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The Final Report on computational gear mechanics is presented. This is an expository report summarizing the research efforts and results. Research on gear geometry, gear stress, and gear dynamics is discussed. Current research and planned future efforts are also discussed. A comprehensive bibliography is presented.
The real noise reduction benefits which may be obtained through the use of one gear tooth form as compared to another is an important design parameter for any geared system, especially for helicopters in which both weight and reliability are very important factors. The design and testing of nine sets of gears which are as identical as possible except for their basic tooth geometry are described. Noise measurements were made at various combinations of load and speed for each gear set so that direct comparisons could be made. The resultant data was analyzed so that valid conclusions could be drawn and interpreted for design use.
Advanced-design spiral-bevel gears were tested in an OH-58D helicopter transmission using the NASA 500 hp Helicopter Transmission Test Stand. Four different gear designs were tested. The four designs tested were the current design of the OH-58D transmission, a higher-strength design the same as the current but with an increased fillet radius to reduce gear tooth bending stress, and two versions of a lower-noise design the same as the high-strength but with modified tooth geometry to reduce transmission error and noise. Noise, vibration, and tooth strain tests were performed and significant gear stress and noise reductions were achieved.
A comprehensive procedure in predicting faults in gear transmission systems under normal operating conditions is presented. Experimental data was obtained from a spiral bevel gear fatigue test rig at NASA Lewis Research Center. Time synchronous averaged vibration data was recorded throughout the test as the fault progressed from a small single pit to severe pitting over several teeth, and finally tooth fracture. A numerical procedure based on the Winger-Ville distribution was used to examine the time averaged vibration data. Results from the Wigner-Ville procedure are compared to results from a variety of signal analysis techniques which include time domain analysis methods and frequency analysis methods. Using photographs of the gear tooth at various stages of damage, the limitations and accuracy of the various techniques are compared and discussed. Conclusions are drawn from the comparison of the different approaches as well as the applicability of the Wigner-Ville method in predicting gear faults.
An advanced design methodology is proposed for the face-milled spiral bevel gears with modified tooth surface geometry that provides a reduced level of noise and has a stabilized bearing contact. The approach is based on the local synthesis of the gear drive that provides the 'best' machine-tool settings. The theoretical aspects of the local synthesis approach are based on the application of a predesigned parabolic function for absorption of undesirable transmission errors caused by misalignment and the direct relations between principal curvatures and directions for mating surfaces. The meshing and contact of the gear drive is synthesized and analyzed by a computer program. The generation of gears with the proposed geometry design can be accomplished by application of existing equipment. A numerical example that illustrates the proposed theory is presented.
Method of precise grinding of spiral bevel gears involves automated inspection of gear-tooth surfaces followed by adjustments of machine-tool settings to minimize differences between actual and nominal surfaces. Similar to method described in "Computerized Inspection of Gear-Tooth Surfaces" (LEW-15736). Yields gears of higher quality, with significant reduction in manufacturing and inspection time.
NASA-GRA computer program designed to solve for steady-state dynamic responses of multigeared rotor systems. Based on transfer-matrix method combined with harmonic-balance method. Includes accurate gear-mesh model for spur and helical gears, containing time-varying mesh stiffnesses, gear-mounting errors, and gear-profile errors. Also includes accurate disk model containing inertia-based dynamic coupling terms due to mass and skew unbalances and massless-elastic-shaft model and linearly coupled fluid-film bearing model. Written in FORTRAN 77.
This document presents an approach for modeling and simulating landing gear systems. Specifically, a nonlinear model of an A-6 Intruder Main Gear is developed, simulated, and validated against static and dynamic test data. This model includes nonlinear effects such as a polytropic gas model, velocity squared damping, a geometry governed model for the discharge coefficients, stick-slip friction effects and a nonlinear tire spring and damping model. An Adams-Moulton predictor corrector was used to integrate the equations of motion until a discontinuity caused by a stick-slip friction model was reached, at which point, a Runga-Kutta routine integrated past the discontinuity and returned the problem solution back to the predictor corrector. Run times of this software are around 2 mins. per 1 sec. of simulation under dynamic circumstances. To validate the model, engineers at the Aircraft Landing Dynamics facilities at NASA Langley Research Center installed one A-6 main gear on a drop carriage and used a hydraulic shaker table to provide simulated runway inputs to the gear. Model parameters were tuned to produce excellent agreement for many cases.
DANST is a FORTRAN computer program for static and dynamic analysis of spur gear systems. The program can be used for parametric studies to predict the static transmission error, dynamic load, tooth bending stress and other properties of spur gears as they are influenced by operating speed, torque, stiffness, damping, inertia, and tooth profile. DANST performs geometric modeling and dynamic analysis for low- or high-contact-ratio spur gears. DANST can simulate gear systems with contact ratios ranging from one to three. It was designed to be easy to use and it is extensively documented in several previous reports and by comments in the source code. This report describes installing and using a new PC version of DANST, covers input data requirements and presents examples.
The authors have extended the application of double circular-arc helical gears for internal gear drives. The geometry of the pinion and gear tooth surfaces has been determined. The influence of errors of alignment on the transmission errors and the shift of the bearing contact have been investigated. Application of a predesigned parabolic function for the reduction of transmission errors was proposed. Methods of grinding of the pinion-gear tooth surfaces by a disk-shaped tool and a grinding worm were proposed.
This paper describes a method that was developed to detect gear tooth damage that does not require a priori knowledge of the frequency characteristic of the fault. The basic idea of the method is that a few damaged teeth will cause transient load fluctuations unlike the normal tooth load fluctuations. The method attempts to measure the energy in the lower side bands of the modulated signal caused by the transient load fluctuations. The method monitors the energy in the frequency interval which excludes the frequency of the lowest dominant normal tooth load fluctuation and all frequencies above it. The method reacted significantly to the tooth fracture damage results documented in the Lewis data sets which were obtained from tests of the OH-58A transmission and tests of high contact ratio spiral bevel gears. The method detected gear tooth fractures in all four of the high contact ratio spiral bevel gear runs. Published results indicate other detection methods were only able to detect faults for three out of four runs.
A comprehensive procedure in predicting faults in gear transmission systems under normal operating conditions is presented. Experimental data were obtained from a spiral bevel gear fatigue test rig at NASA/Lewis. Time-synchronous-averaged vibration data were recorded throughout the test as the fault progressed from a small single pit to severe pitting over several teeth, and finally tooth fracture. A numerical procedure based on the Wigner-Ville distribution was used to examine the time-averaged vibration data. Results from the Wigner-Ville procedure are compared to results from a variety of signal analysis techniques that include time-domain analysis methods and frequency analysis methods. Using photographs of the gear tooth at various stages of damage, the limitations and accuracy of the various techniques are compared and discussed. Conclusions are drawn from the comparison of the different approaches as well as the applicability of the Wigner-Ville method in predicting gear faults.
An exploratory simulation study of a novel approach to pitch control for a tilt wing aircraft was conducted in 1990 on the NASA-Ames Vertical Motion Simulator. The purpose of the study was to evaluate and compare the handling qualities of both a conventional and a geared flap tilt wing control configuration. The geared flap is an innovative control concept which has the potential for reducing or eliminating the horizontal pitch control tail rotor or reaction jets required by prior tilt wing designs. The handling qualities results of the geared flap control configuration are presented in this paper and compared to the conventional (programmed flap) tilt wing control configuration. This paper also describes the geared flap concept, the tilt wing aircraft, the simulation model, the simulation facility and experiment setup, and the pilot evaluation tasks and procedures.
As part of a project to encourage the use of shape memory alloy actuators for space actuators, this mechanism uses a nitinol ribbon to provide the necessary motion to help retract the proposed extended nose landing gear (ENLG) for the space shuttle. Initial proof-of-concept design of the ENLG did not include the ability to retract the gear automatically. One proposed actuator for this purpose was designed at Johnson Space Center and uses resistive heating to rotate the ribbon around a cylinder. This rotation then allows the assembly to pull down a wedge that is used to hold the landing gear strut in place, thus returning the landing gear to its previous height before extension. The presentation will follow the design of this assembly from working with the nitinol ribbon to providing mechanical connections and allowing minimal friction for motion of three wraps around a cylinder. Also to be presented is preliminary work on design of a shape memory alloy gripper, a design project to demonstrate uses of NiTi.
In this report, we propose a new geometry for low-noise, increased-strength helical gears of the Novikov-Wildhaber type. Contact stresses are reduced as a result of their convex-concave gear tooth surfaces. The gear tooth surfaces are crowned in the profile direction to localize bearing contact and in the longitudinal direction to obtain a parabolic function of transmission errors. Such a function results in the reduction of noise and vibrations. Methods for the generation of the proposed gear tooth surfaces by grinding and hobbing are considered, and a tooth contact analysis (TCA) computer program to simulate meshing and contact is applied. The report also investigates the influence of misalignment on transmission errors and shift of bearing contact. Numerical examples to illustrate the developed approaches are proposed. The proposed geometry was patented by Ford/UIC (Serial Number 09-340-824, pending) on June 28, 1999.
Spiral bevel gears are an important drive system components of rotorcraft (helicopters) currently in use. In this application the spiral bevel gears are required to transmit very high torque at high rotational speed. Available experimental data on the operational characteristics for thermal and structural behavior is relatively small in comparison to that found for parallel axis gears. An ongoing test program has been in place at NASA Glenn Research Center over the last ten years to investigate their operational behavior at operating conditions found in aerospace applications. This paper will summarize the results of the tests conducted on face-milled spiral bevel gears. The data from the pinion member (temperature and stress) were taken at conditions from slow-roll to 14400 rpm and up to 537 kW (720 hp). The results have shown that operating temperature is affected by the location of the lubricating jet with respect to the point it is injected and the operating conditions that are imposed. Also the stress measured from slow-roll to very high rotational speed, at various torque levels, indicated little dynamic affect over the rotational speeds tested.
NA4 is a vibration diagnostic parameter, developed by researchers at NASA Glenn Research Center, for health monitoring of gears in helicopter transmissions. The NA4 reacts to the onset of gear pitting damage and continues to react to the damage as it spreads. This research also indicates NA4 reacts similarly to load variations. The sensitivity of NA4 to load changes will substantially affect its performance on a helicopter gearbox that experiences continuously changing load throughout its flight regimes. The parameter NA4 has been used to monitor gear fatigue tests at constant load. At constant load, NA4 effectively detects the onset of pitting damage and tracks damage severity. Previous research also shows that NA4 reacts to changes in load applied to the gears in the same way it reacts to the onset of pitting damage. The method used to calculate NA4 was modified to minimize these load effects. The modified NA4 parameter was applied to four sets of experimental data. Results indicate the modified NA4 is no longer sensitive to load changes, but remains sensitive to pitting damage.
The purpose of this paper was to verify, when using an oil debris sensor, that accumulated mass predicts gear pitting damage and to identify a method to set threshold limits for damaged gears. Oil debris data was collected from 8 experiments with no damage and 8 with pitting damage in the NASA Glenn Spur Gear Fatigue Rig. Oil debris feature analysis was performed on this data. Video images of damage progression were also collected from 6 of the experiments with pitting damage. During each test, data from an oil debris sensor was monitored and recorded for the occurrence of pitting damage. The data measured from the oil debris sensor during experiments with damage and with no damage was used to identify membership functions to build a simple fuzzy logic model. Using fuzzy logic techniques and the oil debris data, threshold limits were defined that discriminate between stages of pitting wear. Results indicate accumulated mass combined with fuzzy logic analysis techniques is a good predictor of pitting damage on spur gears.