VTechWorks Repository :: Browsing by Author "Mabie, Hamilton H."

Browsing by Author "Mabie, Hamilton H."

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Analysis of spur gear teeth for static deflections
Caldwell, Sherwood McCraw (Virginia Tech, 1966-03-17)
The problem of the deflection of spur gear teeth has been previously investigated analytically by several authors. Two of the papers dealing with this topic were written by Timoshenko and Baud (18)t and Marin and Shenk (11). Both papers employ the cantilever beam approach in which the spur gear tooth is represented as a rigidly supported, cantilever beam of uniform thickness tapered in the plane of load application. Deflection is considered to be caused by bending moment, shearing force, and Hertzian pressure at the point of load application. Two additional papers were written by Weber (25) and Attia (3) in which the actual involute gear tooth was considered to be an elastically supported cantilever beam rather than rigidly clamped at the root of the tooth. Likewise, circumferential deformation of the gear body was considered. However, the derived equations for the total deflection due to these effects are exceedingly complicated and require the use of numerical methods for their solution since some of the equations are in integral form.
An analytical study and computer analysis of three-dimensional, steady-state vibration of multishaft geared-rotor systems
Blanding, James Michael (Virginia Polytechnic Institute and State University, 1985)
A unique multifrequencied transfer matrix method performs three-dimensional harmonic, steady-state response calculations on geared-rotor systems. The full six degrees-of-freedom method includes physical branching to accommodate multiple shafting and frequency branching to simultaneously accommodate multiple frequencies and their interdependence resulting from time-varying mesh stiffness. Areas of emphasis include development of a modified transfer matrix to handle multiple frequencies and shafting; description of the time-varying stiffness tensor representing the involute spur gear mesh based on bending, shear, compression, and local contact deformation; development of the mesh transfer matrix; development of an automatic system solver to allow the engineer to analyze systems of arbitrary construction; and the development of a matrix solver to efficiently handle large systems. A computer analysis demonstrates the significance of terms included in the stiffness evaluation as compared with less rigorous treatment in the literature. An analytical example problem illustrates the automated model generation through complete rotor system dynamic response analysis produced by the current work with special attention to the significance of parametric excitation due to the gear mesh.
Application of the finite element method in high-side gondola rail car design
Schmidt, Gerald (Virginia Tech, 1987-10-14)
Finite element models of four design configurations of a proposed composite aluminum-steel high-side coal gondola rail car were developed. The designs were analyzed for compliance with the loadings set forth by the Association of American Railroads. Each of the first three designs were analyzed to check design concepts and alternatives with the fourth design being the final design planned for a prototype car. The results of the finite element analyses indicate that the final design is acceptable. However, two areas exist where results taken literally indicate a negative margin of safety. These areas are in the end sill to draftsill connection and in the draftsill casting. These conditions appear to be inconsequential since in the end sill case, the high stress is apparently caused by modeling constraints and the draftsill casting is a traditional design and is in common use on current cars and therefore should not cause any service problems. Step-by-step application of the finite element method to this design process is presented along with discussion of some significant element formulation assumptions and modeling methods.
A CAD/CAM interface for computer-aided design of cams
Gandhi, Ashit R. (Virginia Tech, 1985-12-15)
The purpose of this thesis is to provide a complete package for the design and three dimensional modeling display of cams. The software produced as a part of this work will operate as a module of CADAM to produce cam designs and enter the resulting cam as a CAD model and produce the graphical display of the cam. In addition to the introductory material, this thesis is divided into four sections. The section on the graphics packages used in this thesis includes a brief history and capabilities of each of the packages. The second section details the procedure to be adopted in order to design a cam. The next section details ANICAM, the program that has been developed to incorporate the design and display procedure. The fourth section of this thesis contains recommendations for further work in this area. The theoretical work in this project is a combination of original derivations and applications of the theory in the design literature.
Contact area between cylinders in rolling contact
Carroll, Michael David (Virginia Tech, 1976-11-07)
The contact area between two rollers or cylinders was investigated both theoretically and experimentally. The theoretical investigation was based on Hertzian theory, while the experimental method used was based on the measurement of contact resistances. The variables in the investigation were the applied force, skew angles between roller axes, and roller diameters. The experimental results showed contact areas much smaller than predicted by Hertzian theory. This was expected, as Hertzian theory does not account for the rough surfaces of real bodies. Extensive tables of Hertzian contact areas for various roller sizes and skew angles are included.
The development of an instrument to control the oxygen concentration and flow rate of an air-oxygen mixture
Fletcher, J. Robert (Virginia Tech, 1977-10-05)
The equipment as designed and constructed is a workable solution to the problem of mixing air and oxygen at selectable oxygen concentrations and flow rates. Control of the flow of the individual gases is adequate with the metering elements as designed. The laminated brass stock and shim stock is easily fabricated and works well. The mechanical linkage is the weakest link in the design. The hysteresis in setting concentration and the inaccuracies in setting concentration are primarily related to poor design in the linkage. Ways to possibly improve the linkage are discussed in the Recommendation section of this thesis. The only problem with the read-out design is at low flow rates, i. e., less than 5000 cm³/min (5 -(min)) the scale sticks at times.
The effect of hydrogen on the fatigue life of high strength steel
Wilson, James H. (Virginia Tech, 1978-08-05)
Torsional fatigue tests were conducted on 4370 steel oil quenched and tempered at 1000° F in (l) the uncharged state, (2) the hydrogen charged state, and (3) in a hydrogen environment. The tests were conducted on both smooth (K_t = l.l) and V-notch (K_t = 3.8) test specimens. A statistical analysis conducted at the 99% confidence limit for the smooth test specimens indicated that precharging with hydrogen increased the fatigue life of the material and also the fracture surface of the test specimens changed from a circumferential crack to a 45° diagonal crack. At a 90% confidence limit, charging with hydrogen did not affect the fatigue life of the V-notched specimens. At a 99% confidence limit for both the smooth and V-notched test specimens, testing in a hydrogen environment increased the fatigue life of the material. Bending fatigue tests were also conducted on the same material and the results indicated that charging with hydrogen decreased fatigue life of smooth test specimens (K_t = l.l) but increased the fatigue life for V-notched specimens (K_t = 2.4 and 3.8).
The effects of rubber modification on friction and wear of epoxy networks
Chitsaz-Zadeh, Majid R. (Virginia Polytechnic Institute and State University, 1987)
An epoxy resin (Epon 828) was chemically modified with two different elastomers, poly(dimethyl-co-diphenyl) siloxane (PSX) and carboxyl-terminated butadiene-acrylonitrile (CTBN), to enhance its fracture toughness. The friction and wear of specimens modified with different amounts of elastomer were investigated in a pin-on-disk wear machine. An attempt was made to correlate the fracture toughness of the epoxy material to its fatigue wear rate for experiments in which a steel ball was sliding on a modified epoxy disk. A different type of experiment, modified epoxy pin sliding on an abrasive disk, was performed to detect whether abrasive wear of modified epoxies responds differently than fatigue wear to the fracture toughness. Other experiments were performed in which the wear debris produced during sliding was blown out of the interface to study its influence on friction and wear behavior. The effect of surface morphology on friction and wear was also studied. The results indicated that a marked improvement in fracture toughness was achieved for samples with higher elastomer content. Regardless of the type of the experiment, epoxy pin-on-abrasive disk or steel ball-on-epoxy disk, wear rates correlated positively with inverse of fracture toughness. Both friction coefficient and wear rate were found to be influenced by the removal of the wear debris, especially for samples with higher elastomer content. The friction coefficient was reduced for samples with higher elastomer content and this was attributed to the low surface energy of the elastomer. CTBN-modified epoxies exhibited lower friction coefficients than epoxies modified with polysiloxane. It was found that sample morphology had a significant effect on both friction coefficient and wear rate; the sample with approximately the same domain size but the least number of elastomeric domains exhibited the highest friction coefficient and the highest wear rate.
A fabrication stress model for axisymmetric filament wound composite structures
Nguyen, Vinh Dinh (Virginia Polytechnic Institute and State University, 1988)
A comprehensive fabrication stress model was developed to compute fiber stresses in axisymmetric filament wound composite structures at any stage of the fabrication process, a prerequisite for the evaluation of the performance of the composite structures from fabrication process variables. The stress model uses an isoparametric axisymmetric finite element formulation and a double-layered composite element to model the mechanical behavior of the composite material in any cure state. An incremental finite element formulation was used to model the winding and mandrel removal stages. A thermo-mechanical formulation was used to model the curing stage. Also, all major physical phenomena occurring in the fabrication stages which significantly affect the fiber stresses are taken into account: instantaneous tension loss in winding, tension loss due to multiple circuit winding, tension loss due to fiber motion through the uncured resin, material cure transition, and fiber stiffness degradation in a compressive strain state. Two case studies were selected to evaluate and to illustrate the use of the fabrication stress model: the space shuttle booster Joint overwrap and a filament wound composite bottle. The analysis results of the overwrap case study show excellent agreement with experimental hoop strain data. The fabrication stresses from the analysis indicate that the overwrap should experience no strength degradation due to adverse fabrication stresses and strains. Very favorable residual stress results were also predicted by the model for the overwrap. The analysis results of the bottle case study, while having no experimental data to compare with, show very reasonable behaviors, which can be readily explained by a qualitative consideration of the actual winding problem. The stress and strain results from the case study show that the bottle would experience strength degradation when a sand/PVA mandrel is used, but it would retain maximum strength when a steel mandrel is used.
Fatigue limit analysis involving biaxial stress components
Munday, Edgar Gray (Virginia Polytechnic Institute and State University, 1984)
Biaxial stress fatigue data is carefully examined in order to determine how much foundation exists for a rational approach to classical stress-based fatigue limit analysis involving biaxial stress components. A review is given of the methods presently in vogue, and new methods are suggested for obtaining equivalent mean and equivalent alternating stresses. Some groundwork is laid for the consideration of stress gradient influence on fatigue behavior. There are also some observations concerning the Distortional Energy and Tresca criteria and how they are incorporated in fatigue design procedures. The work is restricted to cases in which the alternating principal stress axes have fixed orientation.
Finite element analysis of subregions using a specified boundary stiffness/force method
Jara-Almonte, C. C. (Virginia Polytechnic Institute and State University, 1985)
The accurate finite element analysis of subregions of large structures is difficult to carry out because of uncertainties about how the rest of the structure influences the boundary conditions and loadings of the subregion model. This dissertation describes the theoretical development and computer implementation of a new approach to this problem of modeling subregions. This method, the specified boundary stiffness/force (SBSF) method, results in accurate displacement and stress solutions as the boundary loading and the interaction between the stiffness of the subregion and the rest of the structure are taken into account. This method is computationally efficient because each time that the subregion model is analyzed, only the equations involving the degrees of freedom within the subregion model are solved. Numerical examples are presented which compare this method to some of the existing methods for subregion analysis on the basis of both accuracy of results and computational efficiency. The SBSF method is shown to be more accurate than another approximate method, the specified boundary displacement (SBD) method and to require approximately the same number of computations for the solution. For one case, the average error in the results of the SBD method was +2.75% while for the SBSF method the average error was -0.3%. The comparisons between the SBSF method and the efficient and exact zooming methods demonstrate that the SBSF method is less accurate than these methods but is computationally more efficient. In one example, the error for the exact zooming method was -0.9% while for the SBSF method it was -3.7%. Computationally, the exact zooming method requires almost 185% more operations than the SBSF method. Similar results were obtained for the comparison of the efficient zooming method and the SBSF method. Another use of the SBSF method is in the analysis of design changes which are incorporated into the subregion model but not into the parent model. In one subregion model a circular hole was changed to an elliptical hole. The boundary forces and stiffnesses from the parent model with the circular hole were used in the analysis of the modified subregion model. The results of the analysis of the most refined mesh in this example had an error of only -0.52% when compared to the theoretical result for the modified geometry. The results of the research presented in this dissertation indicate that the SBSF method is better suited to the analysis of subregions than the other methods documented in the literature. The method is both accurate and computationally efficient as well as easy to use and implement. The SBSF method can also be extended to the accurate analysis of subregion models with design changes which are not incorporated into the parent model.
Nonlinear axial stiffness characteristics of axisymmetric bolted joints
Grosse, Ian R. (Virginia Polytechnic Institute and State University, 1987)
A critical assessment of the current design theory for bolted joints which is based on a linear, one-dimensional stiffness analysis is presented. A detailed nonlinear finite element analysis of a bolted joint conforming to ANSI standards was performed. The finite element results arc presented in the classical bolted joint diagram and compared with the linear theory. The results revealed that the joint stiffness is highly dependent on the magnitude of the applied load. The joint stiffness changes continuously from extremely high for small applied loads to extremely low for large applied loads, contrary to the constant joint stiffness of the linear theory. The linear theory is shown to be extremely inadequate in characterizing the joint stiffness. The significance of the results in terms of the failure of bolted joints is discussed. Straight-forward analytical procedures are proposed for establishing estimates of the nonlinear stiffness description and the associate bolt loading in fatigue environments. The linear theory should be discarded and the more accurate nonlinear joint description be used. These results also provide the finite element community an improved model for the interconnection of substructures. The two-dimensional, axisymmetric finite element model includes bilinear gap elements to model the interfaces. Special orthotropic elements were used to model the bolt/nut thread interaction. A free-body-diagram approach was taken by applying loads to the outer diameter of the joint model which correspond to internal, uniformly distributed line-shear and line-moment loads in the joint. A number of convergence studies were performed to validate the solution.
A prediction of polymer wear using polymer mechanical properties and surface characterization parameters
Warren, Jeffery Howard (Virginia Tech, 1976-08-15)
Polymers were slid on rough hard steel surfaces with normal loads which caused full penetration (real and apparent areas equal) and partial penetration (real less than apparent area). Wear data for polyvinylchloride (PVC) and polychlorotrifluoroethylene (PCTFE) was obtained on a pin-on-disk machine using neutron activation analysis A (NAA). Observations of the wear process were made in the scanning electron microscope (SEM) both before, during, and after the wear experiment. It was observed that these polymers along with Nylon 6-6 tend to wear in discrete sites rather than continuous films. At these discrete sites the polymer shears at an angle which is dependent on the mechanical properties of the polymer and on the asperity angle. There appears to be a minimum shear angle beyond which no wear occurs.
Prediction of the running torque of instrument ball bearings at high speed under combined radial and axial loads
Clarke, George Edward (Virginia Tech, 1968-08-05)
The purpose of this investigation was to develop an expression to represent the torque versus speed behavior of instrument ball bearings between 1000 and 40,000 rpm with various combinations of radial and axial load ranging between 0 and 200 grams. Because of the lack of experimental data for instrument bearings over any range of speeds, loads and sizes, it was necessary to construct a suitable bearing tester and accumulate the required data. The testers used were based on previous work by H.H. Mabie at Sandia Corporation and G.E. Clarke at V.P.I. The driving source was a small air turbine developed by Mabie which performed smoothly and reliably between 0 and 50,000 rpm. The torque measuring system employed strain gages on a very small beam which was used to sense forces on the stationary outer race of the bearing while the inner race was driven at speed. Each test was conducted from 0 to 40,000 rpm. The radial load took on va1ues of 50, 100, and 200 grams. The axial load was 0, 50, 100, and 200 grams. All combinations of these loads were used for each size bearing. The sizes tested were R-2, R-3, R-4. Six bearings of each size were used with all six bearings of each size undergoing the same test program in order to yield statistically reasonable averages. Investigation of analytical methods of predicting the running torque indicated that production tolerances of ball bearings rendered such an approach impractical. This led to the development of an empirical expression to predict the running torque within the same range of sizes, loads, and speeds for which experimental test data was obtained. Such an empirical expression was successfully developed and the reSUlting torque predictions compared with the experimental values of torque. The empirical expression proved capable of predicting the running torques within the envelope of the sample standard deviations for a given bearing size and loading in most cases. During the investigation of supplementary topics, it was determined that frictional heating was insignificant during the conduct of the torque tests which had a duration of approximately two minutes. All tests were at ambient temperature. All tests conducted were with oil lubricant and ribbon retainer ba1l bearings. There was no evidence that the empirical expression for friction torque developed here was valid when extrapolated beyond the limits of size, load, and speed used in its development.
A radio-tracer study of the effect of surface finish on the transfer of polychlorotrifluoroethylene sliding on mild steel
Doolittle, Stephen D. (Virginia Tech, 1974-08-05)
The effect of surface finish on the transfer of polychlorotrifluoroethylene (PCTFE) to mild steel was studied using a radio-tracer technique. A pin-on-disk apparatus was used in conjunction with neutron activation of PCTFE to study the initial stages of transfer. Quantitative transfer and friction data were obtained as functions of surface finish and the number of repeated passes of polymer over mild steel. Qualitative supporting evidence for postulated transfer mechanisms was obtained using scanning electron microscopy. The results showed that bulk transfer of PCTFE to mild steel does occur at room temperature. Initial transfer to polished (0.10 um - rms) surfaces, abraded (0.81 um - rms) surfaces, and glass bead blasted (1.73 um - rms) surfaces was attributed to an abrasive wear mechanism. An apparent translation to adhesive wear was observed during later stages of transfer. This transition occurred much sooner with the polished surface than with the rough surfaces. This work also demonstrated that a radio-tracer technique could be effectively applied to the study of polymer wear. The minimum mass detection limit with this technique was 0.3 ug. This sensitivity is at least one order of magnitude better than that obtained with reported polymer wear measurement methods.
Roll vibration of a reciprocating air compressor
Herold, John Henry (Virginia Tech, 1977-08-05)
The rigid-body rotational vibration of a resiliently mounted air compressor about an axis parallel to the axis of the rotor is investigated. An analysis of the motion of the compressor base is conducted using empirical acceleration data. The effect on roll vibration of changing various compressor design parameters is studied using a computer simulation program, PABEWE. This digital simulation incorporating slider-crank linkage analysis employs the strict equations of motion. Control theory is used to control the roll vibration. The control theory is applied to simplified equations of motion and incorporates various feedbacks. Recommendations are offered for the reduction of roll vibration levels.
Structural modification utilizing beam elements
Elliott, Kenny B. (Virginia Polytechnic Institute and State University, 1985)
This study presents a concept that provides a structural dynamicist the ability to analyze the effects of making sophisticated (beam-type) structural changes to a structural system whose modal database is known. The modification technique combines the Dual Modal Space Modification Method (DMSM) and the Transfer-Matrix Method to institute general beam modifications. The DMSM method is employed to implement the beamtype modification, while the transfer-matrix method is used to formulate the modification element. The use of transfer-matrix methods provides the ability to model virtually any beam modification a designer might consider in terms of the two points being connected without the loss of any dynamic information between the points. The result is a modification scheme which is both flexible and universal. Two numerical examples are considered. One example demonstrated the performance of the modification scheme in instituting a severe structural change. The second example demonstrated a change to a complex structure. In both cases, continuum beams were used as modification elements. The results of these two examples show that the modification scheme provides very promising results, providing an adequate modal database was used. Modal truncation was determined to be the primary source of error.
Synthesis and design of the RSSR spatial mechanism for function generation
Williams, Robert L. (Virginia Tech, 1985-08-05)
The purpose of this thesis is to provide a complete package for the synthesis and design of the RSSR spatial function generating mechanism. In addition to the introductory material this thesis is divided into three sections. The section on background kinematic theory includes synthesis, analysis, link rotatability, transmission quality, and branching analysis. The second division details the computer application of the kinematic theory. The program RSSRSD has been developed to incorporate the RSSR synthesis and design theory. An example is included to demonstrate the computer-implemented theory. The third part of this thesis includes miscellaneous mechanism considerations and recommendations for further research. The theoretical work in this project is a combination of original derivations and applications of the theory in the mechanism literature.
Transverse vibrations of double-tapered cantilever beams with end support and with end mass
Mabie, Hamilton H.; Rogers, C. B. (Acoustical Society of America, 1974)
The free vibrations of a double-tapered cantilever beam with (1) end support and (2) end mass have been investigated using the Bernoulli-Euler equation. The beam was tapered linearly in the horizontal and in the vertical planes simultaneously with the taper ratio in the horizontal plane equal to that in the vertical plane. A table is presented for the first case from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios. A chart, plotted from this table, shows the effect of taper ratio on the various harmonics. For the second case, a table and resulting charts show the effect of taper ratio and ratio of end mass to beam mass on the fundamental frequency and higher harmonies. Although previously presented, the case of the beam with free end is also included for purposes of comparison.
The vibration of instrument ball bearings in a controlled environment and the effect of the resulting fretting corrosion on bearing torque
Hite, Gregory Charles (Virginia Tech, 1970-08-05)
Fretting corrosion is a form of wear which occurs at the interface of two contacting solid materials as the result of small, relative vibratory motion. It is generally identified by the presence of a red oxide, Fe203. Previously, the majority of the investigators studied the fretting corrosion between two flat specimens or between a single ball and a flat plate held in contact by a normal force. There are a number of interrelated influencing factors involved in fretting corrosion including: the vibration frequency and amplitude, the environmental conditions, the characteristics of the material, and the type of lubrication. The present investigation was conducted in order to investigate the effects of frequency and amplitude of axial vibration and the consequent accelerations acting to produce fretting damage within an unlubricated instrument ball bearing. The effect of bearing axial play on the fretting damage was also examined. The reproducibility of the damage resulting from these variables was determined.

Browsing by Author "Mabie, Hamilton H."

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