In the past, manufacturing straight bevel gears was only possible on dedicated machines, which is no longer the case thanks to a revolutionary new process. Gleason explains.

Bevel gears with straight teeth have an increasing popularity for certain applications. Before the development of the six-axis CNC machining process of straight bevel gears in 2006 by The Gleason Works, there was no modern machinery available to cut or grind straight bevel gears. In the past the manufacturing of straight bevel gears was only possible on specially dedicated mechanical machines. Such machines are by nature difficult to set up, with limited ability to precisely repeat the setup. Mechanical machine setup has historically been slow and time consuming. New developments allow the use of the straight bevel gear cutting system known as CONIFLEX on the PHOENIX® free form machine. This patented methodology takes advantage of the PHOENIX free form flexibility and reduces setup time to a minimum, while applying the CONIFLEX cutting system used previously on mechanical machines. The process introduced in 2006 was a wet cutting process, using traditional high-speed steel cutting tools.

CONIFLEX straight bevel gears are cut with a circular cutter with a peripheral blade arrangement. The CONIFLEX cutters are arranged in the machine under an angle of e.g. 24° to a plane that is perpendicular to the generating plane or cradle plane [1]. The upper cutter disc is inclined to point down with the cutting zone of the blades, and the lower cutter is inclined to point up (Figure 1). The blades of the lower cutter move through the gaps between the blades of the upper cutter while rotating, and vice versa. This pair of cutter disks and the arrangement in the cutting machine is called the interlocking cutter system.

Figure 1: Interlocking CONIFLEX cutters.

The upper cutter cuts the upper flank only, and is therefore equipped with blades that have their cutting edges toward the top of the figure. The lower cutter in turn cuts the lower flank and is equipped with blades that have their cutting edges toward the bottom of the figure. The two cutters generate a combination of profile and length crowning in the flank surfaces. A side effect of the cutter arrangement is a curved root line, depending on the cutter diameter.

The two cutters represent one tooth of a generating gear, which subsequently requires the setup possibilities for a variety of job designs. The cutters can be moved away from the center of the cradle to achieve a certain mean cone distance. Since the CONIFLEX flank line tangents point to the pitch apex, it is necessary to adjust the angle of the flank line tangent with the so-called space angle. To control the slot width using existing cutters, the cutters can be shifted independently apart or toward each other. Some CONIFLEX machines allow an additional freedom to adjust both cutters in order to modify the length crowning (swing angle). CONIFLEX is a completing process which, compared to spiral bevel gear wet cutting, is considered a rather fast process. Figure 2 shows a Gleason No. 2A CONIFLEX generator with the interlocking cutters engaged in a slot of a ring gear.

In the case of a 20° pressure angle system and a tilt angle of 20° for each cutter, the planes of the cutter disks would generate flank surfaces that consist of precise spherical involutes. However, in straight bevel gears a located flank contact is desired which leads to a modified cutter and cutter tilt design. If in the case of a 20° pressure angle system the tilt angle of the cutter disks is 24° and the cutting edge, rather then being part of the cutter disk plane, forms an internal cone of 86° cone angle (90°-4°), then the internal cone generates a certain length crowning. This effect, in connection with root angle tilt, is used to produce the crowning in straight bevel gears. As mentioned before, it is always a pair of cutters—one left hand, and one right hand cutter—that are required to realize the interlocking arrangement in the cutting machine in order to cut both flanks of a slot at the same time.

There is still a considerable demand for straight bevel gears and machines for their manufacture. However, there was never a full CNC machine developed to satisfy the present demand. Manufacturers of straight bevel gears were relying on remanufactured mechanical machines, some of which are equipped with partial CNC functions like cradle roll, sliding base, ratio of roll, and indexing. The reason why no CONIFLEX CNC free form machine was designed becomes evident after studying the geometrical concept in Figure 2. It is not possible to utilize a six-axis machine because of the double tilted cutter spindles and the interlocking cutter arrangement. To configure a regular six-axis free form machine with the CONIFLEX double spindle head including an automated head setup would have introduced six additional axes with complicated setup actuators. The cost to build such a machine is between 150-200 percent of today’s regular PHOENIX free form generator.

Figure 2: View into the work chamber of a Gleason No. 104 CONIFLEX machine [2].

Motivation of CONIFLEX Cutting on Free Form Machines

Manufacturers of straight bevel gears are mostly processing low quantities and a high variety of different designs. The applications are axle drives and differential gears for special equipment, machine tool applications, marine propulsion units, and aircraft actuation systems. The demand for higher quality straight bevel gears has been raised, together with the desire to apply a defined hard finishing method such as grinding.

Manufacturers with a high job variety and many changeovers between jobs would invest in a modern machine tool for their straight bevel gear needs if it was also possible to put the machine to different uses: e.g. to cut spiral bevel gears. A six-axis free form machine can present a tool in every desired position and angular inclination to a workpiece. This is the basis for the ideas that realized CONIFLEX cutting on PHOENIX free form machines. It is only possible to use one cutter, which makes the original completing process  “semi completing.” The PHOENIX cycle time in case of high-speed steel cutters is longer than in the mechanical machine because of the need to index twice around the circumference. However, it is still acceptable since the free form machine with direct spindle motors indexes extremely fast, and since the higher stiffness of a PHOENIX machine allows fast movements.

There are additional features like independent correction of upper and lower flank (even using different ratio of roll, root angle, tilt angle, and more), summary storage and fast setups, and the possibility to implement cutter disks with carbide tips that would allow a high speed dry cutting of CONIFLEX gear sets.

Figure 3: Vector diagram of CONIFLEX setup (upper cutter).

Conversion of CONIFLEX Summaries to PHOENIX Basic Settings

CONIFLEX summaries which have been calculated for the Gleason machine Nos. 2A, 102, 104, and 114 can be converted to general basic settings in order to perform CONIFLEX cutting on PHOENIX free form machines. The procedure that has been developed is as follows:

• Conversion of CONIFLEX summary into general basic settings;
• Conversion of upper and lower CONIFLEX cutter separately;
• Calculation of start and end roll angles;
• Calculation of setover phase angle between lower and upper cutting;
• Calculation of fin removal roll position;
• Calculation of vector feed angles in case of plunge-roll cycle.

CONIFLEX straight bevel gear cutting summaries that use interlocking cutters contain the following gear geometry relevant settings. The settings of group 1 are initially identical for the upper and lower cutter but may be changed in the course of contact optimizations on the mechanical machine. The settings of group 2 are always identical for the upper and lower cutter in the mechanical machine. In a free form machine all settings of group 1 and 2 may be changed in order to optimize a pinion or gear:

Summary Settings Group 1
Space Angle
Cutter Offset
Cutter Cone Distance
Cutter Swing Angle

Summary Settings Group 2
Cradle Test Roll
Work Test Roll
Start Roll Position
End Roll Position
Machine Root Angle
Sliding Base

For the correct positioning of the cutter in the machine, the tool related dimensions of group 3 are required:

Summary Settings Group 3
Actual Cutter Diameter
Cutter Reference Height

In order to convert a summary of a mechanical machine into basic settings, the machine constants of group 4 are additionally required:

Summary Settings Group 4
Cutter Tilt Angle
Swing Axis Constant
Cutter Gage Reference Radius

Figure 4: Cycle diagram mechanical machine (top) and free form machine.

With all the information from groups 1 through 4 available, the basic machine setup can be calculated according to the vector diagram in Figure 3. The first step after the cutter is positioned with the tip of the RW vector in the origin of the coordinate system (cutter axis parallel to Y-axis) is a cutter tilt rotation around the Z-axis, followed by a movement of the cutter tip RW to the cutter cone distance (vector Rm1). Then the cutter tip is moved in X-axis direction about the cutter offset ET and rotated around the Y-axis about Θs to achieve the space angle inclination. The lower diagram in Figure 3 shows the movement XB in direction of the Y-axis to the proper sliding base position. In some cases there is a swing angle setting (not shown in Figure 3), which requires an additional rotation of the cutter around the X-axis. Also, the adjustment of the work root angle is not shown in the diagrams; it requires a rotation of the work around the X-axis. A similar conversion is done for the lower cutter setup. Although initially the lower cutter arrangement is a mirror image of the upper cutter setup (mirror in a horizontal plane that contains the cradle axis), the conversions are done separately and independently. If corrections have been made to the theoretical summary the upper and lower cutter setup may differ from each other, and the independent conversion will correctly transfer those corrections into the free form machine setup [3].

Cutting Cycle and Generating Roll Strategy

A basic cycle comparison is shown in Figure 4. The upper diagram represents the cycle of a No. 102 CONIFLEX machine. Roll angle changes are plotted along the abscissa plunge advances of the cutter are plotted along the ordinate. The cycle starts with a first plunge, followed by a rough roll to the start roll position. The next step is a set in plunge to full depth, followed by a finish roll from the start roll to the end roll position. The cutter is then withdrawn to the index position, the cradle rolls back to center of roll and the indexing to the next slot occurs.

Figure 5: “Roll only” cycle.

The lower diagram shows the cycle of cutting the same bevel gear on a free form machine. The green vectors represent the cutting of the first cut lower slots. It begins at the right start position with a “roll only” motion from top to root (green start to green end) in the lower cutting position. Withdraw and lower index prepare the machine and tool for the next slot cutting. After all the flanks in the lower position are finished, a setover of the cutter in the upper position and a setover rotation of the work occurs. Now the cutter starts to approach the part with rapid roll first (air cutting) and the nominal roll rate from first cutting action to the end roll position.

The lower diagram in Figure 4 leaves some questions unanswered, such as how a cutter with only “outside” blades can perform a slotting operation without damage and how the roll angle required on a free form machine is related to the roll range of a mechanical machine with interlocking cutters.

As the lower slot is cut first it is important to approach the work with the cutter in a manner to prevent the cutting edge from any cutting action in the start roll position. Figure 5 shows schematic the cutter in the theoretical start roll position. In order to prevent this first contact, the roll angle for cutter tip clearance has to be calculated (about -5° in this example). The first rolling in the lower position is a roughing and finishing. The relative movement of the cutter versus the work piece leaves enough stock on the opposite flank for the upper rolling portion. It is also important that only the tip and the cutting edges of the blades are subjected to any chip load in order to prevent damage to the clearance side blade edges and assure an efficient and smooth cutting action. The process is repeated in the upper position (Figure 5) for the opposite flank. Since the slot already exists, the first move from the tool clearance position to the theoretical start roll angle can be faster than the active generating roll itself.

The root overlap and the additional roll angle between the clearance position and the theoretical start roll position will amount to about 65 percent of the mechanical machine’s roll travel.

Figure 6: Roll angle relation interlocking cutters versus single cutter.

Figure 6 shows the roll diagram for the interlocking cutters at bottom. To fully generate both flanks in case of a mechanical machine it is required to plunge at 0° and roll to +20° first (roughing) and then roll backwards from +20° to -20° which amounts to a total roll range of 60°. In a free form machine it is only necessary to roll either cutter through the required range for the particular flank, which is for the lower cutter from 0° to -20° of roll and for the upper cutter from 0° to +20° of roll, plus some root overlap and some additional roll for cutter clearance at the start roll position. This amounts to a total roll range of about 50° in the shown example. The possible different roll ranges in Figure 6 are:

Free Form Machine

• Seamless rolling between -20° to 0° of lower position and 0° to +20° of upper position
• Gap between lower and upper roll range
• Overlap between lower and upper roll range 

Mechanical Machine
• Plunge cycle at 0°, followed by a rough roll e.g. to +20°, followed by
• Roll from -20° to + 20° of interlocking cutters

Cycle times on modern free form machines are always expected to be lower than those on older mechanical machines. The interlocking cutter arrangement of the CONIFLEX machines involves two cutters simultaneously in the chip removing action. The free form machine uses only one cutter, and it therefore has only half the number of cutting edges in action (applying in both cases the same surface speed). This relationship would basically tell that the cutting time on a free form machine is about twice that of a mechanical machine. However, the two cutters of a mechanical machine are not always both part of the active chip removal except during the plunge part of the cycle. During the roll of flank No. 1, the opposite lower cutter idles with respect to chip removal. In case of rolling flank No. 2, the upper cutter does not remove any chips. The free form machine on the other hand constantly removes chips with its single cutter during the entire cutting cycle, which makes it an efficient process, but the cutting times are still 10-20 percent greater than the mechanical machine with interlocking cutters.

Figure 7: Basic machine setup: left generated, right FORMATE.

Conversion of CONIFLEX Summaries to PHOENIX Machines

In order to reduce the CONIFLEX cutting time, especially of the ring gear, a new feature of the Gleason CONIFLEX PHOENIX program was developed that allows the conversion of every suitable job into FORMATE™. A switch in the input screen can be set to “FORMATE” in order to establish the non-generated version of the job. This means the pinion is generated with additional profile curvature, using the ring gear as generating gear. The gear in turn is simply plunge cut, which greatly reduces the cutting time.

Figure 7 shows a graphic of the typical basic setting of the pinion that mates with a generated gear member at left. The generating gear is a flat disc that rotates around the Y4, five-axis in a plane, perpendicular to the paper, containing the Z4,5 axis. The FORMATE conversion rotates the pinion together with the cutter head and the connection of the cutter head to the cradle around an axis, perpendicular to the presentation plane (X4-axis) until the angle between the pinion axis Z1,2,3 and the cradle axis Y4, 5 is equal to the shaft angle between pinion and gear. In Figure 1 the Z1,2,3-axis matches the direction of the Z4-axis which delivers an inclination of 90° to the cradle axis Y4,5. In this case, the shaft angle between pinion and gear is also 90°. The generating gear is now the mating ring gear itself, which rotates around the cradle axis Y4,5 in order to generate the pinion flank surfaces.

The right configuration in Figure 7 allows users to calculate all required basic settings like cutter tilt and swivel angle, radial distance, and sliding base position. The ratio of roll is calculated from the number of teeth of the mating gear divided by the number of pinion teeth. If the ratio of roll was manipulated in the original generated summary in order to achieve the correct pressure angles, then an additional factor has to be considered to achieve the correct new pinion ratio of roll. In order to achieve the correct pressure angles in a case of non-matching blade and pressure angles in the non-generated ring gear, an incremental cutter tilt is applied.

Figure 8: Vector feed plunge cutting of FORMATE member.

In the FORMATE ring gear cutting process, first the lower position plunging is conducted while the tool is following a predetermined vector feed with a single ramp plunging feed rate (end chip). The plunge position at the bottom of Figure 8 already forms flank 1 and the corresponding root fillet area. It also removed enough material from the slot in order to justify finishing parameters in the upper position cutting, similar to the “roll only cycle.” The feed diagram in the center of Figure 8 shows a double ramp for the upper cutting with the first ramp being a rapid tool approach before tool contact occurs.

Figure 9 shows in the first vertical sequence a tooth contact analysis (TCA) for a generated CONIFLEX set. The TCA after the conversion into FORMATE (second sequence in Figure 2) shows more potential profile contact and lesser profile crowning. The third sequence in Figure 2 represents the TCA result of a profile crowning optimization using Modified Roll second order. All investigations with the new CONIFLEX FORMATE process showed that the transverse contact ratio increase and the rolling characteristics improve versus the generated version.


The new CONIFLEX®Plus cutter system is the world’s first peripheral stick blade cutter system with positive blade seating, which results in a great reduction in cutting time combined with improvements in gear quality and rolling characteristics. CONIFLEX Plus allows the use of coated carbide blades in high-speed dry cutting of straight bevel gears. The new process is at least three times as fast as the traditional cutting, avoids the use of any cutting oils, and only consumes about 25 percent of the electrical energy of straight bevel gear cutting, while at the same time presenting a significant leap in environmentally friendly manufacturing of straight bevel gears.

Figure 9: TCAs, top generated, middle FORMATE, bottom FORMATE optimized.

With the development of three sizes of CONIFLEX Plus cutters—4.25 inch, 9 inch, and 15 inch—the final step to a modern, economical straight bevel gear cutting process was concluded. Figure 10 shows the 9” version of the new cutter generation. The “iris” look of the blade ends at the inside of the peripheral cutter head achieves a higher number of blades in the cutter and preserves the blade length for a maximum number of resharpenings.

The cycle time improvements with the high speed dry cutting process of generated and FORMATE parts is reflected in the chart in Figure 11. In all real cutting applications, the significant cycle time improvement went along with better part quality. The new dry cutting process also provides the option (on the machine control) to remove the root fin in cases of small blade point or large slot width taper.

Figure 10: Top view (top) and front view (bottom) of new CONIFLEX Plus cutter.

It can be concluded that the time savings on CNC free form machines, with respect to setup changes during one work week and the productivity increase from the high speed dry cutting, may result in the replacement of up to 14 conventional straight bevel gear cutting machines with a single PHOENIX free form generator. 

Measurements Before Setup

As input items to the PHOENIX CONIFLEX summary, it is required to measure the stacking height of cutter and adaptor to gain the cutter reference height. Figure 12 shows the new Gleason peripheral cutter build stand. On the right side, a simple height measurement gauge is used to find the cutter reference height from the mounting surface to the blade high point. This is the only value from the actual cutter head setup, which has to be entered into the machine summary. The left side of Figure 12 shows the measurement and adjustment of the radial blade stick out. In case of CONIFLEX Plus cutters, the blades are always adjusted to the nominal diameter.

Figure 11: Cycle time improvements with CONIFLEX Plus tools.

In the case of solid high speed steel cutters, the actual outer diameter of the cutter has to be measured and entered into the CONIFLEX summary calculation program since it influences the basic settings. This measurement is done between two opposite blades using a vernier caliper and finding the high point, as shown in Figure 13.

TCA Flank Form Generation and Closed Loop Corrections

The CONIFLEX desktop software receives a transfer file from the Gleason Straight Bevel Gear Software and converts the mechanical CONIFLEX machine settings in PHOENIX basic settings. From this point the CONIFLEX software is used to conduct tooth contact analysis (TCA), undercut checks, and flank for generation, including a download file for coordinate measurement and flank form correction (G-AGE). Figure 14 shows a typical CONIFLEX TCA. The ease-off of the coast and drive side includes each length and profile crowning. The tooth contact patterns show a square contact pattern with a neutral bias path of contact direction. The G-AGE correction after manufacturing and 3D measurement cover all zero and first order geometry features (Figure 15). The corrective delta settings can be transferred to the manufacturing machine via flash drive or network in order to establish a closed correction loop.

Figure 12: Measuring of cutter reference height.

The results of an example correction of a spiral angle error on flank 1 and a spiral and pressure angle error in flank 2 are demonstrated in Figure 16a, Figure 16b. The CMM output graphic on top contains deviations in the vicinity of 18 microns. The selection in the correction interface for this case is:

• Spiral angle concave correction;
• Pressure angle convex correction;
• Spiral angle convex correction.

Even in cases of small or zero deviation on one of the two flanks, all correction switches in Figure 15 can be activated. A gear engineer often likes to address a single side or a single feature, however, which is possible by the activation of independent switches. The correction result is shown in the bottom portion of Figure 16b. This result is a good demonstration that CONIFLEX freedoms are ideal for flank form control without noticeable side effects.

Figure 13: Measuring of outer diameter.

Hard Finishing of CONIFLEX Gears

The PHOENIX method of cutting with a single cutter can be applied to grinding also. However, even with a single grinding wheel that duplicates the enveloping internal cone surface of the cutting edges, a major obstacle occurs with respect to the dressing removal and the compensation thereof. The cutting edges of a CONIFLEX cutter form an internal cone, which makes dressing in radial direction impossible, even if a diameter change was acceptable within limits. Also, dressing in the axial direction is not a possibility because the difference between maximal and minimal blade point would only allow a few re-dressings. Since the geometry changes due to redressing, thus eliminating the possibility of dressable grinding wheels, a permanent CBN coated steel grinding disk seems the only realistic tool for the task of grinding CONIFLEX gears.

A galvanically coated CBN steel wheel can be manufactured to duplicate the enveloping surface of the cutting edges in a free form grinding machine, which allows a defined hard finishing of straight bevel gears preserving the identical flank form. The grinding technology will allow the use of CONIFLEX gears in many applications where grinding as a hard finishing process is required, like in many aircraft gears. Often when straight bevel gears are the gears of choice for a certain application but grinding is required to fulfill the requirements in accuracy, ZEROL® gears are used instead because they are the closest to straight bevel gears. Ground straight bevel gears have been machined in the past on Maag two-wheel generators or on Heidenreich & Harbeck grinders until those mechanical vintage machines were not available anymore. Today’s demand in ground straight bevel gears could be covered with the possibility of CONIFLEX grinding. Figure 17 shows the first CBN coated grinding wheel (right) next to a 4.25 inch cutter.

Figure 14: Graphical results of a CONIFLEX tooth contact analysis.

Using the CONIFLEX Plus carbide cutter system for the soft cutting operation opens up a second hard finishing possibility, which is skiving using the same cutter head equipped with three-face ground carbide blades that feature a cutting edge facet with a 20° negative side rake angle. Particularly in the case of skiving it is important to apply the Gleason semi-finish strategy, which provides relief to the root fillet transition and also assures that the skiving blades will not cut with their tips at the root bottom. Those factors considered, skiving is the process of choice for the small batch manufacturer, because soft cutting and hard finishing can be performed on the same machine tool using the same cutter head with only the change of the cutting blades. This presents a minimal investment for the manufacture of high quality straight bevel gear sets.

CONIFLEX gear sets present many advantages in their geometry, some of which are controllable contact size and location. With the possibility of grinding or skiving of CONIFLEX gears, a complete new field of applications will open up for this revitalized and well-established kind of bevel gear.


In the past, the manufacturing of straight bevel gears was only possible on specially dedicated machines. One type of straight bevel gear is cut with a circular cutter with a peripheral blade arrangement. The machines and cutters used to manufacture these gears are known by the Gleason trademark, CONIFLEX. The cutters are arranged in the machine under an angle in an interlocking arrangement, which allows a completing cutting process. The two interlocking cutters have to be adjusted independently during setup, which is complicated and time consuming.

Figure 15: Measuring of outer diameter.

The outdated mechanical machines have never been replaced by full CNC machines, but there is still a considerable demand in a high variety of low quantities of straight bevel gears. It was recently discovered that it is possible to connect one of the interlocking straight bevel gear cutter disks to a free form bevel gear generator and cut straight bevel gears of identical geometry compared to the dedicated mechanical straight bevel gear generator. A conversion based on a vector approach delivers basic settings as they are used in modern free form machines. The cutter is mounted to a shaft, which is connected to the cutter spindle. Additional features like reverse cutter mounting, vector feed and root limited roll finally enabled the straight bevel cutting process on modern free form machines. The advantages are quick setup, high accuracy, easy corrections, and high repeatability.

Figure 14 shows a conventional 4.25 inch CONIFLEX cutter to the left, and a cutter with increased number of blades to the right. Since the interlocking principle is not utilized on the PHOENIX machines, it is possible to increase the number of blades and achieve a productivity level, comparable or even higher than on the conventional mechanical machines.

Because of the use of a single cutter disk, it is possible to grind CONIFLEX bevel gears on standard free form grinding machines. A second possibility of hard finishing is a skiving process which can be performed on the same machine as the soft cutting, using the same CONIFLEX Plus cutter heads equipped with specially ground and coated skiving blades.  


1) N.N., Operating Instructions for No. 2A Straight Bevel Generator, The Gleason Works, Rochester, New York, 1961
2) N.N., Calculating Instructions Generated Straight Bevel CONIFLEX® Gears (No. 2A, 102, 104, 114 and 134 Straight Bevel CONIFLEX Generators). The Gleason Works, Rochester, New York, 1961
3) Stadtfeld, H.J., Straight Bevel Gears on Phoenix Machines Using CONIFLEX Tools. Company Publication, The Gleason Works, Rochester, New York, 2007