Windage Effects Research Articles

Investigations on the power losses and thermal effects in gear transmissions

It is generally accepted that the total power loss in gears can be decomposed into contributions of friction between the teeth, lubrication (churning and/or jet lubrication that could induce gas—oil trapping in inter-tooth spaces), and gear windage effects. For low- to medium-speed transmissions, tooth friction is recognized as the main source of dissipation for gears and can significantly influence the temperature equilibrium of a gearbox. In this article, a model to predict power losses due to tooth friction combined with a thermal network to describe the temperature distribution in a geared transmission are presented. The numerical results compare favourably with experimental measurements from a gear test rig.

Investigations on power losses in high-speed gears

Power losses in high-speed gears come from the friction between the teeth (sliding and rolling), the lubrication process (dip or jet lubrication), the pumping of a gas-lubricant mixture during the meshing, and the losses associated with windage effects. The authors have developed different approaches to analyse the contribution of each power loss source, namely: (a) the windage losses based on simplified air flow models neglecting the influence of the lubricant, which compare well with the experimental evidence from a specific test bench; (b) an original model of gas trapping in the intertooth time-varying spaces, which has been validated using the experimental findings on a spur gear test rig in which pressure transducers have been placed at the bottom of the space between two teeth; (b) tooth friction, by introducing into a three-dimensional dynamic model of gears a new traction law based on measurements from a two-disc machine which accounts for lubricant properties and surface finish. The combination of the three models allows for the prediction of gear efficiency over a wide range of speeds and loads for jet-lubricated geared units. This approach also makes it possible to improve tooth geometry and gearbox design to minimize power losses and heat generation. The procedure is illustrated in several industrial applications.

Windage Losses in High Speed Gears—Preliminary Experimental and Theoretical Results

Power losses in high-speed gears come from the friction between the teeth (sliding and rolling), the lubrication process (dip or jet lubrication), the pumping of a gas-lubricant mixture during the meshing and the losses associated with windage effects. The objective of this paper is to present a number of preliminary experimental and theoretical findings on the prediction of windage losses. Experiments were conducted on a test bench whose principle consists in driving a gear to a given speed and then measuring its deceleration once it has been disconnected from the motor. Results are presented for a disk and 4 different gears with no enclosure and in the absence of lubricant at speeds ranging from 0 to 12, 000 rpm. Two different theoretical approaches have been developed: i) a dimensional analysis based upon the dimensionless groups of terms which account for the flow characteristics (Reynolds number), the gear geometry (tooth number, pitch diameter, face width) and the speed, ii) a quasi-analytical model considering in detail the fluid flow on the gear faces and inside the teeth. It is found that both approaches give good results in comparison with the experimental evidence and two analytical formulas aimed at predicting windage losses in high-speed gears are proposed.

Flow and Heat Transfer in an Industrial Rotor-Stator Rim Sealing Cavity

Flow and heat transfer in the row-1 upstream rotor-stator disk cavity of a large 3600-rpm industrial gas turbine was investigated using an integrated approach. A two dimensional axisymmetric transient thermal analysis using aeroengine-based correlations was performed to predict the steady-state metal temperatures and hot running seal clearances at ISO rated power condition. The cooling mass flow and the flow pattern assumption for the thermal model were obtained from the steady-state two dimensional axisymmetric CFD study. The CFD model with wall heat transfer was validated using cavity steady-state air temperatures and static pressures measured at inlet to the labyrinth seal and four cavity radial positions in an engine test which included the mean annulus static pressure at hub radius. The predicted wall temperature distribution from the matched thermal model was used in the CFD model by incorporating wall temperature curve-fit polynomial functions. Results indicate that although the high rim seal effectiveness prevents ingestion from entering the cavity, the disk pumping flow draws air from within the cavity to satisfy entrainment leading to an inflow along the stator. The supplied cooling flow exceeds the minimum sealing flow predicted from both the rotational Reynolds-number-based correlation and the annulus Reynolds number correlation. However, the minimum disk pumping flow was found to be based on a modified entrainment expression with a turbulent flow parameter of 0.08. The predicted coefficient of discharge (Cd) of the industrial labyrinth seal from CFD was confirmed by modifying the carryover effect of a correlation reported recently in the literature. Moreover, the relative effects of seal windage and heat transfer were obtained and it was found that contrary to what was expected, the universal windage correlation was more applicable than the aeroengine-based labyrinth seal windage correlation. The CFD predicted disk heat flux profile showed reasonably good agreement with the free disk calculated heat flux. The irregular cavity shape and high rotational Reynolds number (in the order of 7×107) leads to entrance effects that produce a thicker turbulent boundary layer profile compared to that predicted by the 1/7 power velocity profile assumption.

Rotor Power Losses in Planar Radial Magnetic Bearings—Effects of Number of Stator Poles, Air Gap Thickness, and Magnetic Flux Density

Rotor Power losses in magnetic bearings cannot be accurately calculated at this time because of the complexity of the magnetic field distribution and several other effects. The losses are due to eddy currents, hysteresis, and windage. This paper presents measured results in radial magnetic bearing configurations with eight pole and 16 pole stators and two laminated rotors. Two different air gaps were tested. The rotor power losses were determined by measuring the rundown speed of the rotor after the rotor was spun up to speeds of approximately 30,000 rpm, DN = 2,670,000 mm-rpm, in atmospheric air. The kinetic energy of the rotor is converted to heat by magnetic and air drag power loss mechanisms during the run down. Given past publications and the opinions of researchers in the field, the results were quite unexpected. The measured power losses were found to be nearly independent of the number of poles in the bearing. Also, the overall measured rotor power loss increased significantly as the magnetic flux density increased and also increased significantly as the air gap thickness decreased. A method of separating the hysteresis, eddy current and windage losses is presented. Eddy current effects were found to be the most important loss mechanism in the data analysis, for large clearance bearings. Hysteresis and windage effects did not change much from one configuration to the other.

Comparison of Predicted and Measured Rotor Losses in Planar Radial Magnetic Bearings

The rotor loss mechanisms associated with magnetic bearings have yet to be adequately characterized or quantified and thus pose a problem for the designer and user of magnetic bearings. Accurate calculations of losses associated with the operation of magnetic bearings is particularly important for high speed applications where the rotor losses are expected to be large and for aerospace applications where low power consumption of components is critical. Rotor losses in magnetic bearings are due to both windage effects and iron losses. The iron losses are the result of three different mechanisms including the generation of eddy currents and the occurrence of both alternating and rotational hysteresis effects in the magnetic material. While theoretical models for these losses exist for transformer and electric motor applications, they have not been adequately modified for magnetic bearings. This paper presents the results from a low speed experimental test rig and compares them to calculated values from a new modification of previous theory. Experimental data was taken over a range of 1.5 Hz (90 rpm) to 46.7 Hz (2800 rpm) for several bias currents, two different pole configurations, and for both a linear power amplifier and a switching power amplifier. With certain assumptions, agreement between measured and calculated power losses was within 10 percent for speed comparisons greater than 25 Hz and within 25 percent for the comparison at the 8.3 Hz speed. This body of work represents the foundation for upcoming extensive high speed tests on a larger scale. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in San Francisco, California, October 13–17, 1996

Description and Performance of Finescale Drifters for Coastal and Estuarine Studies

The authors have designed and built a differential Global Positioning System (DGPS)-positioned Lagrangian drifter system to study complex nearshore, estuarine, and inner shelf flows with strong gradients and small scales. Various measures of the accuracy of the positioning system were assessed experimentally, as were the windage effects of antennas and floats. The DGPS-indicated position of a fixed drifter has a standard deviation of less than 1 m (over 600 samples) at a distance from the base station of up to 20 km. Windage effects are linear with a slope of about 0.002 drift-to-wind velocity ratio, which is about half the theoretical value.

Windage Heating of Air Passing Through Labyrinth Seals

The viscous drag on rotating components in gas turbine engines represents both a direct loss of power from the cycle and an input of heat into the secondary (cooling) air system. Hotter cooling air in turn means increased flow requirements. The effects of windage on performance are therefore compounded. To facilitate accurate temperature predictions of highly stressed components, information is needed on windage characteristics of all elements in the secondary cooling system. Much information is available in the literature for disks, cones, cylinders, bolts, etc., but little has been published on windage heating in high-speed seals. Results are presented for experiments carried out (at representative nondimensional conditions) on different designs of labyrinth seals. The results are compared with values calculated from the simple momentum balance theory suggested by McGreeham and Ko [13] and with several values determined from CFD analysis.

A Comparison of ship drift, drifting buoy, and current meter mooring velocities in the Pacific South Equatorial Current

In this note we compare mean seasonal cycles of zonal and meridional velocity in the Pacific South Equatorial Current based on current meter mooring data, drifting buoy data, and ship drift data. Monthly averages of ship drift and drifting buoy data were computed over 2° latitude by 10° longitude rectangles centered at the positions of multiyear current meter moorings near 0°, 110°W, and 0°, 140°W. All three representations of the flow field show the basic character of the annual mean and its variations, provided that the sampling characteristics associated with each measurement technique are taken into account. In particular we find that more than 15 days of drifter data (regardless of year) are required on a 2° latitude by 10° longitude basis to produce monthly mean estimates that agree with moored estimates to within about 5–10 cm s−1 rms. We also infer that windage affects climatological monthly mean ship drift velocities, although uncertainties in the data limit a precise determination of the windage magnitude. An upper bound appears to be about 3% of the surface wind speed, though the actual effect of windage may be considerably smaller.

Surface current distributions in the tropical Indian Ocean derived from compilations of surface buoy trajectories

Three different satellite‐tracked drifting buoy data sets are compiled and used to generate a monthly climatology of surface currents in the tropical Indian Ocean. Buoys were deployed between 1975 and 1987. The data density is maximum on and near the equator and decreases poleward. Drift characteristics of the different buoy configurations are compared using a structure function analysis. The differences in windage effects are consistent with the buoy designs and small compared with the signals studied. The currents in the tropical Indian Ocean during boreal winter and spring can be characterized as two counterrotating gyres. A southern clockwise rotating gyre bounded on the south by the South Equatorial Current (SEC) and on the north during winter by the Equatorial Countercurrent (ECC) and during spring by the Equatorial Jet (EJ). A northern counterclockwise rotating gyre is bounded on the south by the ECC and EJ, depending on season, and on the north by the North Equatorial Current (NEC). The two gyre systems break down during boreal summer. During this season, the SEC is located closer to the equator, and the NEC is replaced by the eastward flowing Indian Monsoon Current (IMC). The western boundary circulation becomes more complicated from late spring through early autumn with the observation of two intense smaller scale gyres. The large‐scale southern gyre reappears during boreal autumn with the reappearance of the EJ. The northern gyre begins to reappear in December, with the reversal of the IMC and the reappearance of the NEC. The monthly buoy speeds are compared with a monthly climatology generated from ship drift reports. Differences between the two climatologies are in general small except in regions of few trajectories. The annual cycles in amplitudes and phases of the major currents in the region are thus comparable.

Closure to “Discussions of ‘Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears’” (1975, ASME J. Eng. Ind., 97, pp. 1272–1273)

Closure to “Discussions of ‘Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears’” (1975, ASME J. Eng. Ind., 97, pp. 1272–1273)

Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears

Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears

Discussion: “Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears” (Akin, L. S., and Mross, J. J., 1975, ASME J. Eng. Ind., 97, pp. 1266–1272)

Discussion: “Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears” (Akin, L. S., and Mross, J. J., 1975, ASME J. Eng. Ind., 97, pp. 1266–1272)

Discussion: “Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears” (Akin, L. S., and Mross, J. J., 1975, ASME J. Eng. Ind., 97, pp. 1266–1272)

Discussion: “Theory for the Effect of Windage on the Lubricant Flow in the Tooth Spaces of Spur Gears” (Akin, L. S., and Mross, J. J., 1975, ASME J. Eng. Ind., 97, pp. 1266–1272)

Study of Lubricant Jet Flow Phenomena in Spur Gears

Lubricant jet flow impingement and penetration depth into a gear tooth space were measured at 4920 and 2560 using a 8.89-cm- (3.5-in.) pitch dia 8 pitch spur gear at oil pressures from 7 × 104 to 41 × 104 N/m2 (10 psi to 60 psi). A high speed motion picture camera was used with xenon and high speed stroboscopic lights to slow down and stop the motion of the oil jet so that the impingement depth could be determined. An analytical model was developed for the vectorial impingement depth and for the impingement depth with tooth space windage effects included. The windage effects on the oil jet were small for oil drop size greater than 0.0076 cm (0.003 in.). The analytical impingement depth compared favorably with experimental results above an oil jet pressure of 7 × 104 N/m2 (10 psi). Some of this oil jet penetrates further into the tooth space after impingement. Much of this post impingement oil is thrown out of the tooth space without further contacting the gear teeth.