The most exhaustive experimental study quantifying gear tooth friction is by Yoshizaki , in which spur gears with various geometries were operated in a power re-circulating test rig and frictional losses were measured. Various lubricants and additives were also evaluated and tooth surface finishes (Rmax) ranging from 0.5 to 4 μm were considered. In Britton , another experimental study, that specifically evaluated the effect of superfinishing on gear tooth friction on a power re-circulating gear test rig is described. A 30 percent reduction in frictional losses is measured and documented. In another experimental study on gear tooth friction, Petry-Johnson  measured frictional losses in a power re-circulating test rig operating ground and chemically polished gears with two different tooth sizes in three different lubricants. This data was further utilized to define guide lines for the design of gear meshes and transmissions. Martins  experimentally measured the friction coefficient in FZG (ground) gears utilizing two lubricants. Several attempts to model and predict the friction losses , ,  are also evident in literature, where the experimental effort is utilized to correlate to analytical results.
Based on the available literature, a comprehensive experimental study to compare gear mesh friction losses with different tooth surface conditions, different lubricants and under various operating conditions was considered a worthwhile effort. In this study, the special variables being evaluated include superfinishing and a W-DLC coating compared to a ground base line. Two lubricants are also evaluated.
A high-speed, power re-circulating (four-square) gear test rig was utilized for the purpose of this experimental study. This rig consists of a test gear box connected to a reversing gear box, as shown in Figure 1. An electrohydraulic torque applicator establishes and measures the torque within the four-square loop and consequently the load on the gear teeth. The motor driving the four-square kinematic loop is only supplying the power to overcome the frictional losses in the test gear box mesh and the reversing gear box mesh. This input torque, outside the four-square loop, was measured with a precision, bearing-less, digital torque-meter, under different experimental conditions to establish a comparative measure of the frictional losses in the test gear mesh under those experimental conditions.
As stated above the four-square gear test rig consists of a test gear box and a reversing gear box. The reversing gear box consists of very high accuracy helical gears with a face width of 100 mm. The gears in the test gear box are 28 teeth, 3.175 module, 20 degree pressure angle, 6.25 mm face width, spur gears fabricated from AMS 6308 steel, carburized and hardened to 60-64 on the Rockwell C scale. Due to the significant difference in face widths between the gears in the test gear box and the reversing gear box, gear failure in fatigue testing is restricted to the test gear box only. Figure 2 illustrates the test gears mounted in the test gear box with the direction of rotation illustrated by the arrow. Oil jet lubrication was employed in the tests and the “oil into the mesh” nozzle is at the bottom and the “oil out of the mesh” nozzle is at the top in Figure 2.
As the test gear box and the reversing gear box are dissimilar, the total frictional losses cannot be precisely assigned to either of the two gear boxes. However, a comparative estimate of changes in gear tooth frictional losses due to surface condition or lubricant change can be assessed. Further, an arbitrary assignment of frictional losses attributable to the two gear boxes allows an approximate assessment of the changes of frictional losses due to the variables of surface and lubricant.
The initial effort focused on characterization of the surface of the test gears. Negatives of the tooth surface were first fabricated using surface replication epoxy (accuracy experimentally verified to be better than 0.1 micron). These replicas were analyzed utilizing optical interferometry to obtain surface characteristics of ground, superfinished and coated gears. The results of the surface characterizations are summarized in Table 1 and are considered to be consistent with what is normally obtained in industry.
A typical data output from one test run is illustrated in Figure 3. The blue line represents the measured loop torque within the four-square test rig and the orange line represents the input torque as measured by the torque transducer on the power input shaft. This particular figure shows the input and loop torques while operating with superfinished gears at 8,000 rpm in SHC 626 lubricant. Depending on the test conditions and the thermal inertia of this test rig, the set up requires up to an hour of operation before the input torque stabilizes for measurement purposes.
The repeatability of the measurements was evaluated. Figure 4 illustrates torque recordings of three different repetitions of superfinished gears operating at 8,000 rpm in SHC 626 lubricant. The range of the stabilized input torque in the three repetitions was 0.09 N-m. This computes to less than +/-1% of the measured torque of 6.95 N-m and was considered acceptable. The tests conducted are detailed in Table 2 with their respective pitch line velocities.
Results and Discussions
In order to provide an adequate tribological basis for the collected data it was decided to compute and document the range of specific film thickness λ for the experimental effort . The bulk temperature of the gear tooth in mesh was interpolated from an earlier experimental effort  in order to obtain the lubricant parameter that is required for the computation of the λ ratio. Based on an oil inlet temperature of 40.5ºC, the range of computed λ ratios for the MIL-PRF 23699 lubricant ranged from 0.31 to 2.5. For the SHC 626 lubricant the computed λ ratios ranged from 0.50 to 4.3. The lowest λ ratios are associated with ground gears at high torques and low speeds while the highest λ ratios are associated with superfinished gears at low torques and high speeds. The λ ratios for the coated gears could not be determined due to lack of experimental data on tooth bulk temperature and lack of coefficient of friction data to compute the same.
Tests were conducted with the various gear pairs in the test gear box and under load, speed and lubricants as defined in Table 2. One typical set of results is shown in Figure 5. As can be seen from Figure 5, the ground gears had the highest measured input torque at all speeds at 192 N-m with MIL-PRF-23699 lubricant.
The results of all the tests conducted are summarized in Table 3. To examine these results analytically, the measured input torque for the ground gear pair was subtracted from the measured input torques for the superfinished and coated gear pairs, under the same load, speed and with the same lubricant. These changes in input torques can be entirely attributed to the change in the surface condition of the gear pair under test and the change in frictional losses at the tooth flank, as all test conditions are otherwise identical. The frictional loss changes range from -0.72 N-m (ID No. 6) to +0.08 N-m (ID No. 2), as shown in Table 3.
The superfinished and coated gears generally required lower input torques (compared to ground) except for one instance where the coated gear had a higher input torque (ID No. 2) than the ground gear set. As this experiment was the first test conducted with the coated gear, some “breaking in” of the coating may have influenced the measurement. If time and budget allowed, the test would be repeated with new gears for better characterization of the break in process or to confirm an anomaly in the data. The ground and superfinished gears were also new at the start of testing. No data was observed that would indicate a similar break in characteristic.
A comparison between superfinished and coated gears was inconsistent. In some instances the superfinished gears had a lower or the same input torque as the coated gear. In some instances the coated gear performed better with a lower loss measurement. The more viscous SHC 626 oil appears to play a greater role in reducing frictional losses at lower speeds and higher loads at the same speeds. The MIL-PRF-23699 appears to more effective at reducing losses at higher speeds and lower loads. As all other conditions are maintained the same, this difference in input torques at each speed, each loop torque and utilizing the same lubricant is entirely due to the changes in frictional losses in the meshing gear teeth mesh.
As the input torque measurement includes the losses in the reversing gear box, which is very dissimilar to the test gear box, an assumption on the amount of losses in the reversing gear box was necessary in order to compute the input loss change as a percentage of the loss with a pair of ground gears. Splits of 50% split and 67% in the losses between the test gear box and reversing gear box were assumed, with the 67% split being more appropriate (large face width, helical gears in the reversing gear box). The percentage reductions in losses are listed in %%0615_REM_Tab2%% based on the loss split assumption model. Based on a 67% split model, superfinishing alone provided a reduction in frictional losses of up to 26% (ID No. 5) while the addition of this coating increase this reduction to 28% (ID No. 6).
The test tooth surfaces were characterized after testing with the same tooth negative optical interferometry technique that was used for pre-test inspection. A reduction in surface finish (Ra) of approximately 0.005 to 0.010 microns was observed for both the superfinished and the W-DLC coated gears. A similar reduction was measured for the corresponding superfinished mate gears. The ground gears were damaged during the 10,000 RPM testing. As expected, the post-test surface characterizations of the ground gears showed an increase in roughness of 0.02 to 0.07 microns (Ra).
The impact of surface treatments such as superfinishing and coating on frictional losses is of significant interest since this loss is converted into heat that has to be accounted for. This experimental effort described above demonstrates that these surface treatments can reduce frictional losses by as much as 28% over ground gears, based on an assumption of the loss split between the two gear boxes on the four-square test rig. Considering that this reduction can be obtained at each gear pair and most gear boxes have many gear meshes, the total impact on the heat generated by the gear box can be significant. It is difficult to state, based on this study if W-DLC coating has any added benefit on frictional losses, though it may improve contact fatigue life and oil out performance of the gear pair.
In order to obtain a more precise estimate of the impact of the surface treatments on gear losses it is necessary to obtain an accurate measure of the losses in the reversing gear box. It would then be possible to isolate the actual losses in the test gear box. From a measurement of total losses a more precise estimate of changes in frictional losses due to surface treatments could be estimated. Identifying the losses solely in the test gear box and eliminating other losses would also lead to an estimate of the effective coefficient of friction at the tooth flank and the impact of the surface treatment on this parameter. This effort, to measure the actual losses in the reversing gear box of the four-square test rig and estimate the effective coefficient of friction at the test gear tooth flank, is currently underway.
The first two authors would like to thank REM Surface Engineering for supporting this experimental effort.
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** 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.