Tumble mills are hollow cylindrical shells of large diameter carrying grinding media (a combination of rock/iron ore/chemical flakes and metal balls/rods), which, upon rotation of the mill, will be ground into fine powder. These mills rotate at low speeds using a gear reduction unit and often have vibration problems. These vibration problems result in increased gear wear and occasional catastrophic failures resulting in production loss. The objective of this research is to investigate the effect of oscillation of grinding media on torsional vibrations of the mill. A theoretical model was developed to determine the oscillating frequency of the grinding media. A 12" (0.3 m) diameter tumble mill test rig was built with a 0.5 hp DC motor. The rig is tested with sand and iron bb balls to simulate the industry process application. At low volume levels the grinding media oscillates like a rigid body as compared to higher volumes. It is shown that tumbling action of grinding media causes torsional excitation and hence its effect has to be considered in torsional vibration analysis. At starting, the load on the gears is much higher due to this oscillation.

Torsional vibration can be characterized as the cyclic variation of shaft speed, which can cause various failures in rotating machines, such as: gear-tooth breakage, blade-off due to blade fatigue in steam turbines, break-off of shafts, and overloading of components fitted onto the shaft. Commercially, there are only a few systems available that measure this type of vibration as compared to lateral vibration measurement systems. Most of these systems required modifications to the rotating machine, which in some cases are unacceptable. Therefore, it has become common practice to develop in-house torsional vibration measurement systems. A common measurement technique, called Time Interval Measurement (TIMS), calculates the instantaneous speed of the shaft from a frequency modulated carrier wave. Since torsional vibration is the cyclic variation of shaft speed, the shaft speed can be used to determine torsional vibration. Noise can be easily introduced into this type of system masking the torsional vibration; this was apparent in the measurement system developed by Kar, which was used as a baseline for the experiments conducted in this thesis. Various techniques were employed to reduce the effects of the noise in the measurement system, such as (1) created an algorithm, different than the one used by Kar, to calculate shaft speed, (2) increased the sampling rate of the data acquisition boards, (3) resampled the shaft speed into the order domain in order to remove harmonic noise, and (4) created an algorithm that corrects the shaft speed calculation to account for unequal spacing of encoder segments. These noise reducing techniques were compiled into a LabVIEW™ program in order to develop a robust measurement system. Each technique was tested individually on two test rigs constructed at the Turbomachinery Laboratory. Each technique proved to reduce the noise introduced into the system, but the geometric compensation algorithm proved to be the most effective in reducing the noise. This thesis proved that an in-house measurement system could be developed at a relatively low cost and with relative ease.

Torsional vibration can be characterized as the cyclic variation of shaft speed, which can cause various failures in rotating machines, such as: gear-tooth breakage, blade-off due to blade fatigue in steam turbines, break-off of shafts, and overloading of components fitted onto the shaft. Commercially, there are only a few systems available that measure this type of vibration as compared to lateral vibration measurement systems. Most of these systems required modifications to the rotating machine, which in some cases are unacceptable. Therefore, it has become common practice to develop in-house torsional vibration measurement systems. A common measurement technique, called Time Interval Measurement (TIMS), calculates the instantaneous speed of the shaft from a frequency modulated carrier wave. Since torsional vibration is the cyclic variation of shaft speed, the shaft speed can be used to determine torsional vibration. Noise can be easily introduced into this type of system masking the torsional vibration; this was apparent in the measurement system developed by Kar, which was used as a baseline for the experiments conducted in this thesis. Various techniques were employed to reduce the effects of the noise in the measurement system, such as (1) created an algorithm, different than the one used by Kar, to calculate shaft speed, (2) increased the sampling rate of the data acquisition boards, (3) resampled the shaft speed into the order domain in order to remove harmonic noise, and (4) created an algorithm that corrects the shaft speed calculation to account for unequal spacing of encoder segments. These noise reducing techniques were compiled into a LabVIEW™ program in order to develop a robust measurement system. Each technique was tested individually on two test rigs constructed at the Turbomachinery Laboratory. Each technique proved to reduce the noise introduced into the system, but the geometric compensation algorithm proved to be the most effective in reducing the noise. This thesis proved that an in-house measurement system could be developed at a relatively low cost and with relative ease.

Tumble mills are hollow cylindrical shells of large diameter carrying grinding media (a combination of rock/iron ore/chemical flakes and metal balls/rods), which, upon rotation of the mill, will be ground into fine powder. These mills rotate at low speeds using a gear reduction unit and often have vibration problems. These vibration problems result in increased gear wear and occasional catastrophic failures resulting in production loss. The objective of this research is to investigate the effect of oscillation of grinding media on torsional vibrations of the mill. A theoretical model was developed to determine the oscillating frequency of the grinding media. A 12" (0.3 m) diameter tumble mill test rig was built with a 0.5 hp DC motor. The rig is tested with sand and iron bb balls to simulate the industry process application. At low volume levels the grinding media oscillates like a rigid body as compared to higher volumes. It is shown that tumbling action of grinding media causes torsional excitation and hence its effect has to be considered in torsional vibration analysis. At starting, the load on the gears is much higher due to this oscillation.

This thesis focuses on the torsional-lateral interactions seen in gear coupled rotors. Of particular interest are cases where the torsional stiffness parameters affect the lateral critical speeds and where lateral stiffness and damping parameters affect torsional critical speeds and amplitudes. A common procedure for critical speed calculations has been to solve lateral and torsional systems separately. This procedure is tested through an eigenvalue analysis. It is shown in this thesis, however, that torsional-lateral interactions play major roles in each other's critical speeds. Some research has seemingly uncoupled two lateral degrees of freedom from the gear system by choosing bearing forces and a coordinate system pointing along the line of action and normal to the line of action. This simplification method has been tested for cases when the lateral bearing stiffness becomes asymmetric. The force generated by a rotating imbalance also creates a variable moment arm as the center of mass rotates about the geometric center of the gear. This variable moment arm is commonly neglected, but is included in the last case study and its effects are displayed in the results section of this thesis.

The modeling of Sand Asphalt and experiments to measure their rheological properties are of vital concern to many industrial processes especially highway and roadway pavement construction industry. A variety of hot mix asphalt mixtures are used in highway and runway pavement construction, with each mixture catering to a specific need. These mixtures vary in type and percentage of aggregates and asphalt used and consequently exhibit marked differences in their response. The main thrust of this research is to provide experimental data which would be helpful in determining the efficacy of the constitutive models that have been developed for these hot mix asphalt mixtures. Here we attempt to provide experimental data in the raw form for Sand Asphalt mixtures that would be helpful in the theoretical modeling efforts involving asphalt materials using a continuum point of view. For example the data obtained can be of immense help to evaluate the constitutive model developed by Murali Krishnan and Rajagopal. The Sand Asphalt mixture in their model is modeled as `homogenized' single constituent due to the peculiarity of its makeup. The constitutive model of Murali Krishnan and Rajagopal is based on a thermodynamical framework for materials possessing multiple natural configurations (multiple stress free states) to derive the constitutive equations. Recently an Orthogonal Rheometer was built to characterize the granular solids by Gupta and Rajagopal which was later used by Baek in the torsional mode. In this work we have used the same Torsional Rheometer with some minor modifications in the design to measure some general properties of Sand Asphalt mixtures. Sand Asphalt mixtures, due to their non-linear viscoelastic character, exhibit `normal stress effects' and `stress relaxation'. The Rheometer that we used was able to capture these responses with high precision. We have laid out proper procedures for the further testing of asphalt related mixtures. A typical sand asphalt mixture sample in cylindrical shape was used as the test specimen. From this work some interesting data was obtained. A remarkable observation was that as the shear rate is increased, the normal force and torque generated initially decrease, but beyond a certain shear rate they attain a constant value.

The modeling of Sand Asphalt and experiments to measure their rheological properties are of vital concern to many industrial processes especially highway and roadway pavement construction industry. A variety of hot mix asphalt mixtures are used in highway and runway pavement construction, with each mixture catering to a specific need. These mixtures vary in type and percentage of aggregates and asphalt used and consequently exhibit marked differences in their response. The main thrust of this research is to provide experimental data which would be helpful in determining the efficacy of the constitutive models that have been developed for these hot mix asphalt mixtures. Here we attempt to provide experimental data in the raw form for Sand Asphalt mixtures that would be helpful in the theoretical modeling efforts involving asphalt materials using a continuum point of view. For example the data obtained can be of immense help to evaluate the constitutive model developed by Murali Krishnan and Rajagopal. The Sand Asphalt mixture in their model is modeled as `homogenized' single constituent due to the peculiarity of its makeup. The constitutive model of Murali Krishnan and Rajagopal is based on a thermodynamical framework for materials possessing multiple natural configurations (multiple stress free states) to derive the constitutive equations. Recently an Orthogonal Rheometer was built to characterize the granular solids by Gupta and Rajagopal which was later used by Baek in the torsional mode. In this work we have used the same Torsional Rheometer with some minor modifications in the design to measure some general properties of Sand Asphalt mixtures. Sand Asphalt mixtures, due to their non-linear viscoelastic character, exhibit `normal stress effects' and `stress relaxation'. The Rheometer that we used was able to capture these responses with high precision. We have laid out proper procedures for the further testing of asphalt related mixtures. A typical sand asphalt mixture sample in cylindrical shape was used as the test specimen. From this work some interesting data was obtained. A remarkable observation was that as the shear rate is increased, the normal force and torque generated initially decrease, but beyond a certain shear rate they attain a constant value.

This thesis deals with modification of an existing four-cylinder diesel engine to a singlecylinder research engine. The work is divided into four main parts. The first part is theoretical, briefly describes research engines, their individual types and provides an overview of their functions. The second part of the work includes the modification of a four-cylinder diesel engine to a single-cylinder research engine, focusing mainly on balancing inertia forces. The third, most extensive chapter contains the structural analysis of the crankshaft. The last part contains the design of a torsional coupling, which ensures the connection of the engine with the dynamometer.

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