ML17318A693

Rotors for Large Steam Turbines.

ML17318A693
Person / Time
Site:	Cook
Issue date:	03/17/1980
From:	Hohn A BBC BROWN BOVERI, INC. (FORMERLY BROWN BOVERI CORP.
To:
Shared Package
ML17318A689	List: ML17318A690 ML17318A691 ML17318A693 ML17318A706 ML17318A707
References
CH-T-060-053-E, CH-T-60-53-E, NUDOCS 8004220027
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Rotors or BBC BROWN BQVERI Large Steam Turbines Publication No. CH-T 060053 E

Rotors for Large Steam Turbines A. Hohn Rotor Configurations As the unit capacity of steam turbosets Increases, so too does the sfse of the rotor, and hence also the stresses The designs current today are restricted to the forms applied to it. The various designs of rotor are discussed and shown in Fig. l:

results of stress calculations given. Rotor materials are considered briefly, followed by comment on the future -Diagram a shows two rotors, each produced from a development of rotor design for large steam turbines. single forging.

-Shrinking discs on to a central shai? which transmits the torque gives rise to the composite construction of diagram b.

In diagram c, separate discs have been welded together to form a drum. type rotor [I],

Each configuration has its own advantages and disad-vantages as regards production of the'teel, heat treatment, machining and testing, but these will not be dealt with specifically here. Distinctive differences in the matter of stresses are considered in the following

'two sectlolls.

Statics of Rotors under the Influence of Speed, Disc Geometry and Temperature The Disc under the influence of Rotation introduction All designers of turbomachines use thc rotating disc in onc form or thc other as a basic component of the rotor.

Steam turbines today are remarkable particularly for The following remarks on the rotating disc, which arc of their size: unit capacities of more than l000 MW are now an elementary nature and can be pursued further in (2, 3, to be found both in conventional power stations with 4] for example, are therefore applicable to all, with fossil-fuelled boilers and also in nuclear power plant. For account taken of the boundary conditions particular to a a number of reasons, unit capacities will rise even further specific design.

in future, and it would bc premature at the moment to Ifthe equilibrium of forces in the radial direction is taken speak of any limit. Machines of this size represent a on a rotating disc element of constant thickness, al-substantial financial commitment and in thc event of lowance is made for the relationship between radial and failure cause serious disruption of the power supply to tangential expansion in thc disc and Hooke's law for both domestic and industrial users. It is therefore under- biaxial stress is introduced, we obtain the diflerential standable that the manufacturer of such machines does as equation of the'rotating disc in terms of a< with the much as the latest state of the technology will allow in general solution:

order to ensure that these large machines are reliable in service. ti cot (3 .')

This article is concerned with the heart of the machine, o ~Ci~ a Cs 8

the rotor, and reference is made to the various rotor designs and the difiercnces between them. Full treatment of the subject would have to include thc static behaviour Disregarding any external tension for thc time being, the in steady-state operation and under transient conditions, curves of radial and tangential stress are found to be as and also the dynamics of the rotor under the influence of follows for:

the flow of steam. This, however, would go beyond thc scope of an article, and therefore the main focus of a. a solid disc:

attention here is on steady-state operation which at all events constitutes the basis of the mechanical design, and t. ~'(3+v) (.. (2) on which all other phenomena arc superimpose* 8

and since crt = (r d

rtr) + (2 centre of the solid disc, i.e. with err clt = (l rs'co'3 + <<)/8.

Thc result can be seen in Fig. 2. To illustrate more clearly

'Z r'o'l'2 the mutual infiuences of radial and tangential stress,

~ cos (3 ~ <<) /rr I + 3 << Fig. 2 also includes the dimensionless comparative stress 2rt 8 ( 3+. Sv on thc assumption of constant work of deformation, thus:

b. a perforated disc:

(2 cos (3 + <<) t I r r Xr22 rr

- y;*+;*-;.,

trr s

2 q r2 rz (4) 8 clv I. utld Sv ~

(2 rs'o'3 + 2) ts cos (3 + <<) rt's'  ; 3 <<

I."'+ "'*+ ,

I s I 2

" 3+. From Fig. 2 wc can draw a first conclusion:

In order to show equations (2) to (5) in general form they For the same dimension (rs), the same material ((2) and are made dimensionless with the stress prevailing at the thc same speed (co), the perforated disc will exhibit a Fig. I - Dlirerent types of rotor construction Fig. 2 - Dimensionless radial, tangential and combined stresses ol'iscs of equal width 1,8't 2,0 Ol 02 03 04 05

r2

~ 0,6 St 126'rl Stt Sv 1,4 rs 1,2 1.0 0,9 0,8 07 0,6 rt 0,2 0.5 rs 0,4 O,l S 0.3 0.4 0,2 osr 06 O,I

/ r 0.1 0,2 0,3 0,4 0.5 0,6 0.7 0,8 0.9 1,0 rs

-Sr ~ 8 or 8 or era er (3 +v) +<<)

- Sv ~ 8 ov 0 r22 ars (3 + r)

Ors er (3

higher loading than the solid disc. A measure of this is radius rt the sum of disc, expansion and shalt compres-the mean tangential stress. sion must equal the degree of shrinkage du, i.e.

This result also remains essentially unchanged when the additional loads caused by blade tension, steam pressure rtw rts Utw + Uts and shrinkage are superimposed on the rotational S treSseS. With this it is now possible to construct a "spring The considerations presented so far are suFIcient for diagram" of the shrunk joint (Fig. 3), and within this the determining the rotational stresses in the case of a solid relative degree of shrinkage hrjr can bc determined fora disc. For the perforated and shrunk-on disc of Fig. lb, given geometry (rt, r1) and a desired shrinkage force o<t.

however, deformation also has to be taken into account, Thc shrinkage force is chosen in the light of the two owing to the diFerent stiffness of the central shaft and the following points:

disc. Only then can onc define the required degree of shrinkage, which in turn has an infiuence on the choice of - Expansion of the disc due to rotation may only be large material. enough to <<nsure that a positive fixing is maintained when run at overspeed (normally l 2 x operating speed),

i.e. the disc must not come loose. Publications by Deformation Affecting the Perforated Disc manufacturers of this type of construction indicate that the liAwFspeed (zero-shrinkage) lies approximatefy 35%

Here we can again start from Eq. (I) and determine the above the normal operating speed [5).

integration constants C< and Ct appropriate to the - It must also be ascertained whether, at normal operat-boundary conditions. With thc aid of thc calcuhted ing speed, thc shrunk-on disc is f'ully capable of trans-stresses it is possible to determine the radial expansion, ferring thc bhde torque to thc central shaft. Generally and hence also thc radial displacement U for any radius of speaking, this requirement is always met if the overspeed the central shaA or of the shrunk-on disc. Of particular condition is satisfied.

interest are the relative displacements Ut of shaA and disc at the point of attachment with radius r1. Thc result of Our considerations regarding the shrunkwn disc can thus considering deformation in this way can bc read from thc bc summarized as follows:

Table. Thus, any expansion of disc orshaA is proportion- At standstill the disc is stretched because it was undersize al to the forces. art and ars which cause it. There is a when fitted on-the shaft, and the shaA is compressed by square-law relationship between the expansion and rota- thc shrinkage. Owing to'ts own rotation and the tensile tion ru. Here it must bc noted that for different speeds thc force exerted by the blades the disc expands more than external tension ars also varies as the square of the speed. the central shaft. The shrinkage force is thus reduced. A The shrunkwn body has to satisfy the following condi- residual degree of shrinkage must be retained when the tions: at the point of contact between disc and shaA at rotor is run at ovcrspeed.

Expansion of shaft and disc Shrinkag force Rotation External tension NON> I ~

8) mru ii CO B) tt1) er1icu'(I -r)

( ri Juan, 4a Disc rii I'ii (S

x (I r)+ r11 (I +r) X + r) +(I rt

[ rli

Figurc 3 shows these relauonships for standstill (co = 0), oct operating speed (co), overspeed (co ~ co') and liftofspeed E (co' I 35co) for a disc of uniform width with a radius 2,$ ~ IO 3 ratio of rr/ri ~ 3. In this diagram thc elasticity properties 2,0 of the disc and thc central shaft have been determined in accordance with the Table. On the abscissa thc point of origin is the desired degree of shrinkage (&/ri)o, which is selected according to the residual shrinkage (ordinate) I,O desired at the overspeed condition. The individual com- O,S ponents of the disc and shaft expansion due to rotation Us and external tension ore have also been taken from the I 2 3 4 ri pg Table. In order to establish the order of magnitude of the Uis I

Usw compressive forces ori involved, and also the residual ps rI shrinkage, the diagram was compiled using realistic conditions such as occur in the case of I.p. rotors for half-speed steam turbines: n 1500 rev/min, equivalent to co = 157 s-', overspeed co' 12 co; blade tension eris being taken as 8 kgf/mrna at the normal operating speed.

The residual shrinkage for any speeds can be obtained directly from Fig. 3 by means of thc following conversion from the stationary shrinkage diagram. The basic prin-ciples of this are explained in [6].

We have:

(9) co ~ 0 Since the residual shrinkage du at operating speed co is given by (10) for the residual shrinkage we obtain co ~

cu'I I I) -

Fig. 3 Shrinkage diagram for shrunken discs under dlirereni operating eondiiions Thus it can be seen from Fig. 3 that an extremely large degree of shrinkage (4 15 x 10-') is necessary to achieve a lift-offspeed of co' I 35 co, taking into account the blade tension.

If for the example in Fig. 3 it had been stipulated that liiboff is to occur at 135% of operating speed without allowance for the external tension etre (i.e. without blad- uniform strength or the perforated disc will be given a ing), this would result in the standstill shrinkage diagram hyperbolic meridian similar to y = c/rn, in order to make shown by the broken line in Fig.3, with a standstill the best possible usc of the material. This then results in a shrinkage of 2 6 x 10-s. In this case, however, the bladed more gentle disc characteristic than shown in Fig. 3, and rotor would lose its residual shrinkage even at small hence in a reduction of the necessary shrinkage force. But overspeeds (9% in this instance), owing to the blade here, too, a very tight shrink fit will still be needed for a tension, and some means such as keys would be needed great variety of disc meridian shapes, which is one reason to prevent the disc from slipping. The reserve of speed up why highly tempered materials are chosen for the discs.

to liftwifmentioned here is determined by thc residual There are a number of methods (e.g. [2]) for calculating shrinkage obtained with Eq. (11). the stress in a disc of any technically feasible contour.

The method of finite elements has recently come to be used for this purpose, even going to the extent of not only influence of Disc Geometry determining the stress conditions in the individual parts (discs) of the rotor, but also of considering the rotor as The above statements are of a fundamental nature and an entity and taking into account the interactions be-aid one's understanding when comparing dificrent tween neighbouring parts of the discs. A very good designs. But in practice the shrunk-on disc is not of overall investigation of the rotor is always possible with constant width. The disc meridian will therefore be the method of finite elements, the fundamentals of which shaped in some way, it will be formed to yield a disc of can bc found described in [6]. Detailed investigations,

FISA-Grid for cnlcttlctinsttretics R Inttnl ln n I.p. rotor hy the 5nhe dctncnt method l3 ~ to l2 C IC'4 />" in such as in the slots of blade fixings, need more refined calculation applied over a very fine grid, while the aid of .

where a'tr (l3) photoelastic techniques must bc enlisted for assessing the surface stress in thc grooves. In this manner one can Before setting about solving this equation one must know account for all the stress components involved. the boundary conditions, e.g. surface temperature, heat supplied and removed.

In practice, the rotor geometry does not follow a simple shape and the temperature distribution at the surface is Injfuenee of Temperature complex, owing the cooling eKect of the stcam. Con-sequently, one cannot expect a complete solution to the Under normal operating conditions the rotors of large heat conduction equation. There are nevertheless two steam turbines arc in general exposed to a steady-state practical ways of solving this problem:

temperature field: after start-up and settling down to normal load an isothermal distribution becomes estab- - Thc isotherms in the rotor are found with the aid of an lished in the respective rotors which varies only slightly in electrical analogue model, in which case thc rotational response to moderate load fluctuations. symmetry of the rotor is accounted for by selecting A knowledge of the isotherm distribution in the rotor is suitable resistances (perforations) on the twMimensional necessary for two reasons: model.

The conduction of an electrical current through a body is first, onc needs to know the local temperature in order described by the equation to compare thc local stress present with the characteristic temperature,

of thc material (e.g. long-time strength) valid at this local aU ~ hU at c (l4)

-second, the isothermal condition gives rise to a stress field which it may be important to calculate for the total and is thus analogous to the heat conduction equation loading on thc rotor. (l2). Here, U is the applied voltage, C the electrical capacitance and x thc electrical conductivity of thc This mises the question of how one determines the material. Lines of equal voltage U, or equal potential, arc isotherm distribution in the rotor. Basically this is a an analogue of the isotherms T ~ constant.

problem of thermal conduction P] in a rotationally symmetrical body described by the Fourier equation -Another possible way of determining thc temperature distribution in the rotor is to solve the heat conduction aT ~ arhT ar (12) equation by numerical methods. This possibility has gained greatly in significance in recent years with. the usc

Fig. S- Von Mlscs'combined ttrcss Md of tha toUd Ip. rotor shown 3t immi la Fig. ta Values 20 to 47 it//mm~.

-.~20.~

1000 20'-

I I 47 40 of finite elements for calculating stress. One has thc It will be seen that owing to the abrupt change of cross-advantage that the results of calculating temperature in section from the central shah portion to thc disc, stress this way lie on the same lattice as the subsequent stress concentrations as high as 31 kgf/mme occur. Stress con-calculation, and thus can be used as a direct input for centrations of this kind are always to be found when the computing the termal stress. force field is disturbed as a result of changes in cross-section. Fig. 5 also shows the stress level at thc inner Finally, as regards determining the isotherms it must be bore, with a radius ratio of rt/rs ~015. At47kgf/mm said that without thc subsequent stress calculation it will the stress herc reaches a very high value, although it is always be fragmentary and yield only moderately useful still always below that of shrunken discs. Results of information. calculating the stresses in shrunk-on discs arc shown in Fig. 6. Owing to the larger central bore for the shaft a much higher stress of 68 kgf/mm's found here, other-Practical Results of Stress Calculations wise the conditions are the same as in Fig.5. At the transition from thc slim part of the disc to the broad Rorarlonal Stresses in Dig@rent LP Rotor Designs outer shoulder one can again see a stress concentration in the corner of the divergence, attaining local values of 70 to The discussion in the previous section on stress calcula- 80 kgf/mme and caused chiefly by disruption of the radial tion in rotors of different constructions is now illustrated stress pattern.

below with the aid of a few practical examples. A technique often used in the past was to secure the Figure4 shows thc grid imposed on a I.p. rotor for shrunk-on discs with extra keys. This inevitably gives rise determining the mechanical stresses by the finite element to stress concentrations in the keyway which in the most method. All the basic designs depicted in Fig. I werc favourable case have a stress concentration factor of calculated in a similar manner. about three. What this means with the high basic stress When computing the stresses, the speed and blade tension level of a perforated disc is easy to appreciate: from thc were kept constant for all types of rotor. Shape, dimen- start a plastic zone will form round the slot which, if thc sions, speed and blade tension correspond to values properties of the material are less than ideal, can lead to

'ound in practice. cracking and hence to failure of the disc when it is Figure 5 illustrates thc comparative stress field for a I.p. rotating. Sufficient instances of this have unfortunately rotor machined from the solid as shown in Fig. Ia. Here occurred in the past [9, IO). In order to meet the the comparative stress has been taken as according to von standards, of reliability required in power stations, there-Miscs: fore, it is essential that no keys of any kind should bc av ~ ~ (ar at)'+(at az) +'(ar ar) .'arr'15) provided as an extra means of securing the discs.

As already explained in connection with Fig. 2, thc solid disc will show the most favourable stress characteristics.

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4L) 4L4 44$ $1 j 5L1 $ IJ ltj 41j

$ 4) $ 47 40.l 41 44J 447 SLl SIA ltj Figure 7 illustrates the combined str<<ss distribution (aAer tic feature of steady-state operation that the isotherms von Mises) in a welded drum rotor of a type found in run almost perpendicular to thc axis of rotation, and on machines of over 1000 MW. Tlie boundary conditions- the basis of the isotherm distribution one can predict that outside diameter and bladntension- are comparable with the thermal strcsscs will be very small compared to the.

the designs shown in Fig. 5 and 6, the speed being taken stresses caused by rotation. In this example they in fact as 1800 rcv/min in all the cases shown. It will bc noticed amount to only some 5 to 10% of the mechanical stresses.

that with a rotor of this kind, which is composed of solid In contrast to the cold low-pressure section, thc mechani-discs, thc greatest stress is roughly between 40% (Fig. 5) cal design of rotors exposed to high temperatures in-and 60% (Fig. 6) lower than for rotors machined from cludes their behaviour in relation to time. Because of the solid or for shrunken discs. This fact will again be creep phenomena, which will be discussed in more detail important when considering the choice of material and in the next section, the material ages in the course of thc bursting speed. time. This ageing process is a function of the material, temperature and stress, as well as time, and therefore in order to assess the suitability of a design one must know HP and IP Rotors, Including Temperature sects all these parameters, i.e.

Figurc 8 shows the isotherms in a welded h.p. rotor under - the behaviour of the material as a function of loading, conditions of full load. Here onc can see thc charactcris- temperature and time,

Fig. 7 - Combined stress IIel a welded drum rotor as shown in Fig. Ic Values 20 to 28 ltgf/mme.

I 20 I I 000

/

+2g 20 26

- thc isotherm distribution in the rotor, and little creep, uniform heat treatment, adequate long-term the stresses in the rotor. ductility, low notch sensitivity and good resistance to scale.

An example of a detailed study of a high-pressure blade Nuclear power stations at present do not raise any fixing is shown in Fig. 9. Using photoelastic techniques, problems of temperature because the turbines run on the edge stresses in the lateral grooves are determined saturated steam, and even the high-temperature reactors under diFerent loads and added as supplementary in- for large power stations will not exceed the live steam formation to the results of a refined stress calculation temperature of conventional plant, at least in the near (Fig.9). In this way, together with allowance for the future.

behaviour of the material and stringent production quali- Figurc l0 shows two typical rotor steels [11] used for h.p.

ty control, it is possible to guarantee the performance of and i.p. turbines. To allow internationally consistent the rotor over many years. comparisons, the long-time rupture values for l00000 hours are taken as a basis for mechanical design pur-poses.

The Rotor IVlaterial The following remarks survey briefly the behaviour of rotor materials under thc influence of temperature, stress High-Pressure and Intermediate-Pressure Rotors and time.

The rotors of modern large steam turbines are,all of Ifa test bar is subjected to a load att and at thc same time fcrritic material. This is related to the fact that for a temperature Te, it will in time undergo plastic elonga-conventional plant the world over the live steam tempera- tion (creep) and finally break. For the same loading the ture has become established at 538 'C. With this material bar will fail earlier with a higher test temperature one can expect good long-time properties, no softening, )

Tt Te than with a lower temperature.

Fig.g - Isotherm distribution in a welded h.p. rotor

$ 00 450 5 I0 'C 460'00 10 I

fig. 9- Combined stresses in I ti a I

I grooves of h.p. blade Axing the

'the Agura denote the von Miscs combmcd stress m ltgtimms.

r I 3 500 'C 505 C 5IO C sls C The creep process is illustrated in Fig. Il. We can which in practice makes it easier to assess the rotor after distinguish three main phases of creep; primary (I), a long period in service. Every time the turbine is secondary (II) and tertiary (III), in which the bar rapidly inspected, specially provided control diameters are reaches breaking point. All high.pressure and interme- measured and the results compared with measurements of diate.pressure rotors operate within the secondary phase, previous years. Here,'however, account must bc taken and the designer has to make sure that his design has an of the fact that thc creep rate within a disc varies adequate reserve with respect to the tertiary stage. In the widely from inside to outside owing to variations in secondary phase the rate of creep i ~ de/dt is constant, the stress.

-

fig.lo I.ong-time fnptUre cnrvcs eea in hgrtmms and chemical Lo~~pressure Rotors eomposi tion of steels 24 CrMov 55 and 2l CrMov 5 I I 70 60 Whereas for high-temperature conditions the number of 50 diHcrent rotor materials used by the various manufac-2I Cr Mo V5ll turers is limited, the selection of materials for low-40 pelt'0 ooo pressure rotors is much wider. This is not all that o ~

remarkable when one remembers the variety of l.p. rotor 25 designs, because the material is principally matched to iso.

20 the dill'erent stress conditions of the individual types of construction. Furthermore, because these rotors are 24 Cr Mo V55 essentially cool, the factors governing the choice of J ~ 'material will only be the yield point, ultimate strength, IO 9 elastic limit and notch toughness. Here it is assumed that g

1 the rotor operates in the upper part of the notch-6 toughness range, i.e. thc fracture appearance transition 5 temperature is below thc operating temperature.

4 Recently, and not the least of thc reasons being several cases of explosive failure of solid and shrunkMisc rotors, which also extended to nuclear stations [IOJ, there has been a tendency to base the choice of material on additional criteria in order to avoid such instances of brittle fracture. For this, the rotor is considered from the standpoint of fracture mechanics, the aim being to arrive IO io'O

<<h I05 at appropriate values of crack resistance and rate of propagation for subcritical crack growth Without going

into the fundamentals of fracture mechanics the subject IO

failure of all control and safety systems. In this hypothet-ical situation, rejection of the electrical load would cause the rotor speed to run away, possibly resulting in ex-rt)ro rt)ro ro plosive failure.

Our own studies have shown that h.p. and i.p. rotors

/ have a much higher bursting speed than I.p. rotors. The reason for this is that the high and intermediate-pressure

/ rotors stretch radially less than the low-pressure rotors, and while the material characteristic governing bursting is r

the yield point, h.p. and i.p. rotors are generally designed tr0 dl ) const.

do

/ to withstand long-time failure. Since the value for long-time failure is only a fraction of the corresponding yield point. depending on the temperature, these rotors have a larger reserve with respect to the bursting speed than do I.p. rotors.

/z In order to study the behaviour of diFerent disc designs in relation to the bursting speed wc again use the disc of uniform width as a starting point. Grammel has shown

[14) that the mean tangential stress in the disc is suitable as a measure of the resistance to explosive failure. The IOltN I mean tangential stress trtM is given by fig. 1 I - Creep curves for difFerent temperatures and loads (schematic) rs crt dr (16) is treated in (12) and [13), for example it should be crt à fs rt mentioned that this aspect of mechanics was originally evolved for high-strength, relatively brittle materials. and can be written in dimensionless form as follows:

However, it is only suitable for describing a crack which already exists, and takes no account of the actual forma- n 8 trt tion of the crack. At the same time it should not be dr forgotten that turbine rotors consist of ductile materials g res tos (3 + t) (17) which have the ability, if need be, to fiow locally and StM fs rt disperse stress peaks, thus preventing cracks from form-ing, or at least greatly delaying their onset. For trt we then use Eq. (3) for a solid disc and Eq. (5) for It can, of course, happen that there is some justification a perforated disc. If we now write the ratio of the mean, f'r examining a rotor from a fracture mechanics view- tangential stress Stwr, of the perforated disc to the mean point. This will always be so if, because of the high level tangential stress Stlv of the solid disc, we have of disc stresses, one has to resort to high-strength materials or when, as in the case of solid low-pressure rotors, the large dimensions, make it very difficult to (18) detect faults inside the forging. It may then be of 'he advantage to assume a fault of a certain size in a certain ratio of thc bursting speeds of perforated disc to position and check to see what the consequences might be solid disc is then described by in the course of time.

<BRL Bursting Speed ir BRV I+ + (19)

In recent years, and initially at the request of the US Atomic Energy Commission, manufacturers of large tur- Equations (18) and (19) are shown graphically iri Fig. I?

bines for nuclear power plant have had to analyse the As examination will quickly show, for rt(rs ~ I they will extent of damage to the turboset in the event of total of course provide the bursting speed ratio for the thin ring.

2,0 Figure 13 shows in qualitative terms the behaviour of two diff'erent I.p. rotor constructions at elevated speed. For the same size. blade tension and operating speed, thc l,g e sax, Sets tangential stress for the drum rotor will follow curve I.

asar Soir The same applies to the disc rotor, but at thc bore l.g diameter chosen this rotor shows a stress roughly double that of thc drum rotor. In the elastic region there is proportionality between the stress and the square of the speed. If the speed is raised relative to the normal speed by a factor of I 4, for example, the stresses increase by a V g factor of 196 (curve 2). The inner portion of thc per-1,2 forated disc is then already beyond the yield point, and the corresponding zone relaxes.

l.o Owing to plastic deformation, therefore, the elastic heal. I / 1 curve 2 gives way to curve 2'nd thc parts of the disc

( l+ "+( which are still elastic arc thus subjected to additional, O,g ,"j',6 stress. According to what has been said.so far, a measure of the rcscrve with respect to fracture is the ratio of the.

yield point to the mean tangential stress, i.e.essentially.

the area in Fig. 13 contained between curves I and the yield point. The root of this area ratio represents the.

0 0,2 0.4 rt 0,6 relationship of the bursting speed of thc two designs Ps shown in Fig.13. If one wishes to compensate the Fig. lz - Ratios of mean tangential stress and berating speed lor disadvantage of the lower fracture speed of a perforated perforated and solid discs disc by using more highly tempered material, the increase-in yieltI point required for a perforated disc can also be.

found with Eq. (18) (Fig. 12). It can bc seen that with the radius ratios occurring in practice it is difficult to achieve a perforated disc of such a quality that it is equivalent to a solid disc as regards its bursting speed. This would mean high-strength material has to be used, with the consequent higher risk of brittle fracture.

Outlook Fig. ls - Behaviour of tteo types of I.p. rotor at <<lerated speed As mentioned earlier, the unit capacity of large steam di

~t turbosets will continue to risc in thc foreseeable future, di and hence.influencc the demands made of the rotors. A decisive, and to solne extent limiting, factor over the past decade was the final stage, which ifthe vacuum was good 2

l had to handle enormous flow volumes. All manufacturers dl of steam turbines therefore carefully developed longer final blades and introduced these to the market. But longer blades also means a larger rotor diameter, accom-panied by higher centrifugal loadings on both blades and rotor. To keep stresses below the limit, the speed of the machines was halved. The technique employed in the USA was to run thc high and intermediate-prcssure sections at thc full speed of 3600 rev/min, and combine di Pa the low-pressure units with a 4-pole generator on a second shaft string running at 1800 rev/min. Europe later adopted the idea of the half-speed machine, although in 12

single-shaft form and only for nuclear plant. By halving disposal a design concept sufficientl flcxible to allow him the speed in this way. and at the same time doubling, the an adequate margin of safety in designing rotors for the size, the stresses in full-speed and half-speed machines high-pressure section as unit capacities continue to risc.

were kept the same, but the corresponding exhaust area of the final blades increased fourfold.

A feature of recent years has been a growing worldwide shortage of cooling water [15]. In the industrialized countries, and these if only because of their. power distribution networks are the potential buyers of large Symbols machines. it is becoming no longer possible to usc fresh water for cooling purposes. Future large power stations F. = Modulus of elasticity will therefore be equipped mainly with wet or dry cooling L = Perforated disc

- Dimensionless radial stress towers. which means the turbine vacuum will be rclativcly S<

poor and the steam exhaust volume correspondingly Si = Dimensionless tangential stress smaller. It may thus well be that the final blade lengths Sist =- Dimensionless mean tangential stress and I.p. rotor dimensions customary today will be ade- Sv ~ Dimensionless equivalent voltage quate for some time to come, without being tied to half- T = Tempcraturc speed I.p. sections because of thc stresses, even with large U = Radial displacement capacities. It is likely that large machines for nuclear V = Solid disc power stations, with poor vacuum, will also be built for a = Thermal conductivity full speed and still be able to cope with thc stresses in the c = Specific heat of rotor material blades and rotor. nnn =. Bursting speed The possibility of making the I.p. rotor relatively small r = Considered disc radius also improves the chances of the solid-rotor design to ri = Inner radius of perforated disc some degree. Great advances in forging technology have ri Outer radius of disc been made over the past few years, and this has increased hr = Degree of shrinkage confidence in the use of forged one-piece shafts. Finished weights of over 200 t have been achieved to date. These

~

du ti Relative degree of shrinkage rotors require an ingot weighing morc than 400t and r ~ Time with the associated risks can be produced only in Japan e< Radial expansion and the United States. It is improbable that the steel- = Tangential expansion works will contemplate a further increase in rotor size. = Conductivity of rotor material with the correspondingly heavy investment needed to deal ~ Transverse contraction ratio with larger ingots, because the market for these large = Specific mass of disc material forgings is too restricted. The concept of the large one- e< = Radial stress piece rotor can therefore be extrapolated into the future e<i = Shrinkage force to only a limited extent. e~ =. Blade tension applied at radius rs Thc situation is slightly different for the high-pressure (ri Tangential stress section. On the assumption that future nuclear power %st = Mean tangential stress over meridional area of stations will also operate with steam conditions such as blade are found today in conventional plant (I50 to 250 bar, d! = Axial stresses in rotor 538'C), the very size of the I.p. rotor could present a CO = Angular velocity of rotation stress problem. Overcoming this can be approached in OP = Overspeed two different ways: the material and the design. yp 4 = Lift-offspeed There is no likelihood in the near future of finding a different material for h.p. rotors which has substantially better long-term properties and does not forfeit the advantages of the low alloy steels used at present. Much more probable is that stresses in the h.p. rotor can be Indices kept in check through suitable design: the large steam turbine today is quite clearly following thc path taken W = Central shaft many years ago by the gas turbine towards cooling the S = Disc rotor by means of steam. The designer thus has at his 0 = Standstill 13

Bibliography

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Weld. J. June 1968.

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[4] K. Lofter: Die Bcrechnung von rotierenden Scheiben und Schalen. Springer 1961.

[5] A. Bald: Besonderheiten grosser NassdampAurbo-sgtze. Mitt. Vereinig. Grosskesselbesitzer S2 1972 (4).

[6] 0.C. Zleriklewlczr The finite element method in struc-tural and continuum mechanics. McGraw-Hill, London 1967.

[7] B. Bauler Die Mathematik des Naturforschers und Ingenieurs, vol. IV. Hitzel 1952.

[S]H. Lelpholz: Festigkeitslehre fur den Konstrukteur.

Springer 1969.

[9] H.D. Enunerr Investigation of large turbine spindle failure. ASME Paper 55 A 17?-

[IO] D. Calderonr Stcam turbine failure at Hinkley Point.

Proc. Inst. mech. Engrs 186.

[I I] Stghte fQr grQssere SchmiedestQcke (GQtevorschrift).

Stahl-Eisen-Werkstoffblatt 550- S7.

[12] K. Hecke/: EinfQhrung in die technische Anwendung der Bruchmechanik. Hanser 1970.

[13] D. Radaj: Grundlegendc Beziehungen der lincar-elastischen Bruchmechanik. Schweissen u. Schneidcn 23 1971 (IO).

[14] R. Grammel: Die Erklarung des Problems der hohen Sprengfestigkeit umlaufender Scheiben. Ingenieur-Archiv 16 1947 (I).

"

[IS] H. Flohn, D. Hensehler, H. Schuller: Der Wasser-haushalt der Erde. Aus: Mensch und Umwelt. Tech.

Rdsch. 64 1972 (47).

14

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