Producing gear teeth with high form accuracy and fine surface

finish using water-lubricated chemical reactions

K. Oobayashia, K. Iriea, F. Hondab,*

aAISIN AW CO., LTD, 10 Takane, Fujii-cho, Anjo, Aichi 444-1192, JapanbToyota Technological Institute, 2 Hisakata, Tempaku, Nagoya 468-8511, Japan

Abstract

A new method was investigated for high-accuracy fine finishing of gear teeth surfaces using a water-lubricated tribo-chemical technique. A

pair of shaved gears with rather low surface roughness was rotated in water lubricant for 30 min so that the gear tooth surface contacting the

mating tooth was ‘worn’ to a mirror surface and ideal tooth profile, due to the mechano-chemical mild erosion of the contact area. The wear

rate was 2.0 mm per 20,000 meshings, corresponding to a wear of one atomic radius thickness per meshing. Oxidation of the steel surface by

water molecules is proposed as the dominant wear process. Operation noise from the gear pair rotation was drastically reduced to lower than

about 10–15 dB compared to conventionally machined gear surfaces (30 dB in average), as a result of the wear of the tooth surface to form a

best-fit profile. The noise increased with further processing of the gear pair. Thus, there is an appropriate number of rotations for suitable

surface wear treatment. This new and simple procedure for surface treatment assures saving in energy, and does not require expensive honing

techniques or high-accuracy grinding tools.

The wear mechanisms used in this process are discussed along with the application of the technique to other processes for precision

finishing.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Water-lubrication; Tribo-chemistry; Mild wear; Fine finishing; Gear tooth; Low noise; Mirror surface

1. Introduction

For the machining of accurate and fine gear teeth, the

numerically best-fit profile of the tooth has been developed

using sophisticated calculations [1,2]. Manufacturing of the

tooth shape near a best-fit involute curve profile can be

carried out through the rough cutting, shaving, honing, and

fine finishing procedures using rather high-accuracy cutting

tools. Additional and final finishing involves a running-in

process to obtain the best-fit pair contact alignment and of

the lowest noise during gear revolution. Each of these

processes and the manufacturing time accounts for a great

percentage of the total energy of gear production. For

example, after the honing process, a variety of GRz 2.5 mm

still remains between the produced surface profile and the

numerically ideal one.

Only a small fraction of a tooth surface requires a high-

accuracy profile to contact the mating gear surface, so

0301-679X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.triboint.2004.08.022

* Corresponding author.

the high-accuracy finishing can be limited to a small contact

area. The remaining area (outside of the contacted area) on

the tooth can remain relatively rough.

The important parameter to monitor the fitness of the

surface profile is the noise level of the pair of gears in

operation. Many experiments and simulation studies [3]

have been carried out to reduce the noise level but are not

completed due to the non-linear combined effects of mutual

relationships among complicated shapes, vibration and

friction. An additional objective of the surface finishing of

the gear would be improvement of the mechanical strength

of the finished surface layers. A high-energy fluctuating load

applied to the gear tooth in operation induces surface fatigue

or undesirable exfoliation of the stressed dedendum surface

layers on the gear [4,5]. Micro-cracks on the machined

surface must usually be minimized to maintain the longer

service life of the gear.

In this report, we present the results of a wear process

by which a pair of gear teeth are worked in water, thereby

using the tribo-chemical oxidation for the fine machining.

Tribology International 38 (2005) 243–248

www.elsevier.com/locate/triboint

Fig. 1. Systematic diagram of the test bench for water-lubricated surface

finishing.

K. Oobayashi et al. / Tribology International 38 (2005) 243–248244

We monitored the wear rate as a function of the number of

teeth meshings and examined the wear process for obtaining

the best conditions for the oxidation reaction with water [6].

2. Experimental procedure

A pair of gears (120 mm in diameter) was mounted on a

bench tester designed especially for the tribological and

noise monitoring tests during rotation, using water as the

lubricant. The apparatus is designed to apply a variable load

between the drive and driven teeth (190–1500 N). Fig. 1

shows the schematic diagram of the tester. The geometric

alignment of the contacted position of each gear and the

distance between the two gears are adjustable. Distilled

water (1000 ml/min) was supplied continuously between the

mating gear teeth under contact. The gears were not

immersed in water, to avoid additional rotation resistance.

The applied load, rotation rate, and noise level were

measured continuously by sensors. The noise sensor signal

was analyzed in the range from 0 to 10 KHz at the point

closest to the gears.

The gears were made of alloy steel (JIS SCM420H

standard steel which almost corresponds SAE 5120, and

DIN 20CR4), forged, and shaved to a surface roughness of

Rz 2.5, and then carburized. The hardness of the curburized

surface was 750 Hv. After testing at a given rotation number

and load, the tooth surfaces were analyzed by a high-

accuracy profilometer, measuring surface roughness, wear

Fig. 2. Surface roughness of the water-finished gear tooth, along and across the p

grinding is presented for reference.

position and tooth profile at the contact area. The wear

position and profile of the contacted surface clearly showed

great changes as a function of the number of gear meshings

(i.e. calculated from the number of revolutions). The

numerically ideal involute curve of the gear was referred

to, in evaluating the wear surface.

3. Results and discussion

3.1. Surface roughness of worn teeth

The surface roughness of the water-lubricated gear tooth

(referred to as ‘tribo-assisted oxidation for fine finishing’:

TOFF) is shown in Fig. 2, compared with surfaces after the

procedures previous to TOFF. The first row in Fig. 2 indicates

the roughness along the profile direction (across the pitch-

line), and the second row indicates the lead direction (along

the pitch-line) of the tooth, together with the quantitative

expression of roughness Rz. These are results for a reference

condition of 500 rpm, 415 N of load, and 20,000 revolutions.

The contacted regions on the surface had a mirror surface (Rz

0.5 mm), much better than that before finishing (Rz 2.5 mm).

The mirror-smooth area expanded to a larger area by

increasing the number of gear revolution.

In Fig. 3, the profile of (a) the shaved surface is shown,

plus the results of (b) worn surface after 20,000 revolutions,

and (c) after 50,000 revolutions. The straight lines in Fig. 3

indicate the ideal involute curve. The involute curve is

exactly three-dimensional curve but mathematically

expressed by a straight line to simplify the deviation of

the measured surface from the ideal involute profile. Both

ends of the gear profile are manufactured to deviate largely

from the involute curve for smooth release of the load

during meshings. Therefore, a profile closest to the straight

line (excluding the both gear ends) in Fig. 3 is a best-fit

profile. A smooth profile closest to the ideal involute profile

was obtained between 15,000 and 20,000 revolutions. Over

this range, the entire tooth surface was smooth but the

profiles became worn beyond the calculated ideal involute

curve by 50,000 revolutions, as is shown in Fig. 3(c).

itch-line. Average surface roughness before finishing and after honing and

Fig. 3. Two-dimensional profiles of the water-lubricated gears as a function of the number of mesh contacts. Profiles across and along the pitch-line are

presented.

K. Oobayashi et al. / Tribology International 38 (2005) 243–248 245

Fig. 4 presents three-dimensional maps of the surfaces

(a) before water-lubrication and (b) after 20,000 evolutions

showing close to the best-fit profile, while (c) reveals

the over-worn surface after 50,000 revolutions. Fig. 4(b)

indicates that the suitably treated tooth surface is very

Fig. 4. Three-dimensional surface profile of drive and driven surfaces. Excess

smooth in local area with the mesoscopical roughness and

matches well macroscopic involute curve. In Fig. 4(c), the

roughness in local regions is still fairly smooth, but

measurements show high waviness especially in dedendum.

In addition to drive and driven gear surface profiles,

wear is observed after 30,000 mesh contacts with the mating gear tooth.

K. Oobayashi et al. / Tribology International 38 (2005) 243–248246

the third row in Fig. 4 indicates the mathematical

summation of the two surface profiles. Therefore, the third

row do not show any real gear profile but realizes that the

highest points in these maps are the closest points between

the gears which come into contact at first. The relatively

smooth surface suggests mild wear.

From the area of the mirror surface and profiles before

and after the wear-test operation, the wear rate was

determined within an accuracy of G0.1 mm. The load was

fixed here at 415 N. The observed result of this wear rate

was 2.0 mm per 20,000 revolutions, corresponding to a wear

of 0.10 nm thickness in the surface layer per revolution. An

average thickness of a single atomic radius of iron surface is

thus removed only from the meshing area of the tooth.

Fig. 5 shows the tooth profile after running under high

load of 1132 N. The worn surface area was larger under

increasing load in comparison with the results of the same

number of meshings and load of 415 N, as is shown in

Fig. 5(a) and (b). The wear rate, in term of thickness,

however, was almost the same, equivalent as determined by

the profile. Based on these results, the mating tooth surfaces

apparently were deformed under high load and that the area

of gear contact between the mating surfaces increased, yet

the wear ‘thickness’ on the surface did not change.

In the contact mode examined here, a tooth surface mates

once per gear revolution. The tooth pair in contact is not

fixed because each gear has different number of teeth.

The best-fit contact condition, therefore, is averaged on all

Fig. 5. Tooth profiles as a result of high load contact. The mirror-finish area increas

the tooth pair of the gear. It is reasonable to consider that the

highest spot on the tooth surface comes into contact

preferentially and undergoes mechano-chemical wear,

depleting layer-by-layer [7,8] beginning from the top-most

atomic layer on the tooth surfaces. By scanning electron

microscope (SEM) observations, at least, no etch pit or

micro-cracks were observed on the smooth contacted

surfaces. The time interval between each mating until the

next mating contact is 0.12 s at 500 rpm, and 0.01 s at

6000 rpm. This is long enough for the clean (intrinsic) iron

surface to react with the surrounding water molecules,

because the rate of water adsorption to a clean surface is

known to be of the order of 1 ms (1 Langmuir). The surface

top-most iron atoms are allowed to react with water

molecules during one turn of the gear mating contact, and

the reaction product layer is removed from the surface. We

assumed that the surface structure is composed of Fe–O or

Fe–OH bonds on the adsorbed surface of two-dimensional

layer, because two-dimensional adsorbed structure cannot

be defined as compounds such as FeO, Fe2O3, and Fe3O4

have been identified on the slid surfaces in water [6]. If

reaction products were accumulated as oxide layers and

formed crystalline oxides, multiplayer of oxides can be

removed from the contacted area, due to weak shear strength

in the oxide layers. In this contact condition, wear do not

proceed layer-by-layer and do not make smooth metallic

surface. In the relevant wear of gear surface, meshing

number determined the wear rate as half-monolayer per

ed with the load, but the wear rate was almost equal to the result at low load.

Fig. 6. The typical noise level observed on the test bench. First- and second-order noise decreased abruptly at minimum.

K. Oobayashi et al. / Tribology International 38 (2005) 243–248 247

contact of the iron surface, on an average. The wear

mechanism is still unclear by our experimental results but

the surface observations suggested the wear proceed layer-

by-layer, which is different from the sliding tests in water.

3.2. Noise level of gear revolution

The ideal smooth profile produced a minimum noise

level under repeated meshing and unmeshing of the gear

teeth surfaces. The noise level could, therefore, be an

important diagnostic parameter in determining the most

desirable surface profile. Fig. 6(a) shows a typical result of

the first- and second-order vibration observed on the TOFF

tester. Starting from 25 dB of the first-order vibration, the

noise decreased to 12 dB at minimum, and the second-order

noise showed the same decrease to 20,000 revolutions. The

noise reduction of K13 dB on the test bench correspond to a

noise reduction from 96 to 85 dB in an automatic

transmission (AT) assembly (87 dB is the standard noise

limit for compliance). The minimum noise appeared after

about 20,000 revolutions from the test start for both

vibration modes in the case of Fig. 6(a), but in some

cases, the primary noise minimum was reached at 18,000

revolutions as shown in Fig. 6(b). For some specimens (c),

even two minimum stages appeared in the secondary noise.

If one presumes this to be due to some size-fluctuation

particular to various original specimens, at an average of

between 15,000 and 27,000 meshings, a minimum noise

would appear, and minor hump of secondary noise would

Fig. 7. Noise level observed on an automatic transmission assembly, after

finishing treatment on the test bench.

depend on the original surface profile. The noise drop by the

TOFF treatment was rather drastic compared to other

treatment such as honing and shaving, so the profile closest

to the ideal one was very effective for noise suppression.

When TOFF tested gears were placed into an AT

assembly, the noise level was found to be lower than with

conventional gears. This is shown in Fig. 7, which is a graph

of gear noise as a function of gear revolution rate. Within

the observed range of revolution rate, the noise levels were

suppressed satisfactorily, especially the sympathetic

vibrations at 700 and 1200 rpm. A small percentage of the

tested specimens, however, showed almost the same noise

level. This is probably due to misalignment of the gear pair

and/or inhomogeneous deformation during transfer from

the TOFF device to the AT assembly. The exact same

geometric configuration on a TOFF device is very difficult

to reproduce on the AT assembly; results showed some

fluctuation on the best-fit contact reproduction. As has been

indicated above, the best-fit profile of a tooth appears after

almost the same number of revolution: 15,000–22,000.

Thus, it is reasonable to consider that the three-dimensional

best-fit profile of the tooth produces the lowest noise

condition. Monitoring of the vibration in the TOFF

operation is therefore recommended.

Operation beyond the minimum noise stage resulted in

smooth surfaces but the worn profile emitted higher noise as

before the TOFF treatment.

In this report, we supplied plain distilled water to the gear

surface mating points so that the reactions with water were

obviously accelerated tribologically. In fact, an area on the

gear surface not contacted is not oxidized or worn visually

at least. No rust on the surface is observed after a few hours

of running water. The wear rate of plain distilled water was

suitable for controlling for the relevant purpose. For general

application of this finishing technique to other complex

shapes of surface and/or inner surface of work to be

polished, one could use combinations of planetary gears, or

smaller size rotators could be inserted inside the work.

4. Conclusions

When water-lubricated boundary condition was used

between gear teeth in finishing, a very smooth metallic

surface was obtained as follows.

K. Oobayashi et al. / Tribology International 38 (2005) 243–248248

(1)

The tooth surface was finished with a profile extremely

close to the numerically designed best-fit profile, or to a

profile of best-fit curve for a pair of gears. The mesh

contact had a mirror finish.

(2)

The wear of the tooth surface proceeded layer-by-layer

as a linear function of the number of mesh contacts and

preferentially at the contact point or area.

(3)

The noise level abruptly decreased from 25 to 12 dB on

the test bench at minimum, on the best-fit tooth profile

of the gear.

The new procedure introduced in this study reduced the

total energy for fine, high-accuracy finishing of gear teeth

and other surfaces, with applying minimum shear stress on

the surfaces.

Acknowledgements

The authors express their gratitude to AISIN AW Co, Ltd

and Toyota-Shokki Co Ltd, for their generous financial

support for our study.

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