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Holding fixture that holds the thread gage and three wires in the proper relationship facilitates the measurement of the pitch diameter of the tapered threads of a pipe thread gage. Modified, this device can be used to hold involute spur gears.
Tests were conducted with two groups of 8.89-centimeter (3.5-in.) pitch diameter spur gears with standard 20 deg involute profile with tip relief made of CVM Super-Nitralloy (5Ni-2Al) and CVM AISI M-50 at a temperature of 350 K (170 F). Super-Nitralloy gears with tip relief had a life 150 percent that of gears without tip relief. An increased scoring phenomenon was noted with the Super-Nitralloy gears with tip relief. Through-hardened AISI M-50 gears with tip relief failed due to tooth fracture. AISI M-50 gears without tip relief had a life approximately 40 times greater than the AISI M-50 gears with tip relief.
Design and fabrication of gear drives for rocket engine turbopumps are described in the sequence encountered during the design process as follows: (1) selection of overall arrangement; (2) selection of gear type; (3) preliminary sizing; (4) lubrication system design; (5) detail tooth design; (6) selection of gear materials; and (7) gear fabrication and testing as it affects the design. The description is oriented towards the use of involute spur gears, although reference material for helical gears is also cited.
The paper examines RNA-ribosomal changes observed in protozoa and fixed postmitotic cells, as well as the characteristics of intermitotic cells. Attention is given to a discussion of the implications of the reported ribosomal changes as to the senescent deterioration of protein synthesis and physiological functions. A survey of the literature suggests that, while the data on ribosomal change in dividing cells both in vivo and in vitro are inconclusive, there is strong histological and biochemical evidence in favor of some degree of quantitative ribosomal loss in fixed postmitotic cells. Since these decreases in ribosomes are demonstrated in differential cells from nematodes, insects and mammals, they may represent a universal manifestation of cytoplasmic senescence in certain types of fixed postmitotic animal cells. The observed variability in ribosomal loss for cells belonging to the same type suggests that this involution phenomenon is rather related to the wear and tear suffered by a particular cell.
An analysis and computer program called TELSGE were developed to predict the variations of dynamic load, surface temperature, and lubricant film thickness along the contacting path during the engagement of a pair of involute spur gears. The analysis of dynamic load includes the effect of gear inertia, the effect of load sharing of adjacent teeth, and the effect of variable tooth stiffness which are obtained by a finite-element method. Results obtained from TELSGE for the dynamic load distributions along the contacting path for various speeds of a pair of test gears show patterns similar to that observed experimentally. Effects of damping ratio, contact ratio, tip relief, and tooth error on the dynamic load were examined. In addition, two dimensionless charts are included for predicting the maximum equilibrium surface temperature, which can be used to estimate directly the lubricant film thickness based on well established EHD analysis.
The fundamental geometrical characteristics of spiral bevel gear tooth surfaces are discussed. The parametric representation of an ideal spiral bevel tooth is developed based on the elements of involute geometry, differential geometry, and fundamental gearing kinematics. A foundation is provided for the study of nonideal gears and the effects of deviations from ideal geometry on the contact stresses, lubrication, wear, fatigue life, and gearing kinematics.
This paper discusses the fundamental geometrical characteristics of spiral bevel gear tooth surfaces. The parametric representation of an ideal spiral bevel tooth is developed. The development is based on the elements of involute geometry, differential geometry, and fundamental gearing kinematics. A foundation is provided for the study of nonideal gears and the effects of deviations from ideal geometry on the contact stresses, lubrication, wear, fatigue life, and gearing kinematics.
The tooth surface principal radii of curvature of crown (flat) gears were determined. Specific results are presented for involute, straight, and hyperbolic cutter profiles. It is shown that the geometry of circular cut spiral bevel gears is somewhat simpler than a theoretical logarithmic spiral bevel gear.
Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory.
An analysis of the surface geometry of spiral bevel gears formed by a circular cutter is presented. The emphasis is upon determining the tooth surface principal radii of curvature of crown (flat) gears. Specific results are presented for involute, straight, and hyperbolic cutter profiles. It is shown that the geometry of circular cut spiral bevel gears is somewhat simpler than a theoretical logarithmic spiral bevel gear.
Analysis and computer program (TELSGE) predict variations of dynamic load and surface temperature and lubricant film thickness along contacting path of pair of involute spur gears. Analysis of dynamic load includes effect of gear inertia, effect of load sharing of adjacent teeth, and effect of variable tooth stiffness obtained by element method. TELSGE written in FORTRAN IV.
The modifications and testing of a standard Stirling engine, required for connection to a 25 kW induction alternator, for use with a solar thermal parabolic dish electric module is described. Power was absorbed by a GE induction alternator connected to the utility grid. Also included are the results from recent testing of another solar engine at the DOE-Georgia Tech solar site. It was done in parallel with the testing at Edwards for the purpose of comparing performance of two solar-only receivers, which were based on the standard 4-95 involute heat exchanger.
The magnitude and variation of tooth pair compliance with load position affects the dynamics and loading significantly, and the tooth root stressing per load varies significantly with load position. Therefore, the recently developed time history, interactive, closed form solution for the dynamic tooth loads for both low and high contact ratio spur gears was expanded to include improved and simplified methods for calculating the compliance and stress sensitivity for three involute tooth forms as a function of load position. The compliance analysis has an improved fillet/foundation. The stress sensitivity analysis is a modified version of the Heywood method but with an improvement in the magnitude and location of the peak stress in the fillet. These improved compliance and stress sensitivity analyses are presented along with their evaluation using test, finite element, and analytic transformation results, which showed good agreement.
Static analysis, dynamic analysis, and computer programs are discussed. Spur gear formulae and involute profile development and deflection are also discussed.
A number of applications of elastohydrodynamic film thickness expressions were considered. The motion of a steel ball over steel surfaces presenting varying degrees of conformity was examined. The equation for minimum film thickness in elliptical conjunctions under elastohydrodynamic conditions was applied to roller and ball bearings. An involute gear was also introduced, it was again found that the elliptical conjunction expression yielded a conservative estimate of the minimum film thickness. Continuously variable-speed drives like the Perbury gear, which present truly elliptical elastohydrodynamic conjunctions, are favored increasingly in mobile and static machinery. A representative elastohydrodynamic condition for this class of machinery is considered for power transmission equipment. The possibility of elastohydrodynamic films of water or oil forming between locomotive wheels and rails is examined. The important subject of traction on the railways is attracting considerable attention in various countries at the present time. The final example of a synovial joint introduced the equation developed for isoviscous-elastic regimes of lubrication.
Necessary and sufficient conditions for a nonlinear system of equations to be locally equivalent, in a neighborhood of the origin in the real number system, to a controllable linear system are combined with several versions of the global inverse function theorem to define sufficient conditions for transforming the nonlinear system into a linear system. Additionally, a technique is introduced for developing a transformation under the assumptions that the columns of a controllability matrix span an n-dimensional space. Finally, the n-l form of the controllability matrix columns is demonstrated to be involutive
A method to analyze the static and dynamic loads in a planetary gear train was developed. A variable-variable mesh stiffness (VVMS) model was used to simulate the external and internal spur gear mesh behavior, and an equivalent conventional gear train concept was adapted for the dynamic studies. The analysis can be applied either involute or noninvolute spur gearing. By utilizing the equivalent gear train concept, the developed method may be extended for use for all types of epicyclic gearing. The method is incorporated into a computer program so that the static and dynamic behavior of individual components can be examined. Items considered in the analysis are: (1) static and dynamic load sharing among the planets; (2) floating or fixed Sun gear; (3) actual tooth geometry, including errors and modifications; (4) positioning errors of the planet gears; (5) torque variations due to noninvolute gear action. A mathematical model comprised of power source, load, and planetary transmission is used to determine the instantaneous loads to which the components are subjected. It considers fluctuating output torque, elastic behavior in the system, and loss of contact between gear teeth. The dynamic model has nine degrees of freedom resulting in a set of simultaneous second order differential equations with time varying coefficients, which are solved numerically. The computer program was used to determine the effect of manufacturing errors, damping and component stiffness, and transmitted load on dynamic behavior. It is indicated that this methodology offers the designer/analyst a comprehensive tool with which planetary drives may be quickly and effectively evaluated.
Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory. Previously announced in STAR as N82-32733