Kerr, Thomas Chandler (2017-12). Static and Dynamic Coefficient Measurements for a Thrust Collar Used in an Integrally Geared Compressor. Master's Thesis.
Thesis
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 ???v?? 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 ???v?? = 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 ??v?? on the pinion shaft and measuring the relative displacement between the BG and the TC (??v??). 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 ???v?? and ??v?? values to create a static, load/ relative displacement curve and the slope is the measured static stiffness coefficient (???v?? ). 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 ??v???? = ???v???v?? - ??v???v?? where ?????? is the reaction force of the TC, and ???? is the axial damping coefficient. The trends and the magnitudes of the measured ???v?? values and the predicted values from San Andres code for ??v?? 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 (??), ???v?? test condition for averaging purposes. A one degree of freedom damped motion model uses ?v??(??) measurements to determine the damped natural frequency (????) and damping factor (??) for each test point. The thrust collar mass ??v???? and the measured ?? were then used to calculate ??v?? and ??v?? . The ???? values obtained in this fashion were consistently (and markedly) smaller than the static ???v?? values. Based on the results, the author uses the following model ??v???? = ???v???v?? ? ??v???v?? ? ? ??v????v?? that includes the virtual-mass coefficient (??v??). The Cable et al. model was based on the Reynolds equation and accordingly did not produce a virtual-mass term. The ??v?? term is calculated for each test point using ???v?? , ??v??, and ??. ??v?? increases as a function ?? and ???v?? . 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 ??v?? with increasing ???v?? . The test rig produced damping coefficients that increased for increasing ??, while the predicted values decreased. The magnitude of ??v?? was lower than the predicted damping by a factor of 2 - 10.
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 ???v?? 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 ???v?? = 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 ??v?? on the pinion shaft and measuring the relative displacement between the BG and the TC (??v??). 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 ???v?? and ??v?? values to create a static, load/ relative displacement curve and the slope is the measured static stiffness coefficient (???v?? ).
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
??v???? = ???v???v?? - ??v???v??
where ?????? is the reaction force of the TC, and ???? is the axial damping coefficient. The trends and the magnitudes of the measured ???v?? values and the predicted values from San Andres code for ??v?? 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 (??), ???v?? test condition for averaging purposes. A one degree of freedom damped motion model uses ?v??(??) measurements to determine the damped natural frequency (????) and damping factor (??) for each test point. The thrust collar mass ??v???? and the measured ?? were then used to calculate ??v?? and ??v?? . The ???? values obtained in this fashion were consistently (and markedly) smaller than the static ???v?? values. Based on the results, the author uses the following model
??v???? = ???v???v?? ? ??v???v?? ? ? ??v????v??
that includes the virtual-mass coefficient (??v??). The Cable et al. model was based on the Reynolds equation and accordingly did not produce a virtual-mass term.
The ??v?? term is calculated for each test point using ???v?? , ??v??, and ??. ??v?? increases as a function ?? and ???v?? . 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 ??v?? with increasing ???v?? . The test rig produced damping coefficients that increased for increasing ??, while the predicted values decreased. The magnitude of ??v?? was lower than the predicted damping by a factor of 2 - 10.