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A new method for cutting straight bevel 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.
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.
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.
Klingelnberg's new tool and machine concept allow for precise production.
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.
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.
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.
In today's economy, when purchasing a new state-of-the-art gear shaper means a significant capital investment, common sense alone dictates that you develop strategies to get the most for your money. One of the best ways to do this is to take advantage of the sophistication of the machine to make it more than just a single-purpose tool.
The objective, according to Dr.- Ing. Hansjörg Geiser, head of development and design for gear machines at Liebherr, was to develop and design a combined turning and hobbing machine in which turning, drilling and hobbing work could be carried out in the same clamping arrangement as the hobbing of the gearings and the subsequent chamfering and deburring processes.
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.
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.
Previews of manufacturing technology related to gears that will be on display at IMTS 2012.
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?
Booth previews from exhibitors showing products and services for the gear industry.
Physical Vapor Deposited (PVD) coatings such as TiN (Titanium nitride) have been a boon for cutting tool manufacturers. They reduce wear and, therefore, extend tool life, which in turn reduces production costs. But PVD coatings are expensive, and when they fail, they cost both time and money, and they causes of the failure are not always readily apparent.
This article summarizes the development of an improved titanium nitride (TiN) recoating process, which has, when compared to conventional recoat methods, demonstrated tool life increases of up to three times in performance testing of hobs and shaper cutters. This new coating process, called Super TiN, surpasses the performance of standard TiN recoating for machining gear components. Super TiN incorporates stripping, surface preparation, smooth coating techniques and polishing before and after recoating. The combination of these improvements to the recoating process is the key to its performance.
A gear shaper cutter is actually a gear with relieved cutting edges and increased addendum for providing clearance in the root of the gear being cut. The maximum outside diameter of such a cutter is limited to the diameter at which the teeth become pointed. The minimum diameter occurs when the outside diameter of the cutter and the base circle are the same. Those theoretical extremes, coupled with the side clearance, which is normally 2 degrees for coarse pitch cutters an d1.5 degrees for cutters approximately 24-pitch and finer, will determine the theoretical face width of a cutter.
The cutting tool is basic to gear manufacturing. Whether it's a hob, broach, shaper cutter or EDM wire, not much gets done without it. And the mission of the tool remains the same as always; removing material as quickly, accurately and cost-effectively as possible. Progress in the field tends to be evolutionary, coming gradually over time, but recently, a confluence of emerging technologies and new customer demands has caused significant changes in the machines, the materials and the coatings that make cutting tools.
Fig. 1 shows the effects of positive and negative rake on finished gear teeth. Incorrect positive rake (A) increase the depth and decreases the pressure angle on the hob tooth. The resulting gear tooth is thick at the top and thin at the bottom. Incorrect negative rake (B) decreases the depth and increases the pressure angle. This results in a cutting drag and makes the gear tooth thin at the top and thick at the bottom.
What Is Whisker-Reinforced Ceramic? Whisker-reinforced ceramic as applied to cutting tool inserts comprises a matrix of aluminum oxide into which approximately 50% by volume of high-purity silicon carbide "whiskers" are randomly dispersed. The "whiskers" are, in fact, single crystals having dimensions of approximately 0.6 microns in diameter x 10-80 microns in length. These "whiskers" have a tensile strength on the order of 1,000,000 psi (690 MPa). The composite material that is the best known and most widely applied using this technology is designated WG-300 and manufactured by the Greenleaf Corporation of Saegertown, PA.
The cutting tool industry has undergone some serious changes in the last couple of years in both technology and the way the industry does business. The emerging technology today, as well as for the foreseeable future, is dry cutting, especially in high volume production settings. Wet cutting continues to be as popular as ever with lubrication advances making it more economical and environmentally friendly. There has also developed a process called "near dry cutting." this process offers many of the benefits of fluids while eliminating many of hte associated problems.
Economic production is one of the main concerns of any manufacturing facility. In recent years, cost increases and tougher statutory requirements have increasingly made cutting fluids a problematic manufacturing and cost factor in metalworking. Depending on the cutting fluid, production process and supply unit, cutting-fluid costs may account for up to 16% of workpiece cost. In some cases, they exceed tool cost by many times (Ref. 1). The response by manufacturers is to demand techniques for dry machining (Ref. 2).
In order to increase the load carrying capacity of hardened gears, the distortion of gear teeth caused by quenching must be removed by precision cutting (skiving) and/or grinding. In the case of large gears with large modules, skiving by a carbide hob is more economical than grinding when the highest accuracy is not required.
Users of gear-cutting tools probably do not often consciously consider the raw material from which those hobs, broaches or shavers are made. However, a rudimentary awareness of the various grades and their properties may allow tool users to improve the performance or life of their tools, or to address tool failures. The high-speed steel from which the tool is made certainly is not the only factor affecting tool performance, but as the raw material, the steel may be the first place to start.
Quality gear manufacturing depends on controlled tolerances and geometry. As a result, ferritic nitrocarburizing has become the heat treat process of choice for many gear manufacturers. The primary reasons for this are: 1. The process is performed at low temperatures, i.e. less than critical. 2. the quench methods increase fatigue strength by up to 125% without distorting. Ferritic nitrocarburizing is used in place of carburizing with conventional and induction hardening. 3. It establishes gradient base hardnesses, i.e. eliminates eggshell on TiN, TiAIN, CrC, etc. In addition, the process can also be applied to hobs, broaches, drills, and other cutting tools.
Sandvik presents the latest in gear milling technologies.
In the past, the blades of universal face hobbing cutters had to be resharpened on three faces. Those three faces formed the active part of the blade. In face hobbing, the effective cutting direction changes dramatically with respect to the shank of the blade. Depending on the individual ratio, it was found that optimal conditions for the chip removal action (side rake, side relief and hook angle) could just be established by adjusting all major parameters independently. This, in turn, results automatically in the need for the grinding or resharpening of the front face and the two relief surfaces in order to control side rake, hook angle and the relief and the relief angles of the cutting and clearance side.
the gear industry is awash in manufacturing technologies that promise to eliminate waste by producing gears in near-net shape, cut production and labor costs and permit gear designers greater freedom in materials. These methods can be broken down into the following categories: alternative ways to cut, alternative ways to form and new, exotic alternatives. Some are new, some are old and some are simply amazing.
The dimensions of the worm and worm gear tooth surfaces and some of the worm gear drive parameters must be limited in order to avoid gear undercutting and the appearance of the envelope of lines of contact on the worm surface. The author proposes a method for the solution of this problem. The relations between the developed concept and Wildhaber's concept of the limit contact normal are investigated. The results of computations are illustrated with computer graphics.
Rolled out at EMO 2007, the Scudding process is a continuous cutting operation that uses a tool design similar to a helical shaper cutter. It can be used for a wide range of gear applications...
Environmentally friendly cutting fluids aren't just good for the environment. They can also be good for performance.
Indexable carbide insert cutting tools for gears are nothing new. But big gears have recently become a very big business. The result is that there's been a renewed interest in carbide insert cutting tools.
A brief introduction to the subject of Thin Film Coatings and their application to gear hobs and shaper cutters is followed by a detailed description of the Chemical Vapor Deposition Process and the Physical Vapor Deposition Process. Advantages and disadvantages of each of these processes is discussed. Emphasis is placed upon: application engineering of coated gear tools based on laboratory and field test results. Recommendations are suggested for tool design improvements and optimization of gear cutting operations using coated tools. Productivity improvements potentially available by properly utilizing coated tools are considered in terms of both tool cost and machining cost.
As we approach the problem of hard gear processing, it is well to take a look at the reason for discussing it at this time. In our present economic atmosphere throughout the world, more and more emphasis is being placed upon efficiency which is dictated by higher energy costs.
The gear hobbing process is a generating type of production operation. For this reason, the form of the hob tooth is always different from the form of the tooth that it produces.
Hobbing is probably the most popular gear manufacturing process. Its inherent accuracy and productivity makes it a logical choice for a wide range of sizes.
Indexable carbide insert (ICI) cutting tools continue to play a pivotal role in gear manufacturing. By offering higher cutting speeds, reduced cycle times, enhanced coatings, custom configurations and a diverse range of sizes and capabilities, ICI tools have proven invaluable for finishing and pre-grind applications. They continue to expand their unique capabilities and worth in the cutting tool market.
Hobs, broaches, shaper cutters, shaver cutters, milling cutters, and bevel cutters used in the manufacture of gears are commonly made of high speed steel. These specialized gear cutting tools often require properties, such as toughness or manufacturability, that are difficult to achieve with carbide, despite the developments in carbide cutting tools for end mills, milling cutters, and tool inserts.
Universal machines capable of cutting both spur and helical gears were developed in 1910, followed later by machines capable of cutting double helical gears with continuous teeth. Following the initial success, the machines were further developed both in England and France under the name Sunderland, and later in Switzerland under the name Maag.
The higher load carrying capacities, compact dimensions and longer life of hardened gears is an accepted fact in industry today. However, the costs involved in case hardening and subsequent finishing operations to achieve these advantages are considerable. For example, in order to achieve desired running properties on larger gears, it has been necessary to grind the tooth flanks. This costly operation can now be replaced, in many cases, by a new Hard Cutting (HC) process which permits the cutting of hardened gears while maintaining extremely low tooling costs.
Question: I have just become involved with the inspection of gears in a production operation and wonder why the procedure specifies that four involute checks must be made on each side of the tooth of the gear being produced, where one tooth is checked and charted in each quadrant of the gear. Why is this done? These particular gears are checked in the pre-shaved, finish-shaved, and the after-heat-treat condition, so a lot of profile checking must be done.
Today's high technology hobs are visible different from their predecessors. Gear hobs have taken on a different appearance and function with present day technology and tool and material development. This article shows the newer products being offered today and the reasons for investigating their potential for use in today's modern gear hobbers, where cost reduction and higher productivity are wanted.
Not long ago, many manufacturing managers thought sensitivity to environmental protection standards meant additional expenses, decreased productivity, and a plethora of headaches and hassles.
The hob is a perfect example of how a little manufacturing ingenuity can make a reliable, highly productive cutting tool. It's an engineering specimen that creates higher cutting speeds, better wear resistance and increases rigidity. The cutting tool alone, however, can't take all the credit for its resourcefulness. Advanced coating technology from companies like Sulzer, Oerlikon Balzers, Ionbond, Seco Tools and Cemecon helps improve cutting tools by reducing overall costs, increasing tool life and maintaining the highest levels of productivity. The following is a quick recap of new technologies and the latest information in the coating market.
Cutter Sharpening Cutter sharpening is very important both during manufacturing and subsequently in resharpening after dulling. Not only does this process affect cutter "over cutting edge" quality and the quality of the part cut, but it can also affect the manner in which chip flow takes place on the cutter face if the surface finished is too rough or rippled.
The last decade has been a period of far-reaching change for the metal working industry. The effect of higher lubricant costs, technical advances in machine design and increasing competition are making it essential that manufacturers of gears pay more attention to testing, selecting and controlling cutting fluid systems. Lubricant costs are not a large percentage of the process cost relative to items such as raw materials, equipment and labor, and this small relative cost has tended to reduce the economic incentive to evaluate and to change cutting fluids.
Gear shaping is one of the most popular production choices in gear manufacturing. While the gear shaping process is really the most versatile of all the gear manufacturing methods and can cut a wide variety of gears, certain types of gears can only be cut by this process. These are gears closely adjacent to shoulders; gears adjacent to other gears, such as on countershafts; internal gears, either open or blind ended; crown or face gears; herringbone gears of the solid configuration of with a small center groove; rack; parts with filled-in spaces or teeth, such as are used in some clutches.
The paper describes a procedure for the design of internal gear pairs, which is a generalized form of the long and short addendum system. The procedure includes checks for interference, tip interference, undercutting, tip interference during cutting, and rubbing during cutting.
Okay, so you want to make some high quality gears for your customers, and you want to make a profit for your company, but you don't want to make a mess of the environment. What can you do?
Manufacturing involute gears using form grinding or form milling wheels are beneficial to hobs in some special cases, such as small scale production and, the obvious, manufacture of internal gears. To manufacture involute gears correctly the form wheel must be purpose-designed, and in this paper the geometry of the form wheel is determined through inverse calculation. A mathematical model is presented where it is possible to determine the machined gear tooth surface in three dimensions, manufactured by this tool, taking the finite number of cutting edges into account. The model is validated by comparing calculated results with the observed results of a gear manufactured by an indexable insert milling cutter.
Question: We are contemplating purchasing a hobbing machine with dry hobbing capabilities. What do we need to know about the special system requirements for this technology?
Gear grinding is one of the most expensive and least understood aspects of gear manufacturing. But with pressures for reduced noise, higher quality and greater efficiency, gear grinding appears to be on the rise.
In the process of developing gear trains, it occasionally occurs that the tip of one gear will drag in the fillet of the mating gear. The first reaction may be to assume that the outside diameter of the gear is too large. This article is intended to show that although the gear dimensions follow AGMA guidelines, if the gear is cut with a shaper, the cutting process may not provide sufficient relief in the fillet area and be the cause of the interference.
The International Manufacturing Technology Show provided one of the biggest ever marketplaces for buying and selling gear-making equipment, with 121601 attenders, making it the largest IMTS ever. The show took place September 4-11 at McCormick Place in Chicago, IL.
In today's industrial marketplace, deburring and chamfering are no longer just a matter of cosmetics. The faster speeds at which transmissions run today demand that gear teeth mesh as smoothly and accurately as possible to prevent premature failure. The demand for quieter gears also requires tighter tolerances. New heat treating practices and other secondary gear operations have placed their own set of demands on manufacturers. Companies that can deburr or chamfer to these newer, more stringent specifications - and still keep costs in line - find themselves with a leg up on their competition.
In the quest for ever more exacting and compact commercial gears, precision abrasives are playing a key production role - a role that can shorten cycle time, reduce machining costs and meet growing market demand for such requirements as light weights, high loads, high speed and quiet operation. Used in conjunction with high-quality grinding machines, abrasives can deliver a level of accuracy unmatched by other manufacturing techniques, cost-effectively meeting AGMA gear quality levels in the 12 to 15 range. Thanks to advances in grinding and abrasive technology, machining has become one of the most viable means to grind fast, strong and quiet gears.
Gearing for Munchkins Gene Kasten, president of Repair Parts, Inc., of Rockford, IL, is the proud owner of a miniature Barber-Colman hobber, the only one of its kind in the world. The machine, a replica of the old B-C "A" machine, was built between 1933 and 1941 by W. W. Dickover, who devoted 2, 640 hours of his spare time to the project.
Question: We are interested in purchasing our first gear hobbing machine. What questions should we ask the manufacturer, and what do we need to know in order to correctly specify the CNC hardware and software system requirements?
Question: When we purchase our first CNC gear hobbing machine, what questions should we ask about the software? What do we need to know to correctly specify the system requirements?
The chamfering and deburring operations on gear teeth have become more important as the automation of gear manufacturing lines in the automotive industry have steadily increased. Quieter gears require more accurate chamfers. This operation also translates into significant coast savings by avoiding costly rework operations. This article discusses the different types of chamfers on gear teeth and outlines manufacturing methods and guidelines to determine chamfer sizes and angles for the product and process engineer.
Broaching is a process in which a cutting tool passes over or through a part piece to produce a desired form. A broach removes part material with a series of teeth, each one removing a specified amount of stock.
This machine concept facilitates highly productive profile grinding for large workpieces. The range for external and internal gears comprises models for manufacturing workpieces up to 2,000 millimeters – for industrial gear units, wind power, and marine propulsion applications
It’s been said that the best ideas are often someone else's. But with rebuilt, retrofitted, re-controlled or remanufactured machine tools, buyer beware and hold onto your wallet. Sourcing re-work vendors and their services can require just as much homework, if not necessarily dollars, as with just-off-the-showroom-floor machines.
Whether you spent time at Gear Expo in Indianapolis or EMO in Hannover, there was certainly new technology attracting attention. Machine tools are faster, more efficient and can integrate numerous functions in a single setup. Grinding technology is turning science upside down and inside out with high-speed removal rates and increased throughput.
The grinding/abrasives market is rapidly changing, thanks to new technology, more flexibility and an attempt to lower customer costs. Productivity is at an all-time high in this market, and it’s only going to improve with further R&D. By the time IMTS 2014 rolls around this September, the gear market will have lots of new toys and gadgets to offer potential customers. If you haven’t upgraded any grinding/abrasives equipment in the last five years, now might be a good time to consider the investment.
By virtue of collected anecdotal accounts, equations and problem solving, balancing is discussed as more math and common sense, and less smoke and mirrors.
Gear shaving is a free-cutting gear finishing operation which removes small amounts of metal from the working surfaces of gear teeth. Its purpose is to correct errors in index, helix angle, tooth profile and eccentricity. The process also improves tooth surface finish and eliminates by means of crowned tooth forms the danger of tooth end load concentrations in service.
Rotary gear honing is a crossed-axis, fine, hard finishing process that uses pressure and abrasive honing tools to remove material along the tooth flanks in order to improve the surface finish (.1-.3 um or 4-12u"Ra), to remove nicks and burrs and to change or correct the tooth geometry. Ultimately, the end results are quieter, stronger and longer lasting gears.
The trend toward moving coordinate measuring machines to the shop floor to become an integral part of the manufacturing operations brings real time process control within the reach of many companies. Putting measuring machines on the shop floor, however, subjects them to harsh environmental conditions. Like any measuring system, CMMs are sensitive to any ambient condition that deviates from the "perfect" conditions of the metrology lab.
Product announcements so often trumpet minor, incremental advances with works like "revolutionary" and "unique" that even the best thesaurus can fail to offer a fresh alternative to alert the reader when something really innovative and important is introduced. In the case of Mitsubishi's new CNC gear shaper, the ST25CNC, both terms apply.
NC and CNC machines are at the heart of manufacturing today. They are the state-of-the-art equipment everybody has (or is soon going to get) that promise to lower costs, increase production and turn manufacturers into competitive powerhouses. Like many other high tech devices (such as microwaves and VCRs), lots of people have and use them - even successfully - without really knowing much about how they operate. But upgrading to CNC costs a lot of money, so it's crucial to separate the hype from the reality.
These days it's hard to get through breakfast without reading or hearing another story about how the computer is changing the way we live, sleep, eat, breathe, make things and do business. The message is that everything is computerized now, or, if it isn't, it will be by next Tuesday at the latest, Well, maybe.
Modern gearboxes are characterized by high torque load demands, low running noise and compact design. In order to fulfill these demands, profile and lead modifications are being applied more often than in the past. This paper will focus on how to produce profile and lead modifications by using the two most common grinding processes—threaded wheel and profile grinding. In addition, more difficult modifications—such as defined flank twist or topological flank corrections—will also be described in this paper.
Several innovations have been introduced to the gear manufacturing industry in recent years. In the case of gear hobbing—the dry cutting technology and the ability to do it with powder-metallurgical HSS—might be two of the most impressive ones. And the technology is still moving forward. The aim of this article is to present recent developments in the field of gear hobbing in conjunction with the latest improvements regarding tool materials, process technology and process integration.
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.
Part I of this series focused on gear shaving, while Part II focuses on gear finishing by rolling and honing.
Faster, more efficient manufacturing offered with table-top design from American Broach & Machine.
The complete Product News section from the May 2009 issue of Gear Technology.
The complete Industry News section from the November/December 2014 issue.
Sentences that start off with some variance of “I don’t want to brag, but…” are generally a good indicator that it’s precisely what the speaker intends to do and typically end with bold proclamations that are immediately and eminently quotable — the kind of quotes perfect for beginning a feature story with an eye-catching artistic flourish.
The proper design or selection of gear cutting tools requires thorough and detailed attention from the tool designer. In addition to experience, intuition and practical knowledge, a good understanding of profile calculations is very important.
In our last issue, we covered the basic principles of gear shaving and preparation of parts for shaving. In this issue, we will cover shaving methods, design principles and cutter mounting techniques.
Machine tool companies are expanding capabilities to better accommodate the changing face of manufacturing. Customers want smaller-sized equipment to take up less valuable floor space, multifunctional machines that can handle a variety of operations and easy set-up changes that offer simplified operation and maintenance.
Gear hobbing is a generating process. The term generating refers to the fact that the gear tooth form cut is not the conjugate form of the cutting tool, the hob. During hobbing both the hob and the workpiece rotate in a continuous rotational relationship. During this rotation, the hob is typically fed axially with all the teeth being gradually formed as the tool traverses the work face (see Fig. 1a).
The Shaping Process - A Quick Review of the Working Principle. In the shaping process, cutter and workpiece represent a drive with parallel axes rotating in mesh (generating motion) according to the number of teeth in both cutter and workpiece (Fig. 1), while the cutter reciprocates for the metal removal action (cutting motion).
For environmental and economic reasons, the use of coolant in machining processes is increasingly being questioned. Rising coolant prices and disposal costs, as well as strains on workers and the environment, have fueled the debate. The use of coolant has given rise to a highly technical system for handling coolant in the machine (cooling, filtering) and protecting the environment (filter, oil-mist collector). In this area the latest cutting materials - used with or without coolant - have great potential for making the metal-removal process more economical. The natural progression to completely dry machining has decisive advantages for hobbing.
Robots, computers and other signs of high technology abounded at IMTS 94, supporting the claim by many that this was one of the best shows ever. Many of the machines on display had so many robotic attachments and computer gizmos that they looked more like they belonged in some science fiction movie than on the floor of a machine shop.
Grinding is a technique of finish-machining, utilizing an abrasive wheel. The rotating abrasive wheel, which id generally of special shape or form, when made to bear against a cylindrical shaped workpiece, under a set of specific geometrical relationships, will produce a precision spur or helical gear. In most instances the workpiece will already have gear teeth cut on it by a primary process, such as hobbing or shaping. There are essentially two techniques for grinding gears: form and generation. The basic principles of these techniques, with their advantages and disadvantages, are presented in this section.
Today, as part of filling a typical gear hobbing or shaping machine order, engineers are required to perform an SPC acceptance test. This SPC test, while it is contractually necessary for machine acceptance, is not a machine acceptance test. It is a process capability test. It is an acceptance of the machine, cutting tool, workholding fixture, and workpiece as integrated on the cutting machine, using a gear measuring machine, with its work arbor and evaluation software, to measure the acceptance elements of the workpiece.
Q&A with Liebherr's Dr. Alois Mundt.
There are a number of companies working to change the way broaching is perceived, and over the past 10 years, they’ve incorporated significant technological changes to make the process more flexible, productive and accurate.
The Raso 200 Dynamic has been developed to offer all the characteristics of a gear shaving machine with a competitive price.
Recently, a new type of hob with carbide inserts has been introduced, providing higher cutting speeds, longer tool life and higher feed rates when compared to re-grindable, high-speed steel hobs. But with this kind of hob, new challenges occur due to positional errors of the cutting edges when mounted on the tool. These errors lead to manufacturing errors on the gear teeth which must be controlled. In this paper, the tooth quality of a gear manufactured by hobs with different quality classes is analyzed using a simulation model in combination with Monte Carlo methods.
The cutting process consists of either a roll only (only generating motion), a plunge only or a combination of plunging and rolling. The material removal and flank forming due to a pure generating motion is demonstrated in the simplified sketch in Figure 1 in four steps. In the start roll position (step 1), the cutter profile has not yet contacted the work. A rotation of the work around its axis (indicated by the rotation arrow) is coupled with a rotation of the cutter around the axis of the generating gear (indicated by the vertical arrow) and initiates a generating motion between the not-yet-existing tooth slot of the work and the cutter head (which symbolizes one tooth of the generating gear).
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.
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.
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
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.
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.
Tribology Aspects in Angular Transmission Systems, Part 2
Impact Technologies considers commercial version of software package.
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.
"General Explanations on Theoretical Bevel Gear Analysis" is part 1 of an eight-part series from Gleason's Dr. Hermann Stadtfeld.
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.
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.
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.
Rules and Formula for worm gears, bevel gears and strength of gear teeth.
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.
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.
I am currently writing a design procedure for the correct method for setting up bevel gears in a gearbox for optimum performance...
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.
Spiral-bevel gears, found in many machine tools, automobile rear-axle drives, and helicopter transmissions, are important elements for transmitting power.
This paper acknowledges the wide variety of manufacturing processes--especially in grinding--utlized in the production of bevel gears...
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.
The bevel gear grinding process, with conventional wheels, has been limited to applications where the highest level of quality is required.
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.
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 presents a summary of all factors that contribute to efficient and economical high-speed cutting of bevel and hypoid gears.
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 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.
How the latest techniques and software enable faster spiral bevel and hypoid design and development.
Spiral bevel and hypoid gear cutting has changed significantly over the years. The machines, tools, processes and coatings have steadily advanced.
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.
Studies to evaluate low-noise Formate spiral bevel gears were performed. Experimental tests were conducted on a helicopter transmission test stand...
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.
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.
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.
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.
More strength, less noise. Those are two major demands on gears, including bevel and hypoid gears.
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.
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.
This month, German automakers will receive the first three units of Klingelnberg's new automated blade checker designed for the shop floor.
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.
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
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.
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.
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.
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.
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?
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.
In this installment of Ask the Expert, Dr. Stadtfeld describes the best methods for measuring backlash in bevel gears.
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...
THE FINAL CHAPTER This is the last in the series of chapters excerpted from Dr. Hermann J. Stadtfeld’s Gleason Bevel Gear Technology — a book written for specialists in planning, engineering, gear design and manufacturing. The work also addresses the technical information needs of researchers, scientists and students who deal with the theory and practice of bevel gears and other angular gear systems. While all of the above groups are of course of invaluable importance to the gear industry, it is surely the students who hold the key to its future. And with that knowledge it is reassuring to hear from Dr. Stadtfeld of the enthusiastic response he has received from younger readers of these chapter installments.
To meet the future goals of higher productivity and lower production costs, the cutting speeds and feeds in modern gear hobbing applications have to increase further. In several cases, coated carbide tools have replaced the commonly used high speed steel (HSS) tools.
The method of cutting teeth on a cylindrical gear by the hobbing process has been in existence since the late 1800s. Advances have been made over the years in both the machines and the cutting tools used in the process. This paper will examine hob tool life and the many variables that affect it. The paper will cover the state-of-the-art cutting tool materials and coatings, hob tool design characteristics, process speeds and feeds, hob shifting strategies, wear characteristics, etc. The paper will also discuss the use of a common denominator method for evaluating hob tool life in terms of meters (or inches) per hob tooth as an alternative to tool life expressed in parts per sharpening.
Bevel Gear Technology Chapter 6
Could you explain to me the difference between spiral bevel gear process face hobbing-lapping, face milling-grinding and Klingelnberg HPG? Which one is better for noise, load capacity and quality?
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.
In the previous sections, the development of conjugate bevel gearsets via hand calculations was demonstrated. The goal of this exercise was to encourage the reader to gain a basic understanding of the theory of bevel gears. This knowledge will help gear engineers to better judge bevel gear design and their manufacturing methods. In order to make the basis of this learning experience even more realistic, this chapter will convert a conjugate bevel gearset into a gearset that is suitable in a real-world application. Length and profile crowning will be applied to the conjugate flank surfaces. Just as in the previous chapter, all computations are demonstrated as manual hand calculations. This also shows that bevel gear theory is not as complicated as commonly assumed.
Chapter 2, Continued In the previous sections, development of conjugate, face milled — as well as face hobbed — bevel gearsets — including the application of profile and length crowning — was demonstrated. It was mentioned during that demonstration that in order to optimize the common surface area, where pinion and gear flanks have meshing contact (common flank working area), a profile shift must be introduced. This concluding section of chapter 2 explains the principle of profile shift; i.e. — how it is applied to bevel and hypoid gears and then expands on profile side shift, and the frequently used root angle correction which — from its gear theoretical understanding — is a variable profile shift that changes the shift factor along the face width. The end of this section elaborates on five different possibilities to tilt the face cutter head relative to the generating gear, in order to achieve interesting effects on the bevel gear flank form. This installment concludes chapter 2 of the Bevel Gear Technology book that lays the foundation of the following chapters, some of which also will be covered in this series.
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.
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.
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.
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.
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.
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?
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.
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.
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
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.
Our experts comment on reverse engineering herringbone gears and contact pattern optimization.
What are the manufacturing methods used to make bevel gears used in automotive differentials?
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.
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.
The purpose of this paper was to verify, when using an oil debris sensor, that accumulated mass predicts gear pitting damage and to identify a method to set threshold limits for damaged gears.
Face-milled hypoid pinions produced by the three-cut, Fixed Setting system - where roughing is done on one machine and finishing for the concave-OB and convex-IB tooth flanks is done on separate machines with different setups - are still in widespread use today.
The configuration of flank corrections on bevel gears is subject to relatively narrow restrictions. As far as the gear set is concerned, the requirement is for the greatest possible contact zone to minimize flank compression. However, sufficient reserves in tooth depth and longitudinal direction for tooth contact displacement should be present. From the machine - and particularly from the tool - point of view, there are restrictions as to the type and magnitude of crowning that can be realized. Crowning is a circular correction. Different kinds of crowning are distinguished by their direction. Length crowning, for example, is a circular (or 2nd order) material removal, starting at a reference point and extending in tooth length or face width.
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.
Some results of evaluation by this method in the automotive industry.