Coe, H. H. | Engineering Papers

NASA NTRS1998

Effects of Planetary Speed Reduction Ratio on Mean Service Life

Planetary gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increase, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed reduction ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

NASA NTRS1998

Effects of Planetary Speed-Reduction Ratio on Mean Service Life

Planetary-gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed-reduction ratio, input speed, power and materials. The planetary-gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

NASA NTRS1996

Effects of Planetary Gear Ratio on Mean Service Life

Planetary gear transmissions are compact, high-power speed reductions which use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane transmission, the planet gear has no size at a ratio of two. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary with a fixed size, gear ratio, input speed power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

NASA NTRS1995

Bending strength model for internal spur gear teeth

Internal spur gear teeth are normally stronger than pinion teeth of the same pitch and face width since external teeth are smaller at the base. However, ring gears which are narrower have an unequal addendum or are made of a material with a lower strength than that of the meshing pinion may be loaded more critically in bending. In this study, a model for the bending strength of an internal gear tooth as a function of the applied load pressure angle is presented which is based on the inscribed Lewis constant strength parabolic beam. The bending model includes a stress concentration factor and an axial compression term which are extensions of the model for an external gear tooth. The geometry of the Lewis factor determination is presented, the iteration to determine the factor is described, and the bending strength J factor is compared to that of an external gear tooth. This strength model will assist optimal design efforts for unequal addendum gears and gears of mixed materials.

Savage, Michael↗

NASA NTRS1992

Maximum Life Spur Gear Design

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Savage, M.↗

NASA NTRS1992

Maximum life spiral bevel reduction design

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ratio under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed backcone distance of the spiral bevel gear set for a specified speed reduction, shaft angle, input torque, and power. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

Savage, M.↗

NASA NTRS1992

Maximum life spiral bevel reduction design

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ratio under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque, and power. Significant parameters in the design are: the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear, and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

Savage, M.↗

NASA NTRS1992

Optimal design of compact spur gear reductions

The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Savage, M.↗

NASA NTRS1991

Maximum life spur gear design

Optimization procedures allow one to design a spur gear reduction for maximum life and other end use criteria. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial guess values. The optimization algorithm is described, and the models for gear life and performance are presented. The algorithm is compact and has been programmed for execution on a desk top computer. Two examples are presented to illustrate the method and its application.

Savage, M.↗

NASA NTRS1991

Maximum life spur gear design

Optimization procedures allow one to design a spur gear reduction for maximum life and other end use criteria. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial guess values. The optimization algorithm is described, and the models for gear life and performance are presented. The algorithm is compact and has been programmed for execution on a desk top computer. Two examples are presented to illustrate the method and its application.

Savage, M.↗

NASA NTRS1986

Testing of UH-60A helicopter transmission in NASA Lewis 2240-kW (3000-hp) facility

The U.S. Army's UH-60A Black Hawk 2240-kW (3000-hp) class, twin-engine helicopter transmission was tested at the NASA Lewis Research Center. The vibration and efficiency test results will be used to enhance the data base for similar-class helicopters. Most of the data were obtained for a matrix of test conditions of 50 to 100 percent of rated rotor speed and 20 to 100 percent of rated input power. The transmission's mechanical efficiency at 100 percent of rated power was 97.3 and 97.5 percent with its inlet oil maintained at 355 and 372 K (180 and 210 F), respectively. The highest vibration reading was 72 g's rms at the upper housing side wall. Other vibration levels measured near the gear meshes are reported.

Mitchell, A. M.↗

NASA NTRS1986

Effect on interference fits on roller bearing fatigue life

An analysis was performed to determine the effects of inner-ring speed and press fits on roller bearing fatigue life. The effects of the resultant hoop and radial stresses on the principal stresses were considered. The maximum shear stresses below the Hertzian contact were determined for different conditions of inner-ring speed and load, and were applied to a conventional roller bearing life analysis. The effect of mean stress was determined using Goodman diagram approach. Hoop stresses caused by press fits and centrifugal force can reduce bearing life by as much as 90 percent. Use of a Goodman diagram predicts life reductions of 20 to 30 percent. The depth of the maximum shear stress remains virtually unchanged.

Coe, H. H.↗

NASA NTRS1985

Lubrication and performance of high-speed rolling-element bearings

Trends in aircraft engine operating speeds have dictated the need for rolling-element bearings capable of speeds to 3 million DN. A review of high-speed rolling-element bearing state-of-the-art performance and lubrication is presented. Through the use of under-race lubrication and bearing thermal management bearing operation can be obtained to speeds of 3 million DN. Jet lubricated ball bearings are limited to 2.5 million DN for large bore sizes and to 3 million DN for small bore sizes. Current computer programs are able to predict bearing thermal performance.

Zaretsky, E. V.↗

NASA NTRS1985

Effect of speed and press fit on fatigue life of roller-bearing inner-race contact

An analysis was performed to determine the effects of inner ring speed and press fit on the rolling element fatigue life of a roller bearing inner race contact. The effects of the resultant hoop and radial stresses on the principal stresses were considered. The maximum shear stresses below the Hertzian contact were determined for different conditions of inner ring speed, load, and geometry and were applied to a conventional ring life analysis. The race contact fatigue life was reduced by more than 90 percent for some conditions when speed and press fit were considered. The depth of the maximum shear stress remained virtually unchanged.

Coe, H. H.↗

NASA NTRS1985

Lubrication and performance of high-speed rolling-element bearings

Trends in aircraft engine operating speeds have dictated the need for rolling-element bearings capable of speeds to 3 million DN. A review of high-speed rolling-element bearing state-of-the-art performance and lubrication is presented. Through the use of under-race lubrication and bearing thermal management bearing operation can be obtained to speeds of 3 million DN. Jet lubricated ball bearings are limited to 2.5 million DN for large bore sizes and to 3 million DN for small bore sizes. Current computer programs are able to predict bearing thermal performance.

Zaretsky, E. V.↗

NASA NTRS1984

Thermal analysis of a planetary transmission with spherical roller bearings operating after complete loss of oil

Planetsys and Spherbean, two computer programs developed for the analysis of rolling element bearings, were used to simulate the thermal performance of an OH-58 helicopter main rotor transmission. A steady state and a transient thermal analysis were made and temperatures thus calculated were compared with experimental data obtained from a transmission that was operated to destruction, which occurred about 30 min after all the oil was drained from the transmission. Temperatures predicted by Spherbean were within 3% of the corresponding measured values at 15 min elapsed time and within 9% at 25 min. Spherbean also indicates a potential for high bearing cage temperatures with misalignment and outer ring rotation.

Coe, H. H.↗

NASA NTRS1983

Predicted and experimental performance of large-bore high-speed ball and roller bearings

The values of inner and outer race temperature, cage speed, and heat transferred to the lubricant or bearing power loss, calculated using the computer programs Shaberth and Cybean, with the corresponding experimental data for the large bore ball and roller bearings were compared. After the development of computer program, it is important that values calculated using such program are compared with actual bearing performance data to assess the programs predictive capability. Several comprehensive computer programs currently in use are capable of predicting rolling bearing operating and performance characteristics. These programs accept input data of bearing internal geometry, bearing material and lubricant properties, and bearing operating conditions. The programs solve several sets of equations that characterize rolling element bearings. The output produced typically consists of rolling element loads and Hertz stresses, operating contact angles, component speed, heat generation, local temperatures, bearing fatigue life, and power loss. Two of these programs, Shaberth and Cybean were developed.

Coe, H. H.↗

NASA NTRS1980

Calculated and experimental data for a 118-mm bore roller bearing to 3 million DN

Operating characteristics for a 118-mm bore cylindrical roller bearing were calculated using the computer program CYBEAN. The predicted results of inner and outer-race temperatures and heat transferred to the lubricant generally compared well with experimental data for shaft speeds to 3 million DN (25,500 rpm), radial loads to 8900 N (2000 lb), and total lubricant flow rates to 0.0102 cu m/min (2.7 gal/min).

Coe, H. H.↗