Part II: 35-Year Old Splined-Disc Rotor Design For Large Gas Turbine
By Manfred J. Janssen and John S. Joyce
Part I of this article appeared in the October 1996 issue of Electricity Today
The design principles of the splined-disc-type rotor with Hirth-serration couplings used in all Siemens heavy-duty gas turbines since 1960 are reviewed. The benefits of this rotor construction are elaborated against the operational requirements imposed on rotors by present day large advanced gas turbines for electric power generation. Details of the stress assessment, analysis and testing underlying the design, as well as a description of the assembly of the rotor are also presented, using mostly the 170 MW-class 3600 rpm Model V84.3A gas turbine to illustrate the most recent technology.
Linear-Elastic Fracture-Mechanical Analysis
It must be assumed that all the rotor components contain flaws which lie below the detection threshold of the employed ultrasonic testing equipment. The higher the danger potential the greater is the necessity to appraise carefully the effect of detectable permissible flaws in conjuction with assumed unrecognizable flaws. Very special care must, therefore, be taken in evaluating the condition of each and every gas turbine rotating part.
Fracture-mechanical analysis allows the behavior of flaws to be predicted. Fracture mechanics enable the stress to be linked with the component geometry to define a stress magnitude which is called the stress intensity factor. (K). The safety margin between the permissible flaw size at the end of the design life of the component and the critical flaw size can be determined by applying the appropriate material property characteristic values that govern stable and instable crack propagation. The K concept of linear-elastic fracture mechanics forms the basis for performing the analysis of all rotor components. The following equation is valid for all possible failure mechanisms involving both stable and instable crack propagation:
(D)K=(D)s . Öa . M
in which (D)K equals the (cyclic) stress intensity factor, (D)s the (cyclic) normal stress, a the characteristic fault size and M the form factor which is a function of the geometry of the component, the flaw and the stress.
Where linear-plastic analysis does not suffice in the case of ductile materials, which tend when loaded to suffer large localized plasticities, the two-criteria method is applied. This method is an engineering tool to evaluate the behavior of cracked structures from materials that range from being highly brittle to fully plastic. It yields a failure curve that delineates the range, behond which instable failure of cracked components must be reckoned with.
The schematic diagram in Fig. 9 shows the procedure that is followed in the fracture-mechanical design of all cyclically highly stressed components. The stress components and the critical flaw size in accordance with the above equation are determined at every intersection point of the finite element grid (Step 2). The maximum permissible flaw size at the end of the component design life is then calculated with a highly conservative safety margin (Step 3).
The permissible initial flaw size is determined by means of a crack-propagation computation from the maximum permissible final flaw size. The result at each finite-element grid intersection point is entered into the so-called permissible flaw-size map of the component (Step 4). Such maps form the basis for the non-destructive quality-assurance testing prescribed for each rotating part. A typical permissible flaw-size map of a compressor disc is presented in Fig. 10.
If the determined permissible flaw size lies below the detection threshold of the prescribed ultrasonic testing equipment or if the calculated number of load cycles for barely detectable flaws is too low, then a more precise analysis of the area in question is carried out (Step 5). This locally applied fracture-mechanical analysis considers the stress gradient in the direction of crack propagation, as well as the changing flaw shape in the course of crack propagation. If this in-depth analysis does not permit a detectable flaw size or an adequate number of load cycles for a barely detectable flaw, then the component geometry must be redesigned.
With regard to LCF stressing a safety margin of at least 1.5 must be ensured for both the permissible number of load cycles and fracture toughness (KI). A safety factor of 2 is required with respect to critical-crack depth. These three requirements must be fulfilled simultaneously.
Rotor Vibration Analysis
A finite-element calculation method is applied to model and simulate the dynamic performance of the gas turbine-generator shaft system. Special programs for rotor dynamic analysis are employed. The emphasis in the simulation calculations is placed on:
- bending and torsional-mode natural frequencies
- vibration response to discrete imbalances
- vibration response to various electrical faults
- bending stresses and movements
- torsional stresses
Figure 11 shows an example of a shafting model comprising a large number of shaft elements. The coupling of the shafting to the foundation is represented by spring elements which reflect the stiffness not only of the journal bearings but also of the bearing supports, machine casings and foundations.
The spring and damping coefficients of the bearing supports, casings and foundations are determined by detailed finite-element calculation of these individual components. In addition, the stiffness values are verified by measurements made on prototype gas turbines in the factory full-load testing facility.
The journal bearing characteristics are determined on the basis of Prof. Glienicke's bearing theories. The characteristics and Glienicke coefficients of the journal bearings employed in all Siemens gas turbines were determined experimentally both in Siemens laboratories and in Prof. Glienicke's research institute in Karlsrune .
Figures 12 and 13 reproduce just a few of the copious results of a computer simulation of the shaft-vibration response to discrete imbalances (denoted by U) in the form of resultant half-amplitude (zero-to-peak) vibrations over the entire speed range up to 4500 rpm (75 Hz). The first and second bending modes were excited by appropriately located imbalances. In both cases, the pair of curves show the vibration-response magnitude (larger semiaxis) at each shaft journal.
The vibration response peaks at 31 Hz and 73 Hz indicate the first and second bending natural frequencies in the vertical direction respectively. The corresponding responses in the horizontal direction occur at 20 Hz and 35 Hz. The last mentioned value is of little significance because of the heavy damping due to the soft horizontal support. The calculated natural modes compare well with the actual test measurements reported in Subsection 6.2.
The simulation and test results clearly reveal the remarkably low tuning of the rotating system, i.e. only one subsynchronous critical speed at just over half rated speed with the second critical speed occurring well above the overspeed-trip setting (108 per cent rated speed) of the emergency governor. This is attributable to the combination of light-weight construction (many voids between uniformly thin-walled discs and in the central drum section) with high stiffness due to the rotor having a large diameter compared with its length, the ratio of its bearing span to its average drum diameter being only roughly 5.
Experimental Investigations
Measurements on rotors while being balanced and tested in the factory overspeed bunker and on rotors in prototype gas turbines driving the 170 MW nominally rated water-friction brake in the Berlin factory test facility are used to check the rotor performance characteristics predicted by theoretical considerations and calculation methods. Metal temperatures and rotary stresses, as well as absolute pedestal and relative shaft vibrations, are recorded in addition to aerothermodynamic values.
Rotor Balancing and Overspeeding
The operational safety of a gas turbine rotor is ensured by the design, which takes into account all the effects of normal and abnormal operation, as also the material properties, as well as by comprehensive quality assurance in the course of manufacture. In addition, each rotor is subjected to a 20 per cent overspeed test, with it being run at 120 per cent rated speed for two minutes. The purpose of this overspeeding is to set all the jointed and shrunk-on components of the rotor so as to minimize any changes in balance during operation at normal running speeds. Furthermore, it causes limited partially plastic material deformation of the notches which results in prestressing them, thereby prolonging useful life, and in improving the transmission of forces through the jointed parts.
Each gas turbine is balanced first at low speed. After having been oversped it is then balanced at high speed by inserting balancing weights in four different planes until the factory-internal criteria for satisfactory running performance are met over the entire operating speed range. Since gas turbine rotors are basically elastic, being run above the first critical speed, the fundamental natural frequency is counteracted by a group of three compensating masses which is selected so as not to affect the low-speed running performance of the rotor. The rotating performance characteristics determined in the overspeed bunker are not necessarily the same as those later in the field. Consequently, each rotor is balanced in the factory to considerably more stringent limiting values than those prescribed in the ISO Standard 11342 for flexible rotors.
Verification of the Dynamic Behavior of the Rotor
Exhaustive measurements are made on each prototype gas turbine rotor in the overspeed bunker and in the machine full-load testing facility to investigate the dynamic behavior of the rotor and its tie-rod. They serve to confirm the integrity of the rotating system, and to verify the computational methods and modelling assumptions employed in its design.
A great advantage of the Berlin gas turbine testing facility is that the prototype machines do not drive a generator synchronized with the local electrical system, but instead a dynamometer in the form of a water-friction brake, thus permitting them to be run under load at any selected speed.
In this way the dynamic behavior of the rotor under severe operating conditions can be investigated, e.g. at different loads up to peak load, over an off-frequency range extending from 92 per cent to 108 per cent rated speed and up to the surge limit of the compressor. Such tests demonstrate that the gas turbine can be reliably operated under even more extreme operating conditions than can occur in an actual power plant.
The running performance of prototype gas turbines is investigated in the testing facility in accordance with the API Standard 616. The fundamental natural frequency can be detected by insertion of supplementary balancing weights to create a defined imbalance of the rotor. This test also makes sure that the fundamental natural frequency does not lie close to any resonant speed. The running performance of the rotor is evaluated on the basis of the results of both the absolute pedestal and the relative shaft vibration measurements.
The vibration behavior of the tie-rod up to 120 per cent rated speed in the overspeed bunker is determined by means of strain gauges. The same measuring system is employed in the course of prototype gas turbines being operated under load and at off-frequency in the factory testing facility in order to verify satisfactory dynamic behavior under abnormally extreme conditions.
Two strain gauges were adhered to the tie-rod where the highest alternating bending stresses occur. Both strain gauges registered not only almost constant but also quite low vibrations (around 20 microns/m which correspond to an alternating bending stress of around 4 MPa).
The pedestal and shaft-vibration velocities, displacements and phase angles during a start-up in the test facility are reproduced in Figs. 14 and 15. The recordings of the vibration velocity over the speed range reveal pronounced maxima which indicate casing resonance of about one-third nominal speed (20Hz). They also show the first critical bending natural frequency to occur at slightly over half rated speed which is in good agreement with the calculated value. The associated phase-angle recording shows the 180¡ change that typically occurs when a resonance point is run through. The freedom from resonance from about half speed up to 108 per cent rated speed is confirmed by the measurements. A similar result is shown by a recording of the relative shaft displacement at the turbine bearing.
Rotor Assembly
In the factory the fore-shaft section is first tightly screwed on to the tie-rod threaded end. The tie-rod is then tilted and brought into the vertical position. The fore-shaft section is then secured by means of a precise chuck to the base plate of the stacking stand. Next, the bladed compressor discs are laid horizontally on top of one another. The Hirth teeth ensure exact centering of the individual discs to one another and to the central through-bolt. There is thus no need for additional centering elements or assembly devices. Those discs, which are provided with a tie-rod damping clamp, are stacked with these elements already assembled on them.
An approx. 0.1 mm clearance fit permits trouble-free assembly.
After the turbine discs and aft-shaft section have been stacked, as photographed in Fig. 16, the tie-rod is cold-stretched by means of a hydraulic device which is schematically shown in Fig. 17. It basically consists of an annular cylinder and piston. The former is connected by means of a screw coupling to the tie-rod and the latter is supported against a shoulder of the aft-shaft section. The hydraulic force is gradually applied which not only stretches the tie-rod but also presses all the stacked rotor components very tightly together. The force is increased until the tie-rod elongation is measured to be about 120 per cent the nominal value which amounts to a cold stretch of approx. 0.2 per cent of the bolt length. The locking nut is then tightened by hand. On relaxing the hydraulic press, the tie-rod stretch drops to around the nominal value resulting in utilization of only half the yield strength of the tie-rod material (cf. Fig. 4). The screw coupling has the same fine thread as that at the other end of the tie-rod. The locking nut is conically shaped to ensure uniform loading of the threads. Unlike the fore-shaft section, the locking nut at the aft-shaft end bears no torque-transmission load.
The assembled rotor is then tilted and laid horizontally on floor stands. First, the journals of both shaft bearings are finish-machined in a precision lathe which also permits highly accurate run-out checks to be performed on the rotor. Next, the rotor is balanced in the overspeed bunker. The rotor is provided with seven balancing planes, three of which are accessible when the gas turbine is completely assembled and are thus reserved for insertion of balancing weights in the field in the event of the rotor balance needing refinement. The remaining four balancing planes are available for the static and dynamic balancing of the rotors in the factory. Finally the rotor is subjected to 20 per cent overspeed testing. This two-minute test not only verifies the dynamic behavior of the rotor at high supersynchronous speed, but also causes local plasticity at highly stressed points, thus improving their fatigue strength as explained in Subsection 6.1. The rotor run-out checks are then repeated to ascertain whether any geometrical alterations occurred during overspeeding as a result of any settlement of the Hirth couplings. The remaining imbalance calculated from the run-out deviations measured at 25 locations along the rotor may not exceed a certain prescribed magnitude.
Unlike other disc-type rotors employing short tie-bolts arranged in pitch circles, splined disc-type rotors of the type presented in this paper can be readily dismantled in the power plant, requiring only about 100 man-hours of work, by reversing the above described factory assembly procedures and reassembled, as in the factory, without any need for rebalancing. Such dismantling allows all the rotor components to be checked ultrasonically if required by any official regulatory bodies.
Conclusions
The operating experience with splined-disc rotors featuring Hirth-serration couplings confirms their suitability for gas turbine applications. The underlying principle of the design concept is the clear separation of the function of the single long prestressed tie-rod to preserve rotor integrity from the function of the self-centering Hirth couplings to transmit the torque reliably under all normal and faulted operating conditions without depending on the contact friction between the rotor components. As was in the past common practice, the rotor can be dismantled to allow ultrasonic inspection of the discs and tie-rod, and then reassembled in the field without any need to rebalance it. Furthermore, all the compressor and turbine blades can without exception be individually removed in the field to allow recoating or replacement in minimum time. It is thus never necessary to return a splined-disc rotor of the presented type to the factory for repair of modification.
The long outstanding reliability record of splined-disc-type rotors with Hirth couplings can be attributed to their simple construction and large performance safety margins under all conceivable operating conditions. It can thus be confidently expected that they will continue to satisfy equally well the operating requirements of advanced high-temperature gas turbines in the future.
Manfred Janssen and John Joyce are with Siemens Power Gen-eration. This paper was originally presented at the Inter-national Gas Tur-bine and Aero-engine Congress and Exhibition, in June of 1996.