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Our company manufactures a range of hardened and ground gears. We are looking into using skiving as part of our finishing process on gears in the 4-12 module range made form 17 CrNiMO6 material and hardened to between 58 and 62 Rc. Can you tell us more about this process?
Looking for some simple yet useful advice heading into IMTS 2016? Never second guess your machine tool investment. Flexibility is a mandatory requirement in gear manufacturing today. Accuracy, reliability and efficiency must improve with each new machine tool purchase. Innovation is always the end game. So it comes as no surprise that IMTS 2016 attendees will have plenty of gear grinding technologies to consider this fall.
Crown gearings are not a new type of gear system. On the contrary, they have been in use since very early times for various tasks. Their earliest form is that of the driving sprocket, found in ancient Roman watermills or Dutch windmills. The first principles of gear geometry and simple methods of production (shaper cutting) were developed in the 1940s. In the 1950s, however, crown gears' importance declined. Their tasks were, for example, taken over by bevel gears, which were easier to manufacture and could transmit greater power. Current subject literature accordingly contains very little information on crown gears, directed mainly to pointing out their limitations (Ref. 1).
Recent trends in gear cutting technology have left process engineers searching for direction about which combination of cutting tool material, coating, and process technology will afford the best quality at the lowest total cost. Applying the new technologies can have associated risks that may override the potential cost savings. The many interrelated variables to be considered and evaluated tend to cloud the issue and make hobbing process development more difficult.
Nowadays, finish hobbing (which means that there is no post-hobbing gear finishing operation) is capable of producing higher quality gears and is growing in popularity.
Increased productivity in roughing operations for gear cutting depends mainly on lower production costs in the hobbing process. In addition, certain gears can be manufactured by shaping, which also needs to be taken into account in the search for a more cost-effective form of production.
We are all looking for ways to increase production without sacrificing quality. One of the most cost-effective ways is by improving the substrate material of your hob. Solid carbide hobs are widely used in many applications throughout the world. LMT-Fette was the first to demonstrate the use of solid carbide hobs in 1993 on modern high-speed carbide (HSC) hobbing machines. Since then the process of dry hobbing has been continuously improving through research and product testing. Dry hobbing is proving to be successful in the gear cutting industry as sales for dry hobbing machines have steadily been rising along with the dramatic increase in sales of solid carbide hobs.
I would like to comment on David Arnesen's article, "Dry Hobbing Saves Automaker Money, Improves Gear Quality," in the Nov/Dec, 1996 issue.
It takes confidence to be the first to invest in new manufacturing technology. But the payback can be significant. That has been the experience at the Ford Motor Company's Transmission & Chassis Division plant at Indianapolis, IN, which boasts the world's first production application of dry hobbing.
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.
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?
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?
Chicago- Results of recent studies on residual stress in gear hobbing, hobbing without lubricants and heat treating were reported by representatives of INFAC (Instrumented Factory for Gears) at an industry briefing in March of this year.
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?
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.
The first part of this article, which ran in the September/October 1994 issue, explained the fundamentals of gear hobbing and some of the latest techniques, including methods of hob performance analysis and new tool configurations, being used to solve specific application problems. In this issue, the author continues his exploration of hobbing by describing the effects of progress on requirements in accuracy, as well as the latest in materials, coating and dry hobbing.
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.
Prior to the introduction of titanium nitride to the cutting tool industry in the early 1980s, there was very little progress in the general application of hobbing in the gear cutting industry. The productivity gains realized with this new type of coating initiated a very active time of advancement in the gear manufacturing process.
Flute Index Flute index or spacing is defined as the variation from the desired angle between adjacent or nonadjacent tooth faces measured in a plane of rotation. AGMA defines and provides tolerance for adjacent and nonadjacent flute spacing errors. In addition, DIN and ISO standards provide tolerances for individual flute variation (Fig. 1).
Many people in the gear industry have heard of skiving, a process wherein solid carbide or inserted carbide blade hobs with 15 - 60 degrees of negative rake are used to recut gears to 62 Rc. The topic of this article is the use of neutral (zero) rake solid carbide hobs to remove heat treat distortion, achieving accuracies of AGMA 8 to AGMA 14, DIN 10-5 and improving surface finish on gears from 8 DP - 96 DP (.3 module - .26 m.).
Can a gear profile generated by the hobbing method be an ideal involute? In strictly theoretical terms - no, but in practicality - yes. A gear profile generated by the hobbing method is an approximation of the involute curve. Let's review a classic example of an approximation.
We make a lot of single-start worm and worm gear sets, and it always seems as though we're buying another special hob. We also do a lot of spur gear cutting, and the spur gear hobs and the worm gear hobs look alike, so we wonder why we cannot use the standard hobs for cutting worm gears too. Can we do this?
Bodine Electric Co. of Chicago, IL., has a 97-year history of fine-and medium-pitch gear manufacturing. Like anywhere else, traditions, old systems, and structures can be beneficial, but they can also become paradigms and obstacles to further improvements. We were producing a high quality product, but our goal was to become more cost effective. Carbide hobbing is seen as a technological innovation capable of enabling a dramatic, rather than an incremental, enhancement to productivity and cost savings.
Almost any external tooth form that is uniformly spaced around a center can be hobbed. Hobbing is recognized as an economical means of producing spur and helical gears with involute tooth profiles.
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.
I make all the double helical gears that go into a gearbox - four different gears in this unit. If the gear module for the bull gear and the intermediate gear are the same (these are the two individual gears that mate), and the gear module for the high-speed pinion and high-speed gears are the same (these are the other two individual gears that mate in the gear box as well), is it then possible to just use two hobs in this setup to make all four gears, since they mate together with each other? We are currently using a different gear hob for each gear.
Experiencing a Dickensian dilemma in its essence, a Los Angeles based manufacturing company was faced with the good fortune of ever increasing orders for steel gears from a good customer with a new recreational product in very high demand. Confronting the possibility of an untold number of lonely late nights tending to the whims of a 1950s era manual hobber was an unpalatable prospect no one desired.
This paper outlines the basic principles of involute gear generation by using a milling cutter; the machine and cutting tool requirements; similarities and differences with other gear generative methods; the cutting strategy; and setup adjustments options. It also discusses the applications that would benefit the most: for coarse-pitch gears the generative gear milling technologies offer improved efficiency, expanded machine pitch capacity, decreased cutter cost, and a possibility for reducing the number of machining operations.
The latest technological solutions help keep chamfering and deburring operations in-line -- often without increasing cycle times.
I would like some instructions for setting the degrees and minutes on a Liebherr or Barber Colman hob. Our machines use a Vernier scale to match the lead angle of the cutter to the part to form straight teeth. There is a dispute on how to do this task, and I wanted insight from another professional.
A calculation method is developed to estimate tool wear on hobs.
RCD Engineering's switch from manual to CNC hobbing operations breaks gear manufacturing lead time records with Bourn & Koch 100H in their gear production pit crew.
Gear hobbing is one of the most productive manufacturing processes for cylindrical gears. The quality of the gears is a result of the tool quality, the precision of the workpiece, tool clamping and kinematics of the machine. The dry gear hobbing process allows machining of gears with a quality according to the DIN standard up to IT 5. To evaluate which gear quality is possible to machine with a given clamping and hob, it is useful to simulate the process in advance.
Another expert takes a crack at a previously answered question about double-helical gears and universal hobs.
Attached photos (Figs. 1-2) show a bushing to locate one single bore. This will be used to locate one single bore diameter of a gear wheel. What is (the latest) technology for common clamping a bushing to locate multiple bore diameters in hobbing?
Gear Technology interviews Scott Yoders of Liebherr about the latest gear machining technologies of relevance to automotive manufacturers.
Sandvik presents the latest in gear milling technologies.
While designing gear and spline teeth, the root fillet area and the corresponding maximum tensile stress are primary design considerations for the gear designer. Root fillet tensile stress may be calculated using macro-geometry values such as module, minor diameter, effective fillet radius, face width, etc.
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.
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).
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?
I have outsourced gear macrogeometry due to lack of resources. Now I received the output from them and one of the gears is with â€”0.8Ă— module correction factor for m = 1.8 mm gear. Since bending root stress and specific slide is at par with specification, but negative correction factor â€”0.8Ă— module â€” is quite high â€” how will it influence NVH behavior/transmission error? SAP and TIF are very close to 0.05 mm; how will that influence the manufacturing/cost?
The hobbing and generation grinding production processes are complex due to tool geometry and kinematics. Expert knowledge and extensive testing are required for a clear attribution of cause to work piece deviations. A newly developed software tool now makes it possible to simulate the cutting procedure of the tool and superimpose systematic deviations on it. The performance of the simulation software is illustrated here with practical examples. The new simulation tool allows the user to accurately predict the effect of errors. With this knowledge, the user can design and operate optimal, robust gearing processes.
Decades ago, technology shifted from HSS to indexable inserts in turning and milling. This movement wasn't immediately realized in gear hobbing because coated PM-HSS hobs and complex gear profiles remained highly effective and productive methods. Only fairly recently have gear manufacturers started to take a serious look at indexable technology to cut gear teeth.
For two days in Saline, Michigan, Liebherr's clients, customers and friends came together to discuss the latest gear products and technology. Peter Wiedemann, president of Liebherr Gear Technology Inc., along with Dr.-Ing. Alois Mundt, managing director, Dr.-Ing. Oliver Winkel, head of application technology, and Dr.-Ing. Andreas Mehr, technology development shaping and grinding, hosted a variety of informative presentations.
Hobbing is one of the most fundamental processes in gear manufacturing. Its productivity and versatility make hobbing the gear manufacturing method of choice for a majority of spur and helical gears.
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).
This is Part II of a two-part series on the basics of gear hobbing. Part I discussed selection of the correct type of hobbing operation, the design features of hobs and hob accuracy. This part will cover sharpening errors and finish hob design considerations.
The Hobbing Process The hobbing process involves a hob which is threaded with a lead and is rotated in conjunction with the gear blank at a ratio dependent upon the number of teeth to be cut. A single thread hob cutting a 40-tooth gear will make 40 revolutions for each revolution of the gear. The cutting action in hobbing is continuous, and the teeth are formed in one passage of the hob through the blank. See Fig. 1 for a drawing of a typical hob with some common nomenclature.
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.
In this paper, the potential for geometrical cutting simulations - via penetration calculation to analyze and predict tool wear as well as to prolong tool life - is shown by means of gear finish hobbing. Typical profile angle deviations that occur with increasing tool wear are discussed. Finally, an approach is presented here to attain improved profile accuracy over the whole tool life of the finishing hob.
Several innovations have been introduced to the gear manufacturing industry in recent years. In the case of gear hobbingâ€”the dry cutting technology and the ability to do it with powder-metallurgical HSSâ€”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.
Fred Young, CEO of Forest City Gear, talks about sophisticated gear manufacturing methods and how they can help solve common gear-related problems.
Bevel gear manufacturers live in one of two camps: the face hobbing/lapping camp, and the face milling/grinding camp.
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.
New tool from LMT-Fette provides combination of operations.
WithÂ reference toÂ the machining of anÂ involute spur or helical gear by the hobbing process,Â this paper suggests a new criterionÂ for selectingÂ the positionÂ of the hob axis relative toÂ the gear axis.
There are great advantages in dry hobbing, not only for friendliness toward the environment, but also for increasing productivity and for decreasing manufacturing cost. Dry hobbing, however, often causes failures in hob cutting edges or problems with the surface quality of gear tooth flanks. These difficulties are not present when hobbing with cutting oil. Pinching and crushing of generated chips between the hob cutting edge and the work gear tooth flank is considered a major cause of those problems.
This article examines the dry hobbing capabilities of two cutting tool materialsâ€”powder metallurgical high-speed steel (PM-HSS) and cemented carbide. Cutting trials were carried out to analyze applicable cutting parameters and possible tool lives as well as the process reliability. To consider the influences of the machinability of different workpiece materials, a case hardening steel and a tempered steel were examined.
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. Stadtfeldâ€™s upcoming book on the subject, which is scheduled for release in 2011.
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.
The seemingly simple process of placing a uniform chamfer on the face ends of spur and helical gears, at least for the aerospace industry, has never been a satisfactory or cost effective process.
Load-carrying capacity of gears, especially the surface durability, is influenced by their tooth surface roughness in addition to their tooth profiles and tooth traces.
In todayâ€™s manufacturing environment, shorter and more efficient product development has become the norm. It is therefore important to consider every detail of the development process, with a particular emphasis on design. For green machining of gears, the most productive and important process is hobbing. In order to analyze process design for this paper, a manufacturing simulation was developed capable of calculating chip geometries and process forces based on different models. As an important tool for manufacturing technology engineers, an economic feasibility analysis is implemented as well. The aim of this paper is to show how an efficient process designâ€”as well as an efficient processâ€”can be designed.
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.
Some results of evaluation by this method in the automotive industry.
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.
The complete Product News section from the May 2009 issue of Gear Technology.
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.
It is well known that hobs with straight-sided teeth do not cut true involutes. In this paper, the difference between the straight side of a hob tooth and the axial profile of an involute worm is evaluated. It is shown that the difference increases as the diametral pitch increases, to the extent that for fine-pitch gearing, the difference is insignificant.
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 finishingâ€”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.
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.
The quality of the finished gear is influenced by the very first machining operations of the blank. Since the gear tooth geometry is generated on a continuously rotating blank in hobbing or shaping, it is important that the timed relationship between the cutter and workpiece is correct. If this relationship is disturbed by eccentricities of the blank to its operating centerline, the generated gear teeth will not be of the correct geometry. During the blanking operations, the gear's centerline and locating surfaces are established and must be maintained as the same through the following operations that generate the gear teeth.
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?
Question: When cutting worm gears with multiple lead stock hobs we find the surface is "ridged". What can be done to eliminate this appearance or is to unavoidable?
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.
Two questions on hobbing cover the various types of hobs and their unusual names, as well as the importance of hob swivel angle.
The following article is a collection of data intended to give the reader a general overview of information related to a relatively new subject within the gear cutting industry. Although carbide hobbing itself is not necessarily new, some of the methods and types of application are. While the subject content of this article may be quite broad, it should not be considered all-inclusive. The actual results obtained and the speeds, feeds, and tool life used in carbide hobbing applications can vary significantly.
Hobbing is a continuous gear generation process widely used in the industry for high or low volume production of external cylindrical gears. Depending on the tooth size, gears and splines are hobbed in a single pass or in a two-pass cycle consisting of a roughing cut followed by a finishing cut. State-of-the-art hobbing machines have the capability to vary cutting parameters between first and second cut so that a different formula is used to calculate cycle times for single-cut and double-cut hobbing.
This article describes a method of obtaining gear tooth profiles from the geometry of the rack (or hob) that is used to generate the gear. This method works for arbitrary rack geometries, including the case when only a numerical description of the rack is available. Examples of a simple rack, rack with protuberances and a hob with root chamfer are described. The application of this technique to the generation of boundary element meshes for gear tooth strength calculation and the generation of finite element models for the frictional contact analysis of gear pairs is also described.
The newer profile-shifted (long and short addendum) gears are often used as small size reduction gears for automobiles or motorcycles. The authors have investigated the damage to each cutting edge when small size mass-produced gears with shifted profiles are used at high speeds.
Among the various types of gearing systems available to the gear application engineer is the versatile and unique worm and worm gear set. In the simpler form of a cylindrical worm meshing at 90 degree axis angle with an enveloping worm gear, it is widely used and has become a traditional form of gearing. (See Fig. 1) This is evidenced by the large number of gear shops specializing in or supplying such gear sets in unassembled form or as complete gear boxes. Special designs as well as standardized ratio sets covering wide ratio ranges and center distanced are available with many as stock catalog products.
The art of gear hobbing has advanced dramatically since the development and introduction of unique machine and tool features such as no backlash, super rigidity, automatic loading of cutting tools, CNC controls, additional machine power and improved cutter materials and coatings. It is essential to utilize all these features to run the machine economically.
Q&A with Liebherr's Dr. Alois Mundt.
The modern day requirement for precision finished hobbed gears, coupled with the high accuracy characteristics of modern CNC hobbing machines, demands high tool accuracy.
NC and CNC metal cutting machines are among the most popular machine tools in the business today, There is also a strong trend toward using flexible machining centers and flexible manufacturing systems. The same trend is apparent in gear cutting. Currently the trend toward CNC tools has increased, and sophisticated controls and peripheral equipment for gear cutting machines are now available; however, the investment in a CNC gear machine has to be justified on the basis of economic facts as well as technical advantages.
Today it is common practice when climb hobbing to keep the direction of the hob thread the same as that of the helical gear. The same generalization holds true for the mass production of gears for automobiles. It is the authors' opinion, however, that conventional hobbing with a reverse-handed hob is more effective for the high-speed manufacture of comparatively small module gears for automobiles. The authors have proven both experimentally and theoretically that reverse-handed conventional hobbing, using a multi-thread hob with a smaller diameter is very effective for lengthening the life of the hob and for increasing cutting efficiency at high speeds.
The forming of gear teeth has traditionally been a time-consuming heavy stock removal operation in which close tooth size, shape, runout and spacing accuracy are required. This is true whether the teeth are finished by a second forming operation or a shaving operation.
Since we are a high volume shop, we were particularly interested in Mr. Kotlyar's article describing the effects of hob length on production efficiency which appeared in the Sept/Oct issue of Gear Technology. Unfortunately, some readers many be unnecessarily deterred from applying the analysis to their own situations by the formidabilty of the mathematical calculations. I am making the following small suggestion concerning the evaluation of the constant terms.
Helical gears can drive either nonparallel or parallel shafts. When these gears are used with nonparallel shafts, the contact is a point, and the design and manufacturing requirements are less critical than for gears driving parallel shafts.
Gear gashing is a gear machining process, very much like gear milling, utilizing the principle of cutting one or more tooth (or tooth space) at a time. The term "GASHING" today applies to the roughing, or roughing and finishing, of coarse diametral pitch gears and sprockets. Manufacturing these large coarse gears by conventional methods of rough and finish hobbing can lead to very long machining cycles and uneconomical machine utilization.
The objective, according to Dr.- Ing. HansjĂ¶rg 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.
New material technology allows for more efficient and flexible hobbing.
This article provides a guideline for the selection of a suitable standard in connection with the kind of spline to be designed and manufactured. Some basic formulae have been explained, together with a strategy on how to find standard tooling by calculating an appropriate profile shift factor for the spline to be designed.