gears made from nylon 6-6, acetal and UHMWPE (Ultra High Molecular Weight Polyethylene). All the tests are made on a four square testing rig with thermoplastic/steel gear pairs where the plastic gear is the driver. Maximum temperature prediction curves obtained through statistical analysis of the results are presented and compared to data available from literature.
Effective gear designs balance strength, durability, reliability, size, weight, and cost. Even effective designs, however, can have the possibility of gear cracks due to fatigue. In addition, truly robust designs consider not only crack initiation, but also crack propagation trajectories. As an example, crack trajectories that propagate through the gear tooth are the preferred mode of failure compared to propagation through the gear rim. Rim failure will lead to catastrophic events and should be avoided. Analysis tools that predict crack propagation paths can be a valuable aid to the designer to prevent such catastrophic failures.
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.
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 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.
It is becoming increasingly apparent that material properties can and will play a greater role than before in addressing the challenges most transmission manufacturers are facing today. Making use of materials' intrinsic fatigue properties provides a new design tool to support the market changes taking place.
Detection of impending gear tooth failure is of interest to every entity that utilizes geared transmissions. However, it is of particular significance at the Gear Research Institute (GRI), where sponsored efforts are conducted to establish gear material endurance limits, utilizing gear fatigue tests. Consequently, knowing when a gear is about to fail in each and every test, in a consistent manner, is essential for producing reliable and useful data for the gear industry.
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.
Aircraft transmissions for helicopters, turboprops and geared turbofan aircraft require high reliability and provide several thousand hours of operation between overhauls. In addition, They should be lightweight and have very high efficiency to minimize operating costs for the aircraft.
The search for greater gear life involves improvement in cost, weight and increased power output. There are many events that affect gear life, and this paper addresses those relating to fatigue, gear tooth pitting, fatigue strength losses due to the heat treating processes and shot peening technique. The capability of shot peening to increase fatigue strength and surface fatigue life eliminate machine marks which cause stress risers, and to aid in lubrication when properly controlled, suggests increased use and acceptance of the process.
Gear surface fatigue endurance tests were conducted on two groups of 10 gears each of carburized and hardened AlSI 9310 spur gears manufactured from the same heat of material
Spur gear surface endurance tests were conducted to investigate CBN ground AISI 9310 spur gears for use in aircraft applications, to determine their endurance characteristics and to compare the results with the endurance of standard vitreous ground AISI 9310 spur gears. Tests were conducted with VIM-VAR AISI 9210 carburized and hardened gears that were finish ground with either CBN or vitreous grinding methods. Test conditions were an inlet oil temperature of 320 K (116 degree F), an outlet oil temperature of 350 K (170 degree F), a maximum Hertz stress of 1.71 GPa (248 ksi), and a speed of 10,000 rpm. The CBN ground gears exhibited a surface fatigue life that was slightly better than the vitreous ground gears. The subsurface residual stress of the CBN ground gears was approximately the same as that for the standard vitreous ground gears for the CBN grinding method used.
Pitting and micropitting resistance of case-carburized gears depends on lubricants and lubrication conditions. Pitting is a form of fatigue damage. On this account a short time test was developed. The test procedure is described. The "pitting test" was developed as a short time test to examine the influence of lubricants on micropitting. Test results showing the influence of case-carburized gears on pitting and micropitting are presented.
In the 1960's and early 1970's, considerable work was done to identify the various modes of damage that ended the lives of rolling element bearings. A simple summary of all the damage modes that could lead to failure is given in Table 1. In bearing applications that have insufficient or improper lubricant, or have contaminants (water, solid particles) or poor sealing, failure, such as excessive wear or vibration or corrosion, may occur, rather than contact fatigue. Usually other components in the overall system besides bearings also suffer. Over the years, builders of transmissions, axles, and gear boxes that comprise such systems have understood the need to improve the operating environment within such units, so that some system life improvements have taken place.
Our experts comment on reverse engineering herringbone gears and contact pattern optimization.
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.
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.
One of the most effective methods in solving the edge loading problem due to excess misalignment and deflection in aerospace actuation gearing is to localize tooth-bearing contact by crowning the teeth. Irrespective of the applied load, if the misalignment and/or deflection are large enough to cause the contact area to reduce to zero, the stress becomes large enough to cause failure. The edge loading could cause the teeth to break or pit, but too much crowning may also cause the teeth to pit due to concentrated loading. In this paper, a proposed method to localize the contact bearing area and calculate the contact stress with crowning is presented and demonstrated on some real-life examples in aerospace actuation systems.
This article is part four of an eight-part series on the tribology aspects of angular gear drives. Each article will be presented first and exclusively by Gear Technology, but the entire series will be included in Dr. Stadtfeld’s upcoming book on the subject, which is scheduled for release in 2011.
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.
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.
In the majority of spiral bevel gears, spherical crowning is used. The contact pattern is set to the center of the active tooth flank and the extent of the crowning is determined by experience. Feedback from service, as well as from full-torque bench tests of complete gear drives, has shown that this conventional design practice leads to loaded contact patterns, which are rarely optimal in location and extent. Oversized reliefs lead to small contact area, increased stresses and noise, whereas undersized reliefs result in an overly sensitive tooth contact.
This paper deals with analysis of the load sharing percentage between teeth in mesh for different load conditions throughout the profile for both sun and planet gears of normal and HCR gearing—using finite element analysis. (FEA).
An offshore jack-up drilling rig is a barge upon which a drilling platform is placed. The barge has legs that can be lowered to the sea floor to support the rig. Then the barge can be “jacked up” out of the water, providing a stable work platform from which to drill for oil and gas. Jack-up drilling rigs were first introduced in the late 1950s. Rack-and- pinion-type jack-up units were introduced soon after that and have dominated the industry ever since.
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.
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).
After a period of operation, high-speed turbo gears may exhibit a change in longitudinal tooth contact pattern, reducing full face width contact and thereby increasing risk of tooth distress due to the decreased loaded area of the teeth. But this can be tricky—the phenomenon may or may not occur. Or, in some units the shift is more severe than others, with documented cases in which shifting occurred after as little as 16,000 hours of operation. In other cases, there is no evidence of any change for units in operation for more than 170,000 hours. This condition exists primarily in helical gears. All recorded observations here have been with case-carburized and ground gear sets. This presentation describes phenomena observed in a limited sampling of the countless high-speed gear units in field operation. While the authors found no existing literature describing this behavior, further investigation suggests a possible cause. Left unchecked and without corrective action, this occurrence may result in tooth breakage.
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.
This paper will demonstrate that, unlike commonly used low-contact-ratio spur gears, high-contact-ratio spur gears can provide higher power-to-weight ratio, and can also achieve smoother running with lower transmission error (TE) variations.
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.
The most conclusive test of bevel and hypoid gears is their operation under normal running conditions in their final mountings. Testing not only maintains quality and uniformity during manufacture, but also determines if the gears will be satisfactory for their intended applications.
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.
There are several methods available for improving the quality of spur and helical gears following the standard roughing operations of hobbing or shaping. Rotary gear shaving and roll-finishing are done in the green or soft state prior to heat treating.
A major source of helicopter cabin noise (which has been measured at over 100 decibels sound pressure level) is the gearbox. Reduction of this noise is a NASA and U.S. Army goal. A requirement for the Army/NASA Advanced Rotorcraft Transmission project was a 10 dB noise reduction compared to current designs.
This article reviews mathematical models for individual components associated with power losses, such as windage, churning, sliding and rolling friction losses.
The authors have developed a rack-type rolling process in which a rack tool is used to roll gear teeth. The results and analysis show that the proposed method reduces errors.
In high precision and heavily loaded spur gears, the effect of gear error is negligible, so the periodic variation of tooth stiffness is the principal cause of noise and vibration. High contact ration spur gears can be used to exclude or reduce the variation of tooth stiffness.
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.
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.
Analysis of helical involute gears by tooth contact analysis shows that such gears are very sensitive to angular misalignment leading to edge contact and the potential for high vibration. A new topology of tooth surfaces of helical gears that enables a favorable bearing contact and a reduced level of vibration is described. Methods for grinding helical gears with the new topology are proposed. A TCA program simulating the meshing and contact of helical gears with the new topology has been developed. Numerical examples that illustrate the proposed ideas are discussed.
An investigation of transmission errors and bearing contact of spur, helical, and spiral bevel gears was performed. Modified tooth surfaces for these gears have been proposed in order to absorb linear transmission errors caused by gear misalignment and to localize the bearing contact. Numerical examples for spur, helical, and spiral bevel gears are presented to illustrate the behavior of the modified gear surfaces with respect to misalignment and errors of assembly. The numerical results indicate that the modified surfaces will perform with a low level of transmission error in non-ideal operating environments.
Service performance and load carrying capacity of bevel gears strongly depend on the size and position of the contact pattern. To provide an optimal contact pattern even under load, the gear design has to consider the relative displacements caused by deflections or thermal expansions expected under service conditions. That means that more or less lengthwise and heightwise crowning has to be applied on the bevel gear teeth.
Part I of this series focused on gear shaving, while Part II focuses on gear finishing by rolling and honing.
An analytical method is presented to predict the shifts of the contact ellipses on spiral bevel gear teeth under load. The contact ellipse shift is the motion of the point to its location under load. The shifts are due to the elastic motions of the gear and pinion supporting shafts and bearings. The calculations include the elastic deflections of the gear shafts and the deflections of the four shaft bearings. The method assumes that the surface curvature of each tooth is constant near the unloaded pitch point. Results from these calculations will help designers reduce transmission weight without seriously reducing transmission performance.
The complete and accurate solution t the contact problem of three-dimensional gears has been, for the past several decades, one of the more sought after, albeit elusive goals in the engineering community. Even the arrival on the scene in the mid-seventies of finite element techniques failed to produce the solution to any but the most simple gear contact problems.
When manufacturing powder metal (PM) gears lead crowning is not achievable in the compaction process. This has to be accomplished either by shaving, grinding or honing. Each of these processes has their merits and draw backs. When employing rolling using a roll burnishing machine lead crowning can be accomplished but due to errors in profile a hard finishing operation such as grinding is used by the industry. In this paper a helical PM gear that has sufficient tolerance class after rolling has been tested in a test rig for durability and the wear has been studied.