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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).
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.
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).
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.
Helical gear pairs with narrow face width can be theoretically classified into three categories over the contact ration domain whose abscissa is the transverse contact ration and whose ordinate is the overlap contact ratio. There is a direct relation between vibration magnitude and shaft parallelism deviation. To clarify the effect of the tooth deviation types on the vibration behavior of helical gear pairs, performance diagrams on vibration are introduced. the acceleration levels of gear pairs are shown by contour lines on the contact ratio domain. Finally, the performance of gears with bias-in and bias-out modifications is discussed considering the effect of the shaft parallelism deviation with use of the developed simulator on a helical gear unit. It becomes clear that there is an asymmetrical feature on the relation between the vibration magnitude of a gear pair and the direction of each deviation.
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.
Curved face width (CFW) spur gears are not popular in the gear industry. But these non-metallic gears have advantages over standard spur gears: higher contact ratio, higher tooth stiffness, and lower contact and bending stresses.
This paper presents a unique approach and methodology to define the limits of selection for gear parameters. The area within those limits is called the “area of existence of involute gears” (Ref. 1). This paper presents the definition and construction of areas of existence of both external and internal gears. The isograms of the constant operating pressure angles, contact ratios and the maximum mesh efficiency (minimum sliding) isograms, as well as the interference isograms and other parameters are defined. An area of existence allows the location of gear pairs with certain characteristics. Its practical purpose is to define the gear pair parameters that satisfy specific performance requirements before detailed design and calculations. An area of existence of gears with asymmetric teeth is also considered.
Most gear cutting shops have shelves full of expensive tooling used in the past for cutting gears which are no longer in production. It is anticipated that these cutters will be used again in the future. While this may take place if the cutters are "standard," and the gears to be cut are "standard," most of the design work done today involves high pressure angle gears for strength, or designs for high contact ratio to reduce noise. The re-use of a cutter under these conditions requires a tedious mathematical analysis, which is no problem if a computer with the right software is available. This article describes a computerized graphical display which provides a quick analysis of the potential for the re-use of shaving cutters stored in a computer file.
Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ration under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque and power. Significant parameters in the design are the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near-optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.
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.
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.
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.
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 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.
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.
The German National Metrology Institute has developed a novel calibration concept that allows for highly accurate calibration of product-like artifacts.
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.
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.
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.
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.
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 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.
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.
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The “less is more” mantra is certainly a rallying cry in manufacturing. Technologies like multiaxis machining, 3D printing and automation are enabling companies to be more efficient, cost-conscious and flexible on the shop floor.
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Excessive machine tool vibration during a precision grinding operation can result in poor workpiece quality in the form of chatter, rough finishes, burn, etc. One possible reason for excessive vibration is directly associated with the relationship between natural frequencies of a machine tool system and the operating speed of the grinding wheel spindle.
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The complete Product News section from the March/April 2015 issue of Gear Technology.
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.
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.
Powder metal. To gear makers today, the phrase conjures images of low power applications in non-critical systems. As powder metal technology advances, as the materials increase in density and strength, such opinions are changing. It is an ongoing, evolutionary process and one that will continue for some time. According to Donald G. White, the executive director of the Metal Powder Industries Federation, in his State-of-the-P/M Industry - 1999 report. "The P/M world is changing rapidly and P/M needs to be recognized as a world-class process - national, continental and even human barriers and prejudices must be eliminated - we must join forces as a world process - unified in approach and goals."
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.
Our experts tackle the topic of measuring involute masters, including both master gears and gear inspection artifacts.
Modern gear design is generally based on standard tools. This makes gear design quite simple (almost like selecting fasteners), economical, and available for everyone, reducing tooling expenses and inventory. At the same time, it is well known that universal standard tools provide gears with less than optimum performance and - in some cases - do not allow for finding acceptable gear solutions. Application specifies, including low noise and vibration, high density of power transmission (lighter weight, smaller size) and others, require gears with nonstandard parameters. That's why, for example, aviation gear transmissions use tool profiles with custom proportions, such as pressure angle, addendum, and whole depth. The following considerations make application of nonstandard gears suitable and cost-efficient:
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.
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?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
How does one perform a contact analysis for worn gears? Our expert responds.
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.
"Magnetic Filtration" and "Better Blanking from Bar-Stock"
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.
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.
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).
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.
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.
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.
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.
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.
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.
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