Browsing by Subject "Spherical"
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Item Sections of n-dimensional spherical cones(Texas Tech University, 1968-06) Keyton, Nancy E.Many proofs have been given for the proposition: "The intersection of a right circular cone and a plane is a second degree curve (conic)". Among the first mathematicians to have proved it was Apollonius, during the period 262-200 B.C.. In fact the first book in conic sections M8S juritten by Apollonius. In this thesis, first, we supply a vector proof of this proposition, thereby simplifying procedures in the proof. Then we generalize the theorem for sections of a spherical cone in an n-dimensional Euclidean space.Item Static, Rotordynamic, and Thermal Characteristics of a Four Pad Spherical-Seat Tilting Pad Journal Bearing with Four Methods of Directed Lubrication(2014-08-07) Coghlan, DavidStatic, dynamic, and thermal characteristics (measured and predicted) are presented for a 4-pad, spherical-seat, TPJB with 0.5 pivot offset, 0.6 L/D, 101.6 mm nominal diameter, and 0.3 preload in the LBP orientation. One bearing is tested four separate times in the following four different lubrication configurations: (1) flooded single-orifice (SO) at the bearing shell, (2) evacuated leading edge groove (LEG), (3) evacuated spray-bar blocker (SBB), and (4) evacuated spray-bar (SB). The LEG, SBB, and SB are all considered methods of ?directed lubrication?. These methods rely on lubrication injected directly to the pad/rotor interface. The same set of pads is used for every test to maintain clearance and preload; each method of lubrication is added as an assembly to the bearing. Test conditions include surface speeds and unit loads up to 85 m/s and 2.9 MPa respectively. Static data includes measured bearing clearances prior to operation (cold) and immediately after operation (hot), rotor-bearing eccentricities and attitude angles, and a new approach to locating the hot center of a bearing. Dynamic data includes: (1) impedance values calculated from measured accelerations, displacements, and excitation forces; and (2) four sets (one set for each bearing configuration) of direct and cross-coupled rotordynamic coefficients derived from measurements and fit to a frequency independent KCM model. Thermal data include measured temperatures from sixteen bearing thermocouples along with inlet, outlet, stator housing, and ambient thermocouples. Twelve of the bearing thermocouples are embedded in the babbitt layer of the pads while the remaining four are oriented at the leading and trailing edge of the loaded pads exposed to the lubricant. Bearing thermocouples provide a circumferential and axial temperature gradient. The pivot stiffness (pad and pivot in series) is measured and incorporated into predictions. Measured static, dynamic, and thermal values are compared to predictions from XL_TPJB, a computer code developed at the Texas A&M University Turbomachinery Lab for predicting bearing performance. Measurements show significant cross-coupled stiffness terms with opposite signs and magnitudes that are 20-50% of the direct terms, a max axial temperature gradient of 9.6 ?C, and attitude angles as high as 29?; all of these indicate that the tilt motion of the pad may be impeded by friction between the spherical pivot and the pad. Temperature measurements show directed lubrication, coupled with an evacuated bearing housing, reduces max bearing temperatures up to 13.9 ?C for the LEG, 10.2 ?C for the SBB, and 12.8 ?C for the SB. Although the SB and SBB reduce the max bearing temperature as intended, they can also cause an increase in temperatures at the leading and trailing edges of the loaded pads. The LEG typically reduced temperatures at all locations. Compared to the base case of the flooded SO, directed lubrication reduces the max bearing temperature. Additionally, the dynamics of the system can also be significantly impacted. Using directed lubrication can reduce direct stiffness by up to 18% for the LEG, 25% for the SBB, and 20% for the SB. Similarly, the direct damping can be reduced by up to 24% for the LEG, 45% for the SBB, and 34% for the SB.