System for monitoring torsion damage to a composite line of shapes through a driving machine and a driven machine

First and second devices (8,9) measure the speed of rotation at two widely separated points H and J along a line of shafts, e.g. through a turboalternator unit. Parameters representative of the opposing torque are determined by a third device which is responsive to signals derived from said measured speeds and to a signal representative of the travel of a controlling servomotor (7). Apparatus are provided that determine the torsion damage suffered, if any, on the basis of the signals provided by said first, second and third devices. The system avoids the prior art need to use expensive, high-current transformers, and can also provide more accurate measurement of damage suffered.

FIELD OF THE INVENTION 
The present invention relates to a system for monitoring torsion damage to 
a composite line of shafts passing through a driving machine and a driven 
machine (eg. through a turboalternator unit), and in which the driven 
machine is controlled via a servomotor. 
BACKGROUND OF THE INVENTION 
Damaging torques can be imposed on turboalternators by severe system 
disturbances. These can result in oscillations in the line of shafts 
having sufficient amplitude to cause mechanical fatigue, and since fatigue 
is cumulative, it is essential to keep track of the damage suffered in 
various zones of the line of shafts. 
One such a system is described in the article about a line of shafts 
entitled "Torsional Monitor Equipment For Turbo-Generator Units" in the 
American journal "Proceedings of the American Power Conference, 1979, vol. 
41, pp. 1163 to 1169". This system includes a device for measuring the 
opposing torque, which device is in the form of a current transformer and 
a voltage transformer applying output signals to an analog computer. 
However, such special transformers are expensive since they are required to 
pass very high currents without distortion, and furthermore, they provide 
inaccurate measurements since they are incapable of taking account of 
non-linear phenomena between the rotor and the stator of the alternator. 
The monitoring system of the present invention uses less expensive means 
and can provide a more accurate result. 
SUMMARY OF THE INVENTION 
The present invention provides a system for monitoring torsion damage to a 
composite line of shafts through a driving machine and a driven machine, 
said driven machine being controlled by a servomotor, said system 
including first and second devices providing signals V.sub.H and V.sub.J 
representative of the speeds of rotation at two widely separated points H 
and J along the line of shafts, a third device determining parameters of 
the opposing torque, means using the signals provided by the first, second 
and third devices to determine the values of stresses in various zones M 
of the line of shafts, and means responsive to said stress values to 
determine metal damage in said zones M, the improvement wherein the device 
determining the parameters of the opposing torque comprises: 
first means responsive to the signals V.sub.H and V.sub.J to provide a 
signal .DELTA..phi..sub.T (t) representative of the angle of twist between 
the points H and J; 
second means supplied with the signal .DELTA..phi..sub.T (t) and with a 
signal dL(t)/dt which is the derivative of a signal L(t) proportional to 
the travel of the servomotor to provide a signal .DELTA..phi..sub.m (t) 
representative of the portion of the angle of twist due to the driving 
torque; 
third means serving to take the difference between the signal 
.DELTA..phi..sub.T (t) and the signal .DELTA..phi..sub.m (t) to provide a 
signal .DELTA..phi.(t) representative of the twist angle due to the 
opposing torque; 
fourth means responsive to the signal .DELTA..phi.(t) to provide the 
parameters of the opposing torque; 
a first threshold device supplied with the signal d.DELTA..phi..sub.T 
(t)/dt to trigger the second means when said signal exceeds a given 
threshold; and 
a second threshold device supplied with the signal dL(t)/dt to trigger the 
second means when said signal exceeds a given threshold.

DETAILED DESCRIPTION OF THE INVENTION 
FIG. 1 is a diagram of a line of shafts in a turboalternator which 
comprises an alternator 1, a turbine 2 including a high pressure (HP) 
portion 3, a mid pressure (MP) portion 4 and two low pressure (LP) 
portions 5 and 6. 
The HP or header portion 3 is fed with fluid under pressure via an 
adjustable valve actuated by a servomotor 7 whose travel as a function of 
time is noted L(t). The position of the servomotor is varied to control 
the performance of the alternator. 
A first instantaneous speed pickup 8 is disposed ahead of the HP portion 3 
at a point H and a second instantaneous speed pickup 9 is disposed behind 
the alternator 1 at a point J. 
The pickups 8 and 9 provide output signals which are applied to a decoder 
10 which provides a signal .DELTA..phi..sub.T (t) representative of the 
instantaneous angle of twist between the points H and J, and signals 
.DELTA..phi..sub.T '(t) and .DELTA..phi..sub.T "(t) respectively 
representative of the difference in speed and the difference in 
acceleration between H and J. 
FIG. 2 shows second means 11 which provide a signal .DELTA..phi..sub.m (t) 
representative of the difference in angle between H and J due to the 
driving torque, and third means 12 which provide a signal .DELTA..phi.(t) 
representative of the difference in angle between H and J due to the 
opposing torque. 
FIG. 2 also shows a differentiator 14' which is supplied with the signal 
.DELTA..phi..sub.T (t) and which supplies the signal d.DELTA..phi..sub.T 
(t)/dt to a first threshold device 14. When this signal exceeds a given 
threshold, the device 14 operates a switch 15 to actuate w blocks Mi 
(where 1.ltoreq.i.ltoreq.w) to calculate .alpha..sub.im (0) where w is the 
number of resonant modes in the line of shafts taken into account, eg. 
about ten. The blocks Mi together with the switch 15 constitute a part of 
the second means 11. 
The blocks Mi receive the signal .DELTA..phi..sub.T (t) continuously, but 
they make use only of the signal .DELTA..phi..sub.T (0), where the instant 
0 is the instant the switch 15 is operated. There is a fixed linear 
relationship between C.sup.r.sub.m (0) and .DELTA..phi..sub.T (0), and the 
coefficients of this relationship are stored in the blocks Mi. 
The formula for .alpha..sub.im (0) is as follows: 
##EQU1## 
where: 
##EQU2## 
where: Cu=reference torque 
I.sub.T =calculated moment of inertia for the complete line of shafts 
r=index of the driving rotor under consideration 
l.sub.r =active length of the rotor r 
.phi..sub.i (z)=resonant mode i 
z=distance along the line of shafts from the point H 
.DELTA..phi..sub.i =angle of twist between the points H and J as calculated 
for mode i C.sub.m.sup.r (0)=the driving torque existing on rotor r before 
the instant t.sub.0 at which the threshold device 14 activates the 
memories Mi. This torque is given once only as a function of the permanent 
value .DELTA..phi..sub.T (0) between the two measuring tracks. This torque 
is given in terms of the reference torque. 
.omega..sub.i *=.omega..sub.i .sqroot.1-.nu..sub.i.sup.2 where: 
.omega..sub.i is angular frequency of order i in conservative, and 
.nu..sub.i is the Lehr damping corresponding to mode i and is 
experimentally determined. In particular, .nu..sub.i includes damping due 
to the driving fluid. 
FIG. 2 also shows a second threshold device 16 which is supplied with the 
signal dL(t)/dt from a differentiator 17 which itself receives a signal 
L(t) representative of the travel of the servomotor 7. 
The second means 11 further include a switch 18 and a switch 18' which are 
operated by the threshold circuit 16 when the signal dL(t)/dt exceeds a 
predetermined threshold. The instant at which the signal dL(t)/dt exceeds 
the threshold is noted t.sub.1, a certain length of time after t.sub.1 the 
servomotor is stopped and the instant it stops is noted t.sub.2. The 
travel of the servomotor at instant t.sub.2 is noted L.sub.2, and the 
instant 0 is, as mentioned above, the instant at which d.DELTA..phi..sub.T 
(t)/dt exceeds its predetermined threshold. 
The switch 18 activates w function generator groups 19 which constitute a 
part of the second means 11. 
Each group 19 comprises function generators g.sub.i1 (t), g.sub.i2 (t), and 
g.sub.i3 (t). The second means further include w blocks 20 for generating 
a function f.sub.im (t). Each of the blocks 20 is supplied with the signal 
dL(t)/dt obtained from the output of the differentiator 17, and with 
signals from the associated group of function generators 19. The signal 
dL(t)/dt is applied to the blocks 20 only when the switch 18' is operated. 
These functions are as follows: 
##EQU3## 
where: 
##EQU4## 
with a=(dL(t)/dt).sub.t =0 L.sub.o =servomotor travel associated with 
torques C.sub.m.sup.r (o) 
with t=t-t.sub.1 in g.sub.i1 and g.sub.i2 
and t=t-t.sub.2 in g.sub.i3 
n.sub.i =.omega..sub.i .multidot..nu..sub.i 
ko=transient driving torque damping constant determined experimentally. 
The outputs from the blocks 20 are connected to inputs of a summing circuit 
21 which performs the signal sum: 
##EQU5## 
to supply a signal .DELTA..phi..sub.m (t) which is representative of the 
difference in angle of twist between the two tracks H and J due to the 
driving torque. 
Two differentiators 22 and 23 provide the signals .DELTA..phi..sub.m '(t) 
and .DELTA..phi..sub.m "(t). 
The third means 12 include three subtractors 24, 25, and 26. The subtractor 
24 takes the difference between the signals .DELTA..phi..sub.T (t) and 
.DELTA..phi..sub.m (t) to provide a signal .DELTA..phi.(t) representative 
of the difference in angle between the two tracks H and J due to the 
opposing torque, where: 
EQU .DELTA..phi.(t)=.DELTA..phi..sub.T (t)-.DELTA..phi..sub.m (t) 
Likewise the subtractors 25 and 26 provide signals: 
EQU .DELTA..phi.'(t)=.DELTA..phi..sub.T '(t)-.DELTA..phi..sub.m '(t); 
and 
EQU .DELTA..phi."(t)=.DELTA..phi..sub.T "(t)-.DELTA..phi..sub.m "(t) 
The fourth means 13 shown in FIG. 3 serve to calculate the electrical 
torque by using the mode base of the line of shafts. The mode base is 
established by testing and by calculation. In the chosen method, Cr is 
represented by a set of polynomials of degree 5. 
##EQU6## 
with 0.ltoreq.k.ltoreq.5, and v representing time between t.sub.n-1 and 
t.sub.n, time being divided into equal slices u with t.sub.n -t.sub.n-1 
=u, n with 0.ltoreq.v.ltoreq.u and v.sup.k representing successive powers 
of v: 1, v, v.sup.2, v.sup.3, v.sup.4, v.sup.5. 
The first division 27 of the fourth means 13 provides discrete values for 
the functions .DELTA..phi.(t), .DELTA..phi.'(t), .DELTA..phi."(t) and 
calculates the functions of the resonant mode characteristics. 
The calculation increment u and the following constants for each resonant 
mode of order i (shown as a block 28 marked C.sub.i) are defined once and 
for all after adjustments performed in situ: 
.omega..sub.i, .nu..sub.i, n.sub.i, p.sub.i1, q.sub.i1 
a.sub.i1.sup.u, a.sub.i2.sup.u, c.sub.i1.sup.u, c.sub.i2.sup.u, 
.beta..sub.i 
as mentioned above u represents the time interval over which each of the 
successive expressions of the opposing torque is valid. 
.omega..sub.i, .nu..sub.i, and n.sub.i have already been defined 
##EQU7## 
with l.sub.A being the active length of the rotor over which the opposing 
torque is exerted. 
The division 27 includes w generators 29 of functions F.sub.i. 
Each function generator 29 is constituted by eighteen blocks (B1) numbered 
1 to 18. 
The block 1 (Bl.sub.i) shown in FIG. 6 calculates the constants P.sub.i2 to 
p.sub.i6 and q.sub.i2 to q.sub.i6 as functions of p.sub.i1 and q.sub.i1 
from the following formulae: 
##EQU8## 
The constants N.sup.k and h.sub.iR.sup.k are calculated by the block 2 
(Bl.sub.i2) shown in FIG. 7, using the following formulae in which the R 
in the index of h.sub.i.sup.k means the real part and k is an integer in 
the range 0 to 5: 
##EQU9## 
where u, u.sup.2, u.sup.3, u.sup.4, and u.sup.5 represent successive 
powers of u both in these formulae and in the following formulae. 
##EQU10## 
The constants 0.sub.i.sup.k and h.sub.iJ.sup.k (where J in the index of 
h.sub.i.sup.k means the imaginary part) are calculated by the block 3 
(Bl.sub.i3) shown in FIG. 8 using formulae which are the same as those 
used in block Bl.sub.i2 except that the following substitutions are made: 
q.sub.i,k+1 for p.sub.i,k+1 
0.sub.i.sup.k for N.sub.i.sup.k 
h.sub.iJ.sup.k for h.sub.iR.sup.k 
The constants A.sub.i.sup.k and B.sub.i.sup.k are calculated by the block 4 
(Bl.sub.i4) shown in FIG. 9 using the following formulae: 
##EQU11## 
The constants L.sub.i1.sup.k and L.sub.i2.sup.k are calculated by the block 
5 (Bl.sub.i5) shown in FIG. 10 using the following formulae: 
##EQU12## 
The function l.sub.i1.sup.n is calculated as a function of l.sub.i1.sup.n-1 
and the coefficients .gamma..sub.k.sup.n-1 by the block 6 (Bl.sub.i6) 
shown in FIG. 11, where: 
n is an index which varies from 0 to infinity 
##EQU13## 
with l.sub.i1.sup.0 =0 
The function l.sub.i2.sup.n is calculated by the block 6 (Bl.sub.i6) shown 
in FIG. 12, using the following formula: 
##EQU14## 
with l.sub.i2.sup.0 =0 
The constants a.sub.i1.sup.n and a.sub.i2.sup.n are calculated by the block 
8 (Bl.sub.i8) shown in FIG. 13, using the following formulae: 
##EQU15## 
with a.sub.i1.sup.0 =0 and a.sub.i2.sup.0 =1 
The constants c.sub.i1.sup.n and c.sub.i2.sup.n are calculated by the block 
9 (Bl.sub.i9) shown in FIG. 14, using the following formulae: 
##EQU16## 
with c.sub.i1.sup.0 =1 and c.sub.i2.sup.0 =0 
The constants a'.sub.i1.sup.n, a'.sub.i2.sup.n, a".sub.i1.sup.n, and 
a".sub.i2.sup.n are calculated by the block 10 (Bl.sub.i10) shown in FIG. 
15, using the following formulae: 
##EQU17## 
The functions C.sub.i.sup.n and D.sub.i.sup.n are calculated by the block 
11 (Bl.sub.i11) shown in FIG. 16, using the following formulae: 
##EQU18## 
The functions C'.sub.i.sup.n and D'.sub.i.sup.n are calculated by the block 
12 (Bl.sub.i12) shown in FIG. 17, using the formulae for block Bl.sub.i11 
except that the following substitutions are made: 
for C.sub.i.sup.n put C'.sub.i.sup.n 
for D.sub.i.sup.n put D'.sub.i.sup.n 
for a.sub.i1.sup.n put a'.sub.i1.sup.n 
for a.sub.i2.sup.n put a'.sub.i2.sup.n 
The functions C".sub.i.sup.n and D".sub.i.sup.n are calculated by the block 
13 (Bl.sub.i13) shown in FIG. 18, using the formulae for block Bl.sub.i11 
except that the following substitutions are made: 
for C.sub.i.sup.n put C".sub.i.sup.n 
for D.sub.i.sup.n put D".sub.i.sup.n 
for a.sub.i1.sup.n put a".sub.i1.sup.n 
for a.sub.i2.sup.n put a".sub.i2.sup.n 
The constants A.sub.i.sup.n and B.sub.i.sup.n are calculated by the block 
14 (Bl.sub.i14) shown in FIG. 19, using the following formulae: 
##EQU19## 
Functions p.sub.ik.sup.n are calculated by the block 15 (Bl.sub.i15) shown 
in FIG. 20, using the following formula: 
##EQU20## 
Functions Q.sub.ik.sup.n are calculated by the block 16 (Bl.sub.i16) shown 
in FIG. 21, using the following formula: 
##EQU21## 
Functions R.sub.ik.sup.n are calculated by the block 17 (Bl.sub.i17) shown 
in FIG. 22, using the following formula: 
##EQU22## 
Functions E.sub.i.sup.1n, E.sub.i.sup.2n, E.sub.i.sup.3n, are calculated by 
the block 18 (Bl.sub.i18) shown in FIG. 23, using the following formulae: 
##EQU23## 
The division 27 is supplied with the signals .gamma..sub.0.sup.n-1 to 
.gamma..sub.5.sup.n-1 representative of the opposing torque during time 
interval n (ie. between t.sub.n-1 and t.sub.n). 
The division 27 includes means supplied with the functions .DELTA..phi.(t), 
.DELTA..phi. (t), and .DELTA..phi."(t) and which supply sequences of 
discrete values .DELTA..phi..sup.n (t), .DELTA..phi.'.sup.n (t), and 
.DELTA..phi.".sup.n (t) representative of these functions at instant 
t.sub.n, with .DELTA..phi..sup.n (t)=.DELTA..phi.(t.sub.n), 
.DELTA..phi.'.sup.n (t)=.DELTA..phi.'(t.sub.n), and .DELTA..phi.".sup.n 
(t)=.DELTA..phi."(t.sub.n). 
The division 27' receives the signals from the division 27 and it also 
receives the signals .gamma..sub.0.sup.n-1 to .gamma..sub.5.sup.n-1 
representative of the electrical torque during the interval n-1, and 
serves to calculate signals .gamma..sub.0.sup.n to .gamma..sub.5.sup.n 
representative of the opposing torque during interval n. 
The division 27' includes 11 blocks numbered Bl'1 to Bl'11. The block Bl"1 
shown in FIG. 24 receives the signal .DELTA..phi..sup.n+1, and the w 
signals E.sub.i.sup.1n-1, and supplies a signal E.sub.i.sup.n using the 
following formula: 
##EQU24## 
the block Bl'2 (FIG. 25) supplies a signal E.sub.2.sup.n using the formula: 
##EQU25## 
the block Bl'3 (FIG. 26) supplies a signal E.sub.3.sup.n using the formula: 
##EQU26## 
The block Bl'4 (FIG. 27) provides signals P.sub.k.sup.n, where: 
##EQU27## 
the block Bl'5 (FIG. 28) provides signals Q.sub.k.sup.n, where: 
##EQU28## 
the block Bl'6 (FIG. 29) provides signals R.sub.k.sup.n, where: 
##EQU29## 
The block Bl'7 (FIG. 30) calculates the signals .gamma..sub.0.sup.n, 
.gamma..sub.0.sup.n, and .gamma..sub.0.sup.n using the following formulae: 
##EQU30## 
The block Bl'8 (FIG. 31) calculates the signal S.sub.1.sup.n using the 
following formula: 
##EQU31## 
The block Bl'9 (FIG. 32) calculates the signal S.sub.2.sup.n using the 
following formula: 
##EQU32## 
The block Bl'10 (FIG. 33) calculates the signal S.sub.3.sup.n using the 
following formula: 
##EQU33## 
The block Bl'11 (FIG. 34) calculates the signals .gamma..sub.3.sup.n, 
.gamma..sub.4.sup.n, and .gamma..sub.5.sup.n using the formulae: 
##EQU34## 
The starting coefficients .gamma..sub.1.sup.0, .gamma..sub.2.sup.0, and 
.gamma..sub.3.sup.0 are obtained from the three formulae above by putting 
n=0 and by diminishing the lower index of the terms in .gamma., P, Q, and 
R by two. 
.gamma..sub.4.sup.0 and .gamma..sub.5.sup.0 are taken to be zero. 
Finally .gamma..sub.0.sup.0 is taken to be equal to 
##EQU35## 
The opposing torque 
##EQU36## 
may be used by monitoring equipment such as described in French patent 
specification FR-B-No. 7629133 or in the above-mentioned article 
"Torsional monitor equipment for turbo-generator units". Alternatively, 
means 30 may be used for determining stress values, as described with 
reference to FIG. 4. 
The means 30 use the results from the division 27' together with some of 
the magnitudes provided by the division 27. 
Functions Sy.sub.1 and S.sub.y2.sup.k are synthesized in a first division 
31 of the means 30. 
The synthesizer Sy.sub.1 provides functions a.sub.i1 (v) and a.sub.i2 (v) 
a.sub.i1 (v) and a.sub.i2 (v) have the same expressions as a.sub.i1.sup.u 
and a.sub.i2.sup.u but in which u is replaced by v. 
v represents time, with 0.ltoreq.v.ltoreq.u 
10 w functions N.sub.i.sup.k (v) and 0.sub.i.sup.k (v) are provided by the 
synthesizers Sy.sub.2, and similarly they replace u by v, but in the 
expressions N.sub.i.sup.k and 0.sub.i.sup.k, with 0.ltoreq.v.ltoreq.u 
These functions are independent of the index n. 
Functions L.sub.i1.sup.k (v) and L.sub.i2.sup.k (v) are generated by a 
second division 32 of the means 30 by means of a block shown in FIG. 35, 
in which: 
##EQU37## 
Functions V.sub.ik.sup.n (v) are also generated in this second division 32 
by means of a block shown in FIG. 36, in which: 
##EQU38## 
The sum of the six functions V.sub.ik.sup.n (v) is performed by a block 
shown in FIG. 37 and providing: 
##EQU39## 
The division 32 includes a block (FIG. 38) which provides the function: 
##EQU40## 
This function W.sub.iM.sup.n (v) is the contribution of the resonant mode i 
to the torsion stress at point M. 
The means 30 include a third division 33 which determines the value of the 
torsion stress at each point M. 
It includes a block (FIG. 39) which provides the function: 
##EQU41## 
where: K.sub.M =1/2D.sub.M .multidot.G.sub.M .multidot.k.sub.M 
D.sub.M is the diameter of the rotor at point M 
G.sub.M is the shear modulus, and 
k.sub.M is the contraction coefficient at M. 
Further, T.sub.M.sup.In =J.sub.M .DELTA..phi.(0) is determined by the block 
shown in FIG. 39 which receives the signal .DELTA..phi.(0), and where the 
term J.sub.M is a coefficient depending on the point M, the index In 
meaning that it exists with instant 0. 
The output from this block provides the signal: 
##EQU42## 
in which n takes all values from zero to infinity, and in which the signal 
is representative of the stress behaviour in the zone M as a function of 
time. 
FIG. 5 shows means 34 for deriving the damage to the metal in the zones M 
on the basis of the stress behaviour T.sub.M (t) in said zones. 
The sixth division serves to calculate the damage produced at each point M 
by the transient behaviour of T.sub.M (t). 
It includes an analog-to-digital converter 35 which transforms the analog 
signal T.sub.M (t) into a digital signal. 
The digital signal is supplied to a block 36 which determines a sequence of 
relative maxima and minima and thus enables a sequence of half cycles to 
be established in terms of their average values T.sub.pM and their 
amplitudes A.sub.p. 
These two magnitudes are compared with values held in a table 37 which 
supplies a magnitude representative of the damage suffered during each 
half cycle. 
This damage is summed in a summing circuit 38 over the entire time 
corresponding to a torsion transient from its appearance at instant t=0. 
The overall damage d.sub.MJ is applied to a summing circuit 39 which keeps 
track of the damage accumulated at the point M during the life of the 
machine, and supplies a magnitude d.sub.M representative thereof. 
This division also includes a threshold device 40 for triggering the 
turbine-alternator unit when the function T.sub.M (t) reaches a 
predetermined value.