When developing its first heavy-duty gas turbines in the 1950s Siemens selected the splined-disc rotor concept which features a single central through-bolt or tie-rod and individual bladed discs which are splined together by radial facial serrations known as Hirth teeth. The basic design principle is that the central tie-rod does not transmit any torque, but only holds the multi-disc rotor tightly together by an adequate compressive prestress force. The full torque developed by the power turbine is transmitted to the compressor by the Hirth couplings which connect adjacent discs by means of their form-locking splines.
The first commercial machine equipped with such a splined-disc rotor was an 8 MW blast-furnace-fired gas turbine compressor drive which was placed in service in a Ruhr District steel mill back in 1960. It is still in operation, having accumulated nearly 120,000 service hours and been started up more than 1000 times. The design of and experience with this type of rotor for heavy- duty gas turbines was first presented to ASME and in the English technical press in 1981. Earlier publication in the German technical press dates back to 1970 . The same basic rotor construction can be seen in Fig. 1 which illustrates the design of the 170 MW-class 3600 rpm Model V84.3A gas turbine that demonstrated a 38 per cent efficiency in December 1994 in the course of a comprehensive full-load testing program in the Berlin factory.
Design Objectives
Large gas turbines for electric power generation are rarely deployed in the simple-cycle operating
mode, but predominantly in combined-cycle configurations to obtain a higher energy-conversion
efficiency than is possible with any other type of thermal power plant. Coupling the generator to
the cold (compressor) end of the gas turbine possess the obvious advantage that the turbine
exhaust gas can be discharged through a simple axial diffuser which can be connected directly in
line with any heat-recovery system. This arrangement has proved ideal for all cogeneration and
combined-cycle applications of gas turbines over the past 30 years. The cold-end drive is
particularly well suited to single-shaft combined-cycle power blocks which are being widely
adopted by electrical utilities worldwide.
The cold-end drive virtually doubles the torque that normally has to be transmitted to the gas turbine compressor because the power turbine does not drive the generator directly, as is the case with hot-end drive, but through the compressor. The useful power to the generator (roughly half the mechanical output of the power turbine) must, therefore, be transmitted through the compressor in addition to the torque required to drive the compressor itself. It is equally important that all fault torques, no matter how severe, arising from electrical disturbances, e.g. malsynchronization and clearance of system short circuits, be carried in the same reliable defined manner without depending on the contact friction between the individual discs to transmit the normal operating torque and on the shearing resistance of multiple tie-bolts to withstand the much greater electrical-fault torques.
The Hirth-serration couples are designed so that their form-locking teeth can safely transmit the maximum possible torque, which can occur as a result of generator malsynchronization, without relying on the friction between the contacting tooth surfaces. In other words, the inherent frictional component provides a considerable additional safety margin in the transmission of torque through the machine under all operating conditions.
The sharp rise in gas turbine efficiency over recent years is mainly attributable to the adoption of increasingly higher turbine inlet gas temperature levels which require internal cooling of nearly all the turbine blades. The air to cool the moving-blade rows is extracted at different pressure levels from appropriate stages of the compressor. Unlike welded rotors, disc-type rotors lend themselves to providing internal passages through which these air extraction can be led from the compressor to the power turbine. These internal air flows heat the webs of some of the rear compressor discs, thus promoting rapid equalization of the temperature throughout the discs from their rims to their hubs during start-up. Since the other discs, through which no extraction air flows, are not internally warmed up and cooled down so fast, an unavoidably high magnitude (up to 1.5mm) of differential thermal expansion or contraction of the bladed discs occurs in advanced gas turbines. Restraint of this relative thermal movement between neighbouring rotor components results in very high stresses which can lead to rotor eccentricity and bowing, with resultant poor running performance, or even to component cracking.
All the Hirth serrations are thus precisely machined with an orientation to the shaft centerline (tie- rod axis) so that the individual discs are free to move radially in a self-centering manner relative to one another during non-steady-state operation, e.g. fast start-up and loading regime, thus precluding the possibility of overstressing any rotor component due to thermal expansion being inhibited.
The Hirth couplings can, however, only permit free self-centering differential thermal movement of the bladed discs because all the rotor components are held together by a central prestressed tie- rod. The use of several tie-bolts arranged circumferentially on a pitch circle through the disc webs would impede such necessary relative movement of the discs.
By not relying on contact friction to transmit the maximum possible torque, the single long tie-rod need not be prestressed beyond half of the yield strength of its material. Unlike multiple tie-bolts, which must be very carefully tensioned in the course of rotor assembly to ensure a circumferentially uniform prestress, and thus acceptable run-out values, as otherwise the rotor will be susceptible to vibrations particularly during start-up, the actual degree of stretching the single central tie-rod is not critical because it cannot result in non-uniform pressure being exerted on the rotor components.
Another advantage of the single central tie-rod is that it is virtually only statically stressed and not subjected to appreciable cyclic stress due to the rotor sag. In contrast, multiple tie-bolts are cyclically stressed by being elongated to a varying degree with each revolution of the rotor, from a maximum when at the bottom (greatest sag) to a minimum when at the top (least sag). The larger the pitch circle, on which the bolts arranged, the greater is the high-cycle fatigue stressing of the bolts.
Finally, an important design goal is to obtain a low-tuned turbine-generator rotating system with only one single subsynchronous critical speed to minimize the susceptibility to vibrations under any operating conditions. Since splined-disc rotors combine low weight with high stiffness, they only exhibit one subsynchronous critical speed which occurs at around half rated operating speed; the second critical speed lies beyond the overspeed-trip setting of the emergency governor.
Basic Rotor Design
The longitudinal section in Fig. 2 depicts an unbladed Model V84.3A gas turbine rotor. It
consists of individual discs, the number of which is equal to the number of compressor (15) and
turbine (4) stages, a drum section between compressor and turbine, and two shaft-end sections
with journals. All 22 components are clamped tightly together by the tie-rod.
It should be noted that the diameter of the center-bore in each disc is greater than that of the tie- rod, i.e. the discs are not in contact with the tie-rod. It is supported at a few locations from the discs by means of patented damping elements in the form of clamps. Their location is selected to ensure that the first bending-mode natural frequency of the tie-rod lies above the rated speed of the gas turbine. The torque is transmitted by means of the Hirth teeth on both faces at the outer diameter of each disc and drum section (21 Hirth couplings in the case of the illustrated Model V84.3A gas turbine rotor). The drawing in Fig. 3 shows the location of the Hirth teeth, cooling- air extraction holds and damping-element groove on a compressor disc.
The annular clearances between the disc center-bores and the tie-rod permit air circulation to worm up the disc webs and hubs as fast as their external rims in the course of starting up, thereby minimizing thermal stresses and low-cycle fatigue. The pin-hole apertures formed by the slightly flattened serration tips of the Hirth couplings admit air to circulate between the discs. The extraction-air flows to cool the turbine moving-blade rows are also very effective in internally warming up the discs in the compressor rear stages. They equalize the thermal radial expansion of the rotor drum with that of the machine casing during start-up and shutdown conditions, thus permitting extremely small radial blade-tip clearances to be safely adopted.
In addition to achieving the design goals outlined in Section 1, the splined-disc rotor construction possesses other important advantages that contribute favorably to lowering operating stress levels, enhancing machine efficiency and easing maintenance. The contouring, arrangement and manufacture of the bladed discs ensure outstandingly uniform distribution of the tangential and radial stresses. There are, for instance, no stress risers in the disc webs because of the absence of holes that would be required with the use of multiple tie-bolts. An adequate supply of cooling air to the turbine moving-blade roots and profiles is secured with minimum pressure losses by conveying it through carefully dimensioned internal passages from appropriately selected compressor stages. The disc rims do not cover the side-entry roots of either the compressor or turbine blading. With the axial clearances between the blade rows being adequately large, both the compressor and turbine blades can thus be individually removed for recoating or replacement purposes.
Stress Assessment Concept
A gas turbine rotating system is loaded with time by the changes in stress levels as a result of
start-up and shutdown procedures, i.e. low-cycle fatigue (LCF), as well as by steady forces
caused by rotation (centrifugal stress) and thermal gradients, as also by high-cycle fatigue(HCF) in
the course of normal operating conditions. The integrity of the rotating system must also be
ensured for all emergency conditions, such as blade failures and electrical faults. However, long-
term interaction between creep\relaxation and fatigue damage need not be considered due to the
rotor metal temperature not exceeding 400íC. A brief overview of the design methodology is
presented below along with some relevant details for two decisively important components, i.e.
the single tie-rod and the Hirth coupling between the fore-shaft section and compressor first-stage
disc, under faulty operating conditions.
Fatigue Design Methodology
The safety standards and design codes of the Kerntechnis-cher Ausschub (Nuclear Safety
Commission) are generally applied. The procedures established therein, which basically
correspond to the ASME Boiler and Pressure Vessel Code, Section III, are mainly based on time-
independent linear-elastic material properties. The simplified analysis is performed in three steps:
1) Computation of stresses using elastic material properties.
2) Determination of the elastic-plastic strain range due to a stress range calculated by linear- elastic methods by means of a strain concentration factor, i.e. Neubers rule is applied.
3) Calculation of the LCF cycle number. (The stresses calculated in Step 1 provide the basis for the linear-elastic fracture - mechanical analysis discussed in Section 4.)
Concept for Structural Integrity of the Tie-Rod
The maximum stead-state metal temperature of the tie-rod in operation is around 300 degrees C which
rules out creep. The tie-rod is designed to withstand the fatigue caused by 10,000 start/stop
cycles. A typical such mechanical and thermal load cycle is depicted in Fig.4.
The continuous line indicates the change in tie-rod stress during a normal load cycle covering start-up, steady-state operation and shutdown. The initial condition is the cold prestress of the tie-bolt established during rotor assembly. The tie-bolt stress drops from this 50 per cent level down to approximately 45 per cent, when the rotor is accelerated to full speed within four minutes of the start-up command, because of the transverse contraction of the disc rims. Subsequently, it begins to rise and reaches a maximum value of approximately 60 per cent about 15 minutes later due to the rotor drum being heated up faster than the tie-rod. The start-up procedure that gives rise to a maximum variation in tie-rod stress of only 15 per cent of the material yield strength. During steady-state operating conditions the tie-rod stress reverts almost to the cold prestress level. The controlled shut-down procedure results in a tid-rod stress-reduction variation of less than 8 per cent of yield strength.
The greatest possible variation in tie-rod stress occurs if the gas turbine is tripped shortly after the rotor drum has been heated up in the course of the start-up procedure. The dashed in Fig. 4 indicates that the tie-rod stress can peak at approx. 65 per cent, thus raising the stress swing to about 20 per cent of yield strength. This extreme case provides stress values that are employed in verifying the structural integrity of the tie-rod which includes consideration of the maximum equivalent (Mises) stress, as well as low and high-cycle fatigue.
As shown in Fig. 4, the average axial stress, which is equal to the equivalent stress, is less than the maximum permissible value of 67 per cent of the yield strength at 300C to obtain a safety factor of 1.5. This maximum tensional stress level is also not exceeded when the tie-bolt is stretched hydraulically in the course of the rotor assembly. Application of a linear-elastic fracture- mechanical analysis, which is explained in Section 4, results in a number of fatigue cycles that exceeds the design-life cycle number. The stress range due to vibrations during normal operating conditions is derived from full-lead test measurements. The allowable HCF-stress leading (Haigh Diagram) for the steel under consideration is about three times that of the measured value. The measurements are discussed in Section 6.
The fine-thread screw coupling fixing the end of the tie-rod to the fore-shaft section was checked in addition to the tie-rod itself.
The core diameter of the threads at both ends of the tie-rod is larger than the actual rod diameter in order to reduce the stresses on the threads. Detailed finite-element computations show how the load on the screw coupling can best be distributed. This is accomplished by providing the fact of the fore-shaft section with a special contour which yields to a certain defined extent in the region of the lower threads. This results in a highly uniform loading of all the screw-coupling threads. This textbook-design principle is illustrated in Fig. 5, in which the uneven loading of crew threads as a result of employing a conventional rigid nut is contrasted with the thread-lead uniformity that is achievable with a relatively flexible inverted nut. In the case of the tie-rod screw couplings the attained load uniformity precludes plastic deformation of any of the threads.
Pull tests were carried out on a 1:8 scale mode in order to demonstrate that the tie-bolt fails before the screw coupling is damaged. A sketch of the experimental set-up is reproduced in Fig. 6. Attention was focused mainly on the tendency of the fore-shaft stub to turn inside out and on the verification of the finite-element simulation by applying a large number of strain gauges, the locations of which are indicated in Fig. 6.
The measured results from two of the test strain gauges on the fore-shaft stub are compared in Fig. 7 with the corresponding computed values of tangential expansion as a function of the stretching force. The continuous line shows the measurement derived from No.2 strain gauge (cf. Fig. 6) located very close to the screw coupling. The relatively large widening of the fore-shaft stub demonstrates its flexibility and the consequent unloading of the lower threads. The corresponding widening measured in the vicinity of the Hirth serrations by No. 1 strain gauge (dashed line) is only about one-quarter the magnitude registered by the other strain gauge. It can be seen that the calculated predictions agree well with the measured values from No. 1 strain gauge.
In the other case, however, the calculated values are about 20 per cent lower than the No.2 strain-gauge measurement results. This deviation is due to the necessity to simplify the complex geometry of the screw-coupling fine threads for finite-element analysis.
The stretching force was increased until the tie-rod ruptured (F=F max). The subsequent inspection of the screw coupling revealed no significant damage to the threads.
Hirth Couplings under Emergency Loading Conditions
The full torque from the power turbine is transmitted by the radial serrations in the Hirth
couplings connecting the individual rotor elements. Two possible failure modes due to
overloading can
be postulated:
1) The tooth flanks slip relative to one another as a result of tie-rod elongation. This does not necessarily cause deformation of the teeth. The relative movement could extend over several teeth if the torque would be maintained. This would mostly likely lead to damage of the tips of the teeth. Couplings with flatly shaped teeth could fail in this way because of their tooth flanks not being very steep.
2) Extreme torque deforms the teeth as a result of an excessive circumferential force causing a circumferential displacement due to plastic deformation of the metal. The centre of this turning motion (fulcrum) need not lie on the centerline of the rotor because neither the tie- rod nor any form of centering establishes a fulcrum for the deformation of the teeth. If the fulcrum should coincide with the center of the rotor, all the teeth would be uniformly deformed. It is should lie on the teeth themselves, however, much less shear force would be required because fewer teeth would be plastically deformed simultaneously. Consequently this type of deformation is more likely to occur. In this case, the tip of a tooth cannot deform the neighbouring tooth as long as it is firmly supporting in its notch. The teeth would thus be deformed at about half their height. Particularly couplings with steep tooth-flank angles could fail in this manner.
The geometry of the Hirth teeth on the generator-end face of the compressor first-stage disc of a Model V84.3A gas turbine is illustrated in Fig. 8. Each of the 180 teeth corresponds to two angular degrees at the outer circumference of the disc. The included angle of the serrations (b = 127í) results in relatively flatly shaped teeth. Consequently, the possibility of the first failure scenario of tooth slippage should be investigated.
It is assumed that the most unfavorable (105í out-of-phase)generator synchronization could require that roughly eight times the normal full-load torque, i.e. 2.1 Ñ 103 kNm, must be borne by the highest loaded Hirth coupling connecting the fore-shaft section with the first compressor disc. The necessary slip torque to overcome the radial serrations and the contact friction between the tooth flanks can be approximated by the equation:
Mslip = Fv Ñ tan (a+f)* rm
in which Fv equals the prestress force, f the flank angle(f = 90í- b/2), rm the average radium of the Hirth teeth and a the angle of friction. The values of the Model V84.3A gas turbine result in
Mslip = 5.9 Ñ 103 kNm
If one neglects the friction component (a = 0), then
Mslip = 3.2 Ñ 103 kNm
This simple estimate proves that a large safety margin prevents the most heavily loaded Hirth coupling from slipping as a result of the most severe electrical fault even without any reliance being placed on the friction between the interlocking teeth.
More detailed theoretical investigations reveal that also no plastic deformation of the Hirth teeth
occurs under these extreme loading assumptions. Other theoretical and experimental
investigations have shown that even higher torque loadings would lead first to a failure of the
shaft coupling between the generator and the gas turbine, thereby ensuring the integrity of the gas
turbine itself.
Part 2 of this article will appear in the November/December issue of Electricity Today.
Manfred J. Janssen and John S. Joyce are with Siemens Electric.