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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 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.
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.
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 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).
The German National Metrology Institute has developed a novel calibration concept that allows for highly accurate calibration of product-like artifacts.
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.
Super-reduction hypoid gears (SRH) are bevel worm gears with certain differences regarding hypoid gears. If two axes are positioned in space and the task is to transmit motion and torque between them using some kind of gears with a ratio above 5 and even higher than 50, the following cases are commonly known. Tribology Aspects in Angular Transmission Systems, Part VIII.
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.
With the aim of reducing the operating noise and vibration of planetary gear sets used in automatic transmissions, a meshing phase difference was applied to the planet gears that mesh with the sun and ring gears.
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.
"Magnetic Filtration" and "Better Blanking from Bar-Stock"
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?
When designing gears, the engineer is often faced with the problem of selecting the number of teeth in each gear, so that the gear train will provide a given speed ratio
Our question this issue deals with high-ratio hypoid gears, and it should be noted here that this is a tricky area of gearing with a dearth of literature on the topic. That being the case, finding “experts” willing to stick their necks out and take on the subject was not a given.
As a result of extensive research into the vibration characteristics of gear drives, a systematic approach has evolved, by which damaging resonances can be eliminated. The method combines finite element techniques with experimental signature and modal analyses. Implementation of the bulk of the method can be carried out early in the design stage. A step-by-step description of the approach, as it was applied to an existing accessory drive, is given in the text. It is shown how premature bearing failures were eliminated by detuning the torsional oscillations of a gearshaft. A dramatic reduction in vibration levels was achieved as a result of detuning the problem gear. The proposed approach can be extended to other types of rotating machines.
Planetary gear transmissions are compact, high-power speed reducers that use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane transmission, the planet gear has no size of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary transmission with a fixed size, gear ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives, which point to an optimal planetary reduction ratio in the neighborhood of four to five.
Jules Kish responds to comments about his article on finding a hunting ratio, and Dr. Sante Basili argues that shaving is still the best way to finish a rough-cut gear.
Our experts tackle the topic of measuring involute masters, including both master gears and gear inspection artifacts.
It has been documented that epicyclic gear stages provide high load capacity and compactness to gear drives. This paper will focus on analysis and design of epicyclic gear arrangements that provide extremely high gear ratios. Indeed, a special, two-stage planetary arrangement may utilize a gear ratio of over one hundred thousand to one. This paper presents an analysis of such uncommon gear drive arrangements and defines their major parameters, limitations, and gear ratio maximization approaches. It also demonstrates numerical examples, existing designs, and potential applications.
News from Around the Gear Industry
The complete Product News section from the March/April 2015 issue of Gear Technology.
Gleason Corporation has announced that agreement has been reached on all terms to acquire for approximately $36 million in cash the Hermann Pfauter Group, including, among other operations, Hermann Pfauter GmbH & Co., a privately held leading producer of gear equipment based in Ludwigsburg, Germany; its 76% interest in Pfauter-Maad Cutting Tools, a leading cutting tool manufacturer basked in Loves Park, IL; and Pfauter-Maag management's 24% ownership interest in that company. The acquisition includes all assets and liabilities, including the assumption of approximately $56 million in bank debt.
When designing a gear set, engineers usually want the teeth of the gear (Ng) and the pinion (Np) in a "hunting" mesh. Such a mesh or combination is defined as one in which the pinion and the gear do not have any common divisor by a prime number. If a mesh is "hunting," then the pinion must make Np x Ng revolutions before the same pinion tooth meshes with the same gear space. It is often easy to determine if a mesh is hunting by first determining if both the pinion and the gear teeth are divisible by 2,3,5,7,etc. (prime numbers). However, in this age of computerization, how does one program the computer to check for hunting teeth? A simple algorithm is shown below.
Selection of the number of teeth for each gear in a gear train such that the output to input angular velocity ratio is a specified value is a problem considered by relatively few published works on gear design.
Our experts comment on reverse engineering herringbone gears and contact pattern optimization.
Sub: 'Finding Tooth Ratios' article published in Nov/Dec 1985 issue Let us congratulate you and Orthwein, W.C. for publishing this superb article in Gear Technology Journal. We liked the article very much and wish to impliment it in our regular practice.
This article presents an efficient and direct method for the synthesis of compound planetary differential gear trains for the generation of specified multiple speed ratios. It is a train-value method that utilizes the train values of the integrated train components of the systems to form design equations which are solved for the tooth numbers of the gears, the number of mating gear sets and the number of external contacts in the system. Application examples, including vehicle differential transmission units, rear-end differentials with unit and fractional speed ratios, multi-input functions generators and robot wrist joints are given.
The American Society of Mechanical Engineers (ASME) announced at Gear Expo '95 that a national service for the calibration of involute artifacts is now available at the Department of Energy's Y-12 Plant in Oak Ridge, TN.
The finished gear engineer, the man who is prepared for all emergencies, must first of all know the basic design principles. Next he must be well versed in all sorts of calculations which come under the heading of "involute trigonometry."
This paper presents an approach that provides optimization of both gearbox kinematic arrangement and gear tooth geometry to achieve a high-density gear transmission. It introduces dimensionless gearbox volume functions that can be minimized by the internal gear ratio optimization. Different gearbox arrangements are analyzed to define a minimum of the volume functions. Application of asymmetric gear tooth profiles for power density maximization is also considered.
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.
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.
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.
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 is part II of a two-part paper that presents the results of extensive test programs on the RCF strength of PM steels.
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.
If you are like most navigators of the printed page, the first thing you read in this final 2013 issue of Gear Technology was our State of the Gear Industry Survey. And who would blame you? It’s not Sabermetrics, but once you’ve read it you’ll have a pretty clear snapshot of last year and a peek into the next. But if you also like to get a little closer to the bone about things, what follows are the collected opinions of five well-regarded people in the gear industry speaking to a number of issues with relevance.
Gear Technology speaks with David Goodfellow, president of American Pfauter, L.P., and Pfauter-Maag Cutting tools, L.P., to get his impressions about the state of the gear industry and its prospects for the future.
High demands for cost-effectiveness and improved product quality can be achieved via a new low pressure carburizing process with high pressure gas quenching. Up to 50% of the heat treatment time can be saved. Furthermore, the distortion of the gear parts could be reduced because of gas quenching, and grinding costs could be saved. This article gives an overview of the principles of the process technology and the required furnace technology. Also, some examples of practical applications are presented.
In most transmission systems, one of the main power loss sources is the loaded gear mesh. In this article, the influences of gear geometry parameters on gear efficiency, load capacity, and excitation are shown.
A reflection by Michael Goldstein, Publisher & Editor-in-Chief.
It has previously been demonstrated that one gear of an interchangeable series will rotate with another gear of the same series with proper tooth action. It is, therefore, evident that a tooth curve driven in unison with a mating blank, will "generate" in the latter the proper tooth curve to mesh with itself.
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.
This article summarizes results of research programs on RCF strength of wrought steels and PM steels.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.