The vortex track of the rotor is prescribed as a circular orbit with a fixed radius. The lateral force, F(t), can be considered as the sum of two forces: the constant force, F 0 , that the runner would feel if he were in the center of the spiral, which arises from the asymmetry in the flow around the rotor in the spiral, and the unsteady force due to the eccentric rotor movements represented by the force matrix [A]; x(t) is the rotor displacement vector from the spiral center. The interchangeable helix tongue had a significant effect on the force on the runner.
The impeller deflections in the lateral plane were measured by two eddy current probes.
Section 8-B
The force on the runner is measured by a Wheatstone bridge dynamometer mounted on the drive shaft behind the runner. This determined the correct orientation and location of the rotor needed to synchronize the data acquisition system. In the laboratory reference system, Figure 4.1), where m is the mass of the rotor and mounting spindle, and g is the gravitational constant.
IMPELLER X DRY
IMPELLER X DRY 2000 RPM
7 Magnitude spectra for (a) bridge l and (b) bridge 6 on the dynamometer with impeller X in volute A at 2000 RPM for non-cavitating design flow at a swirl ratio of 0/w=.l. To extract the hydrodynamic forces from the measurements in water, the dynamic behavior of the dynamometer must be known through the frequencies of interest. The response in magnitude and phase error of the lateral forces F1 and F2 must be flat (see Eq.
For all measurements taken without a vortex, the impeller was placed at the top of the vortex path. Measurements of the weight of Impeller R by rotating the shaft in air are shown in fig. When the force components are transformed out of the rotating dynamometer frame, the resonance disappears.
The parallelism of the sleeves separating the inner and outer bearing pairs of the eccentric drive mechanism was not within the tolerance suggested by the manufacturer. Two accelerometers were mounted on the drive shaft side of the eccentric drive mechanism on the plate pictured. The peaks above the background correspond to the peculiarities of the dynamometer response in the rotating frame.
The purpose of this chapter is to provide some documentation of the dynamic behavior of the apparatus.
IMPELLER R DRY
IMPELLER R
VOLUTE E
OLUTE E
IMPELLER R VOLUTE E
IMPELLER X
ACCELEROMETER
IMPELLER DRY
At O/w = .6, the tangential force stabilized again (see Figures 7.9a-7.11a in the next chapter), consequently tests at higher swirl ratios were unnecessary. For two swirl ratios in the destabilizing swirl region, O/w = 0.1 and 0.3, measurements were made from non-cavitating conditions through the decomposition of the pressure head rise across the pump for the three flow coefficients. This force is presented in the next section for the above tests in terms of the uniform force F O and the unsteady force due to eccentric motion.
The dependence of the magnitude and direction of the uniform force F O and the uniform moment M0 on the flow coefficient is shown in the figure. The angle of the force and moment vectors is measured from the spiral tongue in the direction of rotation of the main shaft. Where Fn > 0, the hydrodynamic force tends to increase the radius of eddy motion.
This corresponds to the decrease of the negative stiffness and the added mass (zero crossing value and the 02 term of Fn) of the hydrodynamic force. The effect of cavitation on the steady force and moment by breaking down the head rise over the pump is shown in Fig. The steady force component in the direction of the full tongue, Fox, was more affected by cavitation.
Nw is the number of swirl ratios for which the variance of the elements of [A] was available.
X VOLUTE A
IMPELLER X VOLUTE A
IMPELLER X YOLUTE A
IMPELLER X NOH-CAVITATING
IMPELLER X VOLUTE A HOH-CAVITATIHG 3000 RPM
10% HEAD LOSS
The measured force is the result of pressure and shear stress acting on the surface of the rotor body. Using a control volume for the momentum equation replaces the contribution of the internal hub and housing walls and blade surfaces with the flow of stress and momentum through the rotor inlet and outlet and the non-uniform fluid momentum in the machine. The operating point reflects the pressure distribution on the pressure and suction surfaces of the rotor blades.
The unsteady forces are associated with the slope of the wing force relative to the changing angle of attack. The presence of cavitation on the blade will affect the slope of the blade force. Consequently, integration of a perturbation of the force on the impeller blades due to the imposed vorticity to obtain the unsteady rotor force requires the inclusion of the changing flow exit angle.
Mt = Zshroud Fn, shroud + Zblade Fn, blade. with the z-axis pointing upstream from the plane at the center of the impeller discharge. The contribution of the impeller volute can be discussed in terms of the force on the impeller blades, because cavitation occurring in the machine would first affect the contribution of the internal surfaces. A simple description of the effect of cavitation on the lever arms is that cavitation will influence the contribution to the integrated forces and moments from the impeller blades before the contribution from the external shroud surfaces, which would have a larger lever arm.
An integral over the moment of the axial compressive force element, rxpn21 dS, will contribute to the lateral moment.
IMPELLER X HOH-GAVIT
2000 RPM
IMPELLER X NON-CAVIT
IMPELLER X HOH-CAVIT
D Dynamics of a Flexible Rotor in Magnetic Bearings," Proceedings of the Fourth Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 2443, str. Proceedings of the First Workshop on Rotordynamic Instability Problems in High- Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 2133, str. A Nova oblika blažilnika za turbostroje," Proceedings of the Fourth Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery , Teksaška univerza A&M, College Station, Teksas, NASA CP 2443, str.
W Force and Moment Rotordynamic Coefficients for Pump- Impeller Shroud Surfaces," Proceedings of the Fourth Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 2443, s. Colding- JS,?jrgensen, J Effekt af væskekræfter på rotorstabilitet af centrifugalkompressorer og pumper," Proceedings of the First Workshop on Rotordynamic Instability Problemer in High-Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 2133, s. Franz, R., og Arndt, N., 1986a, "Measurements of Hydrodynamic Forces on the Impeller of the HPOTP of the SSME," Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, rapport nr.
34;Rotordynamic Forces on Centrifugal Pump Impellers," Proceedings of the Eighth Conference on Fluid Machinery, Akademiai Kiad6, Budapest, Hungary, Vol. J Squeeze-Film Dampers for Turbomachinery Stabilization," Proceedings of the Third Workshop on Rotordynamic Instability. Problems in High Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 2338, pp. Proceedings of the Fifth Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 3026, pp.
W Influence of Thrust Shroud Forces on Turbopump Rotor Dynamics,” Proceedings of the Fifth Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Texas A & M University, College Station, Texas, NASA CP 3026, p.
L TfP
A model is then used to calculate the finite stiffness of the elastic dynamometer-axle system. To obtain the elements of the hydrodynamic force matrix [A] evaluate the Fourier coefficients of Cos and sin of Eqn. The forces and moments are nondimensionalized by the product of the dynamic head using the impeller exit tip velocity and the impeller discharge area.
The deflection and rotation of the shaft on the disk (x, y, 'Px, 'Py) are related to the applied force and moment via the coefficients of the deflection matrix. When the dynamometer is placed between the bearing and the impeller, forces applied to the impeller deform the dynamometer bars. First, the equations of the forces and moments at the center of mass of the disk are written for the impeller rotating and swirling in the air.
Let r = x + e, where x is the elastic deflection of the shaft in the thruster and e is the displacement due to the imposed circular orbit. Let Zcrn be the distance of the center of mass of the "disc" from the calibration plane. Since the hydrodynamic forces contributed significantly to the forces experienced by the propellant in wet motions, the equations used to calculate the hydrodynamic forces and moments were reused, including the above model for the stiffness of the dynamometer-axle system.
The finite stiffness of the dynamometer-axle system is not included in the processing of forces and moments presented in previous chapters.
I RIGID 2000 RPM 0-:4,37
The data acquisition system consists of the frequency multiplier/divisor, two closed loop motor controllers and the data taker. The reinforced dynamometer bridges, pressure transducers and accelerometers are read by the data taker channel selector. Once the conversion is complete, the sample-and-hold is released to obtain the signal from the channel indicated by the AIS.
From the rear panel of the motor control box, two cables go to the interface box, the stop and start relay signals and the control signal with associated power lines. A block diagram will be discussed and then selected elements of the control system will be further discussed with reference to circuit drawings. The input command clock and reference index (SYNC IN) for resetting the internally derived command index are connected to the front panel of the engine control box, fig.
If speed but not spindle phase is to be controlled then either the SYNC IN BNC must be grounded or the jumper next to 4040 (U22) on the DAC up/down card must be removed. If the DAC up/down approaches the limits of the DAC output voltage range (±5V), the window detector in Fig. The behavior of the control system can be monitored by connecting the DAC up/down and integrator outputs accessible from the front panel to a strip chart recorder.
D .5 Circuit diagram of the interface board with the isolation amplifier and the stop-and-start relay.
AGND
