Abstract:
A method for measuring a shafting mechanical fatigue of a turbine generator set, which involves determining a lumped mass model of a turbine generator set and its parameters; calculating a model frequency and a mode shape of the turbine generator set; acquiring an angular velocity change at a machine end; calculating a torque at a calculating section of shafting based on the model frequency, a mode shape curve and an equivalent rigidity of the lumped mass model, so as to obtain a torque-time history curve at the calculating section of the shafting; calculating a fatigue damage accumulative value for a dangerous section of a set shafting under a certain malfunction or disturbance, that is, the shafting mechanical fatigue of the turbine generator set.

Description:
TECHNICAL FIELD 
     The present invention relates to measurement mechanism of shafting mechanical fatigue which is applied to the industry field with turbine-generator and motor of large capability. e.g., large power plant. 
     BACKGROUND 
     Large thermal turbine-generator technique is a crucial part of important equipment in our nation. The shafting of high-power unit takes advantages of lighter, softer, more support, longer span, higher section power density. The higher material utilized coefficient in generator, the higher section power density in shafting. Additionally, the length of shafting is increased, which results in a lower spring constant, a higher fixed shafting spectrum density and a lower energy threshold of oscillation. Furthermore, series capacitor will be widely applied in the future grid to support super high voltage transmission and larger coverage. 
     Subsynchronous oscillation (SSO) could be caused by series capacitor compensation in the transmission line, HVDC, improper installation of the power system stabilizer (PSS), the feedback action of generator excitation system, silicon controlled system, electro-hydraulic control system and so on. The rotors of the turbine generator have big inertia, and are more sensitive to torsional oscillation modes and thus assume the forced state of low cycle fatigue and high stress. When an electromechanical disturbance occurs, balance between the turbine driving torque and the generator magnetic braking torque is broken, torsional stress acting on the shafting is also changed, the fatigue of the rotor will be increased, and the useful life will be decreased. When the torsional stress is great to a certain level, the shafting will be damaged or even ruptured. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is to provide a real-time measuring method of mechanical fatigue in turbine-generator shafting in power plants, which can measure the mechanical fatigue caused by uncertain disturbances in the turbine-generator shafting. The present invention is applicable to large turbo-unit such as 300 MW, 600 MW, 1000 MW, and is also applicable to smaller turbo-units with capacities of 300 MW and below, as well as to large capacity motors. The Cross-section, the dangerous cross-sections and number of rotors depends on the shafting size. Cross-section as used herein denotes interfaces between mass blocks. Dangerous cross-sections stand for the shaft collar of all the rotors of this shafting. For example, as illustrated in  FIG. 1 , in a typical 600 MW turbine generator, the cross-section J1 is between high and intermediate pressure rotor (HIP) and the low pressure rotor A (ALP), where the torque T1 and the dangerous cross-section is between the #2 and #3 shaft bushing. Similarly, the cross-section J2 is between the low pressure rotor A (ALP) and the low pressure rotor B (BLP), where the torque T2, the dangerous cross-section is between the #4 and #5 shaft bushing. The cross-section J3 is between the low pressure rotor B (BLP) and generator (GEN), where the torque T3 and the dangerous cross-section is between the #6 and #7 shaft bushing. 
     The real-time measuring method of mechanical fatigue in turbine-generator shafting is detailed in the following steps: 
     1. Compute torsional mode and vibration curve based on lumped mass model of turbo-unit. 
     1). Determine the lumped mass model. According to number of rotors, the exemplary typical 600 MW set turbine generator is defined as four lumped mass blocks and three massless springs, which are named as shafting vibration system. See  FIG. 1 . 
     2). Determine the parameters of the lumped mass model, i.e., the equivalent inertias of the mass blocks and the spring constants of the springs. 
     3). Compute the frequency-vibration curve of the shafting. 
     According to the moment of inertia M1, M2, M3, M4, rotational speed ω1, ω2, ω3, ω4, rotational angle δ1, δ2, δ3, δ4 and the spring constant K12, K23, K34 between mass pairs, the free motion per unit equation for each mass block can be acquired : 
     
       
         
           
             { 
             
               
                 
                   
                     
                       
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           * 
                           δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             1 
                             ′′ 
                           
                         
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           12 
                           ⁢ 
                           
                             ( 
                             
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               - 
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           * 
                           δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             2 
                             ′′ 
                           
                         
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           12 
                           ⁢ 
                           
                             ( 
                             
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                               - 
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           23 
                           ⁢ 
                           
                             ( 
                             
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                               - 
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           * 
                           δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             3 
                             ′′ 
                           
                         
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           23 
                           ⁢ 
                           
                             ( 
                             
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                               - 
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           34 
                           ⁢ 
                           
                             ( 
                             
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                               - 
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 4 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       0 
                     
                   
                 
                 
                   
                     
                       
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                           * 
                           δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             4 
                             ′′ 
                           
                         
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           34 
                           ⁢ 
                           
                             ( 
                             
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 4 
                               
                               - 
                               
                                 δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       0 
                     
                   
                 
               
                 
             
           
         
       
     
     We can rewrite the formula as 
     
       
         
           
             
               Δδ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 1 
                 ′′ 
               
             
             = 
             
               
                 - 
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     Δδ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   - 
                   
                     Δδ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               Δδ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 2 
                 ′′ 
               
             
             = 
             
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
               - 
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
               - 
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
               + 
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
             
           
         
       
       
         
           
             
               Δδ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 3 
                 ′′ 
               
             
             = 
             
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
               - 
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
               - 
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
               + 
               
                 
                   
                     K 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   
                     M 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 ⁢ 
                 Δδ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
           
         
       
       
         
           
             
               Δδ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 4 
                 ′′ 
               
             
             = 
             
               
                 
                   K 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   34 
                 
                 
                   M 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     Δδ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   - 
                   
                     Δδ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 ) 
               
             
           
         
       
     
     Which takes matrix form as 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       Δδ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         1 
                         ′′ 
                       
                     
                   
                 
                 
                   
                     
                       Δδ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         2 
                         ′′ 
                       
                     
                   
                 
                 
                   
                     
                       Δδ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         3 
                         ′′ 
                       
                     
                   
                 
                 
                   
                     
                       Δδ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         4 
                         ′′ 
                       
                     
                   
                 
               
               ] 
             
             = 
             
               
                 
                   [ 
                   
                     
                       
                         
                           - 
                           
                             
                               K 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               12 
                             
                             
                               M 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             K 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             12 
                           
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       
                         0 
                       
                       
                         0 
                       
                     
                     
                       
                         
                           
                             K 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             12 
                           
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       
                         
                           
                             - 
                             
                               
                                 K 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 12 
                               
                               
                                 M 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                           - 
                           
                             
                               K 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               23 
                             
                             
                               M 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             K 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             23 
                           
                           
                             M 
                             ⁢ 
                             
                                 
                             
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                             2 
                           
                         
                       
                       
                         0 
                       
                     
                     
                       
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                             K 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             23 
                           
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                       
                         
                           
                             - 
                             
                               
                                 K 
                                 ⁢ 
                                 
                                     
                                 
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                                 23 
                               
                               
                                 M 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                           
                           - 
                           
                             
                               K 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               34 
                             
                             
                               M 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                         
                       
                       
                         
                           
                             K 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             34 
                           
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                     
                     
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           
                             K 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             34 
                           
                           
                             M 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       
                         
                           - 
                           
                             
                               K 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               34 
                             
                             
                               M 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                         
                       
                     
                   
                   ] 
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         
                           Δδ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                     
                     
                       
                         
                           Δδ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                     
                       
                         
                           Δδ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                     
                     
                       
                         
                           Δδ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                     
                   
                   ] 
                 
               
               . 
             
           
         
       
     
     Where [K] and [I] represent the coefficient matrix and Identity matrix, respectively. The dynamic model of the rotors is 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         Δδ 
                         ⁢ 
                         
                             
                         
                       
                       ′ 
                     
                   
                 
                 
                   
                     
                       Δω 
                       ′ 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 [ 
                 
                   
                     
                       0 
                     
                     
                       I 
                     
                   
                   
                     
                       K 
                     
                     
                       0 
                     
                   
                 
                 ] 
               
               ⁡ 
               
                 [ 
                 
                   
                     
                       
                         Δδ 
                         ⁢ 
                         
                             
                         
                       
                     
                   
                   
                     
                       Δω 
                     
                   
                 
                 ] 
               
             
           
         
       
     
     Then we can obtain the frequency-vibration curve of the shafting, as shown in  FIGS. 2.1  to  2 . 3 . 
     2. Compute the torques of the cross-section 
     1) According to the vibration curve of different modes, compute the corresponding various relative torsional angles of mass blocks in different modes. As illustrated in  FIGS. 2.1  to  2 . 3 , the various relative torsional angles of four mass blocks in three modes:
 
θ11,θ12,θ13,
 
θ21,θ22,θ23,
 
θ31,θ32,θ33;
 
     2) Compute the torques excited by unit signal on cross-section of the shafting are (as illustrated in  FIGS. 2.1  to  2 . 3 ): 
     The torque between the first and the second mass block in mode 1 is : t 1,1 =K 1,2 ×θ 1,1    
     The torque between the second and the third mass block in mode 1 is : t 1,2 =K 2,3 ×θ 1,2    
     The torque between the third and the fourth mass block in mode 1 is : t 1,3 =K 3,4 ×θ 1,3    
     The torque between the first and the second mass block in mode 2 is : t 2,1 =K 1,2 ×θ 2,1    
     The torque between the second and the third mass block in mode 2 is : t 2,2 =K 2,3 ×θ 2,2    
     The torque between the third and the fourth mass block in mode 2 is : t 2,3 =K 3,4 ×θ 2,3    
     The torque between the first and the second mass block in mode 3 is : t 3,1 =K 1,2 ×θ 3,1    
     The torque between the second and the third mass block in mode 3 is : t 3,2 =K 2,3 ×θ 3,2    
     The torque between the third and the fourth mass block in mode 3 is : t 3,3 =K 3,4 ×θ 3,3 . 
     3) By acquisition of the changes of palstance, compute the torques of the cross-section of shafting. Capture the changes of palstance Δω, then obtain different mode signal Δω1, Δω2, Δω3 by filtering. 
     With
 
Δω k   =A   k ω k  cos(ω k   t ),  k∈ [1,2,3]
 
obtain the terminal rotation angle in different modes are
 
Δθ k =Δω k   t=A   k  sin(ω k   t )=Δω k *sin(ω k   t )/[ω k *cos(ω k   t )],
 
where, k∈[1,2,3], ω k =2πf k , Δθ k  is rotation angle in different modes.
 
     Consequently, the corresponding torque which the input signal act on different cross-section can by computed:
         the torque corresponding to cross-section J 1  is: T 1 =T 1,1 +T 2,1 +T 3,1      the torque corresponding to cross-section J 2  is: T 2 =T 1,2 +T 2,2 +T 3,2      the torque corresponding to cross-section J 3  is : T 3 =T 1,3 +T 2,3 +T 3,3 ,
 
Where
   the torque corresponding to cross-section J1 in mode 1 is T 1,1 =t 1,1 ×Δθ 1      the torque corresponding to cross-section J1 in mode 2 T 2,1 =t 2,1 ×Δθ 2      the torque corresponding to cross-section J1 in mode 3 is T 3,1 =t 3,1 ×Δθ 3      the torque corresponding to cross-section J2 in mode 1 is T 1,2 =t 1,2 ×Δθ 1      the torque corresponding to cross-section J2 in mode 2 is T 2,2 =t 2,2 ×Δθ 2      the torque corresponding to cross-section J2 in mode 3 is T 3,2 =t 3,2 ×Δθ 3      the torque corresponding to cross-section J3 in mode 1 is T 1,3 =t 1,3 ×Δθ 1      the torque corresponding to cross-section J3 in mode 2 is T 2,3 =t 2,3 ×Δθ 2      the torque corresponding to cross-section J3 in mode 3 is T 3,3 =t 3,3 ×Δθ 3  
 
We can substitute Δω into the above formulas to obtain the torque T, which further result in the torque-time history plot.
       

     3. Compute the cumulative fatigue values of all the cross-sections of the shafting caused by a perturbation, which is the mechanical fatigue of turbine-generator shafting.
         1) According to the algorithm in step 2, we can obtain torque-time history plot in shafting section of all the cross-sections of the shafting;   2) Find out the stress cycle in the history plot by utilizing real time rain-flow method;   3) Compute equivalent stress magnitude corresponding to each stress cycle by utilizing linear averaging method;   4) Look up the components spring S-N curve (Stress-Fatigue Life curve) in the dangerous cross-sections, to obtain the fatigue damage value caused by a single stress cycle;   5) The cumulative fatigue value of the specific dangerous cross-section with respect to the vibration is obtained by summing linearly all the fatigue values over all the stress cycle at this dangerous cross-section.       

     The present invention discloses a real-time measuring method of mechanical fatigue in large turbine-generator shafting, which measures the mechanical fatigue in turbine-generator shafting well and truly. With the application of high-capacity turbine-generator and super high voltage transmission, The Subsynchronous oscillation (SSO) occurs more severely in turbo-unit and power grid. Accurate measurement of shafting mechanical fatigue is crucial to suppress the subsynchronous oscillation and to protect turbine-generator and other electrical equipment. The invention discloses a real-time measuring method of mechanical fatigue in large turbine-generator shafting for the first time, which is of great significance to solve the problem of subsynchronous oscillation in power plant and power grid. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates that a lumped mass model which is determined by a classic turbo-unit (600 MW) according to the number of rotors of its shafting. 
         FIGS. 2.1  to  2 . 3  illustrates the vibration mode and inherent frequency of this turbo-unit shafting, wherein 
         FIG. 2.1  denotes the vibration curve at the first order frequency f 1 =15.5 Hz; 
         FIG. 2.2  denotes the vibration curve at the second order frequency f 2 =25.98 Hz; 
         FIG. 2.3  denotes the vibration curve at the third order frequency f 3 =29.93 Hz; 
         FIGS. 3.1  to  3 . 3  are schematic drawings which show different changes of the palstance in varies modes.  FIGS. 3.1 ,  3 . 2  and  3 . 3  corresponds to mode 1, 2 and 3, respectively. 
         FIGS. 4.1  and  4 . 2  show torsional power (y axis, unit MW)−time (x, unit s) curve of the specific cross-section on a perturbation, where sampling frequency is 1000 Hz.  FIG. 4.1  shows a torsional power−time curve, where the statistic time is 8 seconds, and the sampling frequency is 1000 Hz. Note  FIG. 4.2  is to zoom in the first 2 seconds of  FIG. 4.1 . 
         FIG. 5  shows the S-N curve of the rotors of the turbo, which reflects material fatigue value. 
         FIG. 6  shows the architecture of the exampled fatigue measurement system. 
         FIG. 7  shows the protection circuits of the shaft torsional mode. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The invention is further illustrated in conjunction with the appended drawings, referring to the drawings. 
     The working process of this invention is as follows: Capture the changes of palstance of turbo-unit&#39;s engine end, then obtain the instantaneous torsional angle of turbo-unit&#39;s engine end. According to the mode frequency, vibration curve, compute torques on each cross-sections of the shafting which is created by input signal, obtain the load-time history plot on the cross-sections of the shafting. Obtain stress cycles with the rain-flow method, looking up S-N curve of corresponding material part to get the fatigue damage, and then calculate the cumulative fatigue damage of each dangerous cross-section with respect to the vibration or fault at each dangerous cross-section, that is, the shafting mechanical fatigue of turbine-generator. 
     In the S-N curve of the rotors of the turbo, as shown in  FIG. 5 . The invention gives only the S-N curves of the #2 and #3 shaft bushing which are between HIP and ALP, and the S-N curves of locating bearing and shaft coupling which connect two rotors. The y axis denotes tolerant torque, represented in per-unit value of power. 1 per-unit value denotes 314.6 MW power. The x axis denotes cycle times, represented in logarithmic coordinates. For example, to compute damage in the #2 shaft bushing of the cross-section J1, when torque of the cross-section J1 is calculated as 1.85 per-unit value, the tolerant cycle times is 10000, that is, the shafting damage which caused in the #2 shaft bushing is 1/10000. 
     We take a typical 600 MW set turbine generator of one domestic power plant as an example. 
     Determine the lumped mass model which is illustrated in  FIG. 1 . The 4 lumped mass blocks consists of high and intermediate pressure rotor (HIP), the low pressure rotor A (ALP), the low pressure rotor B (BLP), generator (GEN), which are named as shafting vibration system. Note M1, M2, M3 and M4 represent 4 mass blocks. k12, k23 and k34 stands for the massless springs. 
     Determine the parameters of the lumped mass model, i.e., the equivalent inertias of the mass blocks and the spring constants of the springs as shown in Table 1. 
     Compute the frequency-vibration curve of the shafting, we can deduce the free motion per unit equation for each mass block as: 
             {                 M   ⁢           ⁢   1   *   δ   ⁢           ⁢     1   ′′       +     K   ⁢           ⁢   12   ⁢     (       δ   ⁢           ⁢   1     -     δ   ⁢           ⁢   2       )         =   0                   M   ⁢           ⁢   2   *   δ   ⁢           ⁢     2   ′′       +     K   ⁢           ⁢   12   ⁢     (       δ   ⁢           ⁢   2     -     δ   ⁢           ⁢   1       )       +     K   ⁢           ⁢   23   ⁢     (       δ   ⁢           ⁢   2     -     δ   ⁢           ⁢   3       )         =   0                   M   ⁢           ⁢   3   *   δ   ⁢           ⁢     3   ′′       +     K   ⁢           ⁢   23   ⁢     (       δ   ⁢           ⁢   3     -     δ   ⁢           ⁢   2       )       +     K   ⁢           ⁢   34   ⁢     (       δ   ⁢           ⁢   3     -     δ   ⁢           ⁢   4       )         =   0                   M   ⁢           ⁢   4   *   δ   ⁢           ⁢     4   ′′       +     K   ⁢           ⁢   34   ⁢     (       δ   ⁢           ⁢   4     -     δ   ⁢           ⁢   3       )         =   0                       
Which takes matrix form as:
 
               [           Δδ   ⁢           ⁢     1   ′′                 Δδ   ⁢           ⁢     2   ′′                 Δδ   ⁢           ⁢     3   ′′                 Δδ   ⁢           ⁢     4   ′′             ]     =         [           -       K   ⁢           ⁢   12       M   ⁢           ⁢   1                 K   ⁢           ⁢   12       M   ⁢           ⁢   1           0       0               K   ⁢           ⁢   12       M   ⁢           ⁢   2               -       K   ⁢           ⁢   12       M   ⁢           ⁢   2         -       K   ⁢           ⁢   23       M   ⁢           ⁢   2                 K   ⁢           ⁢   23       M   ⁢           ⁢   2           0           0           K   ⁢           ⁢   23       M   ⁢           ⁢   3               -       K   ⁢           ⁢   23       M   ⁢           ⁢   3         -       K   ⁢           ⁢   34       M   ⁢           ⁢   3                 K   ⁢           ⁢   34       M   ⁢           ⁢   3               0       0           K   ⁢           ⁢   34       M   ⁢           ⁢   4             -       K   ⁢           ⁢   34       M   ⁢           ⁢   4               ]     ⁡     [           Δδ   ⁢           ⁢   1               Δδ   ⁢           ⁢   2               Δδ   ⁢           ⁢   3               Δδ   ⁢           ⁢   4           ]       .           
Let [K] and [I] represent the coefficient matrix and Identity matrix, respectively. Consequently, the dynamic model of the rotors is
 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         Δδ 
                         ⁢ 
                         
                             
                         
                       
                       ′ 
                     
                   
                 
                 
                   
                     
                       Δω 
                       ′ 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 [ 
                 
                   
                     
                       0 
                     
                     
                       I 
                     
                   
                   
                     
                       K 
                     
                     
                       0 
                     
                   
                 
                 ] 
               
               ⁡ 
               
                 [ 
                 
                   
                     
                       
                         Δδ 
                         ⁢ 
                         
                             
                         
                       
                     
                   
                   
                     
                       Δω 
                     
                   
                 
                 ] 
               
             
           
         
       
     
     Then we can obtain the frequency-vibration curve of the shafting, as shown in  FIGS. 2.1 ,  2 . 2 ,  2 . 3 . Note that these 3 figures represent 3 secondary synchronization frequencies, i.e., 15.5 Hz, 25.98 Hz and 29.93 Hz, which denotes the 3 vibration modes of this shafting. 
     According to the vibration curve, compute the corresponding various relative torsional angles θ ij (i=1,2,3; j=1,2,3). As illustrated in Table 2. 
     According to the mode frequency, vibration curve, lumped mass model, compute the torques excited by unit signal on cross-section of the shafting t i,j  (i=1,2,3; j=1,2,3) as Illustrated in Table 3. 
     Emulate of one given fault, capture the changes of palstance Δω, then obtain different mode signal Δω1, Δω2, Δω3 by filtering. 
     With
 
Δω k   =A   k ω k  cos(ω k   t ), Δθ k =Δω k   t=A   k  sin(ω k   t )=Δω k *sin(ω k   t )/[ω k *cos(ω k   t )],
 
where, k∈[1,2,3], ω k =2πf k , the rotation angle in different modes are Δθ1, Δθ2, Δω3. As shown in the FIG.  3 . 1 - 3 . 3 , where y axis&#39;s units are MWs, the x axis denotes time record, the length is 8 s, the sampling frequency is 1000 HZ.
 
     According to the torques given in the Table 3, the effect of three modes are added linearly, then is reduced to one cross-section of shafting. In this example, calculate the torque T1 corresponding to cross-section J 1  between the first and the second mass block, T1=T1,1+T2,1+T3,1. Where, T 1,1 =t 1,1 ×Δθ 1 , T 2,1 =t 2,1 ×Δθ 2 , T 3,1 =t 3,1 ×Δθ 3 . Further obtain the torque-time history plot, as illustrated in FIGS.  4 . 1 , 4 . 2 . The y axis denotes torsional power, the y axis&#39;s units are MWs. In  FIG. 4.1 , the statistic time is 8 s, the sampling frequency is 1000 HZ.  FIG. 4.2  is to zoom in the first 2 seconds of  FIG. 4.1 , the sampling frequency is 1000 HZ. 
     Find out the stress cycle in the load-time history plot (see  FIGS. 4.1  and  4 . 2 ) by utilizing real time rain-flow method. Note the number of stress cycle in  FIGS. 4.1  and  4 . 2  is 157, which is given in Table 4. Table 4 also shows the equivalent stress magnitude corresponding to each stress cycle by utilizing linear averaging method. 
     The cross-section J1 has two dangerous cross-sections which are between the #2 and #3 shaft bushing. In our example, we only consider the damage on the #2 shaft bushing. Look up the (S-N) curve on the #2 shaft bushing which is illustrated in  FIG. 5 , to obtain the fatigue damage value on the #2 shaft bushing caused by each stress cycle. Sum all the stress cycles linearly to obtain the cumulative fatigue damage values on the #2 shaft bushing of 600 MW turbine-generator with respect to this perturbation. In our example, the cumulative fatigue damage on the 2#shaft bushing is 0.001072%. The fatigue damage on the other dangerous part of the shafting can be calculated in the same way as the #2 shaft bushing. 
     The architecture of this measurement is illustrated in  FIG. 6 . Both software and hardware elements are flexible and configurable, which consists of 2 power modules (POW), 2 pulse impulse modules (PI), 1 control module (CM), 1 analog input module (AI), 1 digital input module (DI) and 4 digital output modules (DO). The equipment communicates with HMI (Human-Machine Interface) through a specification named O-NET (applicant-specific communication mode), while DP-NET is utilized for the inside communication. All of the modules can be hot-plugged and linked dynamically. The PI captures the impulses which will be processed in the CM to compute the mechanical fatigue value. The DO gives alarm or trip based on the value. 
     The connecting of torsional vibration protector of turbine generator is illustrated in  FIG. 7 . A pair of axis sensors is equipped at the input portion. Redundant rotation sensor transmits rotation velocity to obtain the fatigue damage value which can generate DO signal to alarm or trip when the fatigue damage value is beyond the threshold. Furthermore, the data are transmitted by Ethernet and recorded in HMI. 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Shafting modeling data 
               
             
          
           
               
                   
                 Weight Moment of 
                 Spring Constant 
               
               
                 Lumped Mass Module 
                 Inertia (kg*m2) 
                 K (N*m/rad) 
               
               
                   
               
             
          
           
               
                 HIP 
                 2851 
                   
               
               
                   
                   
                 0.76882E+08 
               
               
                 ALP 
                 15542 
               
               
                   
                   
                 0.13316E+09 
               
               
                 BLP 
                 15235 
               
               
                   
                   
                 0.13232E+09 
               
               
                 GEN 
                 9732 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Relative torsional angle in cross-section between mass blocks 
               
             
          
           
               
                   
                 Relative Torsional Angle in Cross-section between Mass Blocks 
               
             
          
           
               
                 Mode 
                 Frequency (HZ) 
                 between 1 and 2 
                 between 2 and 3 
                 between 3 and 4 
               
               
                   
               
             
          
           
               
                 Mode1 
                 15.5 
                 θ11 = −0.35176 
                 θ12 = −0.92079 
                 θ13 = −0.62897 
               
               
                 Mode2 
                 26.12 
                 θ21 = −0.98820 
                 θ22 = −0.60771 
                 θ23 = 1.21629.93 
               
               
                 Mode3 
                 29.93 
                 θ31 = −1.31161 
                 θ32 = 0.52913 
                 θ33 = −0.35334 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Torque in cross-section between mass blocks 
               
               
                 caused by each mode in unit intension 
               
             
          
           
               
                   
                 Torque in Cross-section Between Mass Blocks 
               
             
          
           
               
                 Mode 
                 Frequency (HZ) 
                 between 1 and 2 
                 between 2 and 3 
                 between 3 and 4 
               
               
                   
               
             
          
           
               
                 Mode1 
                 15.5 
                 t11 = −1.44211 
                 t12 = −6.53824 
                 t13 = −4.43794 
               
               
                 Mode2 
                 26.12 
                 t21 = −−2.43477 
                 t22 = −2.59333 
                 t23 = 5.15.5767 
               
               
                 Mode3 
                 29.93 
                 t31 = −−2.82900 
                 t32 = 1.97669 
                 t33 = −1.31166 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Stress cycles found in torque-time history 
               
               
                 plot of cross-section J1 when fault occurs 
               
             
          
           
               
                 Equivalent Stress 
                   
                   
               
               
                 Amplitude 
                 Peak Point 1 
                 Peak Point 2 
               
               
                   
               
               
                 MEF = 0.00031373 
                 E(i) = −0.00097100 
                 E(i + 1) = −0.00099100 
               
               
                 MEF = 0.00129660 
                 E(i) = 0.00131000 
                 E(i + 1) = −0.00127000 
               
               
                 MEF = 0.00052793 
                 E(i) = 0.00096500 
                 E(i + 1) = 0.00128000 
               
               
                 MEF = 0.00013544 
                 E(i) = −0.00008800 
                 E(i + 1) = −0.00057900 
               
               
                 MEF = 0.00057009 
                 E(i) = 0.00075200 
                 E(i + 1) = −0.00020900 
               
               
                 MEF = 0.00005330 
                 E(i) = −0.00004000 
                 E(i + 1) = 0.00006000 
               
               
                 MEF = 0.00054518 
                 E(i) = 0.00057700 
                 E(i + 1) = −0.00048200 
               
               
                 MEF = 0.00009757 
                 E(i) = 0.00025100 
                 E(i + 1) = 0.00020700 
               
               
                 MEF = 0.00116160 
                 E(i) = −0.00086700 
                 E(i + 1) = 0.00131000 
               
               
                 MEF = 0.00091055 
                 E(i) = 0.00214000 
                 E(i + 1) = 0.00153000 
               
               
                 MEF = 0.00107000 
                 E(i) = 0.00107000 
                 E(i + 1) = −0.00107000 
               
               
                 MEF = 0.00115088 
                 E(i) = −0.00083500 
                 E(i + 1) = 0.00131000 
               
               
                 MEF = 0.00005514 
                 E(i) = −0.00022900 
                 E(i + 1) = −0.00029000 
               
               
                 MEF = 0.00083456 
                 E(i) = −0.00079000 
                 E(i + 1) = 0.00085700 
               
               
                 MEF = 0.00022375 
                 E(i) = 0.00000900 
                 E(i + 1) = 0.00034100 
               
               
                 MEF = 0.00009758 
                 E(i) = −0.00047100 
                 E(i + 1) = −0.00038400 
               
               
                 MEF = 0.00001967 
                 E(i) = −0.00024700 
                 E(i + 1) = −0.00015400 
               
               
                 MEF = 0.00001915 
                 E(i) = −0.00018900 
                 E(i + 1) = −0.00012400 
               
               
                 MEF = 0.00014475 
                 E(i) = −0.00048900 
                 E(i + 1) = −0.00046400 
               
               
                 MEF = 0.00012130 
                 E(i) = −0.00010800 
                 E(i + 1) = 0.00012800 
               
               
                 MEF = 0.00009276 
                 E(i) = −0.00034300 
                 E(i + 1) = −0.00040400 
               
               
                 MEF = 0.00016100 
                 E(i) = −0.00063700 
                 E(i + 1) = −0.00056300 
               
               
                 MEF = 0.02980350 
                 E(i) = −0.24400000 
                 E(i + 1) = −0.07810000 
               
               
                 MEF = 0.03987000 
                 E(i) = −0.27800000 
                 E(i + 1) = −0.20000000 
               
               
                 MEF = 0.02236100 
                 E(i) = −0.01670000 
                 E(i + 1) = −0.09990000 
               
               
                 MEF = 0.07458250 
                 E(i) = 0.12500000 
                 E(i + 1) = 0.02550000 
               
               
                 MEF = 0.12542500 
                 E(i) = 0.23700000 
                 E(i + 1) = 0.30800000 
               
               
                 MEF = 0.01732200 
                 E(i) = −0.07420000 
                 E(i + 1) = −0.19900000 
               
               
                 MEF = 0.01624650 
                 E(i) = 0.04500000 
                 E(i + 1) = 0.04710000 
               
               
                 MEF = 0.01939500 
                 E(i) = −0.20800000 
                 E(i + 1) = −0.35500000 
               
               
                 MEF = 0.31217500 
                 E(i) = −0.24900000 
                 E(i + 1) = 0.34400000 
               
               
                 MEF = 0.00459750 
                 E(i) = −0.02170000 
                 E(i + 1) = −0.05680000 
               
               
                 MEF = 0.05211610 
                 E(i) = 0.00734000 
                 E(i + 1) = −0.14100000 
               
               
                 MEF = 0.11204350 
                 E(i) = −0.15600000 
                 E(i + 1) = 0.08990000 
               
               
                 MEF = 0.09402500 
                 E(i) = 0.16200000 
                 E(i + 1) = 0.22300000 
               
               
                 MEF = 0.15282850 
                 E(i) = 0.26100000 
                 E(i + 1) = 0.06190000 
               
               
                 MEF = 0.03879500 
                 E(i) = −0.30900000 
                 E(i + 1) = −0.21400000 
               
               
                 MEF = 0.07383650 
                 E(i) = 0.05310000 
                 E(i + 1) = −0.11500000 
               
               
                 MEF = 0.04101000 
                 E(i) = −0.17300000 
                 E(i + 1) = −0.22100000 
               
               
                 MEF = 0.04819000 
                 E(i) = 0.14200000 
                 E(i + 1) = 0.14400000 
               
               
                 MEF = 0.09492150 
                 E(i) = 0.09730000 
                 E(i + 1) = −0.09020000 
               
               
                 MEF = 0.03615650 
                 E(i) = 0.09850000 
                 E(i + 1) = 0.08760000 
               
               
                 MEF = 0.02306250 
                 E(i) = −0.08500000 
                 E(i + 1) = −0.07750000 
               
               
                 MEF = 0.02483150 
                 E(i) = 0.07210000 
                 E(i + 1) = 0.06900000 
               
               
                 MEF = 0.06563200 
                 E(i) = −0.06510000 
                 E(i + 1) = 0.06590000 
               
               
                 MEF = 0.06203600 
                 E(i) = 0.06150000 
                 E(i + 1) = −0.06310000 
               
               
                 MEF = 0.01818800 
                 E(i) = 0.05410000 
                 E(i + 1) = 0.05310000 
               
               
                 MEF = 0.01671350 
                 E(i) = 0.04750000 
                 E(i + 1) = 0.04440000 
               
               
                 MEF = 0.01456350 
                 E(i) = 0.04200000 
                 E(i + 1) = 0.03990000 
               
               
                 MEF = 0.00526000 
                 E(i) = −0.03730000 
                 E(i + 1) = −0.02670000 
               
               
                 MEF = 0.00961550 
                 E(i) = −0.03740000 
                 E(i + 1) = −0.03330000 
               
               
                 MEF = 0.03110050 
                 E(i) = 0.03100000 
                 E(i + 1) = −0.03130000 
               
               
                 MEF = 0.01195950 
                 E(i) = 0.03350000 
                 E(i + 1) = 0.03080000 
               
               
                 MEF = 0.00913950 
                 E(i) = −0.02830000 
                 E(i + 1) = −0.02800000 
               
               
                 MEF = 0.00749600 
                 E(i) = 0.02070000 
                 E(i + 1) = 0.02170000 
               
               
                 MEF = 0.00610100 
                 E(i) = −0.02010000 
                 E(i + 1) = −0.01930000 
               
               
                 MEF = 0.01849900 
                 E(i) = 0.01870000 
                 E(i + 1) = −0.01810000 
               
               
                 MEF = 0.00564950 
                 E(i) = 0.01580000 
                 E(i + 1) = 0.01450000 
               
               
                 MEF = 0.01309850 
                 E(i) = −0.01250000 
                 E(i + 1) = 0.01340000 
               
               
                 MEF = 0.00396300 
                 E(i) = 0.01140000 
                 E(i + 1) = 0.01080000 
               
               
                 MEF = 0.00167460 
                 E(i) = −0.00580000 
                 E(i + 1) = −0.00544000 
               
               
                 MEF = 0.01106850 
                 E(i) = 0.01070000 
                 E(i + 1) = −0.01180000 
               
               
                 MEF = 0.00226635 
                 E(i) = −0.00717000 
                 E(i + 1) = −0.00702000 
               
               
                 MEF = 0.00209935 
                 E(i) = −0.00747000 
                 E(i + 1) = −0.00692000 
               
               
                 MEF = 0.00207905 
                 E(i) = 0.00628000 
                 E(i + 1) = 0.00629000 
               
               
                 MEF = 0.00133050 
                 E(i) = 0.00379000 
                 E(i + 1) = 0.00391000 
               
               
                 MEF = 0.00201120 
                 E(i) = −0.00948000 
                 E(i + 1) = −0.00780000 
               
               
                 MEF = 0.00102635 
                 E(i) = −0.00575000 
                 E(i + 1) = −0.00444000 
               
               
                 MEF = 0.00319645 
                 E(i) = −0.00178000 
                 E(i + 1) = 0.00391000 
               
               
                 MEF = 0.00245620 
                 E(i) = 0.00590000 
                 E(i + 1) = 0.00438000 
               
               
                 MEF = 0.00067700 
                 E(i) = 0.00185000 
                 E(i + 1) = 0.00195000 
               
               
                 MEF = 0.00186895 
                 E(i) = −0.00653000 
                 E(i + 1) = −0.00610000 
               
               
                 MEF = 0.00187005 
                 E(i) = −0.00609000 
                 E(i + 1) = −0.00588000 
               
               
                 MEF = 0.00272765 
                 E(i) = 0.00588000 
                 E(i + 1) = 0.00353000 
               
               
                 MEF = 0.00112555 
                 E(i) = 0.00336000 
                 E(i + 1) = 0.00331000 
               
               
                 MEF = 0.00115840 
                 E(i) = 0.00349000 
                 E(i + 1) = 0.00347000 
               
               
                 MEF = 0.00192375 
                 E(i) = 0.00385000 
                 E(i + 1) = 0.00190000 
               
               
                 MEF = 0.00117165 
                 E(i) = −0.00615000 
                 E(i + 1) = −0.00486000 
               
               
                 MEF = 0.00102631 
                 E(i) = 0.00056100 
                 E(i + 1) = −0.00195000 
               
               
                 MEF = 0.00126392 
                 E(i) = −0.00549000 
                 E(i + 1) = −0.00086500 
               
               
                 MEF = 0.00100636 
                 E(i) = −0.00168000 
                 E(i + 1) = 0.00066700 
               
               
                 MEF = 0.00133795 
                 E(i) = 0.00347000 
                 E(i + 1) = 0.00376000 
               
               
                 MEF = 0.00031862 
                 E(i) = 0.00089700 
                 E(i + 1) = 0.00093100 
               
               
                 MEF = 0.00039954 
                 E(i) = 0.00089400 
                 E(i + 1) = 0.00058200 
               
               
                 MEF = 0.00019390 
                 E(i) = −0.00142000 
                 E(i + 1) = −0.00224000 
               
               
                 MEF = 0.00010523 
                 E(i) = 0.00020200 
                 E(i + 1) = 0.00026000 
               
               
                 MEF = 0.00007009 
                 E(i) = −0.00025300 
                 E(i + 1) = −0.00029300 
               
               
                 MEF = 0.00034950 
                 E(i) = −0.00118000 
                 E(i + 1) = −0.00112000 
               
               
                 MEF = 0.00019009 
                 E(i) = −0.00009100 
                 E(i + 1) = 0.00024000 
               
               
                 MEF = 0.00042745 
                 E(i) = 0.00067200 
                 E(i + 1) = 0.00005800 
               
               
                 MEF = 0.00119155 
                 E(i) = −0.00087700 
                 E(i + 1) = 0.00135000 
               
               
                 MEF = 0.00039255 
                 E(i) = −0.00125000 
                 E(i + 1) = −0.00122000 
               
               
                 MEF = 0.00121630 
                 E(i) = 0.00129000 
                 E(i + 1) = −0.00107000 
               
               
                 MEF = 0.00033462 
                 E(i) = 0.00020900 
                 E(i + 1) = −0.00058400 
               
               
                 MEF = 0.00031812 
                 E(i) = 0.00042800 
                 E(i + 1) = −0.00010000 
               
               
                 MEF = 0.00064218 
                 E(i) = 0.00067200 
                 E(i + 1) = −0.00058300 
               
               
                 MEF = 0.00062445 
                 E(i) = 0.00073600 
                 E(i + 1) = −0.00040300 
               
               
                 MEF = 0.00081862 
                 E(i) = 0.00089500 
                 E(i + 1) = −0.00066700 
               
               
                 MEF = 0.00074958 
                 E(i) = 0.00090100 
                 E(i + 1) = −0.00044900 
               
               
                 MEF = 0.00078607 
                 E(i) = −0.00068100 
                 E(i + 1) = 0.00083900 
               
               
                 MEF = 0.22609500 
                 E(i) = 0.20700000 
                 E(i + 1) = −0.26400000 
               
               
                 MEF = 0.17750000 
                 E(i) = 0.15500000 
                 E(i + 1) = 0.34500000 
               
               
                 MEF = 0.46587500 
                 E(i) = −0.41600000 
                 E(i + 1) = 0.49100000 
               
               
                 MEF = 0.42965500 
                 E(i) = −0.42500000 
                 E(i + 1) = 0.43200000 
               
               
                 MEF = 0.01418000 
                 E(i) = −0.44600000 
                 E(i + 1) = −0.24600000 
               
               
                 MEF = 0.11804500 
                 E(i) = 0.31000000 
                 E(i + 1) = 0.26300000 
               
               
                 MEF = 0.09014500 
                 E(i) = 0.19500000 
                 E(i + 1) = 0.11800000 
               
               
                 MEF = 0.02165250 
                 E(i) = −0.11700000 
                 E(i + 1) = −0.09150000 
               
               
                 MEF = 0.03096200 
                 E(i) = 0.08550000 
                 E(i + 1) = 0.07730000 
               
               
                 MEF = 0.01866400 
                 E(i) = −0.07550000 
                 E(i + 1) = −0.06610000 
               
               
                 MEF = 0.01330850 
                 E(i) = −0.04980000 
                 E(i + 1) = −0.04510000 
               
               
                 MEF = 0.01466400 
                 E(i) = 0.03530000 
                 E(i + 1) = 0.02630000 
               
               
                 MEF = 0.00689950 
                 E(i) = 0.01990000 
                 E(i + 1) = 0.02040000 
               
               
                 MEF = 0.01045030 
                 E(i) = −0.01190000 
                 E(i + 1) = 0.00972000 
               
               
                 MEF = 0.00262780 
                 E(i) = −0.00889000 
                 E(i + 1) = −0.00843000 
               
               
                 MEF = 0.00372060 
                 E(i) = 0.00934000 
                 E(i + 1) = 0.01030000 
               
               
                 MEF = 0.00832115 
                 E(i) = −0.00878000 
                 E(i + 1) = 0.00809000 
               
               
                 MEF = 0.00716760 
                 E(i) = 0.00698000 
                 E(i + 1) = −0.00754000 
               
               
                 MEF = 0.00262500 
                 E(i) = 0.00602000 
                 E(i + 1) = 0.00698000 
               
               
                 MEF = 0.00196840 
                 E(i) = −0.00665000 
                 E(i + 1) = −0.00631000 
               
               
                 MEF = 0.00543455 
                 E(i) = 0.00519000 
                 E(i + 1) = −0.00592000 
               
               
                 MEF = 0.00235450 
                 E(i) = 0.00614000 
                 E(i + 1) = 0.00516000 
               
               
                 MEF = 0.00473425 
                 E(i) = −0.00510000 
                 E(i + 1) = 0.00455000 
               
               
                 MEF = 0.00058190 
                 E(i) = 0.00132000 
                 E(i + 1) = 0.00154000 
               
               
                 MEF = 0.00057920 
                 E(i) = −0.00052600 
                 E(i + 1) = 0.00060600 
               
               
                 MEF = 0.00065012 
                 E(i) = 0.00076100 
                 E(i + 1) = −0.00043000 
               
               
                 MEF = 0.00069785 
                 E(i) = 0.00149000 
                 E(i + 1) = 0.00180000 
               
               
                 MEF = 0.00078342 
                 E(i) = 0.00083400 
                 E(i + 1) = −0.00068300 
               
               
                 MEF = 0.00091760 
                 E(i) = −0.00075600 
                 E(i + 1) = 0.00099900 
               
               
                 MEF = 0.00107245 
                 E(i) = −0.00072000 
                 E(i + 1) = 0.00125000 
               
               
                 MEF = 0.03672500 
                 E(i) = −0.22600000 
                 E(i + 1) = −0.33900000 
               
               
                 MEF = 0.02767450 
                 E(i) = 0.07300000 
                 E(i + 1) = 0.06230000 
               
               
                 MEF = 0.02342850 
                 E(i) = 0.05790000 
                 E(i + 1) = 0.04500000 
               
               
                 MEF = 0.00093900 
                 E(i) = −0.02340000 
                 E(i + 1) = −0.01320000 
               
               
                 MEF = 0.01127000 
                 E(i) = 0.01060000 
                 E(i + 1) = −0.01260000 
               
               
                 MEF = 0.00935235 
                 E(i) = −0.00896000 
                 E(i + 1) = 0.00955000 
               
               
                 MEF = 0.00663060 
                 E(i) = 0.00651000 
                 E(i + 1) = −0.00687000 
               
               
                 MEF = 0.00546735 
                 E(i) = −0.00441000 
                 E(i + 1) = 0.00600000 
               
               
                 MEF = 0.00014832 
                 E(i) = −0.00132000 
                 E(i + 1) = −0.00088800 
               
               
                 MEF = 0.00062236 
                 E(i) = −0.00063100 
                 E(i + 1) = 0.00061800 
               
               
                 MEF = 0.00010550 
                 E(i) = −0.00169000 
                 E(i + 1) = −0.00101000 
               
               
                 MEF = 0.00086960 
                 E(i) = 0.00088200 
                 E(i + 1) = −0.00084500 
               
               
                 MEF = 0.00135627 
                 E(i) = −0.00093200 
                 E(i + 1) = 0.00157000 
               
               
                 MEF = 0.20655000 
                 E(i) = 0.23900000 
                 E(i + 1) = 0.43100000 
               
               
                 MEF = 0.01210400 
                 E(i) = −0.07940000 
                 E(i + 1) = −0.05820000 
               
               
                 MEF = 0.01247350 
                 E(i) = 0.02450000 
                 E(i + 1) = 0.01140000 
               
               
                 MEF = 0.00713340 
                 E(i) = 0.00712000 
                 E(i + 1) = −0.00716000 
               
               
                 MEF = 0.00043930 
                 E(i) = 0.00117000 
                 E(i + 1) = 0.00125000 
               
               
                 MEF = 0.11366500 
                 E(i) = −0.41900000 
                 E(i + 1) = −0.38200000 
               
               
                 MEF = 0.00024778 
                 E(i) = −0.00082800 
                 E(i + 1) = −0.00090400 
               
               
                 MEF = 0.00082835 
                 E(i) = 0.00076300 
                 E(i + 1) = 0.00163000 
               
               
                 MEF = 0.00013099 
                 E(i) = −0.00039100 
                 E(i + 1) = 0.00000000 
               
               
                 MEF = 0.00675285 
                 E(i) = 0.00752000 
                 E(i + 1) = −0.00523000 
               
               
                 MEF = 0.00024700 
                 E(i) = −0.00920000 
                 E(i + 1) = −0.01900000 
               
               
                 MEF = 0.12675000 
                 E(i) = −0.02700000 
                 E(i + 1) = 0.17700000 
               
               
                 MEF = 0.18119500 
                 E(i) = 0.27300000 
                 E(i + 1) = 0.41000000 
               
               
                 MEF = 0.48251000 
                 E(i) = 0.64800000 
                 E(i + 1) = −0.15400000 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Fatigue damage in each danger section 
               
               
                 caused by certain disturbance 
               
             
          
           
               
                   
                 Dangerous Cross-sections 
                 Fatigue Damage (%) 
               
               
                   
                   
               
             
          
           
               
                   
                 Position of 2# shaft bushing 
                 0.03548 
               
               
                   
                 Position of 3# shaft bushing 
                 0.0 
               
               
                   
                 Position of 4# shaft bushing 
                 0.00611 
               
               
                   
                 Position of 5# shaft bushing 
                 0.00692 
               
               
                   
                 Position of 6# shaft bushing 
                 0.05248