Two sample cases are presented in order to clarify the spe- cific results obtained from a standard torsional analysis.
2.8.1 MOTOR-GEAR-COMPRESSOR TRAIN Figure 2-3 presents the general layout of a typical motor driven compressor train. For this example a motor, running at 1788 revolutions per minute, drives a speed increasing gear which powers an 8100 revolutions per minute compres- sor. This train is modeled using data normally supplied by vendors of the various components (motor, gear, compressor, nisms (for example, torque pulsations resulting from lateral-
torsional coupling of gear vibrations). The coincidence of any torsional natural frequency with any potential excitation frequency along the reference operating speed line must meet the API separation margin of ± 10 percent.
The corresponding train rotor mode shape for each natural frequency is a plot of relative angular deflection versus axial distance along the coupled rotors. These plots are typically normalized to unity or to the location of maximum angular deflection. In Figure 2-19, Views a–e display train torsional modeshapes calculated for a motor-gear-compressor train.
Mode shape information is important to the proper inter- pretation of the results. Should a torsional interference exist, study of the train mode shape in question can yield informa- tion on nodal point locations and anti-nodal point locations along the deflected rotor train. This information allows the designer to understand where the system is sensitive to flex-
10 15
5
0
400
-400 0 800 1200
Temperature °F
Shear Modulus-KSI x 10-3
Figure 2-16— Variation of Shear Modulus With Temperature
(AISI 4140 and AISI 4340; Typical Compressor and Steam Turbine Shaft Materials)
Structural alloys handbook (static shear modulus)
Aerospace structural metals handbook (ratio determined from dynamic tensile modulus;
Poisson's ratio = 0.290.)
TUTORIAL ON THEAPI STANDARDPARAGRAPHSCOVERINGROTORDYNAMICS ANDBALANCING 95
Figure 2-17—Sample Train Campbell Diagram for a Typical Motor-Gear-Compressor Train
90% speed Motor operating speed 110% speed
1st pinion lateral critical
+10%
2 × electric line frequency –10%
1st compressor lateral critical
1st gear lateral critical
1st motor lateral critical
1st train torsional natural frequency +10%
Electric line frequency –10%
2nd train torsional natural frequency 1 x compressor speed
1 x motor speed
Operating speed (RPM) Range of unacceptable torsional
natural frequencies
Range of acceptable torsional natural frequencies
Torsional Natural frequency (CPM)
Copyright American Petroleum Institute Reproduced by IHS under license with API
1st stage blade natural frequency
3rd train torsional natural frequency
2nd train torsional natural frequency 1st turbine lateral critical
1st train torsional natural frequency 1st compressor lateral critical
90% speed Motor operating speed 110% speed
Figure 2-18—Sample Train Campbell Diagram for a Typical Turbine-Compressor Train
40 x shaft speed (blade pass)
1 x shaft speed
Operating speed (RPM) Range of unacceptable torsional natural frequencies
Range of acceptable torsional natural frequencies
Other blade natural frequencies
Natural frequency (CPM)
TUTORIAL ON THEAPI STANDARDPARAGRAPHSCOVERINGROTORDYNAMICS ANDBALANCING 97
Figure 2-19—Torsional Modeshapes for a Typical Motor-Gear-Compressor Train
1.00.50.0-0.5-1.01.00.50.0-0.5-1.01.00.50.0
0.0 0.0 0.0
-0.5-1.0
Normalized angular displacement (dim)Normalized angular displacement (dim)Normalized angular displacement (dim)
Train Axial Rotor Length (in.)
Low speed couplings Gear Pinion High speed coupling Centrifugal Compressor
Motor
40.0 80.0 120.0 160.0 240.0 280.0
40.0 80.0 120.0 160.0 200.0 240.0 280.0
200.0
40.0 80.0 120.0 160.0 200.0 240.0 280.0
Undamped train torsional natural frequency 1st Mode = 1754 CPM
Undamped train torsional natural frequency 2nd Mode = 3474 CPM
Undamped train torsional natural frequency 3rd Mode = 12165 CPM
Copyright American Petroleum Institute Reproduced by IHS under license with API
1.00.50.0-0.5-1.0
Normalized angular displacement (dim) 1.00.50.0-0.5-1.0
Normalized angular displacement (dim)
40.0 80.0 120.0 160.0 200.0 240.0 280.0
40.0 80.0 120.0 160.0 200.0 240.0 280.0
0.0
0.0
Undamped train torsional natural frequency 4th mode = 15491 CPM
Undamped train torsional natural frequency 5th mode = 16039 CPM
Figure 2-19—Torsional Modeshapes for a Typical Motor- Gear-Compressor Train (Continued)
Train Axial Rotor Length (in.)
Low speed couplings Gear Pinion High speed coupling Centrifugal Compressor
Motor
TUTORIAL ON THEAPI STANDARDPARAGRAPHSCOVERINGROTORDYNAMICS ANDBALANCING 99
Figure 2-20—Sample Train Torsional Campbell Diagram for a Typical Motor-Gear-Compressor Train (With Unacceptable Torsional Natural Frequency Separation Margins)
First mode = 1754 CPM Fourth mode = 15491 CPM
Third mode = 12165 CPM
Second mode = 3474 CPM Fifth mode = 16039 CPM
1 x compressor speed
1 x motor speed
200.0150.0125.050.0175.0100.075.025.00.0 90% speed = 1603 RPM 110% speed = 1959 RPMNormal speed = 1781 RPM
0.0 40.0 80.0 120.0 160.0 200.0 240.0
Reference speed x 101 (RPM) Torsional Natural Frequency x 102(CPM)
Note: Torsional and natural frequency interference with 1x motor speed
Copyright American Petroleum Institute Reproduced by IHS under license with API
Figure 2-21—Sample Train Torsional Campbell Diagram for a Typical
Motor-Gear-Compressor Train (With Acceptable Torsional Natural Frequency Separation Margins)
First mode = 1250 CPM Fourth mode = 15036 CPM
Third mode = 12042 CPM
Second mode = 3173 CPM Fifth mode = 16939 CPM
1 x compressor speed
1 x motor speed
200.0150.0125.050.0175.0100.075.025.00.0 90% speed =1603 RPM 110% speed =1959 RPM
Normal speed =1781 RPM
0.0 40.0 80.0 120.0 160.0 200.0 240.0
Reference speed x 101 (RPM) Torsional natural frequency x 102(CPM)
Note: First mode detuned with 1x motor speed by coupling modification
TUTORIAL ON THEAPI STANDARDPARAGRAPHSCOVERINGROTORDYNAMICS ANDBALANCING 101
2.8.2 TURBINE-COMPRESSOR TRAIN
This example considers a steam turbine directly driving a centrifugal compressor (see Figure 2-6). A torsional analysis is usually not required for this train because the torque char- acteristics of the turbine provides a smooth driver with low amplitude torque pulsations in the frequency range likely to excite a lower torsional natural frequency. Without a major excitation mechanism, torsional natural frequencies will not be significantly amplified. Even in this case, however, a con- servative design approach will ensure that there are no inter- ferences with the 1×operating speed lines, particularly with the fundamental (first) torsional natural frequency.
In Figures 2-22 and 2-23, Views a–c present the train Campbell diagram and first three modeshapes for the tur- bine-compressor train. The Campbell diagram shows no in- terferences between the undamped torsional natural frequencies and the 1×operating speed lines, indicating an acceptable design for this train. Note that the coupling stiff- ness controlled mode lies well below the operating speed range, while the resonant modes corresponding to the partic- ular machines lie above the operating speed range. This is characteristic of most turbine-compressor trains and results in the typically acceptable torsional characteristics for these trains.