CN105574226A - Acquisition method for calculating expansion quantity of steam turbine - Google Patents

Abstract

Does a kind of steam turbine based on reciprocal work theorem swell increment acquisition methods at different levels, the described method comprises the following steps: a. apply equally distributed specific loading on the rotor of steam turbine or the cross section of cylinder , calculate by equally distributed specific loading The axial normal stress of caused rotor or cylinder body ; B. according to steam turbine real load, its axial normal strain is determined ; C. the rotor of steam turbine and the end average displacement of cylinder are calculated separately using end average deformation amount calculation formula With . The present invention calculates turbine rotor according to reciprocal work theorem and cylinder end is displaced, and then obtains the swell increment of turbine rotor and cylinder, has many advantages, such as computational accuracy height, and the speed of service is fast. The method can realize the real-time monitoring of steam turbine differential expansion, guarantee Steam Turbine safe operation, improve the economy of unit.

Description

A kind of acquisition methods calculating turbine expansion amount

Technical field

The present invention relates to a kind of reciprocal work theorem that utilizes and calculate the rotor of steam turbine and the method for cylinder swell increment at different levels, belong to technical field of power generation.

Background technology

Electric power is the main matter basis realizing national economic modernization, and the development degree of power industry has become the important symbol of measurement national economy and social development degree.Along with developing rapidly of economy, to the demand of electric power also in continuous increase.For China, to 2002, national thermoelectricity installed capacity reached 3.85 hundred million kilowatts, and to install the speed increment of 2500 ~ 3,000 ten thousand kilowatts every year on average.Meanwhile, power structure also there occurs marked change, and electrical network peak-valley difference increases day by day, and national each electrical network peak-valley difference has generally reached about the 30%-40% of maximum load all.Adopt little unit in the past as the way of regulating units for subsequent use, can not meet the requirement of electrical network, so the large-sized unit of Large Copacity, high parameter participates in peaking operation become inexorable trend.The Unit Commitment participating in peak regulation is frequent; because the heat conduction of the quality of rotor and cylinder, heat-conducting area, metal is different from the coefficient of heat emission on expansion characteristics and surface; thus unit starting, shutdown and load fluctuation time; rotor and cylinder will produce differential expansion; cause axial dynamic and static gaps to change, when expansion at different levels look into exceed certain limit time, axial dynamic and static gaps can be made to disappear; thus generation rubbing, serious meeting causes cambered axle accident.How to improve thermal power unit operation efficiency in addition, reduce energy consumption, and improve further the security of unit operation, attention that reliability is more and more subject to electric power enterprise, along with electric power valency online unexpectedly, just require that the major equipment of power plant should have higher safety and reliability, the equipment such as steam turbine should possess good peak modulation capacity.There is many problems in this method: first, what differential dilatomater reflected is that the rotor of differential dilatomater measuring point and the swollen value of cylinder are arrived in dead point, it do not reflect at different levels between actual end play, if differential expansion amount is comparatively large and bulk expansion amount is normal time, although differential dilatomater indicating value is safe, may there occurs and touch the accident of rubbing.Modern thermoelectricity large-sized unit often adopts double shell structure in addition, in shutdown process, what sound friction may occur is between rotor and inner casing, and the axial expansion of inner casing and outer shell is general and asynchronous, the measured value obtained from outer shell often can not reflect the truth of rotor and inner casing dynamic and static gaps.Moreover in actual moving process, the error of differential dilatomater is comparatively large, is so just difficult to the actual conditions reflecting the minimum place of end play.As everyone knows, in order to guaranteed efficiency, the dynamic and static gaps of turbine high-pressure admission end flow passage component is relatively little, and when peak load regulation and power condition changing, rotor and the cylinder expansion amount of steam turbine change greatly, this becomes large restraining factors of Unit Commitment dirigibility, and traditional steam turbine rotor and cylinder expansion scale just monitor high pressure cylinder or the maximum differential expansion value of low pressure (LP) cylinder, often cannot reflect the differential expansion situation of the most Dangerous Place of unit operation exactly.Turbine rotor and cylinder expansion value transfinite or deal with improperly and can cause that steam turbine sound rubs, Steam Turbine Vibration exceeds standard, and even cause permanent bending of rotor.In order to strengthen the Real-Time Monitoring to turbine rotor and cylinder expansion amount, many scientific workers do a lot of work.But, the rotor of rotor and cylinder and cylinder expansion amount and temperature rise speed, set structure, material property parameter, steam parameter and steam are relevant to factors such as the coefficient of heat emission of rotor and casing surface, the Changing Pattern of different operating mode lower rotor part and cylinder expansion amount is also not quite similar, and this makes the on-line monitoring of turbine rotor and cylinder expansion amount more difficult.Thus, set up the unstable state thermal expansion mathematical model of turbine rotor and cylinder, simulate the swell increment real-time at different levels of turbine rotor and cylinder and dynamic and static gaps situation of change at different levels truly, become one of Focal point and difficult point of large-sized unit on-line monitoring.When the operating mode of unit changes, provide more accurately steam turbine at different levels between axial displacement and dynamic and static gaps situation of change, and give operations staff with the guidance of necessity and prompting, be very necessary to unit safety reliability service.

Summary of the invention

The object of the invention is to for prior art drawback, a kind of turbine rotor based on reciprocal work theorem and cylinder expansion amount acquisition methods are provided, to realize the Real-Time Monitoring of turbine rotor and cylinder swell increment at different levels, ensure unit safety operation, improve the economy of unit.

Problem of the present invention solves with following technical proposals:

Based on turbine rotor and the cylinder swell increment acquisition methods at different levels of reciprocal work theorem, said method comprising the steps of:

A. on the rotor of steam turbine or the xsect of cylinder, equally distributed specific loading P is applied, calculate distortion and the stress σ of rotor or the cylinder body caused by equally distributed specific loading P, and then obtain the axial normal stress σ of rotor or the cylinder body caused by equally distributed specific loading P _z;

B. according to the real load such as temperature loading T and mechanical load M that the rotor of steam turbine or cylinder act on, determine the distribution ε of its internal strain, and then obtain axial normal strain ε _z;

C. end average deformation amount is calculated as follows:

$u=\underset{\mathrm{\Ω}}{\∫\∫\∫}{\mathrm{\σ}}_z{\mathrm{\ϵ}}_{z}d\mathrm{\Ω}$

Calculate the rotor of steam turbine and the end average displacement u of cylinder respectively ₁and u ₂, Ω is the volume of rotor or cylinder;

The above-mentioned turbine rotor based on reciprocal work theorem and cylinder expansion amount acquisition methods, in order to reduce difficulty in computation, by the rotor of steam turbine or cylinder discrete be n unit, suppose that the axial stress field on each unit is normal stress field, and replace by the mean stress of unit, then end average deformation gauge calculation simplified formula is:

$u=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\σ}}_z^e\underset{e}{\∫\∫\∫}{\mathrm{\ϵ}}_z^{e}dxdydz$

In formula for the average axial normal stress in the unit that caused by equally distributed specific loading P, for the average axial normal strain in the unit that real load causes, x, y, z is respectively the three-dimensional coordinate of unit center point in rectangular coordinate system in space, and wherein, z-axis is parallel to rotor axis.

The above-mentioned turbine rotor based on reciprocal work theorem and cylinder expansion amount acquisition methods, the end average deformation amount of turbine rotor also can be calculated by following formula:

$u=\underset{i=1}{\overset{n}{\Σ}}2{\mathrm{\π\σ}}_z^e{\∫}_z{\∫}_r{\mathrm{\ϵ}}_z^{e}rdrdz$

In formula, r is the distance of unit center point to rotor axis.

The above-mentioned turbine rotor based on reciprocal work theorem and cylinder swell increment acquisition methods at different levels, the rotor caused by equally distributed specific loading P or the distortion of cylinder body and stress are obtained by analysis of finite element method.

The above-mentioned turbine rotor based on reciprocal work theorem and cylinder expansion amount acquisition methods, described equally distributed specific loading P applies in the following manner.

The present invention calculates turbine rotor and cylinder end displacement according to reciprocal work theorem, and then obtains turbine rotor and cylinder swell increment at different levels, has computational accuracy high, the advantages such as travelling speed is fast.The method can realize the Real-Time Monitoring of turbine rotor and cylinder swell increment at different levels, ensures Steam Turbine safe operation, improves the economy of unit.

Accompanying drawing explanation

Below in conjunction with accompanying drawing, the invention will be further described.

Fig. 1 a-Fig. 1 d is the reciprocal work theorem schematic diagram of beam model;

In figure, beam model as shown in the figure, if at point 1 position used load P ₁, cause the displacement of a little 1 position to be δ ₁₁, the displacement of putting 2 positions is δ ₂₁, as shown in Fig. 1 (a); If at point 2 position effect P ₂, cause the displacement of a little 1 position to be δ ₁₂, put the displacement δ of 2 positions ₂₂, as shown in Fig. 1 (b).If by P ₁and P ₂act on lentamente on elastic body, the displacement of final 1 and 2 should be (δ respectively simultaneously ₁₁+ δ ₁₂) and (δ ₂₁+ δ ₂₂), as shown in Fig. 1 (c).Obey Hooke's law at material, under being out of shape very little condition, its deformation energy should be

$U_1=\frac{1}{2}{P}_1({\mathrm{\δ}}_{11}+{\mathrm{\δ}}_{12})+\frac{1}{2}{P}_2({\mathrm{\δ}}_{21}+{\mathrm{\δ}}_{22}),$

If the mode of action changes into first act on P ₁then P is acted on ₂, then at effect P ₁time, P ₁institute's work is P ₁δ ₁₁/ 2, then act on P ₂process in, except P ₂institute's work is P ₂δ ₂₂outside/2, P ₁make again P ₁δ ₁₂merit, as shown in Figure 1 d, so deformation energy is

$U_2=\frac{1}{2}{P}_1{\mathrm{\δ}}_{11}+\frac{1}{2}{P}_2{\mathrm{\δ}}_{22}+P_1{\mathrm{\δ}}_{12},$

Due to the order of deformation energy and load effect, it doesn't matter, so above-mentioned two kinds of different order used loads, the deformation energy of gained should be equal, namely

U ₁＝U ₂，

Just can draw thus

P ₁δ ₁₂＝P ₂δ ₂₁，

Above formula shows, P ₁due to P ₂the displacement δ caused ₁₂upper institute work, equals P ₂due to P ₁the displacement δ caused ₂₁upper institute work, Here it is reciprocal work theorem.

Fig. 2 a-Fig. 2 b is High inter case model schematic;

In figure, High inter case has the model under the real load operating modes such as temperature loading T and mechanical load M as figure (a) is depicted as effect on rotor, correspond to the first state of reciprocal work theorem, when figure (b) has equally distributed specific loading P for end imagination acts on, High inter case model, correspond to the second state of reciprocal work theorem.)

Fig. 3 is cone rotor physical dimension schematic diagram;

Fig. 4 is rotor surface vapor (steam) temperature change curve in time;

Fig. 5 is axial average displacement comparison of computational results figure;

Fig. 6 a-Fig. 6 b is unit rotor structure figure and high-pressure inner cylinder structural representation; (main steam temperature and exhaust temperature of HP curve over time in a Cold Start, first main steam enters governing stage after nozzle sets enters high pressure cylinder, then through the acting of each pressure stage, the temperature and pressure of steam constantly reduces, eventually pass high pressure cylinder steam discharge to discharge, when unit normally runs, main steam temperature and the exhaust temperature of HP temperature difference can reach 300 DEG C, main steam along the flow direction on high pressure rotor surface as Fig. 6 a-Fig. 6 b.

Reheat steam temperature and intermediate pressure cylinder exhaust temperature curve over time in a Cold Start, same reheated steam is done work through each pressure stage after nozzle sets enters intermediate pressure cylinder, temperature and pressure constantly reduces, eventually pass intermediate pressure cylinder steam discharge to discharge, when unit normally runs, reheat steam temperature and the intermediate pressure cylinder exhaust temperature temperature difference also reach nearly 300 DEG C, and reheated steam presses the flow direction of rotor surface also to point out at Fig. 6 a-Fig. 6 b in edge.

Fig. 7 is each pressure stage average displacement of high pressure rotor curve over time;

Fig. 8 is High Pressure Inner Cylinder of Steam Turbine each pressure stage average displacement (rotor and cylinder swell increment at different levels) curve over time;

In figure neutralization literary composition, each symbol inventory is: P is applied to the equally distributed specific loading on the rotor of steam turbine or cylinder, and σ is distortion and the stress of rotor or the cylinder body caused by equally distributed specific loading P, σ _zfor the axial normal stress of the rotor that caused by equally distributed specific loading P or cylinder body, ε is the distribution of rotor or the cylinder internal strain caused by real load, ε _zfor the rotor that caused by real load or the axial normal strain of cylinder internal, u is rotor or cylinder end average deformation amount, u ₁and u ₂be respectively the rotor of steam turbine and the end average displacement of cylinder, Ω is the volume of rotor or cylinder, for the average axial normal stress in the unit that caused by equally distributed specific loading P, for the average axial normal strain in the unit that real load causes, x, y, z is respectively the three-dimensional coordinate of unit center point in rectangular coordinate system in space (z-axis is parallel to rotor axis), and r is the distance of unit center point to rotor axis.

Embodiment

The present invention is directed to the drawback of prior art, utilize reciprocal work theorem, the method for the swell increment calculating obtaining a kind of turbine rotor and cylinder of deriving, this method theory is rigorous, computational accuracy is high, and travelling speed is fast, calculates significant for the swell increment realizing turbine rotor and cylinder.

Beam model as shown in Figure 1, if at point 1 position used load P ₁, cause the displacement of a little 1 position to be δ ₁₁, the displacement of putting 2 positions is δ ₂₁, as shown in Figure 1a; If at point 2 position effect P ₂, cause the displacement of a little 1 position to be δ ₁₂, put the displacement δ of 2 positions ₂₂, as shown in Figure 1 b.If by P ₁and P ₂act on lentamente on elastic body, the displacement of final 1 and 2 should be (δ respectively simultaneously ₁₁+ δ ₁₂) and (δ ₂₁+ δ ₂₂), as shown in Fig. 1 (c).Obey Hooke's law at material, under being out of shape very little condition, its deformation energy should be

$U_1=\frac{1}{2}{P}_1({\mathrm{\δ}}_{11}+{\mathrm{\δ}}_{12})+\frac{1}{2}{P}_2({\mathrm{\δ}}_{21}+{\mathrm{\δ}}_{22})---\left(1\right)$

If the mode of action changes into first act on P ₁then P is acted on ₂, then at effect P ₁time, P ₁institute's work is P ₁δ ₁₁/ 2, then act on P ₂process in, except P ₂institute's work is P ₂δ ₂₂outside/2, P ₁make again P ₁δ ₁₂merit, as shown in Figure 1 d, so deformation energy is

$U_2=\frac{1}{2}{P}_1{\mathrm{\δ}}_{11}+\frac{1}{2}{P}_2{\mathrm{\δ}}_{22}+P_1{\mathrm{\δ}}_{12}---\left(2\right)$

Due to the order of deformation energy and load effect, it doesn't matter, so above-mentioned two kinds of different order used loads, the deformation energy of gained should be equal, namely

U ₁＝U ₂(3)

Just can draw thus

P ₁δ ₁₂＝P ₂δ ₂₁(4)

Above formula shows P ₁due to P ₂the displacement δ caused ₁₂upper institute work, equals P ₂due to P ₁the displacement δ caused ₂₁upper institute work, Here it is reciprocal work theorem.

Reciprocal work theorem is proposed by Betti for 1872, the Betti proposition of reciprocal work theorem for: the summation that the first group of power (comprising external force and inertial force) on elastic body that acts on is done work in second group of corresponding displacement of power equals to act on the summation that on elastic body, second group of power (comprising external force and inertial force) is done work in first group of corresponding displacement of power, and the power wherein related to and displacement are generalized force and generalized displacement.It is worthy of note that two groups of above-mentioned power or two groups of displacements act on same elastic body, in fact reciprocal work theorem is not only applicable to different stressed, but have on the same elastic body of identical constraint, and be applicable to different stressedly to have on the not identical elastic body of two of different constraint.

The displacement of application reciprocal work theorem calculating elastic body under Arbitrary Loads effect is the substance in theory of elasticity.In the present invention, it is generalized to the situation of Thermal Load, application reciprocal work theorem calculates the deflection of the critical component such as turbine rotor and cylinder under temperature loading and mechanical load acting in conjunction.The most it is of concern that rotor and cylinder average deformation in the axial direction in engineering, be called axial expansion amount.

According to engine request and engineering background condition, we choose two states acted on the parts such as rotor or cylinder, the load corresponding to each state and distortion respectively:

First state: the temperature variation T (x, y, z, t) of rotor or cylinder, and the distortion of the rotor caused due to temperature variation under specifying constraint or cylinder and stress, be deformed into u wherein along rotor or cylinder axis direction.In general it is change on xsect, but it is desirable that average deformation amount in engineering, it is the important parameter in steam turbine operation process.

Second state: on the rotor that will calculate average displacement or cylinder xsect, the equally distributed specific loading P of effect, and the distortion of the rotor caused by unit uniformly distributed load or cylinder body and stress.

Here, the power of the first state and distortion are the esoteric truths of turbine rotor or cylinder, and the power of the second state and distortion are analytical calculation and one group of imaginary dummy load introducing.The equally distributed external force of the second state is known, and the rotor thus caused by external force or the static stress and distortion in cylinder body then can be obtained by analysis of finite element method, and retains as the known state parameter of online calculation procedure.

For High inter case, the model under the real load operating modes such as temperature loading T and mechanical load M is had as Fig. 2 (a) is depicted as effect on rotor, High inter case model when Fig. 2 (b) has equally distributed specific loading P for end imagination acts on, they correspond to the first state and second state of reciprocal work theorem respectively.

According to reciprocal work theorem, can draw

$Pu=\underset{\mathrm{\Ω}}{\∫\∫\∫}\mathrm{\σ}\mathrm{\ϵ}d\mathrm{\Ω}---\left(5\right)$

In formula, ε is the distribution of High inter case internal strain under the first state, u is the average deformation amount of High inter case end under the first state, σ is the distribution of High inter case internal stress under the second state, and P is the uniformly distributed load that under the second state, High inter case end void adds.

When added by the second state bottom, load p is equally distributed specific loading, above formula can be reduced to

$u=\underset{\mathrm{\Ω}}{\∫\∫\∫}\mathrm{\σ}\mathrm{\ϵ}d\mathrm{\Ω}---\left(6\right)$

It should be noted that formula (5) comprises ε with the ε in formula (6) _x, ε _yand ε _znormal strain on three directions and γ _xy, γ _yzand γ _zxshearing strain on three directions, σ comprises σ _x, σ _yand σ _zthe normal stress in three directions and τ _xy, τ _yzand τ _zxthe shear stress in three directions.But, the specific loading additional when the present invention's the second state only in the z-direction, so σ _x, σ _yand τ _xy, τ _yzand τ _zxvalue and σ _zcompare very little, the present invention ignores their impact, so the expression formula in (4-6) formula integral sign can be reduced to further

$u=\underset{\mathrm{\Ω}}{\∫\∫\∫}{\mathrm{\σ}}_z{\mathrm{\ϵ}}_{z}d\mathrm{\Ω}---\left(7\right)$

It doesn't matter can to find out the form of formula (7) and structure and load type, so it can be used for solving rotational symmetry and the axial displacement of nonaxisymmetric structure under thermal force, mechanical load and other load acting in conjunction, it is a general computing formula.

Because above formula direct integral is very difficult, Gauss numeric integral can be adopted to obtain high precision solution, but its computation process is by more complicated, the corresponding increase of calculated amount.The present invention has carried out suitable simplification to it, first by discrete for above-mentioned continuous print elastic body, suppose that element subdivision is enough little, then unit vertically area change be not generally very large, so the present invention supposes that the axial stress field on each unit is normal stress field, and replace by the mean stress of unit, the mean stress of each like this unit just can put forward inside integral sign, formula (7) turns to

$u=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\σ}}_z^e\underset{e}{\∫\∫\∫}{\mathrm{\ϵ}}_z^{e}dxdydz---\left(8\right)$

In formula for the mean stress in unit, for the axial strain field in unit.

Especially, when structure is axially symmetric structure, when temperature field is axisymmetric temperature field, the rotor that the present invention analyzes is exactly this situation, and the expression formula of its end average displacement can be written as

$u=\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\σ}}_z^e{\∫}_z{\∫}_r{\∫}_{\mathrm{\θ}}{\mathrm{\ϵ}}_z^{e}rd\mathrm{\θ}drdz---\left(9\right)$

Because structure and strain field all have axisymmetric feature, so strain field is just constant 2 π to the integration of θ, above formula can turn to

$u=\underset{i=1}{\overset{n}{\Σ}}2{\mathrm{\π\σ}}_z^e{\∫}_z{\∫}_r{\mathrm{\ϵ}}_z^{e}rdrdz---\left(10\right)$

In order to reliability and the applicability of the inventive method are described, shown below is the contrast being directed to the inventive method and ansys analog computation result under a certain example, give also the result of calculation of the swell increment at a certain example tubine rotor and cylinder, be namely that it specifically describes simultaneously below.

Embodiment 1

Cone rotor as shown in Figure 3, the displacement vertically of constraint left end, other parts free expansion, physical dimension as shown in the figure.The initial temperature of rotor is 350 DEG C, and the coefficient of heat emission on surface is 20000W/m ²dEG C, its material behavior is as shown in table 1.The extraneous vapor (steam) temperature temperature rise rate of rotor is 5 DEG C/min, and vapor (steam) temperature keeps temperature-resistant after reaching 400 DEG C, and change curve is as shown in Figure 4 in time for rotor surface vapor (steam) temperature.

Table 1 rotor material characteristic

ANSYS and the present invention calculate the contrast of its average displacement as shown in Figure 5.

As can be seen from the figure result of the present invention and ansys result have good consistance, also have very high precision, and the present invention is compared with ANSYS, the subdivision number of its unit is little, under these conditions, its result precision has been enough to the requirement meeting engineering calculation.

Embodiment 2

Be illustrated in figure 6 certain power plant 300MW unit rotor structure figure and high-pressure inner cylinder structural drawing, rotor material is 30CrMoV, and its physical parameter is as shown in table 2, and this unit adopts HP-IP combined casing structure, and thrust bearing is positioned at medium voltage side.High inter case has 16 pressure stages, high-pressure section has nine pressure stages, intermediate pressure section has seven pressure stages, high-pressure section and intermediate pressure section have packing to separate, the each inter-stage of high pressure also has interstage gland, to avoid gas leakage, as Fig. 6 (a) to be shown with arrow mark section be packing position.

Table 2 rotor material characteristic

According to the inventive method can try to achieve respectively rotor each pressure stage average displacement over time curve and high-pressure inner cylinder each pressure stage average displacement (i.e. swell increment at different levels) over time curve see Fig. 7 and Fig. 8.

Claims (4)

1., based on the turbine rotor of reciprocal work theorem and a swell increment acquisition methods for cylinder, it is characterized in that, said method comprising the steps of:

A. on the rotor of steam turbine or the xsect of cylinder, equally distributed specific loading P is applied, calculate distortion and the stress σ of rotor or the cylinder body caused by equally distributed specific loading P, and then obtain the axial normal stress σ of rotor or the cylinder body caused by equally distributed specific loading P _z;

B. according to the real load such as temperature loading T and mechanical load M of the rotor of steam turbine or the upper effect of cylinder, determine the distribution ε of its internal strain, and then obtain axial normal strain ε _z;

C. end average deformation amount computing formula is adopted:

Calculate the rotor of steam turbine and the end average displacement u of cylinder respectively ₁and u ₂, the space of Ω shared by rotor or cylinder.

2. the swell increment acquisition methods of the turbine rotor based on reciprocal work theorem according to claim 1 and cylinder, it is characterized in that, in order to reduce difficulty in computation, by the rotor of steam turbine or cylinder discrete be n unit, suppose that the axial stress field on each unit is normal stress field, and replace by the mean stress of unit, then end average deformation gauge calculation simplified formula is:

In formula for the average axial normal stress in the unit that caused by equally distributed specific loading P, for the average axial normal strain in the unit that real load causes, x, y, z is respectively the three-dimensional coordinate of unit center point in rectangular coordinate system in space (z-axis is parallel to rotor axis).

3. the swell increment acquisition methods of the turbine rotor based on reciprocal work theorem according to claim 2 and cylinder, is characterized in that, the end average deformation amount of turbine rotor also can be calculated by following formula:

In formula, r is the distance of unit center point to rotor axis.

4. the swell increment acquisition methods of the turbine rotor based on reciprocal work theorem according to claim 3 and cylinder, is characterized in that, the rotor caused by equally distributed specific loading P or the distortion of cylinder body and stress are obtained by analysis of finite element method.