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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.
A recent U.S. Army Tank-Automotive Command project, conducted by Battelle's Columbus Laboratories. successfully developed the methodology of CAD/CAM procedures for manufacturing dies (via EDM) for forging spiral bevel gears. Further, it demonstrated that precision forging of spiral bevel gears is a practical production technique. Although no detailed economic evaluation was made in this study, it is expected that precision forging offers an attractive alternative to the costly gear cutting operations for producing spiral bevel gears.
There are different types of spiral bevel gears, based on the methods of generation of gear-tooth surfaces. A few notable ones are the Gleason's gearing, the Klingelnberg's Palloid System, and the Klingelnberg's and Oerlikon's Cyclo Palliod System. The design of each type of spiral bevel gear depends on the method of generation used. It is based on specified and detailed directions which have been worked out by the mentioned companies. However, there are some general aspects, such as the concepts of pitch cones, generating gear, and conditions of force transmissions that are common for all types of spiral bevel gears.
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.
In this article, the authors calculated the numerical coordinates on the tooth surfaces of spiral bevel gears and then modeled the tooth profiles using a 3-D CAD system. They then manufactured the large-sized spiral bevel gears based on a CAM process using multi-axis control and multi-tasking machine tooling. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. Moreover, the gears were meshed with each other and the tooth contact patterns were investigated. As a result, the validity of this manufacturing method was confirmed.
Recently it has been suggested that the transverse plane may be very useful in studying the kinematics and dynamics of spiral bevel gears. The transverse plane is perpendicular to the pitch and axial planes as shown in Fig. 1. Buckingham has suggested that a spiral bevel gear may be viewed as a limited form of a "stepped" straight-tooth gear as in Fig. 2. The transverse plane is customarily used in the study of straight toothed bevel gears.
This paper presents a new approach in roll testing technology of spiral bevel and hypoid gear sets on a CNC roll tester applying analytical tools, such as vibration noise and single-flank testing technology.
Studies to evaluate low-noise Formate spiral bevel gears were performed. Experimental tests were conducted on a helicopter transmission test stand...
This article is the fourth installment in Gear Technology's series of excerpts from Dr. Hermann J. Stadtfeld's book, Gleason Bevel Gear Technology. The first three excerpts can be found in our June, July and August 2015 issues. In the previous chapter, we demonstrated the development of a face-milled spiral bevel gearset. In this section, an analogue face-hobbed bevel gearset is derived.
Recent advances in spiral bevel gear geometry and finite element technology make it practical to conduct a structural analysis and analytically roll the gear set through mesh. With the advent of user-specific programming linked to 3-D solid modelers and mesh generators, model generation has become greatly automated. Contact algorithms available in general purpose finite element codes eliminate the need for the use and alignment of gap elements. Once the gear set it placed in mesh, user subroutines attached to the FE code easily roll it through mesh. The method is described in detail. Preliminary result for a gear set segment showing the progression of the contact line load is given as the gears roll through mesh.
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.
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.
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.
CNC technology offers new opportunities for the manufacture of bevel gears. While traditionally the purchase of a specific machine at the same time determined a particular production system, CNC technology permits the processing of bevel gears using a wide variety of methods. The ideological dispute between "tapered tooth or parallel depth tooth" and "single indexing or continuous indexing" no longer leads to an irreversible fundamental decision. The systems have instead become penetrable, and with existing CNC machines, it is possible to select this or that system according to factual considerations at a later date.
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.
Could the tip chamfer that manufacturing people usually use on the tips of gear teeth be the cause of vibration in the gear set? The set in question is spur, of 2.25 DP, with 20 degrees pressure angle. The pinion has 14 teeth and the mating gear, 63 teeth. The pinion turns at 535 rpm maximum. Could a chamfer a little over 1/64" cause a vibration problem?
In addition to the face milling system, the face hobbing process has been developed and widely employed by the gear industry. However, the mechanism of the face hobbing process is not well known.
Impact Technologies considers commercial version of software package.
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.
Spiral bevel and hypoid gear cutting has changed significantly over the years. The machines, tools, processes and coatings have steadily advanced.
Following is a report on the R&D findings regarding remediation of high-value, high-demand spiral bevel gears for the UH–60 helicopter tail rotor drivetrain. As spiral bevel gears for the UH–60 helicopter are in generally High-Demand due to the needs of new aircraft production and the overhaul and repair of aircraft returning from service, acquisition of new spiral bevel gears in support of R&D activities is very challenging. To compensate, an assessment was done of a then-emerging superfinishing method—i.e., the micromachining process (MPP)—as a potential repair technique for spiral bevel gears, as well as a way to enhance their performance and durability. The results are described in this paper.
Some years back, most spiral bevel gear sets were produced as cut, case hardened, and lapped. The case hardening process most frequently used was and is case carburizing. Many large gears were flame hardened, nitrided, or through hardened (hardness around 300 BHN) using medium carbon alloy steels, such as 4140, to avoid higher distortions related to the carburizing and hardening process.
How the latest techniques and software enable faster spiral bevel and hypoid design and development.
Zerol bevel gears are the special case of spiral bevel gears with a spiral angle of 0°. They are manufactured in a single-indexing face milling process with large cutter diameters, an extra deep tooth profile and tapered tooth depth.
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.
The geometry of the bevel gear is quite complicated to describe mathematically, and much of the overall surface topology of the tooth flank is dependent on the machine settings and cutting method employed. AGMA 929-A06 — Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius — lays out a practical approach for predicting the approximate top-land thicknesses at certain points of interest — regardless of the exact machine settings that will generate the tooth form. The points of interest that AGMA 929-A06 address consist of toe, mean, heel, and point of involute lengthwise curvature. The following method expands upon the concepts described in AGMA 929-A06 to allow the user to calculate not only the top-land thickness, but the more general case as well, i.e. — normal tooth thickness anywhere along the face and profile of the bevel gear tooth. This method does not rely on any additional machine settings; only basic geometry of the cutter, blank, and teeth are required to calculate fairly accurate tooth thicknesses. The tooth thicknesses are then transformed into a point cloud describing both the convex and concave flanks in a global, Cartesian coordinate system. These points can be utilized in any modern computer-aided design software package to assist in the generation of a 3D solid model; all pertinent tooth macrogeometry can be closely simulated using this technique. A case study will be presented evaluating the accuracy of the point cloud data compared to a physical part.
Beveloids are helical gears with nonparallel shafts, with shaft angles generally between 5 degrees and 15 degrees. This is part VI in the Tribology Aspects in Angular Transmission Systems Series
Imagine the flexibility of having one machine capable of milling, turning, tapping and gear cutting with deburring included for hard and soft material. No, you’re not in gear fantasy land. The technology to manufacture gears on non gear-dedicated, mult-axis machines has existed for a few years in Europe, but has not yet ventured into mainstream manufacturing. Deckel Maho Pfronten, a member of the Gildemeister Group, took the sales plunge this year, making the technology available on most of its 2009 machines.
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.
Investment in advanced new manufacturing technologies is helping to reinvent production processes for bevel gear cutters and coarse-pitch hobs at Gleason - delivering significant benefits downstream to customers seeking shorter deliveries, longer tool life and better results.
Today, because of reduced cost of coatings and quicker turnaround times, the idea of all-around coating on three-face-sharpened blades is again economically viable, allowing manufacturers greater freedoms in cutting blade parameters, including three-face-sharpened and even four-face-sharpened blades.
Bevel gear systems are particularly sensitive to improper assembly. Slight errors in gear positioning can turn a well-designed, quality manufactured gear set into a noisy, prone-to-failure weak link in your application.
Hypoid gears are the paragon of gearing. To establish line contact between the pitches in hypoid gears, the kinematically correct pitch surfaces have to be determined based on the axoids. In cylindrical and bevel gears, the axoids are identical to the pitch surfaces and their diameter or cone angle can be calculated simply by using the knowledge about number of teeth and module or ratio and shaft angle. In hypoid gears, a rather complex approach is required to find the location of the teeth—even before any information about flank form can be considered. This article is part seven of an eight-part series on the tribology aspects of angular gear drives.
Spiral-bevel gears, found in many machine tools, automobile rear-axle drives, and helicopter transmissions, are important elements for transmitting power.
In this paper a new method for the introduction of optimal modifications into gear tooth surfaces - based on the optimal corrections of the profile and diameter of the head cutter, and optimal variation of machine tool settings for pinion and gear finishing—is presented. The goal of these tooth modifications is the achievement of a more favorable load distribution and reduced transmission error. The method is applied to face milled and face hobbed hypoid gears.
Transmission of power between nonparallel shafts is inherently more difficult than transmission between parallel shafts, but is justified when it saves space and results in more compact, more balanced designs. Where axial space is limited compared to radial space, angular drives are preferred despite their higher initial cost. For this reason, angular gear motors and worm gear drives are used extensively in preference to parallel shaft drives, particularly where couplings, brakes, and adjustable mountings add to the axial space problem of parallel shaft speed reducers.
This presentation is an expansion of a previous study (Ref.1) by the authors on lapping effects on surface finish and transmission errors. It documents the effects of the superfinishing process on hypoid gears, surface finish and transmission errors.
Computer technology has touched all areas of our lives, impacting how we obtain airline tickets, purchase merchandise and receive medical advice. This transformation has had a vast influence on manufacturing as well, providing process improvements that lead to higher quality and lower costs. However, in the case of the gear industry, the critical process of tooth contact pattern development for spiral bevel gears remains relatively unchanged.
In general, bevel gears and curvic couplings are completely different elements. Bevel gears rotate on nonintersecting axis with a ratio based on the number of teeth. Curvic couplings work like a clutch (Fig. 1).
This article also appears as Chapter 1 in the Gleason Corporation publication "Advanced Bevel Gear Technology." Gearing Principles in Cylindrical and Straight Bevel Gears The purpose of gears is to transmit motion and torque from one shaft to another. That transmission normally has to occur with a constant ratio, the lowest possible disturbances and the highest possible efficiency. Tooth profile, length and shape are derived from those requirements.
James J. Cervinka and Frank E. Pielsticker must've known the future when they named their new business Arrow Gear Co. in 1947. They started out to manufacture gears for hand tools and machine tools, but their business has taken off since then.
Curvic Couplings were first introduced in 1942 to meet the need for permanent couplings and releasing couplings (clutches), requiring extreme accuracy and maximum load carrying capacity, together with a fast rate of production. The development of the Curvic Coupling stems directly from the manufacture of Zerol and spiral bevel gears since it is made on basically similar machines and also uses similar production methods. The Curvic Coupling can therefore lay claim to the same production advantages and high precision associated with bevel gears.
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).
This paper proposes a method for the manufacture of a replacement pinion for an existing, large-sized skew bevel gear using multi-axis control and multitasking machine tool.
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.
Power train designs which employ gears with cone angles of approximately 2 degrees to 5 degrees have become quite common. It is difficult, if not impossible, to grind these gears on conventional bevel gear grinding machines. Cylindrical gear grinding machines are better suited for this task. This article will provide an overview of this option and briefly introduce four grinding variation possibilities.
What are the manufacturing methods used to make bevel gears used in automotive differentials?
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.
High-speed machining using carbide has been used for some decades for milling and turning operations. The intermittent character of the gear cutting process has delayed the use of carbide tools in gear manufacturing. Carbide was found at first to be too brittle for interrupted cutting actions. In the meantime, however, a number of different carbide grades were developed. The first successful studies in carbide hobbing of cylindrical gears were completed during the mid-80s, but still did not lead to a breakthrough in the use of carbide cutting tools for gear production. Since the carbide was quite expensive and the tool life was too short, a TiN-coated, high-speed steel hob was more economical than an uncoated carbide hob.
Our experts comment on reverse engineering herringbone gears and contact pattern optimization.
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.
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.
The question is quite broad, as there are different methods for setting various types of gears and complexity of gear assemblies, but all gears have a few things in common.
The calculation begins with the computation of the ring gear blank data. The geometrically relevant parameters are shown in Figure 1. The position of the teeth relative to the blank coordinate system of a bevel gear blank is satisfactorily defined with...
When Dr. Hermann J. Stadtfeld speaks, people tend to listen. Considered one of the world’s foremost experts on bevel gears, Stadtfeld, the vice president of bevel gear technology at Gleason, recently revealed several cutting-edge advancements that the company has been working on.
Developed here is a new method to automatically find the optimal topological modification from the predetermined measurement grid points for bevel gears. Employing this method enables the duplication of any flank form of a bevel gear given by the measurement points and the creation of a 3-D model for CAM machining in a very short time. This method not only allows the user to model existing flank forms into 3-D models, but also can be applied for various other purposes, such as compensating for hardening distortions and manufacturing deviations which are very important issues but not yet solved in the practical milling process.
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?
The efficiency of a gearbox is the output energy divided by the input energy. It depends on a variety of factors. If the complete gearbox assembly in its operating environment is observed, then the following efficiency influencing factors have to be considered
In this installment of Ask the Expert, Dr. Stadtfeld describes the best methods for measuring backlash in bevel gears.
This article presents some of the findings of cutting investigations at WZL in which the correlation of cutting parameters, cutting materials, tool geometry and tool life have been determined.
Guidelines are insurance against mistakes in the often detailed work of gear manufacturing. Gear engineers, after all, can't know all the steps for all the processes used in their factories.
More strength, less noise. Those are two major demands on gears, including bevel and hypoid gears.
Bevel gear manufacturers live in one of two camps: the face hobbing/lapping camp, and the face milling/grinding camp.
Conical involute gears (beveloids) are used in transmissions with intersecting or skewed axes and for backlash-free transmissions with parallel axes.
Conical involute gears, also known as beveloid gears, are generalized involute gears that have the two flanks of the same tooth characterized by different base cylinder radii and different base helix angles.
This month, German automakers will receive the first three units of Klingelnberg's new automated blade checker designed for the shop floor.
Dana Corp. is developing a process that carburizes a straight bevel gear to a carbon content of 0.8% in 60 fewer minutes than atmosphere carburizing did with an identical straight bevel.
Beveloid gears are used to accommodate a small shaft angle. The manufacturing technology used for beveloid gearing is a special setup of cylindrical gear cutting and grinding machines. A new development, the so-called Hypoloid gearing, addresses the desire of gear manufacturers for more freedoms. Hypoloid gear sets can realize shaft angles between zero and 20° and at the same time, allow a second shaft angle (or an offset) in space that provides the freedom to connect two points in space.
The Pentac Plus is the latest generation of Gleason’s Pentac bevel gear cutting system. It is designed to allow much higher tool life and improved productivity, especially for cutters using multiple face blade geometry.
The bevel gear grinding process, with conventional wheels, has been limited to applications where the highest level of quality is required.
This article presents a summary of all factors that contribute to efficient and economical high-speed cutting of bevel and hypoid gears.
New freedom of motion available with CNC generators make possible improving tooth contact on bevel and hypoid gears. Mechanical machines by their nature are inflexible and require a special mechanism for every desired motion. These mechanisms are generally exotic and expensive. As a result, it was not until the introduction of CNC generators that engineers started exploring motion possibilities and their effect on tooth contact.
This paper acknowledges the wide variety of manufacturing processes--especially in grinding--utlized in the production of bevel gears...
Rules and Formula for worm gears, bevel gears and strength of gear teeth.
The quality of gearing is a function of many factors ranging from design, manufacturing processes, machine capability, gear steel material, the machine operator, and the quality control methods employed. This article discusses many of the bevel gear manufacturing problems encountered by gear manufacturers and some of the troubleshooting techniques used.
The design of any gearing system is a difficult, multifaceted process. When the system includes bevel gearing, the process is further complicated by the complex nature of the bevel gears themselves. In most cases, the design is based on an evaluation of the ratio required for the gear set, the overall envelope geometry, and the calculation of bending and contact stresses for the gear set to determine its load capacity. There are, however, a great many other parameters which must be addressed if the resultant gear system is to be truly optimum. A considerable body of data related to the optimal design of bevel gears has been developed by the aerospace gear design community in general and by the helicopter community in particular. This article provides a summary of just a few design guidelines based on these data in an effort to provide some guidance in the design of bevel gearing so that maximum capacity may be obtained. The following factors, which may not normally be considered in the usual design practice, are presented and discussed in outline form: Integrated gear/shaft/bearing systems Effects of rim thickness on gear tooth stresses Resonant response
Question: Do machines exist that are capable of cutting bevel gear teeth on a gear of the following specifications: 14 teeth, 1" circular pitch, 14.5 degrees pressure angle, 4 degrees pitch cone angle, 27.5" cone distance, and an 2.5" face width?
In robot configurations it is desirable to be able to obtain an arbitrary orientation of the output element or end-effector. This implies a minimum of two independent rotations about two (generally perpendicular) intersecting axes. If, in addition, the out element performs a mechanical task such as in manufacturing or assembly (e.g., drilling, turning, boring, etc.) it may be necessary for the end-effector to rotate about its axis. If such a motion is to be realized with gearing, this necessitates a three-degree-of-freedom, three-dimensional gear train, which provides a mechanical drive of gyroscopic complexity; i.e., a drive with independently controlled inputs about three axes corresponding to azimuth, nutation, and spin.
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.
"General Explanations on Theoretical Bevel Gear Analysis" is part 1 of an eight-part series from Gleason's Dr. Hermann Stadtfeld.
Tribology Aspects in Angular Transmission Systems, Part 2
Klingelnberg's new tool and machine concept allow for precise production.
A new method for cutting straight bevel gears.
I am currently writing a design procedure for the correct method for setting up bevel gears in a gearbox for optimum performance...
The Addendum team was in Chicago in early March, for the National Manufacturing Week show, when it saw something unusual: a bicycle with gears. Real gears, Spiral bevel gears, in fact.
News Items About spiral bevel
1 Mitsui Seiki Machines Cut Spiral Bevels (August 19, 2009)
Several customers of Mitsui Seiki USA have reported success cutting 10-14 class ring gears in low- to mid-volume applications, such as fo... Read News
2 Dontyne Offers Spiral Bevel Gear Design Tools (April 14, 2014)
Dontyne Systems Gear Production Suite (GPS) Bevel Gear Module is not intended to replace Gleason and Klingelnberg designs for all applications... Read News
3 Suhner Spiral Bevel Gears Offer High Power, Low Backlash and Low Noise (August 21, 2015)
Each year, increased engine and motor power require more powerful angle gear heads. Engineers in the tool-making and industrial hand too... Read News