Profile Grinding Large Diameter Gears

By large gear diameter, this paper refers to gears with a module of 12 and higher and diameters of up to 2000 mm or even larger in diameter. The main criterion is that these gears cannot be ground by continuous generating grinding as the path of contact between the threaded grinding wheel and workpiece exceeds the threaded grinding wheel's width.

Illustration 1: Two methods of gear grinding: generating and profile grinding

Illustration 2: Generating grinding vs. profile grinding

Large-diameter gears are found in steel and cement works, mining equipment, large ships, and wind turbines. This article focuses on gears for wind turbines, the most challenging application. Wind turbine gears are subject to the hardest performance standards. Such gears operate at 100 m or more above ground or sea level, often in remote and inaccessible areas. The transmissions of such gears accommodate rotating blades that form a diameter of 120 or more meters. At the time of writing, the largest wind turbine in operation is the General Electric Haliade-X, which stands 260 m (853 ft) tall and has a rotor diameter of 220 m (721 ft). As wind turbines are difficult and expensive to service, companies investing in this technology expect a service life of up to 40 years. For all these reasons, the quality of ground gears has to meet the highest criteria without any burning issues arising from grinding.

The wind turbine gears are made of high chromium and high molybdenum steels like AISI 4320, 4820, 9310, or DIN 17CrNiMo6, 18CrNiMo7-6. Such gears feature extremely large flank line modifications and tip reliefs to compensate for deflection and non-parallelism. These gears are always helical, and serious off-center crown grinding of the tooth geometry is applied to distribute the gear teeth's load properly. For general applications, gear flanks are designed symmetrically. This design means that both gear flanks have the same load-carrying capacity. However, in wind turbines, the gears?experience only uni-directional loading. In such cases, the geometry of the drive side need not be symmetric to the coast side. This fact allows for the design of?gears?with asymmetric teeth.

Illustration 3: Symmetrical and asymmetrical flank design

Gear ratios are up to 1:100, meaning a 15 RPM input is converted to a 1,500 RPM output for the generator. Let us assume a 200 m diameter rotor turning at 15 RPM to get a sense of the power and speed at play. These values result in a peripheral speed at the blade tips of 9420 m/min, which equals 157 m/s, almost half the speed of sound.

The latest wind turbine gearboxes feature up to three planetary gear stages and one or two normal gear stages. The main manufacturers of large wind turbines are the following companies: Siemens-Gamesa, MIH-Vestas, GE Wind Energy, and Dongfang Electric.

Gear profile grinding machines

The following three companies divide the market on the grinding machine tool side: Klingelnberg-H?fler, Kapp-Niles, and Gleason-Pfauter. The typical design of such machines and their axes layout can be seen in Illustration 4 of a Klingelnberg Rapid 2000 machine:

Illustration 4: Layout of a Klingelnberg machine, Rapid 2000, Source: Klingelnberg website, downloadable brochure (PDF)

Workpieces and gearboxes

The following Illustrations 5 and 6 have been added to show the sizes of workpieces and finished gearboxes.

Illustration 5: Planetary gearbox of wind turbine

Illustration 6: Size of turbine gearbox of Adwen AD 8-180 wind turbine

Illustration 6 above shows a gearbox developed by Adwen?and?Winergy, the ?AD 8-180 offshore wind turbine. With an input of close to 10,000 kilonewton-meters (kNm) and a weight of 86 tons, it is the largest wind-torque turbine gearbox ever built in the world. [2]

Gear geometry and terminology,

Clear and precise communication requires a common and shared vocabulary for gears - and everything else. For this reason, the following illustrations 7 to 9 may help:

Illustration 7: Gear Terminology

Illustration 8: Gear terminology

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Illustration 9: Gear Terminology

The most used parameter is the module mn or, for the USA, the pitch diameter DP. These values provide information about the size of the teeth. Together with the module, the number of teeth allows us to establish the gear diameter. Hence, a large module combined with many teeth results in large gear sizes. Inversely, small modules and a low number of teeth equal smaller gears.

?The module is defined by dividing the pitch by PI (π), whereby the pitch is the distance from a given tooth to the adjacent tooth, measured on the pitch diameter.

?The profile (involute) is the distance from the top to the root of the tooth. The profile is the most important value for the definition of gear quality as the meshing gear flank roll against each other to transfer the torque between two meshing gears. Furthermore, any noise (NVH) in the gearbox originates from the deviation of the involute profile during the meshing of a gear set. For this reason, the involute profile is the most widely observed parameter in gear manufacturing.

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Grinding wheels, Selection, and parameters

The author must concede that the best abrasive for large-diameter gear grinding is Cubitron II with precision-shaped grains, also called PSG. This abrasive is manufactured and sold by 3M. The only viable alternative to 3 M's PSG for profile grinding large diameter gears would be grinding wheels with extruded grain shapes, supplied by St. Gobain and 3M.

Illustration 10: Precision-shaped grain Cubitron II?

Illustration 11: Comparison of Cubitron 1 and Cubitron II

Illustration 11 shows the surface of two ceramic grinding wheels. "Ceramic" refers to sintered aluminum oxide. In the author's view, "ceramic" is an unfortunate choice of name as "vitrified" grinding wheels have ceramic bonds that hold them together. Hence, the word "ceramic" may lead to confusion.

Illustration 12: Chip formation of standard and precision-shaped grain?

As defined by DIN Standards, grinding is machining with undefined cutting edges. Since the arrival of Cubitron II, this definition no longer holds. Using standard grains, as shown on the left of Illustration 12, shows the chip forming mechanism of undefined cutting edges. In this instance, the process is divided into three stages: 1. Elastic deformation, 2. Plastic deformation, and 3. Chip formation. For Cubitron II, the first two stages are brief as the shaped grain instantly moves into chip formation, as shown on the right side of Illustration 12.

Wheel speed vc:

roughing: ???????????????????????????????????????24 to 30 m/s

finishing: ???????????????????????????????????????30 to 35 m/s

?As profile grinding has larger contact areas as one may imagine, particularly in the case of helical gears, surface speeds are low to ensure the self-sharpening of the grinding wheels. The effects of changing surface speed are listed in Illustration 13 below.

Illustration 13: Cutting speed vc

?Feedrate vw:

• Standard machines:?????????????????????3,500 mm/min
• H?fler Rapid series:?????????????????????3,000 to 5,000 mm/min
• H?fler Viper series:??????????????????????9,000 to 12,000 (18,000) mm/min
• Gleason-Pfauter Titan::???????????????9,000 to 12,000 (18,000) mm/min

The feedrates are a function of the speed ratio qs, i.e., the ratio between the wheel's surface speed vc and the feedrate vw. In this domain, two schools of thought prevail. The first one takes surface speeds vc of about 3'500 mm/min. The second approach uses very high surface speeds between 9'000 and 20'000 mm/min. Some 20 years ago, or even longer, H?fler showed that the risk of burning the gear flank could be reduced by increasing the feedrates to 9,000, and today, even much higher. The reason for high feedrates is related to the speed ratio qs. In many forms of grinding, including gear grinding, it has been shown that speed ratios between 120 and 1000 should be kept clear to avoid thermal damage issues. See Illustrations 16 to 17.

Illustration 14: Feedrate and reduction of burning risk

?Speed ratio qs

The speed ratio qs refers to the ratio of the grinding wheel's surface speed vc with the speed of the feedrate vw. If we imagine a single grain cutting into the workpiece and generating a wave pattern, as shown in Illustration 15, the lower the speed ratio, the bigger and wider the wave pattern becomes. At high speed ratios, the inverse is true, and finer surface finishes result. Hence, the speed ratio can be used to influence the surface finish. However, there are limitations, and one should not go below a speed ratio of 60 or above 120 to 1000.????????????????????????

Illustration 15: Speed ratio qs between the surface speed of grinding wheel vc & feedrate vw

Illustration 15 shows the usable ranges of speed ratios. The most critical area for burning is between 120 and 1000. This range should be avoided if possible. ?

Illustration16: Permissible ranges of speed ratios

The interplay of surface speed and feedrate results in the speed ratio. The table in Illustration 16 shows the ideal, good, critical, and "to be avoided" ranges.

Illustration 17: Table of speed ratios qs

?Unfortunately, for gear grinding with single rib wheels, this ratio is often between 400 and 600 and falls right into the middle of the critical ranges for the speed ratio. This fact may also explain why the chosen grinding fluid is restricted to pure grinding oil for gear grinding to reduce the risk of burning. Furthermore, this is also why H?fler has produced high-speed feed-rate machines that achieve feedrates of up to 18,000 mm/min (H?fler Viper & Gleason Pfauter Titan). This feedrate allows us to get near the lower end of the thermal risk area, as illustrated below:

?As seen in the following Illustration 17, a ?high feedrate vw of 12,000 mm/min brings down the speed ratio qs to 120, just below the burning zone.?

Theoretical average chip thickness hm

When looking at this parameter, the keyword is "theoretical," as nobody knows the true thickness of a chip and how it is formed as, during the grinding process, chips are compressed, pulled, and/or welded together. However, based on the machining kinematics and parameters, the chip thickness can be calculated theoretically, and a model can be constructed. The resulting model is used as a reference point as looking at many grinding processes, a range of thicknesses has been established. This range of chip thicknesses is as follows:

• ?Finishing:???????????0.10 μm
• Target:????????????????0.25 μm
• Roughing:??????????0.50 μm??????????????upper limit for standard abrasives
• Roughing:??????????0.60 μm??????????????upper limit for ceramic abrasives
• Roughing??????????0.80 μm??????????????upper limit for Cubitron II?

?Illustration 18: Guidelines to the chip thickness hm?

Experience has shown that at average chip thicknesses above 0.5 μm, the conventional grinding wheel structures are broken down. Inversely, at chip thickness below 0.1 μm, "rubbing" replaces chip formation and increases the danger of grinding burn.?

To calculate the theoretical chip thickness, the following formula, which calculates the material removal rate Q'w in the root, must be modified with the sine of the average involute angle (ae x SINα)

• ?ae = infeed (depth of cut) in mm
• vc = cutting or surface speed in m/s
• vw = workpiece speed in mm/min
• SINα = averaged involute angle (see Illustration 20)

Illustration 19: Averaged involute angle α?

Example: Calculation of chip thickness of a given gear:

• 31 teeth, Module 16, pressure angle 20°, helix angle 6.25°
• Radial infeed ae of 0.15 mm
• Feedrate vw of 12,000 mm
• Surface speed 35 m/s
• SIN of pressure angle 20° = 0.35?

Making allowance for the pressure angle of 20°:

In the above case, on the involute, the infeed (depth of cut) ae or the feed-rate vw can be increased until a chip thickness of hm 0.5 μm has been achieved.

?Specific material removal rate Q'w (Q-Prime) (also written Q’w) (mm3/mm/sec)

The specific material removal rate (also known as Q-prime) indicates how many mm3 one (1) mm wheel width removes per second (mm3/mm/sec). The following Illustration taken from surface grinding may give a better understanding of what is meant by Q'w. For the grinding processes such as surface reciprocating and creep-feed grinding, the calculation of Q'w is very simple: (depth of cut ae x feed-rate vw)/60.

MRR (Q’w or Q-Prime):

24 to 30 mm3/mm/sec (case-hardened)

?up to 50 mm3/mm/sec grinding from solid unhardened steel

(MMR stands for material removal rate)

The Q'w rate is a function of the feedrate vw and the depth of cut ae. Calculating Q'w seems straightforward.

This simple formula is also applied to profile gear grinding in many cases. However, as the involute describes a curve, this formula does not reflect the actual values at the individual contact point on the involute. The true depth of cut ae normal continually changes over the full length of the involute and corresponds to the actual radial infeed ae only at the root of the tooth gap. Furthermore, as shown in Illustration xxx, the contact area in profile gear grinding is considerable, with a substantial portion of side grinding. While this image shows a spur gear's contact conditions, the helical gears' contact areas are even larger.?

Illustration 20: Contact area in profile grinding

While one may come across material removal rates Q'w of 7 to 20 mm3/mm/sec, these values came about by the formula: infeed ae (radial) x workpiece speed vw/60.

For this author, this has been a point of contention for many years. This simple formula does not do justice to reality. For this reason, a piece of software was created which looks at five data points along the involute. It becomes easily obvious why the common formula for Q'w is misleading.

For a given gear, 31 teeth, Module 16, pressure angle 20°, helix angle 6.25°, and a radial infeed ae of 0.15 mm and a feed-rate vw of 12,000 mm/min results in a material removal rate of 30 mm3/mm/sec in the root and the material removal Q'w on the involute of only between 1 and 15 mm3/mm/sec.

Illustration 21: Q-Prime (Q'w) along the involute

Illustration 22: Material removal rate Q'w

However, the Q'w formula of Illustration 22 is only correct for the root of the gear gap. On the flanks, Q'w varies across the height of the gear tooth. At every point along the involute line, the pressure angle and the contact conditions change. The radial infeed ae generates a different normal infeed at every point of the height of the tooth, as shown in Illustration 24 below. A thick blue line represents the involute. Five points have been chosen along this line to show the different pressure angles. The angle varies between 8° and 39°. If we take a radial infeed of 0.3 mm as a baseline, the resulting infeed, or depth of cut ae, varies between 0.04 mm to 0.18 mm, by a factor of 4.5! These observations explain why burning often happens in the gear gap's root section. (Here at an angle of 8°). In this region, the grinding wheel is side-grinding and hardly removes any material. Consequently, the abrasive grain does not penetrate the material; only rubbing occurs and no self-sharpening.?

Illustration 23: Infeed ae in radial and normal direction?

To calculate the normal infeed, or depth of cut ae, on the flank, we have to multiply the radial infeed by the SIN of the pressure angle, as shown in Illustration 24.

Illustration 24: Radial vs. normal infeed

Depth of cut ae:

The depth of cut ae or in-feed is a function of Q'w. The depth of cut ae depends on the choice of the grinding process. The choice is between high-speed reciprocating feedrates and the slow feed rates of creepfeed grinding. Both methods have their advantages and disadvantages. Creepfeed combines a deep cut ae with a slow feedrate vw. Reciprocating grinding has shallow cuts in comparison but features much faster feedrates.

?The formula for Q'w on the flank of the gear:

Illustration 25: Reciprocating versus creepfeed grinding

Chip volume V'w

The specific chip volume is a parameter used with single rib wheels to determine dressing cycles. In other words, it has been determined how many mm3 one (1) mm wheel width can remove until a dressing cycle is initiated. ?

• v'w refers to the volume removed until redressing is initiated.
• v'w is given in mm3/mm (volume removed per mm wheel width)
• v'w roughing 2,500 to 6000 mm3/mm, whereas the high value of 6'000 requires Cubitron II
• v'w finishing 300 to 500 mm3/mm
• v'w finishing limited 100 (150) mm3/min for standard wheels.

The table in Illustration 26 lists the v'w value for different wheel specifications and whether the process is roughing or finishing?

Illustration 26: Dressing intervals based on the specific chip volume v'w

??For spur gears, the formula for v'w is as follows:

Whereas

• ae???????????= total radial infeed (mm)
• v'w?????????= removed material per mm wheel (mm3/mm)
• zb???????????= face width of gear (height of gear) (mm)
• z?????????????= number of teeth ground until dressing cycle (number)

?For the v'w of helical gears, the helix angle β has to be considered together with the face width to calculate the total length of the grinding gap:?

Whereas

• ae???????????= total radial infeed (mm)
• β????????????= helix angle of gear tooth
• v'w?????????= removed material volume per mm wheel width (mm3/mm)
• zb???????????= face width of gear (mm)
• z?????????????= Number of teeth ground until next dressing cycle (Number)

?Example: dressing after several tooth gaps z for a spur gear

• ae???????????= 0.15 mm
• v’w?????????= 3,000 mm3/mm
• zb???????????= 371 mm (face width)

After rounding off, in the above case, one would grind fifty-three tooth gaps and start a new dressing cycle.

Dressing of profile grinding wheels

The profile gear grinding wheels are dressed with dressing disks that use CVD diamond inserts. The following parameters are recommended:?

Roughing: Overlap ratio qd 1.5, dress ratio 0.6 synchronous

Finishing: Overlap ratio qd 4 to 6 (8), dress ratio - 0.6 to -0.8 asynchronous. In general, for Cubitron II, the dressing frequency and total dressing amounts are about half as conventional ceramics such as Cubitron 321.?

Illustration 27: Dressing with form rolls?

Illustration 29: dressing of conventional abrasives vs. dressing of Cubitron II ?

Cutting strategy for case-hardened gears:

For large diameter case-hardened gears, the following grinding strategy should be applied:

First pass roughing. (Grinding all gaps, 360° around the gear). Double-flank grinding (the grinding wheel simultaneously engages left and right flanks) is applied. The load is not very high at this stage as the wheel is not always in full contact with the gear flanks due to hardening distortions.

When talking about "passes," it refers to grinding all tooth gaps around a gear. This concept is clarified by the following Illustration 30, showing a gear with 12 teeth, hence 12 tooth gaps.

For helical gears, due to the helix angle β there are larger contact areas and a longer contact line than would be the case for spur gears, or even obvious to the unwary. The larger the contact line, the higher the cutting energy and the higher the risk of burning. Illustration 30 shows the contact line in a tooth gap.

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Illustration 28: Contact line of profile grinding?

Illustration 29: One-flank grinding versus double-flank grinding

Second pass roughing. Again, this is done in double-flank grinding mode. This second pass is the heaviest as the distortion should have been ground off in the first pass, and the wheel will now engage across both tooth flanks. The machine's amp meter may read up to 90% spindle load. While even the Cubitron II wheel may not exceed 90% loading, they work fine at that high limit. Note that the load should never vary by more than 10% between two dressing cycles.

Third pass equalizing. Now the process moves to single-flank grinding as the flanks feature a so-called twist or bias (a.k.a. as "twisted tooth phenomenon," which has to be corrected). The twist is a geometrical distortion of the involute form inherent in two-flank grinding. This error can be eliminated by simultaneous interpolating multiple axes in the gear grinding machine. However, only the single-flank grinding method can be used for this correction. The twist distortion only applies to helical gears. Spur gears, or straight gears, do not feature this complication.

Fourth pass finishing. Again, this is done in single-flank grinding to avoid gear twist. The finishing pass per tooth gap consists of one downward movement in the up-grinding mode and one upward movement in the down-grinding mode. Illustration 29 shows the influence of the four-pass strategy on the spindle load, the material removal rate Q'w, and the surface finish.?

Illustration 29: Four-pass grinding strategy

Down-Grinding versus up-grinding

At first glance, there may not be a significant difference between down-grinding and up-grinding. In down-grinding, the grinding wheel's starting position is below the workpiece. The grinding wheel's starting position is above the workpiece in up-grinding, as shown in Illustration 30.

The depth of cut ae can be taken in down-grinding or up-grinding mode. In down-grinding, the abrasive grain attacks at the full depth of cut, as shown in Illustration 33. The depth of cut gets shallower as the grain moves through the arc of contact. As a rule, down-grinding generates less heat, and if the grinding force on the spindle is measured, it uses about 10% less energy than up-grinding. In up-grinding, the abrasive grain gradually increases the depth of cut as it moves through the arc of contacts. This increase in the depth of cut generates more heat than in the down-grinding process. In down-grinding, the grinding wheel starts below the workpiece and moves up. In contrast, the grinding wheel starts above the workpiece and moves down in up-grinding, as shown in Illustration 31.

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Illustration 31: Down-grinding versus up-grinding

Illustration 32: Down-grinding and up-grinding

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Cutting strategy for non-hardened gears ground from solid

For this process, creepfeed grinding has shown to be the ideal solution. Creepfeed is defined by slow feedrate vw and deep cuts ae, as is shown in Illustration 25.

?Grinding fluid delivery

Gear grinding uses pure oil, never water-based coolants. As in other forms of grinding, the coolant jet should have the same speed as the grinding wheel's surface speed. Preferably, there should be a nozzle for each gear flank and a separate nozzle for the tip of the grinding wheel to cool the root of the tooth gap properly. Additional cleaning nozzles are also recommended. It is ideal to have nozzles on the gear's top and bottom, as shown in Illustration 33.?

Illustration 33: Grinding fluid delivery

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Walter Graf, The Philosopher's Grindstone, Copyright September 2022