Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references. Also available on the World Wide Web.

Thesis (M.S.)--Montana State University--Bozeman, 2007. / Typescript. Chairperson, Graduate Committee: Christopher S. Guy. Includes bibliographical references (leaves 66-72).

In any rotating machinery, the geometry of the seal influences the extent of systemleakage. The path taken by the flow in the clearance volume is dependent on the seal and rotor profile. The clearance between a new "seal-rotor" combination is uniform except for small variations during manufacturing and assembly. With time this annular cross section undergoes further physical changes causing non-uniform flow in the annular volume. This azimuthally varying leakage through the seal-rotor annulus creates unbalanced forces on the rotor causing it to whirl. It is essential to identify the reasons for these unwanted forces. Velocity profiling of the clearance volume flow was performed by Morrison et al. (1992) using 3-D LDA measurements on annular and labyrinth seals operating with 50% dynamic eccentricities and a whirl ratio of one. However, this alone does not provide a complete matrix of data for the conditions prevailing in the clearance zone. Additional information of mean and instantaneous wall pressure distributions for 0%, 10%, 25% and 50% rotor dynamic eccentricity for whirl ratios of zero and one, with positive pre-swirl, no pre-swirl and negative pre-swirl conditions were measured by Robic (1999). The data collected showed that the pressure field on the seal walls reversed itself between the whirling and non-whirling conditions. As a continuance of the earlier works, the present effort investigates the effect of whirl ratio variation for a 50% eccentric smooth annular seal at a leakage Reynolds number of 24000. An attempt has been made to collect pressure data for negative whirl ratios also under similar test conditions. A seal test rig capable of handling different eccentricities and whirl ratios simultaneously was designed and constructed for this purpose. Mean and instantaneous wall pressure data were recorded for 50% eccentricity with whirl ratios between ? 1 for a rotor speed of 1800. For a rotor speed of 2700, whirl ratios tested were between ? 0.6 and for 3600 rotor speed, whirl ratios ranging between ? 0.5 were tested. From the collected data a detailed analysis of wall pressures along the seal surface is performed following the technique described by Winslow (1994) and Robic (1999).

Thesis (M.S.)--Montana State University--Bozeman, 2004. / Typescript. Chairperson, Graduate Committee: Alexander V. Zale. Includes bibliographical references (leaves 48-53).

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 105-115). Also available on the World Wide Web.

Static Whirling Rods: Past researchers suggested that “static instabilities” exist at certain rotational speeds of whirling rods. This thesis shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady state equations of whirling rods are formulated in Lagrangian coordinates. Due to the non-linear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is a close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred “static instabilities”. This approach first solves the “static” problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived. Dynamic Rotating Annuli: In-plane modes of vibration of annular plates are investigated. Two different models of equations one from Bhuta and Jones and the other from Biezeno and Grammel that govern the rotational motions of annuli will be studied. Since Biezeno and Grammel’s model was originally derived in Eulrian coordinates, their model will be transformed to the Lagrangian coordinates for the purpose of comparison with Bhuta and Jones’ model. / The solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the annulus while it is in rotation. Exact and approximate solutions are obtained for the Bhuta and Jones’ model, where the approximate solutions on in-plane displacements and natural frequencies are acquired by ignoring the Coriolis effect. A proposed numerical scheme is implemented to solve the governing equations coupled with radial and circumferential displacements. Uniqueness of solutions will be mentioned although it will not be rigorously derived because it is out of the scope of this thesis. Approximate analytical results show that both radial and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing. The exact and numerical results on both models that take the Coriolis effect into account show that radial natural frequencies are increasing and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing.

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.

Tool chatter in longitudinal turning is addressed with a new perspective using a complex machining model describing the coupled tool-workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut (DOC) and workpiece whirling due to material imbalance. The workpiece is modeled as a system of three rotors: unmachined, being machined and machined, connected by a flexible shaft. The model enables workpiece motions relative to the tool and tool motions relative to the machining surface to be three-dimensionally established as functions of spindle speed, instantaneous DOC, rate of material removal and whirling. Excluding workpiece vibrations from the cutting model is found improper. A rich set of nonlinear behaviors of both the tool and the workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various DOCs is observed. Presented numerical results agree favorably with physical experiments reported in the literature. It is found that whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. The 3D model is explored along with its 1D counterpart, which considers only tool motions and disregards workpiece vibrations. Numerical simulations reveal diverse behaviors for the 3D coupled and 1D uncoupled equations of motion for the tool. Most notably, observations made with regard to the inconsistency in describing stability limits raise the concern for using 1D models to obtain stability charts. The nonlinear 3D model is linearized to investigate the implications of applying linear models to the understanding of machining dynamics. Taylor series expansion about the operating point where optimal machining conditions are desired is applied to linearize the model equations of motion. Modifications are also made to the nonlinear tool stiffness term to minimize linearization errors. Numerical experiments demonstrate inadmissible results for the linear model and good agreement with available physical data in describing machining stability and chatter for the nonlinear model. Effects of tool geometry, feed rate, and spindle speed on cutting dynamics are also explored. It is observed that critical DOC increases with increasing spindle speed and small DOCs can induce cutting instability -- two of the results that agree qualitatively well with published experimental data.

The study of the effect of different orbit paths and whirl ratios on the rotordynamic coefficients of a smooth eccentric annular seal, using Computational Fluid Dynamics (CFD) was performed. The flow was simulated for two different orbits - linear and circular for orbit speeds ranging from 0 to 1. This was done using the FLUENT CFD code with a time - dependent solver which allowed the use of dynamic meshing and User Defined Functions (UDFs). The effect of clearance was also studied by simulating the flow through an eccentric seal with one-tenth the clearance and comparing the results. It was seen that the flow field varies significantly with both the change in orbit and clearance and this in turn affects the forces and rotordynamic coefficients. The linear orbit showed major changes in terms of both the flow fields and the resulting forces. The velocities, pressure magnitudes and forces were much larger than the circular orbit. Another important finding was that the behavior of the flow for the smaller clearance is viscosity dominated compared to the inertia dominated flow seen for large clearances. The computation of rotordynamic coefficients for the circular orbits used Childs' theory and it was seen that for larger clearances the CFD predictions were not in agreement with the expected trends from this theory. The smaller clearance simulations, however, show force predictions from which the rotordynamic coefficients obtained match the theory.

Thesis (PhD)--Montana State University--Bozeman, 2008. / Typescript. Chairperson, Graduate Committee: Billie L. Kerans. Includes bibliographical references.