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A procedure for computer aided design (CAD) of gear teeth is presented. It is developed for generated teeth fabricated by a hob cutter or a shaper. It provides a means for analytically and numerically determining the tooth profile, given the cutter profile. An illustrative example with involute tooth profiles is given. Application with non-standard profiles and with bevel, spiral bevel, and hypoid gears is discussed.
A computer-based analysis of the dynamic effects of spur gear systems is presented. The method of analysis with its associated computer code is capable of determining the dynamic response of spur gear systems having involute tooth profiles and standard contact ratios. Various parameters affecting the system dynamic behavior are examined. Numerical results of the analysis are compared with semi-empirical formulae, AGMA (American Gear Manufacturers Association) formulae, and experimental data. A close correlation with the experimental data is obtained.
How dynamic load affects the surface pitting fatigue life of external spur gears was predicted by using the NASA computer program TELSGE. Parametric studies were performed over a range of various gear parameters modeling low-contact-ratio involute spur gears. In general, gear life predictions based on dynamic loads differed significantly from those based on static loads, with the predictions being strongly influenced by the maximum dynamic load during contact. Gear mesh operating speed strongly affected predicted dynamic load and life. Meshes operating at a resonant speed or one-half the resonant speed had significantly shorter lives. Dynamic life factors for gear surface pitting fatigue were developed on the basis of the parametric studies. In general, meshes with higher contact ratios had higher dynamic life factors than meshes with lower contact ratios. A design chart was developed for hand calculations of dynamic life factors.
An analytical computer simulation program for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the static transmission error of the gears operating under load and uses a fast Fourier transform to generate the frequency spectrum of the static transmission error at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involute) gear pair was compared with that of gears with various profile modifications. Correlations were found between various profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain analysis of the static transmission error of the gears, gave a very good indication of the optimum profile modification to reduce gear dynamic loading. Design curves generated by dynamic simulation at various profile modifications are given for gear systems operated at various loads. Optimum profile modifications can be determined from these design curves for improved gear design.
A data base program to generate statistically significant material-property data for carbon-carbon and carbon phenolic materials to be used in designs of Space Shuttle is described. The program, which will provide data necessary for thermal and stress modeling of Shuttle nozzle and exit cone structures, includes evaluation of tension, compression, shear strength, shear modulus, thermal expansion, thermal conductivity, permeability, and emittance for both materials; the testing of carbon phenolic materials also includes CTE, off-gassing, pyrolysis, and RTG. Materials to be tested will be excised from Space Shuttle inlet, throat, and exit cone billets and modified involute carbon-carbon exit cones; coprocessed blocks, panels, and cylinders will also be tested.
The approximation of a nonlinear system by a feedback linearizable system instead of a linear system is considered. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation. The relationship between these two methods is shown. This provides insight into lower-order invariants in the equivalence problem for two nonlinear systems. The output time responses for a nonlinear system and its feedback linearizable approximation are outlined.
The vibratory excitation arising from a gear pair is widely recognized to be a consequence of the nonuniform transmission of motion by the gear pair. In the preceding paper in this issue, it is shown that a three-component transmission error is required to describe the nonuniform transmission of motion by bevel gears for vibration excitation characterization purposes. The expression for the three-component transmission error derived in that paper is combined in the present paper with an analysis of the mesh forces and mesh elasticity to yield an equation of constraint involving the six degree-of-freedom unknown vibratory displacements of the gear shaft centerliners, the three unknown components of the generalized force transmitted by the mesh, and the geometric deviations of the tooth running surfaces from perfect involute surfaces which are assumed known. This matrix equation can be combined with the equations of motion of a gear system to predict the vibratory response of the system to the generalized transmission error excitation arising from meshing gear pairs within the system.
A method of generating crowned pinion tooth surfaces using a surface of revolution is developed. The crowned pinion meshes with a regular involute gear and has a prescribed parabolic type of transmission errors when the gears operate in the aligned mode. When the gears are misaligned the transmission error remains parabolic with the maximum level still remaining very small (less than 0.34 arc sec for the numerical examples). Tooth contact analysis (TCA) is used to simulate the conditions of meshing, determine the transmission error, and determine the bearing contact.
The topology of a crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is described. The geometry of the modified pinion tooth surface and of the regular involute gear tooth surface is discussed. The tooth contact analysis between the meshing surfaces is also described. Generating a modified pinion tooth surface by a plane whose motion is controlled by a 5-degree-of-freedom system is investigated. The numerical results included indicate that the transmission error remains low as the gears are misaligned.
A method for generation of crowned pinion tooth surfaces using a surface of revolution is developed. The crowned pinion meshes with a regular involute gear and has a prescribed parabolic type of transmission errors when the gears operate in the aligned mode. When the gears are misaligned the transmission error remains parabolic with the maximum level still remaining very small (less than 0.34 arc second for the numerical examples). Tooth Contact Analysis (TCA) is used to simulate the conditions of meshing, determine the transmission error, and the bearing contact.
An analytical computer simulation program for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the static transmission error of the gears operating under load and uses a fast Fourier transform to generate the frequency spectrum of the static transmission error at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involute) gear pair was compared with that of gears with various profile modifications. Correlations were found between various profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain analysis of the static transmission error of the gears, gave a very good indication of the optimum profile modification to reduce gear dynamic loading. Design curves generated by dynamic simulation at various profile modifications are given for gear systems operated at various loads. Optimum profile modifications can be determined from these design curves for improved gear design.
The results obtained during the December 23, 1987 static firing of the DM-9 test article are presented. The DM-9 full-scale static test article employed redesigned solid rocket motor (RSRM) field joint capture feature hardware with J-seal insulation configuration, and nozzle-to-case joint radial bolt design with bonded insulation configuration. The nozzle incorporated RSRM components, including a thicker cowl with involuted outer boot ring. The nozzle employed redundant and verifiable seals in all five joints, and room temperature vulcanization backfill in three joints. With very few exceptions, the DM-9 test article was flight configuration. The test was conducted under extreme weather conditions: temperature of 25 F and wind at 15 to 20 mph. Ballistics performance values were within specification requirements. The RSRM field joint (J-seal) insulation configuration functioned as predicted with no indication of hot gases reaching the capture feature O-rings. There was a blowhole in the polysulfide adhesive in the nozzle-to-case joint, but no evidence of hot gases past the wiper O-ring. Nozzle design changes appeared to perform nominally, with the exception of the outer boot ring, which suffered partial structural breakup late in the test. Field joint heaters maintained the controlling resistance temperature device temperature within the specified requirements during heater operation. The thrust vector control system operated properly. The redesigned water deluge system, temperature conditioning equipment, and other test support equipment performed as planned.
Flex-Gears are being developed as an alternative to brushes and slip rings to conduct electricity across a rotating joint. Flex-Gears roll in the annulus of sun and ring gears for electrical contact while maintaining their position by using a novel application of involute gears. A single Flex-Gear is predicted to transfer up to 2.8 amps, thereby allowing a six inch diameter device, holding 30 Flex-Gears, to transfer over 80 amps. Semi-rigid Flex-Gears are proposed to decrease Flex-Gear stress and insure proper gear meshing.
Analysis of helical involute gears by tooth contact analysis shows that such gears are very sensitive to angular misalignment that leads to edge contact and the potential for high vibration. A new topology of tooth surfaces of helical gears that enables a favorable bearing contact and a reduced level of vibration is described. Methods for grinding of the helical gears with the new topology are proposed. A TCA (tooth contact analysis) program for simulation of meshing and contact of helical gears with the new topology has been developed. Numerical examples that illustrate the proposed ideas are discussed.
Analysis of helical involute gears by tooth contact analysis shows that such gears are very sensitive to angular misalignment that leads to edge contact and the potential for high vibration. A new topology of tooth surfaces of helical gears that enables a favorable bearing contact and a reduced level of vibration is described. Methods for grinding of the helical gears with the new topology are proposed. A TCA (tooth contact analysis) program for simulation of meshing and contact of helical gears with the new topology has been developed. Numerical examples that illustrate the proposed ideas are discussed.
During the year before launch, female frogs will be tested every 3 months for the quantity and quality of eggs produced. Two weeks or more prior to launch, male and female frogs will be transported to the John F. Kennedy Space Center (KSC). During the few weeks before launch, groups will be periodically tested for egg quality to assure that the frogs have adapted to the KSC laboratory environment. About 27 hours before launch, four females will be placed in a damp foam-lined box, called the Adult Frog Box (AFB), through which 100 cc/min of air wil be circulated. The AFB will be lowered into the Spacelab and loaded into the Frog Environmental Unit (FEU) during the final pre-launch preparations. A sperm suspension, for use in flight to fertilize the eggs, will also be prepared and loaded during the pre-launch period. The sperm suspension, together with a kit of syringes containing Human Chorionic Gonadotropin (HCG), will be stored in a refrigerator aboard the shuttle until needed in flight. On the first day of flight, the AFB will be transferred from the FEU to the General Purpose Work Station (GPWS), which is a type of glove box specially designed to allow the crew to use chemicals and biological materials during the flight without contaminating the shuttle/Spacelab environment. Inside the GPWS the four adult frogs will be injected with the HCG hormone and returned to the FEU. Approximately 16 hours after injection, ovulation should have taken place and 15 to 20 eggs from each frog will be placed on each of two egg baskets and covered with sperm for 10 minutes. The egg baskets are inserted into acrylic egg chambers and 50 ml of 'pond water' (20 percent strength Modified Ringers solution (is added. One of the chambers from each frog will be placed on a centrifuge within the FEU and rotated to simulate normal terrestrial gravity (1 g). The remaining chambers are incubated under microgravity conditions within the FEU. Forty minutes after fertilization, the four chambers exposed to 1 g will be removed and observed within the GPWS using a dissecting microscope and camera system. On the basis of egg rotation and egg appearance, the 'best' and 'second best' frogs will be selected to contribute additional eggs. Using the two best frogs, 22 egg chambers will be loaded with eggs and fertilized. Eleven chambers wil be incubated at microgravity and eleven will be incubated on the centrifuge. At various times during the flight, chambers will be removed from the FEU and transferred to the GPWS where a formaldehyde-based fixative will be injected in order to preserve important developmental stages for in depth study following the flight. Five of the 22 chambers plus the eight fertilization test chambers will be returned to Earth with live tadpoles. The swimming behavior of these free swimming tadpoles will be examined within several hours of landing and some will be fixed for a detailed analysis of their inner ear, the otolity, the animals 'balance system.' Lychakov and Vinikov reported an increase in otolith size in tadpoles that developed (but were not fertilized) in space. Live tadpoles from the SL-J flight will be raised through metamorphsis for studies of maturation including an analysis of the effects of space flight on their ability to produce normal progency. Following the flight, the fixed embryos will be serially sectioned and stained using procedures that were developed for this experiment. The embroys fixed at the 2-4 cell stage will be examined for the distribution of cytoplasmic contents, including the various classes of yolk platelets, and the location and shape of the cleavage furrows. The gastrulae will be assessed for the normality of the complex cellular rearrangements that constitute blastopore formation and involution, i.e., the differentiation of the embryo into its specialized body parts. Using a new procedure, the gastrulae will be bleached which will enable the initial sperm entry point (SEP) to be located. The correlation between the SEP and the dorsal lip of the blastopore will be determined. Under normal terrestrial conditions it was shown that the SEP typically is located on the side of the egg opposite the future dorsal side of the embryo. The neurulae will be examined for the normality and completeness of the neural plate and archenteron expansion. The tadpole stages will be used to study the allometry and morphology of the various organ systems.
This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.
An approach for design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.