Figure 4 shows that a small geometric variation in the bearing design can have a great influence on transition behavior. The transition velocity for the best design (inclination angle: 0.5°; slippage: 10%) is about 50% lower than for the worst in the Fig. (inclination angle: 1.0°; slippage: 20%). Assuming constant acceleration during a starting maneuver, the distance to be run under mixed-friction conditions is reduced by the factor 4.
Figure 4 “Border lines” for the transition between mixed friction and full film lubrication for different flat thrust cones based on the experimental data.
What’s more, it becomes obvious that the transitions observed in the test occur within a speed range that is significantly lower than the operational velocities for thrust cone bearings in ICGs (> 100 m/s), and even relevant for gearboxes running with roller bearings.
Gearbox Efficiency in Dependency of the Bearing Concept
To investigate the thrust cones’ ability to reduce friction losses in gearboxes based on roller bearings, a test gearbox (Fig. 5) has been set up. The gearbox is driven by an inverter-fed, asynchronous machine; a torque load can be applied by an adjustable mechanical break coupled to the output shaft. Input and output torque and the rotational speed are recorded via measurement shafts with integrated rotary encoders. Both power input and output can be calculated from the captured data. The difference between input and output is regarded as system losses of the gearbox and the reciprocal quotient as its efficiency. The system losses are the sum of losses caused by several gearbox elements. To evaluate the influence of the bearing concept on the system losses, the gearbox can be equipped with either a set of tapered roller bearings in O-arrangement, or with a combination of thrust cone and ball bearings. All other components contributing to the system losses — gearing, seals, oil level, etc. — are kept constant during the tests.
Figure 5 Test gearbox — equipable with tapered roller bearings (left side) or a combination of thrust cone and ball bearings (right side) as concept drawings (top) and assembled (bottom) (Ref. 6).
By varying torque load and drive speed, characteristic efficiency maps were determined for both bearing concepts (Ref. 6). As an example of the results gained in the comparative tests, efficiency values derived from recorded data at several load levels for drive speeds of 1,200 rpm and 2,400 rpm are plotted over the power input (Fig. 6). Even though the recorded input power values are not exactly the same for both bearing concepts, a benefit of the thrust cone solution is clearly recognizable. Interestingly, the difference between the power losses of the two bearing concepts is hardly varying with the input power. That indicates a nearly load-independent loss mechanism being responsible for the gap between the compared power loss characteristics. Such a mechanism might be explained by drag losses in the bearings, which are highly dependent on the roller geometry and nearly independent from load.
Figure 6 Comparison of the efficiency for a gearbox with tapered roller bearings and a gearbox with a combination of thrust cones and ball.
For all configurations in Figure 6 we can see that the efficiency increases with the transmitted power, since load-independent friction components gain higher weight only in partially loaded operation regions. The highest differences between the bearing concepts occur for both velocities in the lower loaded region. Assuming that other loss mechanisms, e.g. — the friction in the tooth contact — raise with the load, the importance of the nearly static difference between the bearing concepts due to the drag losses is shrinking. Nevertheless the use of thrust cone bearings leads to an average rise in efficiency for the plotted graphs of three to four percent; in the partially loaded regions ascents of about seven percent can be observed.
Bearable Load Under Mixed-Friction Conditions
Despite the achieved reduction of the transition velocity, there remains a speed range in which mixed friction occurs. A functional gearbox design demands thrust cone bearings that reliably endure the estimated mixed -friction phases in the product’s life cycle.
Since, as mentioned, the availability of data on acceptable loads for thrust cone bearings in open literature is limited, a second test series shall provide further insight in bearable loads and influencing parameters. The tests, conducted as well on the thrust cone test bench, are carried out with a constant rotational velocity that belongs to the mixed-friction speed range for all specimens in the transition velocity tests. Starting with a minimum load of 2 kN, the axial force applied to the probes is raised every 50,000 turns by 2 kN until the destruction of the running surfaces is detected or the surfaces withstand the maximum load of 100 kN and passed 2.5 million turns. During the tests cone angle, slip value and contact width are varied for specimens made of 30CrNiMo8 and 34CrMo4. Nitriding of the running surfaces is another parameter in the tests. A high increase of axial accelerations or torque values indicates the surface destruction. To prevent fluid damages the temperature on the contact surface is monitored; if it reaches a critical value, the tests are interrupted for cooling; high temperature-time gradients might indicate a surface destruction as well.
Even though the test series is not yet finished, first observations are nevertheless available. Most of the tested surfaces did not pass the full test cycle without failure. Table 1 presents the maximum load reached in the experiments for 16 specimens arranged as fractional factorial design. Additionally, the equivalent Hertzian pressure is calculated for each test.
The equivalent Hertzian pressure is a common tool for the dimensioning of thrust cone bearings (Refs. 3 and 5). Therefore the flat, conical running surfaces are assumed to be a Hertzian contact of two parallel cylinders with a length that equals the contact width between the thrust cone and the surface on the wheel. The radii of the cylinders are the perpendicular distance between the center of the contact zone and the rotation axis of their shafts.
The only design value for the bearable load of flat thrust cones known from open literature is 50 MPa (Ref. 3). The 16 tests presented clearly exceeded that threshold. Only in one case surface failure occurred at a pressure below 80 MPa; in all other cases the surfaces withstood a load higher than 150 MPa and failed at values three to six times higher than the value known from literature. In four cases the specimen endured the maximum test load of 100 kN without failure. To illustrate the influence of the design parameters under investigation, a main effects diagram is presented (Fig. 7).
Figure 7 Main effects on the bearable equivalent Hertzian pressure under mixed friction conditions based on data given in Table 1 for fractional factorial design of experiments. Note on material abbreviation: A stands for 34CrMo4; B represents 30CrNiMo8.
As expected, low slippage values and the nitriding of running surfaces have a clear, positive effect on the bearable equivalent pressure. The choice of material and the contact width seem to be less important for the contact pressure. Nevertheless the contact width is clearly connected to the absolute bearable load values, which can be seen by comparing the average axial force for both contact sizes (62.0 kN for the 10 mm tracks, and 87.5 kN for the 15 mm surfaces). The strongest effect on the equivalent pressure can be seen for the inclination angle. Interestingly, this parameter has a different emphasis than in the transition velocity tests described previously. While lower inclination angles appeared suitable for early full lubrication, contact with stronger inclined surfaces resists higher loads under mixed-friction conditions. A possible explanation for the observed effect could be seen in deformations induced by the high loads during the mixed-friction test. If the conical surfaces are flattened by the deformation, specimens with initially high inclination angles are hydrodynamically optimized, while the inclination disappears, or at least drops, under a critical minimum for specimens that already started with low angles. Further insight in interactions between the regarded parameters and a regression for their influence on the bearable loads shall be derived when enough tests are conducted to allow a full fractional analysis.
(Editor’s Note: This paper was written in the Spring of 2017. Since that time, the series of tests referred to in the “Bearable Load Under Mixed-Friction Conditions section beginning on page 55 has been completed and results are now available at https://doi.org/10.21268/20170718-120141.)
It must be stated that the values gained thus far should be regarded as a design aid while considering possible extreme load situations for the contact. A permanent bearing operation under the tested conditions does not appear reasonable, since the higher losses in a thrust cone bearing under mixed-friction will not in any way contribute to an efficient gearbox. For “normal” load situations the bearing should be designed for full-film lubrication by using numerical simulations. The presented tests reveal a remarkable load reserve for thrust cone bearings running temporarily under mixed-friction conditions — which is important in enabling a reliable application design.
Conclusions
The conducted experiments on the transition behavior to full lubrication have shown that the transition velocity is highly influenced by geometrical parameters. For flat running surfaces, low inclination angles, and low slippage support early full lubrication.
Comparative efficiency tests on a gearbox revealed a remarkable energy-saving potential for lower-load situations by replacing tapered roller bearings with a combination of thrust cone and roller bearings.
Under mixed-friction conditions thrust cone specimens withstood higher loads than expected by common design values. Nitriding of contacting surfaces and low slippage are suitable to increase the bearable equivalent Hertzian pressure. The surface inclination angle generates an interesting influence, since significant higher load values could be reached with greater angles under mixed-friction conditions. This observation makes a constant value for the equivalent Hertzian pressure, as proposed by literature to date, a doubtable design base. The presented mixed-friction experiments reveal a need for geometry-dependent limits. Furthermore, since lower angles encourage full-film lubrication, an optimization problem results for the design engineer, which might be solved by numerical simulations.
(For more details on the work presented in this article, particularly those pertaining to numerical simulations, can be go to: Hess, Marcel, 2018. Einsatz von Druckkämmen zur Effizienzsteigerung von schrägverzahnten Getrieben. Dissertation TU-Clausthal. ISBN 978-3-86948-624-6.)
Acknowledgements. Financial support from the German Research Foundation (DFG) Priority Programme 1551 Resource Efficient Constructional Elements is gratefully acknowledged.
References
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This paper was first presented at the International VDI Conference on Gears 2017, Garching/Munich [VDI-Berichte 2294, 2017, VDI Verlag GmbH] and is reprinted here with VDI approval.
Dr.- Ing. Marcel Hess studied (2004–2011) mechanical engineering at the Clausthal University of Technology. In 2017 his doctorate degree was awarded by the Faculty of Mathematics/Computer Science and Mechanical Engineering of the Clausthal University of Technology. He worked (2011–2017) as scientific assistant at the Fritz-Süchting-Institute for Mechanical Engineering of the Clausthal University of Technology. Beginning this year (2018), Hess has worked as management assistant at SincoTec Test Systems GmbH, Clausthal.
Prof. Dr.-Ing. Armin Lohrengel studied mechanical engineering at the Clausthal University of Technology and RWTH Aachen University. Until 1999 he was scientific assistant at the chair of machinenelements of RWTH Aachen University. The promotion took place over the life-oriented dimensioning of clutches. From 1999 he was head of machine development at Paul Hartmann AG, Heidenheim. Since 2007 Lohrengel has been a university professor (Department of Mechanical Engineering and Design) and director of the Fritz-Süchting-Institute for Mechanical Engineering of the Clausthal University of Technology.