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.

Thesis deals with the calculation of the crankshaft of the cogeneration unit. It deals with the calculation of equity and forced vibration of the crankshaft. Attention is also paid to the influence of elastic couplings on the shape of its own vibration shaft.

The aim of the thesis is to derive a mathematical model of the engine and driveline in a passenger car, capable of describing the wheel speed disturbances related to the engine and driveline. The thesis is conducted in order to improve the disturbance cancelation algorithm in the indirect tire pressure monitoring system, TPI developed by NIRA Dynamics AB. The model consists of two parts, the model of the engine and the model of the driveline. The engine model uses an analytical cylinder pressure model capable of describing petrol and diesel engines. The model is a function of the crank angle, manifold pressure, manifold temperature and spark timing. The output is the pressure in the cylinder. This pressure is then used to calculate the torque generated on the crankshaft when the pressure acts on the piston. This torque is then applied in the driveline model. Both a two wheel and a four wheel driveline model are presented and they consist of a series of masses and dampers connected to each other with stiff springs. The result is a 14 and 19 degrees of freedom system of differential equations respectively. The model is then validated using measurements collected at LiU during two experiments. Measurements where conducted of the cylinder pressure of a four cylinder petrol engine and on the wheel speed of two different cars when driven in a test rig. The validation against this data is satisfactory and the simulations and measurements show good correlation. The model is then finally used to examine wheels speed disturbance phenomenon discovered in the huge database of test drives available at NIRA Dynamics AB. The effects of the drivelines natural frequencies are investigated and so is the difference between the disturbances on the wheel speed for a petrol and diesel engine. The main reasons for the different disturbance levels on the front and rear wheels in a four wheel drive are also discussed.

The diploma thesis ‚Rubber Torsional Vibration Damper Of a Four-Cylinder Diesel Engine‘ covers all the development phases related to a design of a rubber damper for a specified engine. The individual phases of it are discussed in details throughout the thesis. At first, the construction plan of a crankshaft is given. The computational checks for torsional vibrations and forced torsional vibration are performed then. With regards to it there might be derived the basic parameters and dimensions of a rubber torsional vibration damper. The knowledge of them enables to prepare the constructional plan of a rubber torsional vibration damper. By using this damper construction plan the torsional displacements (deviations) and forced vibrations are calculated. Finally, a mechanical and thermal stress test of this damper is performed and a crankshaft production drawing is produced.

Content of this master thesis is analysis of torsional vibration of the three cylinder engine with balancing shaft. In theoretical part of the thesis the kinematic and dynamic description of the cranktrain mechanism is included. The formation of unbalancing of the engine and methods of balancing are described in the theoretical part as well. In practical part of the thesis the analytical calculation of torsional vibration is provided. Simulation of the engine model in multibody software Adams/Engine was used as the other way of torsional vibration analysis. In the result part of the thesis the comparison of the both way of analysis were discussed. Last step of the thesis was design proposal of the torsional vibration damper done by the analytical calculation.

Drill String dynamic behaviour during the oil drilling operation, was a major source for the failure of the Bottom Hole Assembly (BHA). The behaviour produced torsional vibration, which underpins the stick slip phenomena. Besides threatening the safety of the oil drilling process, such failure cause interruptions in the drilling operations and incurred high maintenance cost to the oil drilling company. This issue can be resolved with the implementation of the optimum control mechanism while operating the drill string. In this research, an optimum control mechanism was proposed to suppress the torsional vibration as well as mitigate the risk of stick slip phenomenon from occurring. The mechanism was proposed through a series of rigorous research strategies i.e. updated-mathematical equation modelling, experimentation and simulation. As the first step, a mathematical equation model describing system dynamics was derived to set the parameter of investigation. Representing the freedom torsional of the two degrees - conventional vertical drill string, the model was used to predict the frictional Torque On Bit (TOB) through non-linear friction force, denoting the ground-formation behaviour during drilling activity. Using a velocity feedback system, the drill-string oscillation was reduced while gradually increasing its velocity via gain scheduling method - allowing fast response to load disturbance. To avoid the motor torque from exceeding the maximum threshold, a Weight On Bit (WOB) was introduced. This approach remarks the novel contribution of this research. Next, an experiment on the preliminary test rig within a controlled laboratory set up was conducted. The rotary drill rig was assembled to identify the dynamics (i.e. parameters) of an individual part of the drill string. The results obtained were then applied in the drill string operation experiment, to identify the optimum control mechanism that can avoid the torsional vibration. To enable triangulation of results, a simulation was conducted by applying the same parameters obtained from the test rig experiment in the model- which is the optimum control mechanism that was proposed in this research to minimise torsional vibration, as well as reducing the chance of drill-string failure due to stick-slip phenomenon.

Torsional vibration is an oscillatory angular twisting motion in the rotating members of a system. It can be deemed quite dangerous in that it cannot be detected as easily as other forms of vibration, and hence, subsequent failures that it leads to are often abrupt and may cause direct breakage of the shafts of the drive train. The need for sufficient analysis during the design stage of a rotating machine is, thus, well justified in order to avoid expensive modifications during later stages of the manufacturing process. In 1998, a project was initiated by the Turbomachinery Research Consortium (TRC) at Texas A&M University, College Station, TX, to develop a suite of computer codes to model torsional vibration of large drive trains. The author had the privilege of developing some modules in Visual Basic for Applications (VBA-Excel) for this suite of torsional vibration analysis codes, now collectively called XLTRC-Torsion. This treatise parleys the theory behind torsional vibration analysis using both the Transfer Matrix approach and the Finite Element approach, and in particular, validates the results generated by XLTRC-Torsion based on those approaches using experimental data available from tests on a 66,000 HP Air Compressor.