After a short introduction about the advantages of herringbone gears (no gap between the two gears) and double helical gears (with a gap) and their areas of application, the article goes into detail on the properties and limits of manufacturing processes for machining these gears. The technology data and the gear quality achieved are listed for selected machining examples so the user is provided with helpful information for daily practice.

For green machining, the focus is on gear shaping and 4- or 5-axis milling, because these two methods replace gear planing (otherwise known as rack-type shaping). Due to the increased quality requirements nowadays, more of these herringbone gears and double helical gears have to be hard finished. From an economic point of view, only 4- or 5-axis hard milling can be used for herringbone gears. Profile grinding has become established for double helical gears if they have a certain gap width.

Due to the development of new and high-performance cutting materials, grinding worms with a very small starting outside diameter of 55 mm can also be used. This makes continuous generating grinding a real alternative to profile grinding for the module range up to 5 mm. Electroplated as well as vitrified-bonded CBN and sintered corundum abrasives in triangular or rod-shaped form are used. Generating grinding has the following advantages over profile grinding:

  • Significantly faster grinding times.
  • More robust against stock deviations and heat-treatment distortions.
  • Lower risk for grinding burn.
  • Economic manufacturing of topological modifications, such as the generated end relief (GER), twist free grinding (TF), etc.
  • Higher apex and indexing accuracy.
  • Very high single and cumulative pitch quality due to the continuous process.
  • Potential for fine grinding and polishing for improved surface roughness.

This will be the first time that the technology development of continuous generating grinding of double helical gears will be presented.

The main objective of this article is to show a state of the technology and the latest developments for machining herringbone gears and double helical gears using the example of different processes and application. The main part of the article is divided into the machining of the herringbone gears with the option to hard finish them with 4-axis milling and green machining of double helical gears. An additional section is about the new technology development for hard finishing of double helical gears by the continuous generating grinding principle.

1 Herringbone and double helical gears

1.1 Determination and application

Spur and helical gears are used most frequently in parallel axis gearboxes. The choice of which of the two gear types is used is linked to the advantages (see Figure 1) of the respective gearing. For example, spur gears are still used for very high and efficient torque transmission. If smooth running and a higher contact ratio is required, helical gears are preferred. If the advantages of spur and helical gears in a transmission have to be taken into account, then herringbone gears (no gap between the two gears) and double helical gears (with a gap) are used.]

Figure 1: Advantages of spur and helical gears.

On the herringbone gear or double helical gear, the entire face width is divided into two halves, each with a right-hand and a left-hand lead direction. Due to this arrangement, the axial force component that arises on a single helical gear is compensated by the opposite lead direction of the second gear. This simplifies the axial bearing of the gear in the gearbox. Therefore, the herringbone and double helical gears are often used in very large workpieces where an axial bearing is difficult to obtain or not available and in smaller workpieces where the space for the axial bearing is very limited.

Typical industries are aerospace (e.g., turbofan planetary transmission, see Figure 2, helicopter transmissions), turbo gearboxes, shipbuilding, mining, cement and raw material industries (e.g., vertical mills), pumps, press, and forging technology.

Figure 2: Power gearbox based on double helical gears. (Copyright: Rolls-Royce plc.)

1.2 Specifics on manufacturing of double helical gears

In the case of a herringbone gear, one helical gear transitions seamlessly into the other (cf. Figure 1, top right picture). In case of a double helical gear, there is a gap between the two helical gears (cf. Figure 1, picture below right). This gap enables gear-cutting processes, such as form milling or hobbing, which require a tool overrun. The individual gear manufacturing processes are discussed in more detail in this report.

In addition to the tool overrun, the following topics are also important from a manufacturing point of view:

1.2.1 Apex point and angular position of the gear teeth

The apex point is the intersection of the two lead traces of the right- and left-handed gear. The location of the apex point reflects the positioning of the double helical gearing during operation in the gearbox. Ideally, with the exception of special lead modifications and corrections, this position is exactly in the center between the two gears. The apex point is shown in many technical drawings with a tolerance that must be adhered to in production. The lead angle deviation fhβ according to ISO 1328-1:2013-09 [2] has an influence on the vertical position. Figure 3 shows this influence schematically.

If the helix angle deviation is the same on both gears, i.e., fhβGear1 = fhβGear2, then the related apex point lies directly on the line of symmetry between the two gears. If the helix angle deviates on one of the two gears, the apex point is shifted up or down depending on the fhβ change (see Figure 3).

Figure 3: Influence of the helix angel deviation on the apex point accuracy.

For the production of a precise double helical gearing, it is important to adhere to the helix angle as precisely as possible, since this also directly influences the position of the apex point. Furthermore, the clamping of the workpiece during the manufacture and measurement of the double helical gear also plays an important role. A face runout error leads to a wobble in the lead (fhβ-variation), which also leads to the vertical position shift of the apex point — as descripted earlier — over the circumference of the gear, which is also known as apex runout error.

Another form of positioning on double helical gears is the angular position or the index of the two helical gears in relation to each other. The positioning is related directly to the left and/or right tooth flank or to the tooth gap center. The indexing of the two gears is preferred when the focus is on the gear mesh, the running and load behavior of the gear flanks. The index accuracy has an influence on the vertical position of the apex point. If both gears have the same helix angle deviation and the tooth gaps are offset against each other, then, as shown in Figure 4, the apex point is shifted up or down depending on the direction of rotation to the right or left.

Figure 4: Angular position (index) of the gears.

The radial offset occurs during the manufacturing of the double helical gear, because one gear is usually machined after the other, and the starting positions of the tooth gaps are not maintained exactly due to re-clamping of the workpiece or a necessary tool change. In such a case, the index error is constant over the gear circumference, and the apex point is constantly shifted to one side. When producing double helical gears, the workpiece should be machined in one clamping, if possible. A precise positioning of the gears to each other can be done with the help of a measuring probe.

Gear cutting tools such as hobs or shaper cutters should have a positioned reference tooth.

The apex point as well as the angular position can be measured on modern gear measuring centers together in one setup after or before a gear measurement (profile, lead, pitch, and runout).

A separate apex point measurement on, for example, an additional coordinate measuring machine, is not necessary.

1.2.2 Interim conclusion from a manufacturing point of view

From a manufacturing point of view, the measurement of the angular position or index is preferable because it allows a very simple and more precise correction to be carried out on a gear-cutting machine. Another advantage of the index is the direct connection between the generation kinematics during gear cutting itself, e.g., the workpiece is clamped on the machine table, which is also used for the alignment of the angular gear position. The influence of the lead angle deviation, in particular the wobble error, on the index is significantly lower than on the position of the apex point. And a conversion of the apex point back into the angular position for a rotation correction, which is required by the machine, is not needed. The index correction can be done together with a lead and tooth thickness correction. This significantly reduces the effort to set up a double helical gear.

1.3 Implementation of tooth flank modifications

The type of application and the resulting load cases and operating temperatures require different tooth trace modifications on herringbone or double helical gears [3]. Simple tooth trace modifications such as lead angle modification, crowning, and conventional tooth end reliefs are known from helical gears and can also be implemented on double helical gears using any gear cutting process.

The combination of different modifications (see Figure 5) [4] also can be implemented with micrometer precision, especially through gear grinding, in particular the established profile grinding.

Figure 5: Deflections, thermal distortion, and the resulting lead modification [4].

More complex modifications that affect the entire tooth flank topology, such as twist or the generated triangular end relief GER (cp. Figure 6), can theoretically be realized using topological generating grinding (DFT) [5].

Figure 6: GER in combination with lead crowning and twist free [5].

The challenge in the practical implementation of generating grinding lies in the use of a grinding worm with a very small outside diameter, which is determined by the gap width on the double helical gear; 4- or 5-axis milling has significantly more manufacturing options and degrees of freedom when designing the tooth flank topography.

2 Machining of herringbone gears

Only gear planing (otherwise known as rack-type shaping), gear shaping and 4- or 5-axis milling can be used to manufacture herringbone gears. Gear planing is being replaced more and more by gear shaping on machines with an electronic helical guide and 4- or 5-axis milling, because the corresponding planing machines, i.e., from the Maag company [6] have not been manufactured for decades.

2.1 Green machining by gear shaping

In the past, herringbone gears were mostly shaped on special herringbone gear-shaping machines. They were often carried out in a horizontal construction, i.e., the workpiece was clamped horizontally for machining (see Figure 7, left), which means the axis of rotation of the gear is also horizontal.

To generate the left and right lead direction, complex mechanical helical guides were used, which allowed the reciprocal shaping (pushing and pulling) over the radial infeed. In this way, the left and right helical gear was generated on the herringbone gear more or less simultaneously (see Figure 7, right).

Figure 7: Special herringbone gear-shaping machine from 1960 and reciprocal shaping [7].

Current and modern gear-shaping machines are usually built in a vertical design with only one shaping spindle. This results in the following machining scenarios for herringbone gears, which also apply to the double helical gears with a gap:

  • Gear shaping of the first gear, turning around the workpiece, shaping the second gear.
  • Gear shaping of the first gear and up-shaping of the second gear.

Depending on the face width, the two necessary shaper cutters can be clamped in one tool holder (see Figure 8). If the face width is too large, the shaper cutter must be changed.

Figure 8: Down- and up-shaping in one clamping.

For shaping herringbone gears, which do not have a tool overrun, it is necessary to use a shaper cutter with a special sharpening in the transverse plane (Figure 9). The shaper cutter has a flute on one side of the rake face, which ensures the chip is rolled up to save space. A chamfer is attached to the opposite side of the shaper cutter, which guides the cutter with stability along the tooth gap due to the high deflection forces encountered when cutting the workpiece material.

Figure 9: Special sharpening in the transverse plane on a shaper cutter [7].

2.2 Multi-axis milling enables both green and hard machining

Herringbone gears can be manufactured on universal turning-milling centers or 4- or 5-axis machines [8]. The gears are created with universal end mills. The required cutter paths are calculated using a CAD/CAM system. Flexible profile and lead modifications can be implemented very easily with this method. Because of this, multi-axis milling is ideal for single-part production and small quantities. Hard machining is also possible. The surface and gear quality achieved with an optimized process is shown in Figure 10.

Figure 10: Hard machining of a herringbone gear.

3 Green machining of double helical gears

3.1 Form milling and hobbing also in combination with 4-axis milling

Very often, double-helical gears have a very small gap or in case of a herringbone gear no gap at all. But in those cases, where the gap is big enough, hobbing or even form milling (sometimes referred to as gashing) can be applied [9]. Usually, there is a hard-finishing process after the hobbing operation, because the grinding discs or grinding worms in the dimension of the hob diameter can be used. In general, hobbing is preferred compared to single index milling due to the faster cycle time and longer tool life. But especially at larger modules, form milling to rough cut the two gears can be beneficial, even if the longer tool life of the hob is not sufficient to cut both gears without a re-sharpening. Since both processes — hobbing as well as form milling — are much faster than 4- or 5-axis milling, they should be applied, if possible or feasible.

Figure 11: Gear hobbing of double helical gears.
Figure 12: 4-axis milling of double helical gears.

It is also possible to apply hobbing or form milling to double helical gears with very small gap sizes, but then the profiling of two gears cannot be completed because of the insufficient tool overrun. The process has then more the function of a roughing process to reduce the tool wear of the roughing tools in 4- or 5-axis milling. Theoretically, this pre-machining should also reduce the necessary cutting time for the following 4-axis milling process, but it makes programming and processing much more complicated, so this is not very common.

Although the 4-axis milling of gears is an especially interesting alternative for producing herringbone or double helical gears, it can also be applied for “standard” cylindrical gears, e.g., for prototypes or single piece production.

Of course, 4-axis milling leads to much longer cycle times compared to hobbing or form milling but is still much more productive than traditional planning. The main advantage is it usually requires only standard respectively on-stock tools. Thus, the production of the parts can start almost immediately without any longer delays, which reduces the lead time a lot.

An example of such standard tools being used for 4-axis milling are shown in Figure 13. Besides the end mills of different diameters for roughing, the radius cutters for machining the root area plus end mills for the finishing are shown.

Figure 13: Standard tools for gear manufacturing.

Due to long cycle times, the high-quality demands of gears are a challenge to the machine tool builders regarding the accuracy and the thermal stability of the accorded machine tools. Machines for gear hobbing and gear milling are built for the highest productivity and the highest quality demands but have been limited regarding their applicability for herringbone or double helical gears with small gap sizes. In order to eliminate this disadvantage, conventional hobbing machines can be equipped with an additional 4-axis milling head (See Figure 14).

Figure 14: Milling head for external and internal gears.

The main feature of this milling head is the very long Y-axis that moves the spindle and the tool tangential to the workpiece. When using cylindrical end mills, this long Y-axis offers the possibility to always position the cutter tangential to the involute profile of the gear to be cut, while keeping the cutter axis parallel to the center distance. Since this cutting strategy takes advantage of the principle of the base-tangent and thus the span-size-measurement, any change in the center distance e.g., due to thermal growth, has no impact on the accuracy of the cut involute. Obviously, this is especially important if the cutting times are very long, which is typically the case in 4-axis-milling of such big gears. Thus, while conventional machining centers are using an additional axis to swivel the tool and make a real 5-axis-machining, the above-mentioned milling head uses only 4 axes to take maximum benefit of the special mathematical properties of the involute. So effectively, the machine is “only” a 4-axis-milling machine, which — in this case — is not a drawback but a proof for deep technological and mathematical understanding of the fantastic benefits of involute form for gear teeth. The second feature of the milling head is the additional internal milling device (to be seen on the right side of the milling head), which can handle end mills or form tools to cut keyways or internal splines. Thus, the external gear can be cut in the same setup with the internal contour to transfer the torque to the shaft. As an application example, the Figure 15 shows the successful machining of a big module double-helical pinion with a module of 25.4 mm (DP 1). This underlines the ability of the milling head and the according machine to handle not only big diameters but also bigger modules. The cutting time of about 24 hours might seem very long, but compared to the traditional shaping or planning process, which takes several days, it can still be considered to be “very fast.”

Figure 15: Application example of a double helical gear (m25.4 DP1).

To underline the accuracy of the machine, the achieved quality is AGMA grade 13-15. Compared to a typical requirement of AGMA 10, this was easily exceeded. When considering the long machining time, the excellent achieved quality level very much proves the functionality of the applied cutting strategy toward thermal stability. As an add-on, the gear teeth can also be deburred and chamfered by using radius cutters in the same setup. This is helpful since the chamfering on such gears is usually done manually, which is demanding and time consuming, especially on typical gears with hundreds of teeth. More details about this machine and additional application examples can be found in [10].

3.2 Increased precision in gear shaping due to gear position measurement

When shaping double helical gears, the exact positioning of the two gears relative to each other often involves a great deal of effort. In order to align both gears exactly to each other before the second machining step, their angular position (index) and their axial position must be precisely determined in an intermediate measurement so the so-called apex point is manufactured within the required tolerance. With conventional, mostly manual measurement technology, this is complex and requires a lot of experience on the part of the operator. This can result in inaccuracies due to alignment or handling errors. An essential part of the coordinated concept of machine, tool and technology is a measuring probe for the correction measurement in the machine, which ensures precision and process reliability.

The probe sits directly on the tool spindle (cp. Figure 16) and is in the same coordinate system as the shaper cutter itself. This reduces inaccuracies that can arise from a tool change or turning around the workpiece and leads to a significant increase in quality and process reliability. In combination with the NC-controlled axes of the shaping machine, a measuring accuracy of up to a few micrometers is achieved. At the same time, the amount of time and handling involved in aligning the two gears with one another is reduced. User-friendly software guides the operator through all process steps.

Figure 16: Measuring probe for position determination and associated process steps.

4 Generating grinding of double helical gears

In addition to multi-axis hard milling and profile grinding, generating grinding can also be used as a hard finishing method for double helical gears. The development of high-performance cutting materials enables the economical use of grinding worms with a starting outside diameter of 55 mm. Triangular or rod- shaped sintered corundum abrasives are used as cutting materials. CBN in electroplated and vitrified bonding [11] is also used. This makes continuous generating grinding in a module range of up to 5 mm a real alternative to established profile grinding. Generating grinding has the following advantages over profile grinding:

  • Significantly faster grinding times.
  • More robust against stock deviations and heat treatment distortions.
  • Lower risk for grinding burn.
  • Economic manufacturing of topological modifications, such as the generated end relief (GER), twist-free grinding (TF), etc.
  • Higher apex and indexing accuracy.
  • Very good single and cumulative pitch quality.
  • Potential for fine grinding and polishing for improved surface roughness.

4.1 Dimensioning and designing of grinding worms

The dimensioning and design of the grinding worm plays an important role in the generating grinding of double helical gears. One aim is to maximize the outside diameter and length of the grinding worm in order to obtain the most economical process possible. The focus is not only on the maximum tool life of the grinding worms. Especially when using grinding worms with small outside diameters, the number of workpieces ground within a dressing interval has a major impact on the proportional dressing time per workpiece and thus also on the total cycle time.

Due to the demanding geometric conditions with all their interfering contours such as the gap width, but also the gear tip diameter, a 3D machine workspace investigation in CAD is used after a simple static tool collision investigation. The latter provides an initial indication of the maximum possible outside diameter of the grinding worm as a function of the number of threads and the gap width. This is then precisely determined in the CAD system depending on the various shift positions.

Depending on the gap width, both gears of the double helical workpiece can be ground with one grinding worm. It should be noted that the tool/gear pairing with the opposite lead direction requires a larger tool overrun due to the larger swivel angle (cp. Figure 17).

Figure 17: Advantages and disadvantages of same and opposite sense of lead.

If this is too large for the given gap width, each gear must be ground with a grinding worm with the same sense of lead. This means the left-handed gear will be ground with a left-handed worm and the right- handed gear with a right-handed worm.

In the case of two grinding worms on a tool arbor, the necessary distance between the two grinding worms and their respective distance to the spindle bearings (main and counter bearing) is determined in the CAD. This then results in the possible total length of the grinding worms.

4.2 Demands on the gear grinding machine

In addition to a very good basic machine, two other requirements are of course very important for the successful implementation of generating grinding of double helical gears: First, a powerful and dynamically stiff grinding head that allows machining with both small and long grinding worms. Second, a software that, in addition to the data input and the mathematically necessary calculations for a double helical gear, also offers the possibility of correcting the two gears individually and the angular position to each other. All points can be achieved with the new designed grinding head GH 240 CB with the proven main and counter bearing design. The maximum spindle speed of 12,000 rpm as standard and 17,000 rpm as an additional option allow an economical cutting speed even with small grinding worm diameters. These high speeds make it necessary for the small grinding worms to be very precisely balanced, even if they are light in weight. This is guaranteed by a two-plane balancing system, which is fully integrated into the main and counter bearing spindle. (See Figure 19)

Figure 18: CAD workspace investigation for the exact determination of the grinding worm.
Figure 16: Measuring probe for position determination and associated process steps.

When developing the software, attention was paid to a simple and easily understandable input method and correction options. In conjunction with the grinding head, which can clamp two grinding worms with different lead directions, a precise process was developed for centering these grinding worms on the respective gears. When setting up the double helical gears, there is the option of first grinding both gears with allowance and aligning them to each other. It is important here that the measuring and reference planes specified on the technical drawings of the double helical workpieces with their measuring heights are also shown in the control (cp. Figure 20) and offset with any necessary corrections. The re-grinding function enables the production of a first part as a good part.

Figure 20: Screen shot of the newly developed software – Data input of the measurement heights.

4.3 Working example double helical gear with module 2.5 mm

The following machining example of a double helical gear with a module of 2.5 mm shows the potential of generating grinding. The two helical gears of the workpiece were each ground with grinding worms with the same sense of lead. Together with a three-thread worm, this leads to the lowest possible tool overrun and thus to a maximum usable outside diameter on the grinding worms of 60 mm for a double helical gear gap width of 26 mm. The total machining time including dressing and idle times is about 14 minutes.

Loading and unloading is done manually. In comparison, the double helical gear in the previous production was profile ground in 90 minutes and, depending on the distortion, even longer. (See Figure 21)

Figure 21: Technology for grinding a double helical gear.

The required gear quality 5 according to ISO 1328 was achieved on the double helical gear (cp. Figure 22). The individual and cumulative pitch achieved are within quality 2.

Figure 22: Achieved gear quality by generating grinding.

The arithmetic mean roughness value Ra is less than 0.4 µm (cp. Figure 23). And the achieved angular position of the two gears to each other is 18 µm or 0.008° in relation to the diameter of 221.9 mm.

Figure 23: Achieved surface roughness quality by generating grinding.

5 Summary

Herringbone and double helical gear are a special application but still can be found in many industrial sectors. From individual production, such as a spare part, to the production of larger quantities, all of these cases can be found in the worldwide gear market.

Table 1 lists the modern gear cutting processes for green and hard machining of double helical gears with their advantages and the qualities that can be achieved. The information in the table gives a rough guideline. Details and more precise information, e.g., the possible minimum gap width must be considered and clarified for each individual case.

Table 1

Multi-axis milling is ideal for single-part production, especially for herringbone gears or double helicals with minimum gap size. The possibility of hard machining is also an advantage of this process. Especially for larger workpiece diameters, the installation of an additional 4-axis milling head on a conventional gear hobbing machine for the single-part production of typical parallel axis gears and double helical gears is ideal. This combines the ability of highest productivity and quality by hobbing and form milling of usual gear designs with the ability of flexible, efficient, and precise production of special applications such as double helical gears. If applicable, the conventional milling head also can be used for roughing the gaps as far as possible before starting 4-axis milling. By using precise measuring sensors, the positional dependency of the two helical gears on the hobbing machines and now also on the gear shaping machines can be significantly improved. Positional accuracies of ±80 µm and better can be maintained during green machining.

If quality-enhancing hard fine machining is required, as shown in the report, continuous generating grinding with small grinding diameter worms up to a module range of up to 5 mm offers a very good qualitative and economically interesting alternative to established profile grinding.

With multi-axis, form milling, and hobbing as well as gear shaping, it is possible to replace the aging specialized shaping and planing machines for the production of herringbone gears. And the hard finishing was supplemented by generating grinding. The modern methods offer the chance to achieve better economic efficiency with higher accuracy. 


  1. Bennet, J. 2017, “Rolls-Royce Sets Record for Most Powerful Turbofan Gearbox In the World,” Popular Mechanics, Hearst Magazine Media, Inc., from gearbox-aircraft-engine/.
  2. ISO 1328-1:2013-09, Cylindrical gears – ISO system of flank tolerance classification – Part 1: Definitions and allowable values of deviations relevant to flanks of gear teeth.
  3. Beinstingel, A., Pinnekamp, B., Heider, M., Stierli, D., Marburg, S., July 2021, “A comparison of an analytical and FEA approach in determining thermal lead correction for high-speed gears,”
  4. Renk-Maag GmbH, Switzerland, “Turbo Gearboxes and its Applications,” from https://renk-
  5. Yoders, S., Mehr, A., 2016, “Efficient hard finishing of asymmetric tooth profiles and topological modifications by generating grinding ,” Fall Technical Meeting, American Gear Manufacturers Association, Pittsburgh.
  6. MAAG Zahnräder AG, 1985, Maag Handbook – Calculation and Manufacturing of gears in Theory and Practice, Second Edition, Zürich, Switzerland.
  7. Verzahntechnik Lorenz GmbH &Co, 1980, Gear Cutting Tools – Manual for Desing and Manufacturing, Third Edition, Ettlingen, Germany.
  8. Kawasaki, K., Tsuji, T., Gunbara, H., 2014, “Manufacturing method of double helical gears using a multi-axis control and multi-tasking machine tool,” International Gear Conference, Lyon, pp. 86–95.
  9. Wolff A., 2008, “Marine Gears – Technology of Cutting Wheel and Pinion,” Trends in Gear Soft Machining, Laboratory for Machine Tools and Production Engineering WZL, Aachen.
  10. Winkel, O., 2019, “5-axis-milling of cylindrical gears on gear cutting machines,” 7th International Conference on Gear and Drivetrain Production (GETPRO), Würzburg.
  11. Reimann, J., Mehr, A., Klocke, F., 2013, “Performance and Technological Potential of Gears Ground by Dressabel cBN Tools,” Fall Technical Meeting, American Gear Manufacturers Association, Indianapolis.

Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the American Gear Manufacturers Association. (AGMA) This paper was presented October 2022 at the AGMA Fall Technical Meeting. 22FTM12