Test rigs that replicate the conditions for thrust collars (TCs) used in an integrally geared compressor (IGC) are scarce. The test rig described here is based on a typical IGC and is the first rig specifically designed to measure the dynamic reaction force coefficients of the lubricated area of the TC. The test rig uses low-speed and high-speed shafts with independently controlled speed and a pneumatically pressurized thrust disk to apply an axial load ̅ to create the hydrodynamic wedge that balances the imposed axial load. The speed ratio between the low-speed shaft (LSS) and the pinion shaft is 11.67.The geometry of the shafts matches that of a typical IGC. Tests were conducted at pinion speeds of 5, 7.5, and 10 krpm and ̅ = 200, 300, and 400 N. The resulting range of applied pressures is smaller than those arising in practice.The author conducts static tests by applying an incrementally-increasing ̅ on the pinion shaft and measuring the relative displacement between the BG and the TC (Δ ̅ ). One test is conducted at each predetermined spin speed. Run-out on the TC as well as the BW obscures the data. Averaging works well to eliminate the effects of run-out.The author uses the averaged ̅ and Δ ̅ values to create a static, load/ relativedisplacement curve and the slope is the measured static stiffness coefficient ( ̅ ). The axial stiffness coefficient results are compared to predictions from a code based on a 2016 model due to Cable et. al. Their dynamic reaction-force model is = − Δ − Δ̇ iii where is the reaction force of the TC, and is the axial damping coefficient. The trends and the magnitudes of the measured ̅ values and the predicted values from San Andres code for agree very well, especially for the 5 krpm test case. The author then conducts dynamic tests involving an applied impulse load to the TC shaft. One hundred impulses are conducted at each spin speed ( ), ̅ test condition for averaging purposes. A one degree of freedom damped motion model uses Δ ( ) measurements to determine the damped natural frequency ( ) and damping factor ( ) for each test point. The thrust collar mass and the measured were then used to calculate and . The values obtained in this fashion were consistently (and markedly) smaller than the static ̅ values. Based on the results, the author uses the following model = − Δ − Δ̇− Δ̈ that includes the virtual-mass coefficient ( ). The Cable et al. model was based on the Reynolds equation and accordingly did not produce a virtual-mass term.The term is calculated for each test point using ̅ , , and . increases as a function and ̅ . It ranges from 0 to 19.5 kg; the mass of the pinion shaft is 12.8 kg.Both predictions and measurements show an increase in with increasing ̅ . The test rig produced damping coefficients that increased for increasing , while the predicted values decreased. The magnitude of was lower than the predicted damping by a factor of 2 -10.iv ACKNOWLEDGEMENTS

A new flexible-pinion-shaft rotor model is presented to predict the response of the pinion shaft of an integrally geared compressor (IGC). The motion of the pinion shaft is driven by: (1) its own imbalance and (2) the axial reaction force developed by relative axial motion at the thrust collar (TC) that connects it to the pinion. The axial reaction force at the TC arises because of the relative axial motion between the pinion shaft and the bull gear (BG) at the overlapping area of the TC. The relative axial motion arises because of: (1) absolute axial motion of the pinion (assumed to be a rigid body), (2) pitch and yaw motion of the pinion at the TC, and (3) absolute axial motion of the BG at the TC overlap area. Because the axial reaction force acts at a radial distance from the mass center of the TC disk, it creates moments that couple the relative axial motion of the pinion and BG shafts to the radial motion of the pinion. The present model includes the local flexural stiffness of the BG. Excitation for the model is provided by: (1) runout from the BG at its running speed, Ω, acting through the axial reaction force of the TC, (2) runout from the pinion at its running speed, ω, acting through the axial reaction force of the TC, and (3) pinion TC mass imbalance at ω. Measured axial runouts of the BG and TC were taken from a test rig at the authors’ laboratory. Predictions for the TC oil-film axial stiffness and damping come from a proprietary Reynolds equation solution to the TC oil-film. The local axial stiffness of the BG at the overlap area was obtained from a finite element analysis of the authors’ test rig. The base rotordynamic model for the pinion was provided for a production IGC pinion by an IGC manufacturer including the bearings and structural dynamics model. Waterfall plots are presented from the model’s predictions of radial motion at the IGC’s Stage 1 compressor impeller. The response is dominated by synchronous response at the pinion speed, ω, and tracking subsynchronous response at the BG speed, Ω. The response at ω comes from the pinion’s imbalance, not the pinion runout at the TC. The response at Ω comes from the BG runout acting across the TC. The IGC manufacturer’s representatives state that predictions from the model are consistent with measurements from real IGCs, particularly in regard to the presence (and amplitudes) of tracking subsynchronous response amplitudes at the BG frequency. Obviously, more detailed models can be developed for the rotordynamics of IGCs, but the authors feel that this relatively simple, one-rotor model, is adequate to predict the observed tracking phenomena in IGCs. The analysis can be produced by modifying an existing rotor code or by simply downloading the rotor’s [M], [K], and [C] matrices over a range of speeds and then using MATLAB or similar codes.

In this retrospective cohort, patients with high-frequency migraine and comorbid mood disorders showed small but not clinically meaningful improvement over baseline on some headache and mood disorder questionnaires after four 45-minute osteopathic manipulative therapy (OMT) sessions. STUDY DESIGN: Retrospective cohort.LEVEL OF EVIDENCE: STEP 4. BRIEF BACKGROUND INFO:OMT is a nonpharmacological treatment used by osteopathic physicians to treat musculoskeletal and other medical complaints. This retrospective study evaluated the effect of OMT in patients with high-frequency migraines and comorbid mood disorders.

Test rigs that replicate the conditions for thrust collars (TCs) used in an integrally geared compressor (IGC) are scarce. The test rig described here is based on a typical IGC and is the first rig specifically designed to measure the dynamic reaction force coefficients of the lubricated area of the TC. The test rig uses low-speed and high-speed shafts with independently controlled speed and a pneumatically pressurized thrust disk to apply an axial load ̅ to create the hydrodynamic wedge that balances the imposed axial load. The speed ratio between the low-speed shaft (LSS) and the pinion shaft is 11.67.The geometry of the shafts matches that of a typical IGC. Tests were conducted at pinion speeds of 5, 7.5, and 10 krpm and ̅ = 200, 300, and 400 N. The resulting range of applied pressures is smaller than those arising in practice.The author conducts static tests by applying an incrementally-increasing ̅ on the pinion shaft and measuring the relative displacement between the BG and the TC (Δ ̅ ). One test is conducted at each predetermined spin speed. Run-out on the TC as well as the BW obscures the data. Averaging works well to eliminate the effects of run-out.The author uses the averaged ̅ and Δ ̅ values to create a static, load/ relativedisplacement curve and the slope is the measured static stiffness coefficient ( ̅ ). The axial stiffness coefficient results are compared to predictions from a code based on a 2016 model due to Cable et. al. Their dynamic reaction-force model is = − Δ − Δ̇ iii where is the reaction force of the TC, and is the axial damping coefficient. The trends and the magnitudes of the measured ̅ values and the predicted values from San Andres code for agree very well, especially for the 5 krpm test case. The author then conducts dynamic tests involving an applied impulse load to the TC shaft. One hundred impulses are conducted at each spin speed ( ), ̅ test condition for averaging purposes. A one degree of freedom damped motion model uses Δ ( ) measurements to determine the damped natural frequency ( ) and damping factor ( ) for each test point. The thrust collar mass and the measured were then used to calculate and . The values obtained in this fashion were consistently (and markedly) smaller than the static ̅ values. Based on the results, the author uses the following model = − Δ − Δ̇− Δ̈ that includes the virtual-mass coefficient ( ). The Cable et al. model was based on the Reynolds equation and accordingly did not produce a virtual-mass term.The term is calculated for each test point using ̅ , , and . increases as a function and ̅ . It ranges from 0 to 19.5 kg; the mass of the pinion shaft is 12.8 kg.Both predictions and measurements show an increase in with increasing ̅ . The test rig produced damping coefficients that increased for increasing , while the predicted values decreased. The magnitude of was lower than the predicted damping by a factor of 2 -10.iv ACKNOWLEDGEMENTS

The incorporation of real-time structural health monitoring has the potential to substantially reduce the inspection burden of advanced composite rotor blades, particularly if impacts can be detected and characterized using operational data. Data-driven impact identification techniques, such as those applied in this work, require that a structural dynamic model of blade frequency response functions (FRFs) be developed for the operational environment. However, the operational characteristics of the rotor system are not accurately described by a model developed and validated in a nonrotating environment. The discrepancies are predominately due to two sources: the change in the blade root boundary condition and the presence of a centrifugal force. This research demonstrates an analytical methodology to compensate for the first of these effects. Derivations of this method are included, as well as analytical and experimental results. Additionally, the theory and experimental results are presented for an approach by which planar impact area and impactor stiffness may be estimated. Applying these techniques, impact location estimation accuracy was improved from 51.6% to 94.2%. Impacts produced by objects of 2–in. diameter were demonstrated to be distinguishable from those of 1 in. or less diameter. Finally, it was demonstrated that the impacts by objects of metallic material were distinguishable from those of rubber material, and that such differentiation was robust to impactor size and impact force magnitude.